Related papers: Interpreting the dependence of mutation rates on a…

We propose a one mutation model for cancer with a mutation rate that increases with time. Under rather general hypotheses the number of mutations is necessarily a (non homogeneous) Poisson process with the prescribed mutation rate. We show…

We study a simple model of DNA evolution in a growing population of cells. Each cell contains a nucleotide sequence which randomly mutates at cell division. Cells divide according to a branching process. Following typical parameter values…

Tumor recurrence, driven by the evolution of drug resistance is a major barrier to therapeutic success in cancer. Resistance is often caused by genetic alterations such as point mutation, which refers to the modification of a single genomic…

Mutation-induced drug resistance in cancer often causes the failure of therapies and cancer recurrence, despite an initial tumor reduction. The timing of such cancer recurrence is governed by a balance between several factors such as…

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…

Most human tumors result from the accumulation of multiple genetic and epigenetic alterations in a single cell. Mutations that confer a fitness advantage to the cell are known as driver mutations and are causally related to tumorigenesis.…

Development of a tumor is known to be a result of accumulation of DNA changes in somatic cells. However, the processes of how DNA changes are produced and how they accumulate in somatic cells are not clear. DNA changes include two types:…

Under constant selection, each trait has a fixed fitness, and small mutation rates allow populations to efficiently exploit the optimal trait. Therefore it is reasonable to expect mutation rates will evolve downwards. However, we find this…

A mathematical model of genome degradation is proposed that takes into account a variable rate of mutation and increasing number of cells in a developing human organism. The model explains known properties of cancer development, in…

We study large deviation events in the timing of disease recurrence. In particular, we are interested in modeling cancer treatment failure due to mutation-induced drug resistance. We first present a two-type branching process model of this…

Stochastic models of sequential mutation acquisition are widely used to quantify cancer and bacterial evolution. Across manifold scenarios, recurrent research questions are: how many cells are there with $n$ alterations, and how long will…

DNA replication is an essential process in biology and its timing must be robust so that cells can divide properly. Random fluctuations in the formation of replication starting points, called origins, and the subsequent activation of…

Cancer progression involves the sequential accumulation of genetic alterations that cumulatively shape the tumour phenotype. In prostate cancer, tumours can follow divergent evolutionary trajectories that lead to distinct subtypes, but the…

Biological cells replicate their genomes in a well-planned manner. The DNA replication program of an organism determines the timing at which different genomic regions are replicated, with fundamental consequences for cell homeostasis and…

As cancer advances, cells often spread from the primary tumor to other parts of the body and form metastases. This is the main cause of cancer related mortality. Here we investigate a conceptually simple model of metastasis formation where…

The GC-content is very variable in different genome regions and species but although many hypothesis we still do not know the reason why. Here we show that a relationship exists with the mutation rate, in particular we noticed a new…

It has been recently claimed that it is possible to predict the rate of de novo mutation of each site in the human genome with almost perfect accuracy (Michaelson et al. (2012) Cell, 151, 1431-1442). We show that this claim is unwarranted.…

Recent methodological advances are enabling better examination of speciation and extinction processes and patterns. A major open question is the origin of large discrepancies in species number between groups of the same age. Existing…

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…

Isogenic Escherichia coli growing exponentially in a constant environment display large variation in growth-rates, division-sizes and generation-times. It is unclear how these seemingly random cell cycles can be reconciled with the precise…