@article {Skolnick2000a, title = {Derivation of protein-specific pair potentials based on weak sequence fragment similarity}, journal = {Proteins: Structure, Function, Bioinformatics}, volume = {38}, year = {2000}, pages = {3{\textendash}16}, abstract = {A method is presented for the derivation of knowledge-based pair potentials that corrects for the various compositions of different proteins. The resulting statistical pair potential is more specific than that derived from previous approaches as assessed by gapless threading results. Additionally, a methodology is presented that interpolates between statistical potentials when no homologous examples to the protein of interest are in the structural database used to derive the potential, to a Go-like potential (in which native interactions are favorable and all nonnative interactions are not) when homologous proteins are present. For cases in which no protein exceeds 30\% sequence identity, pairs of weakly homologous interacting fragments are employed to enhance the specificity of the potential. In gapless threading, the mean z score increases from -10.4 for the best statistical pair potential to -12.8 when the local sequence similarity, fragment-based pair potentials are used. Examination of the ab initio structure prediction of four representative globular proteins consistently reveals a qualitative improvement in the yield of structures in the 4 to 6 A rmsd from native range when the fragment-based pair potential is used relative to that when the quasichemical pair potential is employed. This suggests that such protein-specific potentials provide a significant advantage relative to generic quasichemical potentials.}, keywords = {knowledge-based potentials, potential deriva-, Sequence Analysis, structure prediction, Tertiary, tion}, url = {http://onlinelibrary.wiley.com/doi/10.1002/(SICI)1097-0134(20000101)38:1\%3C3::AID-PROT2\%3E3.0.CO;2-S/full}, author = {Jeffrey Skolnick and Andrzej Koli{\'n}ski and Angel Ortiz} } @article {Skolnick1999c, title = {De novo predictions of the quaternary structure of leucine zippers and other coiled coils}, journal = {International Journal of Quantum Chemistry}, volume = {75}, year = {1999}, pages = {165{\textendash}176}, abstract = {Coiled coils possess a quaternary structure comprised of the side-by-side arrangement of a-helices. Due their inherent structural simplicity, they are ideal model systems for both theoretical and experimental studies. Among the coiled coils are the leucine zippers, which play an important role in the activation of DNA transcription. In contrast to the large amount of available experimental data, an overview of which is presented, there are very few theoretical studies. To address this need, the status of existing theoretical approaches to predict coiled coil quaternary structure is described. Furthermore, to treat the conformational equilibria inherent in these systems, an extension of entropy sampling Monte Carlo simulations is developed that can treat multimers. Here, the approach is applied to GCN4 leucine zippers in the context of a reduced protein model. Not only is the native conformation successfully predicted, but the model also reproduces the experimentally observed helix content in the denatured state and the observed two-state thermodynamic behavior. Such two-state behavior arises from the dissociation of highly helical dimeric chains to form monomers of low, isolated chain helix content.}, keywords = {coiled coil, lattice protein models, Leucine Zippers, protein structure prediction, quaternary structure prediction}, url = {http://cssb.biology.gatech.edu/skolnick/publications/pdffiles/183.pdf}, author = {Jeffrey Skolnick and Andrzej Koli{\'n}ski and Debasisa Mohanty} } @article {Mohanty1999, title = {De novo simulations of the folding thermodynamics of the GCN4 leucine zipper}, journal = {Biophysical Journal}, volume = {77}, number = {1}, year = {1999}, month = {jul}, pages = {54{\textendash}69}, abstract = {Entropy Sampling Monte Carlo (ESMC) simulations were carried out to study the thermodynamics of the folding transition in the GCN4 leucine zipper (GCN4-lz) in the context of a reduced model. Using the calculated partition functions for the monomer and dimer, and taking into account the equilibrium between the monomer and dimer, the average helix content of the GCN4-lz was computed over a range of temperatures and chain concentrations. The predicted helix contents for the native and denatured states of GCN4-lz agree with the experimental values. Similar to experimental results, our helix content versus temperature curves show a small linear decline in helix content with an increase in temperature in the native region. This is followed by a sharp transition to the denatured state. van{\textquoteright}t Hoff analysis of the helix content versus temperature curves indicates that the folding transition can be described using a two-state model. This indicates that knowledge-based potentials can be used to describe the properties of the folded and unfolded states of proteins.