Complete list of papers

Mathematical models in chemistry, biophysics, and soft matter.

Here is a complete list of papers in order of publication year, most recent first. Click on a paper to see the abstract and links to the full text.

Ab Initio Study of Water Polarization in the Hydration Shell of Aqueous Hydroxide: Comparison between Polarizable and Nonpolarizable Water Models

Denis Bucher, Angus Gray-Weale, and Serdar Kuyucak

J. Chem. Theory Comput., 2010, 6 (9), pp 2888–2895

Ab initio simulations of aqueous hydroxide are performed to study the structure and polarization of water molecules in the first solvation shell. Polarization is found to depend on the configuration of the hydrogen-bond (HB) donors. In the most common case of four HB donors, the dipole moment of water molecules is much larger than those in the first shell of monovalent ions. When there are only three HB donors, the water dipole moment exceeds even those in the first shell of a divalent cation. We also show that the dipole fluctuations in the first hydration shell of hydroxide are reduced compared to bulk water, which can provide a rationale for the propensity of hydroxide for interfaces with hydrophobes. Because of its unique properties, hydroxide provides a nontrivial test for benchmarking classical models. Comparison of the ab initio results with those obtained from the classical models indicates that the latter need to be further improved in order to yield reliable results.

A divergent synthesis of modular dendrimers via sequential C–C bond fragmentation thio-Michael addition

Judith Hierold, Angus Gray-Weale and David W. Lupton

Chem. Commun., vol 46, pp 6789-6791 (2010).

The C–C bond fragmentation of carbocycles has been developed as a new method for the divergent synthesis of dendrimers. The scope of this reaction was examined with the preparation of six first generation dendrimers from structurally diverse and readily available fragmentation precursors. By pairing the fragmentation with a thio-Michael reaction, the preparation of a [G4]-ene24 dendrimer has been achieved.

Describing the Structure of a Randomly Hyperbranched Polymer, Konkolewicz D, Gray-Weale A, Perrier S, Macromolecular Theory and Simulations vol. 19 (5) pp. 219-227 (2010).

This paper describes random branching theory, a model for the solution structure of hyperbranched polymers. In this model, the hyperbranched polymer is assumed to be composed of units whose structure is simpler than the resulting polymer. These simple units can have any structure of chemical functionality, from monomers to linear chains or spherical particles. This paper outlines how this theory is constructed, describes the underlying assumptions and parameters, and summarizes the most basic form. It is shown how variations in the parameters change the behavior of the model, and described how to fit an experimental data series. This demonstrates how the model can be used to fit other data series, and how it can be used as a test for whether a polymer is randomly hyperbranched.

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Nature of α and β Particles in Glycogen Using Molecular Size Distributions Mitchell A. Sullivan, Francisco Vilaplana, Richard A. Cave, David Stapleton, Angus A. Gray-Weale, and Robert G. Gilbert Biomacromolecules, in press, 10.1021/bm100074p.

Glycogen is a randomly hyperbranched glucose polymer. Complex branched polymers have two structural levels: individual branches and the way these branches are linked. Liver glycogen has a third level: supramolecular clusters of β particles which form larger clusters of α particles. Size distributions of native glycogen were characterized using size exclusion chromatography (SEC) to find the number and weight distributions and the size dependences of the number- and weight-average masses. These were fitted to two distinct randomly joined reference structures, constructed by random attachment of individual branches and as random aggregates of β particles. The z-average size of the α particles in dimethylsulfoxide does not change significantly with high concentrations of LiBr, a solvent system that would disrupt hydrogen bonding. These data reveal that the β particles are covalently bonded to form α particles through a hitherto unsuspected enzyme process, operative in the liver on particles above a certain size range.

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Hyperbranched Polymers by Thiol-Yne Chemistry: From Small Molecules to Functional Polymers Dominik Konkolewicz, Angus Gray-Weale, and Sébastien Perrier J. Am. Chem. Soc. vol 131 p 18075–18077 (2009).

