A Classical Density-Functional Theory for Describing Water Interfaces

We develop a classical density functional for water which combines the White Bear fundamental-measure theory (FMT) functional for the hard sphere fluid with attractive interactions based on the Statistical Associating Fluid Theory (SAFT-VR). This functional reproduces the properties of water at both long and short length scales over a wide range of temperatures, and is computationally efficient, comparable to the cost of FMT itself. We demonstrate our functional by applying it to systems composed of two hard rods, four hard rods arranged in a square and hard spheres in water

Effects of Sequence Disorder on DNA Looping and Cyclization

Effects of sequence disorder on looping and cyclization of the double-stranded DNA are studied theoretically. Both random intrinsic curvature and inhomogeneous bending rigidity are found to result in a remarkably wide distribution of cyclization probabilities. For short DNA segments, the range of the distribution reaches several orders of magnitude for even completely random sequences. The ensemble averaged values of the cyclization probability are also calculated, and the connection to the recent experiments is discussed.Comment: 8 pages, 4 figures, LaTeX; accepted to Physical Review E; v2: a substantially revised version; v3: references added, conclusions expanded, minor editorial corrections to the text; v4: a substantially revised and expanded version (total number of pages doubled); v5: new Figure 4, captions expanded, minor editorial improvements to the tex

Development of a four-item physical activity index from information about subsistence living in rural African women: a descriptive, cross-sectional investigation

<p>Abstract</p> <p>Background</p> <p>We investigated the criterion validity of a physical activity index (PAI) derived from socio-demographic variables obtained from convenience samples of rural African women.</p> <p>Methods</p> <p>We used a sample (N = 206) from a larger dataset which surveyed adult rural Africans during 1997, and data collected during 2003/4 from 138 adult rural African women. A three-point PAI (low-, medium- and high-subsistence) was constructed from four socio-demographic questions related to electricity, cooking methods, water collection and availability of motorized transport. Criterion measures included measures of adiposity, blood biochemistry, resting blood pressure (RBP), physical fitness (VO_2max) and single-plane accelerometry (ACC).</p> <p>Results</p> <p>Age, educational level and health status were not related to PAI level (p > 0.1). There was a significant negative, linear trend between the PAI level and adiposity level (p < 0.04), and fasting blood glucose concentration (p < 0.0001), while VO_2maxwas positively related to PAI level (p = 0.0190). The PAI level was positively and linearly related to ACC output, namely counts.day^-1(p = 0.0044), steps.day^-1(p = 0.0265), min.day^-1of moderate-to-vigorous activity (p = 0.0040), and the percentage of subjects adhering to physical activity public health guidelines (p = 0.0157). Other criterion measures did not reach significance, but were in the expected direction (sedentary behaviour: p > 0.08, RBP: p > 0.07).</p> <p>Conclusion</p> <p>The PAI derived from a socio-demographic questionnaire is a valid instrument for broadly categorizing levels of physical activity for this specific population of rural African women. As the epidemiological transition progresses, validity will need to be re-established.</p

Steady-state simulations using weighted ensemble path sampling

We extend the weighted ensemble (WE) path sampling method to perform rigorous statistical sampling for systems at steady state. The straightforward steady-state implementation of WE is directly practical for simple landscapes, but not when significant metastable intermediates states are present. We therefore develop an enhanced WE scheme, building on existing ideas, which accelerates attainment of steady state in complex systems. We apply both WE approaches to several model systems confirming their correctness and efficiency by comparison with brute-force results. The enhanced version is significantly faster than the brute force and straightforward WE for systems with WE bins that accurately reflect the reaction coordinate(s). The new WE methods can also be applied to equilibrium sampling, since equilibrium is a steady state

Effect of body mass and physical activity volume and intensity on pedometry-measured activity energy expenditure in rural black South Africans in the Limpopo Province

Objectives. We developed a novel approach to investigate patterns of pedometry-measured total weekly activity energy expenditure (EEAct) in rural black South Africans in the Limpopo Province. Design. We analysed 7-day pedometry data in 775 subjects (female: N=508; male: N=267). Variance components models for EEAct were used to estimate the variance explained by body mass (BM), total weekly steps (volume) and estimated intensity (kcal. kg-1.step-1). Univariate General Linear Models, adjusting for age, BM and physical activity (PA) volume, were used to determine if EEAct was primarily affected by volume or intensity. Results. BM (13.1%), PA intensity (24.4%) and PA volume (56.9%) explained 94.4% of the variance in EEAct. Adjusted EEAct did not differ between sexes (78 kcal.week-1, p =0.2552). There were no significant differences across activity categories (sedentary to very active) for adjusted EEAct (62 - 287 kcal.week-1, p>0.1). Adjusted EEAct for 6 - 7 days of compliance (≥10 000 steps.day-1) differed significantly from 1 - 2 days of compliance (266 - 419 kcal.week-1, p0.30). Conclusions. We have highlighted an intensity effect for days of compliance and at very active ambulatory levels (≥12 500 steps. day-1). A volume effect appeared to dominate between sexes, across activity categories and weight-by-activity categories. It is important that post hoc statistical adjustments be made for body mass and PA volume when comparing EEAct across groups