}, keywords = {Computer Simulation, Dimerization, DNA-Binding Proteins, Fungal Proteins, Fungal Proteins: chemistry, Leucine Zippers, Monte Carlo Method, Protein Conformation, Protein Denaturation, Protein Folding, Protein Kinases, Protein Kinases: chemistry, Protein Structure, Saccharomyces cerevisiae Proteins, Secondary, Temperature, Thermodynamics}, isbn = {6197848821}, issn = {0006-3495}, doi = {10.1016/S0006-3495(99)76872-4}, url = {http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1300312\&tool=pmcentrez\&rendertype=abstract}, author = {Debasisa Mohanty and Andrzej Koli{\'n}ski and Jeffrey Skolnick} } @article {Kolinski1999, title = {Dynamics and thermodynamics of beta-hairpin assembly: insights from various simulation techniques}, journal = {Biophysical Journal}, volume = {77}, number = {6}, year = {1999}, month = {dec}, pages = {2942{\textendash}52}, abstract = {Small peptides that might have some features of globular proteins can provide important insights into the protein folding problem. Two simulation methods, Monte Carlo Dynamics (MCD), based on the Metropolis sampling scheme, and Entropy Sampling Monte Carlo (ESMC), were applied in a study of a high-resolution lattice model of the C-terminal fragment of the B1 domain of protein G. The results provide a detailed description of folding dynamics and thermodynamics and agree with recent experimental findings (. Nature. 390:196-197). In particular, it was found that the folding is cooperative and has features of an all-or-none transition. Hairpin assembly is usually initiated by turn formation; however, hydrophobic collapse, followed by the system rearrangement, was also observed. The denatured state exhibits a substantial amount of fluctuating helical conformations, despite the strong beta-type secondary structure propensities encoded in the sequence.}, keywords = {Amino Acid Sequence, Animals, Biophysical Phenomena, Biophysics, Models, Molecular, Molecular Sequence Data, Monte Carlo Method, Nerve Tissue Proteins, Nerve Tissue Proteins: chemistry, Protein Conformation, Protein Folding, Protein Structure, Proteins, Proteins: chemistry, Secondary, Thermodynamics}, issn = {0006-3495}, doi = {10.1016/S0006-3495(99)77127-4}, url = {http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1300567\&tool=pmcentrez\&rendertype=abstract}, author = {Andrzej Koli{\'n}ski and Bartosz Ilkowski and Jeffrey Skolnick} } @article {Skolnick1997a, title = {Derivation and testing of pair potentials for protein folding. When is the quasichemical approximation correct?}, journal = {Protein Science}, volume = {6}, number = {3}, year = {1997}, month = {mar}, pages = {676{\textendash}688}, abstract = {Many existing derivations of knowledge-based statistical pair potentials invoke the quasichemical approximation to estimate the expected side-chain contact frequency if there were no amino acid pair-specific interactions. At first glance, the quasichemical approximation that treats the residues in a protein as being disconnected and expresses the side-chain contact probability as being proportional to the product of the mole fractions of the pair of residues would appear to be rather severe. To investigate the validity of this approximation, we introduce two new reference states in which no specific pair interactions between amino acids are allowed, but in which the connectivity of the protein chain is retained. The first estimates the expected number of side-chain contracts by treating the protein as a Gaussian random coil polymer. The second, more realistic reference state includes the effects of chain connectivity, secondary structure, and chain compactness by estimating the expected side-chain contrast probability by placing the sequence of interest in each member of a library of structures of comparable compactness to the native conformation. The side-chain contact maps are not allowed to readjust to the sequence of interest, i.e., the side chains cannot repack. This situation would hold rigorously if all amino acids were the same size. Both reference states effectively permit the factorization of the side-chain contact probability into sequence-dependent and structure-dependent terms. Then, because the sequence distribution of amino acids in proteins is random, the quasichemical approximation to each of these reference states is shown to be excellent. Thus, the range of validity of the quasichemical approximation is determined by the magnitude of the side-chain repacking term, which is, at present, unknown. Finally, the performance of these two sets of pair interaction potentials as well as side-chain contact fraction-based interaction scales is assessed by inverse folding tests both without and with allowing for gaps.