Engineering Applications of Artificial Intelligence 14 (2001) 715–726 An agent-based learning framework for modeling microbial growth Santhoji Katare, Venkat Venkatasubramanian* Laboratory for Intelligent Process Systems, School of Chemical Engineering, Purdue University, West Lafayette, IN 47907-1283, USA Received 1 June 2001; received in revised form 1 June 2001; accepted 1 January 2002 Abstract The overall idea of this paper is to study the intelligent behavior of microbes in a binary substrate environment with agent-based learning models. Study of microbial growth enables understanding of industrially relevant processes such as fermentation, biodegradation of pollutants, antibody production using hybridoma cells, etc. Artificial intelligence techniques such as genetic algorithms and agent-based learning methodologies have been used to study microbial growth. Specifically, the objective is to (1) qualitatively model the intelligent growth characteristics of the microbes using a minimal set of generic rules as against algebraic/ differential mathematical relationships and (2) propose a suitable hypothesis that explains the origin of intelligence through learning in the microbes. A microbial cell has been modeled as a collection of agents characterized by a set of resources and an objective to survive and grow. The actions of the agents are governed by generic rules such as survival, growth and division as is common for any individual in a resource-limited competitive environment. The interaction of the agents with the environment and other fellow agents enables them to ‘‘learn’’ and ‘‘adapt’’ to the changes in the environment and thus defines the dynamics of the system. The origin of intelligence in the microbes has been studied by both a simple learning rule of imitation and rule discovery studies. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Agent-based learning model; Multi-agent system; Microbial growth; Complex adaptive systems; Genetic algorithms 1. Introduction to complex adaptive systems and these goals by a sequence of actions. For example, an agent-based models ant in an ant colony possesses the required skills to followother ants along their pheromone trails in order Complex adaptive systems can be considered as to gather food. The inherent non-linearity of these possessing the following characteristics: They are highly systems leads to a highly complex behavior and is not variable and stochastic. They can adapt and learn. They easy to model using traditional mathematical techni- comprise of several individuals, each with their own set ques. Ordinary/partial differential equations or alge- of resources and goals. The system consists of indivi- braic equations cannot be used to describe such systems duals that normally have access to the local information intuitively. and based on a set of guiding rules, they compete in the The local interactions of individuals in highly resource-limited competitive environment to achieve networked systems gives rise to global consequences, their goals. There is no central coordinating agency which cannot be attributed to any single individual in that controls their behavior. Densely populated systems the system. This ‘‘emergent property’’, a characteristic such as bacterial cultures, crowded societies, political of the system as a whole with no significance at the parties, financial institutions, etc. are characterized by individual level, distinguishes a complex system from an large-scale interactions among its members. Every ordinary one. For example, density or entropy is defined individual in each of these systems is unique with only for a statistical ensemble of molecules rather than their own characteristics and traits. Each one has a an individual atom or molecule. Similarly, the electron particular goal and a set of resources/skills to attain structure of hydrogen and oxygen in isolation or for that matter that of the H2O molecule cannot help us explain the overall property of wetness of water, which is a *Corresponding author. Tel.: +1-765-494-0734; fax: +1-765-494- 0805. property emerging from the interaction of several H2O E-mail address: [email protected] (V. Venkatasubramanian). molecules with each other under specific rules of 0952-1976/01/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0952-1976(02)00015-5 716 S. Katare, V. Venkatasubramanian / Engineering Applications of Artificial Intelligence 14 (2001) 715–726 chemistry—valency, bonding, etc. It is clear that this 2. The problem: growth of microbes in a binary substrate property cannot be attributed to a single H2O molecule. environment Agent-based models have been used to study the phenomenon of emergent behavior in complex systems Microbes growin highly competitive and complicated (http://www.santafe.edu/projects/swarm). environments. The growth behavior is controlled by It is interesting to note that a ‘‘reductionist’’ approach thousands of biochemical reactions that change dyna- of looking at the constituents of the system in isolation mically based upon the