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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf,len=1953
+page_content='ExplainableFold: Understanding AlphaFold Prediction with Explainable AI  Juntao Tan 1 Yongfeng Zhang 1  Abstract  This paper presents ExplainableFold, an explain-  able AI framework for protein structure prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Despite the success of AI-based methods such as  AlphaFold in this field, the underlying reasons for  their predictions remain unclear due to the black-  box nature of deep learning models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' To address  this, we propose a counterfactual learning frame-  work inspired by biological principles to generate  counterfactual explanations for protein structure  prediction, enabling a dry-lab experimentation  approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Our experimental results demonstrate  the ability of ExplainableFold to generate high-  quality explanations for AlphaFold’s predictions,  providing near-experimental understanding of the  effects of amino acids on 3D protein structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  This framework has the potential to facilitate a  deeper understanding of protein structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Introduction  The protein folding problem studies how a protein’s amino  acid sequence determines its tertiary structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' It is crucial  to biochemical research because a protein’s structure influ-  ences its interaction with other molecules and thus its func-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Current machine learning models have gain increasing  success on 3D structure prediction (AlQuraishi, 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Tor-  risi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Among them, AlphaFold (Jumper et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=',  2021) provides near-experimental accuracy on structure pre-  diction, which is considered as an importance achievement  in recent years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Nevertheless, one of the important problems  of AlphaFold, as well as other deep models, is that they can-  not provide explanations for their predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Essentially,  the why question still remains largely unsolved: the model  gives limited understanding of why the proteins are folded  into the structures they are, which hinders the model’s ability  to provide deeper insights for human scientists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  However, it is crucial to understand the mechanism of pro-  tein folding from both AI and scientific perspectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' From  1Department of Computer Science, Rutgers University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Corre-  spondence to: Juntao Tan <juntao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='tan@rutgers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='edu>, Yongfeng  Zhang <yongfeng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='zhang@rutgers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='edu>.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Copyright by the author(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  the AI perspective, explainability has long been an important  consideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' State-of-the-art protein structure prediction  models leverage complex deep and large neural networks,  which makes it difficult to explain their predictions or debug  the trained model for further improvement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' From the sci-  entific perspective, scientists’ eager to conquest knowledge  is not satisfied with just knowing the prediction results, but  also knowing the why behind the results (Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  In particular, structural biologists not only care about the  structure of proteins, but also need to know the underlying  relationship between protein primary sequences and tertiary  structures (Dill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Dill & MacCallum, 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  It has been established that certain amino acids play signifi-  cant roles in the protein folding process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' For instance, one  single disorder in the HBB gene can significantly change  the structure of hemoglobin, the protein that carries oxygen  in blood, causing the sickle-cell anaemia (Kato et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Knowing the relationship between amino acids and protein  structure helps scientists to produce synthetic proteins with  precisely controlled structures (Tan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2020) or mod-  ify existing proteins with desired properties (Szymkowski,  2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Mart´ınez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Ackers & Smith, 1985), which  are essential for advanced research directions such as drug  design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Additionally, in certain research tasks, scientists  would like to modify the amino acids without drastically  changing the protein structure, which requires the knowl-  edge of “safe” residue substitutions (Bordo & Argos, 1991),  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', the knowledge of which amino acids are not the most  crucial ones in the folding process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  While currently there are few Explainable AI-based methods  to study the mechanism of protein folding, many previous  biochemical researches have been conducted for this pur-  pose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' One of the best known methods is via site-directed  mutagenesis (Hutchison et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 1978;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Carter, 1986;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Sarkar &  Sommer, 1990).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' To test the role of certain residues in pro-  tein folding, biologists either delete them from the sequence  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', site-directed deletion) (Arpino et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Gl¨uck &  Wool, 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Flores-Ram´ırez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Dominy & An-  drews, 2003) or replace them with other types of amino acids  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', site-directed substitution) (Flores-Ram´ırez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Bordo & Argos, 1991;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Betts & Russell, 2003) and then mea-  sure their influences on the 3D structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' However, these  approaches suffer from several limitations: 1) So far, modi-  fication of such residues can be limited by methods for their  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='11765v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='AI]  27 Jan 2023  ExplainableFold: Understanding AlphaFold Prediction with Explainable AI  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' (a) Some amino acids play crucial roles in protein folding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' By removing the effects of a relative small set of these residues, the  predicted structure will be different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' (b) Some other residues are less important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Despite deleting a large set of these residues, the protein  still folds into a similar structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' (c) Some substitutions are radical to the protein structure and even a small number of such substitutions  can drastically change the structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' (d) Some other