@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 {Skolnick1989, title = {Monte Carlo studies on equilibrium globular protein folding. II. Beta-barrel globular protein models}, journal = {Biopolymers}, volume = {28}, number = {6}, year = {1989}, month = {jun}, pages = {1059{\textendash}95}, abstract = {In the context of dynamic Monte Carlo simulations on a model protein confined to a tetrahedral lattice, the interplay of protein size and tertiary structure, and the requirements for an all-or-none transition to a unique native state, are investigated. Small model proteins having a primary sequence consisting of a central bend neutral region flanked by two tails having an alternating hydrophobic/hydrophilic pattern of residues are seen to undergo a continuous transition to a beta-hairpin collapsed state. On increasing the length of the tails, the beta-hairpin structural motif is found to be in equilibrium with a four-member beta-barrel. Further increase of the tail length results in the shift of the structural equilibrium to the four-member beta-barrel. The random coil to beta-barrel transition is of an all-or-none character, but while the central turn is always the desired native bend, the location of the turns involving the two external strands is variable. That is, beta-barrels having the external stands that are two residues out of register are also observed in the transition region. Introduction into the primary sequence of two additional regions that are at the very least neutral toward turn formation produces an all-or-none transition to the unique, native, four-member beta-barrel. Various factors that can augment the stability of the native conformation are explored. Overall, these folding simulations strongly indicate that the general rules of globular protein folding are rather robust{\textendash}namely, one requires a general pattern of hydrophobic/hydrophilic residues that allow the protein to have a well-defined interior and exterior and the presence of regions in the amino acid sequence that at the very least are locally indifferent to turn formation. Since no site-specific interactions between hydrophobic and hydrophilic residues are required to produce a unique four-member beta-barrel, these simulations strongly suggest that site specificity is involved in structural fine-tuning.}, keywords = {Algorithms, Models, Monte Carlo Method, Protein Conformation, Proteins, Theoretical}, issn = {0006-3525}, doi = {10.1002/bip.360280604}, url = {http://www.ncbi.nlm.nih.gov/pubmed/2730942}, author = {Jeffrey Skolnick and Andrzej Koli{\'n}ski and Robert Yaris} } @article {282, title = {Phenomenological Theory of Polymer Melt Dynamics}, journal = {International Journal of Modern Physics B}, volume = {3}, year = {1989}, pages = {33-64}, abstract = {A particularly interesting problem in polymer physics is the mechanism by which an individual polymer chain moves in a polymer melt or concentrated polymer solution. The first rather successful model of polymer dynamics was the reptation model of de Gennes which asserts that due to the effect of entanglements a polymer finds itself confined to a tube. Thus, the dominant long wavelength motion of the chain should be slithering out the ends of the tube. In order to examine the validity of the reptation model, a series of dynamic Monte Carlo simulations were performed. Although the simulations are on chains sufficiently long that agreement with the experimentally observed scaling with degree of polymerization n of the self diffusion constant and terminal relaxation time is observed, reptation does not appear to be the dominant mechanism of long distance motion. Rather the motion is isotropic, with the slowdown from dilute solution behavior arising from the formation of dynamic entanglements {\textemdash} rare long lived contacts where a given chain drags another chain through the melt for times on the order of longest internal relaxation time. Motivated by the simulations results, a phenomenological theory for the diffusive and viscoelastic behavior is developed that is consistent with both simulations and experiment and which does not invoke reptation. The major conclusions arising from the theoretical approach are described, and comparison is made with experiment.}, doi = {10.1142/S0217979289000038}, author = {Jeffrey Skolnick and Robert Yaris and Andrzej Koli{\'n}ski} } @article {Skolnick1988a, title = {Monte Carlo simulations of the folding of beta-barrel globular proteins}, journal = {Proceedings of the National Academy of Sciences of the United States of America}, volume = {85}, number = {July}, year = {1988}, pages = {5057{\textendash}5061}, abstract = {With the use of dynamic Monte Carlo simulations, the necessary conditions for the collapse from a random-coil denatured state to a structurally unique four-member beta-barrel native state of a model globular protein have been investigated. These systems are free to roam through all of configuration space--both native and nonnative interactions are allowed. The relative importance of hydrophobic and hydrophilic