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Nucleation is the rate-determining step in the kinetics of many self-assembly processes. However, the importance of nucleation in the kinetics of DNA-origami self-assembly, which involves both the binding of staple strands and the folding of the scaffold strand, is unclear. Here, using Monte Carlo simulations of a lattice model of DNA origami, we find that some, but not all, designs can have a nucleation barrier and that this barrier disappears at lower temperatures, rationalizing the success of isothermal assembly. We show that the height of the nucleation barrier depends primarily on the coaxial stacking of staples that are adjacent on the same helix, a parameter that can be modified with staple design. Creating a nucleation barrier to DNA-origami assembly could be useful in optimizing assembly times and yields, while eliminating the barrier may allow for fast molecular sensors that can assemble/disassemble without hysteresis in response to changes in the environment., 28 pages, 17 figures, accepted in Nano Letters with improved text and figure accessibility

Multicomponent self-assembly mixtures offer the possibility of encoding multiple target structures with the same set of interacting components. Selective retrieval of one of the stored structures has been attempted by preparing an initial state that favors the assembly of the required target, through seeding, concentration patterning, or specific choices of interaction strengths. This may not be possible in an experiment where on-the-fly reconfiguration of the building blocks to switch functionality may be required. In this paper, we explore principles of inverse design of a multicomponent, self-assembly mixture capable of encoding two competing structures that can be selected through simple temperature protocols. We design the target structures to realize the generic situation in which one of the targets has the lower nucleation barrier, while the other is globally more stable. We observe that, to avoid the formation of spurious or chimeric aggregates, the number of neighboring component pairs that occur in both structures should be minimal. Our design also requires the inclusion of components that are part of only one of the target structures. We observe, however, that to maximize the selectivity of retrieval, the component library itself should be maximally shared by the two targets, within such a constraint. We demonstrate that temperature protocols can be designed that lead to the formation of either one of the target structures with high selectivity. We discuss the important role played by secondary aggregation products in improving selectivity, which we term "vestigial aggregates."

In this paper, we benchmark a cavity-based simulation method for calculating the relative solubility of large molecules in explicit solvents. The essence of the procedure is the accounting of the Gibbs energy change associated with an alchemical thermodynamic cycle where, in sequence, a cavity is created in a solvent, a solute is inserted in the cavity and the cavity is annihilated. The Gibbs energy change is equated to the excess chemical potential allowing the comparison of solubilities in different solvents. The results obtained using the cavity-based method are compared to direct large-scale molecular dynamics simulations performed using coarse-grained models for calculating the partition coefficient of pyrene between heptane and toluene. We demonstrate the applicability of this cavity-based technique under high pressure/temperature conditions., The authors gratefully acknowledge the generous funding and technical support for this work from BP Plc through the International Centre for Advanced Materials (ICAM) which made this research possible.

The free energy of glasses cannot be estimated using thermodynamic integration, as glasses are intrinsically not in equilibrium. We present numerical simulations showing that, in contrast, plausible free-energy estimates of a Kob-Andersen glass can be obtained using the Jarzynski relation. Using the Jarzynski relation, we also compute the chemical potential difference of the two components of this system, and find that, in the glassy regime, the Jarzynski estimate matches well with the extrapolated value of the supercooled liquid. Our findings are of broader interest as they show that the Jarzynski method can be used under conditions where the thermodynamic integration approach, which is normally more accurate, breaks down completely. Systems where such an approach might be useful are gels and jammed, glassy structures formed by compression., 4 pages, 2 figures

The aim of this paper is to present some of the features of the non-Poissonian statistics of the spread of a disease like COVID19 to a community of chemical-physicists, who are more used to particle-based models. We highlight some of the reasons why creating a ``transferable'' model for an epidemic is harder than creating a transferable model for molecular simulations. We describe a simple model to illustrate the large effect of decreasing the number of social contacts on the suppression of outbreaks of an infectious disease. Although we do not aim to model the COVID19 pandemic, we choose model parameter values that are not unrealistic for COVID19 and we hope to provide some intuitive insight in the role of social distancing. As our calculations are almost analytical, they allow us to understand some of the key factors influencing the spread of a disease. We argue that social distancing is particularly powerful for diseases that have a fat tail in the number of infected persons per primary case. Our results illustrate that a "bad" feature of the COVID19 pandemic, namely that super-spreading events are important for its spread, could make it particularly sensitive to truncating the number of social contacts., EU FET-OPEN 766972-NANOPHLOW Chinese National Science Foundation grant 11874398 Chinese National Science Foundation grant 12034019 Strategic Priority Research Program of the Chinese Academy of Sciences grant XDB33000000, K.~C. Wong Educational Foundation. international collaboration grant

Intracellular liquid-liquid phase separation enables the formation of biomolecular condensates, such as ribonucleoprotein granules, which play a crucial role in the spatiotemporal organization of biomolecules (e.g., proteins and RNAs). Here, we introduce a patchy-particle polymer model to investigate liquid-liquid phase separation of protein-RNA mixtures. We demonstrate that at low to moderate concentrations, RNA enhances the stability of RNA-binding protein condensates because it increases the molecular connectivity of the condensed-liquid phase. Importantly, we find that RNA can also accelerate the nucleation stage of phase separation. Additionally, we assess how the capacity of RNA to increase the stability of condensates is modulated by the relative protein-protein/protein-RNA binding strengths. We find that phase separation and multiphase organization of multicomponent condensates is favored when the RNA binds with higher affinity to the lower-valency proteins in the mixture than to the cognate higher-valency proteins. Collectively, our results shed light on the roles of RNA in ribonucleoprotein granule formation and the internal structuring of stress granules.