}, keywords = {empirical parameter sets, inverse protein folding, protein structural database, protein threading, quasichemical approximation}, issn = {0961-8368}, doi = {10.1002/pro.5560060317}, url = {http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2143667\&tool=pmcentrez\&rendertype=abstract}, author = {Jeffrey Skolnick and Lukasz Jaroszewski and Andrzej Koli{\'n}ski and Adam Godzik} } @article {Kolinski1997a, title = {Determinants of secondary structure of polypeptide chains: Interplay between short range and burial interactions}, journal = {Journal of Chemical Physics}, volume = {107}, number = {3}, year = {1997}, pages = {953{\textendash}964}, abstract = {The effect of tertiary interactions on the observed secondary structure found in the native conformation of globular proteins was examined in the context of a reduced protein model. Short-range interactions are controlled by knowledge based statistical potentials that reflect local conformational regularities seen in a database of three-dimensional protein structures. Long-range interactions are approximated by mean field, single residue based, centrosymmetric hydrophobic burial potentials. Even when pairwise specific long-range interactions are ignored, the inclusion of such burial preferences noticeably modifies the equilibrium chain conformations, and the observed secondary structure is closer to that seen in the folded state. For a test set of 10 proteins (belonging to various structural classes), the accuracy of secondary structure prediction is about 66\% and increases by 9\% with respect to a related model based on short-range interactions alone [Kolinski et al., J. Chem. Phys. 103, 4312 (1995)]. The increased accuracy is due to the interplay between the short-range conformational propensities and the burial and compactness requirements built into the present model. While the absolute level of accuracy assessed on a per residue basis is comparable to more standard techniques, in contrast to these approaches, the conformation of the chain now has a better defined geometric context. For example, the assumed spherical domain protein model that simulates the segregation of residues between the hydrophobic core and the hydrophilic surface allows for the prediction of surface loops/turns where the polypeptide chain changes its direction. The implications of having such self-consistent secondary structure predictions for the prediction of protein tertiary structure are briefly discussed.}, doi = {10.1063/1.474448}, url = {http://smartech.gatech.edu/handle/1853/27033}, author = {Andrzej Koli{\'n}ski and Jeffrey Skolnick} } @article {Olszewski1996, title = {Does a backwardly read protein sequence have a unique native state?}, journal = {Protein Engineering}, volume = {9}, number = {1}, year = {1996}, month = {jan}, pages = {5{\textendash}14}, abstract = {Amino acid sequences of native proteins are generally not palindromic. Nevertheless, the protein molecule obtained as a result of reading the sequence backwards, i.e. a retro-protein, obviously has the same amino acid composition and the same hydrophobicity profile as the native sequence. The important questions which arise in the context of retro-proteins are: does a retro-protein fold to a well defined native-like structure as natural proteins do and, if the answer is positive, does a retro-protein fold to a structure similar to the native conformation of the original protein? In this work, the fold of retro-protein A, originated from the retro-sequence of the B domain of Staphylococcal protein A, was studied. As a result of lattice model simulations, it is conjectured that the retro-protein A also forms a three-helix bundle structure in solution. It is also predicted that the topology of the retro-protein A three-helix bundle is that of the native protein A, rather than that corresponding to the mirror image of native protein A. Secondary structure elements in the retro-protein do not exactly match their counterparts in the original protein structure; however, the amino acid side chain contract pattern of the hydrophobic core is partly conserved.