A General Algorithm for Sampling Rare Events in Non-Equilibrium and Non-Stationary Systems

Although many computational methods for rare event sampling exist, this type of calculation is not usually practical for general nonequilibrium conditions, with macroscopically irreversible dynamics and away from both stationary and metastable states. A novel method for calculating the time-series of the probability of a rare event is presented which is designed for these conditions. The method is validated for the cases of the Glauber-Ising model under time-varying shear flow, the Kawasaki-Ising model after a quench into the region between nucleation dominated and spinodal decomposition dominated phase change dynamics, and the parallel open asymmetric exclusion process (p-o ASEP). The method requires a subdivision of the phase space of the system: it is benchmarked and found to scale well for increasingly fine subdivisions, meaning that it can be applied without detailed foreknowledge of the physically important reaction pathways.Comment: 11 pages, 6 figure

Free Energies by Thermodynamic Integration Relative to an Exact Solution, Used to Find the Handedness-Switching Salt Concentration for DNA

Sets of free energy differences are useful for finding the equilibria of chemical reactions, while absolute free energies have little physical meaning. However finding the relative free energy between two macrostates by subtraction of their absolute free energies is a valuable strategy in certain important cases. We present calculations of absolute free energies of biomolecules, using a combination of the well-known Einstein Molecule method (for treating the solute) with a conceptually related method of recent genesis for computing free energies of liquids (to treat the solvent and counterions). The approach is based on thermodynamic integration from a detailed atomistic model to one which is simplified but analytically solvable, thereby giving the absolute free energy as that of the tractable model plus a correction term found numerically. An example calculation giving the free energy with respect to salt concentration for the B- and Z-isomers of all-atom duplex DNA in explicit solvent and counterions is presented. The coexistence salt concentration is found with unprecedented accuracy.Comment: Supplementary derivations and convergence data were uploaded as two pdf file

Crystal nucleation mechanism in melts of short polymer chains under quiescent conditions and under shear flow

We present a molecular dynamics simulation study of crystal nucleation from undercooled melts of n-alkanes, and we identify the molecular mechanism of homogeneous crystal nucleation under quiescent conditions and under shear flow. We compare results for n-eicosane(C20) and n-pentacontahectane(C150), i.e. one system below the entanglement length and one above. Under quiescent conditions, we observe that entanglement does not have an effect on the nucleation mechanism. For both chain lengths, the chains first align and then straighten locally. Then the local density increases and finally positional ordering sets in. At low shear rates the nucleation mechanism is the same as under quiescent conditions, while at high shear rates the chains align and straighten at the same time. We report on the effects of shear rate and temperature on the nucleation rates and estimate the critical shear rates, beyond which the nucleation rates increase with the shear rate. We show that the viscosity of the system is not affected by the crystalline nuclei.Comment: 9 page

The Early Crystal Nucleation Process in Hard Spheres shows Synchronised Ordering and Densification

We investigate the early part of the crystal nucleation process in the hard sphere fluid using data produced by computer simulation. We find that hexagonal order manifests continuously in the overcompressed liquid, beginning approximately one diffusion time before the appearance of the first `solid-like' particle of the nucleating cluster, and that a collective influx of particles towards the nucleation site occurs simultaneously to the ordering process: the density increases leading to nucleation are generated by the same individual particle displacements as the increases in order. We rule out the presence of qualitative differences in the early nucleation process between medium and low overcompressions, and also provide evidence against any separation of translational and orientational order on the relevant lengthscales

Free Energies by Thermodynamic Integration Relative to an Exact Solution, Used to Find the Handedness-Switching Salt Concentration for DNA

Sets of free energy differences are useful for finding the equilibria of chemical reactions, while absolute free energies have little physical meaning. However finding the relative free energy between two macrostates by subtraction of their absolute free energies is a valuable strategy in certain important cases. We present calculations of absolute free energies of biomolecules, using a combination of the well-known Einstein molecule method (for treating the solute) with a conceptually related method of recent genesis for computing free energies of liquids (to treat the solvent and counterions). The approach is based on thermodynamic integration from a detailed atomistic model to one which is simplified but analytically solvable, thereby giving the absolute free energy as that of the tractable model plus a correction term found numerically. An example calculation giving the free energy with respect to salt concentration for the B- and Z-isomers of all-atom duplex DNA in explicit solvent and counterions is presented. The coexistence salt concentration is found with unprecedented accuracy