substitutions are conservative and have small effect on the protein structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  installation and the chemistry available for reaction, and  the modification of some residues can be very challenging  (Spicer & Davis, 2014), 2) Wet-lab methods for determin-  ing protein structures are very difficult and time-consuming  (Ilari & Savino, 2008), and 3) The wet lab experiments de-  scribed above have many prerequisites and obstacles, and  may not be completely safe for many researchers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Recently, AI-based dry-lab methods such as AlphaFold pro-  vide near-experimental protein structure predictions (Jumper  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2021), which sheds light on the possibility to gen-  erate insightful understandings of protein folding by ex-  plaining AlphaFold’s inference process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Such (Explainable)  AI-driven dry-lab approach will largely overcome the afore-  mentioned limitations and can be very helpful for human  scientists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Furtunately, we observe that the process of testing  the effects of residues on protein structure by site-directed  mutagenesis is fundamentally similar to counterfactual rea-  soning, a commonly used technique for generating explana-  tions for machine learning models (Tan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Goyal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Tolkachev et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Cito et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Intuitively, counterfactual reasoning perturbs parts of the  input data, such as interaction records of a user (Tan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=',  2021), nodes or edges of a graph (Tan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2022), pixels  of an image (Goyal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2019), or words of a sentence  (Tolkachev et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2022), and then observes how the model  output changes accordingly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  In this paper, we propose ExplainableFold, a counterfac-  tual explanation framework that generates explanations for  protein structure prediction models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' ExplainableFold mim-  ics existing biochemical experiments by manipulating the  amino acids in a protein sequence to alter the protein struc-  ture through carefully designed optimization objectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' It  provides insights about which residue(s) of a sequence is cru-  cial (or indecisive) to the protein’s structure and how certain  changes on the residue(s) will change the structure, which  helps to understand, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', what are the most impactful amino  acids on the structure, and what are the most radical (or safe)  substitutions when modifying a protein structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' An exam-  ple of applying our framework on CASP14 target protein  T1030 is shown in Figure 1, which shows that deletion or  substitution of a small number of residues can result in sig-  nificant changes to the protein structure, while some other  deletions or substitutions may have very small effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' We  evaluate the framework based on both standard explainable  AI metrics and biochemical heuristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Experiments show  that the proposed method produces more faithful explana-  tions compared to previous statistical baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Meanwhile,  the predicted relationship between protein amino acids and  their structures are highly positively correlated with wet-lab  biochemical experimental results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Related Work  The essential idea of the proposed method is to integrate  counterfactual reasoning and site-directed mutagenesis anal-  ysis in a unified machine learning framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' We discuss  the two research directions in this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Residue Effect Analysis by Site-directed Mutagenesis  Many studies in molecular biology, such as those involv-  ing genes and proteins, rely on the use of human-induced  mutation analysis (Stenson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Early metagenesis  methods were not site-specific, resulting in entirely random  and indiscriminate mutations (Egli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' In 1978,  a) Most Intolerant Deletion:  c) Most Radical Substitution:  TM-score: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='47 Changed # of Residues: 80 / 273 (29%)  b) Most Tolerant Deletion:  d) Most Conservative Substitution:  TM-score: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='66 Changed # of Residues: 142 / 273 (52%)  TM-score: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='57 Changed # of Residues: 82 / 273 (30%)ExplainableFold: Understanding AlphaFold Prediction with Explainable AI  Hutchison et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' proposed the first method that can modify  biological sequences at desired positions with specific inten-  tions, which is known as site-directed mutagenesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Later,  more precise and effective tools were constantly developed  (Motohashi, 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Doering et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Site-directed muta-  genesis is widely utilized in biomedical research for various  applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' In this section, we focus on the use of site-  directed mutagenesis to study the impact of amino acid  mutations on protein structures (Studer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Two common approaches to site-directed mutagenesis are  amino acid deletion and substitution (Choi & Chan, 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  The deletion approach deletes certain residues from the  sequence and observes the effects on the structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' For in-  stance, Gl¨uck & Wool (2002) identified the amino acids that  are essential to the action of the ribotoxin restrictocin by  systematic deletion of its amino acids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Flores-Ram´ırez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  (2007) proposed a random deletion approach to measure the  amino acids’ effects on the longest loop of GFP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Arpino et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  (2014) conducted experiments to measure the the protein’s  tolerance to random single amino acid deletion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' The substi-  tution approach, on the other hand, replaces one or multiple  residues with other types of amino acids to test their influ-  ence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' For example, Clemmons (2001) substituted a small  domain of the IGF-binding protein to measure weather spe-  cific domains account for specific structures and functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' (2018) mutated a specific amino acid on the  surface of a Pin1 sub-region, known as the WW domain, and  observed significant structural change on the protein struc-  ture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Guo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' (2004) randomly replaced amino acids to  test proteins’ tolerance to substitution at different positions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  When developing our framework, we draw insights from the  aforementioned biochemical methods, which were proven  effective in wet-lab experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' We aim to translate the  wet-lab methods for understanding protein structures into a  