arXiv subjects

Jonathan P. K. Doye

Publications and source records attributed to Jonathan P. K. Doye.

At least 73 records · Page 4Linked to original sources

arXiv2010

The stability of a crystal with diamond structure for patchy particles with tetrahedral symmetry

The phase diagram of model anisotropic particles with four attractive patches in a tetrahedral arrangement has been computed at two different values for the range of the potential, with the aim of investigating the conditions under which a diamond crystal can be formed. We find that the diamond phase is never stable for our longer-ranged potential. At low temperatures and pressures, the fluid freezes into a body-centred-cubic solid that can be viewed as two interpenetrating diamond lattices with a weak interaction between the two sublattices. Upon compression, an orientationally ordered face-centred-cubic crystal becomes more stable than the body-centred-cubic crystal, and at higher temperatures a plastic face-centered-cubic phase is stabilized by the increased entropy due to orientational disorder. A similar phase diagram is found for the shorter-ranged potential, but at low temperatures and pressures, we also find a region over which the diamond phase is thermodynamically favored over the body-centred-cubic phase. The higher vibrational entropy of the diamond structure with respect to the body-centred-cubic solid explains why it is stable even though the enthalpy of the latter phase is lower. Some preliminary studies on the growth of the diamond structure starting from a crystal seed were performed. Even though the diamond phase is never thermodynamically stable for the longer-ranged model, direct coexistence simulations of the interface between the fluid and the body-centred-cubic crystal and between the fluid and the diamond crystal show that, at sufficiently low pressures, it is quite probable that in both cases the solid grows into a diamond crystal, albeit involving some defects. These results highlight the importance of kinetic effects in the formation of diamond crystals in systems of patchy particles.

cond-mat.mtrl-sci↗

arXiv2010

The effect of scale-free topology on the robustness and evolvability of genetic regulatory networks

We investigate how scale-free (SF) and Erdos-Renyi (ER) topologies affect the interplay between evolvability and robustness of model gene regulatory networks with Boolean threshold dynamics. In agreement with Oikonomou and Cluzel (2006) we find that networks with SFin topologies, that is SF topology for incoming nodes and ER topology for outgoing nodes, are significantly more evolvable towards specific oscillatory targets than networks with ER topology for both incoming and outgoing nodes. Similar results are found for networks with SFboth and SFout topologies. The functionality of the SFout topology, which most closely resembles the structure of biological gene networks (Babu et al., 2004), is compared to the ER topology in further detail through an extension to multiple target outputs, with either an oscillatory or a non-oscillatory nature. For multiple oscillatory targets of the same length, the differences between SFout and ER networks are enhanced, but for non-oscillatory targets both types of networks show fairly similar evolvability. We find that SF networks generate oscillations much more easily than ER networks do, and this may explain why SF networks are more evolvable than ER networks are for oscillatory phenotypes. In spite of their greater evolvability, we find that networks with SFout topologies are also more robust to mutations than ER networks. Furthermore, the SFout topologies are more robust to changes in initial conditions (environmental robustness). For both topologies, we find that once a population of networks has reached the target state, further neutral evolution can lead to an increase in both the mutational robustness and the environmental robustness to changes in initial conditions.

q-bio.PE↗

arXiv2009

DNA nanotweezers studied with a coarse-grained model of DNA

We introduce a coarse-grained rigid nucleotide model of DNA that reproduces the basic thermodynamics of short strands: duplex hybridization, single-stranded stacking and hairpin formation, and also captures the essential structural properties of DNA: the helical pitch, persistence length and torsional stiffness of double-stranded molecules, as well as the comparative flexibility of unstacked single strands. We apply the model to calculate the detailed free-energy landscape of one full cycle of DNA 'tweezers', a simple machine driven by hybridization and strand displacement.

