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We consider reversible breaking of adhesion bonds or folding of proteins under the influence of a constant external force. We discuss the stochastic properties of the unbinding/rebinding events and analyze their mean number and their…
We derive exact solutions of simplified models for the temporal evolution of the protein concentration within a cell population arbitrarily far from the stationary state. We show that monitoring the dynamics can assist in modeling and…
Protein molecules in cells are synthesized by macromolecular machines called ribosomes. According to recent experimental data, we reduce the complexity of the ribosome and propose a model to express its activity in six main states. Using…
In this paper, we proposed a stochastic model which describes two species of particles moving in counterflow. The model generalizes the theoretical framework describing the transport in random systems since particles can work as mobile…
Many aspects of the study of protein folding and dynamics have been affected by the recent advances in machine learning. Methods for the prediction of protein structures from their sequences are now heavily based on machine learning tools.…
Increasing evidence suggests that chromosome folding and genetic expression are intimately connected. For example, the co-expression of a large number of genes can benefit from their spatial co-localization in the cellular space.…
Understanding protein solubility is essential for their functional applications. Computational methods for predicting protein solubility are crucial for reducing experimental costs and enhancing the efficiency and success rates of protein…
We investigate a diffusion process in heterogeneous media where particles stochastically reset to their initial positions at a constant rate. The heterogeneous media is modeled using a spatial-dependent diffusion coefficient with a…
We introduce a mathematical model for ultrasound modulated optical tomography and present a simple reconstruction scheme for recovering the spatially varying optical absorption coefficient from scanning measurements with narrowly focused…
Enzyme engineering enables the modification of wild-type proteins to meet industrial and research demands by enhancing catalytic activity, stability, binding affinities, and other properties. The emergence of deep learning methods for…
A computational method is developed to work on an inverse equilibrium problem with an interest towards applications with protein folding. In general, we are given a set of equilibrium confgiurations and want to derive the most probable…
In recent years, there has been a surge in the development of 3D structure-based pre-trained protein models, representing a significant advancement over pre-trained protein language models in various downstream tasks. However, most existing…
Molecular motion through pores plays a crucial role in various natural and industrial processes. One of the most fascinating features of biological channel-facilitated transport is a stochastic gating process, when the channels dynamically…
The inverse problem of backward diffusion is known to be ill-posed and highly unstable. Backward diffusion processes appear naturally in image enhancement and deblurring applications. It is therefore greatly desirable to establish a…
The mathematical formulation of the model for molecular movement of single motor proteins driven by cyclic biochemical reactions in an aqueous environment leads to a drifted Brownian motion characterized by coupled diffusion equations. In…
Snapshot matrices built from solutions to hyperbolic partial differential equations exhibit slow decay in singular values, whereas fast decay is crucial for the success of projection- based model reduction methods. To overcome this problem,…
The motion involved in barrier crossing for protein folding are investigated in terms of the chain dynamics of the polymer backbone, completing the microscopic description of protein folding presented in the previous paper. Local reaction…
Inverse protein folding is a fundamental task in computational protein design, which aims to design protein sequences that fold into the desired backbone structures. While the development of machine learning algorithms for this task has…
We develop a systems approach based on an energy-landscape concept to differentiate interactions involving redox activities and conformational changes of proteins and nucleic acids interactions in multi-layered protein-DNA regulatory…
A recent experiment [Sadoon AA, Wang Y. 2018 Phys. Rev. E 98, 042411] has revealed that nucleoid associated proteins (i.e., DNA-binding proteins) exhibit highly heterogeneous diffusion processes in bacteria where not only the diffusion…