Time Scale Gap Research Articles

Performance Analysis of Guidance Laws Based on Timescale Gap

An analytical treatment of performance analysis of guidance laws is possible only in simplistic scenarios. As the complexity of the guidance system increases, a search for analytical solutions becomes quite impractical. In this paper, a new performance measure, based upon the notion of a timescale gap that can be computed through numerical simulations, is developed for performance analysis of guidance laws. Finite time Lyapunov exponents are used to define the timescale gap. It is shown that the timescale gap can be used for quantification of the rate of convergence of trajectories to the collision course. Comparison between several guidance laws, based on the timescale gap, is presented. Realistic simulations to study the effect of aerodynamics and atmospheric variations on the timescale gap of these guidance laws are also presented.

Quantitative Protein Dynamics from Dominant Folding Pathways

We develop a theoretical approach to the protein-folding problem based on out-of-equilibrium stochastic dynamics. Within this framework, the computational difficulties related to the existence of large time scale gaps are removed, and simulating the entire reaction in atomistic details using existing computers becomes feasible. We discuss how to determine the most probable folding pathway, identify configurations representative of the transition state, and compute the most probable transition time. We perform an illustrative application of these ideas, studying the conformational evolution of alanine dipeptide, within an all-atom model based on the empiric GROMOS96 force field.

Coarse-grained protein molecular dynamics simulations

A limiting factor in biological science is the time-scale gap between experimental and computational trajectories. At this point, all-atom explicit solvent molecular dynamics (MD) are clearly too expensive to explore long-range protein motions and extract accurate thermodynamics of proteins in isolated or multimeric forms. To reach the appropriate time scale, we must then resort to coarse graining. Here we couple the coarse-grained OPEP model, which has already been used with activated methods, to MD simulations. Two test cases are studied: the stability of three proteins around their experimental structures and the aggregation mechanisms of the Alzheimer's Abeta16-22 peptides. We find that coarse-grained isolated proteins are stable at room temperature within 50 ns time scale. Based on two 220 ns trajectories starting from disordered chains, we find that four Abeta16-22 peptides can form a three-stranded beta sheet. We also demonstrate that the reptation move of one chain over the others, first observed using the activation-relaxation technique, is a kinetically important mechanism during aggregation. These results show that MD-OPEP is a particularly appropriate tool to study qualitatively the dynamics of long biological processes and the thermodynamics of molecular assemblies.

IFold: a platform for interactive folding simulations of proteins

We built a novel web-based platform for performing discrete molecular dynamics simulations of proteins. In silico protein folding involves searching for minimal frustration in the vast conformational landscape. Conventional approaches for simulating protein folding insufficiently address the problem of simulations in relevant time and length scales necessary for a mechanistic understanding of underlying biomolecular phenomena. Discrete molecular dynamics (DMD) offers an opportunity to bridge the size and timescale gaps and uncover the structural and biological properties of experimentally undetectable protein dynamics. The iFold server supports large-scale simulations of protein folding, thermal denaturation, thermodynamic scan, simulated annealing and p(fold) analysis using DMD and coarse-grained protein model with structure-based Gō-interactions between amino acids. http://ifold.dokhlab.org

Clusters of interacting receptors can stabilize synaptic efficacies

Synaptic weights store memories that can last a lifetime. Yet, memory depends on synaptic protein receptors that are recycled in and out of the membrane at a fast rate, possibly several times an hour. Several proposals to bridge this vast gap in time scales between memory and its molecular substrate have relied on bistable molecular switches. Here, we propose an alternative to this approach based on clusters of interacting receptors in the synaptic membrane. We show that such clusters can be metastable and that the lifetime of such clusters can be many orders of magnitude larger than the lifetime of the receptors of which they are composed. We also demonstrate how bidirectional synaptic plasticity can be implemented in this framework.