}, keywords = {Amino Acid Sequence, Computer Simulation, Models, Molecular, Molecular Sequence Data, Monte Carlo Method, Protein Conformation, Protein Engineering, Protein Folding, Protein Structure, Secondary, Staphylococcal Protein A, Staphylococcal Protein A: chemistry, Tertiary}, issn = {0269-2139}, url = {http://www.ncbi.nlm.nih.gov/pubmed/9053902}, author = {Krzysztof A. Olszewski and Andrzej Koli{\'n}ski and Jeffrey Skolnick} } @article {Skolnick1995, title = {De novo simulations of the folding of GCN4 and its mutants}, journal = {Modeling of Biomolecular Structures and Mechanisms}, volume = {8}, year = {1995}, pages = {95{\textendash}98}, abstract = {A hierarchical approach to protein folding is employed to examine the folding pathway and predict the quaternary structure of the GCN4 leucine zipper. Structures comparable in quality to experiment have been predicted. In addition, the equilibrium between dimers, trimers and tetramers of a number of GCN4 mutants has been examined. In most of the cases, the simulation results are in accord with the experimental studies of Harbury et al.}, keywords = {Leucine Zippers/computer, Protein folding/GCN4, protein models, simulations/lattice}, url = {http://cssb.biology.gatech.edu/skolnick/publications/pdffiles/124.pdf}, author = {Jeffrey Skolnick and Michal Vieth and Andrzej Koli{\'n}ski and Charles L. Brooks III} } @article {Skolnick1994a, title = {De Novo Prediction of Protein Tertiary Structure}, journal = {Polymer Preprints}, volume = {35}, year = {1994}, pages = {82{\textendash}83}, author = {Jeffrey Skolnick and Andrzej Koli{\'n}ski} } @article {Sikorski1994, title = {Dynamics of star branched polymers in a matrix of linear chains{\textemdash}a Monte Carlo study}, journal = {Macromolecular Theory and Simulations}, volume = {3}, year = {1994}, pages = {715{\textendash}729}, abstract = {A simple cubic lattice model of the melt of 3-arm star-branched polymers of various length dissolved in a matrix of long linear chains (n1 = 800 beads) is studied using a dynamic Monte Carlo method. The total polymer volume fraction is equal to 0,5, while the volume fraction of the star polymers is about ten times smaller. The static and dynamic properties of these systems are compared with the corresponding model systems of isolated star-branched polymers and with the melt of linear chains. It has been found that the number of dynamic entanglements for the star polymers with arm length up to 400 segments is too small for the onset of the arm retraction mechanism of polymer relaxation. In this regime dynamics of star-branched polymers is close to the dynamics of linear polymers at corresponding concentration and with equivalent chain length. The entanglement length for star polymers appears to be somewhat larger compared with linear chains.}, doi = {10.1002/mats.1994.040030407}, url = {http://onlinelibrary.wiley.com/doi/10.1002/mats.1994.040030407/abstract}, author = {Andrzej Sikorski and Andrzej Koli{\'n}ski and Jeffrey Skolnick} } @article {Godzik1993, title = {De novo and inverse folding predictions of protein structure and dynamics}, journal = {Journal of Computer-Aided Molecular Design}, volume = {7}, year = {1993}, pages = {397{\textendash}438}, abstract = {In the last two years, the use of simplified models has facilitated major progress in the globular protein folding problem, viz., the prediction of the three-dimensional (3D) structure of a globular protein from its amino acid sequence. A number of groups have addressed the inverse folding problem where one examines the compatibility of a given sequence with a given (and already determined) structure. A comparison of extant inverse protein-folding algorithms is presented, and methodologies for identifying sequences likely to adopt identical folding topologies, even when they lack sequence homology, are described. Extension to produce structural templates or fingerprints from idealized structures is discussed, and for eight-membered beta-barrel proteins, it is shown that idealized fingerprints constructed from simple topology diagrams can correctly identify sequences having the appropriate topology. Furthermore, this inverse folding algorithm is generalized to predict elements of supersecondary structure including beta-hairpins, helical hairpins and alpha/beta/alpha fragments. Then, we describe a very high coordination number lattice model that can predict the 3D structure of a number of globular proteins de novo; i.e. using just the amino acid sequence. Applications to sequences designed by DeGrado and co-workers [Biophys. J., 61 (1992) A265] predict folding intermediates, native states and relative stabilities in accord with experiment. The methodology has also been applied to the four-helix bundle designed by Richardson and co-workers [Science, 249 (1990) 884] and a redesigned monomeric version of a naturally occurring four-helix dimer, rop. Based on comparison to the rop dimer, the simulations predict conformations with rms values of 3-4 A from native. Furthermore, the de novo algorithms can assess the stability of the folds predicted from the inverse algorithm, while the inverse folding algorithms can assess the quality of the de novo models. Thus, the synergism of the de novo and inverse folding algorithm approaches provides a set of complementary tools that will facilitate further progress on the protein-folding problem.