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Computational chemistry allows researchers to experiment in sillico: by running a computer simulations of a biological or chemical processes of interest. Molecular dynamics with molecular mechanics model of interactions simulates N-body…
In mesh-based numerical simulations, sweep is an important computation pattern. During sweeping a mesh, computations on cells are strictly ordered by data dependencies in given directions. Due to such a serial order, parallelizing sweep is…
All simulation approaches eventually face limits in computational scalability when applied to large spatiotemporal domains. This challenge becomes especially apparent in molecular-level particle simulations, where high spatial and temporal…
Our long term goal is to execute General Purpose computation on homogeneous computing media consisting of millions of small identical Processing Elements (PE) communicating locally. We proceed by simulating the Self-Development of a Network…
In experiments on model membranes, a formation of large domains of different lipid composition is readily observed. However, no such phase separation is observed in the membranes of intact cells. Instead, a structure of small transient…
The dynamic interplay between collective cell movement and the various molecules involved in the accompanying cell signalling mechanisms plays a crucial role in many biological processes including normal tissue development and pathological…
Cell plasma membranes display a dramatically rich structural complexity characterized by functional sub-wavelength domains with specific lipid and protein composition. Under favorable experimental conditions, patterned morphologies can also…
Modeling membrane interactions with arbitrarily shaped colloidal particles, such as environmental micro- and nanoplastics, at the cell scale remains particularly challenging, owing to the complexity of particle geometries and the need to…
Lipid membranes are abundant in living organisms, where they constitute a surrounding shell for cells and their organelles. There are many circumstances in which the deformations of lipid membranes are involved in living cells: fusion and…
Computational meshes, as a way to partition space, form the basis of much of PDE simulation technology, for instance for the finite element and finite volume discretization methods. In complex simulations, we are often driven to modify an…
Since its foundations, more than one hundred years ago, the field of structural biology has strived to understand and analyze the properties of molecules and their interactions by studying the structure that they take in 3D space. However,…
Membrane phase-separation is a mechanism that biological membranes often use to locally concentrate specific lipid species in order to organize diverse membrane processes. Phase separation has also been explored as a tool for the design of…
Membranes are present in all cells and tissues. Mathematical models of cells and tissues need a compact mathematical description of membranes with a resolution of about 1 nm. Membranes isolate cells because ions have difficulty penetrating…
Spherical symmetry is ubiquitous in nature. It's therefore unfortunate that spherical system simulations are so hard, and require complete spheres with millions of interacting particles. Here we introduce an approach to model spherical…
A model of multicellular systems with several types of cells is developed from the phase field model. The model is presented as a set of partial differential equations of the field variables, each of which expresses the shape of one cell.…
Lipid membranes and membrane deformations are a long-standing area of research in soft matter and biophysics. Computer simulations have complemented analytical and experimental approaches as one of the pillars in the field. However, setting…
Animal cells are both encapsulated and subdivided by lipid bilayer membranes. Beyond just acting as boundaries, these membranes' shapes influence the function of cells and their compartments. Physically, membranes are two-dimensional fluids…
A variety of models for the membrane-mediated interaction of particles in lipid membranes, mostly well-established in theoretical physics, is reviewed from a mathematical perspective. We provide mathematically consistent formulations in a…
The operations drip and mate considered in (mem)brane computing resemble the operations cut and recombination well known from DNA computing. We here consider sets of vesicles with multisets of objects on their outside membrane interacting…
A mechanical model and numerical method for structural membranes implied by all isosurfaces of a level-set function in a three-dimensional bulk domain are proposed. The mechanical model covers large displacements in the context of the…