Unraveling Bacteriorhodopsin

Unraveling Bacteriorhodopsin

A molecular view of Tanner's law: molecular dynamics simulations of droplet spreading

By truncating the range of van der Waals forces in our molecular dynamics model we reduce the lengthscale and timescale gap between the outer (wedge) and inner (precursor) regions in droplet spreading simulations. This results in a molecular model which combines atomic-scale resolution with the ability to capture large-scale behaviour as manifested by the Tanner spreading law. Our results show that Tanner's law can be recovered, even if van der Waals effects and the resulting precursor film are limited to distances of the order of three atomic diameters from the substrate. In other words, removal of the singularity is not necessary up to a few atomic diameters from the contact line. The very good quantitative agreement with theory and experiments suggests that the original precursor theory of de Gennes can be generalized to precursors of molecular thickness in which flow is not characterized by the continuum (Stokes) model. Gravity current simulations are also in excellent agreement with the theory of Huppert and recent experimental results showing lubrication scalings at small capillary numbers.

Theoretical studies of the mechanical unfolding of the muscle protein titin: Bridging the time-scale gap between simulation and experiment

Brute-force, fully atomistic simulations of single molecule mechanical unfolding experiments are not feasible because current simulation time scales are about six orders of magnitude shorter than the time scales explored by experiments. To circumvent this difficulty, we have constructed a model, in which the unfolding dynamics of the I27 domain of the muscle protein titin is described as diffusive motion along a single unfolding coordinate R (equal to the domain extension) in the presence of an external driving potential and the potential of mean force G(R). The effect of the remaining degrees of freedom is described in terms of a viscous force with a friction coefficient η. The potential of mean force G(R) is computed from a series of equilibrium molecular dynamics trajectories performed with constrained values of R and η is extracted from a series of steered molecular dynamics simulations, in which R is increased at a constant rate and the mechanical response of the molecule is monitored as a function of time. The estimated G(R) allows us to calculate the force-dependent unfolding rate via transition-state theory and—by performing kinetic Monte Carlo simulations—to predict unfolding force distributions in experimentally relevant regimes. We compare the computed unfolding free energy profile with that deduced from atomic force microscopy studies of titin and find that, while the unfolding free energy barrier at zero force is nearly identical to the experimental value, the force dependence of the barrier is nonlinear, in contrast to most phenomenological models of titin unfolding. Because of this, the value ku(0) of the unfolding rate extrapolated to zero unfolding force, as well as the location of the unfolding transition state, differ from those previously estimated from experimental data. In particular, our estimate of ku(0) is several orders of magnitude lower than the unfolding rate measured in chemical denaturation experiments, suggesting that the two experimental techniques may probe different unfolding pathways. At the same time, the distribution of the unfolding force as well as its dependence on the pulling rate predicted by our simulations are found to be in agreement with atomic force microscopy experiments.

Time-Trimming Tricks for Dynamic Simulations: Splitting Force Updates to Reduce Computational Work

Time-Trimming Tricks for Dynamic Simulations: Splitting Force Updates to Reduce Computational Work

Biomolecular dynamics at long timesteps: bridging the timescale gap between simulation and experimentation.

Innovative algorithms have been developed during the past decade for simulating Newtonian physics for macromolecules. A major goal is alleviation of the severe requirement that the integration timestep be small enough to resolve the fastest components of the motion and thus guarantee numerical stability. This timestep problem is challenging if strictly faster methods with the same all-atom resolution at small timesteps are sought. Mathematical techniques that have worked well in other multiple-timescale contexts--where the fast motions are rapidly decaying or largely decoupled from others--have not been as successful for biomolecules, where vibrational coupling is strong. This review examines general issues that limit the timestep and describes available methods (constrained, reduced-variable, implicit, symplectic, multiple-timestep, and normal-mode-based schemes). A section compares results of selected integrators for a model dipeptide, assessing physical and numerical performance. Included is our dual timestep method LN, which relies on an approximate linearization of the equations of motion every delta t interval (5 fs or less), the solution of which is obtained by explicit integration at the inner timestep delta tau (e.g., 0.5 fs). LN is computationally competitive, providing 4-5 speedup factors, and results are in good agreement, in comparison to 0.5 fs trajectories. These collective algorithmic efforts help fill the gap between the time range that can be simulated and the timespans of major biological interest (milliseconds and longer). Still, only a hierarchy of models and methods, along with experimentational improvements, will ultimately give theoretical modeling the status of partner with experiment.