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[
"The structures of compounds bound to E7R have been deposited in the Protein Data Bank under accession code 4NB3.",
"\n\nIntroduction {#sec1}\n============\n\nReplication protein A (RPA) is a single stranded DNA (ssDNA)--binding protein complex that is essential for DNA replication, damage response, and repair.^[@ref1],[@ref2]^ In response to DNA lesion formation, RPA rapidly coats ssDNA,^[@ref1],[@ref3]^ preventing the formation of aberrant DNA structures at replication foci and recruiting a number of checkpoint proteins to initiate the response to DNA damage.^[@ref4]^ Increased activity of DNA damage response and repair pathways is observed in a number of human cancers and has been linked to resistance to radiation or chemotherapy treatment.^[@ref5]^ Thus, compounds targeting these pathways may have utility in patients undergoing cancer therapy.",
"\n\nRPA70 is the largest of the RPA subunits and contains three high-affinity ssDNA binding domains that serve as the DNA-anchoring core of the entire complex (RPA70A, -B, -C).^[@ref1],[@ref2]^ Binding to ssDNA is mediated by oligosaccharide/oligonucleotide binding (OB) folds that are present on all subunits.^[@ref6]−[@ref8]^ The basic cleft in the OB fold present on the N-terminal domain, RPA70N, binds to several partner proteins that are important for mediating the response to DNA damage, including ATRIP (ATR-interacting protein), RAD9, MRE11, and p53.^[@ref4],[@ref9]−[@ref11]^ We hypothesize that the selective inhibition of the RPA70N basic cleft will specifically disrupt these protein--protein interactions, leading to the inhibition of a subset of RPA functions, attenuation of the DNA damage response, and the selective killing of cancer cells.",
"\n\nToward the discovery of a probe molecule that binds tightly to RPA70N and inhibits its interaction with other proteins, we and others have previously reported small molecules that bind to RPA70N.^[@ref12]−[@ref14]^ We used an NMR-based screen to identify fragments that bind to RPA70N, and, on the basis of X-ray structures of the screening hits and analogues when bound to the protein, have obtained analogues with improved affinity. ",
"Recently, we have discovered compounds that bind to RPA70N with submicromolar affinity^[@ref12]^ that were obtained by linking together small molecules that bind to two adjacent sites.",
"\n\nAn alternative approach for targeting protein--protein interactions is the use of stapled helix peptides. ",
"Hydrocarbon stapling has been shown to increase the affinity, stability, and cellular permeability of peptide sequences that bind to protein targets.^[@ref15]−[@ref17]^ NMR experiments have demonstrated that homologous peptides derived from the partner proteins ATRIP, RAD9, and MRE11 bind competitively to the basic cleft of RPA70N.^[@ref18]^ Further, the three peptides share a region of similar primary sequence with p53 and contain a mix of conserved acidic and hydrophobic amino acid residues.^[@ref19]^ An X-ray crystal structure of a chimeric protein containing portions of RPA70N and p53 reveals that a part of the p53 transactivation domain (residues 47--57) folds into helices that bind into the basic cleft in the OB fold of RPA70N.^[@ref19]^ These binding interactions in the cleft are stabilized by both electrostatic and hydrophobic interactions. ",
"We have previously measured the binding affinity of these peptides to RPA70N and found that the ATRIP-derived sequence binds more tightly than the Rad9, MRE11, and p53 peptides.^[@ref20]^\n\nHere we describe the discovery of stapled helix peptides, based on the ATRIP sequence, that bind tightly to the protein--protein interaction site in the basic cleft of RPA70N and inhibit the interactions of RPA70N with other peptides/proteins. ",
"The binding affinity was optimized by traditional methods, as well as a novel method that can efficiently select and incorporate unnatural amino acids into the peptides. ",
"Peptides in which an unnatural amino acid was incorporated displayed a 1--2 orders of magnitude improvement in binding affinity compared to peptides with natural amino acids, penetrate cells, and may serve as useful tools for studying RPA function and the therapeutic potential of inhibiting RPA.",
"\n\nResults and Discussion {#sec2}\n======================\n\nAlanine Scanning of the ATRIP Peptide {#sec2.1}\n-------------------------------------\n\nTo better understand the peptide structure--activity-relationships (SARs) of the ATRIP-derived peptide and to elucidate the sequence positions suitable for affinity-optimizing point mutations, we performed an alanine scan in which each amino acid was replaced by an alanine residue (Table [1](#tbl1){ref-type=\"other\"}). ",
"Affinity of the mutated peptides was measured using an FPA competition assay with FITC-ATRIP as a probe.^[@ref20]^\n\n###### Alanine Scan of an ATRIP-Derived Peptide\n\n![](",
"jm-2013-01730y_0011){#GRAPHIC-d518e377-autogenerated}\n\nAlanine mutations are shown in bold red.",
"\n\n*K*~d~ values derived from IC~50~ values measured in an FPA competition assay.",
"\n\nSouza-Fagundes et al.^[@ref20]^\n\nResidues D1, F2, T3, D6, L7, E9, L10, D11, and L13 were found to be important for binding to RPA70N, as replacement of each of these with an alanine resulted in a significant loss of binding affinity. ",
"Interestingly, although D5 is conserved in the ATRIP and corresponding RAD9, MRE11, and p53 sequences, replacement with an alanine leads to a peptide equipotent with the parent, suggesting that this residue does not contribute significantly to binding to RPA70N. Similarly, despite the conservation of E8 in three out of the four RPA70N binding partners, no loss of binding was observed when E8 was replaced with alanine. ",
"In contrast, an almost complete loss of binding was observed when F2 was replaced with an alanine (peptide-02). ",
"Two ATRIP amino acid mutations led to a slight improvement in affinity: E8A (peptide-07, *K*~d~ = 22 μM) and T12A (peptide-11, *K*~d~ = 17 μM). ",
"However, when combined into one peptide sequence (peptide-14), the individual positive effects on the binding affinity were not additive.",
"\n\nATRIP Amino Acid Substitutions Inspired by p53 {#sec2.2}\n----------------------------------------------\n\nIn an attempt to improve the binding affinity of the ATRIP peptide, we substituted the hydrophobic residues WF from the p53 peptide into the corresponding positions of the ATRIP peptide (Table [2](#tbl2){ref-type=\"other\"}). ",
"These residues form a hydrophobic motif within p53 (IEQWF) that is not present within the ATRIP sequence. ",
"Although individual substitution of L10 or D11 with W or F, respectively, did not improve binding relative to peptide-14 (peptide-15 and peptide-16), a 10-fold improvement in affinity was observed when these replacements were combined (peptide-17, *K*~d~ = 2.7 μM). ",
"This effect may be attributed to a clustering of the two residues, leading to the formation of a hydrophobic binding core.^[@ref19],[@ref21]^ To further optimize the potency, we substituted positions 8 and 12 of peptide-17 with alanines, as those mutations were found to increase the binding affinity to RPA70N. Whereas the E8A mutation results in a dramatic loss of affinity in the context of the WF motif (peptide-18), the binding of peptide-19 (T12A mutation) was increased by a factor of 2 relative to peptide 17. ",
"A FITC moiety was attached to peptide-19 to facilitate direct measurement of binding affinity to RPA70N; the new peptide-20 has an affinity of 480 nM (approximately an additional 3-fold increase). ",
"While the basis for the binding improvement due to the FITC label is not well understood, a similar effect was noted with the ATRIP peptide.^[@ref20]^\n\n###### Amino Acid Substitutions\n\n![](",
"jm-2013-01730y_0012){#GRAPHIC-d518e438-autogenerated}\n\nSubstituted residues are indicated in bold red.",
"\n\n*K*~d~ values derived from IC~50~ values measured in an FPA competition assay.",
"\n\nSouza-Fagundes et al.^[@ref20]^\n\n*K*~d~ values of FITC-labeled peptides determined by direct binding experiments.",
"\n\nReduction of Overall Peptide Charge {#sec2.3}\n-----------------------------------\n\nPeptide-20 has a net negative charge of −6. ",
"Empirical evidence has suggested that a neutral or positive overall charge is optimal for achieving cellular penetrance.^[@ref17]^ We therefore examined the relative importance of the negatively charged residues in peptide-19 by replacing aspartic and glutamic acid residues with their amide analogues. ",
"In addition, we tested the replacement of D and E residues with alanines (in the context of the optimized WFA containing peptide-19) to elucidate which negatively charged amino acids could be substituted with an uncharged residue without leading to an unacceptable decrease in RPA70N affinity (Table [3](#tbl3){ref-type=\"other\"}). ",
"While replacement of some negatively charged amino acids is tolerated, other substitutions are accompanied by a severe drop in binding affinity, as might be expected for a peptide binding to a protonated basic cleft. ",
"For example, changing D1 to an asparagine was tolerated with a relatively minimal loss of affinity (peptide-21), an alanine substitution of D5 did not reduce the potency compared to an N substitution (peptide-22 and peptide-23), and substitution of D6 with an asparagine produced better binding than the corresponding alanine (peptide-24 and peptide-25). ",
"However, for E8, an alanine substitution sharply reduced the binding affinity (peptide-26), while minimal loss of affinity was observed for substituting E9 with either an alanine or glutamine (peptide-27 and peptide-28). ",
"On the basis of these results, we combined the least deleterious amino acid substitutions to produce a FITC-labeled peptide (peptide-29) with a net negative charge of −2. ",
"However, the reduction in charge came at the expense of a nearly 50-fold loss in binding to RPA70N compared to peptide-20.",
"\n\n###### Charge Abrogation of Peptide-19\n\n![](",
"jm-2013-01730y_0006){#GRAPHIC-d518e487-autogenerated}\n\nCharge replacement mutations are shown in bold red. ",
"Amino acid changes incorporated from earlier peptides are shown in blue.",
"\n\n*K*~d~ values derived from IC~50~ values measured in an FPA competition assay unless otherwise noted.",
"\n\n*K*~d~ values determined by direct binding experiments.",
"\n\nShortening of the Peptide Sequence {#sec2.4}\n----------------------------------\n\nConcomitant with our efforts to reduce the net negative charge of the peptides, we examined the effect of peptide length on binding affinity and the possibility of improving the properties of the peptides.^[@ref22]^ If the ATRIP-derived peptides adopt a helix with the same length as p53 upon binding to RPA70N, several N- and the C-terminal residues may not be part of the secondary structure and thus are potential candidates for removal. ",
"The alanine scan revealed that all residues at the N-terminus are essential for interacting with RPA70N (Table [1](#tbl1){ref-type=\"other\"}). ",