Abstract The methodology to simulate transport phenomena in bulk systems is well-established. In contrast, there is no clear consensus about the choice of techniques to model cross-transport phenomena and phoretic transport, mainly because some of the hydrodynamic descriptions are incomplete from a thermodynamic point of view. In the present paper, we use a unified framework to describe diffusio-osmosis(phoresis), and we report non-equilibrium molecular dynamics (NEMD) on such systems. We explore different simulation methods to highlight some of the technical problems that arise in the calculations. For diffusiophoresis, we use two NEMD methods: boundary-driven and field-driven. Although the two methods should be equivalent in the limit of very weak gradients, we find that finite Peclet-number effects are much stronger in boundary-driven flows than in the case where we apply fictitious color forces. Graphic abstract

The existing kinetic theory of gases is based on an analytical approach that becomes intractable for all but the simplest molecules. Here we propose a simple numerical scheme to compute the transport properties of molecular gases in the limit of infinite dilution. The approach that we propose is approximate, but our results for the diffusivity $D$, the viscosity $\eta$ and the thermal conductivity $\lambda$ of hard spheres, Lennard-Jones particles and rough hard spheres, agree well with the standard (lowest order) Chapman-Enskog results. We also present results for a Lennard-Jones-dimer model for nitrogen, for which no analytical results are available. In the case of poly-atomic molecules (we consider n-octane), our method remains simple and gives good predictions for the diffusivity and the viscosity. Computing the thermal conductivity of poly-atomic molecules requires an approximate treatment of their quantized internal modes. We show that a well-known approximation that relates $\lambda$ to $D$ and $\eta$, yields good results. We note that our approach should yield a lower limit to the exact value of $D$, $\eta$ and $\lambda$. Interestingly, the most sophisticated (higher-order) Chapman-Enskog results for rough hard spheres seem to violate this bound.

International audience; We report a numerical study of the diffusiophoresis of short polymers using non-equilibrium molecular dynamics simulations. More precisely, we consider polymer chains in a fluid containing a solute which has a concentration gradient, and examine the variation of the induced diffusiophoretic velocity of the polymer chains as the interaction between the monomer and the solute is varied. We find that there is a non-monotonic relation between the diffusiophoretic mobility and the strength of the monomer-solute interaction. In addition we find a weak dependence of the mobility on the length of the polymer chain, which shows clear difference from the diffusiophoresis of a solid particle. Interestingly, the hydrodynamic flow through the polymer is much less screened than for pressure driven flows. a) Electronic mail: df246@cam.ac.uk 1 arXiv:1909.06352v2 [cond-mat.soft] 8 Apr 2020 Studying polymer diffusiophoresis with Non-Equilibrium Molecular Dynamics

We report simulations of a spherical Janus particle undergoing exothermic surface reactions around one pole only. Our model excludes self-phoretic transport by design. Nevertheless, net motion occurs from direct momentum transfer between solvent and colloid, with speed scaling as the square root of the energy released during the reaction. We find that such propulsion is dominated by the system’s short-time response, when neither the time dependence of the flow around the colloid nor the solvent compressibility can be ignored. Our simulations agree reasonably well with previous experiments.

Conventional Monte Carlo simulations are stochastic in the sense that the acceptance of a trial move is decided by comparing a computed acceptance probability with a random number, uniformly distributed between 0 and 1. Here we consider the case that the weight determining the acceptance probability itself is fluctuating. This situation is common in many numerical studies. We show that it is possible to construct a rigorous Monte Carlo algorithm that visits points in state space with a probability proportional to their average weight. The same approach has the potential to transform the methodology of a certain class of high-throughput experiments or the analysis of noisy datasets., 7 pages, 4 figures

The Lennard-Jones 12-6 potential (LJ) is arguably the most widely used pair potential in molecular simulations. In fact, it is so popular that the question is rarely asked whether it is fit for purpose. In this paper, we argue that, whilst the LJ potential was designed for noble gases such as argon, it is often used for systems where it is not expected to be particularly realistic. Under those circumstances, the disadvantages of the LJ potential become relevant: most important among these is that in simulations the LJ potential is always modified such that it has a finite range. More seriously, there is by now a whole family of different potentials that are all called Lennard-Jones 12-6, and that are all different - and that may have very different macroscopic properties. In this paper, we consider alternatives to the LJ 12-6 potential that could be employed under conditions where the LJ potential is only used as a typical short-ranged potential with attraction. We construct a class of potentials that are, in many respects LJ-like but that are by construction finite ranged, vanishing quadratically at the cut-off distance, and that are designed to be computationally cheap. Below, we present this potential and report numerical data for its thermodynamic and transport properties, for the most important cases (cut-off distance rc = 2σ ("LJ-like") and rc = 1.2σ (a typical "colloidal" potential)).

We examine the mechanism of formation of micelles of dihydroxy bile salts using a coarse-grained, implicit solvent model and Langevin dynamics simulations. We find that bile salt micelles primarily form via addition and removal of monomers, similarly to surfactants with typical head-tail molecular structures, and not via a two-stage mechanism - involving formation of oligomers and their subsequent aggregation to form larger micelles - originally proposed for bile salts. The free energy barrier to removal of single bile monomers from micelles is ≈2kBT, much less than what has been observed for head-tail surfactants. Such a low barrier may be biologically relevant: it allows for rapid release of bile monomers into the intestine, possibly enabling the coverage of fat droplets by bile salt monomers and subsequent release of micelles containing fats and bile salts - a mechanism that is not possible for ionic head-tail surfactants of similar critical micellar concentrations.

