arXiv subjects

Richard P. Sear

Publications and source records attributed to Richard P. Sear.

At least 37 records · Page 2Linked to original sources

arXiv2004

A statistical theory of nucleation in the presence of uncharacterised impurities

First order phase transitions proceed via nucleation. The rate of nucleation varies exponentially with the free-energy barrier to nucleation, and so is highly sensitive to variations in this barrier. In practice, very few systems are absolutely pure, there are typically some impurities present which are rather poorly characterised. These interact with the nucleus, causing the barrier to vary, and so must be taken into account. Here the impurity-nucleus interactions are modelled by random variables. The rate then has the same form as the partition function of Derrida's Random Energy Model, and as in this model there is a regime in which the behaviour is non-self-averaging. Non-self-averaging nucleation is nucleation with a rate that varies significantly from one realisation of the random variables to another. In experiment this corresponds to variation in the nucleation rate from one sample to another. General analytic expressions are obtained for the crossover from a self-averaging to a non-self-averaging rate of nucleation.

cond-mat.stat-mech↗

arXiv2004

Specific protein-protein binding in many-component mixtures of proteins

Proteins must bind to specific other proteins in vivo in order to function. The proteins must bind only to one or a few other proteins of the of order a thousand proteins typically present in vivo. Using a simple model of a protein, specific binding in many component mixtures is studied. It is found to be a demanding function in the sense that it demands that the binding sites of the proteins be encoded by long sequences of bits, and the requirement for specific binding then strongly constrains these sequences. This is quantified by the capacity of proteins of a given size (sequence length), which is the maximum number of specific-binding interactions possible in a mixture. This calculation of the maximum number possible is in the same spirit as the work of Shannon and others on the maximum rate of communication through noisy channels.

q-bio.BM↗

arXiv2003

Solution stability, neutral evolution and variability in a simple model of globular proteins

It is well known amongst molecular biologists that proteins with a common ancestor and that perform the same function in similar organisms, can have rather different amino-acid sequences. Mutations have altered the amino-acid sequences without affecting the function; this is called neutral evolution. A simple model of a protein in which the interactions are encoded by sequences of bits is introduced, and used to study how mutations can change these bits, and hence the interactions, while maintaining the stability of the protein solution. This stability is a simple minimal requirement on our model proteins which mimics part of the requirement on a real protein to be functional. The properties of our model protein, such as its second virial coefficient, are found to vary significantly from one model protein to another. It is suggested that this may also be the case for real proteins in vivo.

cond-mat.soft↗

arXiv2003

Instabilities in complex mixtures with a large number of components

Inside living cells are complex mixtures of thousands of components. It is hopeless to try to characterise all the individual interactions in these mixtures. Thus, we develop a statistical approach to approximating them, and examine the conditions under which the mixtures phase separate. The approach approximates the matrix of second virial coefficients of the mixture by a random matrix, and determines the stability of the mixture from the spectrum of such random matrices.

cond-mat.soft↗

arXiv2003

Protein crystals and charged surfaces: interactions and heterogeneous nucleation

As proteins typically have charges of around 10, they will interact strongly with charged surfaces. We calculate the electrostatic contribution to the interaction of crystals of protein with charged surfaces. The surfaces repel like-charged crystals and attract oppositely-charged crystals, with free energies which can be easily several kT per protein molecule brought into contact with the surface. This means that oppositely charged surfaces can act as a nucleant, they can induce nucleation of a protein crystal by lowering the free energy barrier to heterogeneous nucleation of the crystal from a dilute solution.

cond-mat.soft↗

arXiv2002

The effects of added salt on the second virial coefficients of the complete proteome of E. coli

Bacteria typically have a few thousand different proteins. The number of proteins with a given charge is a roughly Gaussian function of charge - centred near zero, and with a width around ten (in units of the charge on the proton). We have used the charges on E. coli's proteins to estimate the changes in the second virial coefficients of all its proteins as the concentration of a 1:1 salt is increased. The second virial coefficient has dimensions of volume and we find that on average it decreases by about twice the average volume of a protein when the salt concentration is increased from 0.2 to 1 Molar. The standard deviation of the decrease is of the same order. The consequences of this for the complex mixture of proteins inside an E. coli cell, are briefly discussed.