"In contrast, minimal loss of binding affinity was observed when residues at the C-terminus were replaced by alanine (peptide-12 and peptide-13). ",
"Therefore, we tested whether shortening of peptide-20 by one, two, or three residues at the C-terminus would be tolerated (Table [4](#tbl4){ref-type=\"other\"}).",
"\n\n###### Binding Affinity of Shortened Peptides\n\n![](",
"jm-2013-01730y_0007){#GRAPHIC-d518e532-autogenerated}\n\nDeleted residues are indicated by bold red dashes. ",
"3,4-Dichlorophenylalanine is shown as a bold green Z. Amino acid changes incorporated from earlier peptides are shown in blue.",
"\n\n*K*~d~ values determined by direct binding experiments.",
"\n\nRemoving the C-terminal residue (S15) had almost no effect on the binding of peptide-30 to RPA70N, and the removal of the last two C-terminal amino acids (A-S) led to a peptide with improved binding affinity to RPA70N (peptide-31). ",
"However, removing one additional residue (L13) resulted in a 3-fold decrease in binding affinity (peptide-32).",
"\n\nUnnatural Amino Acid Substitutions {#sec2.5}\n----------------------------------\n\nIn order to further improve binding to RPA70N, we explored the possibility of incorporating unnatural amino acids. ",
"Such peptides can be difficult and expensive to synthesize and thus must be carefully designed. ",
"To identify suitable locations for incorporation of a designed unnatural amino acid, we exploited findings from our small molecule discovery efforts. ",
"We have previously reported the use of an NMR-based fragment screen to discover compounds that bind to a hydrophobic pocket near S55,^[@ref12]^ suggesting that this pocket represents an important binding \"hot spot\" on RPA70N (Figure [1](#fig1){ref-type=\"fig\"}A). ",
"Consistent with this finding, that same pocket is occupied by F54 of the WF motif within the p53 peptide (Figure [1](#fig1){ref-type=\"fig\"}B).^[@ref19]^ Optimization of multiple series of fragment hits has established that a 3,4-dichloro-substituted phenyl ring displays significantly improved binding affinity to RPA70N compared to an unsubstituted phenyl group.^[@ref12],[@ref14]^ Thus, we hypothesized that a peptide containing a 3,4-dichloro-substituted phenylalanine in place of a phenylalanine would have improved binding affinity to RPA70N (Figure [1](#fig1){ref-type=\"fig\"}C). ",
"Indeed, a peptide containing an unnatural amino acid with a 3,4-dichlorophenyl moiety (peptide-33) showed a \\>100-fold improvement in affinity (Table [4](#tbl4){ref-type=\"other\"}). ",
"An X-ray structure of peptide-33 when complexed with RPA70N confirmed that the side chain of the 3,4-dichlorophenylalanine binds to the RPA70N hot spot located above S55, in a manner similar to the binding mode of the phenylalanine of p53 (Figure [1](#fig1){ref-type=\"fig\"}D).",
"\n\n![",
"X-ray structures of fragments and peptides in complex with RPA70N reveal a preferred binding site within the basic cleft. (",
"A) Overlay of cocrystal structures of fragments bound to RPA70N. (B) Superpositioned structures of RPA70N bound to fragments and the p53 peptide (red). (",
"C) The dichlorophenyl ring of an elaborated compound (yellow) binds in the same hydrophobic pocket as F54 of the p53 peptide (red). (",
"D) Superposition of RPA70N/p53 peptide (red)^[@ref19]^ and RPA70N/peptide-33 (blue).](jm-2013-01730y_0002){#fig1}\n\nStapled Helix Peptides {#sec2.6}\n----------------------\n\nThe use of a hydrocarbon staple for helical peptides is a promising approach to improve upon the poor characteristics of linear peptides by imparting increased protease resistance, affinity, and cell permeability.^[@ref15]−[@ref17]^ Three stapling patterns have been shown to stabilize helical conformations: *i*, *i* + 3; *i*, *i* + 4; and *i*, *i* + 7.^[@ref17]^ On the basis of the results from the mutational analyses, we employed the *i*, *i* + 4 configuration using residues 5 and 9 to evaluate stapled helix peptides with varying overall net charge (Table [5](#tbl5){ref-type=\"other\"}). ",
"Although peptide-34 had a slightly reduced binding affinity compared to its unstapled counterpart (peptide-31), the negative charge was reduced. ",
"As expected, further reduction of the charge yielded an additional loss in affinity (peptide-35, peptide-36, and peptide-37). ",
"Once again, we compensated for the loss in affinity due to charge abrogation by substituting F12 with a dichlorophenylalanine (peptide-38 and peptide-39). ",
"Incorporation of this motif alone led to a 31- and 175-fold increase in affinity, respectively, resulting in peptides that represent the optimal balance of potency and overall net charge.",
"\n\n###### Binding Affinities of Peptides\n\n![](",
"jm-2013-01730y_0008){#GRAPHIC-d518e630-autogenerated}\n\nα-(4-Pentenyl)alanine staples are depicted as a red X. 3,4-Dichlorophenylalanine is shown as a bold green Z. Amino acid changes incorporated from earlier peptides are shown in blue.",
"\n\n*K*~d~ values determined by direct binding experiments.",
"\n\nSelectivity {#sec2.7}\n-----------\n\nTo verify the utility of the stapled helix peptides as specific inhibitors of the RPA70N protein--protein interactions, we evaluated the ability of the peptides to bind to the other OB-fold-containing domains of RPA that bind to ssDNA.",
"\n\n{#fig2}\n\nBy use of a direct binding FPA assay, peptide-37 and peptide-39 were examined for their ability to bind to RPA70A/B, which contains the core ssDNA binding unit, and RPA70C/32D/14 (Figure [2](#fig2){ref-type=\"fig\"}). ",
"Peptide-37 shows very little selectivity in binding to the different OB-fold containing domains; while this peptide binds to RPA70N with a *K*~d~ of 7.4 μM, it binds the other domains with similar affinity (12--15 μM). ",
"In contrast, peptide-39, which binds to RPA70N with an affinity of 0.042 μM, binds to RPA70A/B and RPA70C/32D/14 with a *K*~d~ of only 2.4 μM, exhibiting 50-fold selectivity for binding to RPA70N. The incorporation of the dichlorophenyl moiety not only produces a significant increase in potency but also appears to impart a significant increase in selectivity for RPA70N over other OB-fold containing domains. ",
"To confirm that peptide-39 does not functionally displace RPA from ssDNA, we conducted an electrophoretic mobility shift assay (EMSA). ",
"Increasing concentrations of peptide-39 were incubated with RPA and ssDNA and subjected to separation on a polyacrylamide gel. ",
"No change in the percent of RPA bound to radiolabeled ssDNA was observed, indicating that although peptide-39 can bind weakly to other OB-fold containing domains in a biochemical assay, this 2 μM binding affinity is not sufficient to displace full-length RPA from ssDNA (Figure [3](#fig3){ref-type=\"fig\"}). ",
"Thus, peptide-39 possesses a suitable selectivity profile for use as a probe of RPA70N function in cells.",
"\n\n{#fig3}\n\nCell Penetrance {#sec2.8}\n---------------\n\nSeveral studies have demonstrated that stapled helix peptides gain entry to mammalian cells through active endocytosis.^[@ref15],[@ref23],[@ref24]^ Further, overall peptide charge is a key determinant of cellular penetrance, with increased positive charge leading to more efficient uptake. ",
"We examined the ATRIP-derived stapled helix peptides for their ability to enter mammalian cells. ",
"Peptides were incubated for 24 h with U2OS cells, fixed, and visualized by confocal microscopy for direct observation of the FITC label (Figure [4](#fig4){ref-type=\"fig\"}). ",
"As expected, peptide-34, with a net charge of −4, was the least efficient at penetrating cells. ",
"In contrast, the remaining peptides were observed inside the cells in a pattern consistent with internalization through endocytosis. ",
"Diffuse cytosolic staining and fluorescence within the nucleus were also observed, as exemplified by peptide-37 and peptide-39.",
"\n\n{#fig4}\n\nConclusions {#sec3}\n===========\n\nTo discover a peptide that binds tightly to RPA70N and penetrates cells, we initiated optimization of a 15 amino acid ATRIP-derived peptide that binds to RPA70N with an affinity of 29 μM and possesses a net charge of −5. ",
"Through alanine scanning, natural amino acid substitutions, and shortening of the peptide sequence, we identified key residues responsible for binding to RPA70N, improved the binding affinity, and ascertained which amino acids could be substituted to reduce the overall negative charge. ",
"However, because of the electrostatic characteristics of the pocket, substitutions that reduced the peptide charge universally led to a decrease in binding affinity. ",
"Despite these improvements and the knowledge gained, the resulting peptides were still unsuitable for use as a chemical probe for the study of RPA70N as a cancer target because of insufficient binding affinity.",
"\n\nTo further improve the binding affinity, we sought to incorporate an unnatural amino acid into our peptides. ",
"Historically, this strategy has not been widely employed because of difficulties in choosing which amino acid to replace and which unnatural amino acid to use as a replacement. ",
"Indeed, most peptide optimizations typically involve only the use of natural amino acid substitutions. ",
"Here we have demonstrated a strategy to efficiently design unnatural amino acid substitutions for peptide optimization. ",
"The optimization process involves the identification of a binding hot spot using a fragment-based screen and subsequent structural characterization of important molecular interactions that might be exploited for affinity improvements. ",
"Structural knowledge of the residue that normally occupies this hotspot, along with SAR information gleaned from fragment hits and optimization of these hits, then guides the efficient targeted replacement of an amino acid with an optimized variant.",
"\n\nWe have demonstrated this strategy by capitalizing on a wealth of SAR and structural information from compounds identified from a NMR-based fragment screen. ",
"In multiple prior instances, the presence of a 3,4-dichlorophenyl moiety has produced improvements in binding affinity.^[@ref12],[@ref14]^ Thus, we applied this substitution pattern to a phenylalanine residue that had been previously determined to occupy the same binding hot spot identified in the fragment screen. ",
"The addition of two halogens produced highly significant gains in binding affinity in both stapled and unstapled peptides.",
"\n\nIn total, by combining peptide optimization studies, small molecule SAR, and structural information on peptide and small molecule binding modes, we improved the affinity of the modified peptide by almost 1000-fold. ",
"The optimized stapled helix peptide obtained from this work binds tightly to RPA70N with an affinity of 0.042 μM, is selective for binding to RPA70N versus other OB folds of RPA, has a reduced overall net negative charge, and penetrates cells. ",
"This compound may serve as a useful tool to study the biology of RPA and validate RPA as a cancer target. ",
"Moreover, the new approach that we have employed to optimize the peptides may be a useful general method for optimizing peptides that bind to other protein targets and thus expand the utility of stapled helix peptides as chemical tools and therapeutic agents.",
