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Error-induced extinction in a multi-type critical birth-death process.
J Math Biol
September 2024
School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh, EH9 3FD, UK.
Extreme mutation rates in microbes and cancer cells can result in error-induced extinction (EEX), where every descendant cell eventually acquires a lethal mutation. In this work, we investigate critical birth-death processes with n distinct types as a birth-death model of EEX in a growing population. Each type-i cell divides independently or mutates at the same rate.
View Article and Find Full Text PDFLearning spatio-temporal patterns with Neural Cellular Automata.
PLoS Comput Biol
April 2024
School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh, United Kingdom.
Neural Cellular Automata (NCA) are a powerful combination of machine learning and mechanistic modelling. We train NCA to learn complex dynamics from time series of images and Partial Differential Equation (PDE) trajectories. Our method is designed to identify underlying local rules that govern large scale dynamic emergent behaviours.
View Article and Find Full Text PDFSequential mutations in exponentially growing populations.
PLoS Comput Biol
July 2023
School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh, United Kingdom.
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 it take for these cells to appear. For exponentially growing populations, these questions have been tackled only in special cases so far.
View Article and Find Full Text PDFInterference with HIV infection of the first cell is essential for viral clearance at sub-optimal levels of drug inhibition.
PLoS Comput Biol
February 2020
Africa Health Research Institute, KwaZulu-Natal, South Africa.
HIV infection can be cleared with antiretroviral drugs if they are administered before exposure, where exposure occurs at low viral doses which infect one or few cells. However, infection clearance does not happen once infection is established, and this may be because of the very early formation of a reservoir of latently infected cells. Here we investigated whether initial low dose infection could be cleared with sub-optimal drug inhibition which allows ongoing viral replication, and hence does not require latency for viral persistence.
View Article and Find Full Text PDFCancer recurrence times from a branching process model.
PLoS Comput Biol
November 2019
School of Mathematics, University of Edinburgh, Edinburgh, United Kingdom.
Article Synopsis
- The study focuses on how cancer cells spread from the main tumor to other parts of the body, leading to metastases, which is a major cause of death in cancer patients.
- Researchers used a model to analyze the relationship between the size of the primary tumor and the formation of metastases, assuming that each metastasis develops independently.
- The findings indicate that early surgical removal of the primary tumor is crucial to prevent cancer recurrence, with even minor delays in surgery increasing the likelihood of metastases being present and undetectable.
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