Comparison of umbrella sampling and steered molecular dynamics methods for computing free energy profiles of aromatic substrates through phospholipid bilayers

Understanding the permeation of molecules through lipid membranes is fundamental for predicting the cellular uptake of solutes and drug delivery mechanisms. In molecular simulations, the usual approach is to compute the free energy (FE) profile of a molecule across a model lipid bilayer, which can then be used to estimate the permeability of the molecule. Umbrella Sampling (US), which involves carrying out a series of biased simulations along a defined reaction coordinate (usually the bilayer normal direction), is a popular method for the computation of such FE profiles. However, US can be challenging to implement because the results are dependent on the strength of the biasing potential and the spacing of windows along the reaction coordinate, which, in practice, are usually optimized by an inefficient trial and error approach. The Steered Molecular Dynamics implementation of the Jarzynski Equality (JE-SMD) has been identified as an alternative to equilibrium sampling methods for measuring the FE change across a reaction coordinate. In the JE-SMD approach, equilibrium FE values are evaluated from the average of rapid non-equilibrium trajectories, thus avoiding the practical issues that come with US. Here, we use three different corrections of the JE-SMD method to calculate the FE change for the translocation of two aromatic substrates, phenylalanine and toluene, across a lipid bilayer and compare the accuracy and computational efficiency of these approaches to the results obtained using US. We show evidence that when computing the free energy profile, the JE-SMD approach suffers from insufficient sampling convergence of the bilayer environment and is dependent on the characteristic of the aromatic substrate itself. We deduce that, despite its drawbacks, US remains the more viable approach of the two for computing the FE profile.

Work probability distribution for a ferromagnet with long-ranged and short-ranged correlations

Work fluctuations and work probability distributions are fundamentally different in systems with short-ranged versus long-ranged correlations. Specifically, in systems with long-ranged correlations the work distribution is extraordinarily broad compared to systems with short-ranged correlations. This difference profoundly affects the possible applicability of fluctuation theorems like the Jarzynski fluctuation theorem. The Heisenberg ferromagnet, well below its Curie temperature, is a system with long-ranged correlations in very low magnetic fields due to the presence of Goldstone modes. As the magnetic field is increased the correlations gradually become short ranged. Hence, such a ferromagnet is an ideal system for elucidating the changes of the work probability distribution as one goes from a domain with long-ranged correlations to a domain with short-ranged correlations by tuning the magnetic field. A quantitative analysis of this crossover behavior of the work probability distribution and the associated fluctuations is presented.

Work, work fluctuations, and the work distribution in a thermal nonequilibrium steady state

Long-ranged correlations generically exist in nonequilibrium fluid systems. In the case of a nonequilibrium steady state caused by a temperature gradient, the correlations are especially long-ranged and strong. The anomalous light scattering predicted to exist in these systems is well-confirmed by numerous experiments. Recently, the Casimir force or pressure due to these fluctuations or correlations has been discussed in great detail. In this paper, the notion of a Casimir work is introduced, and an alternative way to measure the nonequilibrium Casimir force is suggested. In particular, the nonequilibrium Casimir force is related to nonequilibrium heat, and not, as in equilibrium, to a volume derivative of an average energy. The nonequilibrium work fluctuations are determined and shown to be very anomalous compared to equilibrium work fluctuations. The nonequilibrium work distribution is also computed, and it is contrasted with work distributions in systems with short-range correlations. Again, there is a striking difference in the two cases. Formal theories of work and work distributions in nonequilibrium steady states are not explicit enough to illustrate any of these interesting features.

Effect of confinement on DNA, solvent and counterion dynamics in a model biological nanopore

The application of recent advances in nanopore technology to high-throughput DNA sequencing requires a more detailed understanding of solvent, ion and DNA interactions occurring within these pores. Here we present a combination of atomistic and coarse-grained modeling studies of the dynamics of short single-stranded DNA (ssDNA) homopolymers within the alpha-hemolysin pore, for the two single-stranded homopolymers poly(dA)40 and poly(dC)40. Analysis of atomistic simulations along with the per-residue decomposition of protein-DNA interactions in these simulations gives new insight into the very complex issues that have yet to be fully addressed with detailed MD simulations. We discuss a modification of the solvent properties and ion distribution around DNA within nanopore confinement and put it into the general framework of counterion condensation theory. There is a reasonable agreement in computed properties from our all-atom simulations and the resulting predictions from analytical theories with experimental data, and our equilibrium results here support the conclusions from our previous non-equilibrium Brownian dynamics studies with a recently developed BROMOC protocol that cations are the primary charge carriers through alpha-hemolysin nanopores under an applied voltage in the presence of ssDNA. Clustering analysis led to an identification of distinct conformational states of captured polymer and depth of the current blockade. Therefore, our data suggest that confined polymer may act as a flickering gate, thus contributing to excess noise phenomena. We also discuss the extent of water structuring due to nanopore confinement and the relationship between the conformational dynamics of a captured polymer and the distribution of blocked current.