Elsevier

Neurocomputing

Volume 72, Issues 1–3, December 2008, Pages 142-148
Neurocomputing

A lifecycle model for simulating bacterial evolution

https://doi.org/10.1016/j.neucom.2007.12.042Get rights and content

Abstract

This paper presents a lifecycle model (LCM) to simulate bacterial evolution from a finite population of Escherichia coli (E. coli) bacteria. The potential of this approach is in relating the microscopic behaviors of single bacterial cell to the macroscopic effects of bacterial colonies. This can be accomplished via use of an individual-based modeling method under the framework of agent–environment–rule (AER). Here, our study focuses on investigating the behaviors at different developmental stages in E. coli lifecycle and developing a new biologically inspired methodology for static or dynamic systems. The experimental results through a varying environment demonstrates that our model can be used to study under which circumstances a certain bacterial behaviors emerges, and also give an inspiration to design a new biological optimization algorithm being used for optimization problems.

Introduction

Escherichia coli, or E. coli is probably the best-understood microorganism, and well studied in various aspects of microbiology science [16], [4], [5], [15]. Its entire genome has been sequenced into 4639221 A, C, G, and T “letters”—adenosine, cytosine, guanine, and thymine [14]. Understanding of these single-cell organisms is an essential step towards understanding more complex organisms.

In biology, the term lifecycle refers to the various phases an individual passes through from birth to maturity and reproduction. This process often leads to drastic transformations of the individuals with stage-specific adaptations to a particular environment. The lifecycle of E. coli has three major stages: a free swimming stage spent searching for prey in water of soil, a growth stage spent inside the periplasm of the prey bacterium, and a lysis stage spent when getting insufficient nutrition form environment [13].

The fundamental unit of bacterial life, encapsulating action and information interaction as well as variability, is the cell. Therefore, it seems appropriate to construct ecological models in terms of individual cells and their behaviors. The existing extensive literature on modeling cells and their behaviors is almost based on classical mathematical approaches [9], [12]. Those approaches always restricted the minds of modelers. This paper presents a bio-inspired computational model, which simulates a population of individual E. coli bacteria during their whole lifecycle.

There are many bio-inspired computational models, such as genetic algorithm (GA) [10], particle swarm optimization (PSO) [8], [11] and ant system (AS) [6]. GA is a model to mimic the behaviors of evolution process in natural system specifically those that follow Darwin's principle of survival of the fittest. PSO is a collaborative population-based stochastic optimization model, which is inspired by the social behaviors of organisms, such as bird flocks and fish schools. AS algorithm is inspired by the behaviors of real ants finding the shortest path between their nest and a food source.

In the above models, they are all established based on population-based modeling approach. In a population-based model, the individuals follow the same rules and take the same actions simultaneously (all individuals are identical). In addition, the behaviors of a certain individual cannot be controlled and tracked.

Unlike the population-based method, our proposed model—lifecycle model (LCM) is developed using an individual-based modeling (IBM) approach. Compared with the population-based modeling approach, IBM possesses a more flexible and robust capability for simulating bacterial system, where there are a large number of individuals (cells) which have their own behavior dynamics influenced by the other individuals and the environment. In LCM, each individual corresponds to an autonomous artificial bacterium in the simulated domain. They possess different properties and the behaviors of each individual can be controlled and tracked.

The primary objective of the study is to investigate the behaviors at different developmental stages in their lifecycle. The secondary objective is to construction of a biologically inspired artificial ecology being of interest in itself.

The experimental results through a varying environment demonstrates that our model can be used to study under which circumstances a certain bacterial behavior emerge, and also give an inspiration to design a new biological optimization algorithm being used for optimization problems.

The rest of paper is organized as follows: some typical bacterial behaviors during their whole lifecycle are provided in Section 2. A framework of LCM and the mathematical model of bacterial behaviors are described in Section 3. Experimental settings and experimental results are given in Section 4. Finally, Section 5 concludes the paper.

Section snippets

Chemotaxis

A fascinating property of E. coli is their chemotactic behaviors. Chemotaxis (or more accurately, chemokinesis), the process by which a cell alters its speed or frequency of turning in response to an extracellular chemical signal, has been most thoroughly studied in the peritrichous bacterium E. coli [1], [3]. The response to a chemical stimulus in their vicinity helps bacteria find sources of nutrients which are essential for their survival. Bacterial cells will migrate towards environment

Lifecycle model of E. coli bacteria

LCM consists of a number of fundamental elements, which work together to construct an artificial biological ecology system. The framework of this model is based on an agent–environment–rule (AER) schema, i.e., there are three fundamental elements: agent, environment, and rules. The detailed description of it is listed below

  • A: artificial bacteria

  • E: artificial environment

  • R: the environment/organism interaction mechanisms.

