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This collection of studies within the field of statistical mechanics of condensed matter, particularly protein folding, highlights the evolution of computational approaches to model protein dynamics. Dokholyan et al. (1998) and Frauenkron et al. (1998) introduce advanced algorithms such as discrete molecular dynamics and the pruned-enriched Rosenbluth method, demonstrating enhanced efficiency and resolution in simulating protein folding compared to traditional methods. Garel (2003) and Klimov & Thirumalai (1998) explore theoretical perspectives, emphasizing the role of polymer heterogeneity and cooperativity, respectively, in protein folding, with Klimov and Thirumalai introducing a quantitative measure of cooperativity that correlates with experimental data. Collectively, these studies underscore the significance of incorporating both computational efficiency and theoretical insights into understanding the complex thermodynamics and kinetics of protein folding, advancing the field towards more accurate and holistic models.
Background: Many attempts have been made to resolve in time the folding of model proteins in computer simulations. Different computational approaches have emerged. Some of these approaches suffer from the insensitivity to the geometrical properties of the proteins (lattice models), while others are computationally heavy (traditional MD).
Results: We use a recently-proposed approach of Zhou and Karplus to study the folding of the protein model based on the discrete time molecular dynamics algorithm. We show that this algorithm resolves with respect to time the folding --- unfolding transition. In addition, we demonstrate the ability to study the coreof the model protein.
Conclusion: The algorithm along with the model of inter-residue interactions can serve as a tool to study the thermodynamics and kinetics of protein models.
We demonstrate that the recently proposed pruned-enriched Rosenbluth method PERM (P.~Grassberger, Phys.~Rev.~{\bf E 56} (1997)
3682) leads to very efficient algorithms for the folding of simple model proteins. We test it on several models for lattice heteropolymers, and compare to published Monte Carlo studies of the properties of particular sequences. In all cases our method is faster than the previous ones, and in several cases we find new minimal energy states. In addition to producing more reliable candidates for ground states, our method gives detailed information about the thermal spectrum and, thus, allows to analyze static aspects of the folding behavior of arbitrary sequences.
Different aspects of protein folding are illustrated by simplified polymer models. Stressing the diversity of side chains (residues) leads one to view folding as the freezing transition of an heteropolymer. Technically, the most common approach to diversity is randomness, which is usually implemented in two body interactions (charges, polar character,..). On the other hand, the (almost) universal character of the protein backbone suggests that folding may also be viewed as the crystallization transition of an homopolymeric chain, the main ingredients of which are the peptide bond and chirality (proline and glycine notwithstanding). The model of a chiral dipolar chain leads to a unified picture of secondary structures, and to a possible connection of protein structures with ferroelectric domain theory.
We consider equilibrium folding transitions in lattice protein models with and without side chains. A dimensionless measure, $Omega_{c}$, is introduced to quantitatively assess the degree of cooperativity in lattice models and in real proteins. We show that larger values of $Ξ©_{c}$ resembling those seen in proteins are obtained in lattice models with side chains (LMSC). The enhanced cooperativity in LMSC is due to the possibility of denser packing of side chains in the interior of the model protein. We also establish that $Ξ©_{c}$ correlates extremely well with (Ο= (T_ΞΈ -T_{f} )/T_ΞΈ), where (T_ΞΈ) and (T_{f}) are collapse and folding transition temperatures, respectively. These theoretical ideas are used to analyze folding transitions in various real proteins. The values of $Ξ©_{c}$ extracted from experiments show a correlation with $Ο$. We conclude that the degree of cooperativity can be expressed in terms of the single parameter $Ο$, which can be estimated from experimental data.
We show that arguments in the comment by Schwab et al. quant-ph/0503018 on our recent work are invalid.
An exactly solvable model based on the topology of a protein native state is applied to identify bottlenecks and key-sites for the folding of HIV-1 Protease. The predicted sites are found to correlate well with clinical data on resistance to FDA-approved drugs. It has been observed that the effects of drug therapy are to induce multiple mutations on the protease. The sites where such mutations occur correlate well with those involved in folding bottlenecks identified through the deterministic procedure proposed in this study. The high statistical significance of the observed correlations suggests that the approach may be promisingly used in conjunction with traditional techniques to identify candidate locations for drug attacks.
Researchers working in lattice field theory constitute an established community since the early 1990s, and around the same time the online open-access e-print repository arXiv was created. The fact that this field has a specific arXiv section, hep-lat, which is comprehensively used, provides a unique opportunity for a statistical study of its evolution over the last three decades. We present data for the number of entries, $E$, published papers, $P$, and citations, $C$, in total and separated by nations. We compare them to six other arXiv sections (hep-ph, hep-th, gr-qc, nucl-th, quant-ph, cond-mat) and to two socio-economic indices of the nations involved: the Gross Domestic Product (GDP) and the Education Index (EI). We present rankings, which are based either on the Hirsch Index H, or on the linear combination $Ξ£= E + P + 0.05 C$. We consider both extensive and intensive national statistics, i.e. absolute and relative to the population or to the GDP.
The purpose of this paper is to study the shapes and stabilities of bio-membranes within the framework of exterior differential forms. After a brief review of the current status in theoretical and experimental studies on the shapes of bio-membranes, a geometric scheme is proposed to discuss the shape equation of closed lipid bilayers, the shape equation and boundary conditions of open lipid bilayers and two-component membranes, the shape equation and in-plane strain equations of cell membranes with cross-linking structures, and the stabilities of closed lipid bilayers and cell membranes. The key point of this scheme is to deal with the variational problems on the surfaces embedded in three-dimensional Euclidean space by using exterior differential forms.