}, keywords = {Inverse folding, lattice protein models, Molten globule intermediates, Protein folding pathways, tertiary structure prediction}, url = {http://www.springerlink.com/index/QM35800826224081.pdf}, author = {Adam Godzik and Andrzej Koli{\'n}ski and Jeffrey Skolnick} } @article {Kolinski1992, title = {Discretized model of proteins. I. Monte Carlo study of cooperativity in homopolypeptides}, journal = {Journal of Chemical Physics}, volume = {97}, number = {December}, year = {1992}, pages = {9412{\textendash}9426}, abstract = {A discretized model of globular proteins is employed in a Monte Carlo study of the helix{\textendash}coil transition of polyalanine and the collapse transition of polyvaline. The present lattice realization permits real protein crystal structures to be represented at the level of 1 {\r A} resolution. Furthermore, the Monte Carlo dynamic scheme is capable of moving elements of assembled secondary and supersecondary structure. The potentials of mean force for the interactions are constructed from the statistics of a set of high resolution x-ray structures of nonhomologous proteins. The cooperativity of formation of ordered structures is found to be larger when the major contributions to the conformational energy of the low temperature states come from hydrogen bonds and short range conformational propensities. The secondary structure seen in the folded state is the result of an interplay between the short and long range interactions. Compactness itself, driven by long range, nonspecific interactions, seems to be insufficient to generate any appreciable secondary structure. A detailed examination of the dynamics of highly helical model proteins demonstrates that all elements of secondary structure are mobile in the present algorithm, and thus the folding pathways do not depend on the use of a lattice approximation. Possible applications of the present model to the prediction of protein 3D structures are briefly discussed.}, keywords = {Conformational Changes, Coupling, Globular Clusters, Lattice Gas, Molecular Models, Monte Carlo Method, Polypeptides, Proteins, Randomness, Resolution}, doi = {10.1063/1.463317}, url = {http://link.aip.org/link/doi/10.1063/1.463317}, author = {Andrzej Koli{\'n}ski and Jeffrey Skolnick} } @article {Skolnick1991, title = {Dynamic Monte Carlo Simulations of a new lattice model of globular protein folding, structure, and dynamics}, journal = {Journal of Molecular Biology}, volume = {221}, year = {1991}, pages = {499{\textendash}531}, abstract = {A long-standing problem of molecular biology is the prediction of globular protein tertiary structure from the primary sequence. In the context of a new, 24-nearest-neighbor lattice model of proteins that includes both alpha and beta-carbon atoms, the requirements for folding to a unique four-member beta-barrel, four-helix bundles and a model alpha/beta-bundle have been explored. A number of distinct situations are examined, but the common requirements for the formation of a unique native conformation are tertiary interactions plus the presence of relatively small (but not irrelevant) intrinsic turn preferences that select out the native conformer from a manifold of compact states. When side-chains are explicitly included, there are many conformations having the same or a slightly greater number of side-chain contacts as in the native conformation, and it is the local intrinsic turn preferences that produce the conformational selectivity on collapse. The local preference for helix or beta-sheet secondary structure may be at odds with the secondary structure ultimately found in the native conformation. The requisite intrinsic turn populations are about 0.3\% for beta-proteins, 2\% for mixed alpha/beta-proteins and 6\% for helix bundles. In addition, an idealized model of an allosteric conformational transition has been examined. Folding occurs predominantly by a sequential on-site assembly mechanism with folding initiating either at a turn or from an isolated helix or beta-strand (where appropriate). For helical and beta-protein models, similar folding pathways were obtained in diamond lattice simulations, using an entirely different set of local Monte Carlo moves. This argues strongly that the results are universal; that is, they are independent of lattice, protein model or the particular realization of Monte Carlo dynamics. Overall, these simulations demonstrate that the folding of all known protein motifs can be achieved in the context of a single class of lattice models that includes realistic backbone structures and idealized side-chains.