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Multiscale phenomena exhibit complex structure-function relationships, and predicting their macroscopic behavior requires deducing differential equations at different scales. The complexity of these equations and the number of essential…
Cancers are complex adaptive diseases regulated by the nonlinear feedback systems between genetic instabilities, environmental signals, cellular protein flows, and gene regulatory networks. Understanding the cybernetics of cancer requires…
The availability of cancer measurements over time enables the personalised assessment of tumour growth and therapeutic response dynamics. However, many tumours are treated after diagnosis without collecting longitudinal data, and cancer…
Tumor growth, which plays a central role in cancer evolution, depends on both the internal features of the cells, such as their ability for unlimited duplication, and the external conditions, e.g., supply of nutrients, as well as the…
Theoretical and computational tools that can be used in the clinic to predict neoplastic progression and propose individualized optimal treatment strategies to control cancer growth is desired. To develop such a predictive model, one must…
We discuss the mathematical modelling of two of the main mechanisms which pushed forward the emergence of multicellularity: phenotype divergence in cell differentiation, and between-cell cooperation. In line with the atavistic theory of…
How can tissues generate large numbers of cells, yet keep the divisional load (the number of divisions along cell lineages) low in order to curtail the accumulation of somatic mutations and reduce the risk of cancer? To answer the question…
Life systems are complex and hierarchical, with diverse components at different scales, yet they sustain themselves, grow, and evolve over time. How can a theory of such complex biological states be developed? Here we note that for a…
Many biological systems regulate phenotypic heterogeneity as a fitness-maximising strategy in uncertain and dynamic environments. Analysis of such strategies is typically confined both to a discrete set of environmental conditions, and to a…
The evolutionary and ecological dynamics of tumors under immune responses and therapeutic interventions pose major challenges to long-term treatment success. Although treatment may initially achieve short-term disease control, resistant…
Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can…
Cancer is a disease that takes millions of lives every year. Then, to propose treatments, avoid recurrence, and improve the patient's life quality, we need to analyze this disease from a biophysical perspective with a solid mathematical…
It is widely recognized that reciprocal interactions between cells and their microenvironment, via mechanical forces and biochemical signaling pathways, regulate cell behaviors during normal development, homeostasis and disease progression…
Populations of isogenic embryonic stem cells or clonal bacteria often exhibit extensive phenotypic heterogeneity which arises from stochastic intrinsic dynamics of cells. The internal state of the cell can be transmitted epigenetically in…
Since the discovery of a cancer initiating side population in solid tumours, studies focussing on the role of so-called cancer stem cells in cancer initiation and progression have abounded. The biological interrogation of these cells has…
In this article, we will see a new approach to study the impact of a small microscopic population of cancer cells on a macroscopic population of healthy cells, with an example inspired by pathological hematopoiesis. Hematopoiesis is the…
The collective chemotaxis of multicellular clusters is an important phenomenon in various physiological contexts, ranging from embryonic development to cancer metastasis. Such clusters often display interesting shape dynamics and…
Dynamics maintaining diversity of cell types in a multi-cellular system are studied in relationship with the plasticity of cellular states. First, we introduce a new theoretical framework, reaction-diffusion system on `chemical species…
Hierarchical Bayesian methods enable information sharing across multiple related regression problems. While standard practice is to model regression parameters (effects) as (1) exchangeable across datasets and (2) correlated to differing…
Phenotypic variation is a hallmark of cellular physiology. Metabolic heterogeneity, in particular, underpins single-cell phenomena such as microbial drug tolerance and growth variability. Much research has focussed on transcriptomic and…