Related papers: A bulk-surface reaction-diffusion system for cell …
Many reaction-diffusion models produce travelling wave solutions that can be interpreted as waves of invasion in biological scenarios such as wound healing or tumour growth. These partial differential equation models have since been adapted…
Cell adhesion proteins are transmembrane proteins that bind cells to their environment. These proteins typically cluster into disk-shaped or linear structures. Here we show that such clustering patterns spontaneously emerge when the protein…
The self-organization of proteins into enriched compartments and the formation of complex patterns are crucial processes for life on the cellular level. Liquid-liquid phase separation is one mechanism for forming such enriched compartments.…
The response of a model micro-electrochemical system to a time-dependent applied voltage is analyzed. The article begins with a fresh historical review including electrochemistry, colloidal science, and microfluidics. The model problem…
The role of polarization in the topology of quantum emitter chains is investigated theoretically, whereby "polarization" refers to the transition dipole moments of the emitters. We show that, if the chain is zigzag-shaped, different…
Positive feedback regulation is ubiquitous in cell signaling networks, often leading to binary outcomes in response to graded stimuli. However, the role of such feedbacks in clustering, and in spatial spreading of activated molecules, has…
Blebs are cell protrusions generated by local membrane-cortex detachments followed by expansion of the plasma membrane. Blebs are formed by some migrating cells, for example primordial germ cells of the zebrafish. While blebs occur randomly…
We derive the boundary condition for a subdiffusive particle interacting with a reactive boundary with finite reaction rate. Molecular crowding conditions, that are found to cause subdiffusion of larger molecules in biological cells, are…
We consider a system of two reaction-diffusion-advection equations describing the one dimensional directed motion of particles with superimposed diffusion and mutual alignment. For this system we show the existence of traveling wave…
Planar cell polarity (PCP), the coherent in-plane polarization of a tissue on multicellular length scales, provides directional information that guides a multitude of developmental processes at cellular and tissue levels. While it is…
Morphological change of bilayer membrane in vivo is not a spontaneous procedure but modulated by various types of proteins in general. Most of these modulations are associated with the localization of related proteins in the crowded lipid…
We propose a boundary element method for the accurate solution of the cell-by-cell bidomain model of electrophysiology. The cell-by-cell model, also called Extracellular-Membrane-Intracellular (EMI) model, is a system of reaction-diffusion…
In this paper we consider the diffusion of nanoparticles taken up by a semi-permeable spherical cell placed in the path of a diffusive particle field generated by an external planar source. The cell interior and exterior are characterized…
We analyze a class of cell-bulk coupled PDE-ODE models, motivated by quorum and diffusion sensing phenomena in microbial systems, that characterize communication between localized spatially segregated dynamically active signaling…
Model of biological effects of ionizing particles, especially of protons and other ions, is proposed. The model is based on distinguishing the single-particle and collective effects of the underlying radiobiological mechanism. The…
In this paper, we provide well-posedness results for nonlinear parabolic PDEs given by reaction-diffusion equations describing the concentration of oxygen in encapsulated cells. The cells are described in terms of a core and a shell, which…
GTPase molecules are important regulators in cells that continuously run through an activation/deactivation and membrane-attachment/membrane-detachment cycle. Activated GTPase is able to localize in parts of the membranes and to induce cell…
Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…
We prove the existence of solutions of a cross-diffusion parabolic population problem. The system of partial differential equations is deduced as the limit equations satisfied by the densities corresponding to an interacting particles…
Biological, physical, medical, and numerical applications involving membrane problems on different scales are numerous. We propose an extension of the standard Turing theory to the case of two domains separated by a permeable membrane. To…