"\n\nExperimental Details {#sec4}\n====================\n\nProtein Expression and Purification {#sec4.1}\n-----------------------------------\n\nRecombinant RPA70N (RPA70~1--120~), RPA70AB (RPA70~181--422~), and RPA70NAB (RPA70~1--422~) constructs were prepared as described previously.^[@ref20],[@ref25]−[@ref27]^ Proteins were expressed in *Escherichia coli* host Rosetta (RPA70AB, RPA70NAB) or BL21-DE3 (RPA70N) cells (Novagen). ",
"Cells were grown in LB medium containing kanamycin (RPA70AB, RPA70NAB) or ampicillin (RPA70N) at 37 °C, induced with 0.1 M IPTG when the OD reached 0.6, and harvested after 4 h using a JLA 8.1 Beckman rotor at 7500 rpm and 4 °C. ",
"Pellets were stored at −20 °C. ",
"Human RPA70N was purified using a Ni sepharose column (GE Healthcare). ",
"Following His-tag cleavage and a Ni sepharose column repass to remove the cleaved tag, RPA70N was obtained at greater than 95% purity as judged by sodium dodecyl sulfate--polyacrylamide gel electrophoresis (SDS--PAGE) analysis. ",
"Finally, RPA70N samples were dialyzed against assay buffer (50 mM HEPES, 75 mM NaCl, 5 mM DTT, pH 7.5) for use in fluorescence polarization studies. ",
"RPA70AB samples were purified using nickel affinity chromatography in 10 mM HEPES (pH 7.5), 500 mM NaCl, 5 mM BME, and 10% glycerol using an elution gradient from 20 to 300 mM imidazole. ",
"Cleavage of the His tag with TEV protease was performed through overnight dialysis in a buffer containing 10 mM HEPES (pH 7.5), 200 mM NaCl, 5 mM BME. ",
"A second Ni column purification step was used to remove the His tag. ",
"Size exclusion chromatography using a Superdex S75 column equilibrated with the dialysis buffer was used as a last step of purification. ",
"RPA70AB protein was concentrated, and stock solutions were frozen in liquid nitrogen and kept at −80 °C. ",
"A similar procedure described previously^[@ref26]^ was used for RPA70NAB samples using Ni column buffer 30 mM MES (pH 6.5), 500 mM NaCl, 5 mM BME and cleaving with H3C protease. ",
"The size exclusion chromotography step was performed using a Superdex S200 column and a buffer containing 30 mM MES (pH 6.5), 200 mM NaCl, 10 mM BME, 5% glycerol.",
"\n\nPeptide Synthesis {#sec4.2}\n-----------------\n\nAll linear peptides, with and without fluorescein isothiocyanate (FITC), were purchased from GenScript USA Inc. FITC groups were attached to the N-terminus of peptide sequences via an aminohexanoic acid (Ahx) linker. ",
"Hydrocarbon stapled peptides were purchased from New England Peptide LLC. ",
"Staples were incorporated by placing modified α-(4-pentenyl)alanine residues at predetermined locations within the peptide sequence, separated by three amino acids. ",
"Peptides were purified by the manufacturer using high-performance liquid chromatography to \\>95% purity. ",
"Unlabeled peptides were dissolved as 10 mM stock solutions in assay buffer (50 mM HEPES, 75 mM NaCl, 5 mM DTT, pH 7.5). ",
"FITC-labeled peptides were dissolved in DMSO to a final concentration of 1 mM.\n\nFluorescence Polarization Anisotropy Assays {#sec4.3}\n-------------------------------------------\n\n*K*~d~ determination and FPA competition assays were conducted as described previously^[@ref20]^ with minor modifications. ",
"For direct *K*~d~ determination of FITC-labeled peptides, increasing concentrations of purified RPA were added to 25 nM peptide in a total of 50 μL assay buffer. ",
"Anisotropy was measured, and data were fit to a single site binding model using Prism. ",
"For competition experiments, unlabeled peptides were titrated into assay buffer containing RPA70N and FITC-labeled peptide probe. ",
"Assays were conducted at a protein concentration equal to the *K*~d~ of the FITC-peptide--protein interaction. ",
"Therefore, 50 nM FITC-ATRIP was used with 6 μM RPA70N; 25 nM peptide-31 was used with 350 nM RPA70N. Anisotropy was measured and plotted against compound concentration using a four-parameter logistic fit to generate an IC~50~; this value was converted to *K*~d~, as previously described.^[@ref20]^\n\nGel Mobility Shift Assay {#sec4.4}\n------------------------\n\nThe gel mobility shift assays were performed as previously described^[@ref28]^ with the following modifications. ",
"Purified RPA (12 nM final concentration) and increasing concentrations of peptide-39 (0, 0.1, 1, 10, 100 μM final concentration) were incubated with radiolabeled 50-nucleotide ssDNA probe (6 nM final concentration) at room temperature for 20 min. ",
"The samples were separated by electrophoresis prior to autoradiography and quantitation.",
"\n\nFluorescence Microscopy {#sec4.5}\n-----------------------\n\nU2OS cells were plated at 3 × 10^4^ cells/well in eight-chamber slides (BD Falcon). ",
"After 24 h, cells were washed once with PBS and incubated for 24 h with stapled helix peptides in serum-free medium. ",
"Medium was removed, and cells were fixed in 4% paraformaldehyde/PBS for 1 h at room temperature. ",
"Cells were rinsed three times with PBS and mounted on a coverslip with Vectashield (Vector Laboratories) mounting medium containing DAPI. ",
"Slides were imaged on a confocal microscope (Zeiss LSM 710).",
"\n\nCrystallization of RPA70N:Peptide-33 Complex {#sec4.6}\n--------------------------------------------\n\nLyophilized peptide-33 (FITC-Ahx-DFTADDLEEWZAL-NH~2~) was added directly to 700 μM RPA70N E7R at a 2.5:1 (peptide-33/E7R RPA70N) ratio and initially screened against a variety of conditions. ",
"Following optimization of the initial crystallization conditions, the buffer condition of 100 mM Bis-Tris, pH 6.5, 200 mM ammonium acetate, 25% PEG 3350 was found to produce crystals that showed a strong green color, indicative of the presence of FITC. ",
"Prior to data collection, crystals were soaked in mother liquor containing 20% 2-methyl-2,4-pentanediol (MPD) and were flash-frozen in liquid nitrogen. ",
"X-ray diffraction data were initially collected on an in-house rotating anode source and later at sector 21 (Life Sciences Collaborative Access Team, LSCAT) at the Advanced Photon Source. ",
"All data were processed by HKL2000.^[@ref29]^ The proteins crystallized in space group *C*121 and contained two peptide-33:E7R RPA70N complexes in the asymmetric unit. ",
"Initial phases were obtained by molecular replacement with PHASER^[@ref30]^ using the E7R RPA70N structure (4IPC)^[@ref27]^ as a search model. ",
"Iterative cycles of model building and refinement were performed using COOT^[@ref31]^ and Phenix.^[@ref32]^ Following modeling of waters, peptide-33, including its covalently attached FITC, was placed into electron density at the basic cleft and refined. ",
"The structure of this complex has been deposited in the Protein Data Bank under the accession code 4NB3.",
"\n\nCrystallographic results and refinement statistics. ",
"This material is available free of charge via the Internet at <http://pubs.acs.org>.",
"\n\nSupplementary Material\n======================\n\n###### \n\njm401730y_si_001.pdf\n\n^\\#^ A.O.F.: Novartis Institutes for BioMedical Research (NIBR), Global Discovery Chemistry, Emeryville, California 94608, United States.",
"\n\n^∞^ B.V.: The Institute for Applied Cancer Sciences, The University of Texas MD Anderson Cancer Center, Houston, TX, United States.",
"\n\n^¶^ E.M.S.-F.: Physiology and Biophysics Department, Federal University of Minas Gerais, Av. ",
"Antônio Carlos, 6627, Pampulha, Belo Horizonte, MG, 31270-901, Brazil.",
"\n\nThe authors declare no competing financial interest.",
"\n\nThis work was supported by a postdoctoral fellowship from the Deutscher Akademischer Austausch Dienst (DAAD) to A.O.F., a National Institutes of Health National Research Service Award (NRSA) F32 ES021690 to M.D.F., NIH Grant CA102792 to D.C., and funding from the National Council for Scientific and Technological Development---CNPq and Federal University of Minas Gerais/Brazil to E.M.S.-F. We thank Dr. Cheryl Arrowsmith (Ontario Cancer Institute, Toronto, Canada) for kindly providing the ^1^H and ^15^N backbone NMR assignments of RPA70N.\n\nRPA\n\n: replication protein A\n\nFPA\n\n: fluorescence polarization anisotropy\n\nLE\n\n: ligand efficiency\n"
] | {
"pile_set_name": "PubMed Central"
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"Social Media Optimization Trends For 2017\n\nIt’s anticipated that the Development of Snap will Result in new opportunities, which is interesting at least, in 2017. ",
"In the past couple of months Breeze, understood previously and more broadly as Snap Chat, has obtained improved by leaps and bounds. ",
"Experts are predicting big things with this platform at the days beforehand. ",
"Breeze has been effective in altering important trends in addition to user expectations from the sphere of social networking marketing. ",
"Due to Snap, the moment focused perspective of communicating is back. ",
"It has meant more spontaneous and lives content. ",
"It’s helped programmers create more programs that are concentrated towards the mobile platforms.",
"\n\nSnap has also brought forth perpendicular videos and forced them a Portion of the mainstream. ",
"But now it’s seeking to produce products which happen to fall beyond the purview of the attention domain – which of exchanging messages. ",
"It’s seeking to bring about real world eyeglasses because of its customers so that they have the ability to capture visual information about a first-person basis. ",
"So far as.",
"\n\nSocial networking Optimization is worried; Snap will be there right at the center of matters. ",
"It’s also expected to offer a few significant league advertising opportunities also. ",
"Twitter fatigue will get worse Experts believe that maybe not everybody is well with Twitter and moving. ",
"But Many Brands and celebrities active on Twitter. ",
"They are trying to gain Twitter followers in 2017.",
"\n\nTwitter fatigue will get worse\n\nAhead in 2017, it’s not expected to have any better. ",
"Actually, within the past couple of decades, a lot of folks have been stating that Twitter will probably die a natural death. ",
"But, there are also the ones that consider that in most likelihood Twitter will be there for one more year in the least. ",
"But, they’re also stating that Twitter fatigue increases appreciably in 2017. ",
"Twitter is famous for its brief updates delivered at a breakneck speed but in addition, it contributes to a great deal of incoming and outgoing tweets.",
"\n\nWhen it began it was rather fascinating for the simple reason that it was brand new. ",
"But now users are becoming used to it and are requesting something that’s a whole lot different. ",
"They would like it to be larger, have higher details, and have more interesting content. ",
"Additionally, they wish for the speed to become slower. ",
"Instagram actually has already begun to slow down its rate of updates.",
"\n\nMore sensational experiences\n\nYes, this is exactly what users will desire in 2017 and they desire Social media to meet this function, to be the supplier as it had been. ",