cond-mat.soft↗

arXiv2002

Distribution of the second virial coefficients of globular proteins

George and Wilson [Acta. Cryst. D 50, 361 (1994)] looked at the distribution of values of the second virial coefficient of globular proteins, under the conditions at which they crystallise. They found the values to lie within a fairly narrow range. We have defined a simple model of a generic globular protein. We then generate a set of proteins by picking values for the parameters of the model from a probability distribution. At fixed solubility, this set of proteins is found to have values of the second virial coefficient that fall within a fairly narrow range. The shape of the probability distribution of the second virial coefficient is Gaussian because the second virial coefficient is a sum of contributions from different patches on the protein surface.

cond-mat.soft↗

arXiv2002

Flory-Huggins theory for athermal mixtures of hard spheres and larger flexible polymers

A simple analytic theory for mixtures of hard spheres and larger polymers with excluded volume interactions is developed. The mixture is shown to exhibit extensive immiscibility. For large polymers with strong excluded volume interactions, the density of monomers at the critical point for demixing decreases as one over the square root of the length of the polymer, while the density of spheres tends to a constant. This is very different to the behaviour of mixtures of hard spheres and ideal polymers, these mixtures although even less miscible than those with polymers with excluded volume interactions, have a much higher polymer density at the critical point of demixing. The theory applies to the complete range of mixtures of spheres with flexible polymers, from those with strong excluded volume interactions to ideal polymers.

cond-mat.soft↗

arXiv2002

Interfacial tension and nucleation in mixtures of colloids and long ideal polymer coils

Mixtures of ideal polymers with hard spheres whose diameters are smaller than the radius of gyration of the polymer, exhibit extensive immiscibility. The interfacial tension between demixed phases of these mixtures is estimated, as is the barrier to nucleation. The barrier is found to scale linearly with the radius of the polymer, causing it to become large for large polymers. Thus for large polymers nucleation is suppressed and phase separation proceeds via spinodal decomposition, as it does in polymer blends.

cond-mat.soft↗

arXiv2002

Heterogeneous nucleation near a metastable vapour-liquid transition: the effect of wetting transitions

Phase transformations such as freezing typically start with heterogeneous nucleation. Heterogeneous nucleation near a wetting transition, of a crystalline phase is studied. The wetting transition occurs at or near a vapour-liquid transition which occurs in a metastable fluid. The fluid is metastable with respect to crystallisation, and it is the crystallisation of this fluid phase that we are interested in. At a wetting transition a thick layer of a liquid phase forms at a surface in contact with the vapour phase. The crystalline nucleus is then immersed in this liquid layer, which reduces the free energy barrier to nucleation and so dramatically increases the nucleation rate. The variation in the rate of heterogeneous nucleation close to wetting transitions is calculated for systems in which the longest-range forces are dispersion forces.

cond-mat.stat-mech↗

arXiv2001

Scaling theory for the free-energy barrier to homogeneous nucleation of a non-critical phase near a critical point

Homogeneous nucleation of a new phase near an Ising-like critical point of another phase transition is studied. A scaling analysis shows that the free energy barrier to nucleation contains a singular term with the same scaling as the order parameter associated with the critical point. The total magnetisation of the nucleus scales as the response function and so it diverges. Vapour-liquid critical points are in the Ising universality class and so our results imply that near such a critical point the number of molecules in a nucleus of a another phase, such as a crystalline phase, diverges as the isothermal compressibility. The case where symmetry prevents coupling between the nucleus and the order parameter is also considered.

cond-mat.stat-mech↗

arXiv2001

Nucleation of the crystalline phase of proteins in the presence of semidilute non-adsorbing polymer

Starting from a protein solution which is metastable with respect to the crystalline phase, the effect of adding semidilute non-adsorbing polymer is considered. It is found to increase the chemical potential of the protein by a few tenths of kT, which may be enough to lower the barrier to nucleation of the crystalline phase by enough to allow crystallisation. It is also shown that assuming that the polymer induces a pairwise additive attraction leads to qualitatively incorrect results.