dry-lab AI-driven approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' We note that there have been ex-  isting attempts which built models to understand the relation-  ship between protein structures and their residues (Masso  & Vaisman, 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Masso et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Sotomayor-Vivas  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' However, they were mostly based on statistical  analysis on wet-lab experimentation data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Our method is  the first AI-driven machine learning method developed for  understading protein structure predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Counterfactual Reasoning for Explainable AI  Counterfactual explanation is a type of model-agnostic ex-  plainable AI method that tries to understand the underlying  mechanism of a model’s behavior by perturbing its input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  The basic idea is to investigate the difference of the model’s  prediction before and after changing the input data in spe-  cific ways (Wachter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Since counterfactual ex-  planation is well-suited for explaining black-box models,  it has been an important explainable AI method and has  been employed in various applications, including but not  limited to recommender systems (Tan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Ghaz-  imatin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2020), computer vision (Goyal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Vermeire et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2022), natural language processing (Yang  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Lampridis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Tolkachev et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2022),  molecular analysis (Tan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Ying et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Lin  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2021), and software engineering (Cito et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  In this paper, we explore counterfactual explanation to ex-  plain the amino acids’ effects on protein folding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' How-  ever, counterfactual explanation for protein folding exhibits  unique challenges compared with previous tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' For exam-  ple: 1) most of the aforementioned applications are classifi-  cation tasks, for which the explanation goal is very clear –  looking for a minimal change that alter the predicted label.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  However, protein structure prediction is a generation task  in a continuous space, which requires careful design of the  counterfactual reasoning objective;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' 2) protein structure pre-  diction models such as AlphaFold take complicated input  besides the primary sequence, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', the MSA and templates;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  3) it is easier to evaluate the explanations for the classifi-  cation tasks, nevertheless, as a new explainable AI task,  protein structure prediction poses unique challenges on the  evaluation of explanation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' We will show how to overcome  these challenges in the following parts of the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Problem Formulation  In this section, we first provide formulation of the Explain-  ableFold problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Since a protein tertiary (3D) structure is  uniquely determined by its primary structure (amino acid  sequences) (Dill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Wiltgen, 2009), according to  the key idea of counterfactual explanation, we define the ex-  planation as identifying the most crucial residues that cause  the proteins to fold into the structures they are.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Suppose a protein consists of a chain of l residues, where  the i-th residue is encoded as a 21-dimensional one-hot col-  umn vector ri.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' The “1” element in ri indicates the type  of the residue, which can be one of the 20 common amino  acids or an additional dimension for unknown residue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' By  concatenating all the residue vectors, a protein P is de-  noted as P = [r1, r2, · · · , rl], where P ∈ {0, 1}21×l is  called the protein embedding matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Many state-of-the-art  protein structure prediction models predict the 3D struc-  ture not only based on the residue sequence, but also uti-  lize supplementary evolutionary information (Senior et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=',  2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Jumper et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2021) by extracting Multiple Sequence  Alignment (MSA) (Edgar & Batzoglou, 2006) from pro-  tein databases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Suppose m proteins are retrieved from the  evolutionary database based on their similarity with protein  P, the constructed MSAs can be encoded as another ma-  trix M(P ) ∈ {0, 1}m×21×l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' A protein structure prediction  model fθ predicts the protein 3D structure S based on the  ExplainableFold: Understanding AlphaFold Prediction with Explainable AI  residue sequence and MSA embeddings:  S = fθ  �  P , M(P )  �  (1)  where M(P ) can be omitted if the model only takes the  residue sequence information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Though a structure predic-  tion model may predict the positions of all atoms, in many  structural biology research, only the backbone of residues  are used for comparing the similarities of protein structures  (Zhang & Skolnick, 2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Xu & Zhang, 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Zemla,  2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Therefore, we adopt the same idea in this paper,  where S ∈ R3×l only contains the predicted (x, y, z)T co-  ordinates of the α-carbon atom of each amino acid residue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  The explanation is expected to be a subset of residues ex-  tracted from the protein sequence, expressed as E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' The  objective of the ExplainableFold problem is to find the mini-  mum set of E that contains the most influential information  for the prediction of the 3D structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' The ExplainableFold Framework  In biochemistry, the most common methods for studying  the effects of amino acids on protein structure fall into two  categories: amino acid deletion and substitution (Choi &  Chan, 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' We design the ExplainableFold framework  from both of the two perspectives, and we introduce them  separately in the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' The Residue Deletion Approach  The deletion approach simulates the biochemical studies  that detect essential residues for a protein by deleting one or  more residues and measuring the protein’s tolerance to such  deletion (Arpino et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Gl¨uck & Wool, 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Flores-  Ram´ırez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' The key idea is to apply a residue  mask that removes the effect of certain residues from the se-  quence and then measure the change of the protein structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  From the counterfactual machine learning perspective, this  can be considered from two complementary views (Guidotti  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Tan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2022): 