"No more can it suffice users to say social websites they’re attending an Occasion – they should show other people how it seems to be attending that event reside. ",
"This can be achieved by means of live videos and 360-degree graphics.",
"\n\nEven Real-time posting could resolve the conundrum to an extent too. ",
"The fundamental Idea is to create others – that aren’t there – feel a portion of the entire show. ",
"They ought to feel They Are a real and natural part of the whole experience even as it continues to unravel.",
"\n\nSIMILAR NEWS\n\nThere are certain promotional ideas that can truly help you get the website traffic as well as rise success of video clip on buying you Tube comments, However, there is a trouble that this takes a great deal of time to get the sort and also customers for the video. …",
"\n\nAre you planning to Boost YouTube Sights? ",
"There can be any type of a number of factors for services as well as individuals to want to reach a larger target market. ",
"Among the lot more effective means to acquire a bigger target market is to buy YouTube views advertise YouTube …\n\nRunning a picture for your web site is as awesome as running a large range of phrases. ",
"So, you should utilize images from a variety of the things which you may be offering, in addition, to showcase them all working on the online audience. ",
"Because situation applies Instagram as well …"
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"Pierre Karl Péladeau nuit au retour des Nordiques à Québec, a affirmé jeudi le chef de la Coalition avenir Québec, François Legault. ",
"Selon lui, les propriétaires de la Ligue nationale de hockey (LNH) seront réfractaires à accorder une franchise à un homme d'affaires qui dirige un parti indépendantiste.",
"\n\n«Ce que j'entends à Montréal, c'est que tant que M. Péladeau sera là, ce sera difficile de lui donner une équipe», a laissé tomber le chef caquiste avant une réunion de ses députés.",
"\n\nIl dit douter que les propriétaires des autres franchises canadiennes acceptent d'accueillir au sein de leur groupe le chef d'un parti politique voué à l'indépendance du Québec. ",
"M. Péladeau est l'actionnaire de contrôle de Québecor, l'entreprise qui gère l'amphithéâtre de Québec et qui tente de convaincre la Ligue nationale de hockey (LNH) de ramener le hockey professionnel dans la Vieille Capitale.",
"\n\nM. Legault croit que les autres propriétaires useront de leur droit de veto pour barrer la route à M. Péladeau.",
"\n\n«Le fait que M. Péladeau soit un indépendantiste, on sait très bien, que ce soit les propriétaires de Toronto ou du Canadien, ce ne sont pas des indépendantistes et ils n'aiment pas ça, l'indépendance du Québec», a dit M. Legault.",
"\n\nLa sortie de François Legault a été qualifiée de « ridicule » par le député péquiste Pascal Bérubé. ",
"Il note que les Nordiques ont rejoint la LNH en 1979, alors que René Lévesque était au pouvoir et à quelques mois du premier référendum sur l'indépendance.",
"\n\n«Je crois que Québec est une capitale présentement, puis on est une capitale d'un pays, et ça ne changera pas, a dit M. Bérubé. ",
"Cette ville-là est une ville de hockey avec des amateurs de hockey qui aiment le hockey, qui ne mélangent pas ça avec la politique.»",
"\n\nM. Bérubé y voit la preuve que le chef caquiste sent la soupe chaude dans les élections partielles de Chauveau et Jean-Talon, deux circonscriptions vacantes de la région de Québec.",
"\n\nCe n'est pas la première fois qu'un politicien soupçonne le PQ de nuire au retour des Nordiques. ",
"Jean Charest l'avait fait lors de la campagne électorale de 2012. ",
"À l'époque, M. Legault a qualifié ses commentaires de «désespérés».",
"\n\nLe ministre libéral Sam Hamad, responsable de la Capitale nationale, a dit ne pas vouloir nuire aux efforts de Québecor pour ramener le hockey professionnel à Québec, jeudi. ",
"Il a toutefois laissé entendre que l'incertitude économique que pourrait entraîner l'élection d'un gouvernement péquiste risque de jouer dans la décision des autorités de la LNH.",
"\n\n«Il ne faut pas être naïf», a dit M. Hamad. ",
"La condition politique c'est la stabilité et la stabilité, c'est un facteur important pour l'économie.",
"\n\nLorsque Pierre Karl Péladeau s'est lancé en politique, en mars 2014, le commissaire adjoint de la LNH, Bill Daly, a affirmé à Sportsnet que les allégeances politiques de l'homme d'affaires n'auraient pas d'impact sur un éventuel processus d'expansion.",
"\n\nUn porte-parole de la ligue, Frank Brown, a refusé de commenter la sortie de M. Legault jeudi.",
"\n\n«Il n'y a pas de commentaire à faire puisque nous ne sommes pas dans un processus formel d'expansion», a-t-il indiqué dans un courriel."
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"It's very hard to articulate what kind of pain it was – but I rested down on one knee and I remember thinking, 'What the f**k was that?' ",
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"\n\nView photos\n\nPhoto credit: Getty Images\n\nExplaining that he knew something was wrong at that point, Dominic said his stuntman looked at him \"like he had seen a ghost\".",
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"\n\n\"Within two or three days, I was ready to get back to work. ",
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"The Redskins’ Week 15 win at Jacksonville kept Washington’s playoff hopes alive and pushed back relentless offseason talk for at least a few more days. ",
"Regardless, there’s no stopping 2019 free agency and the NFL Draft from occurring. ",
"There’s also no denying some clear needs and concerns for the current roster going forward.",
"\n\nIn conjunction with my latest 2019 first-round NFL mock draft, here’s a quick look at the primary positional concerns for next season. ",
"Have fun quibbling at the order, which likely changes multiple times over the coming weeks. ",
"I've changed my mind three times since starting the list.",
"\n\n<<SEE THE 2019 NFL MOCK DRAFT 6.0>>\n\n1. ",
"Quarterback – Much speculation surrounds Alex Smith’s recovery from his broken right leg including concerns over possible infections from the compound fracture. ",
"From the football perspective, his playing career could be in jeopardy. ",
"Smith’s hefty contract remains on the books with salary cap hits of $20.4 and $21.4 million over the next two years. ",
"That limits Washington’s options since a notable free agent signing or a first round selection makes would put a huge chunk of the team’s asset allocation into one position. ",
"But does Colt McCoy and a Day 2 selection sound appealing?",
"\n\n2. ",
"Inside linebacker – Between Mason Foster’s private messages and Zach Brown seeing the writing on the wall, fair to say that it’s been a rough month for this unit. ",
"That the Redskins risked plenty to claim Reuben Foster shows their level of concern at the position. ",
"Washington needs a speed upgrade inside.",
"\n\n3. ",
"Left guard – The Redskins had a need here this past offseason and never addressed it. ",
"The problem remains. ",
"Don’t expect a Jay Gruden-coached team to select another guard in the first, but fixing this whole is necessary.",
"\n\n4. ",
"Edge rusher – Preston Smith, another 2019 free agent, only has 3.5 sacks and five tackles for loss. ",
"That’s 1.5 sacks more than 2017 second-round pick Ryan Anderson. ",
"Even if Smith stays, the Redskins need more production opposite Ryan Kerrigan. ",
"Edge rusher might be the odds-on-favorite for their first-round pick considering the need and draft strengths.",
"\n\n5. ",
"Cornerback – Washington played this season with two true veterans and four players with a combined one year of NFL experience. ",
"The top option, Josh Norman, enters the fourth year of his five-year, $75 million contract. ",
"He only counts as $6 million in dead cap space, meaning the Redskins could move on if interested.",
"\n\n6. ",
"Wide receiver – Jamison Crowder enters free agency. ",
"Whether the Redskins make retaining the slot threat a priority or not, this group lacks a go-to option.",
"\n\n<<SEE THE 2019 NFL MOCK DRAFT 6.0>>\n\nMORE REDSKINS NEWS:"
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"Q:\n\nМожно ли как то обработать undefined?",
"\n\nЕсть скрипт, который на сайте отображает город посетителя в шапке справа вот в таком вот виде. ",
"Но бывает так, что иногда скрипт вместо города выдаёт undefined. ",
"И собственно вопрос: А можно как-то дописать/переписать скрипт, чтобы если undefined то вместо него показывало например текст: Доставка до вашего места? ",
"Помогите пожалуйста это исправить.",
"\n<!-- ",
"Определение города посетителя -->\n <script src=\"http://code.jquery.com/jquery-1.10.2.min.js\" type=\"text/javascript\"></script>\n <script src=\"https://api-maps.yandex.ru/2.0/?load=package.full&lang=ru-RU\" type=\"text/javascript\"></script>\n <script type=\"text/javascript\">\n $(document).ready(function(){\n ymaps.ready(function(){\n var geolocation = ymaps.geolocation;\n //$('#cou').html('Ваша страна: '+geolocation.country);\n $('#tow').html('Выдача заказов в г. '",
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"Определение города посетителя -->\n\n<span id=\"tow\">... определяется ...</span>\n\nA:\n\nМожно, воспользуемся проверкой if else - если условие внутри if (здесь) верно, то выполнятся команды внутри { } после if. ",
"А если неверно - то выполнятся команды внутри { } после else. ",
"Восклицательный знак является отрицанием, т.е. !",
"= можно прочитать как \"не равно\".",
"\n....\n\nvar geolocation = ymaps.geolocation;\n\nif (geolocation.city !",
"= undefined) { // если не undefined\n\n $('#tow').html('Выдача заказов в г. '",
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"Semi-synthetic DNA-protein conjugates: novel tools in analytics and nanobiotechnology.",
"\nThis article reports on the syntheses, characterization and applications of semi-synthetic conjugates composed of nucleic acids, proteins and inorganic nanoparticles. ",
"For example, self-assembled oligomeric networks consisting of streptavidin and double-stranded DNA are applicable as reagents in immunoassays, model systems for ion-switchable nanoparticle networks as well as nanometer-scaled 'soft material' standards for scanning probe microscopy. ",
"Covalent conjugates of single-stranded DNA and streptavidin are utilized as biomolecular adapters for the immobilization of biotinylated macromolecules at solid substrates via nucleic acid hybridization. ",
"This 'DNA-directed immobilization' allows for reversible and site-selective functionalization of solid substrates with metal and semiconductor nanoparticles or, vice versa, for the DNA-directed functionalization of gold nanoparticles with proteins, such as immunoglobulins and enzymes. ",
"This approach is applicable for the detection of chip-immobilized antigens. ",
"Moreover, covalent DNA-protein conjugates allow for their selective positioning along single-stranded nucleic acids, and thus for the construction of nanometre-scale assemblies composed of proteins and/or nanoclusters. ",
"Examples include the fabrication of functional biometallic nanostructures from gold nanoparticles and antibodies, applicable as diagnostic tools in bioanalytics."