}, keywords = {assembly mechanism, bends and turns, folding pathways, Protein Folding, secondary structures}, doi = {10.1016/0022-2836(91)80070-B}, url = {http://dx.doi.org/10.1016/0022-2836(91)80070-B}, author = {Jeffrey Skolnick and Andrzej Koli{\'n}ski} } @article {Skolnick1990a, title = {Dynamic Monte Carlo Globular Protein Folding and Structure}, journal = {Chemical Design Automation News}, volume = {5}, number = {3}, year = {1990}, pages = {1{\textendash}20}, author = {Jeffrey Skolnick and Andrzej Koli{\'n}ski and Andrzej Sikorski} } @article {284, title = {Dynamic Monte Carlo Simulations of Globular Protein Folding, Structure and Dynamics}, journal = {Comments on Molecular \& Cell Biology}, volume = {6}, year = {1990}, pages = {223-247}, author = {Jeffrey Skolnick and Andrzej Koli{\'n}ski and Andrzej Sikorski} } @article {Sikorski1990, title = {Dynamic Monte Carlo simulations of globular protein folding/unfolding pathways: I. Six-member, Greek Key beta-Barrel proteins}, journal = {Journal of Molecular Biology}, volume = {212}, year = {1990}, pages = {787{\textendash}817}, abstract = {In the context of a simplified diamond lattice model of a six-member, Greek key beta-barrel protein that is closely related in topology to plastocyanin, the nature of the folding and unfolding pathways have been investigated using dynamic Monte Carlo techniques. The mechanism of Greek key assembly is best described as punctuated "on site construction". Folding typically starts at or near a beta-turn, and then the beta-strands sequentially form by using existing folded structure as a scaffold onto which subsequent tertiary structure assembles. On average, beta-strands tend to zip up from one tight bend to the next. After the four-member, beta-barrel assembles, there is a long pause as the random coil portion of the chain containing the long loop thrahes about trying to find the native state. Thus, there is an entropic barrier that must be surmounted. However, while a given piece of the protein may be folding, another section may be unfolding. A competition therefore exists to assemble a fairly stable intermediate before it dissolves. Folding may initiate at any of the tight turns, but the turn closer to the N terminus seems to be preferred due to well-known excluded volume effects. When the protein first starts to fold, there are a multiplicity of folding pathways, but the number of options is reduced as the system gets closer to the native state. In the early stages, the excluded volume effect exerted by the already assembled protein helps subsequent assembly. Then, near the native conformation, the folded parts reduce the accessible conformational space available to the remaining unfolded sections. Unfolding essentially occurs in reverse. Employing a simple statistical mechanical theory, the configurational free energy along the reaction co-ordinate for this model has been constructed. The free energy surface, in agreement with the simulations, provides the following predictions. The transition state is quite near the native state, and consists of five of the six beta-strands being fully assembled, with the remaining long loop plus sixth beta-strand in place, but only partially assembled. It is separated from the beta-barrel intermediate by a free energy barrier of mainly entropic origin and from the native state by a barrier that is primarily energetic in origin. The latter feature is in agreement with the "Cardboard Box" model described by Goldenberg and Creighton but, unlike their model, the transition state is not a high-energy distorted form of the native state.}, url = {http://www.sciencedirect.com/science/article/pii/002228369090238H}, author = {Jeffrey Skolnick and Andrzej Koli{\'n}ski} } @inbook {Skolnick1990, title = {Dynamics of dense polymer systems: Computer simulations and analytic theories}, booktitle = {Advances in Chemical Physics}, volume = {77}, year = {1990}, pages = {223{\textendash}278}, keywords = {Brownian dynamics, Monte Carlo results, relaxation times, Rouse model, unknotted rings}, doi = {10.1002/9780470141274.ch5}, url = {http://books.google.com/books?hl=en\&lr=\&id=D6Ve3CgALtkC\&oi=fnd\&pg=PA223\&dq=Dynamics+of+dense+polymer+systems:+computer+simulations+and+analytic+theories\&ots=19NoqLh3qY\&sig=ONsS49-adBsoKzx\_8nplUSmOIMI}, author = {Jeffrey Skolnick and Andrzej Koli{\'n}ski} } @article {Skolnick1989b, title = {Dynamic Monte Carlo Simulation of a melt of ring polymers}, journal = {Polymer Preprints}, volume = {30}, year = {1989}, pages = {70{\textendash}73}, author = {Jeffrey Skolnick and Andrzej Koli{\'n}ski and