interactions and the presence or absence of statistical bend-forming regions for the formation of a unique native state are examined, and the conditions necessary for a denatured-to-native (and vice versa) conformational transition that is thermodynamically all-or-none and which always results in collapse to the same, four-member beta-barrel are explored. These conditions are found to be a general pattern of hydrophobic/hydrophilic residues that allows the native state to differentiate the interior from the exterior of the protein and the presence of regions that are, at the very least, neutral toward turn formation. The former set of interactions seems to define the mean length of the beta-stretch, and the latter set serves to lock the native state into the lowest free energy state, the native conformation. These folding simulations strongly suggest that the general rules of protein folding are rather robust and that site-specific tertiary interactions are only involved in structural fine tuning. The conditions required for the formation of a structurally unique native state from a manifold of collapsed conformations that are originally quite close in energy is highly suggestive of a mechanism of protein evolution by means of random mutations. The implications of these folding studies for such a mechanism are qualitatively explored.}, url = {http://www.pnas.org/content/85/14/5057.short}, author = {Jeffrey Skolnick and Andrzej Koli{\'n}ski and Robert Yaris} } @article {Skolnick1988, title = {Phenomenological theory of the dynamics of polymer melts. I. Analytic treatment of self-diffusion}, journal = {The Journal of Chemical Physics}, volume = {3}, number = {1}, year = {1988}, pages = {33{\textendash}64}, abstract = {In the context of dynamic Monte Carlo (MC) simulations on dense collections of polymer chains confined to a cubic lattice, the nature of the dynamic entanglements giving rise to the degree of polymerization n, dependence of the self-diffusion constant D~n[superscript -2] is examined. Consistent with our previous simulation results, which failed to find evidence for reptation as the dominant mechanism of polymer melt motion [J. Chem. Phys. 86, 1567, 7164, 7174 (1987)], long-lived dynamic entanglement contacts between pairs of segments belonging to different chains are extremely rare and are mobile with respect to the laboratory fixed frame. It is suggested that dynamic entanglements involve the dragging of one chain by another through the melt for times on the order of the terminal relaxation time of the end-to-end vector. Employing the physical description provided by the MC simulation, the general expression of Hess [Macromolecules 19, 1395 (1986)] for the friction constant increment experienced by a polymer due to the other polymers forms the basis of a phenomenological derivation of D~n[superscript -2] for monodisperse melts that does not require the existence of reptation. Rather, such behavior is dependent on the relatively benign assumptions that the long distance global motions of the chains are uncorrelated, that the dynamic contacts can be truncated at the pair level, and that the propagator describing the evolution between dynamic contacts contains a free Rouse chain component. The mean distance between dynamic entanglements is predicted to depend inversely on concentration, in agreement with experiment. Moreover, as the free Rouse component is frozen out, for chains greater than an entanglement length ne, a molecular weight independent glass transition is predicted. Extension to bidisperse melts predicts that the probe diffusion coefficient Dp depends on the matrix degree of polymerization, nm, as n. Finally, comparison is made between the theoretical expressions and MC results for mono- and bidisperse melts}, doi = {10.1063/1.454212 }, url = {http://link.aip.org/link/JCPSA6/v88/i2/p1407/s1}, author = {Jeffrey Skolnick and Robert Yaris and Andrzej Koli{\'n}ski} } @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} } @article {Skolnick1987, title = {Monte Carlo studies of the long-time dynamics of dense polymer systems. The failure of the reptation model}, journal = {Accounts of Chemical Research}, volume = {20}, number = {9}, year = {1987}, month = {sep}, pages = {350{\textendash}356}, issn = {0001-4842}, doi = {10.1021/ar00141a006}, url = {http://pubs.acs.org/doi/abs/10.1021/ar00141a006}, author = {Jeffrey Skolnick and Andrzej Koli{\'n}ski and Robert Yaris} } @article {Kolinski1987, title = {Monte Carlo studies on equilibrium globular protein folding. I. Homopolymeric lattice models of beta-barrel proteins}, journal = {Biopolymers}, volume = {26}, number = {6}, year = {1987}, month = {jun}, pages = {937{\textendash}62}, abstract = {Dynamic Monte Carlo studies have been performed on various diamond lattice models of β-proteins. Unlike previous work, no bias toward the native state is introduced; instead, the protein is allowed to freely hunt through all of phase space to find the equilibrium conformation. Thus, these systems may aid in the elucidation of the rules governing