Structuring and sampling complex conformation space: Weighted ensemble dynamics simulations

Based on multiple simulation trajectories, which started from dispersively selected initial conformations, the weighted ensemble dynamics method is designed to robustly and systematically explore the hierarchical structure of complex conformational space through the spectral analysis of the variance-covariance matrix of trajectory-mapped vectors. Non-degenerate ground state of the matrix directly predicts the ergodicity of simulation data. The ground state could be adopted as statistical weights of trajectories to correctly reconstruct the equilibrium properties, even though each trajectory only explores part of the conformational space. Otherwise, the degree of degeneracy simply gives the number of meta-stable states of the system under the time scale of individual trajectory. Manipulation on the eigenvectors leads to the classification of trajectories into non-transition ones within the states and transition ones between them. The transition states may also be predicted without a priori knowledge of the system. We demonstrate the application of the general method both to the system with a one-dimensional glassy potential and with the one of alanine dipeptide in explicit solvent.Comment: 13 pages, 7 figures. Phys Rev E 2009 (in press

Investigation on energetic optimization problems of stochastic thermodynamics with iterative dynamic programming

The energetic optimization problem, e.g., searching for the optimal switch- ing protocol of certain system parameters to minimize the input work, has been extensively studied by stochastic thermodynamics. In current work, we study this problem numerically with iterative dynamic programming. The model systems under investigation are toy actuators consisting of spring-linked beads with loading force imposed on both ending beads. For the simplest case, i.e., a one-spring actuator driven by tuning the stiffness of the spring, we compare the optimal control protocol of the stiffness for both the overdamped and the underdamped situations, and discuss how inertial effects alter the irreversibility of the driven process and thus modify the optimal protocol. Then, we study the systems with multiple degrees of freedom by constructing oligomer actuators, in which the harmonic interaction between the two ending beads is tuned externally. With the same rated output work, actuators of different constructions demand different minimal input work, reflecting the influence of the internal degrees of freedom on the performance of the actuators.Comment: 14 pages, 7 figures, communications in computational physics, in pres

Systematically Constructing Kinetic Transition Network in Polypeptide from Top to Down: Trajectory Mapping

<div><p>Molecular dynamics (MD) simulation is an important tool for understanding bio-molecules in microscopic temporal/spatial scales. Besides the demand in improving simulation techniques to approach experimental scales, it becomes more and more crucial to develop robust methodology for precisely and objectively interpreting massive MD simulation data. In our previous work [J Phys Chem B 114, 10266 (2010)], the trajectory mapping (TM) method was presented to analyze simulation trajectories then to construct a kinetic transition network of metastable states. In this work, we further present a top-down implementation of TM to systematically detect complicate features of conformational space. We first look at longer MD trajectory pieces to get a coarse picture of transition network at larger time scale, and then we gradually cut the trajectory pieces in shorter for more details. A robust clustering algorithm is designed to more effectively identify the metastable states and transition events. We applied this TM method to detect the hierarchical structure in the conformational space of alanine-dodeca-peptide from microsecond to nanosecond time scales. The results show a downhill folding process of the peptide through multiple pathways. Even in this simple system, we found that single common-used order parameter is not sufficient either in distinguishing the metastable states or predicting the transition kinetics among these states.</p></div

Comparison between <i>τ</i>_<i>life</i>, <i>τ</i> and <i>τ</i>_<i>eq</i>.

<p>The blue symbols (squares for the ones with error bar, stars for the ones without error bar) denote the estimated <i>τ</i>_<i>life</i> of the metastable states. The green crosses denote the identified timescale of the states. The red diamonds denote the estimated <i>τ</i>_<i>eq</i>. The error bars are estimated where possible. The dotted lines are just for aiding the inspection.</p

The detailed view for some of the state-indicator curves in the trajectory.

<p>The detailed view for some of the state-indicator curves in the trajectory.</p

The equilibration process in metastable states.

<p>In each panel, different color represents different trajectory pieces used to estimate the equilibration process. The solid lines are calculated with simulation data, the dotted lines are the fitted stretched exponential curves.</p

The distributions of the 28 states along various collective variables.

<p>The selected collective variable include total energy of the system (a), the solvation energy (b), the distance between the two ends of the peptide (c), the RMSD relative to a representative conformation in <i>S</i>₄ (d), the first (e) and the second (f) principle component of dihedral angle principle component analysis [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0125932#pone.0125932.ref022" target="_blank">22</a>].</p

The representative structures of <i>S</i>₄, <i>S</i>₇, <i>S</i>₁₆, <i>S</i>₁₇, <i>S</i>₂₀ and <i>S</i>₂₅.

<p>The representative structures of <i>S</i>₄, <i>S</i>₇, <i>S</i>₁₆, <i>S</i>₁₇, <i>S</i>₂₀ and <i>S</i>₂₅.</p

The scaling behavior of ⟨Pavr(q⃗,t)|Pavr(q⃗,t)⟩-1 versus <i>t</i>.

<p>The scaling behavior of </p><p></p><p><mo>⟨</mo><mrow></mrow></p><p><mi>P</mi></p><p><mi>a</mi><mi>v</mi><mi>r</mi></p><p></p><p><mo>(</mo></p><p><mi>q</mi><mo>⃗</mo></p><mo>,</mo><mi>t</mi><mo>)</mo><p></p><mo>|</mo><p><mi>P</mi></p><p><mi>a</mi><mi>v</mi><mi>r</mi></p><p></p><p><mo>(</mo></p><p><mi>q</mi><mo>⃗</mo></p><mo>,</mo><mi>t</mi><mo>)</mo><p></p><mo>⟩</mo><mo>-</mo><mn>1</mn><p></p><p></p> versus <i>t</i>.<p></p