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"Facing off\n\nThis piece represents the opinion of The Bowdoin Orient editorial board.",
"\n\nFebruary 3, 2012\n\nThe students behind Mass Deactivation presented a challenge to the Bowdoin community this week, urging students to deactivate their Facebook accounts for exactly one month starting on February 8. ",
"The premise of the experiment is to re-experience what life would be like without the social network, and creators Tyler Patton '12 and Ruiqi Tang '13 think that Bowdoin—as close-knit as it is tech-saturated—is the perfect environment in which to do so. ",
"And they're right.",
"\n\nThere could not be a better time to participate in this experiment. ",
"Facebook just filed a $5 billion IPO to become a publicly traded company, which means that starting this spring it will be beholden to shareholders, and must find ways to increase profitability by selling even more user information to advertisers and other third parties. ",
"With change afoot, perhaps we should examine just how much of our private information we really want to be converted into currency.",
"\n\nWe are also the last generation of college students that will remember what it was to socialize without Facebook. ",
"Our lives were probably not any simpler without Facebook, but they were certainly less plugged-in. ",
"We had to go to greater lengths to meet people and to keep in touch with friends and family. ",
"Perhaps we took more active roles in building personal relationships before we had a mini-feed to tell us what our friends were doing.",
"\n\nThe most compelling aspect of this experiment is its call for collective action. ",
"As the site points out, deactivating a Facebook account does not completely disconnect you from the online world. ",
"You will inevitably still be surrounded by people posting photos, liking statuses, and creating events. ",
"And as Facebook reminds users who attempt to deactivate, your friends might miss you when you're gone. ",
"As such, this experiment \"could literally be the last time for the rest of your life that you and the people around you exist without Facebook.\" ",
"What would it be like to attend a party no one will see photos of the next day? ",
"Or to approach someone at that party without having done some reconnaissance on their profiles first?",
"\n\nTo achieve the mass participation that will make this experiment meaningful, its creators must extend their advertising campaign such that it reaches more people. ",
"They must push beyond those who already harbor misgivings about Facebook and attempt to attract heavy users who might notice the greatest difference in their lives without an account. ",
"While the cryptic flyers simply reading \"massdeactivation.blogspot.com\" are intriguing, they do not explain the very exciting nature of the project. ",
"It would be unfortunate to lose potential participants just because they forget to look up the mysterious URL upon returning to their dorm rooms.",
"\n\nAdditionally, we urge the creators to survey participants at the end of the experiment and to make the results public. ",
"Did people find that Facebook enriches or compromises their social lives? ",
"Did they feel more or less lonely, bored or connected to people when they did not have an account? ",
"Collecting and distributing this information will be thought-provoking for those who participate in the experiment, as well as for those who choose not to join, and may even prompt similar experiments elsewhere. ",
"Facebook does not make the path to deactivation obvious, but we believe it is worth following, if only for a month."
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"php\n\nnamespace Runalyze\\Tests\\Parser\\Activity\\FileType;\n\nuse Runalyze\\Parser\\Activity\\Common\\Data\\ActivityDataContainer;\nuse Runalyze\\Parser\\Activity\\Common\\Filter\\DefaultFilterCollection;\nuse Runalyze\\Parser\\Activity\\Common\\ParserInterface;\nuse Runalyze\\Parser\\Common\\FileContentAwareParserInterface;\nuse Runalyze\\Parser\\Common\\FileTypeConverterInterface;\n\nabstract class AbstractActivityParserTestCase extends \\PHPUnit_Framework_TestCase\n{\n /** @var null|ActivityDataContainer|ActivityDataContainer[] */\n protected $Container;\n\n /** @var int */\n protected $NumberOfActivities = 0;\n\n /** @var string[] */\n protected $FilesToClear = [];\n\n protected function tearDown()\n {\n foreach ($this->FilesToClear as $file) {\n if (file_exists($file)) {\n unlink($file);\n }\n }\n }\n\n /**\n * @return string\n */\n protected function pathToTestFiles()\n {\n return TESTS_ROOT.'/testfiles/';\n }\n\n /**\n * @param FileTypeConverterInterface $converter\n * @param FileContentAwareParserInterface $parser\n * @param string $file file path relative to 'testfiles/'\n * @param string[] $expectedOutputFiles\n * @param bool $completeAfterwards\n */\n protected function convertAndParseFile(FileTypeConverterInterface $converter, FileContentAwareParserInterface $parser, $file, array $expectedOutputFiles, $completeAfterwards = true)\n {\n $outputFile = $converter->convertFile($this->pathToTestFiles().$file);\n\n if (!",
"is_array($outputFile)) {\n $outputFile = [$outputFile];\n }\n\n $this->FilesToClear = $outputFile;\n $path = $this->pathToTestFiles();\n $outputFile = array_map(function ($file) use ($path) {\n return str_replace($path, '', $file);\n }, $outputFile);\n\n $this->assertEquals($expectedOutputFiles, $outputFile);\n\n $this->parseFiles($parser, $outputFile, $completeAfterwards);\n }\n\n protected function parseFiles(FileContentAwareParserInterface $parser, array $files, $completeAfterwards = true)\n {\n $tmpContainer = [];\n\n foreach ($files as $currentFile) {\n $this->parseFile($parser, $currentFile, $completeAfterwards);\n\n if (!",
"is_array($this->Container)) {\n $tmpContainer[] = $this->Container;\n } else {\n $tmpContainer = $tmpContainer + $this->Container;\n }\n }\n\n $this->NumberOfActivities = count($tmpContainer);\n $this->Container = 1 == $this->NumberOfActivities ? ",
"$tmpContainer[0] : $tmpContainer;\n }\n\n /**\n * @param FileContentAwareParserInterface $parser\n * @param string $file file path relative to 'testfiles/'\n * @param bool $completeAfterwards\n */\n protected function parseFile(FileContentAwareParserInterface $parser, $file, $completeAfterwards = true)\n {\n $this->parseFileContent($parser, file_get_contents($this->pathToTestFiles().$file), $completeAfterwards);\n }\n\n /**\n * @param FileContentAwareParserInterface $parser\n * @param string $fileContent\n * @param bool $completeAfterwards\n */\n protected function parseFileContent(FileContentAwareParserInterface $parser, $fileContent, $completeAfterwards = true)\n {\n $parser->setFileContent($fileContent);\n $parser->parse();\n\n $this->setContainerFrom($parser, $completeAfterwards);\n }\n\n /**\n * @param ParserInterface $parser\n * @param bool $completeAfterwards\n * @param bool $runFilter\n */\n protected function setContainerFrom(ParserInterface $parser, $completeAfterwards = true, $runFilter = true)\n {\n $filterCollection = new DefaultFilterCollection();\n $this->NumberOfActivities = $parser->getNumberOfActivities();\n $this->Container = [];\n\n for ($i = 0; $i < $this->NumberOfActivities; ++$i) {\n $this->Container[] = $parser->getActivityDataContainer($i);\n\n if ($completeAfterwards) {\n $this->Container[$i]->completeContinuousData();\n }\n\n if ($runFilter) {\n $this->Container[$i]->filterActivityData($filterCollection);\n }\n\n if ($completeAfterwards) {\n $this->Container[$i]->completeActivityData();\n }\n }\n\n if (1 == $this->NumberOfActivities) {\n $this->Container = $this->Container[0];\n }\n }\n\n /**\n * @param array $expectedRounds [[duration [s], distance [km]], ...]\n * @param int $deltaDuration [s]\n * @param float $deltaDistance [km]\n */\n protected function checkExpectedRoundData(array $expectedRounds, $deltaDuration = 0, $deltaDistance = 0.0)\n {\n $this->checkExpectedRoundDataFor($this->Container, $expectedRounds, $deltaDuration, $deltaDistance);\n }\n\n /**\n * @param ActivityDataContainer $container\n * @param array $expectedRounds [[duration [s], distance [km]], ...]\n * @param int $deltaDuration [s]\n * @param float $deltaDistance [km]\n */\n protected function checkExpectedRoundDataFor(ActivityDataContainer $container, array $expectedRounds, $deltaDuration = 0, $deltaDistance = 0.0)\n {\n $this->assertEquals(count($expectedRounds), $container->Rounds->count());\n\n foreach ($expectedRounds as $i => $expectedRoundData) {\n $this->assertEquals($expectedRoundData[0], $container->Rounds[$i]->getDuration(), 'Round #'.$i.' ",
"has wrong duration.', ",
"$deltaDuration);\n $this->assertEquals($expectedRoundData[1], $container->Rounds[$i]->getDistance(), 'Round #'.$i.' ",
"has wrong distance.', ",
"$deltaDistance);\n }\n }\n\n /**\n * @param array $expectedPauses [[time index [s], duration [km](, hr start [bpm], hr end [bpm])], ...]\n * @param int $deltaDuration [s]\n */\n protected function checkExpectedPauseData(array $expectedPauses, $deltaDuration = 0)\n {\n $this->assertEquals(count($expectedPauses), $this->Container->Pauses->count());\n\n foreach ($expectedPauses as $i => $expectedPauseData) {\n $this->assertEquals($expectedPauseData[0], $this->Container->Pauses[$i]->getTimeIndex(), 'Pause #'.$i.' ",
"has wrong time index.', ",
"$deltaDuration);\n $this->assertEquals($expectedPauseData[1], $this->Container->Pauses[$i]->getDuration(), 'Pause #'.$i.' ",
"has wrong duration.', ",
"$deltaDuration);\n\n if (isset($expectedPauseData[2]) && isset($expectedPauseData[3])) {\n $this->assertEquals($expectedPauseData[2], $this->Container->Pauses[$i]->getHeartRateAtStart(), 'Pause #'.$i.' ",
