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Neural mass models are used to simulate cortical dynamics and to explain the electrical and magnetic fields measured using electro- and magnetoencephalography. Simulations evince a complex phase-space structure for these kinds of models;…

Mathematical modeling in cancer has been growing in popularity and impact since its inception in 1932. The first theoretical mathematical modeling in cancer research was focused on understanding tumor growth laws and has grown to include…

Cell migration is essential for regulating many biological processes in physiological or pathological conditions, including embryonic development and cancer invasion. In vitro and in silico studies suggest that collective cell migration is…

During developmental processes such as embryogenesis, how a group of cells fold into specific structures, is a central question in biology that defines how living organisms form. Establishing tissue-level morphology critically relies on how…

The compartmental model is a basic tool for studying signal propagation in neurons, and, if the model parameters are adequately defined, it can also be of help in the study of electrical or fluid transport. Here we show that the input…

Motile biological cells in tissue often display the phenomenon of durotaxis, i.e. they tend to move towards stiffer parts of substrate tissue. The mechanism for this behavior is not completely understood. We consider simplified models for…

The behaviour of an organism often reflects a strategy for coping with its environment. Such behaviour in higher organisms can often be reduced to a few stereotyped modes of movement due to physiological limitations, but finding such modes…

Virus trafficking is fundamental for infection success and plasmid cytosolic trafficking is a key step of gene delivery. Based on the main physical properties of the cellular transport machinery such as microtubules, motor proteins, our…

Cancer progression and monotonic accumulation models were developed to discover dependencies in the irreversible acquisition of binary traits from cross-sectional data. They have been used in computational oncology and virology but also in…

Collective cell migration is a multicellular phenomenon that arises in various biological contexts, including cancer and embryo development. "Collectiveness" can be promoted by cell-cell interactions such as co-attraction and contact…

Many agent-based mathematical models of cranial neural crest cell (CNCC) migration impose a binary phenotypic partition of cells into either leaders or followers. In such models, the movement of leader cells at the front of collectives is…

Chemotactic cells establish cell polarity in the absence of external guidance cues. Such self-organized polarity is induced by spontaneous symmetry breaking in the intracellular activities, which produces an emergent memory effect…

A three-dimensional hydrodynamical model for a micro random walker is combined with the idea of chemotactic signaling network of E. coli. Diffusion exponents, orientational correlation functions and their dependence on the geometrical and…

Autologous chemotaxis, in which cells secrete and detect molecules to determine the direction of fluid flow, is thwarted at high cell density because molecules from other cells interfere with a given cell's signal. Using a minimal model of…

Eukaryotic cells can polarize and migrate in response to electric fields via "galvanotaxis," which aids wound healing. Experimental evidence suggests cells sense electric fields via molecules on the cell's surface redistributing via…

Malignant cancers that lead to fatal outcomes for patients may remain dormant for very long periods of time. Although individual mechanisms such as cellular dormancy, angiogenic dormancy and immunosurveillance have been proposed, a…

The migratory dynamics of cells can be influenced by the complex micro-environment through which they move. It remains unclear how the motility machinery of confined cells responds and adapts to their micro-environment. Here, we propose a…

A cellular bleb grows when a portion of the cell membrane detaches from the underlying cortex under the influence of a cytoplasmic pressure. We develop a quantitative model for the growth and dynamics of these objects in a simple…

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.…

Cell shape is an important biomarker that is directly linked to cell function. However, cell morphodynamics, namely the temporal fluctuation of cell shape is much less understood. We study the morphodynamics of MDA-MB-231 cells in type I…