Volume 14 Supplement 8
Biomimicry of quorum sensing using bacterial lifecycle model
© Niu et al.; licensee BioMed Central Ltd. 2013
Published: 9 May 2013
Recent microbiologic studies have shown that quorum sensing mechanisms, which serve as one of the fundamental requirements for bacterial survival, exist widely in bacterial intra- and inter-species cell-cell communication. Many simulation models, inspired by the social behavior of natural organisms, are presented to provide new approaches for solving realistic optimization problems. Most of these simulation models follow population-based modelling approaches, where all the individuals are updated according to the same rules. Therefore, it is difficult to maintain the diversity of the population.
In this paper, we present a computational model termed LCM-QS, which simulates the bacterial quorum-sensing (QS) mechanism using an individual-based modelling approach under the framework of Agent-Environment-Rule (AER) scheme, i.e. bacterial lifecycle model (LCM). LCM-QS model can be classified into three main sub-models: chemotaxis with QS sub-model, reproduction and elimination sub-model and migration sub-model. The proposed model is used to not only imitate the bacterial evolution process at the single-cell level, but also concentrate on the study of bacterial macroscopic behaviour. Comparative experiments under four different scenarios have been conducted in an artificial 3-D environment with nutrients and noxious distribution. Detailed study on bacterial chemotatic processes with quorum sensing and without quorum sensing are compared. By using quorum sensing mechanisms, artificial bacteria working together can find the nutrient concentration (or global optimum) quickly in the artificial environment.
Biomimicry of quorum sensing mechanisms using the lifecycle model allows the artificial bacteria endowed with the communication abilities, which are essential to obtain more valuable information to guide their search cooperatively towards the preferred nutrient concentrations. It can also provide an inspiration for designing new swarm intelligence optimization algorithms, which can be used for solving the real-world problems.
Many agent-based models, inspired by biological phenomenon, have been formulated to provide new approaches for solving realistic optimization problems especially complex NP problems . Two different types of agent-based models, population-based and individual-based models, have been classified based on the viewpoint of biological simulation. In population-based models such as the particle swarm optimization algorithm , all individuals have unique characters and follow the same evolutionary rules. Nevertheless, in individual-based models (IBM) , an individual is regarded as a discrete entity endowed with its own attributes, states and behaviors. Every heterogeneous entity can communicate with each other and then make group decisions by social intelligence.
Early in 1988, Kreft and his colleagues proposed an individual-based model termed BacSim to simulate the evolution process of Escherichia coli (E. coli) from an individual bacterium to a group. As he says, we can see a macroscopic world in the microscopic object . An E-CELL model was illustrated by Tomita et al. in 1999, inspired by developmental processes of Mycoplasma genitalium . Ginovart et al. (2002) designed a discrete IBM called INDISIM to simulate the growth of bacterial cultures . An alternative model based on the COSMIC system to simulate the artificial bacterial interaction and evolution was shown by Paton et al. in 2004 . Soon after, Emonet et al. (2005) developed an IBM termed AgentCell to simulate bacterial chemotactic processes at the single-cell level . Another individual-based model of low-population bacteria cultures in the lag stage was presented by Prats et al. in 2006 . Recently, an IBM termed iDynoMiCS, which employs new bacterial biofilm modelling approaches, was formulated by Lardon et al. (2011) .
In our previous work, we formulated a lifecycle model (LCM) guided by the Agent-Environment-Rule architecture to simulate the bacterial evolution in 2008 . LCM mainly focuses on microscopic and macroscopic evolution processes of bacteria in different growth phases. Three main developmental phases of E. coli including the lag, dynamic and decline phases are studied. Compare with the population-based computational model, the individual-based LCM has improved flexibility where the behaviors of every individual could be investigated and controlled. The original LCM, however, is in its infancy . Recent studies have demonstrated that quorum sensing (QS) systems generally exist in bacteria acting as communication with and between groups . Incorporating intra- and inter-species QS mechanisms into LCM is the primary aim and work of this paper.
