Analytical Approaches for Deriving Friction Coefficients for Selected α-Helical Peptides Based Entirely on Molecular Dynamics Simulations

Abstract

In this paper we derive analytically from molecular dynamics (MD) simulations the friction coefficients related to conformational transitions within several model peptides with α-helical structures. We study a series of alanine peptides with various length from ALA5 to ALA21 as well as their two derivatives, the (AAQAA)3 peptide and a 13-residue KR1 peptide that is a derivative of the (AAQAA)2 peptide with the formula GN(AAQAA)2G. We use two kinds of approaches to derive their friction coefficients. In the local approach, friction associated with fluctuations of single hydrogen bonds are studied. In the second approach, friction coefficients associated with a folding transitions within the studied peptides are obtained. In both cases, the respective friction coefficients differentiated very well the subtle structural changes between studied peptides and compared favorably to experimentally available data.

Effects of Proline on Internal Friction in Simulated Folding Dynamics of Several Alanine-Based α-Helical Peptides

“…In the case of KR1 peptide, it is the contrary, since additional partially folded states stabilized by proline are the ones with a helical region usually in a central portion of the peptide. Thus, glycines at the ends of the KR1 peptide do not help in producing stable partially folded configurations . Comparing all longer than eight aa peptides, there is no systematic trend in either central or terminal partially folded configurations stabilized by proline in the case of the partially folded peptides.…”

“…Following the refs and for helical peptides, the value of f is calculated from the fraction of the helical HBs formed throughout the simulation trajectory f = ∑ i N h i N h max where h i is the number of helical HBs, i.e., the ones present in the folded state, within the i th frame out of N frames in total, and h max is a maximum number of HBs in a folded state. We use a purely distance-based criterion for HB finding, in which an α-helical HB in residue i is formed when the distance O i ... N i +4 is below 0.36 nm, with O i the peptide carbonyl oxygen of residue i and N i +4 the peptide nitrogen of residue i + 4.…”

“…The time series of h i values were also used to calculate the reaction rate constants k according to k normalf normalo normall normald + k normalu normaln normalf normalo normall normald = 1 τ normalf where τ f is the time constant obtained from the h i autocorrelation function, fitted using a mono-exponential decay plus a constant (if needed). The autocorrelation function was defined in the usual way, as given in ref .…”

“…The local friction coefficient pertaining to lasting of a single HBhas been calculated from the fluctuation–dissipation theorem as γ l = k B T D = 2 τ k B T δ 2 where D is the diffusion coefficient obtained from 1-D Brownian motion as D = δ 2 2 τ …”

“…The global friction coefficient pertaining to an energy dissipation during an overall folding reaction for each peptidehas been calculated based on the work of Khatri et al . Using the model derived by Wosztyl et al, the global friction coefficient is γ g = k B T prefixfalse∑ i normalΔ x i 2 ( 1 k normalf normalo normall normald + 1 k normalu normaln normalf normalo normall normald ) where Δ x i is the ensemble-averaged change in the end-to-end distance of the peptide after passing from i to i + 1 HBs along its folding trajectory. More information about calculations of Δ x i will be presented in subsequent sections.…”