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Glycogen phosphorylase (GP) is currently exploited as a target for inhibition of hepatic glycogenolysis under high glucose conditions. Spirohydantoin of glucopyranose and N-acetyl-β-D-glucopyranosylamine have been identified as the most potent inhibitors of GP that bind at the catalytic site. Four spirohydantoin and three β-D-glucopyranosylamine analogs have been designed, synthesized and tested for inhibition of GP in kinetic experiments. Depending on the functional group introduced, the Ki values varied from 16.5 μM to 1200 μM. In order to rationalize the kinetic results, we determined the crystal structures of the analogs in complex with GP. All the inhibitors bound at the catalytic site of the enzyme, by making direct and water-mediated hydrogen bonds with the protein and by inducing minor movements of the side chains of Asp283 and Asn284, of the 280s loop that blocks access of the substrate glycogen to the catalytic site, and changes in the water structure in the vicinity of the site. The differences observed in the K i values of the analogs can be interpreted in terms of variations in hydrogen bonding and van der Waals interactions, desolvation effects, ligand conformational entropy, and displacement of water molecules on ligand binding to the catalytic site. © 2005 Wiley-Liss, Inc. 61 4 966 983 Cited By :21

This chapter describes the organization and use of Proteus, a multitool computational suite for the optimization of protein and ligand conformations and sequences, and the calculation of pKα shifts and relative binding affinities. The software offers the use of several molecular mechanics force fields and solvent models, including two generalized Born variants, and a large range of scoring functions, which can combine protein stability, ligand affinity, and ligand specificity terms, for positive and negative design. We present in detail the steps for structure preparation, system setup, construction of the interaction energy matrix, protein sequence and structure optimizations, pKα calculations, and ligand titration calculations. We discuss illustrative examples, including the chemical/structural optimization of a complex between the MHC class II protein HLA-DQ8 and the vinculin epitope, and the chemical optimization of the compstatin analog Ac-Val4Trp/His9Ala, which regulates the function of protein C3 of the complement system. © Springer Science+Business Media New York 2016. 1414 77 97 Cited By :1

Computational Protein Design (CPD) is a promising method for high throughput protein and ligand mutagenesis. Recently, we developed a CPD method that used a polar-hydrogen energy function for protein interactions and a Coulomb/Accessible Surface Area (CASA) model for solvent effects. We applied this method to engineer aspartyl-adenylate (AspAMP) specificity into Asparaginyl-tRNA synthetase (AsnRS), whose substrate is asparaginyl-adenylate (AsnAMP). Here, we implement a more accurate function, with an all-atom energy for protein interactions and a residue-pairwise generalized Born model for solvent effects. As a first test, we compute aminoacid affinities for several point mutants of Aspartyl-tRNA synthetase (AspRS) and Tyrosyl-tRNA synthetase and stability changes for three helical peptides and compare with experiment. As a second test, we readdress the problem of AsnRS aminoacid engineering. We compare three design criteria, which optimize the folding free-energy, the absolute AspAMP affinity, and the relative (AspAMP-AsnAMP) affinity. The sequences and conformations are improved with respect to our previous, polar-hydrogen/CASA study: For several designed complexes, the AspAMP carboxylate forms three interactions with a conserved arginine and a designed lysine, as in the active site of the AspRS:AspAMP complex. The conformations and interactions are well maintained in molecular dynamics simulations and the sequences have an inverted specificity, favoring AspAMP over AsnAMP. The method is not fully successful, since experimental measurements with the seven most promising sequences show that they do not catalyze at a detectable level the adenylation of Asp (or Asn) with ATP. This may be due to weak AspAMP binding and/or disruption of transition-state stabilization. © 2011 Wiley-Liss, Inc. 79 12 3448 3468 Cited By :12

UV resonance Raman spectroscopy was used to probe the temperature dependence of the conformation of TTR(105-115) in solution. Resonance Raman spectra with excitation at 239.5 nm, show an increase in the absolute resonance Raman cross section of Tyr with an increase in temperature. This trend is associated with an increase in the hydrophobicity of the Tyr local environment, suggesting a conformational change at 28 °C. Excitation at ∼200 nm is known to enhance scattering due to amide vibrations and provides insights as to the secondary structure of a peptide or protein. UVRR spectra at this excitation suggest that in solution the peptide assumes a disordered conformation with frequent formation of β-turns. Explicit-solvent replica-exchange MD simulations of the isolated peptide in the region 15 to 37 °C suggest that the dominant conformation assumed by the peptide corresponds to a coil with β-turns in the central and C-terminal region. In line with the experiments, an increase in temperature induces structural order in the peptide, reflected by an increase in the probability for the formation of β-turns and hydrophobic side-chain contacts, mainly in the 8-11 moiety, and to a lesser extent in the 4-7 moiety. © 2011 American Chemical Society. 115 14 4088 4098 Cited By :4

Peptide and protein self-assembly is related to the fundamental problems of protein folding and misfolding and has potential applications in medicine, materials science and nanotechnology. Sequence repeats from self-assembling proteins may provide useful elementary building blocks of peptide-based nanostructures. Sequences from the adenovirus fiber shaft self-assemble into amyloid-like fibrils outside their native context. In earlier simulations we studied the self-assembly of two shaft sequences, the octapeptide NSGAITIG and the hexapeptide GAITIG. Based on these simulations, cysteine residues were substituted at the first two positions of the octapeptide, yielding amyloid fibrils capable of binding to silver, gold and platinum nanoparticles. Here, we study by implicit-solvent replica-exchange simulations the self-assembly of a longer shaft sequence, the dodecapeptide LSFDNSGAITIG. The simulations provide insights on the molecular organization of the corresponding fibers. Individual molecules tend to adopt hairpin-like conformations in the observed intermolecular β-sheets, in line with the experimentally determined amyloid fiber diameters and the conformation of the peptide in the adenovirus fiber shaft. By analyzing the arrangement of individual peptides in the intermolecular sheets, we suggest possible structural models of the corresponding fibers and interpret their stability by energetic calculations. © 2010 Elsevier B.V.All rights reserved. 357 2 717 722 Cited By :9