LCM=〈A, E, R〉 where A={A1, A2, …, AN} comprise N artificial bacteria. The

Environments setting

Our experiment is conducted in a varying environment with nutrient-noxious distribution. The nutrient distribution of the environment at t=0 is set by the following function:F(x)=5exp-0.1((x1-15)2+(x2-20)2)-2exp-0.08((x1-20)2+(x2-15)2)+3exp-0.08((x1-25)2+(x2-10)2)+2exp-0.1((x1-10)2+(x2-10)2)-2exp-0.5((x1-5)2+(x2-10)2)-4exp-0.1((x1-15)2+(x2-5)2)-2exp-0.5((x1-8)2+(x2-25)2)-2exp-0.1((x1-21)2+(x2-25)2)+2exp-0.5((x1-25)2+(x2-16)2)+2exp-0.5((x1-5)2+(x2-14)2)

It is also illustrated in Fig. 5.

Parameters setting

According

Conclusions and future work

A lifecycle model (LCM) concerned with modeling ecological and evolutionary processes of E. coli bacteria is proposed in this paper. LCM is based on an agent–environment–rule (AER) scheme, in which the complex individual behaviors, including learning and adaptation, can emerge from cells following simple rules in a society. The details of some typical evolutionary behaviors such as chemotaxis, reproduction, extinction, and migration have been described and the detailed algorithm used to model

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant no. 70431003) and the National Basic Research Program of China (Grant no. 2002CB312200).

Ben Niu received his B.Sc. degree in Mechanical Engineering from Hefei Union University, Hefei, China, in 2001. In the same year, he enrolled at the Anhui Agriculture University in Hefei where he earned his M.Sc. degree in Enterprise Information Management in 2004. He is currently pursuing his Ph.D. in Shenyang Institute of Automation of the Chinese Academy of Sciences. His current research interests include swarm intelligence, bioinformatics and computational biology, fuzzy systems and neural

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Ben Niu received his B.Sc. degree in Mechanical Engineering from Hefei Union University, Hefei, China, in 2001. In the same year, he enrolled at the Anhui Agriculture University in Hefei where he earned his M.Sc. degree in Enterprise Information Management in 2004. He is currently pursuing his Ph.D. in Shenyang Institute of Automation of the Chinese Academy of Sciences. His current research interests include swarm intelligence, bioinformatics and computational biology, fuzzy systems and neural networks, with an emphasis on evolutionary and other stochastic optimization methods.

Yunlong Zhu is the Director of the Key Laboratory of Advanced Manufacturing Technology, Shenyang Institute of Automation of the Chinese Academy of Sciences. He received his Ph.D. in 2005 from the Chinese Academy of Sciences, China. He has research interests in various aspects of Enterprise Information Management but he has ongoing interests in artifical intelligence, machine learning, and related areas. Prof. Zhu's research has led to a dozen professional publications in these areas.

Xiaoxian He obtained his B.Sc. degree in Computer Science from the Department of Computer Science and Technology, Hunan Normal University, China, in July 2002. Currently he is a Ph.D. candidate in Shenyang Institute of Automation, Chinese Academy of Sciences. His research interests include swarm intelligence, complex adaptive system, bio-inspired computing and decision making.

Hai Shen earned her B.Sc. and M.Sc in Computer Application Technology in 1998 and 2005, respectively, both from Shenyang University of Technology in Shenyang, Liaoning, China. From 1998 to 2002, she worked as a teacher in Shenyang Normal University. She is currently pursuing her Ph.D. in Shenyang Institute of Automation, Chinese Academy of Sciences. Her research interests include swarm intelligence, evolutionary computation, bio-computing and multi-objective optimization.

Qinghua Wu received his M.Sc. (Eng.) degree in Electrical Engineering from Huazhong University of Science and Technology, China, in 1981. He received his Ph.D. degree from the Queen's University of Belfast (QUB), UK, in 1987. Currently, he is the Chair of Electrical Engineering in the Department of Electrical Engineering and Electronics, The University of Liverpool, UK, acting as the Head of Intelligence Engineering and Automation group. Professor Wu is a Chartered Engineer, Fellow of IEE and Senior Member of IEEE. His research interests include adaptive control, mathematical morphology, neural networks, learning systems, and evolutionary computation and power system control and operation.

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