We have demonstrated a versatile approach to the synthesis of functional hyperbranched polymers. The thiol-yne reaction occurs at room temperature, reaches yields over 95% in less than 2 h, and enables the incorporation of various functionalities in the final product. The reaction applies to both small molecules and linear chains with a thiol and an alkyne. Techniques such as RAFT can be used to synthesize a large library of such linear chains, which can be converted into hyperbranched polymers following the strategy outlined in this paper. We believe the simplicity and versatility of this approach makes the thiol-yne reaction an ideal candidate for the synthesis of hyperbranched polymers.

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Comment on ‘Behaviour of hydroxide at the water/vapor interface’ [Chem. Phys. Lett. 474 (2009) 241]. Gray-Weale. Chemical Physics Letters vol. 481 (1-3) pp. 22-24 (2009).

Application of the Gibbs adsorption isotherm to the available data for the pH-dependence of the surface tension of water leads to two conclusions. First, a strong hydroxide surface affinity implies the surface tension nearly pH-independent near pH 7. Second, surface tension data at high bulk hydroxide concen- tration are consistent with a large surface excess of hydroxide at low bulk concentration. These in part contradict the claims made by Winter et al., but also allow a reinterpretation of their spectra, revealing the essential importance of their conclusion that hydroxide is absent from the top few molecular layers near the water–vapour interface.

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An explanation for the charge on water's surface. Angus Gray-Weale and James K. Beattie. Phys. Chem. Chem. Phys. vol 11 p 10994-1005 (2009).

Measurements with different techniques point to a strong affinity of hydroxide ions for interfaces between water and hydrophobes, but some spectroscopic experiments do not detect excess hydroxide at the interface, while others do. Hydroxide ions are unusual in that they reduce the relative permittivity of an electrolyte solution more than other monovalent, monatomic ions. This implies that they suppress the collective dipole-moment fluctuations of nearby waters. We show that the absence of these fluctuations leads to a Hamaker-like force on the hydroxide ion that attracts it to regions where dipole-moment fluctuations are smaller than in bulk water, in other words, to regions of low relative permittivity. We show also that there is no contradiction between the picture of the basic, negatively charged interface and spectroscopic measurements. This is, in part, because the hydroxides are mostly below the outermost molecular layers. By combining a simple model for this fluctuation force with a modified Poisson–Boltzmann equation, we reproduce the dependence of the

-potential on pH, including the low isoelectric point, the approximate magnitude of the experimental surface charge density, and the Jones–Ray data for the dependence of surface tension on electrolyte concentration. We discuss also the apparent contradiction between molecular-dynamics simulations that deny and experiments that support a basic, negatively charged interface.

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Extracting Physically Useful Information from Multiple-Detection Size-Separation Data for Starch A. Gray-Weale, R. Cave, R. G. Gilbert Bioacromolecules vol 10 p 2708-13 (2009)

A method for interpreting multiple-detection size separation data of complex branched homopolymers [Konkolewicz, D.; Gilbert, R. G.; Gray-Weale, A. Phys. Rev. Lett. 2007, 98, 238301] is applied to starch. The method, whose application is described in detail, uses the sample's weight and number distributions over polymer sizes, along with the Molecular weight distribution of the individual branches (or their average degree of polymerization). The branch-length and number size distributions are used to generate the weight distribution of a hypothetical molecule with the same branch-length and number distributions but where the branches are randomly joined; this reference weight distribution is then compared to the actual one. The method is applied to size-exclusion chromatography (SEC) data for starch from a particular rice variety, the first time such data have been reported for a native starch. Comparison with the randomly branched reference function shows that the amylopectin component is consistent with random branching on the distance scale of this measurement, 10(2)-10(3) run. This implies that on the size scale commensurate with that of a whole amylopectin chain, branching is pseudorandom, even though there is nonrandom branching oil the much smaller scale of individual branches and clusters.

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Searching for Stars Steven L. Brown, Dominik Konkolewicz, Angus Gray-Weale, William B. Motherwell, and Sébastien Perrier Aust. J. Chem. vol 62 p 1533–1536 (2009).

