Multiscale stochastic reaction-diffusion modelling: application to actin dynamics in filopodia

Two multiscale (hybrid) stochastic reaction-diffusion models of actin dynamics in a filopodium are investigated. Both hybrid algorithms combine compartment-based and molecular-based stochastic reaction-diffusion models. The first hybrid model is based on the models previously\ud developed in the literature. The second hybrid model is based on the application of recently developed two-regime method (TRM) to a fully molecular-based model which is also developed in this paper. The results of hybrid models are compared with the results of the molecular-based model. It is shown that both approaches give comparable results, although the TRM model better agrees quantitatively with the molecular-based model

A variational approach to the stochastic aspects of cellular signal transduction

Cellular signaling networks have evolved to cope with intrinsic fluctuations, coming from the small numbers of constituents, and the environmental noise. Stochastic chemical kinetics equations govern the way biochemical networks process noisy signals. The essential difficulty associated with the master equation approach to solving the stochastic chemical kinetics problem is the enormous number of ordinary differential equations involved. In this work, we show how to achieve tremendous reduction in the dimensionality of specific reaction cascade dynamics by solving variationally an equivalent quantum field theoretic formulation of stochastic chemical kinetics. The present formulation avoids cumbersome commutator computations in the derivation of evolution equations, making more transparent the physical significance of the variational method. We propose novel time-dependent basis functions which work well over a wide range of rate parameters. We apply the new basis functions to describe stochastic signaling in several enzymatic cascades and compare the results so obtained with those from alternative solution techniques. The variational ansatz gives probability distributions that agree well with the exact ones, even when fluctuations are large and discreteness and nonlinearity are important. A numerical implementation of our technique is many orders of magnitude more efficient computationally compared with the traditional Monte Carlo simulation algorithms or the Langevin simulations.Comment: 15 pages, 11 figure

Protein structure prediction: Do hydrogen bonding and water-mediated interactions suffice?

The many-body physics of hydrogen bond formation in alpha-helices of globular proteins was investigated using a simple physics-based model. Specifically, a context-sensitive hydrogen bond potential, which depends on residue identity and degree of solvent exposure, was used in the framework of the Associated Memory Hamiltonian codes developed previously but without using local sequence structure matches (“memories”). Molecular dynamics simulations employing the energy function using the context-sensitive hydrogen bond potential alone (the “amnesiac” model) were used to generate low energy structures for three alpha-helical test proteins. The resulting structures were compared to both the X-ray crystal structures of the test proteins and the results obtained using the full Associated Memory Hamiltonian previously used. Results show that the amnesiac Hamiltonian was able to generate structures with reasonably high structural similarity (Q ~ 0.4) to that of the native protein but only with the use of predicted secondary structure information encoding local steric signals. Low energy structures obtained using the amnesiac Hamiltonian without any a priori secondary structure information had considerably less similarity to the native protein structures (Q ~ 0.3). Both sets of results utilizing the amnesiac Hamiltonian are poorer than when local-sequence structure matches are used

Energetics and Vibrational States for Hydrogen on Pt(111)

We present a combination of theoretical calculations and experiments for the low-lying vibrational excitations of H and D atoms adsorbed on the Pt(111) surface. The vibrational band states are calculated based on the full three-dimensional adiabatic potential energy surface obtained from first principles calculations. For coverages less than three quarters of a monolayer, the observed experimental high-resolution electron peaks at 31 and 68meV are in excellent agreement with the theoretical transitions between selected bands. Our results convincingly demonstrate the need to go beyond the local harmonic oscillator picture to understand the dynamics of this system.Comment: In press at Phys. Rev. Lett - to appear in April 200

The Energy Landscape, Folding Pathways and the Kinetics of a Knotted Protein

The folding pathway and rate coefficients of the folding of a knotted protein are calculated for a potential energy function with minimal energetic frustration. A kinetic transition network is constructed using the discrete path sampling approach, and the resulting potential energy surface is visualized by constructing disconnectivity graphs. Owing to topological constraints, the low-lying portion of the landscape consists of three distinct regions, corresponding to the native knotted state and to configurations where either the N- or C-terminus is not yet folded into the knot. The fastest folding pathways from denatured states exhibit early formation of the N-terminus portion of the knot and a rate-determining step where the C-terminus is incorporated. The low-lying minima with the N-terminus knotted and the C-terminus free therefore constitute an off-pathway intermediate for this model. The insertion of both the N- and C-termini into the knot occur late in the folding process, creating large energy barriers that are the rate limiting steps in the folding process. When compared to other protein folding proteins of a similar length, this system folds over six orders of magnitude more slowly.Comment: 19 page

Capturing the essence of folding and functions of biomolecules using Coarse-Grained Models