Lifecycle model (LCM)
A bio-inspired lifecycle model (LCM), according to bacterial evolution processes during their lifecyle, was proposed as a new inspiration to solve optimization problems in 2008 . Behaviors of E. coli in different life phases are concentrated on in LCM. In biological science, behaviors of E. coli have been intensively studied for more than 150 years and four key behavioral patterns of E. coli, i.e. chemotaxis, reproduction, migration and elimination, have been detailed described in .
In absence of gradient information about attractant or repellent chemical concentration, a bacterium runs in a straight line using flagella as propellers for a few seconds, and then tumbles with random directions. The run-tumble-run cycle will be repeated during the whole bacterial lifecycle. A bacterium with gradient information shows distinctly different behaviors. It has been suggested that the bacteria can possess the memory ability so that it can compare current gradient information with previous ones . If the concentration of attractant chemicals raises or the density of repellent chemicals reduces, the frequency of run increases. Otherwise, the frequency of tumble increases. The run-tumble-run cycle is the essential property of bacterial chemotactic behaviors.
When a bacterium obtains sufficient energy from the environment, it has a chance to reproduce. The healthy bacterium splits into two identical daughter cells in the same spatial position. Those with poor nutrients intake may undergo extinction or migrate to new niches for survival . Of course, the population varies between different life phases. In the lagging phase, most bacteria absorb rich nutrients and thus the population of bacteria grows exponentially. The increasing of population size leads to the intensified competition for nutrients. During dynamic phase, the population size of bacterial colony fluctuates markedly in the early stage and then gradually stagnates in a relatively stable state. With the food depleted gradually, some bacteria are not able to find sufficient food sources, which will be eliminated or migrate to new places with good nutrient concentrations, the population size reduces at the decline stage.
Although the theoretical modelling based on individual bacterial behaviors is insufficient. The flexible structure of LCM allows it to retain the potential of incorporating quorum-sensing (or cell-cell communication) mechanisms. This paper chiefly concentrates on the integration of QS systems into LCM for achieving a more accurate biological simulation model. A brief description of QS mechanisms is given as follows.
Quorum-sensing (QS) mechanisms
New microbial discoveries have illustrated that though as the simple unicellular microbes on earth, bacteria can utilize cell-to-cell communication to make group decisions, synthesize beneficial molecules for themselves and so on . Information about other bacteria and the environment can be acquired by an individual bacterium, and interpreted in a 'meaningful' way which finally results in sharing of knowledge . Possessing the sophisticated linguistic communication abilities, bacteria are able to take on some advanced features of social intelligence, such as cooperative foraging and creating complex niches . Such communication process via chemical signals is termed quorum sensing (QS).
Two main kinds of QS systems in individual-wide and population-wide scales are considered and simulated in the paper . It is clear that via the use of intrinsic QS mechanisms, global behaviors of bacterial species are coordinated for maximizing group benefits as well as individual benefits .
LCM with QS mechanisms
The bacterial movement of chemotaxis is run through in the whole lifecyle. During each movement of run or tumble, each bacterium pursues nutrients or avoid noxious. Bacteria with high energy intake will broadcast their search information to other bacteria with low energy level by QS mechanism. When a mass of bacteria congregate together and the local environment becomes overcrowded, they compete with each other instead of cooperated with others. Some bacteria with strong foraging abilities accumulate sufficient nutrients for reproduction. Others that lack competitive edges are easily eliminated. In the proposed model, these dead bacteria are replaced by copies of bacteria possessing the opportunity of reproduction. The rest of bacteria, which have a little energy and average foraging capacities, will migrate to a new region together through interspecies communication. To reduce computational complexity, the lifecycle model with QS mechanisms is divided into three sub-models, which are presented in detail as follows.
Chemotaxis with QS sub-model
It is expected that the integration of QS mechanisms into chemotaxis will facilitate the cooperative search of the global optimum and accelerate the convergence rate. Subsequently, the reproduction and elimination sub-model will been conducted until the number of run and tumble reaches a certain value ( or ). Note that the number of chemotaxis step equals the total number of iterations ().