Selective Desulfurization and Fluorescence Spectroscopy as New Tools in the Search for Cross Termination Side-products in RAFT Polymerization

We present a novel approach to the examination of the ‘controversial’ three-armed stars that are argued to exist in rate-retarded reversible addition–fragmentation chain transfer (RAFT) polymerizations by using a fluorescent carbazole- containing RAFT agent that exhibits classical signs of retardation, and provides a route to polymer-RAFT agent cross termination. We also pioneer the use of an existing desulfurization technique for the purification of polymers by removal of the coloured RAFT derived moiety, with the added benefit of potentially isolating and identifying the presence of cross termination side-products. Our findings suggest that the rate retardation is either due to the RAFT intermediate being sufficiently stable that it does not cross terminate, or that most of cross termination events occur between the intermediate and short radicals. Our findings are consistent with a model proposed earlier by this group for rate retardation in RAFT systems, which assumed a slow rate for long-chain cross termination, and a fast short chain cross termination rate.

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Obtaining Kinetic Information from the Chain-Length Distribution of Polymers Produced by RAFT D Konkolewicz, M Siauw, A Gray-Weale, BS Hawkett, S Perrier J. Phys. Chem. B vol 113 p 7086-94 (2009)

We describe a simple model for the kinetics and chain-length distribution of polymers made by living radical techniques. Living radical methods give good control over the molecular weight of a linear polymer by capping the growing end and forming a dormant chain. The polymer is predominantly capped, and occasionally decaps to form a radical that propagates for a short period before recapping. Our model uses this mechanism to describe the chain-length distribution of polymers made by living radical methods. We focus on oligomers made by reversible addition-fragmentation chain transfer (RAFT) polymerization as model systems. Our model can determine optimal reaction conditions for desired polymer properties and test hypotheses about reaction schemes by using only two parameters, with each parameter related to the kinetics. The first. parameter is the mean number of monomers added when a chain decaps. A broad distribution results if many monomers are added upon decapping. The second parameter is the mean number of times a polymer decaps. Many decapping events indicate high monomer conversion. Our model gives kinetic information by directly fitting to an experimental chain-length distribution, which is the reverse of other kinetic models that generate the distribution from rate coefficients. Our approach has also the advantage of being simpler than previously published kinetic schemes, which use many rate coefficients as inputs. Our model was tested against three monomers (acrylic acid, butyl acrylate, and styrene) and two RAFT agents. In each case, we successfully describe the chain-length distribution, and give information about the kinetics, especially the probability of propagation versus deactivation by the RAFT mechanism. This excellent agreement with a priori expectations and quantum calculations makes our model a powerful tool for predicting the structure of polymers obtained by living radical polymerization.

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Comparative structural analyses of purified glycogen particles from rat liver, human skeletal muscle and commercial preparations Je-Hoon Ryu et al., International Journal of Biological Macromolecules, vol 45 p 478-82 (2009).

Glycogen, a branched polymer of glucose, is a cellular energy store, important for whole body glucose metabolism. The largest stores are located in the liver and skeletal muscle but can also be found in the heart, brain, leukocytes, skin, thymus, retina and adipose tissue [9]. Glycogen accumulation and utilization are under elaborate controls involving covalent phosphorylation and allosteric ligand binding. Control differs between muscle and liver in part due to the existence of different tissue-specific enzymes at key steps. Each glycogen molecule is associated with enzymes and proteins that are tissue specific and necessary for synthesis, degradation and regulation.

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RAFT Polymerization Kinetics: How Long Are the Cross-Terminating Oligomers? D. Konkolewicz, B. S. Hawkett, A. Gray-Weale, S. Perrier. J. Pol. Sci. A: Polymer Chemistry vol 47 (14) p 3455-3466 (2009).

