Related papers: On a Stochastic PDE Model for Epigenetic Dynamics
The phenotypic equilibrium, i.e. heterogeneous population of cancer cells tending to a fixed equilibrium of phenotypic proportions, has received much attention in cancer biology very recently. In previous literature, some theoretical models…
Understanding how microenvironmental heterogeneity influences tumor progression is essential for advancing both cancer biology and therapeutic strategies. In this study, we develop a cellular automata (CA) model to simulate tumor growth…
We investigate a simple quantitative genetics model subjet to a gradual environmental change from the viewpoint of the phylogenies of the living individuals. We aim to understand better how the past traits of their ancestors are shaped by…
Multiple phenotypic states often arise in a single cell with different gene-expression states that undergo transcription regulation with positive feedback. Recent experiments have shown that at least in E. coli, the gene state switching can…
We develop a modeling framework for cancer progression that distinguishes the order of two possible mutations. Recent observations and information on myeloproliferative neoplasms are analyzed within our framework. In some patients with…
We consider a stochastic individual-based population model with competition, trait-structure affecting reproduction and survival, and changing environment. The changes of traits are described by jump processes, and the dynamics can be…
Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees relating species. Along branches, sequence evolution is modelled using a continuous-time Markov process characterised by an instantaneous rate…
We present a general framework to describe the evolutionary dynamics of an arbitrary number of types in finite populations based on stochastic differential equations (SDE). For large, but finite populations this allows to include…
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…
In population genetics, mutation rate is often treated as a homogeneous parameter across the genome. Empirical evidence, however, shows systematic variation across genomic contexts associated with chromatin organization and epigenomic…
The inverse geometric approach to the modeling of the growth of circular objects revealing required features, such as the velocity of the growth and fractal behavior of their contours, is presented. It enables to reproduce some of the…
We built a novel Bayesian hierarchical survival model based on the somatic mutation profile of patients across 50 genes and 27 cancer types. The pan-cancer quality allows for the model to "borrow" information across cancer types, motivated…
Understanding how a diversity of plants in agroecosystems affects the adaptation of pathogens in a key issue in agroecology. We analyze PDE systems describing the dynamics of adaptation of two phenotypically structured populations, under…
We investigate a stochastic version of a simple enzymatic reaction which follows the generic Michaelis-Menten kinetics. At sufficiently high concentrations of reacting species, the molecular fluctuations can be approximated as a realization…
Timing is essential for many cellular processes, from cellular responses to external stimuli to the cell cycle and circadian clocks. Many of these processes are based on gene expression. For example, an activated gene may be required to…
Adaptive therapy is a promising paradigm for treating cancers, that exploits competitive interactions between drug-sensitive and drug-resistant cells, thereby avoiding or delaying treatment failure due to evolution of drug resistance within…
Evolution is a dynamic process. The two classical forces of evolution are mutation and selection. Assuming small mutation rates, evolution can be predicted based solely on the fitness differences between phenotypes. Predicting an…
Two mathematical models of macroevolution are studied. These models have population dynamics at the species level, and mutations and extinction of species are also included. The population dynamics are updated by difference equations with…
Cellular processes do not follow deterministic rules; even in identical environments genetically identical cells can make random choices leading to different phenotypes. This randomness originates from fluctuations present in the…
The pancreatic innervation undergoes dynamic remodeling during the development of pancreatic ductal adenocarcinoma (PDAC). Denervation experiments have shown that different types of axons can exert either pro- or anti-tumor effects, but…