A series of glucopyranosylidene-spiro-isoxazolines was prepared through regio- and stereoselective [3+2]-cycloaddition between the methylene acetylated exo-glucal and aromatic nitrile oxides. The deprotected cycloadducts were evaluated as inhibitors of muscle glycogen phosphorylase b. The carbohydrate-based family of five inhibitors displays Ki values ranging from 0.63 to 92.5 μM. The X-ray structures of the enzyme-ligand complexes show that the inhibitors bind preferentially at the catalytic site of the enzyme retaining the less active T-state conformation. Docking calculations with GLIDE in extra-precision (XP) mode yielded excellent agreement with experiment, as judged by comparison of the predicted binding modes of the five ligands with the crystallographic conformations and the good correlation between the docking scores and the experimental free binding energies. Use of docking constraints on the well-defined positions of the glucopyranose moiety in the catalytic site and redocking of GLIDE-XP poses using electrostatic potential fit-determined ligand partial charges in quantum polarized ligand docking (QPLD) produced the best results in this regard. © 2009 Elsevier Ltd. All rights reserved. 17 20 7368 7380 Cited By :48

4-Phenyl-N-(β-D-glucopyranosyl)-1H-1,2,3-triazole-1-acetamide (glucosyltriazolylacetamide) has been studied in kinetic and crystallographic experiments with glycogen phosphorylase b (GPb), in an effort to utilize its potential as a lead for the design of potent antihyperglycaemic agents. Docking and molecular dynamics (MD) calculations have been used to monitor more closely the binding modes in operation and compare the results with experiment. Kinetic experiments in the direction of glycogen synthesis showed that glucosyltriazolylacetamide is a better inhibitor (Ki = 0.18 mM) than the parent compound α-D-glucose (Ki = 1.7 mM) or β-D-glucose (Ki = 7.4 mM) but less potent inhibitor than the lead compound N-acetyl-β-D-glucopyranosylamine (Ki = 32 μM). To elucidate the molecular basis underlying the inhibition of the newly identified compound, we determined the structure of GPb in complex with glucosyltriazolylacetamide at 100 K to 1.88 Å resolution, and the structure of the compound in the free form. Glucosyltriazolylacetamide is accommodated in the catalytic site of the enzyme and the glucopyranose interacts in a manner similar to that observed in the GPb-α-D-glucose complex, while the substituent group in the β-posi tion of the C1 atom makes additional hydrogen bonding and van der Waals interactions to the protein. A bifurcated donor type hydrogen bonding involving O3H, N3, and N4 is seen as an important structural motif strengthening the binding of glucosyltriazolylacetamide with GP which necessitated change in the torsion about C8-N2 bond by about 62° going from its free to the complex form with GPb. On binding to GP, glucosyltriazolylacetamide induces significant conformational changes in the vicinity of this site. Specifically, the 280s loop (residues 282-288) shifts 0.7 to 3.1 Å (CA atoms) to accommodate glucosyltriazolylacetamide. These conformational changes do not lead to increased contacts between the inhibitor and the protein that would improve ligand binding compared with the lead compound. In the molecular modeling calculations, the GOLD docking runs with and without the crystallographic ordered cavity waters using the GoldScore scoring function, and without cavity waters using the ChemScore scoring function successfully reproduced the crystallographic binding conformation. However, the GLIDE docking calculations both with (GLIDE XP) and without (GLIDE SP and XP) the cavity water molecules were, impressively, further able to accurately reproduce the finer details of the GPb-glucosyltriazolylacetamide complex structure. The importance of cavity waters in flexible receptor MD calculations compared to "rigid" (docking) is analyzed and highlighted, while in the MD itself very little conformational flexibility of the glucosyltriazolylacetamide ligand was observed over the time scale of the simulations. © 2007 Wiley-Liss, Inc. 71 3 1307 1323 Cited By :27

The cyclic 13-residue peptide compstatin is a potential therapeutic agent against the unregulated activation of the complement system. A thorough knowledge of its structural and dynamical properties in solution may assist the design of improved complement inhibitors. NMR studies have suggested that the 5-8 segment of free compstatin folds into a critical for activity 5-8 β turn and the rest of the peptide is mainly disordered. Earlier computational studies of compstatin analogues with a polar-hydrogen/generalized-Born approximation reproduced the 5-8 turn, but also indicated the formation of β-hairpin or α-helical elements and the existence of interactions between certain charged or aromatic sidechains. However, these features are absent or partly present in the NMR spectra, due to extensive conformational averaging. In order to check the compstatin properties with a more rigorous model of the intra- and intermolecular interactions, we conduct here 98-ns all-atom/explicit-water simulations of three compstatin analogues with variable activity a native analogue, the more active mutant V4W/H9A and the inactive mutant Q5G. The 5-8 β-turn population is in good accord with NMR. For the systems studied here, the simulations suggest that the 5-8 turn population does not correlate strictly with activity, in agreement with earlier mutational studies. Furthermore, they show structural differences among the analogues outside the 5-8 region. The possible role of these differences in activity is discussed. The probability of β-hairpin or α-helix elements is much smaller with respect to the polar-hydrogen/GB simulations, and the persistent Trp4-Trp7 or Asp6-Arg11 sidechain interactions of the earlier GB studies are not reproduced. The present simulations extend the NMR data and improve our understanding of the properties of compstatin and related analogues. © 2007 Elsevier Inc. All rights reserved. 26 2 571 580 Cited By :10

The HLA locus is the strongest risk factor for anti-citrullinated protein antibody (ACPA) + rheumatoid arthritis (RA). Despite considerable efforts in the last 35 years, this association is poorly understood. Here we identify (citrullinated) vinculin, present in the joints of ACPA + RA patients, as an autoantigen targeted by ACPA and CD4 + T cells. These T cells recognize an epitope with the core sequence DERAA, which is also found in many microbes and in protective HLA-DRB1∗13 molecules, presented by predisposing HLA-DQ molecules. Moreover, these T cells crossreact with vinculin-derived and microbial-derived DERAA epitopes. Intriguingly, DERAA-directed T cells are not detected in HLA-DRB1∗13 + donors, indicating that the DERAA epitope from HLA-DRB1∗13 mediates (thymic) tolerance in these donors and explaining the protective effects associated with HLA-DRB1∗13. Together our data indicate the involvement of pathogen-induced DERAA-directed T cells in the HLA-RA association and provide a molecular basis for the contribution of protective/predisposing HLA alleles. 6 Cited By :21

We describe an efficient generalized Born (GB) approximation for proteins, in which the interaction energy between two amino acids depends on the whole protein structure, but can be accurately computed from residue-pairwise information. Two results make the scheme pairwise. First, an accurate expression exists for the interaction energy between two residues R and R′ that depends on the product B = BRBR′ of their residue Born solvation radii. Second, this expression is accurately fitted by a parabolic function of B the (three) fitting coefficients depend only on the pair RR′, not on its environment. In effect, the quantity B captures all the information that is relevant about the pair's dielectric environment. The method is tested with calculations on several hundred structures of the proteins trpcage, BPTI, ubiqutin, and thoredoxin. It yields solvation energies in better agreement with Poisson calculations than a traditional GB formulation. We also compute the effect of the protein/solvent environment on the interactions between pairs of charged residues in the active site of the enzyme aspartyl-tRNA synthetase. Our method captures this effect as accurately as traditional GB. Because it is residue-pairwise, the method can be incorporated into efficient protocols for rotamer placement and computational protein design. © 2005 American Chemical Society. 109 47 22667 22673 Cited By :26