"has wrong heart rate at start.');",
"\n $this->assertEquals($expectedPauseData[3], $this->Container->Pauses[$i]->getHeartRateAtEnd(), 'Pause #'.$i.' ",
"has wrong heart rate at end.');",
"\n }\n }\n }\n}\n"
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"---\nabstract: |\n We present a physical model to explain the behavior of long-term, time series measurements of chloride, a natural passive tracer, in rainfall and runoff in catchments \\[[*Kirchner et al.*]{}, [*",
"Nature, 403*]{}(524), 2000\\]. ",
"A spectral analysis of the data shows the chloride concentrations in rainfall to have a white noise spectrum, while in streamflow, the spectrum exhibits a fractal $1/f$ scaling. ",
"The empirically derived distribution of tracer travel times $h(t)$ follows a power-law, indicating low-level contaminant delivery to streams for a very long time. ",
"Our transport model is based on a continuous time random walk (CTRW) with an event time distribution governed by $\\psi(t)\\sim\n A_{\\beta}t^{-1-\\beta}$. The CTRW using this power-law $\\psi(t)$ (with $0<\\beta<1$) is interchangeable with the time-fractional advection-dispersion equation (FADE) and has accounted for the universal phenomenon of anomalous transport in a broad range of disordered and complex systems. ",
"In the current application, the events can be realized as transit times on portions of the catchment network. ",
"The travel time distribution is the first passage time distribution $F(t; l)$ at a distance $l$ from a pulse input (at $t=0$) at the origin. ",
"We show that the empirical $h(t)$ is the catchment areal composite of $F(t; l)$ and that the fractal $1/f$ spectral response found in many catchments is an example of the larger class of transport phenomena cited above. ",
"The physical basis of $\\psi(t)$, which determines $F(t; l)$, is the origin of the extremely long chemical retention times in catchments.",
"\nauthor:\n- 'H. Scher'\n- 'G. Margolin'\n- 'R. Metzler'\n- 'J. Klafter'\n- 'B. Berkowitz'\ntitle: 'The dynamical foundation of fractal stream chemistry: The origin of extremely long retention times'\n---\n\nIntroduction\n============\n\nThe distribution of travel times required for chemical substances to travel through a catchment is an important hydraulic quantity, determining the retention of pollutants until they are eventually released to a stream or lake. ",
"The same distribution controls the transport of chemicals in subsurface hydrological systems. ",
"The nature of this distribution determines the expected ecological impact of contaminants.",
"\n\nIn a long-term catchment study conducted at Plynlimon, Wales, [*Kirchner et al.*]{} ",
"\\[2000\\] (hereafter denoted KFN) compare the (input) time series of the concentration $c_R(t)$ of chloride tracer in the rainfall to the (output) time series of the concentration $c_s(t)$ into the Hafren stream. ",
"They relate the concentrations through the convolution integral $$\\label{conv}\nc_s(t)={\\textstyle\\int_0^\\infty}h(t')c_R(t-t')dt'$$ where the effective travel time distribution $h(t)$ governs the lag time between injection of the tracer through rainfall and outflow to the stream.",
"\n\nKFN observe that the streamflow (volume of water) responds rapidly to storm rainfall inputs while the $c_s(t)$ response is highly damped (i.e., low-level contaminant delivery to streams for a very long time). ",
"The timescales of catchment hydrologic and chemical response are resolved using spectral methods [@duffy] (in which the input/output response can be compared at each (time) wavelength). ",
"The spectral power of the water fluxes of rainfall and streamflow coincide while the spectra of $c_s(t)$ show strong attenuation on all wavelengths less than 5-10 years. ",
"Further, the $c_R(t)$ spectra scale as white noise in sharp contrast to the fractal $1/f$ scaling of the $c_s(t)$ spectra. ",
"Using these results in the Fourier transform of the convolution in (\\[conv\\]), with $f$ denoting frequency, and $C_s$, $H$ and $C_R$ representing the respective Fourier transforms, $$\\label{amp}\nC_s(f)=H(f)C_R(f)$$ and the relation of the power spectra is $$\\label{power}\n|C_s(f)|^2=|H(f)|^2|C_R(f)|^2$$ Since $|C_R(f)|^2$ is nearly a white noise spectrum (a constant) one has $|H(f)|^2 \\propto |C_s(f)|^2$. From the measured power-law scaling of $|C_s(f)|^2\n\\propto f^{-0.97}$, KFN conclude that $$\\label{htail}\nh(t) \\sim t^{-m}$$ (from $H(f)\\sim f^{-(1-m)}$), where $m \\approx 0.5$.\n\nIn order to ensure that $h(t)$ is integrable and possesses a finite average travel time, KFN arbitrarily chose the gamma distribution $$\\label{tddk}\nh(t)=\\frac{t^{\\gamma-1}}{\\varrho^{\\gamma}\\Gamma(\\gamma)}\ne^{-t/\\varrho}$$ with $\\gamma=0.48$ and $\\varrho=1.9$ years, with a characteristic travel time $T_h \\equiv\\int_0^{\\infty}h(t)t dt=\\gamma\\varrho$. Due to the relatively large value of $\\varrho$, essentially the entire data correspond to the power-law $h(t)\\sim t^{\\gamma-1}$ with the power spectrum $|C_s(f)|^2 \\propto|H(f)|^2\\sim f^{-2\\gamma}$. KFN refer to similar scaling between $f^{-0.7}$ and $f^{-1.2}$ found in Scandinavian and North American field sites, which indicates a certain ubiquity to fractal, scale-free forms (which is the issue we address in this letter).",
"\n\nTransport models\n================\n\nThe first step to understanding transport in the catchment is the clarification of the meaning of (\\[conv\\]). ",
"The $h(t)$ is the [*effective*]{} response to a pulse of rain falling on the entire area of the catchment. ",
"Every point of this area is a source of chloride and the stream is a line sink for the chloride. ",
"We simplify the area to be a rectangle of width $\\lambda$ about this stream sink (with periodic boundary conditions on the sides perpendicular to the stream[@ctrw]). ",
"The sink or absorbing boundary ensures the correct “counting rate\" of chloride at the arriving point, i.e., the first passage time distribution $F(t;l)$ is the appropriate travel time distribution from a pulse source at point $l$. In terms of this [*intrinsic*]{} distribution, $$\\label{eq:gen}\nc_{s}(t;l_s) = \\int_0^\\infty \\sum_{l\\in \\Omega}F(t';l-l_s) c_{R}\n(t-t';l)dt'$$ where $c_{s}(t;l_s)$ is the chloride concentration at the stream position $l_s$ at time $t$, $\\Omega$ is the size of the catchment and $c_{R}(t;l)$ the rain-input at a position $l$ in $\\Omega$. We can consider the sampling positions $\\{l_s \\}$ of $c_{s}$ to be a small region compared to $\\Omega$ and hence $c_{s}(t;l_s) \\approx\nc_{s}(t)$. To do the $l$-sum we assume that the rainfall is distributed uniformly in $\\Omega$, $c_{R}(t;l) \\approx\nc_{R}(t)$. Hence, we recover (\\[conv\\]) now with $$\\label{eff}\nh(t) \\equiv \\sum_{l\\in \\Omega}F(t;l)$$ The distribution $F(t;l)$ must be integrable in time and thus so $h(t)$ for a finite $\\Omega$. The basis of comparison for various transport approaches is the computation in (\\[eff\\]).",
"\n\nAdvection-dispersion equation (ADE)\n-----------------------------------\n\nThe textbook approach to transport of passive tracers in both surface and subsurface systems usually focuses on the advection-dispersion equation (ADE) $$\\label{dae}\n\\partial {\\cal W}/\\partial t+v\\partial {\\cal W}/\\partial x=D\\partial^2 {\\cal\nW}/\\partial x^2$$ e.g., for 1d with constant $v$ the average fluid velocity and $D$ the dispersion coefficient. ",
"This equation governs the temporal evolution of the probability density function (pdf) ${\\cal W}(x,t)$ of finding a tracer particle, which undergoes dispersive motion, at a certain position $x$ at time $t$ after release at $t=0$. The pdf ${\\cal W}$ is the normalized concentration profile.",
"\n\nThe travel time distribution belonging to (\\[dae\\]) can be obtained by the Laplace Transform ($LT$) technique. ",
"This yields the $LT$ $\\tilde{{\\cal F}}(u;x)\\equiv\\int_0^{\\infty}{\\cal F}(t;x)e^{-ut}dt$ of the first passage time from $x$ to the absorbing boundary at $x=0$, $\\tilde{{\\cal F}}(u;x)=\n\\exp\\left(x\\left[v-\\sqrt{4Du+v^2}\\right]/(2D)\\right)$. $LT$ inversion delivers the travel time distribution \\[gauss\\] [F]{}(t;x) = () which when inserted for $F(t;x)$ in (\\[eff\\]) yields $$\\begin{aligned}\n\\label{int}\nh(t) \\! \\! \\! \\! &",
"\\propto& \\! \\! \\! \\! ",
"\\int_0^\\lambda {\\cal F}(t;x)dx =\\frac\n{v}{2}\\bigl[{\\rm erf}(z) +{\\rm erf}\\left(\\frac {P_e}{4z}-z \\right) \n\\nonumber \\\\&+&\n\\! \\! \\! \\! ",
"\\frac {\\exp(-z^2)-\\exp\\left(-(\\frac\n{P_e}{4z}-z)^{2}\\right)}{\\sqrt{\\pi}z}\\bigr]\\end{aligned}$$ where the Peclet number $P_e\\equiv \\lambda v/D$, $z \\equiv \\frac {1}{2}\\sqrt{v^{2}t/D}$ and erf$(z)$ is the error function (the same result (\\[int\\]) was also derived in [*Kirchner et al.*]{}, ",
"2001). ",
"For $t<0.1 D/v^2$, $h(t)\\sim t^{-\\frac{1}{2}}$ which is similar to (\\[htail\\]) for $m\n\\approx 0.5$. \\[This upper limit on the time range holds for $P_e\\ge1$; for $P_e<1$ the limit is smaller.\\] The range is estimated by assuming $D$ to be the macrodispersion, $D=v\\alpha$, where $\\alpha$ is the dispersivity. ",
"Assuming $v\\approx 10^2$ m/yr and on the km scale $\\alpha \\sim (1-10^2)$ m, $t<0.1\\alpha/v \\sim (10^{-3}-10^{-1})$ yr. ",
"One needs $v\\approx 10$ m/yr and $\\alpha\n\\sim 10^2$ m in (\\[int\\]), for $h(t) \\sim t^{-\\frac{1}{2}}$ to partially overlap the time range of observation of this dependence [@kirchner]. ",
"Moreover, this behavior is only the same as (\\[htail\\]) in the special case where $m$ (or $\\gamma$) = $\\frac {1}{2}$. The catchment data (spectral power $\\sim \nf^{-2\\gamma}$) quoted above cover a range of $0.7\\leq 2\\gamma\\leq 1.2$.\n\nFor large $t$, $h(t)$ in (\\[int\\]) exhibits an exponential decrease $\\sim t^{-\\frac{3}{2}}$ $\\exp\\left(-v^2(4D)^{-1}t\\right)$ which is faster than (\\[tddk\\]). ",
