Cooperation and Cheating in Exoenzyme Production By

Biotechnol. J. 2010, 5 DOI 10.1002/biot.200900303 www.biotechnology-journal.com Research Article Cooperation and cheating in microbial exoenzyme production – Theoretical analysis for biotechnological applications Stefan Schuster1, Jan-Ulrich Kreft2, Naama Brenner3, Frank Wessely1, Günter Theißen4, Eytan Ruppin5 and Anja Schroeter1 1 Department of Bioinformatics, School of Biology and Pharmaceutics, Friedrich Schiller University of Jena, Jena, Germany 2 Centre for Systems Biology, School of Biosciences, University of Birmingham, Birmingham, UK 3 Department of Chemical Engineering, Technion – Israel Institute of Technology, Technion City, Haifa, Israel 4 Department of Genetics, Friedrich Schiller University of Jena, Jena, Germany 5 School of Computer Sciences and School of Medicine, Tel Aviv University, Tel Aviv, Israel The engineering of microorganisms to produce a variety of extracellular enzymes (exoenzymes), for example for producing renewable fuels and in biodegradation of xenobiotics, has recently attracted increasing interest. Productivity is often reduced by “cheater” mutants, which are deficient in exo- Received 19 January 2010 enzyme production and benefit from the product provided by the “cooperating” cells. We present Revised 25 April 2010 a game-theoretical model to analyze population structure and exoenzyme productivity in terms of Accepted 28 April 2010 biotechnologically relevant parameters. For any given population density, three distinct regimes are predicted: when the metabolic effort for exoenzyme production and secretion is low, all cells cooperate; at intermediate metabolic costs, cooperators and cheaters coexist; while at high costs, all cells use the cheating strategy. These regimes correspond to the harmony game, snowdrift game, and Prisoner’s Dilemma, respectively. Thus, our results indicate that microbial strains engineered for exoenzyme production will not, under appropriate conditions, be outcompeted by cheater mutants. We also analyze the dependence of the population structure on cell density. At low costs, the frac- tion of cooperating cells increases with decreasing cell density and reaches unity at a critical thresh- old. Our model provides an estimate of the cell density maximizing exoenzyme production. Keywords: Biochemical engineering · Evolutionary game theory · Extracellular enzymes · Optimization of enzyme synthesis · Systems biology 1 Introduction nowadays is biofuel production. It often involves the exoenzyme, cellulase, for saccharification [1, 2]. Many biotechnologically relevant processes in- Extracellular bacterial cellulases, xylanases and volve the action of extracellular enzymes (exoen- amylases are important in digestive processes in zymes). An example of high commercial interest many habitats such as the rumen [3]. Saccha- romyces cerevisiae secretes, among others, acid phosphatase [4] and invertase [5]. Further exam- ples are fungal lignolytic enzymes such as lignin Correspondence: Dr. Anja Schroeter, Department of Bioinformatics, peroxidase, laccase, and manganese peroxidase [6]. School of Biology and Pharmaceutics, Ernst-Abbe-Platz 2, Friedrich Exoenzymes play an important role in biodegrada- Schiller University of Jena, 07743 Jena, Germany tion of xenobiotics and, thus, in bioremediation of E-mail: [email protected] Fax: +49-3641-946452 polluted areas. For example, lignolytic enzymes are also active in the breakdown of toxic polycyclic aro- Abbreviation: ESS, evolutionarily stable strategy matic hydrocarbons [6]. © 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim 1 Biotechnology Biotechnol. J. 2010, 5 Journal [14-18] can be used to determine equilibrium states of the population (i.e., mixtures of strategies) when the fitness of an organism depends not only on its own strategy but also on the strategies of others. That theory has been used for analyzing many properties of living organisms such as sex ratios [14], the evolution of cooperation [16, 18–20], biofilms [21], and the selection of biochemical pathways [22, 23]. Moreover, it can be used for clas- sification in data analysis [24]. Game theory is also a well-suited tool for analyzing and optimizing biotechnological setups in which the balance between competition and cooperation determines productivity. Here we present a mathematical framework for modeling exoenzyme production Figure 1. Interplay between microbial cells upon secretion of exoenzymes. based on evolutionary game theory.We analyze the Cheater cells (denoted by ‘Cheat’) do not produce exoenzymes (incised difference in fitness of cooperating and cheating circles) and benefit from the growth substrate (monomers) released by cells in dependence on total cell density and on the the enzyme secreted by cooperating cells (‘Coop’). The initial substrate