Proton binding plays a critical role in protein structure and function. We report pKa calculations for three aspartates in two proteins, using a linear response approach, as well as a "standard" Poisson-Boltzmann approach. Averaging over conformations from the two endpoints of the proton-binding reaction, the protein's atomic degrees of freedom are explicitly modeled. Treating macroscopically the protein's electronic polarizability and the solvent, a meaningful model is obtained, without adjustable parameters. It reproduces qualitatively the electrostatic potentials, proton-binding free energies, Marcus reorganization free energies, and pKa shifts from explicit solvent molecular dynamics simulations, and the pKa shifts from experiment. For thioredoxin Asp-26, which has a large pKa upshift, we correctly capture the balance between unfavorable carboxylate desolvation and favorable interactions with a nearby lysine similarly for RNase A Asp-14, which has a large pKa downshift. For the unshifted thioredoxin Asp-20, desolvation by the protein cavity is overestimated by 2.9 pKa units several effects could explain this. "Standard" Poisson-Boltzmann methods sidestep this problem by using a large, ad hoc protein dielectric but protein charge-charge interactions are then incorrectly downscaled, giving an unbalanced description of the reaction and a large error for the shifted pKa values of Asp-26 and Asp-14. © 2005 by the Biophysical Society. 88 6 3888 3904 Cited By :56

CP320626, a potential antidiabetic drug, inhibits glycogen phosphorylase in synergism with glucose. To elucidate the structural basis of synergistic inhibition, we determined the structure of muscle glycogen phosphorylase b (MGPb) complexed with both glucose and CP320626 at 1.76 Å resolution, and refined to a crystallographic R value of 0.211 (Rfree = 0.235). CP320626 binds at a novel allosteric site, which is some 33 Å from the catalytic site, where glucose binds. The high resolution structure allows unambiguous definition of the conformation of the 1-acetyl-4-hydroxy-piperidine ring supported by theoretical energy calculations. Both CP320626 and glucose promote the less active T-state, thereby explaining their synergistic inhibition. Structural comparison of MGPb-glucose-CP320626 complex with liver glycogen phosphorylase a (LGPa) complexed with a related compound (CP403700) show that the ligand binding site is conserved in LGPa. © 2002 Elsevier Science Ltd. All rights reserved. 10 5 1313 1319 Tradenames: cp 403700 cp320626 Cited By :26

In recent years, molecular dynamics simulations of biomolecular free energy differences have benefited from significant methodological advances and increased computer power. Applications to molecular recognition provide an understanding of the interactions involved that goes beyond, and is an important complement to, experimental studies. Poisson-Boltzmann electrostatic models provide a faster and simpler free energy method in cases where electrostatic interactions are important. We illustrate both molecular dynamics and Poisson-Boltzmann methods with a detailed study of amino acid recognition by aspartyl-tRNA synthetase, whose specificity is important for maintaining the integrity of the genetic code. 35 6 430 437 Cited By :285

The self-assembly of short peptides into fibrous nanostructures (such as fibrils and tubes) has recently become the subject of intense theoretical and experimental scrutiny, as such assemblies are promising candidates for nanobiotechnological applications. The sequences of natural fibrous proteins may provide a rich source of inspiration for the design of such short self-assembling peptides. We describe the self-assembly of the aspartate-rich undecapeptide (NH3+-LSGSDSDTLTV-NH2), a sequence derived from the shaft of the adenovirus fiber. We demonstrate that the peptide assembles experimentally into amyloid-type fibrils according to widely accepted diagnostic criteria. In addition, we investigate an aqueous solution of undecapeptides by molecular dynamics simulations with an implicit (GB) solvent model. The peptides are frequently arranged in intermolecular β-sheets, in line with their amyloidogenic propensity. On the basis of both experimental and theoretical insights, we suggest possible structural models of the fibrils and their potential use as scaffolds for templating of inorganic materials. © 2014 American Chemical Society. 118 7 1765 1774 Cited By :8

Glycogen phosphorylase (GP) is a validated target for the development of new type 2 diabetes treatments. Exploiting the Zinc docking database, we report the in silico screening of 1888 N-acyl-β-d-glucopyranosylamines putative GP inhibitors differing only in their R groups. CombiGlide and GOLD docking programs with different scoring functions were employed with the best performing methods combined in a 'consensus scoring' approach to ranking of ligand binding affinities for the active site. Six selected candidates from the screening were then synthesized and their inhibitory potency was assessed both in vitro and ex vivo. Their inhibition constants' values, in vitro, ranged from 5 to 377 μM while two of them were effective at causing inactivation of GP in rat hepatocytes at low μM concentrations. The crystal structures of GP in complex with the inhibitors were defined and provided the structural basis for their inhibitory potency and data for further structure based design of more potent inhibitors. © 2014 Elsevier Ltd. All rights reserved. 22 17 4810 4825 Cited By :9

Self-assembling peptides that can form supramolecular structures such as fibrils, ribbons, and nanotubes are of particular interest to modern bionanotechnology and materials science. Their ability to form biocompatible nanostructures under mild conditions through non-covalent interactions offers a big biofabrication advantage. Structural motifs extracted from natural proteins are an important source of inspiration for the rational design of such peptides. Examples include designer self-assembling peptides that correspond to natural coiled-coil motifs, amyloid-forming proteins, and natural fibrous proteins. In this chapter, we focus on the exploitation of structural information from beta-structured natural fibers. We review a case study of short peptides that correspond to sequences from the adenovirus fiber shaft. We describe both theoretical methods for the study of their self-assembly potential and basic experimental protocols for the assessment of fibril-forming assembly. © Springer Science+Business Media New York 2014. 1216 53 70 Cited By :4