"The decrease in $h(t)$ at large $t$ ($t>>\\lambda/v$) is due to the finite size of the catchment and not an arbitrary limiting time. ",
"The relation between the operative time range of (\\[htail\\]) and $\\lambda$ will be determined in the following.",
"\n\nContinuous-time random walk and time-fractional-ADE\n---------------------------------------------------\n\nAs shown above the standard treatment of the transport using the ADE yields a marginal accounting of the data. ",
"A transport model must determine a $F(t;l)$ that when inserted in (\\[eff\\]) gives rise to (\\[htail\\]) for over three decades of time [@kirchner]. ",
"As we will show this is best expedited with a non-Gaussian form of $F(t;l)$. A particularly dispersive form of $F(t;l)$ is associated with anomalous transport which has been observed in a wide range of disordered and complex systems: electron hopping/multiple-trapping in amorphous semiconductors [@ctrw], particle migration in fracture networks [@till], contaminant transport in heterogeneous porous media [@bescher], anomalous diffusion[@report], and Hamiltonian chaos[@pt]. ",
"There are key common features in these anomalous transport phenomena, e.g., non-Gaussian propagation of an initial pulse of particles with a mean position $\\ell(t)$ and standard deviation $\\sigma(t)$ exhibiting the same sublinear dependence on $t$ (in the presence of a bias or head). ",
"A continuous time random walk (CTRW) transport process has successfully accounted for these unusual basic features. ",
"The anomalous behavior is an outcome of a CTRW governed by a long-tail distribution of the individual transition times or event times (which have to be defined in each physical context, e.g., trap release), $$\\label{psi}\n\\psi(t)\\sim A_{\\beta}t^{-1-\\beta}$$ where $A_{\\beta}$ is a constant. ",
"Over the observation time range in which (\\[psi\\]) obtains we have for the propagating plume $P(l,t)$ $$\\ell (t) \\sim t^\\beta, \\qquad\\sigma(t) \\sim t^\\beta\\qquad0<\\beta<1$$ The highly dispersive nature of this $P(l,t)$ can be discerned by the ratio $\\sigma(t)/\\ell (t)\\sim$ constant, instead of the familiar $1/\\sqrt{t}$ for a Gaussian plume. ",
"The latter is produced for $\\beta>2$ (while for $1<\\beta<2$ one has an intermediate $t$-dependence).",
"\n\nThe CTRW accounts naturally for the cumulative effects of a sequence of transitions which constitutes the particle transport. ",
"The formalism of the CTRW has been well documented in the literature \\[[*Berkowitz and Scher*]{}, 1998; [*Metzler and Klafter*]{}, 2000\\]. ",
"For brevity we show the key equation for our purpose here in Laplace space (for three dimensions) $$\\label{1stP}\n\\tilde{F}({\\bf s},u)=\\tilde{P}({\\bf s},u)/\\tilde{P}(0,u) \\qquad\n\\qquad {\\bf s} \\ne 0$$ where the particle starts at the origin at $t=0^+$, $\\tilde{P}({\\bf\ns},u)$ is the $LT$ of $P({\\bf s},t)$, the probability density to find the particle on ${\\bf s}$ at time $t$ (plume), and $\\tilde{F}({\\bf s},u)$ is the $LT$ of $F({\\bf s},t)$, the probability per time for the particle to first arrive at ${\\bf s}$ at time $t$.\n\nExplicit evaluations for $\\tilde{F}({\\bf s},u)$ have been determined for symmetric situations (e.g., plane (line) source to plane (line) sink) and with the use of (\\[psi\\]) [@ctrw]. ",
"The symmetric cases allow a reduction of the problem to a one-dimensional form of $F$ which we write as $F(t; x)$ and $$\\label{ltF}\n\\tilde{F}(u;x)=\\exp(-xu^{\\beta}/\\bar{l}) \\qquad(0<\\beta<1)$$ ($u$ dimensionless). ",
"The inverse $LT$ of $\\tilde{F}(u;x)$ has been expressed in terms of a class of Fox $H$-functions [@report], but it is more expedient to work directly with (\\[ltF\\]) in the evaluation of $h(t)$, which will be considered in the next section.",
"\n\nMathematically, the CTRW (in the special case using (\\[psi\\]) and $(0<\\beta<1)$) is interchangeable with the time-fractional advection-dispersion equation (FADE) [@report] $$\\label{fda}\n\\frac{\\partial W}{\\partial t}=\\, _0D_t^{1-\\beta}\\left(-v_{\\beta}\n\\frac{\\partial}{\\partial x}+d_{\\beta}\\frac{\\partial^2}{\\partial x^2}\n\\right)W(x,t)$$ where the Riemann-Liouville operator is defined in terms of the convolution [@report], $$\\label{rl}\n_0D_t^{1-\\beta}W(x,t)=\\frac{1}{\\Gamma(\\beta)}\\frac{d}{dt}\\int_0^tdt'\n\\frac{W(x,t')}{(t-t')^{1-\\beta}},\\, 0<\\beta<1.$$ The form of FADE (\\[fda\\]) is the natural generalization of the ADE (\\[dae\\]) for power-law forms of $\\psi$. The solutions of FADE reproduce those of the CTRW in this special case, and in the spatial continuum limit they form a natural bridge between the CTRW and the ADE [@tipm].",
"\n\nLong Retention Times\n====================\n\nWe proceed to insert (\\[ltF\\]) into the $LT$ of (\\[eff\\]) to obtain $$\\label{eq:lth}\n\\tilde{h}(u) \\propto \\int_0^\\lambda\n\\exp(-lu^{\\beta}/\\bar{l})dl=\\bar{l}u^{-\\beta}(1-\\exp(-\\lambda\nu^{\\beta}/\\bar{l}))$$ where $\\bar{l}$ is the mean step distance. ",
"The expression for $\\tilde{h}(u)$ in (\\[eq:lth\\]) has been thoroughly studied in another context [@ctrw]; the main features are $$h(\\tau)\\sim\\left\\{\\begin{array}{ll}\n\\tau^{\\beta-1}, & \\tau<\\tau^*\\\\\n\\tau^{-\\beta-1}, & \\tau>\\tau^*\n\\end{array}\\right.",
"\n\\label{scaling}$$ ($\\tau$ dimensionless time). ",
"The exponent for $\\tau>\\tau^*$ ensures that $h(\\tau)$ is integrable. ",
"On a log-log plot $h(\\tau)$ is two constant slopes, $\\beta-1$, $-1-\\beta$, with a turnover range between them. ",
"The center time of this range, $\\tau^*$, can be estimated as the time for the argument of the exponent in (\\[eq:lth\\]) to be $\\sim\nO(1)$ (using $u \\sim 1/\\tau$) $$\\label{tau}\n\\tau^{*} \\sim (\\frac {1-\\beta}{\\beta})^{\\frac {1-\\beta}{\\beta}}(\\beta\n\\lambda/\\bar{l})^{\\frac {1}{\\beta}}$$ (The $\\beta$-factors derive from a more detailed analysis \\[[*Scher and Montroll*]{}, 1975, Appendix C\\].) ",
"For $\\beta =\\frac{1}{2}$, in (\\[eq:lth\\]) one can do the inverse $LT$ and obtain $h(\\tau) \\sim (\\pi\n\\tau)^{-\\frac{1}{2}}(1-\\exp(-\\lambda^2 /4\n\\bar{l}^2 \\tau))$, clearly showing (\\[scaling\\])-(\\[tau\\]).",
"\n\nThe change from $\\tau$ to $t$ is model dependent (to be discussed below). ",
"We use $\\tau = v_ot/\\bar{l}\\varepsilon$, where $v_o$ is a characteristic velocity (of the velocity distribution) and $\\varepsilon$ is a constant. ",
"For $\\beta = \\frac{1}{2}$, $v_o \\sim$ 100 m/yr, $\\lambda \\sim \\frac{1}{2}$ km, $\\bar{l} \\sim$ 30 m and $\\varepsilon \\sim \\frac{1}{2}$, one has (from (\\[tau\\]) with $\\tau^* = v_ot^*/\\bar{l}\\varepsilon$), $t^* \\sim$ 10 yr, which is a reasonable time scale for the change from $h(t) \\sim t^{\\beta-1}$. Hence, our scaling result (\\[scaling\\]) agrees with the KFN data (\\[htail\\]) over the measurement time range ($>$ 3 decades for t$\\le$ 10 yrs) with $\\beta=\\gamma$ ($\\equiv 1-m$). ",
"The $t$-“cutoff\" for $h(t)$ in (\\[scaling\\]) is algebraic, $t^{-\\beta-1}$, not exponential as in (\\[tddk\\])! ",
"This behavior of $h(t)$ is indicative of extremely long chemical retention times in catchments. ",
"The turnover to the $t^{-\\beta-1}$ dependence (in (\\[scaling\\])) is a prediction of the CTRW theory and has not yet been observed. ",
"A finite value of $T_h$ depends on a change in the behavior of (\\[psi\\]). ",
"For $t\n\\gg t^*$, the tail of $\\psi(t)$ becomes steeper and for $\\beta>2$, the [*intrinsic*]{} arrival time distribution evolves to ${\\cal F}(t;x)$.\n\nIndependent tests of our transport model can be obtained with experiments using a different tracer (d) and boundary conditions. ",
"For injection of the tracer d at various catchment points $\\{ {\\bf x}\n\\}$, the concentration in the stream $c_{d}(t;{\\bf l_s})$ is proportional to $F({\\bf\nx}-{\\bf l_s},t)$, determined for these boundary conditions. ",
"\\[This result answers the question raised by [*Stark and Stieglitz*]{} \\[2000\\] about a site-specific spill.\\] This is also a method for obtaining a value of $\\beta$, which determines the shape of $F({\\bf x},t)$.\n\nThere are many different physical mechanisms (cf. ",
"Refs. ",
"above) that can give rise to the $\\psi(t)$ in (\\[psi\\]) that has generated our results for $h(t)$. The common features are the representation of the transport process as a series of transitions \\[[*Berkowitz and Scher*]{}, 1998, 2001\\] and the encounter within this series of a sufficient number of transition-times that are much larger than the median one. ",
"These relatively few long-time events, which can be due to release from traps/stagnant-regions and/or passage through low velocity segments, can have a dominant influence on the overall transport. ",
"The relative weighting of these events is expressed by the exponent of the power-law in (\\[psi\\]).",
"\n\nThe hydrologic environments beneath the catchment subregions can contain a sufficient number of these low velocity sections and stagnant dead-ends. ",
"The local slope (and interconnection [@rinaldo]) of the catchment side-channels also affects the velocity distribution. ",
"The subsurface of the catchment basin can be modeled as a heterogeneous porous medium and/or a random fracture network [@bescher]. ",
