9,787 research outputs found

    Ab initio theory of helix-coil phase transition

    Full text link
    In this paper we suggest a theoretical method based on the statistical mechanics for treating the alpha-helix-random coil transition in alanine polypeptides. We consider this process as a first-order phase transition and develop a theory which is free of model parameters and is based solely on fundamental physical principles. It describes essential thermodynamical properties of the system such as heat capacity, the phase transition temperature and others from the analysis of the polypeptide potential energy surface calculated as a function of two dihedral angles, responsible for the polypeptide twisting. The suggested theory is general and with some modification can be applied for the description of phase transitions in other complex molecular systems (e.g. proteins, DNA, nanotubes, atomic clusters, fullerenes).Comment: 24 pages, 3 figure

    Alpha helix-coil phase transition: analysis of ab initio theory predictions

    Full text link
    In the present paper we present results of calculations obtained with the use of the theoretical method described in our preceding paper [1] and perform detail analysis of alpha helix-random coil transition in alanine polypeptides of different length. We have calculated the potential energy surfaces of polypeptides with respect to their twisting degrees of freedom and construct a parameter-free partition function of the polypeptide using the suggested method [1]. From the build up partition function we derive various thermodynamical characteristics for alanine polypeptides of different length as a function of temperature. Thus, we analyze the temperature dependence of the heat capacity, latent heat and helicity for alanine polypeptides consisting of 21, 30, 40, 50 and 100 amino acids. Alternatively, we have obtained same thermodynamical characteristics from the use of molecular dynamics simulations and compared them with the results of the new statistical mechanics approach. The comparison proves the validity of the statistical mechanic approach and establishes its accuracy.Comment: 34 pages, 12 figure

    Statistical Mechanical Treatments of Protein Amyloid Formation

    Full text link
    Protein aggregation is an important field of investigation because it is closely related to the problem of neurodegenerative diseases, to the development of biomaterials, and to the growth of cellular structures such as cyto-skeleton. Self-aggregation of protein amyloids, for example, is a complicated process involving many species and levels of structures. This complexity, however, can be dealt with using statistical mechanical tools, such as free energies, partition functions, and transfer matrices. In this article, we review general strategies for studying protein aggregation using statistical mechanical approaches and show that canonical and grand canonical ensembles can be used in such approaches. The grand canonical approach is particularly convenient since competing pathways of assembly and dis-assembly can be considered simultaneously. Another advantage of using statistical mechanics is that numerically exact solutions can be obtained for all of the thermodynamic properties of fibrils, such as the amount of fibrils formed, as a function of initial protein concentration. Furthermore, statistical mechanics models can be used to fit experimental data when they are available for comparison.Comment: Accepted to IJM

    A Criterion That Determines Fast Folding of Proteins: A Model Study

    Full text link
    We consider the statistical mechanics of a full set of two-dimensional protein-like heteropolymers, whose thermodynamics is characterized by the coil-to-globular (TθT_\theta) and the folding (TfT_f) transition temperatures. For our model, the typical time scale for reaching the unique native conformation is shown to scale as τfF(M)exp(σ/σ0)\tau_f\sim F(M)\exp(\sigma/\sigma_0), where σ=1Tf/Tθ\sigma=1-T_f/T_\theta, MM is the number of residues, and F(M)F(M) scales algebraically with MM. We argue that TfT_f scales linearly with the inverse of entropy of low energy non-native states, whereas TθT_\theta is almost independent of it. As σ0\sigma\rightarrow 0, non-productive intermediates decrease, and the initial rapid collapse of the protein leads to structures resembling the native state. Based solely on {\it accessible} information, σ\sigma can be used to predict sequences that fold rapidly.Comment: 10 pages, latex, figures upon reques

    Equations for Stochastic Macromolecular Mechanics of Single Proteins: Equilibrium Fluctuations, Transient Kinetics and Nonequilibrium Steady-State

    Full text link
    A modeling framework for the internal conformational dynamics and external mechanical movement of single biological macromolecules in aqueous solution at constant temperature is developed. Both the internal dynamics and external movement are stochastic; the former is represented by a master equation for a set of discrete states, and the latter is described by a continuous Smoluchowski equation. Combining these two equations into one, a comprehensive theory for the Brownian dynamics and statistical thermodynamics of single macromolecules arises. This approach is shown to have wide applications. It is applied to protein-ligand dissociation under external force, unfolding of polyglobular proteins under extension, movement along linear tracks of motor proteins against load, and enzyme catalysis by single fluctuating proteins. As a generalization of the classic polymer theory, the dynamic equation is capable of characterizing a single macromolecule in aqueous solution, in probabilistic terms, (1) its thermodynamic equilibrium with fluctuations, (2) transient relaxation kinetics, and most importantly and novel (3) nonequilibrium steady-state with heat dissipation. A reversibility condition which guarantees an equilibrium solution and its thermodynamic stability is established, an H-theorem like inequality for irreversibility is obtained, and a rule for thermodynamic consistency in chemically pumped nonequilibrium steady-state is given.Comment: 23 pages, 4 figure

    Statistical Mechanics of Membrane Protein Conformation: A Homopolymer Model

    Full text link
    The conformation and the phase diagram of a membrane protein are investigated via grand canonical ensemble approach using a homopolymer model. We discuss the nature and pathway of α\alpha-helix integration into the membrane that results depending upon membrane permeability and polymer adsorptivity. For a membrane with the permeability larger than a critical value, the integration becomes the second order transition that occurs at the same temperature as that of the adsorption transition. For a nonadsorbing membrane, the integration is of the first order due to the aggregation of α\alpha-helices.Comment: RevTeX with 5 postscript figure
    corecore