Effective diffusion in one-dimensional rough potential-energy landscapes

Digital nets conformational sampling (DNCS) - an enhanced sampling technique to explore the conformational space of intrinsically disordered peptides

We propose digital nets conformational sampling (DNCS) - an enhanced sampling technique to explore the conformational ensembles of peptides, especially intrinsically disordered peptides (IDPs). The DNCS algorithm relies on generating history-dependent samples of dihedral variables using bitwise XOR operations and binary angle measurements (BAM). The algorithm was initially studied using met-enkephalin, a highly elusive neuropeptide. The DNCS method predicted near-native structures and the energy landscape of met-enkephalin was observed to be in direct correlation with earlier studies on the neuropeptide. Clustering analysis revealed that there are only 24 low-lying conformations of the molecule. The DNCS method has then been tested for predicting optimal conformations of 42 oligopeptides of length varying from 3 to 8 residues. The closest-to-native structures of 86% of cases are near-native and 24% of them have a root mean square deviation of less than 1.00 Å with respect to their crystal structures. The results obtained reveal that the DNCS method performs well, that too in less computational time.

Dynamics, statistics, and task allocation of foraging ants

Ant foraging is one of the most fascinating examples of cooperative behavior observed in nature. It is well studied from an entomology viewpoint, but there is currently a lack of mathematical synthesis of this phenomenon. We address this by constructing an ant foraging model that incorporates simple behavioral rules within three task groups of the ant colony during foraging (foragers, transporters, and followers), pheromone trails, and memory effects. The motion of an ant is modeled as a discrete correlated random walk, with a characteristic zigzag path that is congruent with experimental data. We simulate the foraging cycle, which consists of ants searching for food, transporting food, and depositing chemical trails to recruit and orient more ants (en masse) to the food source. This allows us to gain insights into the basic mechanism of the cooperative interactions between ants and the dynamical division of labor within an ant colony during foraging to achieve optimal efficiency. We observe a disorder-order phase transition from the start to the end of a foraging process, signaling collective motion at the population level. Finally, we present a set of time delay ODEs that corroborates with numerical simulations.

Diffusion in a two-dimensional energy landscape in the presence of dynamical correlations and validity of random walk model

Diffusion in a multidimensional energy surface with minima and barriers is a problem of importance in statistical mechanics and it also has wide applications, such as protein folding. To understand it in such a system, we carry out theory and simulations of a tagged particle moving on a two-dimensional periodic potential energy surface, both in the presence and absence of noise. Langevin dynamics simulations at multiple temperatures are carried out to obtain the diffusion coefficient of a solute particle. Friction is varied from zero to large values. Diffusive motion emerges in the limit of a long time, even in the absence of noise. Noise destroys the correlations and increases diffusion at small friction. Diffusion thus exhibits a nonmonotonic friction dependence at the intermediate value of the damping, ultimately converging to our theoretically predicted value. The latter is obtained using the well-established relationship between diffusion and random walk. An excellent agreement is obtained between theory and simulations in the high-friction limit but not so in the intermediate regime. We explain the deviation in the low- to intermediate-friction regime using the modified random walk theory. The rate of escape from one cell to another is obtained from the multidimensional rate theory of Langer. We find that enhanced dimensionality plays an important role. To quantify the effects of noise on the potential-imposed coherence on the trajectories, we calculate the Lyapunov exponent. At small friction values, the Lyapunov exponent mimics the friction dependence of the rate.

Polymer brushes for friction control: Contributions of molecular simulations

When polymer chains are grafted to solid surfaces at sufficiently high density, they form brushes that can modify the surface properties. In particular, polymer brushes are increasingly being used to reduce friction in water-lubricated systems close to the very low levels found in natural systems, such as synovial joints. New types of polymer brush are continually being developed to improve with lower friction and adhesion, as well as higher load-bearing capacities. To complement experimental studies, molecular simulations are increasingly being used to help to understand how polymer brushes reduce friction. In this paper, we review how molecular simulations of polymer brush friction have progressed from very simple coarse-grained models toward more detailed models that can capture the effects of brush topology and chemistry as well as electrostatic interactions for polyelectrolyte brushes. We pay particular attention to studies that have attempted to match experimental friction data of polymer brush bilayers to results obtained using molecular simulations. We also critically look at the remaining challenges and key limitations to overcome and propose future modifications that could potentially improve agreement with experimental studies, thus enabling molecular simulations to be used predictively to modify the brush structure for optimal friction reduction.

An effective one-dimensional approach to calculating mean first passage time in multi-dimensional potentials

Thermally activated escape processes in multi-dimensional potentials are of interest to a variety of fields, so being able to calculate the rate of escape-or the mean first-passage time (MFPT)-is important. Unlike in one dimension, there is no general, exact formula for the MFPT. However, Langer's formula, a multi-dimensional generalization of Kramers's one-dimensional formula, provides an approximate result when the barrier to escape is large. Kramers's and Langer's formulas are related to one another by the potential of mean force (PMF): when calculated along a particular direction (the unstable mode at the saddle point) and substituted into Kramers's formula, the result is Langer's formula. We build on this result by using the PMF in the exact, one-dimensional expression for the MFPT. Our model offers better agreement with Brownian dynamics simulations than Langer's formula, although discrepancies arise when the potential becomes less confining along the direction of escape. When the energy barrier is small our model offers significant improvements upon Langer's theory. Finally, the optimal direction along which to evaluate the PMF no longer corresponds to the unstable mode at the saddle point.