Individual-Based Modeling of Bacterial Genetic Elements

Abstract

Individual-based computational modeling of biological systems is an important complement to experimental research. The individual-based model (IbM) is a bottom-up approach that considers the fate of individuals, their properties and interactions, and the influence of these interactions, holistically, on properties of the system. This contrasts with population- based models dependent on averaged behaviour of the whole system (DeAngelis & Gross, 1992; Huston, DeAngelis, & Post, 1988). IbMs can track individuals in time so that unusual events can be captured. They are particularly suited to biological simulations, where individuals might represent virtual plants, animals, or microorganisms in differing ecosystems. Lower complexity, coupled with the wealth of genetic knowledge about bacteria, allow for more realistic simulations compared with higher organisms. Accordingly, a lineage of IbMs, including Bacteria Simulator (BacSim) (Kreft, Booth, & Wimpenny, 1998; Kreft, Picioreanu, Wimpenny, & van Loosdrecht, 2001), INDividual DIScrete SIMulation (INDISIM) (Ginovart, Lopez, & Gras, 2005; Ginovart, Lopez, & Valls, 2002; Prats, Lopez, Giro, Ferrer, & Valls, 2006), COmputing Systems of Microbial Interactions and Communications (COSMIC) (Gregory, Paton, Saunders, & Wu, 2004; Paton, Gregory, Vlachos, Saunders, & Wu, 2004), RUle-based BActerial Modeling (RUBAM) (Paton, Vlachos, Wu, & Saunders, 2006; Vlachos, Paton, Saunders, & Wu, 2006) and COSMIC-Rules (Gregory, Saunders, & Saunders, 2006, 2008b), based on COSMIC and RUBAM, has been developed for bacterial simulations. Although all these models are individual-based, underlying simulation mechanisms and aims vary. BacSim was the first to use IbM in a recognizable biological context (Kreft et al., 1998, 2001) aiming to model growth and cell division, quantitatively, at the population level, using a pseudocontinuous 2-dimensional world with restricted nutrients. INDISIM is based on stronger mathematical foundations, and is a discrete space and time stochastic simulation of colony growth, largely based on random variables (Ginovart et al., 2002). Each cell is a set of parameters existing at a discrete location. COSMIC uses pseudocontinuous space and discrete time to model evolution of cells (Gregory et al., 2004). Each cell contains a bit string genome that interacts with itself and the environment. This model is largely deterministic, although random events do have a role. It can run in a parallel machine, though any random effects this creates have been removed. RUBAM is a simplification of COSMIC, with pseudocontinuous space, discrete time, and a much more simplified genome. It aims to model adaptation (Vlachos et al., 2006). The simplified genome allows for comparatively rapid simulations that show adaptation and acquired resistance to antibiotics. COSMIC-Rules is a culmination of IbM modeling design, having an effective balance of modeling detail while being computationally tractable (Gregory et al., 2006, 2008b). Like COSMIC, it is a parallel simulation with pseudocontinuous space and discrete time. It uses a genome abstraction to represent the conditions and outputs of complex biochemical pathways, while incorporating an element of specificity and means of simulating evolution. Like the other IbMs considered here, each individual has its own parameters and state. Unlike the other IbMs, the scope of COSMIC-Rules covers vertical and horizontal gene transfer using populations of millions of cells.