The solubility of a crystalline material can be estimated from the absolute free energy of the solid and the excess solvation free energy. In the earlier work, we presented a general-purpose molecular-dynamics-based methodology enabling solubility predictions of crystalline compounds, yielding accurate estimates of the aqueous solubilities of naphthalene at various pressures and temperatures. In the present work, we investigate a number of prototypical complex materials, including phenanthrene, calcite, and aragonite over a range of temperatures and pressures. Our results provide stronger evidence for the power of the methodology for universal solubility predictions.

If a thermal gradient is applied along a fluid-solid interface, the fluid experiences a thermo-osmotic force. In steady state this force is balanced by the gradient of the shear stress. Surprisingly, there appears to be no unique microscopic expression that can be used for computing the magnitude of the thermo-osmotic force. Here we report how, by treating the mass $M$ of the fluid particles as a tensor in the Hamiltonian, we can eliminate the balancing shear force in a non-equilibrium simulation and therefore compute the thermo-osmotic force at simple solid-fluid interfaces. We compare the non-equilibrium force measurement with estimates of the thermo-osmotic force based on computing gradients of the stress tensor. We find that the thermo-osmotic force as measured in our simulations cannot be derived from the most common microscopic definitions of the stress tensor., 5 pages, 2 figures

In this paper, we explore the strengths and weaknesses of a cavity-based method to calculate the excess chemical potential of a large molecular solute in a dense liquid solvent. Use of the cavity alleviates some technical problems associated with the appearance of (integrable) divergences in the integrand during alchemical particle growth. The excess chemical potential calculated using the cavity-based method should be independent of the cavity attributes. However, the performance of the method (equilibration time and the robustness) does depend on the cavity attributes. To illustrate the importance of a suitable choice of the cavity attributes, we calculate the partition coefficient of pyrene in toluene and heptane using a coarse-grained model. We find that a poor choice for the functional form of the cavity may lead to hysteresis between growth and shrinkage of the cavity. Somewhat unexpectedly, we find that, by allowing the cavity to move as a pseudo-particle within the simulation box, the decay time of fluctuations in the integrand of the thermodynamic integration can be reduced by an order of magnitude, thereby increasing the statistical accuracy of the calculation.

We present numerical simulations of diffusio-osmotic flow, i.e. the fluid flow generated by a concentration gradient along a solid-fluid interface. In our study, we compare a number of distinct approaches that have been proposed for computing such flows and compare them with a reference calculation based on direct, non-equilibrium molecular dynamics simulations. As alternatives, we consider schemes that compute diffusio-osmotic flow from the gradient of the chemical potentials of the constituent species and from the gradient of the component of the pressure tensor parallel to the interface. We find that the approach based on treating chemical potential gradients as external forces acting on various species agrees with the direct simulations, thereby supporting the approach of Marbach et al (2017 J. Chem. Phys. 146 194701). In contrast, an approach based on computing the gradients of the microscopic pressure tensor does not reproduce the direct non-equilibrium results., European Union ( European Training Network NANOTRANS Grant 674979).

Biological membranes typically contain a large number of different components dispersed in small concentrations in the main membrane phase, including proteins, sugars, and lipids of varying geometrical properties. Most of these components do not bind the cargo. Here, we show that such "inert" components can be crucial for the precise control of cross-membrane trafficking. Using a statistical mechanics model and molecular dynamics simulations, we demonstrate that the presence of inert membrane components of small isotropic curvatures dramatically influences cargo endocytosis, even if the total spontaneous curvature of such a membrane remains unchanged. Curved lipids, such as cholesterol, as well as asymmetrically included proteins and tethered sugars can, therefore, actively participate in the control of the membrane trafficking of nanoscopic cargo. We find that even a low-level expression of curved inert membrane components can determine the membrane selectivity toward the cargo size and can be used to selectively target membranes of certain compositions. Our results suggest a robust and general method of controlling cargo trafficking by adjusting the membrane composition without needing to alter the concentration of receptors or the average membrane curvature. This study indicates that cells can prepare for any trafficking event by incorporating curved inert components in either of the membrane leaflets., Herchel Smith scholarship (T.C.), the CAS PIFI fellowship (T.C.), the UCL Institute for the Physics of Living Systems (T.C. and A.Š.), the Austrian Academy of Sciences through a DOC fellowship (P.W.), the European Union Horizon 2020 programme under ETN grant no. 674979-NANOTRANS and FET grant no. 766972-NANOPHLOW (J.D. and D.F.), the Engineering and Physical Sciences Research Council (D.F. and A.Š.), the Academy of Medical Sciences and Wellcome Trust (A.Š.), and the Royal Society (A.Š.).

We present a mean-field theory to explain the thermo-orientation effect in an off-center Stockmayer fluid. This effect is the underlying cause of thermally induced polarization and thermally induced monopoles, which have recently been predicted theoretically. Unlike previous theories that are based either on phenomenological equations or on scaling arguments, our approach does not require any fitting parameters. Given an equation of state and assuming local equilibrium, we construct an effective Hamiltonian for the computation of local Boltzmann averages. This simple theoretical treatment predicts molecular orientations that are in very good agreement with simulation results for the range of dipole strengths investigated. By decomposing the overall alignment into contributions from the temperature and density gradients, we shed further light on how the nonequilibrium result arises from the competition between the two gradients., Erwin Schrödinger Institute for Mathematics and Physics Cambridge Philosophical Society Austrian Science Fund (FWF) [SFB ViCoM, Project F41]

Colloidal particles with DNA `legs' that can bind reversibly to receptors on a surface can be made to `walk' if there is a gradient in receptor concentration. We use a combination of theory and Monte Carlo simulations to explore how controllable parameters, e.g. coating density and binding strength, affect the dynamics of such colloids. We find that competition between thermodynamic and kinetic trends imply that there is an optimal value for both, the binding strength and the number of `legs' for which transport is fastest. Using available thermodynamic data on DNA binding, we indicate how directionally reversible, temperature-controlled transport of colloidal walkers can be achieved. In particular, the present results should make it possible to design a chromatographic technique that can be used to separate colloids with different DNA functionalization., to appear in Soft Matter

