Individual-Based Modeling of Bacterial Genetic Elements

Individual-Based Modeling of Bacterial Genetic Elements

Venetia A. Saunders (Liverpool John Moores University, UK), Richard Gregory (University of Liverpool, UK) and Jon R. Saunders (University of Liverpool, UK)
DOI: 10.4018/978-1-60566-026-4.ch304
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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.
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Introduction

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.

Key Terms in this Chapter

Bit String Matching: Method by which bits in a tagged bit string are compared with bits in another tagged bit string to determine if they are acceptably similar. COSMIC-Rules uses the fast exclusive-or operation followed by counting the number of set bits.

Genome Compression: An abstraction that reduces the complexity of pathways into single components. Each “gene” can represent an otherwise intractable pathway if its external overall effect, behaviour, or input/output relationship can be characterised by probability, mathematical formula, lookup table, logical expression, or a combination of any of these methods.

Bacterial Plasmid: A self-replicating, extrachromosomal genetic element found in bacteria. Plasmids may carry genes for various functions, including antibiotic resistance and virulence.

Individual-Based Model (IbM): Modeling philosophy in which numerical quantities, representing the size of some population, are replaced by individuals that make up the population. Each individual would have its own state, allowing analysis to include both population level crowd effects and individualism. The form of the individual is inherently open-ended and need not be tied to mathematical expressions. The IbM philosophy also allows use of nested levels of individuality.

Bacteriophage (Phage): A virus that specifically infects bacteria. Broadly, there are two types: virulent (or lytic) and temperate (or lysogenic). Upon infection, a virulent phage replicates and releases progeny phages. A temperate phage may enter the lytic cycle or lysogenize the host, with the phage genome remaining dormant. The genome may later become active, directing the synthesis of progeny phages and destruction of the host.

Tagged Bit String: Consists of both a type and a bit string. The type specifies what pathway it abstracts, and what other tags must be present for this pathway abstraction to be active. A bit string provides specificity by adding another (mutable) condition to activation of a pathway. Both tag and bit string exist as an inseparable pair and are passed through both vertical and horizontal inheritance.

Antibiotic: A natural or artificial substance that can kill or inhibit growth of microorganisms.

COSMIC-Rules: Model and modeling framework simulating bacterial adaptation using IbM philosophy and genome compression to achieve realistic and qualitatively accurate simulations of, for example, substance affinity, plasmid transfer, phage spread, and cellular decay.

Bacterial Conjugation: A naturally occurring horizontal gene transfer process in which donor and recipient cells come into direct contact for exchange of genetic material in bacteria.

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