Related papers: Protein Unfolding and the Diffusion Collision Mode…
We present a multiscale approach to model diffusion in a crowded environment and its effect on the reaction rates. Diffusion in biological systems is often modeled by a discrete space jump process in order to capture the inherent noise of…
A general theoretical framework is developed using free energy functional methods to understand the effects of heterogeneity in the folding of a well-designed protein. Native energetic heterogeneity arising from non-uniformity in native…
We consider the problem of simulating diffusion bridges, which are diffusion processes that are conditioned to initialize and terminate at two given states. The simulation of diffusion bridges has applications in diverse scientific fields…
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…
A phase space coalescence description based on the Wigner-function method for cluster formation in relativistic nucleus-nucleus collisions is presented. The momentum distributions of nuclear clusters d,t and He are predicted for central…
Understanding how monomeric proteins fold under in vitro conditions is crucial to describing their functions in the cellular context. Significant advances both in theory and experiments have resulted in a conceptual framework for describing…
In this paper, we propose a tumor growth model to incorporate and investigate the spatial effects of autophagy. The cells are classified into two phases: normal cells and autophagic cells, whose dynamics are also coupled with the nutrients.…
The fusion of two interacting heavy ions traditionally has been interpreted in terms of the penetration of the projectile into the target. Observed rates well below the Coulomb barrier are considerably lower than estimates obtained from…
In this paper, we mathematically describe the time evolution of protein folding features via Iori et al.'s heteropolymer model. More specifically, we identify that the folding amino acid chain evolve according to a power law $D \sim…
Kramer's approach to the rate of the thermally activated escape from a metastable state is extended to field theory. Diffusion rate in the 1+1-dimensional Sine-Gordon model as a function of temperature and friction coefficient is evaluated…
Accurate estimation of mutational effects on protein-protein binding energies is an open problem with applications in structural biology and therapeutic design. Several deep learning predictors for this task have been proposed, but,…
In structure-based models of proteins, one often assumes that folding is accomplished when all contacts are established. This assumption may frequently lead to a conceptual problem that folding takes place in a temperature region of very…
We introduce a simplified protein model where the water degrees of freedom appear explicitly (although in an extremely simplified fashion). Using this model we are able to recover both the warm and the cold protein denaturation within a…
The present work deals with the derivation of corrector estimates for the two-scale homogenization of a thermo-diffusion model with weak thermal coupling posed in a heterogeneous medium endowed with periodically arranged high-contrast…
We study traveling fronts in a system of one dimensional reaction-diffusion-advection equations motivated by problems in reactive flows. In the limit as a parameter tends to infinity, we construct the approximate front profile and determine…
We point out that the correlation between folding times and $\sigma = (T_{\theta } - T_{f})/T_{\theta }$ in protein-like heteropolymer models where $T_{\theta }$ and $T_{f}$ are the collapse and folding transition temperatures was already…
In this paper we introduce a novel method of deriving a pairwise potential for protein folding. The potential is obtained by optimization procedure, which simultaneously maximizes the energy gap for {\it all} proteins in the database. To…
Generative modeling has recently undergone remarkable advancements, primarily propelled by the transformative implications of Diffusion Probabilistic Models (DPMs). The impressive capability of these models, however, often entails…
Different aspects of protein folding are illustrated by simplified polymer models. Stressing the diversity of side chains (residues) leads one to view folding as the freezing transition of an heteropolymer. Technically, the most common…
The dissipation rate due to inelastic collisions between equally charged, insulating particles in a granular gas is calculated. It is equal to the known dissipation rate for uncharged granular media multiplied by a Boltzmann-like factor,…