We extend a new model for the kinetics of reversible addition-fragmenta- tion chain transfer (RAFT) polymerization. The essence of this model is that the ter- mination of the radical intermediate formed by the RAFT process occurs only with very short oligomeric radicals. In this work, we consider cross-termination of oligom- ers up to two monomers and an initiator fragment. This model accounts for the ab- sence of three-armed stars in the molecular weight distribution, which are predicted by other cross-termination models, since the short third arm makes a negligible dif- ference to the polymer’s molecular weight. The model is tested against experiments on styrene mediated by cyano-isopropyl dithiobenzoate, and ESR experiments of the intermediate radical concentration. By comparing our model to experiments, we may determine the significance of cross-termination in RAFT kinetics. Our model suggests that to agree with the known data on RAFT kinetics, the majority of cross-terminat- ing chains are dimeric or shorter. If longer chains are considered in cross-termination reactions, then significant discrepancies with the experiments (distinguishable star polymers in the molecular weight distribution) and quantum calculations will result.

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General Description of the Structure of Branched Polymers A. Gray-Weale and R. G. Gilbert J. Pol. Sci. A: Polymer Chemistry vol 47 p 3914-30 (2009)

A multidimensional distribution function is defined to describe the branching structure of branched homopolymers such as starch and polyacrylates. Averages of this function give distributions which can be measured using, for example, the number and weight distributions as a function of hydrodynamic volume from size-exclusion chromatography and field-flow fractionation, and two-dimensional separation methods. This provides means to plot data to obtain physically meaningful quantities, and to test mechanistic postulates for the (bio)synthesis, of branched polymers. A simple enzyme-kinetic model for a reduced form of this multidimensional distribution for starch biosynthesis is derived and solved. One application is to derive number distributions for the molecular weight distribution of debranched glycogen. Fitting this to experiment gives estimates of this ratio for two forms of glycogen. We propose that number distributions from size separation for starch (which, it is pointed out, are obtained directly from in-line viscometric detection) have a simple and meaningful form when plotted as ln(number distribution) against V-h(p), where V-h is hydrodynamic volume, and p a parameter of order unity determined from multiple-detection size separation measurements. The new function is also used to propose a two-dimensional experiment which can yield an unambiguous measurement of the amylose: amylopectin ratio in starch.

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Correlations in the Structure and Dynamics of Ionic Liquids A. Gray-Weale Aust. J. Chem. vol 62 p 288-297 (2009)

A very great deal of the experimental work on room-temperature ionic liquids was done after high-performance computing became readily available for quantum-chemical or molecular-dynamic calculations. I explore the use of modern computational methods to guide or aid laboratory work, and the importance of 'old-fashioned' theory, from before the age of fast computers. Debye and Huckel published the first really important theoretical work on correlations between charged particles, and the Nernst-Einstein formula is still used to understand electrical conductivities. I assess the usefulness of all these theoretical methods and ideas, and discuss the particular difficulties presented by ionic liquids.

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Models for Randomly Hyperbranched Polymers: Theory and Simulation D. Konkolewicz, O. Thorn-Sheshold and A. Gray-Weale, Journal of Chemical Physics vol 129 p 054901 (2008).

We derive theoretical models for the structures of randomly hyperbranched polymers in solution, and test them against computer simulations. The models are based on the same basic approach: building a structure by the random assembly of ‘simple units’, which may be monomers, linear chains, or larger branched species. Comparisons to simulation reported here show that the conformations of hyperbranched species, i.e. their radii of gyration and full density proﬁles, are accurately described by this approach. These stringent tests complement previous tests against experiment. We include the eﬀects of solvent quality at the mean-ﬁeld level. Our model works best for hyperbranched structures, but also reproduces very well the simulated density proﬁles of dendrimers. The models reported here provide a simple, but realistic, picture of the physical inﬂuences that aﬀect the conformations of hyperbranched species.

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RAFT Polymerization Kinetics: Combination of Apparently Conﬂicting Models D. Konkolewicz, B. S. Hawkett, A. Gray-Weale, S. Perrier Macromolecules, accepted for publication 16/5/2008.