1) Identify the minimal dele-  tion that will alter the predicted structure and the deleted  residues will be the necessary explanation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' 2) Identify the  maximal deletion that still keeps the predicted structure and  the undeleted residues will be the sufficient explanation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' We  design the counterfactual explanation algorithm from these  two views accordingly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' NECESSARY EXPLANATION (MOST INTOLERANT  DELETION)  From the necessary perspective, we aim to find the minimal  set of residues in the original sequence which, if deleted,  will change the AI model’s (such as AlphaFold’s) predicted  structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' The deleted residues thus contain the most neces-  sary information for the model’s original prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  We can express the perturbation on the original sequence  as a multi-hot vector ∆ = {0, 1}1×l, where δi = 1 means  that the i-th residue will be deleted and δi = 0 means it will  be kept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Then the counterfactual protein embedding matrix  P ∆ can be expressed as:  P ∆ = P ⊙ (1 − ∆) + U ⊙ ∆  (2)  where ⊙ is the element-wise product and U ∈ {0, 1}21×l  denotes an “unknown” matrix of the same shape with P ,  but with all elements being 0 except for the last row being 1  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', unknown type amino acid).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Thus, for δi = 0, the i-th  residue in the original sequence will be preserved, while for  δi = 1, the i-th residue will be treated as an unknown amino  acid without any specific chemical property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Motivated by the Occam’s Razor Principle (Blumer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=',  1987), we aim to find simple and effective explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' The  simpleness can be characterized by the number of residues  that need to be deleted, which should be as few as possi-  ble, while effectiveness means that the predicted protein  structure should be different before and after applying the  deletions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' We can use zero-norm ∥∆∥0 to represent the  number of deletions (for simpleness), while using the TM-  score between the original and the new protein structures  TM(S, S∗) to represent the degree of change on the struc-  ture (for effectiveness).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' TM-score is a standard measure-  ment for comparing aligned protein structures, where TM-  score > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='5 suggests the same folding and TM-score ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='5  suggests different foldings (Zhang & Skolnick, 2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Xu &  Zhang, 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' The counterfactual expxlanation algorithm  then learns the optimal explanation by solving the following  constrained optimization problem:  minimize ∥∆∥0  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' TM(S, S∗) ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='5, ∆ = {0, 1}1×l  where S∗ = fθ(P ∆, M(P ∆))  (3)  where the objective ∥∆∥0 aims to find the minimal dele-  tion, while the constraint guarantees the effectiveness of the  deletion, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', the deletion will change the predicted protein  structure to be different from before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Due to the exponential combinations of sub-sequences for  a given sequence, it is impractical to search for an optimal  solution on the discrete space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' To solve the problem, we use  a continuous relaxation approach to solve the optimization  problem by relaxing the multi-hot vector ∆ to a real-valued  vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' We also relax the hard constraint in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' (3) and  combine them into a single trainable loss function:  L1 = max  �  0, TM(S, S∗) − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='5 + α  �  + λ1∥σ(∆)∥1  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' ∆ ∈ R1×l, where S∗ = fθ(P σ(∆), M(P σ(∆)))  (4)  where the sigmoid function σ(·) is applied so that σ(∆) ∈  (0, 1)1×l approximates the probability distribution between  ExplainableFold: Understanding AlphaFold Prediction with Explainable AI  the original residues and unknown residues, and α is the  margin value of the hinge loss whose default value is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  This relaxation approach has been justified in several previ-  ous studies which also learn explanation on discrete inputs  (Ying et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Goyal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Tan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' The  1-norm regularizer assures the learned perturbation σ(∆)  to be sparse (Candes & Tao, 2005), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', the learned expla-  nation only contains a small set of residues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' λ1 is a hyper-  parameter that controls the trade-off between the complexity  and strength of the generated explanation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' (4) can be  easily optimized with gradient descent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' After optimization,  we convert σ(∆) to a binary vector with the threshold 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' SUFFICIENT EXPLANATION (MOST TOLERANT  DELETION)  Symmetrically, from the sufficiency perspective, we aim to  find the maximal set of residues in the orignal sequence  which, if deleted, will not change the AI model’s predicted  structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' The undeleted residues thus contain the most  sufficient information for the model’s original prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  This can be formulated as a similar but reversed optimization  process as Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' (3), which looks for the maximal perturba-  tion ∆ while keeping the same folding (TM-score > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Therefore, the optimization problem is formulated as:  maximize ∥∆∥0  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' TM(S, S∗) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='5, ∆ = {0, 1}1×l  where S∗ = fθ  �  P ∆, M(P ∆)  �  (5)  Similarly, we relax Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' (5) to a differentiable loss function:  L2 = max  �  0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='5 − TM(S, S∗) + α  �  − λ2∥σ(∆)∥1  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' ∆ ∈ R1×l, where S∗ = fθ(P σ(∆), M(P σ(∆)))  (6)  Contrary to the necessary explanation, the sufficient explana-  tion consists the undeleted residues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Hence, after optimiza-  tion, we filter the residues according to  �  1 − σ(∆)  �  > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='5  and include them into the sufficient explanation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' The Residue Substitution Approach  Another popular approach in biochemistry, site-directed sub-  stitution, studies the influence of the amino acids on protein  folding by replacing certain residues with other known-type  residues (Flores-Ram´ırez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Bordo & Argos, 1991;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Betts & Russell, 2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Different replacements may have  different effects on protein structures, and they can be clas-  sified into two types: conservative substitution and radical  substitution (Zhang, 2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Dagan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' A