Biomedical subjects

Richard P Sear

Publications and source records attributed to Richard P Sear.

15 recordsLinked to original sources

PubMed2006

On the interpretation of quantitative experimental data on nucleation rates using classical nucleation theory.

We consider how experimental data for nucleation rates can be analyzed if it is assumed that classical nucleation theory is a reasonable description of the nucleation. In particular, we consider in detail experimental results for the nucleation of the protein lysozyme. Classical nucleation theory makes predictions for the functional form of the nucleation rate; physically reasonable bounds can be placed on the parameters of this functional form. The experimental data for lysozyme implies values for a parameter (the preexponential factor) that are outside the physically reasonable bounds for homogeneous nucleation but are consistent with heterogeneous nucleation. Also, the functional form of the rate suggests that there is a distribution of barrier heights. Such a distribution is likely for heterogeneous nucleation but not possible for homogeneous nucleation. Modeling experimental data with classical nucleation theory is a generally applicable way of distinguishing between homogeneous and heterogeneous nucleation.

Journal Article↗

PubMed2006

Modeling dual pathways for the metazoan spindle assembly checkpoint.

Using computational modeling, we investigate mechanisms of signal transduction. We focus on the spindle assembly checkpoint, where a single unattached kinetochore is able to signal to prevent cell cycle progression. The inhibitory signal switches off rapidly once spindle microtubules have attached to all kinetochores. This requirement tightly constrains the possible mechanisms. Here we investigate two possible mechanisms for spindle checkpoint operation in metazoan cells, both supported by recent experiments. The first involves the free diffusion and sequestration of cell cycle regulators. This mechanism is severely constrained both by experimental fluorescence recovery data and by the large volumes involved in open mitosis in metazoan cells. By using a simple mathematical analysis and computer simulation, we find that this mechanism can generate the inhibition found in experiment but likely requires a two-stage signal amplification cascade. The second mechanism involves spatial gradients of a short-lived inhibitory signal that propagates first by diffusion but then primarily by active transport along spindle microtubules. We propose that both mechanisms may be operative in the metazoan spindle assembly checkpoint, with either able to trigger anaphase onset even without support from the other pathway.

Anaphase-Promoting Complex-Cyclosome↗

PubMed2006

Heterogeneous nucleation in and out of pores.

We study the nucleation of a new thermodynamic phase in pores and find that the nucleation often proceeds via two steps: nucleation of pore filling, and nucleation out of the pore. These two rates have opposing dependencies on pore size, resulting in a pore size at which the nucleation rate of the new phase is maximal. This finding is relevant to attempts to design and use porous media to crystallize proteins.

Journal Article↗

PubMed2006

Observations of coarsening of air voids in a polymer-highly-soluble crystalline matrix during dissolution.

A combination of magnetic resonance imaging and x-ray microcomputed tomography has been used to visualize the development of the internal micro-structure within compressed tablets made from a combination of insoluble particles (Eudragit, a polymer) and soluble particles (diltiazem hydrochloride, a drug), during dissolution in water. Air voids in the tablet are seen to coarsen. The size distribution of the air voids is well fitted by a log-normal distribution with a mean size that grows linearly with time. There is evidence for both diffusion of voids and sudden collapse of individual voids, presumably as they coalesce. The behavior of the voids is studied and compared with models of coarsening; the implications for tablet dissolution are considered.

Journal Article↗

PubMed2006

Heterogeneous and homogeneous nucleation compared: rapid nucleation on microscopic impurities.

We use computer simulation to calculate the rates of both homogeneous nucleation and heterogeneous nucleation on microscopic impurities. We do so in perhaps the simplest model of fluids and magnets: the two-dimensional Ising model. We expect our results to be qualitatively applicable to many simple and complex fluids. We find that heterogeneous nucleation on an impurity that is not only microscopic but also as small as possible, that is, a single fixed spin, is more than four orders of magnitude faster than homogeneous nucleation. The rate of heterogeneous nucleation then increases by a factor of approximately five for each additional fixed spin in the impurity. These results suggest that impurities as small as single molecules can result in homogeneous nucleation being irrelevant due to heterogeneous nucleation on these microscopic impurities being much faster.

Journal Article↗

PubMed2006

Experiment and theory for heterogeneous nucleation of protein crystals in a porous medium.