cond-mat.soft↗

arXiv2009

Modelling the Self-Assembly of Virus Capsids

We use computer simulations to study a model, first proposed by Wales [1], for the reversible and monodisperse self-assembly of simple icosahedral virus capsid structures. The success and efficiency of assembly as a function of thermodynamic and geometric factors can be qualitatively related to the potential energy landscape structure of the assembling system. Even though the model is strongly coarse-grained, it exhibits a number of features also observed in experiments, such as sigmoidal assembly dynamics, hysteresis in capsid formation and numerous kinetic traps. We also investigate the effect of macromolecular crowding on the assembly dynamics. Crowding agents generally reduce capsid yields at optimal conditions for non-crowded assembly, but may increase yields for parameter regimes away from the optimum. Finally, we generalize the model to a larger triangulation number T = 3, and observe more complex assembly dynamics than that seen for the original T = 1 model.

q-bio.BM↗

arXiv2009

Extracting bulk properties of self-assembling systems from small simulations

For systems that self assemble into finite-sized objects, it is sometimes convenient to compute the thermodynamics for a small system where a single assembly can form. However, we show that in the canonical ensemble the use of small systems can lead to significant finite-size effects due to the suppression of concentration fluctuations. We introduce methods to estimate the bulk-yields from simulations of small systems and to follow the convergence of yields with system size, under the assumptions that the various species behave ideally. We also propose an extension to the umbrella sampling technique that allows the formation of multiple finite-sized objects.

cond-mat.soft↗

arXiv2009

Self-assembly of monodisperse clusters: Dependence on target geometry

We apply a simple model system of patchy particles to study monodisperse self-assembly, using the Platonic solids as target structures. We find marked differences between the assembly behaviours of the different systems. Tetrahedra, octahedra and icosahedra assemble easily, while cubes are more challenging and dodecahedra do not assemble. We relate these differences to the kinetics and thermodynamics of assembly, with the formation of large disordered aggregates a particular important competitor to correct assembly. In particular, the free energy landscapes of those targets that are easy to assemble are funnel-like, whereas for the dodecahedral system the landscape is relatively flat with little driving force to facilitate escape from disordered aggregates.

cond-mat.soft↗

arXiv2009

Monodisperse self-assembly in a model with protein-like interactions

We study the self-assembly behaviour of patchy particles with `protein-like' interactions that can be considered as a minimal model for the assembly of viral capsids and other shell-like protein complexes. We thoroughly explore the thermodynamics and dynamics of self assembly as a function of the parameters of the model and find robust assembly of all target structures considered. Optimal assembly occurs in the region of parameter space where a free energy barrier regulates the rate of nucleation, thus preventing the premature exhaustion of the supply of monomers that can lead to the formation of incomplete shells. The interactions also need to be specific enough to prevent the assembly of malformed shells, but whilst maintaining kinetic accessibility. Free-energy landscapes computed for our model have a funnel-like topography guiding the system to form the target structure, and show that the torsional component of the interparticle interactions prevents the formation of disordered aggregates that would otherwise act as kinetic traps.

cond-mat.soft↗

arXiv2008

The self-assembly of DNA Holliday junctions studied with a minimal model

In this paper, we explore the feasibility of using coarse-grained models to simulate the self-assembly of DNA nanostructures. We introduce a simple model of DNA where each nucleotide is represented by two interaction sites corresponding to the phosphate-sugar backbone and the base. Using this model, we are able to simulate the self-assembly of both DNA duplexes and Holliday junctions from single-stranded DNA. We find that assembly is most successful in the temperature window below the melting temperatures of the target structure and above the melting temperature of misbonded aggregates. Furthermore, in the case of the Holliday junction, we show how a hierarchical assembly mechanism reduces the possibility of becoming trapped in misbonded configurations. The model is also able to reproduce the relative melting temperatures of different structures accurately, and allows strand displacement to occur.

cond-mat.soft↗

arXiv2008

The self-assembly and evolution of homomeric protein complexes

We introduce a simple "patchy particle" model to study the thermodynamics and dynamics of self-assembly of homomeric protein complexes. Our calculations allow us to rationalize recent results for dihedral complexes. Namely, why evolution of such complexes naturally takes the system into a region of interaction space where (i) the evolutionarily newer interactions are weaker, (ii) subcomplexes involving the stronger interactions are observed to be thermodynamically stable on destabilization of the protein-protein interactions and (iii) the self-assembly dynamics are hierarchical with these same subcomplexes acting as kinetic intermediates.