We use the dynamic length and time scale separation in suspensions to formulate a general description of colloidal thermophoresis. Our approach allows an unambiguous definition of separate contributions to the colloidal flux and clarifies the physical mechanisms behind non-equilibrium motion of colloids. In particular, we derive an expression for the interfacial force density that drives single-particle thermophoresis in non-ideal fluids. The issuing relations for the transport coefficients explicitly show that interfacial thermophoresis has a hydrodynamic character that cannot be explained by a purely thermodynamic consideration. Our treatment generalises the results from other existing approaches, giving them a clear interpretation within the framework of non-equilibrium thermodynamics.

Histone tails and their epigenetic modifications play crucial roles in gene expression regulation by altering the architecture of chromatin. However, the structural mechanisms by which histone tails influence the interconversion between active and inactive chromatin remain unknown. Given the technical challenges in obtaining detailed experimental characterizations of the structure of chromatin, multiscale computations offer a promising alternative to model the effect of histone tails on chromatin folding. Here we combine multi-microsecond atomistic molecular dynamics simulations of dinucleosomes and histone tails in explicit solvent and ions, performed with three different state-of-the-art force fields and validated by experimental NMR measurements, with coarse-grained Monte Carlo simulations of 24-nucleosome arrays to describe the conformational landscape of histone tails, their roles in chromatin compaction, and the impact of lysine acetylation, a widespread epigenetic change, on both. We find that while the wild-type tails are highly flexible and disordered, the dramatic increase of secondary-structure order by lysine acetylation unfolds chromatin by decreasing tail availability for crucial fiber-compacting internucleosome interactions. This molecular level description of the effect of histone tails and their charge modifications on chromatin folding explains the sequence sensitivity and underscores the delicate connection between local and global structural and functional effects. Our approach also opens new avenues for multiscale processes of biomolecular complexes.

A concentration gradient along a fluid-fluid interface can cause flow. On a microscopic level, this so-called Marangoni effect can be viewed as being caused by a gradient in the pressures acting on the fluid elements, or as the chemical-potential gradients acting on the excess densities of different species at the interface. If the interfacial thickness can be ignored, all approaches should result in the same flow profile away from the interface. However, on a more microscopic scale, the different expressions result in different flow profiles, only one of which can be correct. Here we compare the results of direct non-equilibrium Molecular Dynamics simulations with the flows that would be generated by pressure and chemical potential gradients. We find that the approach based on the chemical potential gradients agrees with the direct simulations, whereas the calculations based on the pressure gradients do not., 5 pages, 4 figures

The process of homogeneous bubble nucleation is almost impossible to probe experimentally, except near the critical point or for liquids under large negative tension. Elsewhere in the phase diagram, the bubble nucleation barrier is so high as to be effectively insurmountable. Consequently, there is a severe lack of experimental studies of homogenous bubble nucleation under conditions of practical importance (e.g., cavitation). Here we use a simple geometric relation to show that we can obtain information about the homogeneous nucleation process from Molecular Dynamics studies of bubble formation in solvophobic nanopores on a solid surface. The free energy of pinned nanobubbles has two extrema as a function of volume: one state corresponds to a free-energy maximum ("the critical nucleus"), the other corresponds to a free-energy minimum (the metastable, pinned nanobubble). Provided that the surface tension does not depend on nanobubble curvature, the radius of the curvature of the metastable surface nanobubble is independent of the radius of the pore and is equal to the radius of the critical nucleus in homogenous bubble nucleation. This observation opens the way to probe the parameters that determine homogeneous bubble nucleation under experimentally accessible conditions, e.g. with AFM studies of metastable nanobubbles. Our theoretical analysis also indicates that a surface with pores of different sizes can be used to determine the curvature corrections to the surface tension. Our conclusions are not limited to bubble nucleation but suggest that a similar approach could be used to probe the structure of critical nuclei in crystal nucleation.

Cells can often be recognized by the concentrations of receptors expressed on their surface. For better (targeted drug treatment) or worse (targeted infection by pathogens), it is clearly important to be able to target cells selectively. A good targeting strategy would result in strong binding to cells with the desired receptor profile and barely binding to other cells. Using a simple model, we formulate optimal design rules for multivalent particles that allow them to distinguish target cells based on their receptor profile. We find the following: (i) It is not a good idea to aim for very strong binding between the individual ligands on the guest (delivery vehicle) and the receptors on the host (cell). Rather, one should exploit multivalency: High sensitivity to the receptor density on the host can be achieved by coating the guest with many ligands that bind only weakly to the receptors on the cell surface. (ii) The concentration profile of the ligands on the guest should closely match the composition of the cognate membrane receptors on the target surface. And (iii) irrespective of all details, the effective strength of the ligand-receptor interaction should be of the order of the thermal energy [Formula: see text], where [Formula: see text] is the absolute temperature and [Formula: see text] is Boltzmann's constant. We present simulations that support the theoretical predictions. We speculate that, using the above design rules, it should be possible to achieve targeted drug delivery with a greatly reduced incidence of side effects.

