A rigorous formalism for the extraction of state-to-state transition functions from a Boltzmann-weighted ensemble of microcanonical molecular dynamics simulations has been developed as a way to study the kinetics of protein folding in the context of a Markov chain. Analysis of these transition functions for signatures of Markovian behavior is described. The method has been applied to an example problem that is based on an underlying Markov process. The example problem shows that when an instance of the process is analyzed under the assumption that the underlying states have been aggregated into macrostates, a procedure known as lumping, the resulting chain appears to have been produced by a non-Markovian process when viewed at high temporal resolution. However, when viewed on longer time scales, and for appropriately lumped macrostates, Markovian behavior can be recovered. The potential for extracting the long time scale behavior of the folding process from a large number of short, independent molecular dynamics simulations is also explored.

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In this work we demonstrate the use of a rigorous formalism for the extraction of state-to-state transition functions as a way to study the kinetics of protein folding in the context of a Markov chain. The approach is illustrated by its application to two different systems: a blocked alanine dipeptide in a vacuum and the C-terminal β-hairpin motif from protein G in water. The first system displays some of the desired features of the approach, whereas the second illustrates some of the challenges that must be overcome to apply the method to more complex biomolecular systems. For both example systems, Boltzmann weighted conformations produced by a replica exchange Monte Carlo procedure were used as starting states for kinetic trajectories. The alanine dipeptide displays Markovian behavior in a state space defined with respect to φ-ψ torsion angles. In contrast, Markovian behavior was not observed for the β-hairpin in a state space where all possible native hydrogen bonding patterns were resolved. This may be due to our choice of state definitions or sampling limitations. Furthermore, the use of different criteria for hydrogen bonding results in the apparent observation of different mechanisms from the same underlying data: one set of criteria indicate a zipping type of process, but another indicates more of a collapse followed by almost simultaneous formation of a large number of contacts. Analysis of long-lived states observed during the simulations of the β-hairpin suggests that important aspects of the folding process that are not captured by order parameters in common use include the formation of non-native hydrogen bonds and the degree and nature of salt bridge formation. † Part of the special issue "Hans C. Andersen Festschrift".

Cholesterol's preference for specific fatty acid chains is investigated at the atomic level in a 20 ns molecular dynamics computer simulation of a lipid bilayer membrane consisting of cholesterol and 1-stearoyl-2-docosahexaenoyl-sn-glycero-3-phosphocholine (SDPC) in a 1:3 ratio. These simulations reproduce experimental measurements suggesting that cholesterol prefers to be solvated by saturated acyl chains and has a low affinity for polyunsaturated fatty acids. Analyses of the simulation trajectory provide a detailed picture of both the transverse and lateral structures of the lipid bilayer membrane, along with a description of lipid and cholesterol dynamics at high temporal resolution. Comparison with a previous simulation of a pure phospholipid bilayer allows an atomic-level description of the changes in membrane structure and dynamics resulting from incorporation of cholesterol. The observed differential cholesterol interactions with saturated and polyunsaturated lipids provide a mechanism for the formation of laterally inhomogeneous membranes; thus, the simulation provides molecular-level insight into the formation of lipid rafts.

We present a 118-ns molecular dynamics simulation of rhodopsin embedded in a bilayer composed of a 2:2:1 mixture of 1-stearoyl-2-docosahexaenoyl-phosphatidylcholine (SDPC), 1-stearoyl-2-docosahexaenoyl-phosphatidylethanolamine (SDPE), and cholesterol, respectively. The simulation demonstrates that the protein breaks the lateral and transverse symmetry of the bilayer. Lipids near the protein preferentially reorient such that their unsaturated chains interact with the protein, while the distribution of cholesterol in the membrane complements the variations in rhodopsin's transverse profile. The latter phenomenon suggests a molecular-level mechanism for the experimental finding that cholesterol stabilizes the native dark-adapted state of rhodopsin without binding directly to the protein.