Biological applications of the theory of birth-and-death processes

In this review, we discuss the applications of the theory of birth-and-death processes to problems in biology, primarily, those of evolutionary genomics. The mathematical principles of the theory of these processes are briefly described. Birth-and-death processes, with some straightforward additions such as innovation, are a simple, natural formal framework for modeling a vast variety of biological processes such as population dynamics, speciation, genome evolution, including growth of paralogous gene families and horizontal gene transfer, and somatic evolution of cancers. We further describe how empirical data, e.g., distributions of paralogous gene family size, can be used to choose the model that best reflects the actual course of evolution among different versions of birth-death-and-innovation models. It is concluded that birth-and-death processes, thanks to their mathematical transparency, flexibility and relevance to fundamental biological process, are going to be an indispensable mathematical tool for the burgeoning field of systems biology.Comment: 29 pages, 4 figures; submitted to "Briefings in Bioinformatics

Comparing System Dynamics and Agent-Based Simulation for Tumour Growth and its Interactions with Effector Cells

There is little research concerning comparisons and combination of System Dynamics Simulation (SDS) and Agent Based Simulation (ABS). ABS is a paradigm used in many levels of abstraction, including those levels covered by SDS. We believe that the establishment of frameworks for the choice between these two simulation approaches would contribute to the simulation research. Hence, our work aims for the establishment of directions for the choice between SDS and ABS approaches for immune system-related problems. Previously, we compared the use of ABS and SDS for modelling agents' behaviour in an environment with nomovement or interactions between these agents. We concluded that for these types of agents it is preferable to use SDS, as it takes up less computational resources and produces the same results as those obtained by the ABS model. In order to move this research forward, our next research question is: if we introduce interactions between these agents will SDS still be the most appropriate paradigm to be used? To answer this question for immune system simulation problems, we will use, as case studies, models involving interactions between tumour cells and immune effector cells. Experiments show that there are cases where SDS and ABS can not be used interchangeably, and therefore, their comparison is not straightforward.Comment: 8 pages, 8 figures, 2 tables, International Summer Computer Simulation Conference 201

Evolutionarily stable anti-cancer therapies by autologous cell defection

Game theory suggests an anti-cancer treatment based on the use of modified cancer cells that disrupt cooperation within the tumor. Cancer cells are harvested from the patient, the genes for the production of essential growth factors are knocked out in vitro and the cells are then reinserted in the tumor, where they lead to its collapse. Background and objectives: Current anti-cancer drugs and treatments based on gene therapy are prone to the evolution of resistance, because cancer is a process of clonal selection: resistant cell lines have a selective advantage and therefore increase in frequency, eventually conferring resistance to the whole tumor and leading to relapse. An effective treatment must be evolutionarily stable, that is, immune to the invasion of resistant mutant cells. This study shows how such a treatment can be achieved by autologous cell therapy using modified cancer cells, knocked out for genes coding for diffusible factors like growth factors. Methodology: The evolutionary dynamics of a population of cells producing diffusible factors are analyzed using a nonlinear public goods game in a structured population in which the interaction neighborhood and the update neighborhood are decoupled. The analysis of the dynamics of the system reveals what interventions can drive the population to a stable equilibrium in which no diffusible factors are produced. Results: A treatment based on autologous knockout cell therapy can be designed to lead to the spontaneous collapse of a tumor, without targeting directly the cancer cells, their growth factors or their receptors. Critical parameters that can make the therapy effective are identified. Concepts from evolutionary game theory and mechanism design, some of which are counterintuitive, can be adopted to optimize the treatment. Conclusions and implications: Although it shares similarities with other approaches based on gene therapy and RNA interference, the method suggested here is evolutionarily stable under certain conditions. This method, named autologous cell defection, can be carried out using existing molecular biology and cell therapy techniques