The solubility of a crystalline substance in the solution can be estimated from its absolute solid free energy and excess solvation free energy. Here, we present a numerical method, which enables convenient solubility estimation of general molecular crystals at arbitrary thermodynamic conditions where solid and solution can coexist. The methodology is based on standard alchemical free energy methods, such as thermodynamic integration and free energy perturbation, and consists of two parts: (1) systematic extension of the Einstein crystal method to calculate the absolute solid free energies of molecular crystals at arbitrary temperatures and pressures and (2) a flexible cavity method that can yield accurate estimates of the excess solvation free energies. As an illustration, via classical Molecular Dynamic simulations, we show that our approach can predict the solubility of OPLS-AA-based (Optimized Potentials for Liquid Simulations All Atomic) naphthalene in SPC (Simple Point Charge) water in good agreement with experimental data at various temperatures and pressures. Because the procedure is simple and general and only makes use of readily available open-source software, the methodology should provide a powerful tool for universal solubility prediction.

Thermo-osmotic slip -- the flow induced by a thermal gradient along a surface -- is a well-known phenomenon, but curiously there is a lack of robust molecular-simulation techniques to predict its magnitude. Here, we compare three different molecular simulation techniques to compute the thermo-osmotic slip at a simple solid-fluid interface. Although we do not expect the different approaches to be in perfect agreement, we find that the differences are barely significant for a range of different physical conditions, suggesting that practical molecular simulations of thermo-osmotic slip are feasible., 6 pages, 4 figures

In the standard DNA brick set-up, distinct 32-nucleotide strands of single-stranded DNA are each designed to bind specifically to four other such molecules. Experimentally, it has been demonstrated that the overall yield is increased if certain bricks which occur on the outer faces of target structures are merged with adjacent bricks. However, it is not well understood by what mechanism such `boundary bricks' increase the yield, as they likely influence both the nucleation process and the final stability of the target structure. Here, we use Monte Carlo simulations with a patchy particle model of DNA bricks to investigate the role of boundary bricks in the self-assembly of complex multicomponent target structures. We demonstrate that boundary bricks lower the free-energy barrier to nucleation and that boundary bricks on edges stabilize the final structure. However, boundary bricks are also more prone to aggregation, as they can stabilize partially assembled intermediates. We explore some design strategies that permit us to benefit from the stabilizing role of boundary bricks whilst minimizing their ability to hinder assembly; in particular, we show that maximizing the total number of boundary bricks is not an optimal strategy., This work was supported by the Engineering and Physical Sciences Research Council [Programme Grant EP/I001352/1]. HKWS acknowledges support from the Winston Churchill Foundation of the United States. Research carried out in part at the Center for Functional Nanomaterials, Brookhaven National Laboratory, which is supported by the US Department of Energy, Office of Basic Energy Sciences, under Contract No. DE-SC0012704.

A decades-old proposal that all distinct packings are equally probable in granular media has gone unproven due to the sheer number of packings involved. Numerical simulation now demonstrates that it holds — precisely at the jamming threshold. In the late 1980s, Sam Edwards proposed a possible statistical-mechanical framework to describe the properties of disordered granular materials1. A key assumption underlying the theory was that all jammed packings are equally likely. In the intervening years it has never been possible to test this bold hypothesis directly. Here we present simulations that provide direct evidence that at the unjamming point, all packings of soft repulsive particles are equally likely, even though generically, jammed packings are not. Typically, jammed granular systems are observed precisely at the unjamming point since grains are not very compressible. Our results therefore support Edwards’ original conjecture. We also present evidence that at unjamming the configurational entropy of the system is maximal.

Nucleation processes are at the heart of a large number of phenomena, from cloud formation to protein crystallization. A recently emerging area where nucleation is highly relevant is the initiation of filamentous protein self-assembly, a process that has broad implications in many research areas ranging from medicine to nanotechnology. As such, spontaneous nucleation of protein fibrils has received much attention in recent years with many theoretical and experimental studies focussing on the underlying physical principles. In this paper we make a step forward in this direction and explore the early time behaviour of filamentous protein growth in the context of nucleation theory. We first provide an overview of the thermodynamics and kinetics of spontaneous nucleation of protein filaments in the presence of one relevant degree of freedom, namely the cluster size. In this case, we review how key kinetic observables, such as the reaction order of spontaneous nucleation, are directly related to the physical size of the critical nucleus. We then focus on the increasingly prominent case of filament nucleation that includes a conformational conversion of the nucleating building-block as an additional slow step in the nucleation process. Using computer simulations, we study the concentration dependence of the nucleation rate. We find that, under these circumstances, the reaction order of spontaneous nucleation with respect to the free monomer does no longer relate to the overall physical size of the nucleating aggregate but rather to the portion of the aggregate that actively participates in the conformational conversion. Our results thus provide a novel interpretation of the common kinetic descriptors of protein filament formation, including the reaction order of the nucleation step or the scaling exponent of lag times, and put into perspective current theoretical descriptions of protein aggregation., We acknowledge support from the Human Frontier Science Program and Emmanuel College (A.Š.), St John’s and Peterhouse Colleges (T.C.T.M.), the Swiss National Science Foundation (T.C.T.M.), the Biotechnology and Biological Sciences Research Council (T.P.J.K.), the Frances and Augustus Newman Foundation (T.P.J.K.), the European Research Council (T.C.T.M., T.P.J.K., and D.F.), and the Engineering and Physical Sciences Research Council (D.F.).

We propose an efficient Monte Carlo method for the computation of the volumes of high-dimensional bodies with arbitrary shape. We start with a region of known volume within the interior of the manifold and then use the multistate Bennett acceptance-ratio method to compute the dimensionless free-energy difference between a series of equilibrium simulations performed within this object. The method produces results that are in excellent agreement with thermodynamic integration, as well as a direct estimate of the associated statistical uncertainties. The histogram method also allows us to directly obtain an estimate of the interior radial probability density profile, thus yielding useful insight into the structural properties of such a high-dimensional body. We illustrate the method by analyzing the effect of structural disorder on the basins of attraction of mechanically stable packings of soft repulsive spheres., Comment: 5 pages, 2 figures, supplemental material

My least favorite opening sentence of a scientific article is: “Recently there has been much interest in….” Unless the sentence goes on to explain why there is so much interest in the topic, it is unlikely to excite the curiosity of the reader.

