Exact enumerations of self-avoiding lattice walks with different nearest-neighbor contacts

Ishinabe, Takao; Chikahisa, Yoshiaki

doi:10.1063/1.451345

Cited by 22 publications

(11 citation statements)

References 41 publications

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“…The expected packing density is found to decrease with chain length, which is consistent with the scaling relationship of void size and chain length shown in Figure 8c. The compactness ρ of chain polymer has been the subject of several studies [41,12]. The asymptotic value of ρ we found is 0.18, slightly different from that reported in [41] (ρ = 0.16), and is within the range of 0.16 -0.24 reported in [12].…”

Section: Voids Distribution Of Long Chainscontrasting

confidence: 71%

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Statistical geometry of packing defects of lattice chain polymer from enumeration and sequential Monte Carlo method

Liang

Zhang

Chen

2002

The Journal of Chemical Physics

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Voids exist in proteins as packing defects and are often associated with protein functions. We study the statistical geometry of voids in two-dimensional lattice chain polymers. We define voids as topological features and develop a simple algorithm for their detection. For short chains, void geometry is examined by enumerating all conformations. For long chains, the space of void geometry is explored using sequential Monte Carlo importance sampling and resampling techniques. We characterize the relationship of geometric properties of voids with chain length, including probability of void formation, expected number of voids, void size, and wall size of voids. We formalize the concept of packing density for lattice polymers, and further study the relationship between packing density and compactness, two parameters frequently used to describe protein packing. We find that both fully extended and maximally compact polymers have the highest packing density, but polymers with intermediate compactness have low packing density. To study the conformational entropic effects of void formation, we characterize the conformation reduction factor of void formation and found that there are strong end-effect. Voids are more likely to form at the chain end. The critical exponent of end-effect is twice as large as that of self-contacting loop formation when existence of voids is not required. We also briefly discuss the sequential Monte Carlo sampling and resampling techniques used in this study.

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Section: Voids Distribution Of Long Chainscontrasting

confidence: 71%

“…The compactness ρ of chain polymer has been the subject of several studies [41,12]. The asymptotic value of ρ we found is 0.18, slightly different from that reported in [41] (ρ = 0.16), and is within the range of 0.16 -0.24 reported in [12].…”

Section: Voids Distribution Of Long Chainscontrasting

confidence: 71%

Statistical geometry of packing defects of lattice chain polymer from enumeration and sequential Monte Carlo method

Liang

Zhang

Chen

2002

The Journal of Chemical Physics

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“…Topological contacts of various orders are operative in the ensemble of conformations belonging to the high density regime under study. In conformity with previous work (Ishinabe and Chikahisa, 1986;Chan and Dill, 1989a, b;Chan and Dill, 1990a, b;Bahar and Jernigan, 1994), a topological contact refers to the occupancy of two adjacent sites in the lattice by a pair of non-bonded residues, assuming the residues along the chain to be connected to each other by virtual bonds. The contact order refers to the number of intervening bonds in the sequence between a pair of residues in contact.…”

Section: Introductionsupporting

confidence: 76%

“…On-lattice simulations of self-avoiding walks (SAWs) have proven to be quite informative in previous studies of highly compact polymeric structures (Wall and Whittington, 1969;Barber and Ninham, 1970;McKenzie, 1973;Schmalz et al, 1984;Ishinabe and Chikahisa, 1986). Entire allocation of space without violation of the volume exclusion requirement and complete sampling of the conformational subspace of compact states are the two main advantages of this approach.…”

Section: Model and Methods Lattice Simulations Of Model Proteinsmentioning

confidence: 99%

Cooperative structural transitions induced by non-homogeneous intramolecular interactions in compact globular proteins

Bahar¹,

Jernigan²

1994

Biophysical Journal

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The role played by non-homogeneous interactions in stabilizing cooperative structural changes in proteins was investigated by exhaustive simulations of all compact conformations compatible with several well-defined globule-like shapes in three dimensions. Conformational free energies corresponding to the association of residues i and j were computed both for the unperturbed system, all subject to identical intramolecular interactions, and for the perturbed system in which a single pair of residues is probed by changing its interactions with an attractive or repulsive interaction. The high packing density leads to strong coupling between residues so that specific interactions between a given pair of residues are accompanied by considerable enthalpy changes. Relatively weak, about 1-2 kcal/mol, attractive interactions can exert a dramatic effect on the free energy distribution. Usually, central positions in the sequence most affect the conformational characteristics. Some of these interaction pairs appear to be capable of effecting major conformation transitions because of the high level of cooperativity in the dense state. Effects of repulsive interactions, however, do not depend so strongly on residue pair and cause more localized structural changes. This approach can suggest more, or less, sensitive loci for amino acid substitution.

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“…Thus, there is a negative correlation between the global and local stiffnesses. Figure 5 also shows points corresponding to the self-avoiding walk (ε → 0) and neighbor-avoiding walk (ε → ∞) [27,35,36]. The inset of Fig.…”

Section: Negative Energetic Elasticitymentioning

confidence: 99%

Negative Energetic Elasticity of Lattice Polymer Chain in Solvent

Shirai¹,

Sakumichi²

2022

Preprint

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Negative internal energetic contribution to elastic modulus (negative energetic elasticity) has recently been observed in polymer gels. This finding challenges the conventional notion that the elastic moduli of rubberlike materials are determined mainly by entropic elasticity. However, the microscopic origin of negative energetic elasticity has not yet been clarified. Here, we consider the nstep interacting self-avoiding walk on a cubic lattice as a model of a single polymer chain (a subchain of a network in a polymer gel) in a solvent. We show the occurrence of negative energetic elasticity based on an exact enumeration up to n = 20 and analytic expressions for arbitrary n in three cases where the chain is highly stretched. Furthermore, we demonstrate that the negative energetic elasticity of this model originates from the attractive polymer-solvent interaction, which locally stiffens the chain and conversely softens the stiffness of the entire chain. This model qualitatively reproduces the temperature dependence of negative energetic elasticity observed in the polymer-gel experiments, indicating that the analysis of a single chain can explain the properties of negative energetic elasticity in polymer gels.

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Exact enumerations of self-avoiding lattice walks with different nearest-neighbor contacts

Cited by 22 publications

References 41 publications

Statistical geometry of packing defects of lattice chain polymer from enumeration and sequential Monte Carlo method

Statistical geometry of packing defects of lattice chain polymer from enumeration and sequential Monte Carlo method

Cooperative structural transitions induced by non-homogeneous intramolecular interactions in compact globular proteins

Negative Energetic Elasticity of Lattice Polymer Chain in Solvent

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