Related papers: Mathematical models for cell migration: a nonlocal…
Intracellular transport processes are essential to the healthy development of many organisms as well as more generally to healthy cellular function. The complex dynamics and interactions between protein molecules and filaments on different…
The main purpose of this work is the mathematical modelling of large populations of cells under different deterministic interactions among themselves, in balance with naturally random diffusion. We focus on cell-cell adhesion mechanisms for…
Recent biological experiments have shown that certain types of cells are able to move in structured and confined environment even without the activation of focal adhesion. Focusing on this particular phenomenon and based on previous works,…
Cells perform directed motion in response to external stimuli that they detect by sensing the environment with their membrane protrusions. In particular, several biochemical and biophysical cues give rise to tactic migration in the…
Cell-cell adhesion is widely hypothesised to maintain cohesion within the long streams of follower cells that trail leader subpopulations during collective migration, including in neural crest cell migration, angiogenesis, and cancer cell…
Computational modeling of cancer can help unveil dynamics and interactions that are hard to replicate experimentally. Thanks to the advancement in cancer databases and data analysis technologies, these models have become more robust than…
Cell proliferation and cell movement are fundamentally stochastic processes which lead to variability in the growth and spatial structure of cell populations in many biological settings, such as cell invasion, wound healing, and tumour…
This paper provides a unified mathematical analysis of a family of non-local diffuse interface models for tumor growth describing evolutions driven by long-range interactions. These integro-partial differential equations model cell-to-cell…
Populations are heterogeneous, deviating in numerous ways. Phenotypic diversity refers to the range of traits or characteristics across a population, where for cells this could be the levels of signalling, movement and growth activity, etc.…
The inclusion of cognitive processes, such as perception, learning and memory, are inevitable in mechanistic animal movement modelling. Cognition is the unique feature that distinguishes animal movement from mere particle movement in…
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…
We give a very short introduction to discrete and continuum models for the evolutionary and spatial dynamics of cancer through two case studies: a model for the evolutionary dynamics of cancer cells under cytotoxic therapy and a model for…
This paper concerns a model for tumor cell migration through the surrounding extracellular matrix by considering mass balance phenomena involving the chemical interactions produced on the cell surface. The well-posedness of this model is…
Self-organisation of individuals within large collectives occurs throughout biology. Mathematical models can help elucidate the individual-level mechanisms behind these dynamics, but analytical tractability often comes at the cost of…
In this survey article, a variety of systems modeling tumor growth are discussed. In accordance with the hallmarks of cancer, the described models incorporate the primary characteristics of cancer evolution. Specifically, we focus on…
We introduce a generic, purely mechanical model for environment sensitive motion of mammalian cells that is applicable to chemotaxis, haptotaxis, and durotaxis as modes of motility. It is able to theoretically explain all relevant…
We propose a non-local model for contact guidance and steric hindrance depending on a single external cue, namely the extracellular matrix, that affects in a twofold way the polarization and speed of motion of the cells. We start from a…
Mathematical models are vital interpretive and predictive tools used to assist in the understanding of cell migration. There are typically two approaches to modelling cell migration: either micro-scale, discrete or macro-scale, continuum.…
In this paper we develop mathematical models for collective cell motility. Initially we develop a model using a linear diffusion-advection type equation and fit the parameters to data from cell motility assays. This approach is helpful in…
Cells crawling through tissues migrate inside a complex fibrous environment called the extracellular matrix (ECM), which provides signals regulating motility. Here we investigate one such well-known pathway, involving mutually antagonistic…