DNA partitions into triplets under tension in the presence of organic cations, with sequence evolutionary age predicting the stability of the triplet phase

Using atomistic simulations, we show the formation of stable triplet structure when particular GC-rich DNA duplexes are extended in solution over a timescale of hundreds of nanoseconds, in the presence of organic salt. We present planar-stacked triplet disproportionated DNA (Σ DNA) as a possible solution phase of the double helix under tension, subject to sequence and the presence of stabilising co-factors. Considering the partitioning of the duplexes into triplets of base pairs as the first step of operation of recombinase enzymes like RecA, we emphasise the structure-function relationship in Σ DNA. We supplement atomistic calculations with thermodynamic arguments to show that codons for 'phase 1' amino acids (those appearing early in evolution) are more likely than a lower entropy GC-rich sequence to form triplets under tension. We further observe that the four amino acids supposed (in the 'GADV world' hypothesis) to constitute the minimal set to produce functional globular proteins have the strongest triplet-forming propensity within the phase 1 set, showing a series of decreasing triplet propensity with evolutionary newness. The weak form of our observation provides a physical mechanism to minimise read frame and recombination alignment errors in the early evolution of the genetic code

Amyloid Evolution: Antiparallel Replaced by Parallel

Several atomic structures have now been found for micrometer-scale amyloid fibrils or elongated microcrystals using a range of methods, including NMR, electron microscopy, and X-ray crystallography, with parallel β-sheet appearing as the most common secondary structure. The etiology of amyloid disease, however, indicates nanometer-scale assemblies of only tens of peptides as significant agents of cytotoxicity and contagion. By combining solution X-ray with molecular dynamics, we show that antiparallel structure dominates at the first stages of aggregation for a specific set of peptides, being replaced by parallel at large length scales only. This divergence in structure between small and large amyloid aggregates should inform future design of molecular therapeutics against nucleation or intercellular transmission of amyloid. Calculations and an overview from the literature argue that antiparallel order should be the first appearance of structure in many or most amyloid aggregation processes, regardless of the endpoint. Exceptions to this finding should exist, depending inevitably on the sequence and on solution conditions.ISSN:0006-3495ISSN:1542-008

Evolution of Conformation, Nanomechanics, and Infrared Nanospectroscopy of Single Amyloid Fibrils Converting into Microcrystals

Nanomechanical properties of amyloid fibrils and nanocrystals depend on their secondary and quaternary structure, and the geometry of intermolecular hydrogen bonds. Advanced imaging methods based on atomic force microscopy (AFM) have unravelled the morphological and mechanical heterogeneity of amyloids, however a full understanding has been hampered by the limited resolution of conventional spectroscopic methods. Here, it is shown that single molecule nanomechanical mapping and infrared nanospectroscopy (AFM-IR) in combination with atomistic modelling enable unravelling at the single aggregate scale of the morphological, nanomechanical, chemical, and structural transition from amyloid fibrils to amyloid microcrystals in the hexapeptides, ILQINS, IFQINS, and TFQINS. Different morphologies have different Young's moduli, within 2-6 GPa, with amyloid fibrils exhibiting lower Young's moduli compared to amyloid microcrystals. The origins of this stiffening are unravelled and related to the increased content of intermolecular beta-sheet and the increased lengthscale of cooperativity following the transition from twisted fibril to flat nanocrystal. Increased stiffness in Young's moduli is correlated with increased density of intermolecular hydrogen bonding and parallel beta-sheet structure, which energetically stabilize crystals over the other polymorphs. These results offer additional evidence for the position of amyloid crystals in the minimum of the protein folding and aggregation landscape.ISSN:2198-384