We propose a model for the kinetics of reversible addition-fragmentation chain transfer (RAFT) polymerization. The essence of this model is that the termination of the radical intermediate formed by the RAFT process occurs only with the shortest active radicals. This model accounts for the absence of 3-armed stars predicted by other cross-termination models since the short radical makes a negligible difference to the overall molecular weight. The model is tested against experiments on styrene at 60 °C with cyanoisopropyl dithiobezoate (CPDB) as the RAFT agent. The predicted rate coefficients are consistent with slow fragmentation of the RAFT intermediate, and the overall concentration of radicals is consistent with ESR experiments. Overall, it demonstrates that the two conflicting models that have been proposed so far can actually coexist.

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Statistical Mechanical Theory for Steady State Systems VIII: General Theory for a Brownian Particle Driven by a Time- and Space-Varying Force P. Attard and A. Gray-Weale, Journal of Chemical Physics, vol 128 p 114509 (2008).

A Brownian particle subject to a time- and space-varying force is studied with the second entropy theory for nonequilibrium statistical mechanics. A ﬂuctuation expression is obtained for the second entropy of the path, and this is maximized to obtain the most likely path of the particle. Two approaches are used, one based on the velocity correlation function and one based on the position correlation function. The approaches are a perturbation about the free particle result and are exact for weak external forces. They provide a particularly simple way of including memory effects in time-varying driven diffusion. The theories are tested against computer simulation data for a Brownian particle trapped in an oscillating parabolic well. They accurately predict the phase lag and amplitude as a function of drive frequency, and they account quantitatively for the memory effects that are important at high frequencies and that are missing in the simplest Langevin equation.

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Screening and strain in superionic conductors A. Gray-Weale, Faraday Discussions vol 134 p 297-313 (2007).

I calculate the screening length and its relation to elastic constants from mean-ﬁeld models of superionic conductors. The Debye formula for a continuous ﬂuid’s screening length is replaced by one that accounts for the discrete nature of the lattice. Interactions alter the screening length and in some cases give oscillations in the charge structure. The screening lengths derived here are exact not only at low temperature where there are few defects, but also at high temperature where the eﬀective interaction strength is small. The mean-ﬁeld treatment correctly gives the decrease in an elastic constant observed at the superionic transition for a variety of crystals. This decrease is best explained by a change in the defect creation entropy with density. The eﬀect of doping on the elastic constant also agrees well with experiment. The extension to the mean-ﬁeld models given here provides a consistent picture of the response of a superionic crystal to electrical, mechanical and thermal stresses, as well as to doping.

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Time Correlations and the Second Entropy A. Gray-Weale and P. Attard, Journal of Chemical Physics vol 127 p 044503 (2007).

The authors study the transport of mass and heat in simulations of a Lennard-Jones ﬂuid and demonstrate the calculation of transport coefﬁcients, and of both the ﬁrst and second entropies. These entropies are calculated from time correlation functions, as are the transport coefﬁcients. They discuss the role of the second entropy in providing a physical explanation for the link between dynamic ﬂuctuations and response. They illustrate the physical signiﬁcance of the various contributions to the second entropy and how they simplify in the case of relaxation by steady-state ﬂow. Certain approximations proposed for the calculation of the ﬁrst entropy, common in the literature, are shown to break down under certain circumstances, and they give an improved method of calculation. They pay particular attention to the coupling between variables of opposite time parity in the transport matrix, and show that in general this cannot be neglected.

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Randomly Hyperbranched Polymers D. Konkolewicz, R. G. Gilbert and A. Gray-Weale, Physical Review Letters vol 98 p 238301-4 (2007).

We describe a model for the structures of randomly hyperbranched polymers in solution, and ﬁnd a logarithmic growth of radius with polymer mass. We include segmental overcrowding, which puts an upper limit on the density. The model is tested against simulations, against data on amylopectin, a major component of starch, on glycogen, and on polyglycerols. For samples of synthetic polyglycerol and glycogen, our model holds well for all the available data. The model reveals higher-level scaling structure in glycogen, related to the β-particles seen in electron microscopy.