conser-  vative substitution is considered as a “safe” substitution for  which the amino acid replacement usually have no or minor  effects on the protein structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' A radical substitution is  considered “unsafe,” which usually causes significant struc-  tual changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Based on the above concepts, we design the  substitution approach from these two different perspectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' RADICAL SUBSTITUTION EXPLANATION  From the radical substitution perspective, we aim to find the  mimimal set of residue replacements which will lead to a  different folding, and then the learned substitutions are the  most radical substitutions for the protein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  For a target protein with binary embedding matrix P , we  learn a counterfactual binary protein embedding P ′, which  has the same shape as the original embedding matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' The  number of substitutions is represented by ∥P −P ′∥0, which  is the 0-norm of the difference between the two matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  To find the minimal residue substitution that changes the  original folding, the optimization problem is defined as:  minimize ||P − P ′||0  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' TM(S, S′) ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='5, P ′ ∈ {0, 1}21×l  where S′ = fθ  �  P ′, M(P ′)  �  (7)  Due to the exponential search space of the substitutions,  we use the similar continuous relaxation method as in the  deletion approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' First, we relax the binary counterfactual  embedding matrix P ′ to continuous space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' We also relax  the hard constraint in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' (7) and define the differentiable  loss function as:  L3 = max  �  0, TM(S, S′) − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='5 + α  �  + λ3∥P − σ(P ′)∥1  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' P ′ ∈ R21×l, where S′ = fθ  �  P ′, M(P ′)  �  (8)  After optimization, we convert the learned continuous ma-  trix σ(P ′) into binary by setting the maximum value of each  column as 1 and others as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Then, the changed residues  between P and P ′ are the radical substitution explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' CONSERVATIVE SUBSTITUTION EXPLANATION  From the conservative substitution perspective, we aim to  find the maximal set of residue replacements which how-  ever lead to the same folding, and then the learned substitu-  ions are the most conservative substitutions for the protein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  On the contrary to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' (7), we formulate an inverse optimiza-  tion problem as:  maximize ||P − P ′||0  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' TM(S, S′) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='5, P ′ ∈ {0, 1}21×l  where S′ = fθ  �  P ′, M(P ′)  �  (9)  With the same relaxation process, the loss function is:  L4 = max  �  0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='5 − TM(S, S′) + α  �  − λ4∥P − σ(P ′)∥1  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' P ′ ∈ R21×l, where S′ = fθ  �  P ′, M(P ′)  �  (10)  ExplainableFold: Understanding AlphaFold Prediction with Explainable AI  After learning σ(P ′) and getting the binary matrix, again,  the changed residues between P and P ′ are the conservative  substitution explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Phased MSA Re-alignment  It is impractical to re-compute MSAs in each training step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Therefore, we propose a phased MSA re-alignment strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  When learning the explanations, we fix the generated MSAs  and only learn the changes on the sequence embedding for  t training steps (t = 100 by default), which is one pahse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Then, we re-align the MSAs and start another training phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Experiments  We first introduce the datasets and implementation details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Then, we introduce the evaluation results of the deletion  approach and substitution approach, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Datasets  We test the ExplainableFold framework on the 14th Criti-  cal Assessment of protein Structure Prediction (CASP-14)  dataset1 (Moult et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' CASP consecutively establishes  protein data with detailed structural information as a stan-  dard evaluation benchmark for protein structure prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Following Jumper et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' (2021), we remove all sequences  for which fewer than 80 amino acids had the alpha carbon  resolved and remove duplicated sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' After filtering,  55 protein sequences are selected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Implementation Details  Though the ExplainableFold framework can be applied on  any model that predicts protein 3D structures, we choose  Alphafold2 (Jumper et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2021), the state-of-the-art model,  as the base model in the experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' More specifically, we  use the OpenFold (Ahdritz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2022) implementation and  load the official pre-trained AlphaFold parameters2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  When learning the explanations, the pre-trained parame-  ters of AlphaFold are fixed, and only the perturbation vec-  tor on the input (∆ for the deletion approach and P ′ for  the substitution approach) will be optimized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' However, it  still requires computing the gradient through the entire Al-  phafold network, as a result, the learning process requires  extensive memory consumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' To solve the problem, we  follow exactly the same training procedure as introduced in  the original AlphaFold paper (Jumper et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' More  specifically, we use the gradient checkpointing technique to  reduce the memory usage (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Meanwhile,  if a protein has more than 384 residues, we cut it to differ-  ent chunks for each consecutive 384 residues, and generate  1https://predictioncenter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='org/casp14/  2https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='com/deepmind/alphafold  explanations for each of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  We employ the same training strategy for both deletion and  substitution explanation methods: for each training phase  between MSA re-alignments, we optimize the purturbation  vector for 100 steps with Adam optimizer (Kingma & Ba,  2014) and learning rate 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' After each training loop, we re-  align the MSAs with the AlphaFold HHblits/JackHMMER  pipeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' We repeat the training and alignment process for  3 phases when generating explanations for each protein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  All experiments are conducted on NVIDIA A5000 GPUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  The entire training process (including all 3 phases) for one  protein takes approximately 5 hours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' We set α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='1 and  λ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='01 in Equations (4)(6)(8)(10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' To realize an incre-  mental substitution process, we initialize the counterfactual  protein embedding matrix as a duplication of the original  protein embedding matrix, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', we initialize ∆ with all 0’s  and initialize σ(P ′) equal to the original P .