The ability of biological molecules to replicate themselves, achieved with the aid of a complex cellular machinery, is the foundation of life. However, a range of aberrant processes involve the self-replication of pathological protein structures without any additional factors. A dramatic example is the autocatalytic replication of pathological protein aggregates, including amyloid fibrils and prions, involved in neurodegenerative disorders. Here, we use computer simulations to identify the necessary requirements for the self-replication of fibrillar assemblies of proteins. We establish that a key physical determinant for this process is the affinity of proteins for the surfaces of fibrils. We find that self-replication can only take place in a very narrow regime of inter-protein interactions, implying a high level of sensitivity to system parameters and experimental conditions. We then compare our theoretical predictions with kinetic and biosensor measurements of fibrils formed from the Aβ peptide associated with Alzheimer's disease. Our results show a quantitative connection between the kinetics of self-replication and the surface coverage of fibrils by monomeric proteins. These findings reveal the fundamental physical requirements for the formation of supra-molecular structures able to replicate themselves, and shed light on mechanisms in play in the proliferation of protein aggregates in nature.

We report Monte Carlo simulations of a simple off-lattice patchy-particle model for DNA 'bricks'. We relate the parameters that characterise this model with the binding free energy of pairs of single-stranded DNA molecules. We verify that an off-lattice potential parameterised in this way reproduces much of the behaviour seen with a simpler lattice model we introduced previously, although the relaxation of the geometric constraints leads to a more error-prone self-assembly pathway. We investigate the self-assembly process as a function of the strength of the non-specific interactions. We show that our off-lattice model for DNA bricks results in robust self-assembly into a variety of target structures., This work was supported by the Engineering and Physical Sciences Research Council [Programme Grant EP/I001352/1]. Research carried out in part at the Center for Functional Nanomaterials, Brookhaven National Laboratory, which is supported by the US Department of Energy, Office of Basic Energy Sciences, under Contract No. DE-SC0012704., This is the final version of the article. It first appeared from the Royal Society of Chemistry via https://doi.org/10.1039/C6SM01031H

Gelation and densification of calcium–silicate–hydrate take place during cement hydration. Both processes are crucial for the development of cement strength, and for the long-term evolution of concrete structures. However, the physicochemical environment evolves during cement formation, making it difficult to disentangle what factors are crucial for the mechanical properties. Here we use Monte Carlo and Molecular Dynamics simulations to study a coarse-grained model of cement formation, and investigate the equilibrium and arrested states. We can correlate the various structures with the time evolution of the interactions between the nano-hydrates during the preparation of cement. The novel emerging picture is that the changes of the physicochemical environment, which dictate the evolution of the effective interactions, specifically favour the early gel formation and its continuous densification. Our observations help us understand how cement attains its unique strength and may help in the rational design of the properties of cement and related materials., Georgetown University, French Research National Agency (A*MIDEX Project ANR-11-IDEX- 0001-02), French Research National Agency (ICoME2 Labex Project ANR-11-LABX-0053)

When neutral nanoparticles are heated or cooled in a polar liquid, they will interact with each other as if they carry an electrostatic charge that is proportional to the temperature difference between the particle and the surrounding fluid. The same should hold for suspensions of asymmetric ferromagnetic particles, in which case the heated nanoparticles should behave as magnetic monopoles. However, the analogy with electrostatics/magnetostatics is not complete: heated/cooled nanoparticles do not move under the influence of an applied homogeneous field. They should, however, interact as monopoles with each other and should move in inhomogeneous fields.

Nanoactuators and nanomachines have long been sought after, but key bottlenecks remain. Forces at submicrometer scales are weak and slow, control is hard to achieve, and power cannot be reliably supplied. Despite the increasing complexity of nanodevices such as DNA origami and molecular machines, rapid mechanical operations are not yet possible. Here, we bind temperature-responsive polymers to charged Au nanoparticles, storing elastic energy that can be rapidly released under light control for repeatable isotropic nanoactuation. Optically heating above a critical temperature [Formula: see text] = 32 °C using plasmonic absorption of an incident laser causes the coatings to expel water and collapse within a microsecond to the nanoscale, millions of times faster than the base polymer. This triggers a controllable number of nanoparticles to tightly bind in clusters. Surprisingly, by cooling below [Formula: see text] their strong van der Waals attraction is overcome as the polymer expands, exerting nanoscale forces of several nN. This large force depends on van der Waals attractions between Au cores being very large in the collapsed polymer state, setting up a tightly compressed polymer spring which can be triggered into the inflated state. Our insights lead toward rational design of diverse colloidal nanomachines.

By exploiting the exquisite selectivity of DNA hybridization, DNA-Coated Colloids (DNACCs) can be made to self-assemble in a wide variety of structures. The beauty of this system stems largely from its exceptional versatility and from the fact that a proper choice of the grafted DNA sequences yields fine control over the colloidal interactions. Theory and simulations have an important role to play in the optimal design of self- assembling DNACCs. At present, the powerful model-based design tools are not widely used, because the theoretical literature is fragmented and the connection between different theories is often not evident. In this Perspective, we aim to discuss the similarities and differences between the different models that have been described in the literature, their underlying assumptions, their strengths and their weaknesses. Using the tools described in the present Review, it should be possible to move towards a more rational design of novel self-assembling structures of DNACCs and, more generally, of systems where ligand-receptors bonds are used to control interactions., Comment: Pre-refereed version (some small differences with final one, nothing major) Phys. Chem. Chem. Phys., 2016

The self-assembly of structures with "addressable complexity", where every component is distinct and is programmed to occupy a specific location within a target structure, is a promising route to engineering materials with precisely defined morphologies. Because systems with many components are inherently complicated, one might assume that the chances of successful self-assembly are extraordinarily small. Yet recent advances suggest otherwise: addressable structures with hundreds of distinct building blocks have been designed and assembled with nanometer precision. Despite this remarkable success, it is often challenging to optimize a self-assembly reaction to ensure that the intended structure is kinetically accessible. In this Perspective, we focus on the prediction of kinetic pathways for self-assembly and implications for the design of robust experimental protocols. The development of general principles to predict these pathways will enable the engineering of complex materials using a much wider range of building blocks than is currently possible.

