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Register a new userModeling evolution in a Long Time Evolution Experiment with E. Coli
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Dario Alejandro Leon
Publication date
2018
fields
Biology
and research's language is
English
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Taking into account an evolutionary model of mutations in term of Levy Fights that was previously constructed, we designed an algorithm to reproduce the evolutionary dynamics of the Long-Term Evolution Experiment (LTEE) with E. Coli bacteria. The algorithm enables us to simulate mutations under natural selection conditions. The results of simulations on competition of clones, mean fitness, etc., are compared with experimental data. We attained to reproduce the behavior of the mean fitness of the bacteria cultures, get our own interpretations and more tuned descriptions of some phenomena taking part within the experiment, such as fixation and drift processes, clonal interference and epistasis.
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We revisit the model by Wiser, Ribeck, and Lenski (Science textbf{342} (2013), 1364--1367), which describes how the mean fitness increases over time due to beneficial mutations in Lenskis long-term evolution experiment. We develop the model further both conceptually and mathematically. Conceptually, we describe the experiment with the help of a Cannings model with mutation and selection, where the latter includes diminishing returns epistasis. The analysis sheds light on the growth dynamics within every single day and reveals a runtime effect, that is, the shortening of the daily growth period with increasing fitness; and it allows to clarify the contribution of epistasis to the mean fitness curve. Mathematically, we explain rigorous results in terms of a law of large numbers (in the limit of infinite population size and for a certain asymptotic parameter regime), and present approximations based on heuristics and supported by simulations for finite populations.
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Biological systems are typically highly open, non-equilibrium systems that are very challenging to understand from a statistical mechanics perspective. While statistical treatments of evolutionary biological systems have a long and rich history, examination of the time-dependent non-equilibrium dynamics has been less studied. In this paper we first derive a generalized master equation in the genotype space for diploid organisms incorporating the processes of selection, mutation, recombination, and reproduction. The master equation is defined in terms of continuous time and can handle an arbitrary number of gene loci and alleles, and can be defined in terms of an absolute population or probabilities. We examine and analytically solve several prototypical cases which illustrate the interplay of the various processes and discuss the timescales of their evolution. The entropy production during the evolution towards steady state is calculated and we find that it agrees with predictions from non-equilibrium statistical mechanics where it is large when the population distribution evolves towards a more viable genotype. The stability of the non-equilibrium steady state is confirmed using the Glansdorff-Prigogine criterion.
The world evolution of the Severe acute respiratory syndrome coronavirus 2 (SARS-Cov2 or simply COVID-19) led the World Health Organization to declare it a pandemic. The disease appeared in China in December 2019, and it has spread fast around the world, specially in european countries like Italy and Spain. The first reported case in Brazil was recorded in February 26, and after that the number of cases growed fast. In order to slow down the initial growth of the disease through the country, confirmed positive cases were isolated to not transmit the disease. To better understand the early evolution of COVID-19 in Brazil, we apply a Susceptible-Infectious-Quarantined-Recovered (SIQR) model to the analysis of data from the Brazilian Department of Health, obtained from February 26, 2020 through March 25, 2020. Based on analyical and numerical results, as well on the data, the basic reproduction number is estimated to $R_{0}=5.25$. In addition, we estimate that the ratio unidentified infectious individuals and confirmed cases at the beginning of the epidemic is about $10$, in agreement with previous studies. We also estimated the epidemic doubling time to be $2.72$ days.
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