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Thus, the  optimal explanations are gradually learned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Evaluation of the Deletion Approach  Counterfactual explanations can be evaluated by their com-  plexity, sufficiency and necessity (Glymour et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Tan  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' First, according to the Occam’s Razor Princi-  ple (Blumer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 1987), we hope an explanation can be as  simple as possible so that it is cognitively easy to understand  for humans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' This can be evaluated by the complexity of the  explanation, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', the percentage of residues that are included  in the explanation:  Complexity = |E|/l  (11)  where l is the length of the protein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Sufficiency and necessity measure how crucial the generated  explanations are for the protein structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' We follow the def-  inition in causal inference theory (Glymour et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2016) and  existing explainable AI research (Tan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2022) and mea-  sure the explanations with two causal metrics: Probability  of Necessity (PN) and Probability of Sufficiency (PS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  PN measures the necessity of the explanation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' A set of  explanation residues is considered a necessary explanation  if, by removing their effects from the protein sequence,  the predicted structure of the protein will have a different  folding (TM-score < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Suppose there are N proteins in  the testing data, then PN is calculated as:  PN =  �N  k=1 PNk  N  , PNk =  �  1, if TM(Sk, S∗  k) ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='5  0, else  (12)  Intuitively, PN measures the percentage of proteins whose  explanation residues, if removed, will change the protein  structure, and thus their explanation residues are necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  PS measures the sufficiency of the explanation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' A set of  explanation residues is considered a sufficient explanation if,  ExplainableFold: Understanding AlphaFold Prediction with Explainable AI  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' PN Evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Deletion∗ is the necessity optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Ave Exp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Ave Comp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Ave TM-score  PN  Size (|E|) ↓  (|E|/l) ↓  TM(S, S∗) ↓  score↑  Random  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='31  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='83  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='07  Evo (Masso et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2006)  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='42  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='33  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='77  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='16  Deletion (necessity)∗  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='54  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='29  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='48  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='44  Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' PS Evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Deletion∗ is the sufficiency optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Ave Exp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Ave Comp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Ave TM-score  PS  Size (|E|) ↓  (|E|/l) ↓  TM(S, S∗) ↑  score↑  Random  102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='40  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='38  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='31  Evo (Masso et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2006)  104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='95  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='42  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='41  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='40  Deletion (sufficiency)∗  95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='37  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='61  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='62  by removing all of the other residues and only keeping the  explanation residues, the protein still has the same folding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Similarty, PS is calculated as:  PS =  �N  k=1 PSk  N  , PSk =  �  1, if TM(Sk, S∗  k) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='5  0, else  (13)  Intuitively, PS measures the percentage of proteins whose  explanation residues alone can keep the protein structure  unchanged, and thus their explanation resides are sufficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' BASELINES  We compare the model performance with a common com-  putational biology baseline (Masso et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2006), which  analyzes a protein’s tolerance to the change on each residue  by extracting the data from evolutionary database.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' More  specifically, proteins are not tolerate to the mutations at evo-  lutionary conserved positions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' However, they are capable  of withstanding certain mutations at other positions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' When  implementing the baseline, we refer to a protein’s MSAs  and select the evolutionary conserved residues as the expla-  nation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' This is illustrated in Figure 2 using protein CASP14  target T1030 as an example, where for each residue position,  we count the number of MSAs that conserve the residue  at this position, and show the top 30% and 40% conserved  residues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' We also randomly select residues as explanation  and compute PN and PS scores as another baseline to mea-  sure the general difficulty of the evaluation task, and more  details are provided in the following subsection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' RESULTS  The results of PN and PS evaluation are reported in Table  1 and Table 2, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' The explanation complexity  of our method (29% for necessary explanation and 37%  for sufficient explanation) are automatically decided by our  optimization process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' However, the baselines do not have  the ability to decide the optimal explanation complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' For  fair comparison, we set the complexities of the baselines  to be slightly larger than our method (30% for necessary  explanation and 40% for sufficient explanation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Therefore,  the baselines will have a small advantage over our method  (a) Top 30% conserved residues (b) Top 40% conserved residues  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Evolutionary conserved residues are considered more  important for the protein structures (the residues marked red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  because they are allowed to use more residues to achieve  the necessity or sufficiency goals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  For PN