Search

Ligand diffusion through a protein interior is a fundamental process governing biological signaling and enzymatic catalysis. A complex topology of channels in proteins leads often to difficulties in modeling ligand escape pathways by classical molecular dynamics simulations. In this paper, two novel memetic methods for searching the exit paths and cavity space exploration are proposed: Memory Enhanced Random Acceleration (MERA) Molecular Dynamics (MD) and Immune Algorithm (IA). In MERA, a pheromone concept is introduced to optimize an expulsion force. In IA, hybrid learning protocols are exploited to predict ligand exit paths. They are tested on three protein channels with increasing complexity: M2 muscarinic G-protein-coupled receptor, enzyme nitrile hydratase, and heme-protein cytochrome P450cam. In these cases, the memetic methods outperform simulated annealing and random acceleration molecular dynamics. The proposed algorithms are general and appropriate in all problems where an accelerated transport of an object through a network of channels is studied.

The method calculating the effective diffusion coefficient in an arbitrary periodic two-dimensional channel, presented in our previous paper [P. Kalinay, J. Chem. Phys. 141, 144101 (2014)], is generalized to 3D channels of cylindrical symmetry, as well as to 2D or 3D channels with particles driven by a constant longitudinal external driving force. The next possible extensions are also indicated. The former calculation was based on calculus in the complex plane, suitable for the stationary diffusion in 2D domains. The method is reformulated here using standard tools of functional analysis, enabling the generalization.

Network representations are becoming increasingly popular for analyzing kinetic data from techniques like Milestoning, Markov State Models, and Transition Path Theory. Mapping continuous phase space trajectories into a relatively small number of discrete states helps in visualization of the data and in dissecting complex dynamics to concrete mechanisms. However, not only are molecular networks derived from molecular dynamics simulations growing in number, they are also getting increasingly complex, owing partly to the growth in computer power that allows us to generate longer and better converged trajectories. The increased complexity of the networks makes simple interpretation and qualitative insight of the molecular systems more difficult to achieve. In this paper, we focus on various network representations of kinetic data and algorithms to identify important edges and pathways in these networks. The kinetic data can be local and partial (such as the value of rate coefficients between states) or an exact solution to kinetic equations for the entire system (such as the stationary flux between vertices). In particular, we focus on the Milestoning method that provides fluxes as the main output. We proposed Global Maximum Weight Pathways as a useful tool for analyzing molecular mechanism in Milestoning networks. A closely related definition was made in the context of Transition Path Theory. We consider three algorithms to find Global Maximum Weight Pathways: Recursive Dijkstra's, Edge-Elimination, and Edge-List Bisection. The asymptotic efficiency of the algorithms is analyzed and numerical tests on finite networks show that Edge-List Bisection and Recursive Dijkstra's algorithms are most efficient for sparse and dense networks, respectively. Pathways are illustrated for two examples: helix unfolding and membrane permeation. Finally, we illustrate that networks based on local kinetic information can lead to incorrect interpretation of molecular mechanisms.

In this paper, we present a theoretical approach to construct a fluctuating quantum model of the CO vibration in heme-CO proteins and its interaction with external laser fields. The methodology consists of mixed quantum-classical calculations for a restricted number of snapshots, which are then used to construct a parametrized quantum model. As an example, we calculate the infrared absorption spectrum of carboxy-hemoglobin, based on a simplified protein model, and found the absorption linewidth in good agreement with the experimental results., (© 2011 American Institute of Physics)

The dynamics of many biological processes of interest, such as the folding of a protein, are slow and complicated enough that a single molecular dynamics simulation trajectory of the entire process is difficult to obtain in any reasonable amount of time. Moreover, one such simulation may not be sufficient to develop an understanding of the mechanism of the process, and multiple simulations may be necessary. One approach to circumvent this computational barrier is the use of Markov state models. These models are useful because they can be constructed using data from a large number of shorter simulations instead of a single long simulation. This paper presents a new Bayesian method for the construction of Markov models from simulation data. A Markov model is specified by (τ,P,T), where τ is the mesoscopic time step, P is a partition of configuration space into mesostates, and T is an N(P)×N(P) transition rate matrix for transitions between the mesostates in one mesoscopic time step, where N(P) is the number of mesostates in P. The method presented here is different from previous Bayesian methods in several ways. (1) The method uses Bayesian analysis to determine the partition as well as the transition probabilities. (2) The method allows the construction of a Markov model for any chosen mesoscopic time-scale τ. (3) It constructs Markov models for which the diagonal elements of T are all equal to or greater than 0.5. Such a model will be called a "consistent mesoscopic Markov model" (CMMM). Such models have important advantages for providing an understanding of the dynamics on a mesoscopic time-scale. The Bayesian method uses simulation data to find a posterior probability distribution for (P,T) for any chosen τ. This distribution can be regarded as the Bayesian probability that the kinetics observed in the atomistic simulation data on the mesoscopic time-scale τ was generated by the CMMM specified by (P,T). An optimization algorithm is used to find the most probable CMMM for the chosen mesoscopic time step. We applied this method of Markov model construction to several toy systems (random walks in one and two dimensions) as well as the dynamics of alanine dipeptide in water. The resulting Markov state models were indeed successful in capturing the dynamics of our test systems on a variety of mesoscopic time-scales.