Biological mixtures such as the cytosol may consist of thousands of distinct components. There is now a substantial body of evidence showing that, under physiological conditions, intracellular mixtures can phase separate into spatially distinct regions with differing compositions. In this article we present numerical evidence indicating that such spontaneous compartmentalization exploits general features of the phase diagram of a multicomponent biomolecular mixture. In particular, we show that demixed domains are likely to segregate when the variance in the intermolecular interaction strengths exceeds a well-defined threshold. Multiple distinct phases are likely to become stable under very similar conditions, which can then be tuned to achieve multiphase coexistence. As a result, only minor adjustments to the composition of the cytosol or the strengths of the intermolecular interactions are needed to regulate the formation of different domains with specific compositions, implying that phase separation is a robust mechanism for creating spatial organization. We further predict that this functionality is only weakly affected by increasing the number of components in the system. Our model therefore suggests that, for purely physico-chemical reasons, biological mixtures are naturally poised to undergo a small number of demixing phase transitions.

We report a numerical calculation of the total number of disordered jammed configurations $\Omega$ of $N$ repulsive, three-dimensional spheres in a fixed volume $V$. To make these calculations tractable, we increase the computational efficiency of the approach of Xu et al. (Phys. Rev. Lett. 106, 245502 (2011)) and Asenjo et al. (Phys. Rev. Lett. 112, 098002 (2014)) and we extend the method to allow computation of the configurational entropy as a function of pressure. The approach that we use computes the configurational entropy by sampling the absolute volume of basins of attraction of the stable packings in the potential energy landscape. We find a surprisingly strong correlation between the pressure of a configuration and the volume of its basin of attraction in the potential energy landscape. This relation is well described by a power law. Our methodology to compute the number of minima in the potential energy landscape should be applicable to a wide range of other enumeration problems in statistical physics, string theory, cosmology and machine learning, that aim to find the distribution of the extrema of a scalar cost function that depends on many degrees of freedom., Comment: 18 pages, 7 figures

We report canonical and grand-canonical lattice Monte Carlo simulations of the self-assembly of addressable structures comprising hundreds of distinct component types. The nucleation behaviour, in the form of free-energy barriers to nucleation, changes significantly as the co-ordination number of the building blocks is changed from 4 to 8 to 12. Unlike tetrahedral structures - which roughly correspond to DNA bricks that have been studied in experiment - the shapes of the free-energy barriers of higher co-ordination structures depend strongly on the supersaturation, and such structures require a very significant driving force for structure growth before nucleation becomes thermally accessible. Although growth at high supersaturation results in more defects during self-assembly, we show that high co-ordination number structures can still be assembled successfully in computer simulations and that they exhibit self-assembly behaviour analogous to DNA bricks. In particular, the self-assembly remains modular, enabling in principle a wide variety of nanostructures to be assembled, with a greater spatial resolution than is possible in low co-ordination structures., Comment: Faraday Discussions 2015

Molecular imprinting is the process whereby a polymer matrix is cross-linked in the presence of molecules with surface sites that can bind selectively to certain ligands on the polymer. The cross-linking process endows the polymer matrix with a chemical 'memory', such that the target molecules can subsequently be recognized by the matrix. We present a simple model that accounts for the key features of this molecular recognition. Using a combination of analytical calculations and Monte Carlo simulations, we show that the model can account for the binding of rigid particles to an imprinted polymer matrix with valence-limited interactions. We show how the binding multivalency and the polymer material properties affect the efficiency and selectivity of molecular imprinting. Our calculations allow us to formulate design criteria for optimal molecular imprinting.

We present simulations of an equilibrium statistical-mechanics model that uniformly samples the space of quiescent states of a periodically sheared suspension. In our simulations, we compute the structural properties of this model as a function of density. We compare the results of our simulations with the structural data obtained in the corresponding non-equilibrium model of Corté et al. [Nat. Phys. 4, 420 (2008)]. We find that the structural properties of the non-equilibrium model are very different from those of the equilibrium model, even though the two models have exactly the same set of accessible states. This observation shows that the dynamical protocol does not sample all quiescent states with equal probability. In particular, we find that, whilst quiescent states prepared in a non-equilibrium protocol can be hyperuniform [see D. Hexner and D. Levine, Phys. Rev. Lett. 114, 110602 (2015); E. Tjhung and L. Berthier, Phys. Rev. Lett. 114, 148301 (2015); and J. H. Weijs et al., Phys. Rev. Lett. 115, 108301 (2015)], ergodic sampling never leads to hyperuniformity. In addition, we observe ordering phase transitions and a percolation transition in the equilibrium model that do not show up in the non-equilibrium model. Conversely, the quiescent-to-diffusive transition in the dynamical model does not correspond to a phase transition, nor a percolation transition, in the equilibrium model.

