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A fundamental issue discussed in evolutionary biology is the transition from unicellular to multicellular organisms. Here we develop non-robust models provided in [1] and attempt to get robust models investigated how differentiation of…
Do biological cells sense time by the number of their divisions, a process that ends at senescence? We consider the question "can the cell's perception of time be expressed through the length of the shortest telomere?" The answer is that…
The rate at which individual bacterial cells grow depends on the concentrations of cellular components such as ribosomes and proteins. These concentrations continuously fluctuate over time and are inherited from mother to daughter cells,…
The reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or die out. Thresholds for disease extinction contribute crucial knowledge on disease control, elimination, and mitigation…
Resource Balance Analysis (RBA) is a framework for predicting steady-state cellular growth under resource constraints. However, classical RBA formulations are static and do not capture the dynamic regulation of biosynthetic resources or…
This chapter is an overview of foundational results in the mathematical theory of replicator systems. Its primary aim is to provide a unified framework for the mathematical formalisation of evolutionary processes in the spirit of…
Stem cell regeneration is a crucial biological process for most self-renewing tissues during the development and maintenance of tissue homeostasis. In developing the mathematical models of stem cell regeneration and tissue development, cell…
We propose a two-component reaction-transport model for the migration-proliferation dichotomy in the spreading of tumor cells. By using a continuous time random walk (CTRW) we formulate a system of the balance equations for the cancer cells…
Optimization-based models have been used to predict cellular behavior for over 25 years. The constraints in these models are derived from genome annotations, measured macro-molecular composition of cells, and by measuring the cell's growth…
We present a statistical analysis of biological evolution processes. Specifically, we study the stochastic replication-mutation-death model where the population of a species may grow or shrink by birth or death, respectively, and…
We consider the Wright-Fisher model for a population of $N$ individuals, each identified with a sequence of a finite number of sites, and single-crossover recombination between them. We trace back the ancestry of single individuals from the…
A sufficiently advanced extraterrestrial civilization can send out a swarm of self-replicating probes for space exploration. Given the fast-growing number of such a probe, even if there is only one extraterrestrial civilization sending out…
We present a three-stage probabilistic model for the progression of Chronic Myeloid Leukemia (CML), as manifested by the leukemic stem cells, progenitor cells and mature leukemic cells. This progression is captured through the process of…
Ecology and evolution under changing environments are important in many subfields of biology with implications for medicine. Here, we explore an example: the consequences of fluctuating environments on the emergence of antibiotic…
We study a branching random walk on $\r$ with an absorbing barrier. The position of the barrier depends on the generation. In each generation, only the individuals born below the barrier survive and reproduce. Given a reproduction law,…
Competitive birth-death processes often exhibit an oscillatory behavior. We investigate a particular case where the oscillation cycles are marginally stable on the mean-field level. An iconic example of such a system is the Lotka-Volterra…
The self-organization of cells into complex tissues relies on a tight coordination of cell behavior. Identifying the cellular processes driving tissue growth is key to understanding the emergence of tissue forms and devising targeted…
The discovery of two fundamental laws concerning cellular dynamics with recursive growth is reported. First, the chemical abundances measured over many cells are found to obey a log-normal distribution and second, the relationship between…
A model of mutation rate evolution for multiple loci under arbitrary selection is analyzed. Results are obtained using techniques from Karlin (1982) that overcome the weak selection constraints needed for tractability in prior studies of…
A dynamic model for cell differentiation is studied, where cells with internal chemical reaction dynamics interact with each other and replicate. It leads to spontaneous differentiation of cells and determination, as is discussed in the…