Dielectric relaxation plays an important role in many chemical processes in proteins, including acid-base titration, ligand binding, and charge transfer reactions. Its complexity makes experimental characterization difficult, and so, theoretical approaches are valuable. The comparison of molecular dynamics free energy simulations with simpler models such as a dielectric continuum model is especially useful for obtaining qualitative insights. We have analyzed a charge insertion process that models deprotonation or mutation of an important side chain in the active site of the enzyme aspartyl-tRNA synthetase. Complexes with the substrate aspartate and the analogue asparagine were studied. The resulting dielectric relaxation was found to involve both ligand and side chain rearrangements in the active site and to account for a large part of the overall charging free energy. With the continuum model, charge insertion is performed along a two-step pathway: insertion into a static environment, followed by relaxation of the environment. These correspond to different physical processes and require different protein dielectric constants. A low value of ∼1 is needed for the static step, consistent with the parametrization of the molecular mechanics charge set used. A value of 3-6 (depending on the exact insertion site and the nature of the ligand) is needed to describe the dielectric relaxation step. This moderate value indicates that, for this system, the local protein polarizability in the active site is within at most a factor of 2 of that expected at nonspecific positions in a protein interior. 123 44 11047 11056 Cited By :49

1 online ID: 1032 In: Journal of computational chemistry, Vol. 34, no. 28 ( 2013), p.2472-2484. Summary: Abstract We describe an automated procedure for protein design, implemented in a flexible software package, called Proteus. System setup and calculation of an energy matrix are done with the XPLOR modeling program and its sophisticated command language, supporting several force fields and solvent models. A second program provides algorithms to search sequence space. It allows a decomposition of the system into groups, which can be combined in different ways in the energy function, for both positive and negative design. The whole procedure can be controlled by editing 2–4 scripts. Two applications consider the tyrosyl‐tRNA synthetase enzyme and its successful redesign to bind both O‐methyl‐tyrosine and D‐tyrosine. For the latter, we present Monte Carlo simulations where the D‐tyrosine concentration is gradually increased, displacing L‐tyrosine from the binding pocket and yielding the binding free energy difference, in good agreement with experiment. Complete redesign of the Crk SH3 domain is presented. The top 10000 sequences are all assigned to the correct fold by the SUPERFAMILY library of Hidden Markov Models. Finally, we report the acid/base behavior of the SNase protein. Sidechain protonation is treated as a form of mutation it is then straightforward to perform constant‐pH Monte Carlo simulations, which yield good agreement with experiment. Overall, the software can be used for a wide range of application, producing not only native‐like sequences but also thermodynamic properties with errors that appear comparable to other current software packages.Copyright © 2013 Wiley Periodicals, Inc.

We have used a novel human retinal pigmented epithelial (RPE) cell-based model that mimics drusen biogenesis and the pathobiology of age-related macular degeneration to evaluate the efficacy of newly designed peptide inhibitors of the complement system. The peptides belong to the compstatin family and, compared to existing compstatin analogs, have been optimized to promote binding to their target, complement protein C3, and to enhance solubility by improving their polarity/hydrophobicity ratios. Based on analysis of molecular dynamics simulation data of peptide-C3 complexes, novel binding features were designed by introducing intermolecular salt bridge-forming arginines at the N-terminus and at position-1 of N-terminal dipeptide extensions. Our study demonstrates that the RPE cell assay has discriminatory capability for measuring the efficacy and potency of inhibitory peptides in a macular disease environment.© 2013 Elsevier Ltd. 116 96 108 Cited By :15

Specific ion effects on oligopeptide conformations in solution are attracting strong research attention, because of their impact on the protein-folding problem and on several important biological-biotechnological applications. In this work, we have addressed specific effects of electrolytes on the tendency of oligopeptides toward formation and propagation of helical segments. We have used replica-exchange molecular dynamics (REMD) simulations to study the conformations of two short hydrophobic peptides [Ace-(AAQAA) 3-Nme (AQ), and Ace-A8-Nme (A8)] in pure water and in aqueous solutions of sodium chloride (NaCl) and sodium iodide (NaI) with concentrations of 1 and 3 M. The average helicities of the AQ peptide have been analyzed to yield Lifson-Roig (LR) parameters for helix nucleation and helix propagation. The salt dependence of these parameters suggests that electrolytes tend to stabilize the helical conformations of short peptides by enhancing the helix nucleation parameter. The helical conformations of longer oligopeptides are destabilized in the presence of salts, however, because the helix propagation parameters are reduced by electrolytes. On top of this general trend, we observe a significant specific salt effect in these simulations. The hydrophobic iodide ion in NaI solutions has a high affinity for the peptide backbone, which reflects itself in an enhanced helix nucleation and a reduced helix propagation parameter with respect to pure water or NaCl solutions. The present work thus explains the computational evidence that electrolytes tend to stabilize the compact conformations of short peptides and destabilize them for longer peptides, and it also sheds additional light on the specific salt effects on compact peptide conformations. © 2013 American Chemical Society. 117 34 9866 9876 Cited By :5

We report the computational and rational design of new generations of potential peptide-based inhibitors of the complement protein C3 from the compstatin family. The binding efficacy of the peptides is tested by extensive molecular dynamics-based structural and physicochemical analysis, using 32 atomic detail trajectories in explicit water for 22 peptides bound to human, rat or mouse target protein C3, with a total of 257 ns. The criteria for the new design are: (i) optimization for C3 affinity and for the balance between hydrophobicity and polarity to improve solubility compared to known compstatin analogs and (ii) development of dual specificity, human-rat/mouse C3 inhibitors, which could be used in animal disease models. Three of the new analogs are analyzed in more detail as they possess strong and novel binding characteristics and are promising candidates for further optimization. This work paves the way for the development of an improved therapeutic for age-related macular degeneration, and other complement system-mediated diseases, compared to known compstatin variants. © 2012 John Wiley & Sons A/S. 79 5 703 718 Cited By :16

We examine computationally the dipeptide and tetrapeptide of alanine in pure water and solutions of sodium chloride (NaCl) and iodide (NaI), with salt concentrations up to 3 M. Enhanced sampling of the configuration space is achieved by the replica exchange method. In agreement with other works, we observe preferential sodium interactions with the peptide carbonyl groups, which are enhanced in the NaI solutions due to the increased affinity of the less hydrophilic iodide anion for the peptide methyl side-chains and terminal blocking groups. These interactions have been associated with a decrease in the helicities of more complex peptides. In our simulations, both salts have a small effect on the dipeptide, but consistently stabilize the intramolecular hydrogen-bonding interactions and "α-helical" conformations of the tetrapeptide. This behavior, and an analysis of the intermolecular interaction energies show that ion-peptide interactions, or changes in the peptide hydration due to salts, are not sufficient determining factors of the peptide conformational preferences. Additional simulations suggest that the observed stabilizing effect is not due to the employed force-field, and that it is maintained in short peptides but is reversed in longer peptides. Thus, the peptide conformational preferences are determined by an interplay of energetic and entropic factors, arising from the peptide sequence and length and the composition of the solution. © 2011 American Chemical Society. 115 45 13389 13400 Cited By :16