conditions in the environment. cannot explain the emergent behavior of the system as a The system can exhibit a variety of behaviors ranging whole. When we try to model complex systems from simultaneous utilization of all substrates to essentially what we do is to model their emergent sequential utilization of substrates, resulting in multi- behavior through the local interactions of the agents. exponential growth phases (Kompala et al., 1984). Hence, it is essential to look at these systems using a Analyzing the growth behavior of microbes has been holistic approach and the concept of ‘‘Agent-based an important issue from the perspective of under- Models’’ (http://www.red3d.com/cwr/ibm.html) enables standing industrially relevant processes such as fermen- us to do so. This technique models the individual entities tation, biological pollution control, antibody of the system that we call as agents. An agent is an production using hybridoma cells, etc. autonomous, self-acting entity capable of attaining a set The ability of cells to learn and adapt (Ramkrishna of goals by utilizing resources at its disposal. Every et al., 1987) to their ever-changing environment has agent in a multi-agent system is unique and is enabled the growth and proliferation of complex characterized by a set of goals, resources and its actions. ecosystems. Based upon several years of evolution, The interaction of an agent with other fellow agents and microbes have developed an advanced internal regula- its immediate environment is the key aspect of an agent- tory system (Kompala et al., 1984) that optimizes based modeling framework. The natural modularity as substrate uptake and maximizes growth. It is our aim evident in this framework helps one to exploit all the to analyze this evolutionary aspect of the cells that has advantages characteristic of an object-oriented para- led to the development of their optimization machinery digm. In addition, this technique also enables the in order to understand the cellular growth behavior and modeler to impart ‘‘intelligence’’ to each of the hopefully to control it. individuals in the system and a means by which they The current work is an attempt to model microbial can change and hence affect or be affected by the growth to study the adaptable nature of cells using the vagaries of the environment—in other words to make agent-based modeling technique as a first-cut attempt to them learn. Essentially, the system would consist of rules analyze more complex systems. Our objective in this that define the way the agents interact with its work is as follows: to study the feasibility of using agent- neighborhood—the environment and other agents— based models to qualitatively study the growth behavior of and would characterize the ‘‘visibility’’ of the agents in microbes using a set of generic rules and to analyze the the system. Agent-based systems have been designed to role of intelligence, learning and adaptation in the growth model vehicular traffic (Burmeister et al., 1997), optimal process of cells. This has been achieved by qualitatively power flow networks (Talukdar and Ramesh, 1994), modeling glucose effect: sequential utilization of sub- ecological systems (http://www.santafe.edu/Bpth/echo/), strates in order of their growth supporting capabilities. bacterial colony growth (Kreft et al., 1998), information Fig. 1 shows the schematic of the growth pattern of exchange in supply chains (Strader et al., 1998), financial cells in a binary substrate environment. Consumption of 1 institutions (Tesfatsion, 1997), human use of the land S1 results in the production of more biomass as and its resources (Polhill et al., 2001) and other complex compared to that produced when the same amount of systems. S2 is consumed. Region I corresponds to the growth The current work deals with the study of intelligent resulting from the uptake of faster growing substrate S1. behavior of microbes in a batch culture in a binary When S1 is exhausted, the cells regulate their internal substrate environment using an agent-based model. metabolic machinery to produce enzymes to consume The rest of this paper is organized as follows. The the other available substrate, S2. The time taken in important characteristics of microbial growth in a switching the regulatory process is known as the diauxie binary substrate environment and the problem consid- lag (Monod, 1942) and is represented by Region II. ered in this work are explained in the next section. Region III shows the growth of cells on substrate S2.As Section 3 details the schematic of the model and is evident from Fig. 1, the slope of the growth curve in our agent-based solution approach using predefined Region III is smaller than that of the slope in Region I. rules. Section 4 presents the rule discovery studies to model learning and intelligent growth behavior of the 1 A binary substrate environment has two substrates that support microbes. We present our conclusions in the final growth at different rates. We denote the faster growth-supporting section.