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Toward a more general solution to the band-broadening problem in size-separation of polymers D. Konkolewicz, J. Taylor, P. Castignolles, A. Gray-Weale, R. G. Gilbert, Macromolecules vol 40 p 3477-87 (2007).

The molecular weight distributions (MWDs) and hydrodynamic volume distributions of polymers can reveal considerable mechanistic information on the polymerization process, and have significant effects on physical properties such as viscosity. While the broadening function for a particular SEC setup can be found using ultranarrow standards, these are extremely difficult to obtain. The present paper implements and tests a suggested technique (Aust. J. Chem. 2005, 58, 178) to enable the deconvolution of size distributions using broad standards, synthesized under conditions which are expected to produce a number MWD P(M) which is a single exponential. Broad standards with a wide range of Mh n were synthesized for both styrene and methyl methacrylate (MMA), using low-conversion free-radical polymerization with appropriate choice of chain transfer agent (CTA) and initiator concentrations; standards with high Mh nwere synthesized at 25 °C without added initiator. The broadening function was obtained by assuming a flexible functional form (exponential Gaussian hybrid) and least-squares fitting its parameters so that the “theoretical” exponential P(M) curves for each sample, with exponents obtained experimentally, matched the experimental SEC distribution for styrene. The procedure was tested by using the same band-broadening function to deconvolute data for the original polystyrene “standards” and the polyMMA samples, using the Ishige deconvolution method. This method tends to amplify noise, and too tight a tolerance can lead to spurious structure in the deconvoluted distributions. Nevertheless, a tolerance range could be found which led to stable solutions, where the deconvoluted P(M) curves for both were indeed single exponential over the range of molecular weights where data with acceptable accuracy could be obtained. This suggests that this is a generally applicable method to correct for band broadening for a wide range of systems, although improved deconvolution methods are needed to obtain truly converged and stable solutions.

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Interpreting size-exclusion data for highly branched biopolymers by reverse Monte-Carlo simulations C. Watts, A. Gray-Weale and R. G. Gilbert. Biomacromolecules vol 8 p 455-63 (2007).

Size-exclusion chromatography with multiple detection provides data on the distributions of various properties in a branched polymer sample, for example, distributions of the number, average mass, mean-squared mass, and branching fraction against hydrodynamic volume. A method is developed that provides a basis to use such data for obtaining structural and biosynthetic information on highly branched polymers, such as amylopectin. We generate by simulation a reference distribution of randomly branched polymers from the experimental distribution of debranched chains of the target polymer. We then select from these simulated chains a set with the same number (or other) distribution as the actual polymer sample, using reverse Monte Carlo simulations. Properties of these model polymers are used to interpret the differences with experiment as due to correlations in branching structure. The same methodology can be applied to data from other separation techniques such as field-flow fractionation and high-performance anionic exchange chromatography.

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Nanoparticle enhanced conductivity in organic ionic plastic crystals: Space charge versus strain induced defect mechanism Y. Shekibi, A. Gray-Weale, D. MacFarlane, A. Hill, M. Forsyth, Journal of Physical Chemistry C vol 111 p 11463-8 (2007).

High conductivity in solid-state electrolytes is a critical requirement for many advanced energy and other electrochemical applications. Plastic crystalline materials have shown promise in this regard, and the inclusion of nanosized inorganic particles in both amorphous and crystalline materials has indicated order of magnitude enhancements in ion transport induced by space charge or other defect enhancement. In this paper we present conductivity enhancements in the plastic crystal N,N′-ethylmethylpyrrolidinium bis(trifluoromethanesulfonyl)- amide ([C2mpyr][NTf2]) induced by nanosized SiO₂ particles. The addition of the nanoparticles dramatically increases plasticity and ion mobility. Positron annihilation lifetime spectroscopy (PALS) measurements indicate an increase in mean defect size and defect concentration as a result of nanoparticle inclusion. The scaling of the conductivity with size suggests that a “trivial space charge” effect is operable, although a strain induced enhancement of defects (in particular extended defects) is also likely given the observed increase in plasticity.

