Nonextensive statistical mechanics applied to protein folding problem: kinetics aspects

Abstract

A reduced (stereo-chemical) model is employed to study kinetic aspects of globular protein folding process, by Monte Carlo simulation. Nonextensive statistical approach is used: transition probability p i j between configurations i → j is given by p i j = [1 + (1 − q)∆G i j /k B T ] 1/(1−q) , where q is the nonextensive (Tsallis) parameter. The system model consists of a chain of 27 beads immerse in its solvent; the beads represent the sequence of amino acids along the chain by means of a 10-letter stereo-chemical alphabet; a syntax (rule) to design the amino acid sequence for any given 3D structure is embedded in the model. The study focuses mainly kinetic aspects of the folding problem related with the protein folding time, represented in this work by the concept of first passage time (FPT). Many distinct proteins, whose native structures are represented here by compact self avoiding (CSA) configurations, were employed in our analysis, although our results are presented exclusively for one representative protein, for which a rich statistics was achieved. Our results reveal that there is a specific combinations of value for the nonextensive parameter q and temperature T, which gives the smallest estimated folding characteristic time t . Additionally, for q = 1.1, t stays almost invariable in the range 0.9 ≤ T ≤ 1.3, slightly oscillating about its average value t = 27 ±σ, where σ = 2 is the standard deviation. This behavior is explained by comparing the distribution of the folding times for the Boltzmann statistics (q → 1), with respect to the nonextensive statistics for q = 1.1, which shows that the effect of the nonextensive parameter q is to cut off the larger folding times present in the original (q → 1) distribution. The distribution of natural logarithm of the folding times for Boltzmann statistics is a triple peaked Gaussian, while, for q = 1.1 (Tsallis), it is a double peaked Gaussian, suggesting that a log-normal process with two characteristic times replaced the original process with three characteristic times. Finally we comment on the physical meaning of the present results, as well its significance in the near future works.

Effect of local thermal fluctuations on folding kinetics: A study from the perspective of nonextensive statistical mechanics

“…These specificities are achieved through the specification of which pairs of residues are allowed to get closer, as first neighbors, and its main consequence is to select folding and unfolding pathways through the configurational space. The set of inter-monomer constraints is fixed for each monomer pair, that is, it does not depend on the particularities of the native structure [2,22].…”

“…Differently of most polymers, each natural protein folds over itself in a specific 3−D structural conformation, its native structure. The series of events that drive a polypeptidic chain into its native structure, the folding process, is not yet fully understood: protein systems involve many complex interactions, and presents several remarkable properties that seems to require new experiments [1], theoretical, and computational approaches [2][3][4].…”

q-distributions in complex systems: a brief review

“…(1) has been employed in a growing number of theoretical and empirical works on a large variety of themes. Examples include scale-free networks [10][11][12][13][14], dynamical systems [15][16][17][18][19][20][21][22][23][24][25][26][27], algebraic structures [28][29][30][31] among other topics in statistical physcics [32][33][34][35][36].…”

Entropic formulation for the protein folding process: Hydrophobic stability correlates with folding rates

“…Black curve, standard MA: when we apply Boltzmann weight the folding process may follow alternative folding routes with some lag; here this condition is described by three decaying exponentials of different characteristic times: τ ≅30; 160 and 890 (MCt). Details for data treatment to reproduce the ensemble behavior of the folding process can be found in our previous works [10,11,28,29].…”