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The proper functioning of multicellular organisms requires the robust establishment of precise proportions between distinct cell-types. This developmental differentiation process typically involves intracellular regulatory and stochastic…
Cancer, as the uncontrollable cell growth, is related to many branches of biology. In this review, we will discuss three mathematical approaches for studying cancer biology: population dynamics, gene regulation, and developmental biology.…
We investigate a model of cell division in which the length of telomeres within the cell regulate their proliferative potential. At each cell division the ends of linear chromosomes change and a cell becomes senescent when one or more of…
Mathematical and computational models can assist in gaining an understanding of cell behavior at many levels of organization. Here, we review models in the literature that focus on eukaryotic cell motility at 3 size scales: intracellular…
According to the universally accepted concept of the development of life on the Earth, multicellular organisms initially emerged as a result of either the union of identical unicellular organisms with the following functional…
During development, spatio-temporal patterns ranging from checkerboard to engulfing occur with precise proportions of the respective cell fates. Key developmental regulators are intracellular transcriptional interactions and intercellular…
Uncovering the quantitative laws that govern the growth and division of single cells remains a major challenge. Using a unique combination of technologies that yields unprecedented statistical precision, we find that the sizes of individual…
Boolean network models of strongly connected modules are capable of capturing the high regulatory complexity of many biological gene regulatory circuits. We study numerically the previously introduced basin entropy, a parameter for the…
Viral infectious diseases, such as HIV virus growth, cause an important health concern. Study of intracellular viral processes can provide us to develop drug and understanding the drug dose to decrease the HIV virus in during growth.…
The concept of entropy in nonequilibrium macroscopic systems is investigated in the light of an extended equation of motion for the density matrix obtained in a previous study. It is found that a time-dependent information entropy can be…
Entropy is a very useful concept from physics that tries to explain how a system behaves from a point of view of the thermodynamics. However, there are two ways to explain entropy, and it depends on if we are studying a microsystem or a…
In this work we develop and analyze a mathematical model of biological control to prevent or attenuate the explosive increase of an invasive species population in a three-species food chain. We allow for finite time blow-up in the model as…
Recent experiments have been able to visualise chromosome organization in fast-growing E.coli cells. However, the mechanism underlying the spatio-temporal organization remains poorly understood. We propose that the DNA adopts a specific…
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 order to survive, reproduce and (in multicellular organisms) differentiate, cells must control the concentrations of the myriad different proteins that are encoded in the genome. The precision of this control is limited by the inevitable…
Cell division is an essential biological process, and regulation of cell division is of relevance for many important fields of biology and medicine. Introducing exogenous substances, such as nanoparticles, into the nucleus, has been…
Cells employ control strategies to maintain a stable size. Dividing at a target size (the `sizer' strategy) is thought to produce the tightest size distribution. However, this result follows from phenomenological models that ignore the…
The outstanding problem of controlling complex networks is relevant to many areas of science and engineering, and has the potential to generate technological breakthroughs as well. We address the physically important issue of the energy…
The expansion of biological species in natural environments is usually described as the combined effect of individual spatial dispersal and growth. In the case of aquatic ecosystems flow transport can also be extremely relevant as an extra,…
We study the classification of cellular-automaton update rules into Wolfram's four classes. We start with the notion of the input entropy of a spatiotemporal block in the evolution of a cellular automaton, and build on it by introducing two…