@article {Rutkowska2007,
	title = {Why do proteins divide into domains? Insights from lattice model simulations},
	journal = {Biomacromolecules},
	volume = {8},
	year = {2007},
	month = {nov},
	pages = {3519{\textendash}24},
	abstract = {<p>It is known that larger globular proteins are built from domains, relatively independent structural units. A domain size seems to be limited, and a single domain consists of from few tens to a couple of hundred amino acids. Based on Monte Carlo simulations of a reduced protein model restricted to the face centered simple cubic lattice, with a minimal set of short-range and long-range interactions, we have shown that some model sequences upon the folding transition spontaneously divide into separate domains. The observed domain sizes closely correspond to the sizes of real protein domains. Short chains with a proper sequence pattern of the hydrophobic and polar residues undergo a two-state folding transition to the structurally ordered globular state, while similar longer sequences follow a multistate transition. Homopolymeric (uniformly hydrophobic) chains and random heteropolymers undergo a continuous collapse transition into a single globule, and the globular state is much less ordered. Thus, the factors responsible for the multidomain structure of proteins are sufficiently long polypeptide chain and characteristic, protein-like, sequence patterns. These findings provide some hints for the analysis of real sequences aimed at prediction of the domain structure of large proteins.</p>},
	keywords = {Computer Simulation, Models, Molecular, Polymers, Polymers: chemistry, Protein Structure, Proteins, Proteins: chemistry, Temperature, Tertiary},
	issn = {1525-7797},
	doi = {10.1021/bm7007718},
	url = {http://www.ncbi.nlm.nih.gov/pubmed/17929971},
	author = {Aleksandra Rutkowska and Andrzej Koli{\'n}ski}
}
@inbook {252,
	title = {Theoretical models and simulations of polymer chains},
	booktitle = {Physical Properties of Polymers Handbook},
	year = {2006},
	publisher = {Springer},
	organization = {Springer},
	address = {New York},
	keywords = {Polymers},
	issn = {978-0-387-69002-5},
	author = {Andrzej Kloczkowski and Andrzej Koli{\'n}ski and James E. Mark}
}
@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 {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}
}
@article {277,
	title = {Monte Carlo study of dynamics of the multichain polymer system on the tetrahedral lattice},
	journal = {The Journal of Chemical Physics},
	volume = {79},
	year = {1983},
	pages = {1523-1526},
	publisher = {AIP},
	abstract = {Diffusion of the chain molecules in the concentrated solutions was studied by means of the computer simulation method. The computations were made for various chain lengths and polymer concentrations. It was observed that the rate of diffusion of the polymer chains strongly depends on the chain length according to the relation D∝n-b. It was found that the value of exponent b increases with the polymer concentration.},
	keywords = {Chains, Computerized Simulation, Diffusion, dynamics, Monte Carlo Method, Polymers, solutions},
	doi = {10.1063/1.445944},
	url = {http://link.aip.org/link/?JCP/79/1523/1},
	author = {Andrzej Koli{\'n}ski and Piotr Romiszowski}
}