is costs of enzyme production and secretion. indicated by dimers (e.g., sucrose), even though it may consist of poly- mers such as cellulose. Besides this “desirable” substrate, other sub- In game theory, a number of typical games can strates may be present. A possibly present periplasmic space is represent- be distinguished. Probably the most famous is the ed by the double envelope. Note that the concentration of the growth Prisoner’s Dilemma [25]. In the traditional Prison- substrate is higher near cooperating cells in this spatially heterogeneous er’s Dilemma, defection (cheating) is the only sta- system. ble strategy. Thus, much work has been done on how cooperation can evolve in a Prisoner’s Dilem- The total production of extracellular enzymes ma setting, for example, by stochastic or spatial ef- by a population of microorganisms is often dimin- fects or iteration of the game [15, 16, 26, 27]. An- ished by the existence of a subpopulation of non- other game is the snowdrift game, also known as producing cells [3, 7]. These cells do not invest the game of chicken or hawk-dove game [14, 15, 18, 20]. metabolic costs of producing and secreting these The name snowdrift originates from a cover story enzymes, but benefit from the substrates released in which two car drivers got stuck in a blizzard, and by the action of the exoenzymes generated by oth- shoveling snow by one of them is sufficient for both er cells (Fig. 1). An illustrative example is provided to move on.There, cooperation occurs naturally be- by yeast invertase, encoded by the SUC genes. cause that game leads to two Nash equilibria, in Some strains of S. cerevisiae carry a non-function- which one player cooperates and the other one de- al SUC2 as the only SUC gene [8]. Moreover, the fects. Nash equilibria are situations where none of species S. italicus does not harbor any SUC gene the players would benefit from switching strategy [9], but benefits from the extracellular glucose gen- unilaterally [15, 28]. In the snowdrift game, the pay- erated by the invertase secreted by other Saccha- off for the cooperating player would be reduced romyces species. Greig and Travisano [10] studied when switching to defection because this player wild-type cells of S. cerevisiae and cells in which would then – in the cover story – remain stuck in the gene SUC2 had been deleted. They observed the snowdrift.An example from everyday life is the coexistence between both cell types (although the situation where two people want to pass a narrow subpopulations were generated artificially in that door. In the two Nash equilibria, one person goes case). Another example is provided by Candida al- first while the other waits a moment. In a popula- bicans. The activity of extracellular enzymes such tion, the two equilibria in the snowdrift game imply as proteinase and phospholipase differs signifi- that defectors and cooperators can coexist. Anoth- cantly among three different genotypic strains [11, er relevant game is the harmony game [23, 26], also 12] and among karyotypes of that fungus [13]. called mutually beneficial game, in which the only Secretion of exoenzymes and partial or com- stable solution is where all players cooperate. plete failure to do so can be regarded as different An advantage of using game theory rather than strategies of cells in an evolutionary “game” on fit- traditional dynamic simulation or other techniques ness (growth rates). The strategies correspond to is that the complicated process of finding the stable genetic or epigenetic states, and switches between solution is not considered. For example, it usually them can occur, for example, by mutations or gene takes some communication and, thus, some time, silencing, respectively. Evolutionary game theory until the players agree upon the Nash equilibrium, 2 © 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Biotechnol. J. 2010, 5 www.biotechnology-journal.com as we know from the situation of passing a door. fitness of cheaters on total cell density in Greig and Only the final situation is determined. For the pres- Travisano’s experiment [10]. ent calculations, we use the concept of “evolution- The presented approach has a wide range of po- arily stable strategy” (ESS) [14, 15]. It is a general- tential applications. This includes the economical- ization of the Nash equilibrium to n-player situa- ly important production of renewable biofuels such tions with large n. An ESS is a strategy which, if as ethanol from non-food sources. For this purpose, chosen by a population of agents (e.g., microbial various microorganisms can be engineered to se- cells), cannot be outcompeted by any alternative crete exoenzymes for degrading celluloses and strategy that is initially rare. The ESSs can be at- hemicelluloses

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