Foldamer dynamics expressed via Markov state models. I. Explicit solvent molecular-dynamics simulations in acetonitrile, chloroform, methanol, and water

Abstract

In this article, we analyze the folding dynamics of an all-atom model of a polyphenylacetylene (pPA) 12-mer in explicit solvent for four common organic and aqueous solvents: acetonitrile, chloroform, methanol, and water. The solvent quality has a dramatic effect on the time scales in which pPA 12-mers fold. Acetonitrile was found to manifest ideal folding conditions as suggested by optimal folding times on the order of approximately 100-200 ns, depending on temperature. In contrast, chloroform and water were observed to hinder the folding of the pPA 12-mer due to extreme solvation conditions relative to acetonitrile; chloroform denatures the oligomer, whereas water promotes aggregation and traps. The pPA 12-mer in a pure methanol solution folded in approximately 400 ns at 300 K, compared relative to the experimental 12-mer folding time of approximately 160 ns measured in a 1:1 v/v THF/methanol solution. Requisite in drawing the aforementioned conclusions, analysis techniques based on Markov state models are applied to multiple short independent trajectories to extrapolate the long-time scale dynamics of the 12-mer in each respective solvent. We review the theory of Markov chains and derive a method to impose detailed balance on a transition-probability matrix computed from simulation data.

Building Markov state models along pathways to determine free energies and rates of transitions

“…Short trajectories for MM construction were similarly initiated in previous work. 16,17 Lastly, we have not addressed the question of how many states should be used in a given MM, i.e., no prescription was given for choosing the density of centroids along the string and within each basin. This will depend on the system under study.…”

“…8,12,16 In the context of an effort aimed at mapping out the transition between two welldefined conformational states of a large biomolecular structure, however, the effectiveness of this strategy quickly becomes limited.…”

“…Failure to define appropriate states can severely affect the accuracy and usefulness of a MM. 7,8,16,17 An important requirement of Markov states is that they are defined by a set of collective variables which are "good" reaction coordinates, e.g., coordinates along which a system progresses slowly relative to degrees of freedom orthogonal to them. [18][19][20] While a set of collective variables discriminating between stable states may be enough to describe the thermodynamics of a system, good reaction coordinates are needed to describe the kinetics of transitions between those stable states in order to build a reliable model.…”

Transition Path Sampling Simulations of Biological Systems

“…However, this approach requires a lot of knowledge about the process. The use of Markovian state models or equilibrium kinetic networks might help in this respect [23]. Also, the difficulty of sampling multiple pathways still exists.…”

“…While this approach can yield valuable insights into the properties of biomolecular systems [20,21], it is limited in its applicability due to the exponential growth of the number of stationary points with system size. Stochastic transitions between metastable states consisting of almost invariant subsets of conformations, rather than single potential energy minima, are considered in Markovian state models [22,23].…”