Energy landscape of a small peptide revealed by dihedral angle principal component analysis

Abstract

A 100 ns molecular dynamics simulation of penta-alanine in explicit water is performed to study the reversible folding and unfolding of the peptide. Employing a standard principal component analysis (PCA) using Cartesian coordinates, the resulting free-energy landscape is found to have a single minimum, thus suggesting a simple, relatively smooth free-energy landscape. Introducing a novel PCA based on a transformation of the peptide dihedral angles, it is found, however, that there are numerous free energy minima of comparable energy (less than or approximately 1 kcal/mol), which correspond to well-defined structures with characteristic hydrogen-bonding patterns. That is, the true free-energy landscape is actually quite rugged and its smooth appearance in the Cartesian PCA represents an artifact of the mixing of internal and overall motion. Well-separated minima corresponding to specific conformational structures are also found in the unfolded part of the free energy landscape, revealing that the unfolded state of penta-alanine is structured rather than random. Performing a connectivity analysis, it is shown that neighboring states are connected by low barriers of similar height and that each state typically makes transitions to three or four neighbor states. Several principal pathways for helix nucleation are identified and discussed in some detail.

Nonparametric variational optimization of reaction coordinates

“…The polynomial f (x, y) has n 2 coefficients and, correspondingly, matrices A, C, and D (Eqs. (21) and (22)) have n 4 elements, which means that the computational cost for each iteration scales with n as O(n 4 ). An optimal value of n is a compromise between the approximation power, which grows with n and the computational cost.…”

“…The dynamics is then described as diffusion on a low-dimensional free energy landscape, with both diffusion coefficient and free energy being functions of the coordinates. Examples of such dimensionality reductions can be found in a wide range of problems from many different scientific fields: in molecular dynamics simulations, 12,15,[17][18][19][20][21] order parameters in physics, 11,22 physically based RCs in single molecular experiments, 23,24 biomarkers in medicine, 25 analysing the game of chess, 26 to name a few.…”

“…They satisfactorily partition the configuration space into major free energy minima; however, they do not accurately describe important regions such as transition states and intermediate states. 11 Other popular methods for selection of RC include various variants of principle component analysis (PCA), 21,29,30 diffusion maps, [31][32][33] Isomap, 34 sketch-map, 20 and full correlation analysis; 35 see also recent reviews. [36][37][38] Systematic methods to determine optimal RCs have only started to be developed recently.…”

Effect of the Tottori Familial Disease Mutation (D7N) on the Monomers and Dimers of Aβ40 and Aβ42

“…For the monomers, we used dihedral principal component analysis (dPCA). 83 For the dimers, we used the first two principal components obtained from principal component analysis using the inverse distances between the interpeptide side chain contacts. For detailed characterization of the free energy minima, we calculated several properties using all snapshots belonging to a state, and not just a single representative structure of a state.…”

A theoretical model for the collective motion of proteins by means of principal component analysis

“…However, the standard PCA on the Cartesian coordinates has been proven to be a useful method on studying the internal motion of the proteins and its validity has also been checked against experimentally derived data [67]. The intention of this paper is to describe the dynamics of the collective coordinates, or the essential degrees of freedom, which characterize the reduced dimensional space of the system, and it is independent on the method of how these essential degrees of freedom are determined, hence, other more promising methods [68][69][70] can equally be used in this context. These representative points are distributed in the phase space during a MD trajectory production.…”