arXiv subjects
Publications and source records attributed to Jayanth R. Banavar.
We present the results of a self-consistent, unified molecular dynamics study of simple model heteropolymers in the continuum with emphasis on folding, sequence design and the determination of the interaction parameters of the effective potential between the amino acids from the knowledge of the native states of the designed sequences.
When a mixture of two viscous liquids flows past a solid wall there is an ambiguity in the use of the no-slip boundary condition. It is not obvious whether the mass-averaged velocity, the volume-averaged velocity, the individual species velocities, all or none of the above, or none of the above should exhibit no-slip. Extensive molecular dynamics simulations of the Poiseuille flow of mixtures of coexisting liquid species past an atomistic wall indicate that the velocity of each individual liquid species satisfies the no-slip condition and, therefore, so do mass and volume averages.
A simple lattice model for proteins that allows for distinct sizes of the amino acids is presented. The model is found to lead to a significant number of conformations that are the unique ground state of one or more sequences or encodable. Furthermore, several of the encodable structures are highly designable and are the non-degenerate ground state of several sequences. Even though the native state conformations are typically compact, not all compact conformations are encodable. The incorporation of the hydrophobic and polar nature of amino acids further enhances the attractive features of the model.
The exact determination of ground states of small systems is used in a scaling study of the random-field Ising model. While three variants of the model are found to be in the same universality class in 3 dimensions, the Gaussian and bimodal models behave distinctly in 4 dimensions with the latter apparently having a discontinuous jump in the magnetization. A finite-size scaling analysis is presented for this transition.
The sensitivity of the native states of protein-like heteropolymers to mutations modelled as perturbations in the interaction potential between amino acids is studied. The stability threshold against mutations is shown to be zero for random heteropolymers on a lattice in two dimensions, whereas a design procedure modelling evolution produces a non-zero threshold. We introduce an evolution-like protein design procedure based on an optimization of the stability threshold that is shown to naturally ensure thermodynamic stability as well.
The relation between a recently introduced dynamical real space renormalization group and the fluctuation-dissipation theorem is discussed. An apparent incompatibility is pointed out and resolved.
The effects of erosion, avalanching and random precipitation are captured in a simple stochastic partial differential equation for modelling the evolution of river networks. Our model leads to a self-organized structured landscape and to abstraction and piracy of the smaller tributaries as the evolution proceeds. An algebraic distribution of the average basin areas and a power law relationship between the drainage basin area and the river length are found.
A novel exact dynamical real space renormalization group for a Langevin equation derivable from a Euclidean Gaussian action is presented. It is demonstrated rigorously that an algebraic temporal law holds for the Green function on arbitrary structures of infinite extent. In the case of fractals it is shown on specific examples that two different fixed points are found at variance with periodic structures. Connection with growth dynamics of interfaces is also discussed.