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The peptide compstatin and its derivatives inhibit the complement-component protein C3 in primate mammals and are potential therapeutic agents against the unregulated activation of complement in humans, but are inactive against C3 from lower mammals. Recent molecular dynamics (MD) simulations showed that the most potent compstatin analog comprised entirely of natural amino acids (W4A9) had a smaller affinity for rat C3, due to reproducible changes in the rat protein structure with respect to the human protein, which eliminated or weakened specific protein-ligand interactions seen in the human C3:W4A9 complex. Here, we study by MD simulations three W4A9 complexes with the mouse C3 protein, and two "transgenic" mouse derivatives, containing a small number (6-9) of human C3 substitutions. The mouse complex experiences the conformational changes and affinity reduction of the rat complex. In the "transgenic" complexes, the conformation remains closer to that of the human complex, the protein-ligand interactions are improved, and the affinity for compstatin becomes "human-like." The present work creates new avenues for a compstatin-sensitive animal model. A similar strategy, involving the comparison of a series of complexes by MD simulations, could be used to design "transgenic" sequences in other systems. © 2011 Wiley-Liss, Inc. 79 11 3166 3179 Cited By :14

With an aim toward glycogenolysis control in Type 2 diabetes, we have investigated via kinetic experiments and computation the potential of indirubin (IC 50 > 50 μM), indirubin-3'-oxime (IC 50 = 144 nM), KT5720 (K i = 18.4 nM) and staurosporine (K i = 0.37 nM) as phosphorylase kinase (PhKγtrnc) ATP-binding site inhibitors, with the latter two revealed as potent inhibitors in the low nM range. Because of lack of structural information, we have exploited information from homologous kinase complexes to direct in silico calculations (docking, molecular dynamics, and MM-GBSA) to predict the binding characteristics of the four ligands. All inhibitors are predicted to bind in the same active site area as the ATP adenine ring, with binding dominated by hinge region hydrogen bonds to Asp104:O and Met106:O (all four ligands) and also Met106:NH (for the indirubins). The PhKγtrnc-staurosporine complex has the greatest number of receptor-ligand hydrogen bonds, while for the indirubin-3'-oxime and KT5720 complexes there is an important network of interchanging water molecules bridging inhibitor-enzyme contacts. The MM-GBSA results revealed the source of staurosporine's low nM potency to be favorable electrostatic interactions, while KT5720 has strong van der Waals contributions. KT5720 interacts with the greatest number of protein residues either by direct or 1-water bridged hydrogen bond interactions, and the potential for more selective PhK inhibition based on a KT5720 analogue has been established. Including receptor flexibility in Schrödinger induced-fit docking calculations in most cases correctly predicted the binding modes as compared with the molecular dynamics structures the algorithm was less effective when there were key structural waters bridging receptor-ligand contacts. © 2010 Wiley-Liss, Inc. 79 3 703 719 Tradenames: kt 5720 Cited By :37

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The acid/base properties of proteins are essential in biochemistry, and proton binding is a valuable reporter on electrostatic interactions. We propose a constant-pH Monte Carlo strategy to compute protonation free energies and pKas. The solvent is described implicitly, through a generalized Born model. The electronic polarizability and backbone motions of the protein are included through the protein dielectric constant. Side chain motions are described explicitly, by the Monte Carlo scheme. An efficient computational algorithm is described, which allows us to treat the fluctuating shape of the protein/solvent boundary in a way that is numerically exact (within the GB framework) this contrasts with several previous constant-pH approaches. For a test set of six proteins and 78 titratable groups, the model performs well, with an rms error of 1.2 pH units. While this is slightly greater than a simple Null model (rms error of 1.1) and a fully empirical model (rms error of 0.9), it is obtained using physically meaningful model parameters, including a low protein dielectric of four. Importantly, similar performance is obtained for side chains with large and small pKa shifts (relative to a standard model compound). The titration curve slopes and the conformations sampled are reasonable. Several directions to improve the method further are discussed. © 2010 American Chemical Society. 114 32 10634 10648 Cited By :20

The development of compounds to regulate the activation of the complement system in non-primate species is of profound interest because it can provide models for human diseases. The peptide compstatin inhibits protein C3 in primate mammals and is a potential therapeutic agent against unregulated activation of complement in humans but is inactive against nonprimate species. Here, we elucidate this species specificity of compstatin by molecular dynamics simulations of complexes between the most potent natural compstatin analog and human or rat C3. The results are compared against an experimental conformation of the human complex, determined recently by X-ray diffraction at 2.4-å resolution. The human complex simulations provide information on the relative contributions to stability of specific C3 and compstatin residues. In the rat simulations, the protein undergoes reproducible conformational changes, which eliminate or weaken specific interactions and reduce the complex stability. The simulation insights can be used to design improved compstatin-based inhibitors for human C3 and active inhibitors against lower mammals. © 2010 Wiley-Liss, Inc. 78 12 2655 2667 Cited By :19

The self-assembly of peptides and proteins into nanostructures is related to the fundamental problems of protein folding and misfolding and has potential applications in medicine, materials science and nanotechnology. Natural peptides, corresponding to sequence repeats from self-assembling proteins, may constitute elementary building blocks of such nanostructures. In this work, we study by implicit-solvent replica-exchange simulations the self-assembly of two amyloidogenic sequences derived from the naturally occurring fiber shaft of the adenovirus, the octapeptide NSGAITIG (asparagine-serine-glycine-alanine- isoleucine-threonine-isoleucineglycine) and its hexapeptide counterpart, GAITIG. In accordance with their amyloidogenic capacity, both peptides form readily intermolecular β-sheets, stabilized by extensive main- and side-chain contacts involving the C-terminal moieties (segments 3-8 and 2-6, respectively). The structural and energetic properties of these sheets are analyzed extensively. The N-terminal residues Asn1 and Ser2 of the octapeptide remain disordered in the sheets, suggesting that these residues are exposed at the exterior of the fibrils and accessible. On the basis of insight provided by the simulations, cysteine residues were recently substituted at positions 1 and 2 of NSGAITIG the newly designed peptides maintain their amyloidogenic properties and can bind to silver, gold and platinum nanoparticles [Kasotakis et al. Biopolymers 2009, 92, 164-172]. Computational investigation can identify suitable positions for rational modification of peptide building blocks, aiming at the fabrication of novel biomaterials © 2009 American Chemical Society. 113 47 15639 15647 Cited By :22

CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecular simulation program. It has been developed over the last three decades with a primary focus on molecules of biological interest, including proteins, peptides, lipids, nucleic acids, carbohydrates and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. In addition, the CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numerous platforms in both serial and parallel architectures. This paper provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM paper in 1983.