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Molecular weight distributions from size-separation data for hyperbranched polymers D. Konkolewicz, A. Gray-Weale, R. G. Gilbert, J. Pol. Sci. A: Polymer Chemistry vol 45 p 3112-5 (2007).

Size separation techniques for polymer characterization include size-exclusion chromatography (SEC) and field-flow fractionation. These techniques separate on hydrodynamic volume V_h, a quantity with dimensions of volume, proportional to the product [g]w Mn, where [η]_w and M_n are respectively, the weight-average intrinsic viscosity and number-average molecular weight. The characterization of branched polymers is challenging, because (even in the hypothetical case of an SEC system without band broadening) a sample of branched polymers with the same V_h in general contains chains with a range of molecular weights. This effect is called variously ‘‘imperfect resolution,’’‘‘structural polydispersity,’’ or ‘‘local polydispersity,’’ the term used here.

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Theory of multiple-detection size-exclusion chromatography of complex branched polymers M. Gaborieau, R. G. Gilbert, A. Gray-Weale, J. Hernandez, P. Castignolles, Macromolecular Theory and Simulations vol 16 p 13-28 (2007).

SEC separates complex branched polymers by hydrodynamic volume, rather than by mol- ecular weight or branching characteristics. Equations relating the response of different types of detectors are derived including band broadening, by defining a distribution function N0(M,Vh), the number of chains with molecular weight M and hydrodynamic volume Vh. While the true molecular weight distribution of com- plex polymers cannot be determined by SEC, irrespective of the detector used, the formalism enables multiple detection SEC data to be pro- cessed to both analyze the polymer sample and reveal mechanistic information about polymer synthesis. The formalism also shows how the true weight- and number-average molecular weight, Mw and Mn, can be obtained from correct processing of the hydrodynamic volume distributions.

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Role of Protein Flexibility in ion Permeation T. Bastug, A. Gray-Weale, S. Patra, S. Kuyucak, Biophysical Journal vol 90 p 2285-96 (2006).

Proteins have a ﬂexible structure, and their atoms exhibit considerable ﬂuctuations under normal operating conditions. However, apart from some enzyme reactions involving ligand binding, our understanding of the role of ﬂexibility in protein function remains mostly incomplete. Here we investigate this question in the realm of membrane proteins that form ion channels. Speciﬁcally, we consider ion permeation in the gramicidin A channel, and study how the energetics of ion conduction changes as the channel structure is progressively changed from completely ﬂexible to a ﬁxed one. For each channel structure, the potential of mean force for a permeating potassium ion is determined from molecular dynamics (MD) simulations. Using the same molecular dynamics data for completely ﬂexible gramicidin A, we also calculate the average densities and ﬂuctuations of the peptide atoms and investigate the correlations between these ﬂuctuations and the motion of a permeating ion. Our results show conclusively that peptide ﬂexibility plays an important role in ion permeation in the gramicidin A channel, thus providing another reason—besides the well-known problem with the description of single ﬁle pore water—why this channel cannot be modeled using continuum electrostatics with a ﬁxed structure. The new method developed here for studying the role of protein ﬂexibility on its function clariﬁes the contributions of the ﬂuctuations to energy and entropy, and places limits on the level of detail required in a coarse-grained model.

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The energy landscape of a fluorite-structured superionic conductor A. Gray-Weale and P. A. Madden, The Journal of Physical Chemistry B vol 108 p 6634-42 (2005).

In a recent paper, we described similarities between the superionic transition in certain crystals and the glass transition in fragile, supercooled liquids. We now examine the underlying energy landscapes of the fluorides of lead(II) and calcium, by minimizing the potential energy from configurations along molecular-dynamics trajectories. The resulting inherent structures are characterized by the number of defects they contain and the interactions of these defects. We propose a simple explanation for the clustering of these defects, related to the lattice’s strain energy, and discuss its implications for the mechanism of conduction. We also consider the vibrational densities of states of the inherent structures and test the possibility that an increase in the harmonic vibrational entropy upon defect formation stabilizes the superionic state. A mean-field model with an interaction term varying with the cube-root of the defect concentration describes the inherent structure defect populations well, and also reproduces the energy and entropy over a significant temperature range. However, a direct examination of the way in which the inherent structure energy depends on the defect concentration shows that this does not mean that the physical picture used to construct the mean-field free energy is correct.