evaluation, the results of the random baseline shows  that protein structures tend to be robust to residue deletions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  For example, when randomly removing the effects of 30%  residues, only 7% of the proteins fold into different struc-  tures, which indicates that finding necessary explanations  is a challenging problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' The evolutionary baseline is able  to select more necessary residues with a PN score of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='16,  which is 128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='6% better than random selection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Compared to  them, our method shows much better performance: with a  smaller number of residues, the generated explanations are  able to cause 44% of the proteins fold into different struc-  tures, outperforming the evolutionary baseline by 175%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  For PS evaluation, the evolutionary baseline is not notice-  ably better than randomly selecting residues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' The reason  may be that despite the proteins’ less tolerance to the evo-  lutionary conserved residues, there is no guarantee that the  evolutionary conserved residues alone contain sufficient in-  formation to preserve the protein structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' In comparison,  our method does generate more sufficient explanations, out-  performing the evolutionary baseline by 55% according to  the PS score with less complex explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Meanwhile,  our TM score is > 50%, indicating that the protein structure  is indeed preserved under our sufficient explanation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Additionally, we show the learning curve of the optimization  for CASP14 target protein T1030 in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' For necessary  optimization, the algorithm gradually deletes the protein  residues until the TM-score is smaller than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='4 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='5−α,  see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='(4)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Then, the explanation complexity slightly drops  back while keeping the TM-score at the same level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' For  sufficient optimization, the L1-loss drastically increases at  the beginning, which suggests that the algorithm is trying  to delete as many residues as possible while keeping the  original folding structure unchanged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' However, after re-  computing MSAs, the TM-score becomes too low.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Thus,  the algorithm increases the number of preserved residues  to keep TM-score larger than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='6 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='5 + α, see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' (6)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Note that the TM-scores change sharply when re-computing  MSAs at the end of each training loop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' The more frequently  175  150  MSAs Num  125  100  75  50  25  0  20  40  60  80  0  100  120  Residue Position175  150  iSAs Num  125  100  75  50  25  20  40  60  80  0  100  120  Residue PositionExplainableFold: Understanding AlphaFold Prediction with Explainable AI  (a) Necessary Optimization  (b) Sufficient Optimization  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Learning Curves of the Deletion Approach  we re-align MSAs, the smoother the optimization will be.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Evaluation of the Substitution Approach  The substitution approach identifies the most radical or con-  servative amino acid substitutions, which are of particular  interest in biochemical research (Zhang, 2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Previously,  it was impractical to conduct wet-lab experiments to investi-  gate the relative “safety” of replacing specific residues with  alternative amino acids due to their prohibitive cost (Bordo  & Argos, 1991).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Alternatively, scientists infer the exchange-  ability of two types of amino acids either through the use of  heuristics based on their physical or chemical properties or  through the analysis of evolutionary data, such as:  Epstein’s distance(Epstein, 1967): Predict the impact of  switching two amino acids based on their size and polarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Miyata’s distance (Miyata et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 1979): Predict the impact  based on their volume and polarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Evolutionary indicator (Bordo & Argos, 1991): Detect  “safe” substitutions based on evolutionary data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Note that these indicators are rather suggestions than ground-  truth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' They provide general trends that are better than ran-  dom selection but cannot be expected to be precise in every  scenario (Bordo & Argos, 1991).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' These methods are not  perfectly consistent with each other, but are linearly related.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Therefore, we utilize the amino acid substitution data gener-  ated by our method to caculate the pair-wise exchangeability  between the amino acids, and test the correlation between  our exchangeability with the above three existing exchange-  ability indicators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' The details of the pair-wise substitution  statistics and the calculation of pair-wise exchangeability  are provided in the Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  In Table 3, we report the correlation of our generated pair-  wise exchangeability with the three aforementioned indica-  tors by a non-parametric method: Pearson’s correlation r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Besides, the correlation among the three biochemical meth-  ods themselves range from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='438 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='578.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Additionally,  the correlation is also visualized in Figure 4, where darker  color indicates higher correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' For Pearson’s correlation,  a value greater than 0 indicates a positive association, where  r > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='1, r > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='3, r > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='5 represents small, medium, and  Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Correlation between our method and each of the biochem-  ical indicators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Metrics with “*” are originally distance metrics,  for which we take the inverse to reprenst the exchangeability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' The  results are significant at p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='001 under two-tailed test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Epstein∗  Miyata∗  Evolution  Radical  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='388  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='602  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='382  Conservative  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='494  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='796  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='405  (a) Corr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' w/ Epstein’s distance  (b) Corr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' w/ Miyata’s distance  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' The correlation