Studies of peptide-based nanostructures provide general insights into biomolecular self-assembly and can lead material engineering toward technological applications. The diphenylalanine peptide (FF) self-assembles into discrete, hollow, well ordered nanotubes, and its derivatives form nanoassemblies of various morphologies. Here we demonstrate for the first time, to our knowledge, the formation of planar nanostructures with β-sheet content by the triphenylalanine peptide (FFF). We characterize these structures using various microscopy and spectroscopy techniques. We also obtain insights into the interactions and structural properties of the FF and FFF nanostructures by 0.4-μs, implicit-solvent, replica-exchange, molecular-dynamics simulations of aqueous FF and FFF solutions. In the simulations the peptides form aggregates, which often contain open or ring-like peptide networks, as well as elementary and network-containing structures with β-sheet characteristics. The networks are stabilized by polar and nonpolar interactions, and by the surrounding aggregate. In particular, the charged termini of neighbor peptides are involved in hydrogen-bonding interactions and their aromatic side chains form "T-shaped" contacts, as in three-dimensional FF crystals. These interactions may assist the FF and FFF self-assembly at the early stage, and may also stabilize the mature nanostructures. The FFF peptides have higher network propensities and increased aggregate stabilities with respect to FF, which can be interpreted energetically. © 2009 by the Biophysical Society. 96 12 5020 5029 Cited By :97

Structure prediction and computational protein design should benefit from accurate solvent models. We have applied implicit solvent models to two problems that are central to this area. First, we performed sidechain placement for 29 proteins, using a solvent model that combines a screened Coulomb term with an Accessible Siurface Area term (CASA model). With optimized parameters, the prediction quality is comparable with earlier work that omitted electrostatics and solvation altogether. Second, we computed the stability changes associated with point mutations involving ionized sidechains. For over 1000 mutations, including many fully or partly buried positions, we compared CASA and two generalized Born models (GB) with a more accurate model, which solves the Poisson equation of continuum electrostatics numerically. CASA predicts the correct sign and order of magnitude of the stability change for 81% of the mutations, compared to 97% with the best GB. We also considered 140 mutations for which experimental data are available. Comparing to experiment requires additional assumptions about the unfolded protein structure, protein relaxation in response to the mutations, and contributions from the hydrophobic effect. With a simple, commonly-used unfolded state model, the mean unsigned error is 2.1 kcal/mol with both CASA and the best GB. Overall, the electrostatic model is not important for sidechain placement CASA and GB are equivalent for surface mutations, while GB is far superior for fully or partly buried positions. Thus, for problems like protein design that involve all these aspects, the most recent GB models represent an important step forward. Along with the recent discovery of efficient, pairwise implementations of GB, this will open new possibilities for the computational engineering of proteins. © 2007 Wiley-Liss, Inc. 67 4 853 867 Cited By :40

The proteins of the pancreatic ribonuclease A (RNase A) family catalyze the cleavage of the RNA polymer chain. The development of RNase inhibitors is of significant interest, as some of these compounds may have a therapeutic effect in pathological conditions associated with these proteins. The most potent low molecular weight inhibitor of RNase reported to date is the compound 5′-phospho-2′-deoxyuridine-3-pyrophosphate (P→5)-adenosine-3- phosphate (pdUppA-3′-p). The 3′,5′-pyrophosphate group of this compound increases its affinity and introduces structural features which seem to be unique in pyrophosphate-containing ligands bound to RNase A, such as the adoption of a syn conformation by the adenosine base at RNase subsite B 2 and the placement of the 5′-β-phosphate of the adenylate (instead of the α-phosphate) at subsite P1 where the phosphodiester bond cleavage occurs. In this work, we study by multi-ns molecular dynamics simulations the structural properties of RNase A complexes with the ligand pdUppA-3′-p and the related weaker inhibitor dUppA, which lacks the 3′ and 5′ terminal phosphate groups of pdUppA-3′-p. The simulations show that the adenylate 5′-β-phosphate binding position and the adenosine syn orientation constitute robust structural features in both complexes, stabilized by persistent interactions with specific active-site residues of subsites P1 and B2. The simulation structures are used in conjunction with a continuum-electrostatics (Poisson-Boltzmann) model, to evaluate the relative binding affinity of the two complexes. The computed relative affinity of pdUppA-3′-p varies between -7.9 kcal/mol and -2.8 kcal/mol for a range of protein/ligand dielectric constants (εp) 2-20, in good agreement with the experimental value (-3.6 kcal/mol) the agreement becomes exact with εep = 8. The success of the continuum-electrostatics model suggests that the differences in affinity of the two ligands originate mainly from electrostatic interactions. A residue decomposition of the electrostatic free energies shows that the terminal phosphate groups of pdUppA-3′-p make increased interactions with residues Lys7 and Lys66 of the more remote sites P2 and P0, and His119 of site P1. © 2007 by the Biophysical Society. 92 5 1659 1672 Cited By :9

Recent experiments and simulations show that large chaotropic anions favor solvation at the water surface, mainly due to induction interactions dominated by ionic polarizabilities. We compare the solvation free-energy components of iodide at the water surface and bulk with a recent, polarizable force field. The bulk position is stabilized by the interaction between the iodide permanent charge and the solvent permanent dipole moments the surface is favored by the iodide polarizability and the reduced cavity accommodating the solute. The ionic solvation is not described satisfactorily by linear response the non-linearity of the iodide induced dipole moment is discussed. © 2005 Elsevier B.V. All rights reserved. 420 1-3 199 203 Cited By :27

