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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…
The rules governing cell division and differentiation are central to understanding the mechanisms of development, aging and cancer. By utilising inducible genetic labelling, recent studies have shown that the clonal population in transgenic…
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…
We explore the role of cellular life cycles for viruses and host cells in an infection process. For this purpose, we derive a generalized version of the basic model of virus dynamics (Nowak, M.A., Bangham, C.R.M., 1996. Population dynamics…
The state of chromatin in individual cells is directly related to the state of the whole organism and may be used for assessment of the state of the whole organism. Many hereditary diseases are connected with chromatin rearrangements.…
Local stresses in a tissue, a collective property, regulate cell division and apoptosis. In turn, cell growth and division induce active stresses in the tissue. As a consequence, there is a feedback between cell growth and local stresses.…
Modelling, analysing and inferring triggering mechanisms in population reproduction is fundamental in many biological applications. It is also an active and growing research domain in mathematical biology. In this chapter, we review the…
Cells grown in culture act as a model system for analyzing the effects of anticancer compounds, which may affect cell behavior in a cell cycle position-dependent manner. Cell synchronization techniques have been generally employed to…
Active loop extrusion - the process of formation of dynamically growing chromatin loops due to the motor activity of DNA-binding protein complexes - is firmly established mechanism responsible for chromatin spatial organization at different…
This paper demonstrates a new regeneration processes technology making use of positive stable distributions. We study the asymptotic behavior of branching processes with a randomly controlled migration component. Using the new method, we…
A mathematical model of radiotherapy is proposed. The study used the classical 24 hours way of fractionation with a weekend pause. We introduce the matrices of ``radiotherapy'' and ``growth''. We developed an equation of the fraction cell…
The origin of allometric scaling of metabolic rate is a long-standing question in biology. Several models have been proposed for explaining the origin; however, they have advantages and disadvantages. In particular, previous models only…
The emergence of a predominant phenotype within a cell population is often triggered by a rare accumulation of DNA mutations in a single cell. For example, tumors may be initiated by a single cell in which multiple mutations cooperate to…
In this work, we investigate the population dynamics of tumor cells under therapeutic pressure. Although drug treatment initially induces a reduction in tumor burden, treatment failure frequently occurs over time due to the emergence of…
In this review, we discuss recent advances on the plasticity of cancer stem cells and highlight their relevance to understand the metastatic process and to guide therapeutic interventions. Recent results suggest that the strict hierarchical…
Genome replication, a key process for a cell, relies on stochastic initiation by replication origins, causing a variability of replication timing from cell to cell. While stochastic models of eukaryotic replication are widely available, the…
Faithful segregation of genetic material during cell division requires alignment of chromosomes between two spindle poles and attachment of their kinetochores to each of the poles. Failure of these complex dynamical processes leads to…
Various rod-shaped bacteria such as the canonical gram negative Escherichia coli or the well-studied gram positive Bacillus subtilis divide symmetrically after they approximately double their volume. Their size at division is not constant,…
A new approach to the modular, complex systems analysis of nonlinear dynamics in cell cycling network transformations involved in carcinogenesis is proposed. Carcinogenesis is a complex process that involves dynamically inter-connected…
Stem cell heterogeneity is essential for the homeostasis in tissue development. This paper established a general formulation for understanding the dynamics of stem cell regeneration with cell heterogeneity and random transitions of…