The distances over which biological molecules and their complexes can function range from a few nanometres, in the case of folded structures, to millimetres, for example during chromosome organization. Describing phenomena that cover such diverse length, and also time scales, requires models that capture the underlying physics for the particular length scale of interest. Theoretical ideas, in particular, concepts from polymer physics, have guided the development of coarse-grained models to study folding of DNA, RNA, and proteins. More recently, such models and their variants have been applied to the functions of biological nanomachines. Simulations using coarse-grained models are now poised to address a wide range of problems in biology.Comment: 37 pages, 8 figure

Setting benchmarks for modelling gas–surface interactions using coherent control of rotational orientation states

A fundamental and predictive understanding of molecule-surface interactions is challenging to obtain. Here the authors report an experimental technique allowing direct measurement of the scattering matrix, which reports on the coherent evolution of quantum states of a molecule scattering from a surface

Prediction of native-state hydrogen exchange from perfectly funneled energy landscapes

Simulations based on perfectly funneled energy landscapes often capture many of the kinetic features of protein folding. We examined whether simulations based on funneled energy functions can also describe fluctuations in native-state protein ensembles. We quantitatively compared the site-specific local stability determined from structure-based folding simulations, with hydrogen exchange protection factors measured experimentally for ubiquitin, chymotrypsin inhibitor 2, and staphylococcal nuclease. Different structural definitions for the open and closed states based on the number of native contacts for each residue, as well as the hydrogen-bonding state, or a combination of both criteria were evaluated. The predicted exchange patterns agree with the experiments under native conditions, indicating that protein topology indeed has a dominant effect on the exchange kinetics. Insights into the simplest mechanistic interpretation of the amide exchange process were thus obtained.Fil: Craig, Patricio Oliver. Fundación Instituto Leloir; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Bioquimicas de Buenos Aires; Argentina. University of California San Diego. Department of Chemistry and Biochemistry; Estados UnidosFil: Lätzer, Joachim. Rutgers University. BioMaPS Institute; Estados UnidosFil: Weinkam, Patrick. University of California at San Francisco. Department of Bioengineering and Therapeutic Sciences; Estados UnidosFil: Hoffman, Ryan M. B.. University Of California At San Diego; Estados UnidosFil: Ferreiro, Diego. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Química Biológica de la Facultad de Ciencias Exactas y Naturales; ArgentinaFil: Komives, Elizabeth A.. University Of California At San Diego; Estados UnidosFil: Wolynes, Peter G.. University Of California At San Diego; Estados Unido

Inversion of the balance between hydrophobic and hydrogen bonding interactions in protein folding and aggregation.

Identifying the forces that drive proteins to misfold and aggregate, rather than to fold into their functional states, is fundamental to our understanding of living systems and to our ability to combat protein deposition disorders such as Alzheimer's disease and the spongiform encephalopathies. We report here the finding that the balance between hydrophobic and hydrogen bonding interactions is different for proteins in the processes of folding to their native states and misfolding to the alternative amyloid structures. We find that the minima of the protein free energy landscape for folding and misfolding tend to be respectively dominated by hydrophobic and by hydrogen bonding interactions. These results characterise the nature of the interactions that determine the competition between folding and misfolding of proteins by revealing that the stability of native proteins is primarily determined by hydrophobic interactions between side-chains, while the stability of amyloid fibrils depends more on backbone intermolecular hydrogen bonding interactions

Rationalization and Design of the Complementarity Determining Region Sequences in an Antibody-Antigen Recognition Interface

Protein-protein interactions are critical determinants in biological systems. Engineered proteins binding to specific areas on protein surfaces could lead to therapeutics or diagnostics for treating diseases in humans. But designing epitope-specific protein-protein interactions with computational atomistic interaction free energy remains a difficult challenge. Here we show that, with the antibody-VEGF (vascular endothelial growth factor) interaction as a model system, the experimentally observed amino acid preferences in the antibody-antigen interface can be rationalized with 3-dimensional distributions of interacting atoms derived from the database of protein structures. Machine learning models established on the rationalization can be generalized to design amino acid preferences in antibody-antigen interfaces, for which the experimental validations are tractable with current high throughput synthetic antibody display technologies. Leave-one-out cross validation on the benchmark system yielded the accuracy, precision, recall (sensitivity) and specificity of the overall binary predictions to be 0.69, 0.45, 0.63, and 0.71 respectively, and the overall Matthews correlation coefficient of the 20 amino acid types in the 24 interface CDR positions was 0.312. The structure-based computational antibody design methodology was further tested with other antibodies binding to VEGF. The results indicate that the methodology could provide alternatives to the current antibody technologies based on animal immune systems in engineering therapeutic and diagnostic antibodies against predetermined antigen epitopes