GP catalyzes the phosphorylation of glycogen to Glc-1-P. Because of its fundamental role in the metabolism of glycogen, GP has been the target for a systematic structure-assisted design of inhibitory compounds, which could be of value in the therapeutic treatment of type 2 diabetes mellitus. The most potent catalytic-site inhibitor of GP identified to date is spirohydantoin of glucopyranose (hydan). In this work, we employ MD free energy simulations to calculate the relative binding affinities for GP of hydan and two spirohydantoin analogues, methyl-hydan and n-hydan, in which a hydrogen atom is replaced by a methyl- or amino group, respectively. The results are compared with the experimental relative affinities of these ligands, estimated by kinetic measurements of the ligand inhibition constants. The calculated binding affinity for methyl-hydan (relative to hydan) is 3.75 ± 1.4 kcal/mol, in excellent agreement with the experimental value (3.6 ± 0.2 kcal/mol). For n-hydan, the calculated value is 1.0 ± 1.1 kcal/mol, somewhat smaller than the experimental result (2.3 ± 0.1 kcal/mol). A free energy decomposition analysis shows that hydan makes optimum interactions with protein residues and specific water molecules in the catalytic site. In the other two ligands, structural perturbations of the active site by the additional methyl- or amino group reduce the corresponding binding affinities. The computed binding free energies are sensitive to the preference of a specific water molecule for two well-defined positions in the catalytic site. The behavior of this water is analyzed in detail, and the free energy profile for the translocation of the water between the two positions is evaluated. The results provide insights into the role of water molecules in modulating ligand binding affinities. A comparison of the interactions between a set of ligands and their surrounding groups in X-ray structures is often used in the interpretation of binding free energy differences and in guiding the design of new ligands. For the systems in this work, such an approach fails to estimate the order of relative binding strengths, in contrast to the rigorous free energy treatment. © 2005 Wiley-Liss, Inc. 61 4 984 998 Cited By :24

Background: The complement protein C5a acts by primarily binding and activating the G-protein coupled C5a receptor C5aR (CD88), and is implicated in many inflammatory diseases. The cyclic hexapeptide PMX53 (sequence Ace-Phe-[Orn-Pro-dCha-Trp-Arg]) is a full C5aR antagonist of nanomolar potency, and is widely used to study C5aR function in disease. Results: We construct for the first time molecular models for the C5aR:PMX53 complex without the a priori use of experimental constraints, via a computational framework of molecular dynamics (MD) simulations, docking, conformational clustering and free energy filtering. The models agree with experimental data, and are used to propose important intermolecular interactions contributing to binding, and to develop a hypothesis for the mechanism of PMX53 antagonism. Conclusion: This work forms the basis for the design of improved C5aR antagonists, as well as for atomic-detail mechanistic studies of complement activation and function. Our computational framework can be widely used to develop GPCR-ligand structural models in membrane environments, peptidomimetics and other chemical compounds with potential clinical use. © 2014 Tamamis et al. licensee BioMed Central Ltd. 7 1 Cited By :7

Specific amino acid binding by aminoacyl-tRNA synthetases (aaRS) is necessary for correct translation of the genetic code. Engineering a modified specificity into aminoacyl-tRNA synthetases has been proposed as a means to incorporate artificial amino acid residues into proteins in vivo. In a previous paper, the binding to aspartyl-tRNA synthetase of the substrate Asp and the analogue Asn were compared by molecular dynamics free energy simulations. Molecular dynamics combined with Poisson-Boltzmann free energy calculations represent a less expensive approach, suitable for examining multiple active site mutations in an engineering effort. Here, Poisson-Boltzmann free energy calculations for aspartyl-tRNA synthetase are first validated by their ability to reproduce selected molecular dynamics binding free energy differences, then used to examine the possibility of Asn binding to native and mutant aspartyl-tRNA synthetase. A component analysis of the Poisson-Boltzmann free energies is employed to identify specific interactions that determine the binding affinities. The combined use of molecular dynamics free energy simulations to study one binding process thoroughly, followed by molecular dynamics and Poisson-Boltzmann free energy calculations to study a series of related ligands or mutations is proposed as a paradigm for protein or ligand design. The binding of Asn in an alternate, "head-to-tail" orientation observed in the homologous asparagine synthetase is analyzed, and found to be more stable than the "Asp-like" orientation studied earlier. The new orientation is probably unsuitable for catalysis. A conserved active site lysine (Lys198 in Escherichia coli) that recognizes the Asp side-chain is changed to a leucine residue, found at the corresponding position in asparaginyl-tRNA synthetase. It is interesting that the binding of Asp is calculated to increase slightly (rather than to decrease), while that of Asn is calculated, as expected, to increase strongly, to the same level as Asp binding. Insight into the origin of these changes is provided by the component analyses. The double mutation (K198L,D233E) has a similar effect, while the triple mutation (K198L,Q199E,D233E) reduces Asp binding strongly. No binding measurements are available, but the three mutants are known to have no ability to adenylate Asn, despite the "Asp-like" binding affinities calculated here. In molecular dynamics simulations of all three mutants, the Asn ligand backbone shifts by 1-2 Å compared to the experimental Asp:AspRS complex, and significant side-chain rearrangements occur around the pocket. These could reduce the ATP binding constant and/or the adenylation reaction rate, explaining the lack of catalytic activity in these complexes. Finally, Asn binding to AspRS with neutral K198 or charged H449 is considered, and shown to be less favorable than with the charged K198 and neutral H449 used in the analysis. © 2001 Academic Press. 306 2 307 327 Cited By :92

Continuum solvent models are playing an increasing role in the study of aqueous solutions, particularly those involving protein solutes. To estimate the magnitude of dielectric relaxation and clarify the microscopic meaning of the protein dielectric constant, charge insertion in the active site of the enzyme aspartyl-tRNA synthetase (AspRS) is analyzed using finite-difference Poisson-Boltzmann calculations. The insertion process is a simplified model that mimics qualitatively the mutation of substrate Asp into Asn, studied earlier by free energy simulations. A two-step insertion path gives the relaxation and nonrelaxation ("static") free energy components separately. The assumption of linear response leads to a linear relation between the two components, connecting the explicit structural differences between reactant and product structures with the relaxation free energy calculated from either structure. This relation is verified here only if protein dielectric constants of 1 and 4-8 are used for the static and relaxation free energies, respectively. These are also the only conditions that give reasonable agreement with the Asp → Asn free energy simulated earlier and with a molecular dynamics/linear response estimate of the present charging free energy. The use of two protein dielectric constants represents a significant departure from standard continuum models. The values obtained are physically reasonable: a protein dielectric of 4-8 for relaxation indicates that the active site of AspRS, though highly polar, is only moderately polarizable. A dielectric of one for the static term indicates that the charge set, optimized for explicit solvent simulations, reproduces the equilibrium potential without the need for additional, implicit protein polarization. In contrast to simple charge insertion, the binding free energies of Asp and Asn to AspRS are best calculated with a more standard protocol that uses a single protein dielectric of 4, accurately reproducing free energy simulation results. For this and other binding processes, additional free energy components are involved, related to desolvation of the binding site the optimal dielectric constant represents an empirical compromise among these. A multistep component analysis could also be used to analyze the role of relaxation in these more complex processes. It is suggested that the use of more than one dielectric constant in continuum models will lead to a more consistent and robust description of dielectric phenomena in solution. 103 29 6142 6156