We use a coarse-grained model for generic proteins to investigate the formation of structures with P212121 symmetry, the most prevalent space group of protein crystals. To account for the string directionality of protein-protein interactions that has been suggested by previous studies, we represent proteins as spherical particles that are covered by a large number of small, attractive "patches" that are randomly distributed on the protein surface. Attractive interactions between two proteins can then involve several pairs of patches interacting simultaneously. Our results suggest that the unit cell with the lowest energy is not necessarily the one that grows fastest. Rather, growth is favoured if 1) new particles can attach with enough bonds to the growth front and 2) particles that attach in crystallographically inequivalent positions bind to the surface with similar strength [corrected]. We subsequently study the impact of interactions that are not part of crystalline contacts and find that when these non-specific interactions are few and weaker than the crystal contacts, both nucleation and growth are successful. If the proportion of non-specific interactions is increased, crystal growth is still possible in a small range of model temperature.

We propose a new algorithm for non-equilibrium molecular dynamics simulations of thermal gradients. The algorithm is an extension of the heat exchange algorithm developed by Hafskjold and co-workers [Mol. Phys. 80, 1389 (1993); Mol. Phys. 81, 251 (1994)], in which a certain amount of heat is added to one region and removed from another by rescaling velocities appropriately. Since the amount of added and removed heat is the same and the dynamics between velocity rescaling steps is Hamiltonian, the heat exchange algorithm is expected to conserve the energy. However, it has been reported previously that the original version of the heat exchange algorithm exhibits a pronounced drift in the total energy, the exact cause of which remained hitherto unclear. Here, we show that the energy drift is due to the truncation error arising from the operator splitting and suggest an additional coordinate integration step as a remedy. The new algorithm retains all the advantages of the original one whilst exhibiting excellent energy conservation as illustrated for a Lennard-Jones liquid and SPC/E water., 8 pages, 6 figures

The field of complex self-assembly is moving toward the design of multi-particle structures consisting of thousands of distinct building blocks. To exploit the potential benefits of structures with such `addressable complexity,' we need to understand the factors that optimize the yield and the kinetics of self-assembly. Here we use a simple theoretical method to explain the key features responsible for the unexpected success of DNA-brick experiments, which are currently the only demonstration of reliable self-assembly with such a large number of components. Simulations confirm that our theory accurately predicts the narrow temperature window in which error-free assembly can occur. Even more strikingly, our theory predicts that correct assembly of the complete structure may require a time-dependent experimental protocol. Furthermore, we predict that low coordination numbers result in non-classical nucleation behavior, which we find to be essential for achieving optimal nucleation kinetics under mild growth conditions. We also show that, rather surprisingly, the use of heterogeneous bond energies improves the nucleation kinetics and in fact appears to be necessary for assembling certain intricate three-dimensional structures. This observation makes it possible to sculpt nucleation pathways by tuning the distribution of interaction strengths. These insights not only suggest how to improve the design of structures based on DNA bricks, but also point the way toward the creation of a much wider class of chemical or colloidal structures with addressable complexity., Comment: Accompanying code for computing free-energy landscapes of addressable structures can be found at https://github.com/wmjac/pygtsa

A coarse-grained simulation method to predict NMR spectra of ions diffusing in porous carbons is proposed. The coarse-grained model uses input from molecular dynamics simulations such as the free-energy profile for ionic adsorption, and density-functional theory calculations are used to predict the NMR chemical shift of the diffusing ions. The approach is used to compute NMR spectra of ions in slit pores with pore widths ranging from 2 to 10 nm. As diffusion inside pores is fast, the NMR spectrum of an ion trapped in a single mesopore will be a sharp peak with a pore size dependent chemical shift. To account for the experimentally observed NMR line shapes, our simulations must model the relatively slow exchange between different pores. We show that the computed NMR line shapes depend on both the pore size distribution and the spatial arrangement of the pores. The technique presented in this work provides a tool to extract information about the spatial distribution of pore sizes from NMR spectra. Such information is diffcult to obtain from other characterisation techniques., Comment: 15 pages, 5 figures in the main text, 1 figure in the appendix

We present a technique for calculating free-energy profiles for the nucleation of multicomponent structuresthat contain as many species as building blocks. We find that a key factor is the topology of the graphdescribing the connectivity of the target assembly. By considering the designed interactions separately fromweaker, incidental interactions, our approach yields predictions for the equilibrium yield and nucleation bar-riers. These predictions are in good agreement with corresponding Monte Carlo simulations. We show that afew fundamental properties of the connectivity graph determine the most prominent features of the assemblythermodynamics. Surprisingly, we find that polydispersity in the strengths of the designed interactions stabi-lizes intermediate structures and can be used to sculpt the free-energy landscape for self-assembly. Finally, wedemonstrate that weak incidental interactions can preclude assembly at equilibrium due to the combinatorialpossibilities for incorrect association.Building nanostructures out of multiple, distinct com-ponents offers enormous possibilities for high-fidelitymanufacturing at the molecular level. Such ‘addressable’structures are fundamentally different from conventionalcrystals or ordered clusters, since every building block isdistinct and thus occupies a specific location in the tar-get structure. Because the interactions between buildingblocks are specified independently, it is possible to designfinite-sized, three-dimensional structures that assemblenearly error-free.

We present a numerical study of the effect of hemispherical pores on the nucleation of Lennard–Jones crystals from the vapour phase. As predicted by Page and Sear, there is a narrow range of pore radii, where vapour–liquid nucleation can become a two-step process. A similar observation was made for different pore geometries by Giacomello et al. We find that the maximum nucleation rate depends on both the size and the adsorption strength of the pore. Moreover, a poe can be more effective than a planar wall with the same strength of attraction. Pore-induced vapour–liquid nucleation turns out to be the rate-limiting step for crystal nucleation. This implies that crystal nucleation can be enhanced by a judicious choice of the wetting properties of a microporous nucleating agent.