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

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

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

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

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

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

Stochastic kinetics of ribosomes: single motor properties and collective behavior

Synthesis of protein molecules in a cell are carried out by ribosomes. A ribosome can be regarded as a molecular motor which utilizes the input chemical energy to move on a messenger RNA (mRNA) track that also serves as a template for the polymerization of the corresponding protein. The forward movement, however, is characterized by an alternating sequence of translocation and pause. Using a quantitative model, which captures the mechanochemical cycle of an individual ribosome, we derive an {\it exact} analytical expression for the distribution of its dwell times at the successive positions on the mRNA track. Inverse of the average dwell time satisfies a ``Michaelis-Menten-like'' equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechano-chemical cycle. Extending this formula appropriately, we also derive the exact force-velocity relation for a ribosome. Often many ribosomes simultaneously move on the same mRNA track, while each synthesizes a copy of the same protein. We extend the model of a single ribosome by incorporating steric exclusion of different individuals on the same track. We draw the phase diagram of this model of ribosome traffic in 3-dimensional spaces spanned by experimentally controllable parameters. We suggest new experimental tests of our theoretical predictions.Comment: Final published versio

A phase I trial of beta-all-trans-retinoic acid delivered via a collagen sponge and a cervical cap for mild or moderate intraepithelial cervical neoplasia.

A phase I trial was conducted of the vitamin A derivative beta-all-trans-retinoic acid (vitamin A acid; TRA), delivered via a collagen sponge and cervical cap for mild or moderate intraepithelial cervical neoplasia. On the basis of known skin and mucosal membrane toxicity, a concentration of 0.05% TRA in a cream-based vehicle was selected as the starting dose and was escalated later with the use of a modified Fibonacchi scale. The delivery device and the TRA were changed daily for 4 days, and side effects were assessed on days 1, 2, 3, 4, 8, and 30 by clinical and colposcopic examination. Vaginal, cervical, and systemic toxicity were evaluated in 35 patients. No dose-related systemic effects were found; mild cervical inflammation increased in many patients at higher doses. Unacceptably high vaginal toxicity was reached at a TRA concentration of 0.484%. A concentration of 0.372% TRA is recommended for use in phase II trials in mild and moderate cervical intraepithelial neoplasia

Diffusion-controlled generation of a proton-motive force across a biomembrane

Respiration in bacteria involves a sequence of energetically-coupled electron and proton transfers creating an electrochemical gradient of protons (a proton-motive force) across the inner bacterial membrane. With a simple kinetic model we analyze a redox loop mechanism of proton-motive force generation mediated by a molecular shuttle diffusing inside the membrane. This model, which includes six electron-binding and two proton-binding sites, reflects the main features of nitrate respiration in E. coli bacteria. We describe the time evolution of the proton translocation process. We find that the electron-proton electrostatic coupling on the shuttle plays a significant role in the process of energy conversion between electron and proton components. We determine the conditions where the redox loop mechanism is able to translocate protons against the transmembrane voltage gradient above 200 mV with a thermodynamic efficiency of about 37%, in the physiologically important range of temperatures from 250 to 350 K.Comment: 26 pages, 4 figures. A similar model is used in arXiv:0806.3233 for a different biological system. Minor changes in the Acknowledgements sectio

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