"In the latter the fragment-length distribution, $f(s)$, and the fragment-velocity histogram, $\\Phi({\\bf \\xi})$, are mapped onto the probability rate for a transit time t (through a fragment) with a displacement [**s**]{}, ([**s**]{},t) ([****]{})f(s) where $|{\\bf \\xi}|=1/v$, $\\hat{\\bf \\xi}=\\hat{\\bf v}$, $t=s\\xi$ and $\\psi (t) \\equiv \\sum_s \\psi ({\\bf s},t)$. The anomalous transport observed in the fracture network particle tracking simulations is due to the power-law tail of $\\Phi({\\bf \\xi}) \\rightarrow \\xi^{-1-\\beta}$ at large $\\xi$. This is the expected behavior to be found in the catchment subsurface $\\Phi_c({\\bf \\xi})$ distribution because this hydrologic environment is the same as ones modeled successfully by the CTRW theory \\[[*Berkowitz and Scher*]{}, 1998, 2001\\]. ",
"The experiments outlined above can test these properties.",
"\n\nConclusion\n==========\n\nIn this letter we introduce the phenomenon of anomalous transport into an analysis of the comparison of the power spectra of the time series of chloride in rainfall and in (stream) runoff. ",
"An [*effective*]{} distribution of travel times $h(t)$ is derived (by KFN from the data) which we show is composed of the summation from all sites of the source distribution $F({\\bf s},t)$ in the catchment. ",
"The latter, in turn, is composed of a sequence of transitions governed by a power-law (tail) distribution (\\[psi\\]). ",
"The results agree naturally with the data reported from a number of catchment studies, in the sense of a power-law scaling of $h(t)$ over decades of $t$ in the observational time range (using reasonable parameters). ",
"A consequence of our transport model is a power-law “cutoff” of $h(t)$ predicting extremely long chemical retention times with subsequent impact on the long-term effects of contaminants on these ecosystems.",
"\n\nWe thank James W. Kirchner and Colin Stark for a critical reading of the manuscript. ",
"RM acknowledges the DFG and the European Commission within the Emmy Noether and SISITOMAS programmes, and BB acknowledges the European Commission (Contract EVK1-CT-2000-00062), for financial support.",
"\n\nBerkowitz, B., and H. Scher, Theory of anomalous chemical transport in fracture networks, [*Phys. ",
"Rev. E*]{}, [*57*]{}(5), 5858-5869, 1998.",
"\n\nBerkowitz, B., and H. Scher, The role of probabilistic approaches to transport theory in heterogeneous media, [*Transp. ",
"Porous Media*]{}, [*42*]{}(1-2), 241-263, 2001.",
"\n\nDuffy, C. J., and L. W. Gelhar, A frequency domain approach to water quality modeling in groundwater: Theory, [*Wat. ",
"Resour. ",
"Res.*]{}, [*",
"21*]{}(8), 1175-1184, 1985.",
"\n\nKirchner, J. W., X. Feng and C. Neal, Fractal stream chemistry and its implications for contaminant transport in catchments, [*Nature, 403*]{}, 524-527, 2000.",
"\n\nKirchner, J. W., X. Feng and C. Neal, Catchment-scale advection and dispersion as a mechanism for fractal scaling in stream tracer concentrations, [*J. Hydrol., ",
"254*]{}, 82-101, 2001.",
"\n\nKlafter, J., M. F. Shlesinger, and G. Zumofen, Beyond Brownian motion, [*Phys. ",
"Today, 49*]{}(2), 33-39, 1996.",
"\n\nKosakowski, G., B. Berkowitz and H. Scher, Analysis of field observations of tracer transport in a fractured till, [*J. Contam. ",
"Hydrol.*]{}, [*",
"47*]{}, 29-51, 2001.",
"\n\nMetzler, R., and J. Klafter, The random walk’s guide to anomalous diffusion: A fractional dynamics approach, [*Phys. ",
"Rep.*]{}, [*339*]{}(1), 1-77, 2000 (and refs. ",
"therein).",
"\n\nRodriguez-Iturbe, I., and A. Rinaldo, [*Fractal River Basins: Chance and Self-Organization*]{}, Cambridge Univ. ",
"Press, New York, 1997.",
"\n\nScher, H., and E. W. Montroll, Anomalous transit-time dispersion in amorphous solids, [*Phys. ",
"Rev. B*]{}, [*12*]{}(6), 2455-2477, 1975.",
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"\n"
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"\nUndifferentiated pleomorphic sarcoma was a well-known tumor that usually involves the soft tissues. ",
"However, in the alimentary tract, it was seldom reported. ",
"A 55-year-old man was admitted to our hospital with lower abdominal pain. ",
"Endoscopic examination showed a protruding tumor occupied the lumen of the descending colon. ",
"Because of the colon obstruction by the tumor, a left hemicolectomy with en bloc lymph node dissection was performed. ",
"Main occupied lesion of the tumor was mesenterium and submucosa, with no epithelial dysplasia. ",
"Also, dissemination of the tumor was recognized in the mesenterium and greater omentum. ",
"Based on histological and immunohistological studies, the tumor was diagnosed as undifferentiated pleomorphic sarcoma."
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"pile_set_name": "PubMed Abstracts"
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"Both shortening and its classier cousin, margarine, took off for obvious reasons—who wouldn’t want a butter substitute that was cheaper, lasted longer, and came with free cookbooks? (",
"All the recipes called for Crisco, of course.)",
"\n\nSensing competition, dairy farmers convinced several states to stop allowing the more appetizing-looking, yellow-colored margarine in the early 20th century, but the bans were largely repealed by the late 1950s, and the golden-hued spread once again became the norm.",
"\n\nA 1961 Time magazine article railed against the dangers of saturated fat (the kind found in butter and lard), and eventually some consumers began to view margarine and shortening as healthier alternatives.",
"\n\nOddly, some health groups also trumpeted hydrogenated oil's benefits.",
"\n\nIn the 1980s, some scientists began to associate heart disease with saturated fats, and in response, groups such as the Center for Science in the Public Interest and the National Heart Savers Association (NHSA) began to hound manufacturers for “poisoning America ... by using saturated fats,” and as a result “nearly all targeted firms responded by replacing saturated fats with trans fats,” as David Schleifer wrote in 2012 for the journal Technology and Culture.",
"\n\nAt the time, many restaurants used beef fat for frying, which groups like CSPI believed was far worse than hydrogenated oils, based on the research of the time. ",
"Schleifer writes:\n\n[CSPI’S 1986] Fast-Food Guide specifically criticized Taco Bell, Arby’s, Hardee’s, and Wendy’s for frying in beef fat and tropical oils (that is, coconut and palm oils). ",
"But it praised Burger King for switching to vegetable shortening in 1986, which it described as “a great boon to Americans’ arteries.” ",
"The guide also praised KFC, writing that the chain was “fortunately” frying in “partially saturated soybean oil . . . ",
"that is much less saturated than beef fat.”",
"\n\nTwo years later, the same group released the report Saturated Fat Attack, which described trans fats as “more healthful” than saturated fats, Schleifer wrote.",
"\n\nIn 1990, a New York Times food writer said CSPI’s campaign prompted fast-food chains to “slim down” by switching to frying in shortening.",
"\n\n***\n\nIn the 1990s, the health risks of trans fats began to eclipse those of the saturated variety. ",
"A 1990 New England Journal of Medicine found that they raised “bad” cholesterol levels. ",
"A 1993 Harvard study found that eating partially hydrogenated vegetable oils increased the risk of heart attacks. ",
"Today, it’s estimated that trans fats contribute to thousands of early deaths each year.",
"\n\nThe food industry even funded its own study with the goal of proving that trans fats were perfectly safe. ",
"However, it only confirmed the earlier findings, and food manufacturers quickly began developing alternatives to hydrogenated oils. ",
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"Which means zero, if you use FDA-label math.",
"\n\nSurprisingly, it was the same organization, CSPI, that later urged the FDA to add trans fats to food labels, and nutrition panels have been required to list the substance since 2006. ",
"Though American consumption of trans fat has declined precipitously in recent years, it's still common in food such as microwave popcorn, margarine, and some coffee creamers. ",
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"Four-quadrant gate\n\nA four-quadrant gate is a type of boom barrier gate protecting a grade crossing.",
"\nIt has a gate mechanism on both sides of the tracks for both directions of automotive traffic. ",
"The exit gates blocking the road leading away from the tracks in this application are equipped with a delay, and begin their descent to their horizontal position several seconds after the entrance gates do, so as to avoid trapping highway vehicles on the crossing.",
"\nMany people consider four-quadrant gates to be safer than two-quadrant gates because they prevent drivers from illegally driving their vehicles around lowered gates to try to beat a train.",
"\n\nIn the UK, such crossings are categorised as 'Manually Controlled Barriers' (MCB) because they are always manually controlled, usually from a signal box. ",
"Some are known as MCB-CCTV level crossings, because they are supervised by video link to the signal box from which they are remotely controlled.",
"\n\nThe first four-quadrant gate in the United States was installed in 1952. ",
"They have become common for new installations and replacements since. ",
"Unlike the UK, many are automated by the rail line's signal system. ",
"The first quad gate installation in the country with sensors to detect vehicles stopped in the tracks was installed in Groton, Connecticut in 1998. ",
"Eight of the eleven remaining grade crossings on the Northeast Corridor now have such setups.",
"\n\nReferences\n\nCategory:Level crossings\nCategory:Protective barriers\nCategory:Road infrastructure\nCategory:Street furniture\n\nFurther reading"
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