Related papers: Mesoscopic and continuum modelling of angiogenesis
The space-time dynamics of rigid inhomogeneities (inclusions) free to move in a randomly fluctuating fluid bio-membrane is derived and numerically simulated as a function of the membrane shape changes. Both vertically placed (embedded)…
We present a stochastic model which describes fronts of cells invading a wound. In the model cells can move, proliferate, and experience cell-cell adhesion. We find several qualitatively different regimes of front motion and analyze the…
In these lecture notes, the basic principles of stochastic thermodynamics are developed starting with a closed system in contact with a heat bath. A trajectory undergoes Markovian transitions between observable meso-states that correspond…
Many cellular behaviors are regulated by gene regulation networks, kinetics of which is one of the main subjects in the study of systems biology. Because of the low number molecules in these reacting systems, stochastic effects are…
We consider the modeling of the dynamics of the chemostat at its very source. The chemostat is classically represented as a system of ordinary differential equations. Our goal is to establish a stochastic model that is valid at the scale…
We propose a simple discrete stochastic model for calcium dynamics in living cells. Specifically, the calcium concentration distribution is assumed to give rise to a set of probabilities for the opening/closing of channels which release…
A recently proposed single progenitor cell model for skin cell proliferation [Clayton et al., Nature v446, 185 (2007)] is extended to incorporate homeostasis as a fixed point of the dynamics. Unlimited cell proliferation in such a model can…
Epigenetic Tracking is a mathematical model of biological cells, originally conceived to study embryonic development. Computer simulations proved the capacity of the model to generate complex 3-dimensional cellular structures, and the…
Recent evidence suggests that nongenetic (epigenetic) mechanisms play an important role at all stages of cancer evolution. In many cancers, these mechanisms have been observed to induce dynamic switching between two or more cell states,…
Morphoelasticity represents a foundational theory for tracing back growth, remodelling, and morphogenesis, yet crucial challenges persist. A unified growth law -- independent of a priori assumptions about constitutive relations or specified…
While it is commonly observed that the shape dynamics of mammalian cells can undergo large random fluctuations, theoretical models aiming at capturing cell mechanics often focus on the deterministic part of the motion. In this paper, we…
Metabolic heterogeneity is widely recognised as the next challenge in our understanding of non-genetic variation. A growing body of evidence suggests that metabolic heterogeneity may result from the inherent stochasticity of intracellular…
During angiogenesis, new blood vessels headed by a migrating endothelial tip cell sprout from pre-existing ones. This process is known to be regulated by two signaling pathways concurrently, vascular endothelial growth factor A (VEGFA) and…
The formation and regulation of macromolecular complexes provides the backbone of most cellular processes, including gene regulation and signal transduction. The inherent complexity of assembling macromolecular structures makes current…
The mesoscopic concept is a way to deal with complex materials with an internal structure within continuum mechanics. It consists of extending the domain of the balance equations by mesoscopic variables and of introducing a local…
Mathematical models of biological neural networks are associated to a rich and complex class of stochastic processes. In this paper, we consider a simple {\em plastic} neural network whose {\em connectivity/synaptic strength} $(W(t))$…
Adhesion between cells plays an important role in many biological processes such as tissue morphogenesis and homeostasis, wound healing and cancer cell metastasis. From a mathematical perspective, adhesion between multiple cell types has…
The deformation and flow of disordered solids, such as metallic glasses and concentrated emulsions, involves swift localized rearrangements of particles that induce a long-range deformation field. To describe these heterogeneous processes,…
Nucleation, commonly associated with discontinuous transformations between metastable and stable phases, is crucial in fields as diverse as atmospheric science and nanoscale electronics. Traditionally, it is considered a microscopic process…
We propose a suite of technologies for analyzing the interaction between anisotropic arterial walls and blood flow for subject-specific geometries. Utilizing an established lumen modeling strategy, we present a comprehensive pipeline for…