Related papers: Improvements in continuum modeling for biomolecula…
To maintain homeostasis, living cells process information with networks of interacting molecules. Traditional models for cellular information processing have focused on networks of chemical reactions between molecules. Here, we describe how…
The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying…
Ion transport through narrow channels is described by the coupled Poisson--Nernst--Planck--Stokes equations (PNPS) on a continuum scale. However, direct numerical simulations in two or three dimensions of boundary value problems for small…
In most natural sciences there is currently the insight that it is necessary to bridge gaps between different processes which can be observed on different scales. This is especially true in the field of chemical reactions where the…
The cell-model and its treatment on the Poisson-Boltzmann level are two important concepts in the theoretical description of charged macromolecules. In this brief contribution to the Proceedings of the NATO-ASI on ``Electrostatic Effects in…
Numerous cellular functions rely on protein$\unicode{x2013}$protein interactions. Efforts to comprehensively characterize them remain challenged however by the diversity of molecular recognition mechanisms employed within the proteome. Deep…
Mathematical methods provide useful framework for the analysis and design of complex systems. In newer contexts such as biology, however, there is a need to both adapt existing methods as well as to develop new ones. Using a combination of…
Machine learning potentials have emerged as a means to enhance the accuracy of biomolecular simulations. However, their application is constrained by the significant computational cost arising from the vast number of parameters compared to…
The evolution, regulation and sustenance of biological complexity is determined by protein-protein interaction network that is filled with dynamic events. Recent experimental evidences point out that clustering of proteins has a vital role…
Diffusion probabilistic models have made their way into a number of high-profile applications since their inception. In particular, there has been a wave of research into using diffusion models in the prediction and design of biomolecular…
Heterogeneous multiscale methods (HMM) combine molecular accuracy of particle-based simulations with the computational efficiency of continuum descriptions to model flow in soft matter liquids. In these schemes, molecular simulations…
Detailed modeling and simulation of biochemical systems is complicated by the problem of combinatorial complexity, an explosion in the number of species and reactions due to myriad protein-protein interactions and post-translational…
Systems biology models are useful models of complex biological systems that may require a large amount of experimental data to fit each model's parameters or to approximate a likelihood function. These models range from a few to thousands…
Posttranslational modifications (PTMs) are an integral component to how cells respond to perturbation. While experimental advances have enabled improved PTM identification capabilities, the same throughput for characterizing how structural…
This paper presents a model of coagulation in electrolyte solutions. In this paper, the coagulation process is modeled according to DLVO-theory, which is an atomistic theory. On the other hand, we describe the dynamics in the electrolyte…
Determining the different conformational states of a protein and the transition paths between them is key to fully understanding the relationship between biomolecular structure and function. This can be accomplished by sampling protein…
Composition is a powerful principle for systems biology, focused on the interfaces, interconnections, and orchestration of distributed processes to enable integrative multiscale simulations. Whereas traditional models focus on the structure…
In order to describe the dynamics of crowded ions (charged particles), we use an energetic variation approach to derive a modified Poisson-Nernst-Planck (PNP) system which includes an extra dissipation due to the effective velocity…
Dynamical systems modeling, particularly via systems of ordinary differential equations, has been used to effectively capture the temporal behavior of different biochemical components in signal transduction networks. Despite the recent…
Using the Poisson bracket method, we derive continuum equations for a fluid of deformable particles in two dimensions. Particle shape is quantified in terms of two continuum fields: an anisotropy density field that captures the deformations…