A central challenge of protein electron-transfer theory is to understand how the protein dynamics influences the electron tunneling from donor to acceptor. It is shown that tunneling (as a function of time) through a fluctuating protein bridge is drastically different from tunneling through a chemically identical static bridge. The static two-state approximation that leads to the donor-acceptor matrix element TDA, is therefore inadequate. A time-dependent two-state approximation is found that describes the tunneling dynamics through a fluctuating bridge. The fluctuating system electronic Hamiltonians are constructed from molecular dynamics trajectories at the CNDO-SCF level. 312 2-4 237 246 Cited By :41

Specific amino acid binding by aminoacyl-tRNA synthetases is necessary for correct translation of the genetic code. To obtain insight into the origin of the specificity, the binding to aspartyl-tRNA synthetase (AspRS) of the negatively charged substrate aspartic acid and the neutral analogue asparagine was compared by use of molecular dynamics and free energy simulations. Simulations of the Asn-AspRS complex showed that although Asn cannot bind in the same position as Asp, several possible positions exist 1.5 to 2 Å away from the Asp site. The binding free energy of Asn in three of these positions was compared to that of Asp through alchemical free energy simulations, in which Asp is gradually mutated into Asn in the complex with the enzyme. To correctly account for the electrostatic interactions in the system (including bulk solvent), a recently developed hybrid approach was used, in which the region of the mutation site is treated microscopically, whereas distant protein and solvent are treated by continuum electrostatics. Seven free energy simulations were performed in the protein and two in solution. The various Asn positions and orientations sampled at the Asn endpoints of the protein simulations yielded very similar free energy differences. The calculated Asp→Asn free energy change is 79.8(± 1.5) kcal/mol in solution and 95.1(± 2.8) kcal/mol in the complex with the protein. Thus, the substrate Asp is predicted to bind much more strongly than Asn, with a binding free energy difference of 15.3 kcal/mol. This implies that erroneous binding of Asn by AspRS is highly improbable, and cannot account for any errors in the translation of the genetic code. Almost all of the protein contributions to the Asp versus Asn binding free energy difference arise from an arginine and a lysine residue that hydrogen bond to the substrate carboxylate group and an Asp and a Glu that hydrogen bond to these all four amino acid residues are completely conserved in AspRSs. The protein effectively 'solvates' the Asp side-chain more strongly than water does. The simulations were analyzed to determine the interactions that Asn is able to make in the binding pocket, and which sequence differences between AspRS and the highly homologous AsnRS are important for modifying the amino acid specificity. A double or triple mutation of AspRS that could make it specific for Asn was proposed, and supported by preliminary simulations of a mutant complex. 275 5 823 846 Cited By :68

A method is proposed to include long-range electrostatic interactions in free energy calculations that involve the creation or deletion of net charges in a macromolecule. The vicinity of the mutation site is treated microscopically, while distant bulk solvent is treated macroscopically. A three-step mutation pathway is used. First, the mutation is introduced with a molecular dynamics simulation for the macromolecule, solvated by a limited number of explicit water molecules and surrounded by vacuum. Selected charges may be reduced during this step to mimic the effect of bulk solvent on the dynamics and to obtain a simulation in which the structures sampled are correct. The full effect of bulk solvent is accounted for in the next two steps. In the second step, the reduced charges are increased to their original values and the corresponding free energy change is obtained from continuum electrostatics. In the third step, the system is transferred into bulk solvent, modeled as a dielectric continuum, and the transfer free energy is obtained from continuum electrostatics. A potential-based charge scaling can be used in step I for the selected charges, which reduces each one in proportion to the screening by bulk solvent of its potential at the mutation site. With this method, the a priori scaling of a charged group in step I is formally equivalent to its solvation by bulk solvent in step III. Thus, for a given charged group, a priori scaling or a posteriori bulk solvation should give similar results. The method is illustrated by a calculation of the free energy change associated with the mutation of an aspartate ligand into asparagine in the active site of aspartyl-tRNA synthetase, a process that removes a negative charge. The results of five free energy runs with three different charge scaling schemes are in good agreement. This indicates that the method is robust with respect to implementation details and that the continuum approximation in steps II and III is valid for this case. 101 41 8349 8362 Cited By :104

We study a model of a random heteropolymer with ''secondary structure'' at the level of mean field theory. The randomness in the polymer sequence is represented by a set of quenched disorder variables that describe the monomer-monomer interactions. The secondary structure is represented by a set of Ising-like thermodynamic variables that describe internal states of the monomers. The interactions between the monomers depend on the quenched disorder variables, on the thermodynamic secondary-structure state variables, and also on the polymer configuration. We find that the system can exist in different phases that depend on the heterogeneity and average strength of the interactions, and on the polymer flexibility. At high temperatures the polymer interconverts freely between configurations without a stable secondary structure. At intermediate temperatures there is a transition to phases with one or two (coexisting) stable secondary-structure motifs and with a large number of thermodynamically important spatial configurations. At low enough temperatures (determined by the polymer flexibility) the polymer undergoes a freezing transition into phases with a unique spatial configuration and one or two stable secondary-structure motifs. © 1994 The American Physical Society. 49 4 3109 3123 Cited By :5

A theoretical analysis is made of the decomposition into contributions from individual interactions of the free energy calculated by thermodynamic integration. It is demonstrated that such a decomposition, often referred to as “component analysis,” is meaningful, even though it is a function of the integration path. Moreover, it is shown that the path dependence can be used to determine the relation of the contribution of a given interaction to the state of the system. To illustrate these conclusions, a simple transformation(Cl− to Br− in aqueous solution) is analyzed by use of the Reference Interaction Site Model‐Hypernetted Chain Closure integral equation approach it avoids the calculational difficulties of macromolecular simulation while retaining their conceptual complexity. The difference in the solvation free energy between chloride and bromide is calculated, and the contributions of the Lennard‐Jones and electrostatic terms in the potential function are analyzed by the use of suitably chosen integration paths. The model is also used to examine the path dependence of individual contributions to the double free energy differences (ΔΔG or ΔΔA) that are often employed in free energy simulations of biological systems. The alchemical path, as contrasted with the experimental path, is shown to be appropriate for interpreting the effects of mutations on ligand binding and protein stability. The formulation is used to obtain a better understanding of the success of the Poisson‐Boltzmann continuum approach for determining the solvation properties of polar and ionic systems. © 1994 Wiley‐Liss, Inc. Copyright © 1994 Wiley‐Liss, Inc. 20 1 25 33 Cited By :104