Related papers: Mathematical models for order of mutation problem …
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…
Mathematical modeling allows us to better understand myeloproliferative neoplasms (MPN), a group of blood cancers, emergence and development. We test different mathematical models on an initial cohort to determine the emergence and…
Recent experimental evidence suggests that acute myeloid leukemias may originate from multiple clones of malignant cells. Nevertheless it is not known how the observed clones may differ with respect to cell properties such as proliferation…
Myeloproliferative Neoplasms (MPN) are blood cancers that appear after acquiring a driver mutation in a hematopoietic stem cell. These hematological malignancies result in the overproduction of mature blood cells and, if not treated, induce…
Recent works have stressed the important role that random mutations have in the development of cancer phenotype. We challenge this current view by means of bioinformatic data analysis and computational modelling approaches. Not all the…
Cancer cell mutations occur when cells undergo multiple cell divisions, and these mutations can be spontaneous or environmentally-induced. The mechanisms that promote and sustain these mutations are still not fully understood. This study…
Predicting cancer-associated clinical events is challenging in oncology. In Multiple Myeloma (MM), a cancer of plasma cells, disease progression is determined by changes in biomarkers, such as serum concentration of the paraprotein secreted…
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…
Cancer is a disease that takes millions of lives every year. Then, to propose treatments, avoid recurrence, and improve the patient's life quality, we need to analyze this disease from a biophysical perspective with a solid mathematical…
Multiple myeloma is a plasma cell cancer that leads to a dysregulated bone remodeling process. We present a partial differential equation model describing the dynamics of bone remodeling with the presence of myeloma tumor cells. The model…
Cancer progresses with a change in the structure of the gene network in normal cells. We define a measure of organizational hierarchy in gene networks of affected cells in adult acute myeloid leukemia (AML) patients. With a retrospective…
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…
Mutations can arise from the chance misincorporation of nucleotides during DNA replication or from DNA lesions that are not repaired correctly. We introduce a model that relates the source of mutations to their accumulation with cell…
The appearance of cancer in a tissue is thought to be the result of two or more successive mutations. We propose a stochastic model that allows for an exact computation of the distribution of the waiting time for a second mutation. This…
In this short communication, we shall explore a nonlinear discrete dynamical system that naturally occurs in population systems to describe a transmission of a trait from parents to their offspring. We consider a Mendelian inheritance for a…
We introduce and analyze a waiting time model for the accumulation of genetic changes. The continuous time conjunctive Bayesian network is defined by a partially ordered set of mutations and by the rate of fixation of each mutation. The…
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…
We study growth lemmas and questions of regularity for generators of Markov processes. The generators are allowed to have an arbitrary order of differentiability less than 2. In general, this order is represented by a function and not by a…
We introduce a Markov model for the evolution of a gene family along a phylogeny. The model includes parameters for the rates of horizontal gene transfer, gene duplication, and gene loss, in addition to branch lengths in the phylogeny. The…
In the context of the genome rearrangement problem, we analyze two well known models, namely the reversal and the prefix reversal models, by exploiting the connection with the notion of permutation pattern. More specifically, for any $k$,…