Supercomputer docking with a large number of degrees of freedom.

Docking represents one of the most popular computational approaches in drug design. It has reached popularity owing to capability of identifying correct conformations of a ligand within an active site of the target-protein and of estimating the binding affinity of a ligand that is immensely helpful in prediction of compound activity. Despite many success stories, there are challenges, in particular, handling with a large number of degrees of freedom in solving the docking problem. Here, we show that SOL-P, the docking program based on the new Tensor Train algorithm, is capable to dock successfully oligopeptides having up to 25 torsions. To make the study comparative we have performed docking of the same oligopeptides with the SOL program which uses the same force field as that utilized by SOL-P and has common features of many docking programs: the genetic algorithm of the global optimization and the grid approximation. SOL has managed to dock only one oligopeptide. Moreover, we present the results of docking with SOL-P ligands into proteins with moveable atoms. Relying on visual observations we have determined the common protein atom groups displaced after docking which seem to be crucial for successful prediction of experimental conformations of ligands.

Steady oscillations in aggregation-fragmentation processes.

We report surprising steady oscillations in aggregation-fragmentation processes. Oscillating solutions are observed for the class of aggregation kernels K_{i,j}=i^{ν}j^{µ}+j^{ν}i^{µ} homogeneous in masses i and j of merging clusters and fragmentation kernels, F_{ij}=λK_{ij}, with parameter λ quantifying the intensity of the disruptive impacts. We assume a complete decomposition (shattering) of colliding partners into monomers. We show that an assumption of a steady-state distribution of cluster sizes, compatible with governing equations, yields a power law with an exponential cutoff. This prediction agrees with simulation results when θ≡ν-µ<1. For θ=ν-µ>1, however, the densities exhibit an oscillatory behavior. While these oscillations decay for not very small λ, they become steady if θ is close to 2 and λ is very small. Simulation results lead to a conjecture that for θ<1 the system has a stable fixed point, corresponding to the steady-state density distribution, while for any θ>1 there exists a critical value λ_{c}, such that for λ<λ_{c}, the system has an attracting limit cycle. This is rather striking for a closed system of Smoluchowski-like equations, lacking any sinks and sources of mass.

Oscillations in Aggregation-Shattering Processes.

We observe never-ending oscillations in systems undergoing collision-controlled aggregation and shattering. Specifically, we investigate aggregation-shattering processes with aggregation kernels K_{i,j}=(i/j)^{a}+(j/i)^{a} and shattering kernels F_{i,j}=λK_{i,j}, where i and j are cluster sizes, and parameter λ quantifies the strength of shattering. When 0≤a<1/2, there are no oscillations, and the system monotonically approaches a steady state for all values of λ; in this region, we obtain an analytical solution for the stationary cluster size distribution. Numerical solutions of the rate equations show that oscillations emerge in the 1/2