between the exchangeability provided by  our conservative optimization method and (a) Epstein’s distance  as well as (b) Miyata’s distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  large correlations, accordingly (Cohen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Both  Table 3 and Figure 4 show that our method has clear posi-  tive correlations with all of the three biochemical methods,  indicating that ExplainableFold can provide informative  exchangeability signals (Yampolsky & Stoltzfus, 2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Be-  sides, the results generated by ExplainableFold may further  improve when larger protein datasets are available or applied  on even better base models in the future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Conclusions and Future Work  In this paper, we propose ExplainableFold—an Explain-  able AI framework that helps to understand the deep learn-  ing based protein structure prediction models such as Al-  phaFold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Technically, we develop a counterfactual explana-  tion framework and implement the framework based on two  approaches: the residue deletion approach and the residue  substitution approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Intuitively, ExplainableFold aims to  find simple explanations that are effective enough to keep  or change the protein’s folding structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Experiments are  conducted on CASP-14 protein datasets and results show  that our approach outperforms the results from traditional  biochemical methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' We believe Explainable AI is funda-  mentally important for AI-driven scientific research because  science not only pursues the answers for the “what” ques-  tions but also (or even more) for the “why” questions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' In the  future, we will further improve our framework by consider-  ing more protein modification methods beyond deletion and  substitution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' We will also generalize our framework to other  scientific problems due to the flexibility of our framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
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+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' and Smith, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Effects of site-specific amino  acid modification on protein interactions and biological  function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Annual review of biochemistry, 54(1):597–629,  1985.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Ahdritz, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', Bouatta, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', Kadyan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
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+page_content=', Gerecke,  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', O’Donnell, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', Berenberg, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', Fisk, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', Zanichelli,  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', Zhang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', Nowaczynski, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
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+page_content=', Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', Bonneau, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', and AlQuraishi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Openfold: Retraining alphafold2 yields new insights into  its learning mechanisms and capacity for generalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  bioRxiv, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
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+page_content=' Machine learning in protein structure pre-  diction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Current opinion in chemical biology, 65:1–8,  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Arpino, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
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+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
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+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Random single amino acid deletion  sampling unveils structural tolerance and the benefits of  helical registry shift on gfp folding and structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Struc-  ture, 22(6):889–898, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Betts, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' and Russell, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Amino acid properties  and consequences of substitutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Bioinformatics for  geneticists, 317:289, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Blumer, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', Ehrenfeucht, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', Haussler, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', and Warmuth,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
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+page_content='  Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' and Skolnick, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Scoring function for automated  assessment of protein structure template quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Proteins:  Structure, Function, and Bioinformatics, 57(4):702–710,  2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' and Skolnick, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Tm-align: a protein structure  alignment algorithm based on the tm-score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Nucleic acids  research, 33(7):2302–2309, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  ExplainableFold: Understanding AlphaFold Prediction with Explainable AI  Appendix  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Statistical Analysis of Amino Acid Substitutions  Table 4 shows the total count of each amino acid in the  testing proteins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' In Table 5, we show how many times a  specific type of substitution happens in the generated ex-  planations learned by the conservative substitution method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  For instance, the substitution of A → R happens 19 times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  The exchangeability of X → Y can be easily calculated by  |X → Y |/|X| (Bordo & Argos, 1991;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Masso et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  The same statistics for radical substitution is provided in  Table 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' For radical substitution, the higher the number  in Table 6, the lower the exchangeability, and thus the ex-  changeability of X → Y is calculated as the reciprocal  |X|/|X → Y | (Bordo & Argos, 1991;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Masso et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=', 2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='  Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Total number of each amino acid in testing data  A  R  N  D  C  Q  E  G  H  I  #  782  581  827  776  175  520  848  853  309  904  L  K  M  F  P  S  T  W  Y  V  #  1122  911  273  600  506  916  746  149  595  780  Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content=' Structural Conservative Statistics  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='A  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='R  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='N  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='D  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='C  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
+page_content='Q  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tFKT4oBgHgl3EQfQC0t/content/2301.11765v1.pdf'}
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