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Despite the importance of a thermodynamically stable structure with a conserved fold for protein function, almost all evolutionary models neglect site-site correlations that arise from physical interactions between neighboring amino acid…
Spherical stellar systems such as King models, in which the distribution function is a decreasing function of energy and depends on no other invariant, are stable in the sense of collisionless dynamics. But Weinberg showed, by a clever…
Statistical invariance of Wiener increments under SO(n) rotations provides a notion of gauge transformation of state-dependent Brownian motion. We show that the stochastic dynamics of non gauge-invariant systems is not unambiguously…
A generic model of a random polypeptide chain, with discrete torsional degrees of freedom and Hookean springs connecting pairs of hydrophobic residues, reproduces the energy probability distribution of real proteins over a very large range…
Protein-DNA interactions are crucial for all biological processes. One of the most important fundamental aspects of these interactions is the process of protein searching and recognizing specific binding sites on DNA. A large number of…
A central goal of protein-folding theory is to predict the stochastic dynamics of transition paths --- the rare trajectories that transit between the folded and unfolded ensembles --- using only thermodynamic information, such as a…
Gene products (RNAs, proteins) often occur at low molecular counts inside individual cells, and hence are subject to considerable random fluctuations (noise) in copy number over time. Not surprisingly, cells encode diverse regulatory…
This paper investigates steady state solutions of a vasculogenesis model governed by coupled partial differential equations in a bounded two dimensional domain. Explicit steady state solutions are analytically constructed, and their…
Flocculation is the process whereby particles (i.e., flocs) in suspension reversibly combine and separate. The process is widespread in soft matter and aerosol physics as well as environmental science and engineering. We consider a general…
A theoretical framework is developed to study the dynamics of protein folding. The key insight is that the search for the native protein conformation is influenced by the rate r at which external parameters, such as temperature, chemical…
In this paper, we study the dynamics of a system of $n$ coupled, self-propelled particles: $\ddot r_k = (\alpha-\beta |\dot r_k|^2)\dot r_k - \frac{\gamma}{n}\sum_{m=1}^n(r_k-r_m)$, $r_k\in \mathbb R^2.$ Numerical experiments indicate that,…
The aim of this review is to provide a concise overview of some of the generic approaches that have been developed to deal with the statistical description of large systems of interacting dissipative 'units'. The latter notion includes,…
We study the linear stability properties of spatially localized single- and multi-peak states generated in a subcritical Turing bifurcation in the Meinhardt model of branching. In one spatial dimension, these states are organized in a…
We use a three dimensional cubic lattice model of proteins to study their properties that determine folding to the native state. The protein chain is modeled as a sequence of $N$ beads. The interactions between beads are taken from a…
Cell polarization underlies many cellular processes, such as differentiation, migration, and budding. Many living cells, such as budding yeast and fission yeast, use cytoskeletal structures to actively transport proteins to one location on…
The observation of stacks of distinct layers in a colloidal or liquid mixture in sedimentation-diffusion equilibrium is a striking consequence of bulk phase separation. Drawing quantitative conclusions about the phase diagram is, however,…
We build on the concept of eigenvector continuation to develop an efficient multi-state method for the rigorous and smooth interpolation of a small training set of many-body wavefunctions through chemical space at mean-field cost. The…
We investigate the sequence-dependent properties of proteins that determine the dual requirements of stability of the native state and its kinetic accessibility using simple cubic lattice models. Three interaction schemes are used to…
We study existence, stability, and dynamics of linear and nonlinear stationary modes propagating in radially symmetric multi-core waveguides with balanced gain and loss. We demonstrate that, in general, the system can be reduced to an…
The importance of torsion vibration in the transmission of life information is indicated. The localization of quantum torsion state is proved. Following these analyses a formalism on the quantum theory of conformation-electron system is…