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Dynamical arrest in superionic crystals and supercooled liquids A. Gray-Weale and P. A. Madden, The Journal of Physical Chemistry B vol 108 p 6624-33 (2005).

Phenomenological similarities between the temperature dependence of the thermal and transport properties of supercooled liquids and certain crystalline fast-ion conductors are explored, using information from computer simulations and experiments. The similarities include non-Arrhenius temperature dependence of the transport coefficients, anomalies in the heat capacity, two-step relaxation of the time-correlation functions, and the connection between the mobility and entropy being described by the Adam-Gibbs equation. We use the detailed information available from computer simulation to examine the relationship between these observations and the number of defects in the system. Such defects may be unambiguously identified in a simple geometrical way from the underlying lattice in the superionic system; defects are often invoked in descriptions of supercooled liquid behavior but they are not easily defined in such a strongly disordered system.

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Theoretical calculation of the structure of a polarizable-ionic fluid A. Gray-Weale and P. A. Madden, Molecular Physics vol 101 p 1761-79 (2003).

Much theory of the structures of fluids depends on the assumption of pair-additive forces between the particles. Simulations and experiments have shown that many molten salts, molecular fluids and other systems have structures that depend sensitively on polarization of their electron clouds, or on other internal distortions. In such cases, the forces are not pair additive and the theoretical calculation of structure, expressed as a radial distribution function, g(r), is not possible using the ordinary methods. Part of the problem is that the internal structure is quantum mechanical. A theoretical method for the calculation of the structure of a fluid of polarizable particles is presented here, in a form that may be applied to any one of many structure theories in common use. The method is inspired by work on the simulation of polarizable fluids. It is applied to a simple model of a molten salt with polarizable ions. The theory is applicable to particles carrying any combination of induced electrical multipole moments, along with charges and permanent moments.

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Induced-dipole contributions to the conductivity and dielectric response of molten ZnCl2 Gray-Weale, Madden and Wilson, Journal of Chemical Physics vol 113 p 6782-87 (2000).

A molecular dynamics simulation of molten ZnCl₂ with a realistic interionic potential is used to evaluate the contribution of interaction-induced dipoles to the dielectric response, or equivalently, to the conductivity. The induced dipoles are included self-consistently in the interionic potential. The contribution is found to be signiﬁcant across the accessible range of frequencies, modifying various features of the spectrum ordinarily attributed to elementary translations of the ionic charges, and markedly improving agreement with experimental spectra.

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Transition-state theory model for the diffusion coefficients of small penetrants in glassy polymers A. Gray-Weale, R. Henchman, R. G. Gilbert, M. L. Greenfield and D. N. Theodorou, Macromolecules vol 30 p 7296-306 (1997).

Previous molecular dynamics simulations have shown that the diffusion of a penetrant in a glassy polymer involves occasional jumps between cavities through the opening of a "neck", and thus, because this is a rare event, the diffusion coefficient can be estimated using transition-state theory. We treat this process as a unimolecular rearrangement and develop semiempirical means of estimating the activation energy, frequency factor and jump length. The activation energy is obtained by treating the polymer as a continuous solid and calculating the energy required to expand a neck in that continuum. The model for the frequency factor uses the result from simulations that the distribution of frequencies of the modes in the transition is very similar to that distribution for the reactant state. The frequency factor is estimated by considering only the motion of the penetrant. These motions are treated as harmonic oscillators. The jump length is obtained from simple geometric considerations of the polymer chain. The parameters are readily evaluated from bulk properties of the polymer such as the isothermal compressibility. The model reproduces experimental trends semiquantitatively and could be used to interpolate and extrapolate experimental diffusion data.

Note that the PDF version of this article on the Macromolecules website has had its equations garbled. Email me if you would like corrected equations.

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