Andrzej Sikorski and Robert Yaris} } @article {Skolnick1989c, title = {Dynamic Monte Carlo study of the folding of a six-stranded Greek key globular protein}, journal = {Proceedings of the National Academy of Sciences of the United States of America}, volume = {86}, number = {February}, year = {1989}, pages = {1229{\textendash}1233}, abstract = {To help elucidate the general rules of equilibrium globular protein folding, dynamic Monte Carlo simulations of a model beta-barrel globular protein having the six-stranded Greek key motif characteristic of real globular proteins were undertaken. The model protein possesses a typical beta-barrel amino acid sequence; however, all residues of a given type (e.g. hydrophobic residues) are identical. Even in the absence of site-specific interactions, starting from a high-temperature denatured state, these models undergo an all-or-none transition to a structurally unique six-stranded beta-barrel. These simulations suggest that the general rules of globular protein folding are rather robust in that the overall tertiary structure is determined by the general pattern of hydrophobic, hydrophilic, and turn-type residues, with site-specific interactions mainly involved in structural fine tuning of a given topology. Finally, these studies suggest that loops may play an important role in producing a unique native state. Depending on the stability of the native conformation of the long loop in the Greek key, the conformational transition can be described by a two-state, three-state, or even larger number of multiple equilibrium states model.}, keywords = {all-or-none transition, multiple domain protein, plastocyanin model}, url = {http://www.pnas.org/content/86/4/1229.long}, author = {Jeffrey Skolnick and Andrzej Koli{\'n}ski and Robert Yaris} } @article {Kolinski1987b, title = {Does reptation describe the dynamics of entangled, finite length polymer systems? A model simulation}, journal = {The Journal of Chemical Physics}, volume = {86}, year = {1987}, pages = {1567{\textendash}1585}, abstract = {In order to examine the validity of the reptation model of motion in a dense collection of polymers, dynamic Monte Carlo (MC) simulations of polymer chains composed of n beads confined to a diamond lattice were undertaken as a function of polymer concentration ϕ and degree of polymerization n. We demonstrate that over a wide density range these systems exhibit the experimentally required molecular weight dependence of the center-of-mass self-diffusion coefficient D\~{}n-2.1 and the terminal relaxation time of the end-to-end vector τR\~{}n3.4. Thus, these systems should represent a highly entangled collection of polymers appropriate to look for the existence of reptation. The time dependence of the average single bead mean-square displacement, as well as the dependence of the single bead displacement on position in the chain were examined, along with the time dependence of the center-of-mass displacement. Furthermore, to determine where in fact a well-defined tube exists, the mean-square displacements of a polymer chain down and perpendicular to its primitive path defined at zero time were calculated, and snapshots of the primitive path as a function of time are presented. For an environment where all the chains move, no evidence of a tube, whose existence is central to the validity of the reptation model, was found. However, if a single chain is allowed to move in a partially frozen matrix of chains (where all chains but one are pinned every ne beads, and where between pin points the other chains are free to move), reptation with tube leakage is recovered for the single mobile chain. The dynamics of these chains possesses aspects of Rouse-like motion; however, unlike a Rouse chain, these chains undergo highly cooperative motion that appears to involve a backflow between chains to conserve constant average density. While these simulations cannot preclude the onset of reptation at higher molecular weight, they strongly argue at a minimum for the existence with increasing n of a crossover regime from simple Rouse dynamics in which reptation plays a minor role at best.}, keywords = {Chains, Computerized Simulation, dynamics, Monte Carlo Method, Polymers}, doi = {10.1063/1.452196}, url = {http://link.aip.org/link/JCPSA6/v86/i3/p1567/s1}, author = {Andrzej Koli{\'n}ski and Jeffrey Skolnick and Robert Yaris} } @article {Kolinski1987d, title = {Dynamic Monte Carlo study of the conformational properties of long flexible polymers}, journal = {Macromolecules}, volume = {20}, year = {1987}, pages = {687{\textendash}689}, doi = {10.1021/ma00168a039}, url = {http://pubs.acs.org/doi/abs/10.1021/ma00168a039}, author = {Andrzej Koli{\'n}ski and Jeffrey Skolnick and Robert Yaris} }