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This article reviews the mechanical bidomain model, a mathematical description how the extracellular matrix and intracellular cytoskeleton are coupled by integrin proteins. The fundamental hypothesis is that differences between…
Diffusion of a particle passing over the saddle point of a two-dimensional quadratic potential is studied via a set of coupled Langevin equations and the expression for the passing probability is obtained exactly. The passing probability is…
Consider a network embedded in the 2D plane, where a particle diffuses along the edges of the network. It is clear that over short length scales a particle moves along a single edge and thus undergoes one-dimensional diffusion. However, on…
Polymer translocation is a promising strategy for the next-generation DNA sequencing technologies. The use of biological and synthetic nano-pores, however, still suffers from serious drawbacks. In particular, the width of the membrane layer…
A multiscale approach is used to simulate the translocation of DNA through a nanopore. Within this scheme, the interactions of the molecule with the surrounding fluid (solvent) are explicitly taken into account. By generating polymers of…
The effect of multiple scatterings on the propagation of hard partonic jets in a dense nuclear medium is studied in the framework of deep-inelastic scattering (DIS) off a large nucleus. Power counting arguments based on the Glauber improved…
In many biological systems, the movement of individual agents is commonly characterized as having multiple qualitatively distinct behaviors that arise from various biophysical states. This is true for vesicles in intracellular transport,…
The function of protein, RNA, and DNA is modulated by fast, dynamic exchanges between three-dimensional conformations. Conformational sampling of biomolecules with exact and nullspace inverse kinematics, using rotatable bonds as revolute…
Particles with ligand-receptor contacts bind and unbind fluctuating "legs" to surfaces, whose fluctuations cause the particle to diffuse. Quantifying the diffusion of such "nanoscale caterpillars" is a challenge, since binding events often…
We investigate the obstructed motion of tracer (test) particles in crowded environments by carrying simulations of two-dimensional Gaussian random walk in model fibrinogen monolayers of different orientational ordering. The fibrinogen…
The movement of organisms and cells can be governed by occasional long distance runs, according to an approximate L\'evy walk. For T cells migrating through chronically-infected brain tissue, runs are further interrupted by long pauses, and…
Recent advancements in diffusion models have revolutionized generative modeling. However, the impressive and vivid outputs they produce often come at the cost of significant model scaling and increased computational demands. Consequently,…
The problem of the time required for a diffusing molecule, within a large bounded domain, to first locate a small target is prevalent in biological modeling. Here we study this problem for a small spherical target. We develop uniform in…
Personalized retrieval and segmentation aim to locate specific instances within a dataset based on an input image and a short description of the reference instance. While supervised methods are effective, they require extensive labeled data…
In this paper a lattice model for the diffusional transport of particles in the interphase cell nucleus is proposed. The dynamic behaviour of single chains on the lattice is investigated and Rouse scaling is verified. Dynamical dense…
Score-based diffusion models have demonstrated remarkable empirical success in learning high-dimensional distributions, particularly those exhibiting low-dimensional and multi-modal structures. However, theoretical understanding of their…
Deploying off-the-shelf segmentation networks on biomedical data has become common practice, yet if structures of interest in an image sequence are visible only temporarily, existing frame-by-frame methods fail. In this paper, we provide a…
Measurements of electron transfer rates as well as of charge transport characteristics in DNA produced a number of seemingly contradictory results, ranging from insulating behaviour to the suggestion that DNA is an efficient medium for…
Diffusion models have demonstrated strong generative capabilities across domains ranging from image synthesis to complex reasoning tasks. However, most inference-time scaling methods rely on fixed denoising schedules, limiting their ability…
The mean time required by a transcription factor (TF) or an enzyme to find a target in the nucleus is of prime importance for the initialization of transcription, gene activation or the start of DNA repair. We obtain new estimates for the…