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In this article we shall trace the historical development of tumour growth laws, which in a quantitative fashion describe the increase in tumour mass/volume over time. These models are usually formulated in terms of differential equations…
Cell competition is a quality control mechanism in tissues that results in the elimination of less fit cells. Over the past decade, the phenomenon of cell competition has been identified in many physiological and pathological contexts,…
We aim to understand the evolution of the genetic composition of cancer cell populations. To achieve this, we consider an individual-based model representing a cell population where cells divide, die and mutate along the edges of a finite…
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…
Background. A large number of algorithms is being developed to reconstruct evolutionary models of individual tumours from genome sequencing data. Most methods can analyze multiple samples collected either through bulk multi-region…
The pathogenesis of cancer in human is still poorly understood. With the rapid development of high-throughput sequencing technologies, huge volumes of cancer genomics data have been generated. Deciphering those data poses great…
Cancer is a complex disease driven by dynamic regulatory shifts that cannot be fully captured by individual molecular profiling. We employ a data-driven approach to construct a coarse-grained dynamic network model based on hallmark…
Evolutionary branching is analysed in a stochastic, individual-based population model under mutation and selection. In such models, the common assumption is that individual reproduction and life career are characterised by values of a…
Cancer is viewed as a multistep process whereby a normal cell is transformed into a cancer cell through the acquisition of mutations. We reduce the complexities of cancer progression to a simple set of underlying rules that govern the…
The spread of an advantageous mutation through a population is of fundamental interest in population genetics. While the classical Moran model is formulated for a well-mixed population, it has long been recognized that in real-world…
The problem of the onset and growth of solid tumour in homogeneous tissue is regarded using an approach based on local interaction between the tumoral and the sane tissue cells. The characteristic sizes and growth rates of spherical…
Advances in single-cell omics allow for unprecedented insights into the transcription profiles of individual cells. When combined with large-scale perturbation screens, through which specific biological mechanisms can be targeted, these…
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…
The migratory dynamics of cells in physiological processes, ranging from wound healing to cancer metastasis, rely on contact-mediated cell-cell interactions. These interactions play a key role in shaping the stochastic trajectories of…
Cancer progression is an evolutionary process that is driven by mutation and selection in a population of tumor cells. We discuss mathematical models of cancer progression, starting from traditional multistage theory. Each stage is…
We investigate the dynamics of cancer initiation in a mathematical model with one driver mutation and several passenger mutations. Our analysis is based on a multi type branching process: We model individual cells which can either divide or…
Stochastic dynamics govern many important processes in cellular biology, and an underlying theoretical approach describing these dynamics is desirable to address a wealth of questions in biology and medicine. Mathematical tools exist for…
The evolution of various competing cell types in tissues, and the resulting persistent tissue population, is studied numerically and analytically in a particle-based model of active tissues. Mutations change the properties of cells in…
Electronic properties of DNA are believed to play a crucial role in many phenomena in living organisms, for example the location of DNA lesions by base excision repair (BER) glycosylases and the regulation of tumor-suppressor genes such as…
First, we revisit the stochastic Luria-Delbr\"uck model: a classic two-type branching process which describes cell proliferation and mutation. We prove limit theorems and exact results for the mutation times, clone sizes, and number of…