q-bio.BM↗

arXiv2007

Preferential attachment during the evolution of a potential energy landscape

It has previously been shown that the network of connected minima on a potential energy landscape is scale-free, and that this reflects a power-law distribution for the areas of the basins of attraction surrounding the minima. Here, we set out to understand more about the physical origins of these puzzling properties by examining how the potential energy landscape of a 13-atom cluster evolves with the range of the potential. In particular, on decreasing the range of the potential the number of stationary points increases and thus the landscape becomes rougher and the network gets larger. Thus, we are able to follow the evolution of the potential energy landscape from one with just a single minimum to a complex landscape with many minima and a scale-free pattern of connections. We find that during this growth process, new edges in the network of connected minima preferentially attach to more highly-connected minima, thus leading to the scale-free character. Furthermore, minima that appear when the range of the potential is shorter and the network is larger have smaller basins of attraction. As there are many of these smaller basins because the network grows exponentially, the observed growth process thus also gives rise to a power-law distribution for the hyperareas of the basins.

cond-mat.stat-mech↗

arXiv2007

Reversible self-assembly of patchy particles into monodisperse icosahedral clusters

We systematically study the design of simple patchy sphere models that reversibly self-assemble into monodisperse icosahedral clusters. We find that the optimal patch width is a compromise between structural specificity (the patches must be narrow enough to energetically select the desired clusters) and kinetic accessibility (they must be sufficiently wide to avoid kinetic traps). Similarly, for good yields the temperature must be low enough for the clusters to be thermodynamically stable, but the clusters must also have enough thermal energy to allow incorrectly formed bonds to be broken. Ordered clusters can form through a number of different dynamic pathways, including direct nucleation and indirect pathways involving large disordered intermediates. The latter pathway is related to a reentrant liquid-to-gas transition that occurs for intermediate patch widths upon lowering the temperature. We also find that the assembly process is robust to inaccurate patch placement up to a certain threshold, and that it is possible to replace the five discrete patches with a single ring patch with no significant loss in yield.

cond-mat.soft↗

arXiv2007

Controlling crystallization and its absence: Proteins, colloids and patchy models

The ability to control the crystallization behaviour (including its absence) of particles, be they biomolecules such as globular proteins, inorganic colloids, nanoparticles, or metal atoms in an alloy, is of both fundamental and technological importance. Much can be learnt from the exquisite control that biological systems exert over the behaviour of proteins, where protein crystallization and aggregation are generally suppressed, but where in particular instances complex crystalline assemblies can be formed that have a functional purpose. We also explore the insights that can be obtained from computational modelling, focussing on the subtle interplay between the interparticle interactions, the preferred local order and the resulting crystallization kinetics. In particular, we highlight the role played by ``frustration'', where there is an incompatibility between the preferred local order and the global crystalline order, using examples from atomic glass formers and model anisotropic particles.

cond-mat.soft↗

arXiv2006

Exploring the origins of the power-law properties of energy landscapes: An egg-box model

Multidimensional potential energy landscapes (PELs) have a Gaussian distribution for the energies of the minima, but at the same time the distribution of the hyperareas for the basins of attraction surrounding the minima follows a power-law. To explore how both these features can simultaneously be true, we introduce an ``egg-box'' model. In these model landscapes, the Gaussian energy distribution is used as a starting point and we examine whether a power-law basin area distribution can arise as a natural consequence through the swallowing up of higher-energy minima by larger low-energy basins when the variance of this Gaussian is increased sufficiently. Although the basin area distribution is substantially broadened by this process,it is insufficient to generate power-laws, highlighting the role played by the inhomogeneous distribution of basins in configuration space for actual PELs.

cond-mat.stat-mech↗

arXiv2006

Power-law distributions for the areas of the basins of attraction on a potential energy landscape