protein folding from a given primary sequence; in particular, the interplay of short- vs long-range interaction can be explored. Three distinct models (A[BOND]C) were examined. In model A, in addition to the preference for trans (t) over gauche states (g+ and g-) (thereby perhaps favoring β-sheet formation), attractive interactions are allowed between all nonbonded, nearest neighbor pairs of segments. If the molecules possess a relatively large fraction of t states in the denatured form, on cooling spontaneous collapse to a well-defined β-barrel is observed. Unfortunately, in model A the denatured state exhibits too much secondary structure to correctly model the globular protein collapse transition. Thus in models B and C, the local stiffness is reduced. In model B, in the absence of long-range interactions, t and g states are equally weighted, and cooperativity is introduced by favoring formation of adjacent pairs of nonbonded (but not necessarily parallel) t states. While the denatured state of these systems behaves like a random coil, their native globular structure is poorly defined. Model C retains the cooperativity of model B but allows for a slight preference of t over g states in the short-range interactions. Here, the denatured state is indistinguishable from a random coil, and the globular state is a well-defined β-barrel. Over a range of chain lengths, the collapse is well represented by an all-or-none model. Hence, model C possesses the essential qualitative features observed in real globular proteins. These studies strongly suggest that the uniqueness of the globular conformation requires some residual secondary structure to be present in the denatured state.}, keywords = {Biological, Models, Monte Carlo Method, Protein Conformation, Proteins}, issn = {0006-3525}, doi = {10.1002/bip.360260613}, url = {http://www.ncbi.nlm.nih.gov/pubmed/3607251}, author = {Andrzej Koli{\'n}ski and Jeffrey Skolnick and Robert Yaris} } @article {Kolinski1987c, title = {Monte Carlo studies on the long time dynamic properties of dense cubic lattice multichain systems. II. Probe polymer in a matrix of different degrees of polymerization}, journal = {The Journal of Chemical Physics}, volume = {86}, year = {1987}, pages = {7174{\textendash}7180}, abstract = {The dynamics of a probe chain consisting of nP =100 segments in a matrix of chains of length of nM=50 up to nM=800 at a total volume fraction of polymer ϕ=0.5 have been simulated by means of cubic lattice Monte Carlo dynamics. The diffusion coefficient of the probe chain over the range of nM under consideration decreases by about 30\%, a behavior rather similar to that seen in real melts of very long chains. Furthermore, the analysis of the probe chain motion shows that the mechanism of motion is not reptation-like and that the cage effect of the matrix is negligible. That is, the local fluctuations of the topological constraints imposed by the long matrix chains (even for nM=800) are sufficiently large to provide for essentially isotropic, but somewhat slowed down, motion of the probe, nP =100, chains relative to the homopolymer melt. The results of these MC experiments are discussed in the context of theoretical predictions and experimental findings for related systems.}, keywords = {Chains, Computerized Simulation, dynamics, Liquid Structure, Matrix Isolation, Melts, Monte Carlo Method, Polymerization, Polymers}, doi = {10.1063/1.452367}, url = {http://link.aip.org/link/JCPSA6/v86/i12/p7174/s1}, author = {Andrzej Koli{\'n}ski and Jeffrey Skolnick and Robert Yaris} } @article {Kolinski1987a, title = {Monte Carlo studies on the long time dynamic properties of dense cubic lattice multichain systems. I. The homopolymeric melt}, journal = {The Journal of Chemical Physics}, volume = {86}, year = {1987}, pages = {7164{\textendash}7174}, abstract = {Dynamic Monte Carlo simulations of long chains confined to a cubic lattice system at a polymer volume fraction of ϕ=0.5 were employed to investigate the dynamics of polymer melts. It is shown that in the range of chain lengths n, from n=64 to n=800 there is a crossover from a weaker dependence of the diffusion coefficient on chain length to a much stronger one, consistent with D\~{}n-2. Since the n-2 scaling relation signals the onset of highly constrained dynamics, an analysis of the character of the chain contour motion was performed. We found no evidence for the well-defined tube required by the reptation model of polymer melt dynamics. The lateral motions of the chain contour are still large even in the case when n=800, and the motion of the chain is essentially isotropic in the local coordinates. Hence, the crossover to the D\~{}n-2 regime with increasing chain length of this monodisperse model melt is not accompanied by the onset of reptation dynamics.