cond-mat.soft↗

arXiv2001

Homogeneous nucleation of a non-critical phase near a continuous phase transition

Homogeneous nucleation of a new phase near a second, continuous, transition, is considered. The continuous transition is in the metastable region associated with the first-order phase transition, one of whose coexisting phases is nucleating. Mean-field calculations show that as the continuous transition is approached, the size of the nucleus varies as the response function of the order parameter of the continuous transition. This response function diverges at the continuous transition, as does the temperature derivative of the free energy barrier to nucleation. This rapid drop of the barrier as the continuous transition is approached means that the continuous transition acts to reduce the barrier to nucleation at the first-order transition. This may be useful in the crystallisation of globular proteins.

cond-mat.stat-mech↗

arXiv2000

Phase separation in mixtures of colloids and long ideal polymer coils

Colloidal suspensions with free polymer coils which are larger than the colloidal particles are considered. The polymer-colloid interaction is modeled by an extension of the Asakura-Oosawa model. Phase separation occurs into dilute and dense fluid phases of colloidal particles when polymer is added. The critical density of this transition tends to zero as the size of the polymer coils diverges.

cond-mat.soft↗

arXiv2000

Nucleation of a non-critical phase in a fluid near a critical point

Phase diagrams of some globular proteins have a fluid-fluid transition as well as a fluid-crystal transition. Homogeneous nucleation of the crystal from the fluid phase near the critical point of the fluid-fluid transition is examined. As the fluid-fluid critical point is approached, the number of molecules in the critical nucleus, the nucleus at the top of the free energy barrier to nucleation, is found to diverge as the isothermal compressibility. This divergence is due to a layer of the fluid phase of width equal to the fluid's correlation length which surrounds the core of the nucleus; the number of molecules in a crystalline environment in the nucleus does not diverge. The free energy barrier to nucleation remains finite but its derivative with respect to the chemical potential is equal to minus the number of molecules in the critical nucleus and so diverges.

cond-mat.soft↗

arXiv2000

Molecular dynamics of a dense fluid of polydisperse hard spheres

Slow dynamics in a fluid are studied in one of the most basic systems possible: polydisperse hard spheres. Monodisperse hard spheres cannot be studied as the slow down in dynamics as the density is increased is preempted by crystallisation. As the dynamics slow they become more heterogeneous, the spread in the distances traveled by different particles in the same time increases. However, the dynamics appears to be less heterogeneous than in hard-sphere-like colloids at the same volume fraction. The particles which move least far in a characteristic relaxation time and, particularly, the particles which move farthest in the same time are clustered, not randomly distributed throughout the sample. We study the dynamics at three different widths of the distribution of diameters of the hard spheres. For each width, the relaxation time is the same function of the compressibility factor, suggesting that this determines the relaxation time for hard spheres.

cond-mat.soft↗

arXiv2000

Phase behaviour of a model of colloidal particles with a fluctuating internal state

Colloidal particles are not simple rigid particles, in general an isolated particle is a system with many degrees of freedom in its own right, e.g., the counterions around a charged colloidal particle.The behaviour of model colloidal particles, with a simple phenomenological model to account for these degrees of freedom, is studied. It is found that the interaction between the particles is not pairwise additive. It is even possible that the interaction between a triplet of particles is attractive while the pair interaction is repulsive. When this is so the liquid phase is either stable only in a small region of the phase diagram or absent altogether.

cond-mat.stat-mech↗

arXiv1999

Metastability and nucleation in the dilute fluid phase of a simple model of globular proteins

The dilute fluid phase of model globular proteins is studied. The model possesses a fluid-fluid transition buried within the fluid-crystal coexistence region, as do some globular proteins. If this fluid-fluid transition is not buried deep inside the fluid-crystal coexistence region the crystalline phase does not nucleate within the dilute fluid. We link this lack of nucleation of the crystal to the interactions in our model and speculate that similar interactions between globular proteins are responsible for the difficulty found in crystallising many globular proteins.

cond-mat.soft↗