The determination of high-resolution structures of proteins requires crystals of suitable quality. Because of the new impetus given to structural biology by structural genomics/proteomics, the problem of crystallizing proteins is becoming increasingly acute. There is therefore an urgent requirement for the development of new efficient methods to aid crystal growth. Nucleation is the crucial step that determines the entire crystallization process. Hence, the holy grail is to design a "universal nucleant," a substrate that induces the nucleation of crystals of any protein. We report a theory for nucleation on disordered porous media and its experimental testing and validation using a mesoporous bioactive gel-glass. This material induced the crystallization of the largest number of proteins ever crystallized using a single nucleant. The combination of the model and the experimental results opens up the scope for the rational design of nucleants, leading to alternative means of controlling crystallization.

Animals↗

PubMed2004

Statistical theory of nucleation in the presence of uncharacterized 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 characterized. 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 behavior is non-self-averaging. Non-self-averaging nucleation is nucleation with a rate that varies significantly from one realization 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.

Journal Article↗

PubMed2004

Solution stability and variability in a simple model of globular proteins.

It is well known among 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. 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.

Adenylate Kinase↗

PubMed2004

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 are required to bind to only one or a few other proteins of the few thousand proteins typically present in vivo. To quantify this requirement we introduce a property of proteins called the capability. The capability is the maximum number of specific-binding interactions possible in a mixture, or in other words the size of largest sustainable interactome. This calculation of the maximum number possible is closely analogous to the work of Shannon and others on the maximum rate of communication through noisy channels. Using a simple model of proteins, we find specific binding to be a demanding function in the sense that it demands that the binding sites of the proteins be encoded by long sequences of elements, and the requirement for specific binding then strongly constrains these sequences.

Biophysical Phenomena↗

PubMed2004

Highly specific protein-protein interactions, evolution and negative design.

We consider highly specific protein-protein interactions in proteomes of simple model proteins. We are inspired by the work of Zarrinpar et al (2003 Nature 426 676). They took a binding domain in a signalling pathway in yeast and replaced it with domains of the same class but from different organisms. They found that the probability of a protein binding to a protein from the proteome of a different organism is rather high, around one half. We calculate the probability of a model protein from one proteome binding to the protein of a different proteome. These proteomes are obtained by sampling the space of functional proteomes uniformly. In agreement with Zarrinpar et al we find that the probability of a protein binding a protein from another proteome is rather high, of order one tenth. Our results, together with those of Zarrinpar et al, suggest that designing, say, a peptide to block or reconstitute a single signalling pathway, without affecting any other pathways, requires knowledge of all the partners of the class of binding domains the peptide is designed to mimic. This knowledge is required to use negative design to explicitly design out interactions of the peptide with proteins other than its target. We also found that patches that are required to bind with high specificity evolve more slowly than those that are required only to not bind to any other patch. This is consistent with some analysis of sequence data for proteins engaged in highly specific interactions.

Evolution, Molecular↗

PubMed2003

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 characterize 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.

Journal Article↗

PubMed2003

Continuous freezing in three dimensions.

We analyze the freezing transition in a system of hard particles with a very long-ranged repulsion. The long-range repulsion makes first-order freezing transitions continuous, but leaves the initial stages of the crystallization unchanged: the crystal phase must still nucleate. The coexistence between bulk phases is replaced by microphase separation.

Journal Article↗

PubMed2002

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 from the behavior 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.

Journal Article↗

PubMed2002

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.

Journal Article↗

PubMed2002

Phase transition analogous to Bose-Einstein condensation in systems of noninteracting surfactant aggregates.

Ideal bosons and a classical system of monomers that aggregate forming noninteracting ring polymers are known to have the same partition function. So, the ring polymers have a phase transition, the analogue of Bose-Einstein condensation of bosons. At this phase transition macroscopic polymers are formed. The link between these systems is made via Feynman's path integrals: these integrals are the same for the trajectories of the bosons in imaginary time and for the configurations of the polymers. We show that a transition of this general form occurs within a whole class of aggregating systems. Examples are the lamellae formation in suspensions of disclike micelles or the emulsification failure observed in water-oil-surfactant emulsions. As with bosons, the transition occurs even when aggregates do not interact. The lambda-transition in 4He is believed to be Bose-Einstein condensation modified by interatomic interactions. We suggest that interaggregate interactions too only modify the transition we have found.

Journal Article↗