Bridge Decomposition of Restriction Measures

Motivated by Kesten's bridge decomposition for two-dimensional self-avoiding walks in the upper half plane, we show that the conjectured scaling limit of the half-plane SAW, the SLE(8/3) process, also has an appropriately defined bridge decomposition. This continuum decomposition turns out to entirely be a consequence of the restriction property of SLE(8/3), and as a result can be generalized to the wider class of restriction measures. Specifically we show that the restriction hulls with index less than one can be decomposed into a Poisson Point Process of irreducible bridges in a way that is similar to Ito's excursion decomposition of a Brownian motion according to its zeros.Comment: 24 pages, 2 figures. Final version incorporates minor revisions suggested by the referee, to appear in Jour. Stat. Phy

Stochastic theory of large-scale enzyme-reaction networks: Finite copy number corrections to rate equation models

Chemical reactions inside cells occur in compartment volumes in the range of atto- to femtolitres. Physiological concentrations realized in such small volumes imply low copy numbers of interacting molecules with the consequence of considerable fluctuations in the concentrations. In contrast, rate equation models are based on the implicit assumption of infinitely large numbers of interacting molecules, or equivalently, that reactions occur in infinite volumes at constant macroscopic concentrations. In this article we compute the finite-volume corrections (or equivalently the finite copy number corrections) to the solutions of the rate equations for chemical reaction networks composed of arbitrarily large numbers of enzyme-catalyzed reactions which are confined inside a small sub-cellular compartment. This is achieved by applying a mesoscopic version of the quasi-steady state assumption to the exact Fokker-Planck equation associated with the Poisson Representation of the chemical master equation. The procedure yields impressively simple and compact expressions for the finite-volume corrections. We prove that the predictions of the rate equations will always underestimate the actual steady-state substrate concentrations for an enzyme-reaction network confined in a small volume. In particular we show that the finite-volume corrections increase with decreasing sub-cellular volume, decreasing Michaelis-Menten constants and increasing enzyme saturation. The magnitude of the corrections depends sensitively on the topology of the network. The predictions of the theory are shown to be in excellent agreement with stochastic simulations for two types of networks typically associated with protein methylation and metabolism.Comment: 13 pages, 4 figures; published in The Journal of Chemical Physic

Solid domains in lipid vesicles and scars

The free energy of a crystalline domain coexisting with a liquid phase on a spherical vesicle may be approximated by an elastic or stretching energy and a line tension term. The stretching energy generally grows as the area of the domain, while the line tension term grows with its perimeter. We show that if the crystalline domain contains defect arrays consisting of finite length grain boundaries of dislocations (scars) the stretching energy grows linearly with a characteristic length of the crystalline domain. We show that this result is critical to understand the existence of solid domains in lipid-bilayers in the strongly segregated two phase region even for small relative area coverages. The domains evolve from caps to stripes that become thinner as the line tension is decreased. We also discuss the implications of the results for other experimental systems and for the general problem that consists in finding the ground state of a very large number of particles constrained to move on a fixed geometry and interacting with an isotropic potential.Comment: 7 pages, 6 eps figure

Dynamics of protein-protein encounter: a Langevin equation approach with reaction patches

We study the formation of protein-protein encounter complexes with a Langevin equation approach that considers direct, steric and thermal forces. As three model systems with distinctly different properties we consider the pairs barnase:barstar, cytochrome c:cytochrome c peroxidase and p53:MDM2. In each case, proteins are modeled either as spherical particles, as dipolar spheres or as collection of several small beads with one dipole. Spherical reaction patches are placed on the model proteins according to the known experimental structures of the protein complexes. In the computer simulations, concentration is varied by changing box size. Encounter is defined as overlap of the reaction patches and the corresponding first passage times are recorded together with the number of unsuccessful contacts before encounter. We find that encounter frequency scales linearly with protein concentration, thus proving that our microscopic model results in a well-defined macroscopic encounter rate. The number of unsuccessful contacts before encounter decreases with increasing encounter rate and ranges from 20-9000. For all three models, encounter rates are obtained within one order of magnitude of the experimentally measured association rates. Electrostatic steering enhances association up to 50-fold. If diffusional encounter is dominant (p53:MDM2) or similarly important as electrostatic steering (barnase:barstar), then encounter rate decreases with decreasing patch radius. More detailed modeling of protein shapes decreases encounter rates by 5-95 percent. Our study shows how generic principles of protein-protein association are modulated by molecular features of the systems under consideration. Moreover it allows us to assess different coarse-graining strategies for the future modelling of the dynamics of large protein complexes

Elasticity of Stiff Polymer Networks

We study the elasticity of a two-dimensional random network of rigid rods (``Mikado model''). The essential features incorporated into the model are the anisotropic elasticity of the rods and the random geometry of the network. We show that there are three distinct scaling regimes, characterized by two distinct length scales on the elastic backbone. In addition to a critical rigidiy percolation region and a homogeneously elastic regime we find a novel intermediate scaling regime, where elasticity is dominated by bending deformations.Comment: 4 pages, 4 figure