}, keywords = {Chains, Computerized Simulation, dynamics, Liquid Structure, Melts, Monte Carlo Method, Polymers}, url = {http://link.aip.org/link/JCPSA6/v86/i12/p7164/s1}, author = {Andrzej Koli{\'n}ski and Jeffrey Skolnick and Robert Yaris} } @article {Kolinski1986b, title = {The collapse transition of semiflexible polymers. A Monte Carlo simulation of a model system}, journal = {The Journal of Chemical Physics}, volume = {85}, year = {1986}, pages = {3585{\textendash}3597}, abstract = {Monte Carlo simulations have been performed on a diamond lattice model of semiflexible polymers for a range of flexibilities and a range of chain lengths from 50 to 800 segments. The model includes both repulsive (excluded volume) and attractive segment{\textendash}segment interactions. It is shown that the polymers group into two classes, {\textquoteleft}{\textquoteleft}flexible{\textquoteright}{\textquoteright} and {\textquoteleft}{\textquoteleft}stiff.{\textquoteright}{\textquoteright} The flexible polymers exhibit decreasing chain dimensions as the temperature decreases with a gradual collapse from a loose random coil, high temperature state to a dense random coil, low temperature state. The stiffer polymers, on the other hand, exhibit increasing chain dimensions with decreasing temperature until at a critical temperature there is a sudden collapse to an ordered high density, low temperature state. This difference is due to the relative strength of the segment{\textendash}segment attractive interactions compared to the energetic preference for a trans conformational state over a gauche state. When the attractive interaction is relatively strong (flexible case) the polymer starts to collapse before rotational degrees of freedom freeze out, leading to a disordered dense state. When the attractive interaction is relatively weak (stiff case) the polymer starts to freeze out rotational degrees of freedom before it finally collapses to a highly ordered dense state.}, keywords = {Chains, Computerized Simulation, Conformational Changes, Diamond Lattices, Flexibility, Mathematical Models, Molecular Structure, Monte Carlo Method, Polymers}, doi = {10.1063/1.450930}, url = {http://link.aip.org/link/JCPSA6/v85/i6/p3585/s1}, author = {Andrzej Koli{\'n}ski and Jeffrey Skolnick and Robert Yaris} } @proceedings {Kolinski1986c, title = {Monte Carlo dynamics of diamond-lattice multichain systems}, journal = {AIP Conference Proceedings}, volume = {137}, year = {1986}, pages = {241{\textendash}245}, url = {http://smartech.gatech.edu/handle/1853/27919}, author = {Andrzej Koli{\'n}ski and Jeffrey Skolnick and Robert Yaris} } @article {Kolinski1986a, title = {Monte Carlo simulations on an equilibrium globular protein folding model}, journal = {Proceedings of the National Academy of Sciences of the United States of America}, volume = {83}, number = {19}, year = {1986}, month = {oct}, pages = {7267{\textendash}71}, abstract = {

Monte Carlo simulations were performed on a diamond lattice, globular protein model in which the trans conformational state is energetically favored over the gauche states (thereby perhaps favoring a beta-sheet secondary structure) and in which nonspecific nonbonded nearest-neighbor attractive interactions are allowed. If the attractive interactions are sufficiently weak that the molecule possesses a relatively high fraction of trans states in the denatured state, then on collapse, a beta-barrel tertiary structure, highly reminiscent of the "native" structure seen in beta-proteins, spontaneously forms. If, however, the attractive interactions are dominant, a coil-to-random globule collapse transition is observed. The roles of short-, medium-, and long-range interactions and topological constraints in determining the observed tertiary structure are addressed, and the implications and limitations of the simulations for the equilibrium folding process in renal globular proteins are explored.

}, keywords = {Models, Protein Conformation, Statistics as Topic, Structural, Structure-Activity Relationship, Temperature, Thermodynamics}, issn = {0027-8424}, url = {http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=386697\&tool=pmcentrez\&rendertype=abstract}, author = {Andrzej Koli{\'n}ski and Jeffrey Skolnick and Robert Yaris} } @article {Kolinski1986e, title = {Monte Carlo study of local orientational order in a semiflexible polymer melt model}, journal = {Macromolecules}, volume = {19}, year = {1986}, pages = {2550{\textendash}2560}, doi = {10.1021/ma00164a017}, url = {http://pubs.acs.org/doi/abs/10.1021/ma00164a017}, author = {Andrzej Koli{\'n}ski and Jeffrey Skolnick and Robert Yaris} } @article {Kolinski1986d, title = {Order-Disorder Transitions in Tetrahedral Lattice Polymer Systems}, journal = {Macromolecules}, volume = {19}, year = {1986}, pages = {2560{\textendash}2567}, doi = {10.1021/ma00164a018}, author = {Andrzej Koli{\'n}ski and Jeffrey Skolnick and Robert Yaris} } @article {Kolinski1986, title = {On the short time dynamics of dense polymeric systems and the origin of the glass transition: A model system}, journal = {The Journal of chemical physics}, volume = {84}, number = {3}, year = {1986}, pages = {1922{\textendash}1931}, doi = {10.1021/ma00164a018}, url = {http://link.aip.org/link/JCPSA6/v84/i3/p1922/s1}, author = {Andrzej Koli{\'n}ski and Jeffrey Skolnick and Robert Yaris} }