Document Type : Original Article
Institute of Biochemistry and Biophysics, University of Tehran, Tehran, Iran
School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran
National Institute of Genetic Engineering and Biotechnology, Tehran, Iran;4School of Biological Sciences, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
Cellular decision-making is a key process in which cells with similar genetic and environmental background make dissimilar decisions. This stochastic process, which happens in prokaryotic and eukaryotic cells including stem cells, causes cellular diver- sity and phenotypic variation. In addition, fitness predicts and describes changes in the genetic composition of populations throughout the evolutionary history. Fitness may thus be defined as the ability to adapt and produce surviving offspring. Here, we present a mathematical model to predict the fitness of a cell and to address the fundamental issue of phenotypic variation. We study a basic decision-making scenario where a bacteriophage lambda reproduces in E. coli, using both the lytic and the lysogenic pathways. In the lytic pathway, the bacteriophage replicates itself within the host bacterium. This fast replication overcrowds and in turn destroys the host bacterium. In the lysogenic pathway, however, the bacteriophage inserts its DNA into the host genome, and is replicated simultaneously with the host genome.
Materials and Methods
In this prospective study, a mathematical predictive model was developed to estimate fitness as an index of survived offspring. We then leverage experi- mental data to validate the predictive power of our proposed model. A mathematical model based on game theory was also generated to elucidate a rationale behind cell decision.
Our findings indicate that a rational decision that is aimed to maximize life expec- tancy of offspring is almost identical to bacteriophage behavior reported based on experi- mental data. The results also showed that stochastic decision on cell fate maximizes the expected number of survived offspring.
We present a mathematical framework for analyzing a basic phenotypic variation problem and explain how bacteriophages maximize offspring longevity based on this model. We also introduce a mathematical benchmark for other investigations of phenotypic variation that exists in eukaryotes including stem cell differentiation.