Reproduction and elimination sub-model
where is fitness value of i th bacterium, is a predefined threshold. The asexual reproduction of healthy bacteria doubles the population of the group. Nevertheless, the colony population size may shrink rapidly owing to the sudden death of a mass of unhealthy bacteria. Hence, the total number of artificial bacteria in the proposed model remains unchanged. From the viewpoint of computation, the reproduction and elimination progress may disturb chemotactic processes in the next iteration step. But more importantly, it could improve the computational speed and possibly find the global optimum.
where indicates the lower boundary and donates the upper boundary, d is the number of the dimensions, k is the current chemotatic step. The values of lower and upper boundaries are always determined according to the constraints defined in the realistic optimization problems.
To simplify LCM-QS, it is suggested that the entire migration process will be conducted only if certain migration conditions are satisfied. For instance, if the chemotactic steps reach a predefined threshold value, the migration process will be performed.
Implementation of LCM-QS
Implementation of LCM-QS
For (each loop or iter<iterMax)
// chemotaxis process
For (each bacterium )
If (given probability >random)
Share information with surrounding neighbours
While (current function value Fc< previous function value Fp)
Swim (using Equation 2)
Share the information with two random-choice bacteria
Tumble (using Equation 2)
While (current function value Fc< previous function value Fp)
Swim (using Equation 2)
// reproduction or elimination
If (reproduction conditions meet)
Sort and Split
For (each bacterium)
If (a given probability Nmig > random)
Migrate to a new niche (using Equation 5)
Results and discussion
To measure the search performance of artificial bacteria using the proposed new model, simulation studies have conducted in a 3-D environment with nutrient-noxious distribution. As illustrated above, information exchange mechanism is one of key indicators in swarm optimization, our experimental studies are conducted with four types of information exchange scenarios.
A: Bacterial chemotaxis without information exchange;
B: Bacterial chemotaxis with group information exchange;
C: Bacterial chemotaxis with individual information exchange;
D: Bacterial chemotaxis with individual and group information exchange.
A: Bacterial chemotaxis without information exchange
B: Bacterial chemotaxis with group information exchange
C: Bacterial chemotaxis with individual information exchange
D: Bacterial chemotaxis with individual and group information exchange
In this paper, a new computational model, termed LCM-QS (lifecycle model with quorum sensing mechanism) is proposed to simulate emergent behaviour of bacterial quorum sensing. The communication mechanism is the most important factor to indicate a swarm intelligence system. The artificial bacteria are endowed with communication ability by using the principle of swarm intelligence. Additionally, reproduction, elimination and migration are all viewed as optimization strategies to build the LCM-QS model. To illustrate the performance of the proposed model, four types of communication schemes between individuals or groups are studied by adapting a 3-D artificial environment with nutrient-noxious distribution. The results show that by using quorum sensing mechanism artificial bacteria are able to response quickly to the complex environment and can find the global optimum in a short time.
The primary goal of this paper concentrates on developing a novel individual-based modelling approach to simulate the quorum sensing mechanism among bacterial colonies. Meanwhile, the LCM-QS model is expected to give an inspiration to present a new swarm intelligence optimization algorithm. However, little consideration is given to other factors such as varying population, dynamic environment. Therefore, in our future work, these issues will be focused on and some real-world applications will be considered, such as the design of new evolutionary neural networks [27–30].
This work is partially supported by The National Natural Science Foundation of China (Grants nos. 71001072, 71271140,71210107016, 71240015), The Hong Kong Scholars Program 2012 (Grant no. G-YZ24), China Postdoctoral Science Foundation (Grant nos. 20100480705, 2012T50584), Science and Technology Project of Shenzhen (Grant No. JC201005280492A) and the Natural Science Foundation of Guangdong Province (Grant nos. S2012010008668, 9451806001002294).
This article has been published as part of BMC Bioinformatics Volume 14 Supplement 8, 2013: Proceedings of the 2012 International Conference on Intelligent Computing (ICIC 2012). The full contents of the supplement are available online at http://www.biomedcentral.com/bmcbioinformatics/supplements/14/S8.
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