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Register a new userAccelerated simulation method for charge regulation effects
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The net charge of solvated entities, ranging from polyelectrolytes and biomolecules to charged nanoparticles and membranes, depends on the local dissociation equilibrium of individual ionizable groups. Incorporation of this phenomenon, emph{charge regulation}, in theoretical and computational models requires dynamic, configuration-dependent recalculation of surface charges and is therefore typically approximated by assuming constant net charge on particles. Various computational methods exist that address this. We present an alternative, particularly efficient charge regulation Monte Carlo method (CR-MC), which explicitly models the redistribution of individual charges and accurately samples the correct grand-canonical charge distribution. In addition, we provide an open-source implementation in the LAMMPS molecular dynamics (MD) simulation package, resulting in a hybrid MD/CR-MC simulation method. This implementation is designed to handle a wide range of implicit-solvent systems that model discreet ionizable groups or surface sites. The computational cost of the method scales linearly with the number of ionizable groups, thereby allowing accurate simulations of systems containing thousands of individual ionizable sites. By matter of illustration, we use the CR-MC method to quantify the effects of charge regulation on the nature of the polyelectrolyte coil--globule transition and on the effective interaction between oppositely charged nanoparticles.
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Nanoparticles in solution acquire charge through dissociation or association of surface groups. Thus, a proper description of their electrostatic interactions requires the use of charge-regulating boundary conditions rather than the commonly employed constant-charge approximation. We implement a hybrid Monte Carlo/Molecular Dynamics scheme that dynamically adjusts the charges of individual surface groups of objects while evolving their trajectories. Charge-regulation effects are shown to qualitatively change self-assembled structures due to global charge redistribution, stabilizing asymmetric constructs. We delineate under which conditions the conventional constant-charge approximation may be employed and clarify the interplay between charge regulation and dielectric polarization.
The problem of state selection when multiple metastable states compete for occupation is considered for systems that are accelerated far from equilibrium. The dynamics of the supercurrent in a narrow superconducting ring under the influence of an external electric field is used to illustrate the general phenomenology.
Using a recently developed bead-spring model for semiflexible polymers that takes into account their natural extensibility, we report an efficient algorithm to simulate the dynamics for polymers like double-stranded DNA (dsDNA) in the absence of hydrodynamic interactions. The dsDNA is modelled with one bead-spring element per basepair, and the polymer dynamics is described by the Langevin equation. The key to efficiency is that we describe the equations of motion for the polymer in terms of the amplitudes of the polymers fluctuation modes, as opposed to the use of the physical positions of the beads. We show that, within an accuracy tolerance level of $5%$ of several key observables, the model allows for single Langevin time steps of $approx1.6$, 8, 16 and 16 ps for a dsDNA model-chain consisting of 64, 128, 256 and 512 basepairs (i.e., chains of 0.55, 1.11, 2.24 and 4.48 persistence lengths) respectively. Correspondingly, in one hour, a standard desktop computer can simulate 0.23, 0.56, 0.56 and 0.26 ms of these dsDNA chains respectively. We compare our results to those obtained from other methods, in particular, the (inextensible discretised) WLC model. Importantly, we demonstrate that at the same level of discretisation, i.e., when each discretisation element is one basepair long, our algorithm gains about 5-6 orders of magnitude in the size of time steps over the inextensible WLC model. Further, we show that our model can be mapped one-on-one to a discretised version of the extensible WLC model; implying that the speed-up we achieve in our model must hold equally well for the latter. We also demonstrate the use of the method by simulating efficiently the tumbling behaviour of a dsDNA segment in a shear flow.
The equations of the temperature-accelerated molecular dynamics (TAMD) method for the calculations of free energies and partition functions are analyzed. Specifically, the exponential convergence of the law of these stochastic processes is established, with a convergence rate close to the one of the limiting, effective dynamics at higher temperature obtained with infinite acceleration. It is also shown that the invariant measures of TAMD are close to a known reference measure, with an error that can be quantified precisely. Finally, a Central Limit Theorem is proven, which allows the estimation of errors on properties calculated by ergodic time averages. These results not only demonstrate the usefulness and validity range of the TAMD equations, but they also permit in principle to adjust the parameter in these equations to optimize their efficiency.
A finite element program is presented to simulate the process of packing and coiling elastic wires in two- and three-dimensional confining cavities. The wire is represented by third order beam elements and embedded into a corotational formulation to capture the geometric nonlinearity resulting from large rotations and deformations. The hyperbolic equations of motion are integrated in time using two different integration methods from the Newmark family: an implicit iterative Newton-Raphson line search solver, and an explicit predictor-corrector scheme, both with adaptive time stepping. These two approaches reveal fundamentally different suitability for the problem of strongly self-interacting bodies found in densely packed cavities. Generalizing the spherical confinement symmetry investigated in recent studies, the packing of a wire in hard ellipsoidal cavities is simulated in the frictionless elastic limit. Evidence is given that packings in oblate spheroids and scalene ellipsoids are energetically preferred to spheres.
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