Energy landscape approaches have become increasingly popular for analysing a wide variety of chemical physics phenomena. Basic to many of these applications has been the inherent structure mapping, which divides up the potential energy landscape into basins of attraction surrounding the minima. Here, we probe the nature of this division by introducing a method to compute the basin area distribution and applying it to some archetypal supercooled liquids. We find that this probability distribution is a power law over a large number of decades with the lower-energy minima having larger basins of attraction. Interestingly, the exponent for this power law is approximately the same as that for a high-dimensional Apollonian packing, providing further support for the suggestion that there is a strong analogy between the way the energy landscape is divided into basins, and the way that space is packed in self-similar, space-filling hypersphere packings, such as the Apollonian packing. These results suggest that the basins of attraction provide a fractal-like tiling of the energy landscape, and that a scale-free pattern of connections between the minima is a general property of energy landscapes.

cond-mat.stat-mech↗

arXiv2006

Energy landscapes, scale-free networks and Apollonian packings

We review recent results on the topological properties of two spatial scale-free networks, the inherent structure and Apollonian networks. The similarities between these two types of network suggest an explanation for the scale-free character of the inherent structure networks. Namely, that the energy landscape can be viewed as a fractal packing of basins of attraction.

cond-mat.stat-mech↗

arXiv2006

Thermodynamics of Community Structure

We introduce an approach to partitioning networks into communities that not only determines the best community structure, but also provides a range of characterization techniques to assess how significant that structure is. We study the thermodynamics of community structure by producing equilibrium ensembles of partitions, in which each partition is represented with a well-defined statistical weight. Thus we are able to study the temperature dependence of thermodynamic properties, namely the modularity $Q$ and heat capacity, with particular emphasis on the transition between high-temperature, essentially random partitions and low-temperature partitions with high modularity. We also look at frequency matrices that measure the likelihood that two nodes belong to the same community, and introduce an order parameter to measure the `blockiness' of the frequency matrix, and therefore the uniqueness of the community structure. These methods have been applied to a number of model networks in order to understand the effects of the degree distribution, spatial embedding and randomization. Finally, we apply these methods to a metabolic network known to have strong community structure and find hierarchical community structure, with some communities being more robust than others.

cond-mat.stat-mech↗

arXiv2006

A self-consistent approach to measure preferential attachment in networks and its application to an inherent structure network

Preferential attachment is one possible way to obtain a scale-free network. We develop a self-consistent method to determine whether preferential attachment occurs during the growth of a network, and to extract the preferential attachment rule using time-dependent data. Model networks are grown with known preferential attachment rules to test the method, which is seen to be robust. The method is then applied to a scale-free inherent structure network, which represents the connections between minima via transition states on a potential energy landscape. Even though this network is static, we can examine the growth of the network as a function of a threshold energy (rather than time), where only those transition states with energies lower than the threshold energy contribute to the network.For these networks we are able to detect the presence of preferential attachment, and this helps to explain the ubiquity of funnels on energy landscapes. However, the scale-free degree distribution shows some differences from that of a model network grown using the obtained preferential attachment rules, implying that other factors are also important in the growth process.

cond-mat.stat-mech↗

arXiv2006

The structure of binary Lennard-Jones clusters: The effects of atomic size ratio

We introduce a global optimization approach for binary clusters that for a given cluster size is able to directly search for the structure and composition that has the greatest stability. We apply this approach to binary Lennard-Jones clusters, where the strength of the interactions between the two atom types is the same, but where the atoms have different sizes. We map out how the most stable structure depends on the cluster size and the atomic size ratio for clusters with up to 100 atoms and up to 30% difference in atom size. A substantial portion of this parameter space is occupied by structures that are polytetrahedral, both those that are polyicosahedral and those that involve disclination lines. Such structures involve substantial strains for one-component Lennard-Jones clusters, but can be stabilized by the different-sized atoms in the binary clusters. These structures often have a `core-shell' geometry, where the larger atoms are on the surface, and the smaller atoms are in the core.

cond-mat.other↗