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Cooperation and Cheating in Exoenzyme Cooperation and cheating in exoenzyme production by microorganisms: Theoretical analysis in view of biotechnological applications Stefan Schuster, Jan-Ulrich Kreft, Naama Brenner, Frank Wessely, Günter Theißen, Eytan Ruppin, Anja Schroeter To cite this version: Stefan Schuster, Jan-Ulrich Kreft, Naama Brenner, Frank Wessely, Günter Theißen, et al.. Co- operation and cheating in exoenzyme production by microorganisms: Theoretical analysis in view of biotechnological applications. Biotechnology Journal, Wiley-VCH Verlag, 2010, 5 (7), pp.751. 10.1002/biot.200900303. hal-00552342 HAL Id: hal-00552342 https://hal.archives-ouvertes.fr/hal-00552342 Submitted on 6 Jan 2011 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Biotechnology Journal Cooperation and cheating in exoenzyme production by microorganisms: Theoretical analysis in view of biotechnological applications For Peer Review Journal: Biotechnology Journal Manuscript ID: biot.200900303.R1 Wiley - Manuscript type: Research Article Date Submitted by the 25-Apr-2010 Author: Complete List of Authors: Schuster, Stefan; Friedrich-Schiller-Universität Jena Kreft, Jan-Ulrich; University of Birmingham, Centre for Systems Biology, School of Biosciences Brenner, Naama; Technion – Israel Institute of Technology, Dept. of Chemical Engineering Wessely, Frank; Friedrich Schiller University of Jena, Dept. of Bioinformatics Theißen, Günter; Friedrich Schiller University of Jena, Dept. of Genetics Ruppin, Eytan; Tel Aviv University, School of Computer Sciences & School of Medicine Schroeter, Anja; Friedrich Schiller University of Jena, Dept. of Bioinformatics Primary Keywords: Biochemical Engineering Secondary Keywords: Systems Biology extracellular enzymes, evolutionary game theory, optimization of Keywords: enzyme synthesis Wiley-VCH Page 1 of 23 Biotechnology Journal 1 1 2 3 4 5 biot.200900303 6 7 Research Article 8 9 10 Cooperation and cheating in exoenzyme production by 11 12 microorganisms – Theoretical analysis in view of 13 14 biotechnological applications 15 16 17 1 2 3 1 4 18 Stefan Schuster , Jan-Ulrich Kreft , Naama Brenner , Frank Wessely , Günter Theißen , 19 Eytan Ruppin 5, and Anja Schroeter 1,* 20 For Peer Review 21 22 1Dept. of Bioinformatics, School of Biology and Pharmaceutics, Ernst-Abbe-Platz 2, 23 24 Friedrich Schiller University of Jena, D-07743 Jena, Germany 25 26 e-mail: [email protected] , [email protected] , [email protected] 27 28 2 29 Centre for Systems Biology, School of Biosciences, University of Birmingham, 30 31 Edgbaston, Birmingham B15 2TT, UK 32 e-mail: [email protected] 33 34 35 3Dept. of Chemical Engineering, 36 37 Technion – Israel Institute of Technology, Technion City, Haifa 32000, Israel 38 39 e-mail: [email protected] 40 41 4 42 Dept. of Genetics, Philosophenweg 12, 43 44 Friedrich Schiller University of Jena, D-07743 Jena, Germany 45 e-mail: [email protected] 46 47 48 5School of Computer Sciences & School of Medicine, 49 50 Tel Aviv University, Tel Aviv 69978, Israel 51 52 e-mail: [email protected] 53 54 55 Key words: evolution of cooperation, evolutionary game theory, extracellular enzymes, 56 57 Prisoner’s Dilemma, snowdrift game 58 59 * 60 Correspondence Wiley-VCH Biotechnology Journal Page 2 of 23 2 1 2 3 4 5 Dept. of Bioinformatics, School of Biology and Pharmaceutics, Ernst-Abbe-Platz 2, 6 Friedrich Schiller University of Jena, D-07743 Jena, Germany 7 8 e-mail: [email protected] , Phone: +49 3641 949583, Fax: +49 3641 946452 9 10 11 12 Abstract 13 The engineering of microorganisms to produce a variety of extracellular enzymes, for 14 15 example for producing renewable fuels and in biodegradation of xenobiotics, has 16 17 recently attracted increasing interest. Productivity is often reduced by "cheater" mutants, 18 19 which are deficient in exoenzyme production and benefitting from the product provided 20 For Peer Review 21 by the "cooperating" cells. We present a game-theoretical model to analyze population 22 structure and exoenzyme productivity in terms of biotechnologically relevant 23 24 parameters. For any given population density, three distinct regimes are predicted: when 25 26 the metabolic effort for exoenzyme production and secretion is low, all cells cooperate; 27 28 at intermediate metabolic costs, cooperators and cheaters coexist, while at high costs, all 29 cells use the cheating strategy. These regimes correspond to the harmony game, 30 31 snowdrift game, and Prisoner’s Dilemma, respectively. Thus, our results indicate that 32 33 microbial strains engineered for exoenzyme production will not, under appropriate 34 35 conditions, be outcompeted by cheater mutants. We also analyze the dependence of the 36 population structure on cell density. At low costs, the fraction of cooperating cells 37 38 increases with decreasing cell density and reaches unity at a critical threshold. Our 39 40 model provides an estimate of the cell density maximizing exoenzyme production. 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Wiley-VCH Page 3 of 23 Biotechnology Journal 3 1 2 3 4 5 1 Introduction 6 7 Many biotechnologically relevant processes involve the action of extracellular enzymes. 8 An example of high commercial interest nowadays is biofuel production. It often 9 10 involves the exoenzyme, cellulase, for saccharification [1, 2]. Extracellular bacterial 11 12 cellulases, xylanases and amylases are important in digestive processes in many habitats 13 14 such as the rumen [3]. Saccharomyces cerevisiae secretes, among others, acid 15 phosphatase [4] and invertase [5]. Further examples are fungal lignolytic enzymes such 16 17 as lignin peroxidase, laccase, and manganese peroxidase [6]. Extracellular enzymes play 18 19 an important role in biodegradation of xenobiotics and, thus, in bioremediation of 20 For Peer Review 21 polluted areas. For example, lignolytic enzymes are also active in the breakdown of 22 23 toxic polycyclic aromatic hydrocarbons [6]. 24 The total production of extracellular enzymes by a population of microorganisms is 25 26 often diminished by the existence of a subpopulation of non-producing cells [3, 7]. 27 28 These cells do not invest the metabolic costs of producing and secreting these enzymes 29 30 while nevertheless benefitting from the substrates released by the action of the 31 exoenzymes generated by other cells (Fig. 1). An illustrative example is provided by 32 33 yeast invertase, encoded by the SUC genes. Some strains of S. cerevisiae carry a non- 34 35 functional SUC2 as the only SUC gene [8]. Moreover, the species S. italicus does not 36 37 harbour any SUC gene [9] while it can benefit from the etxracellular glucose generated 38 39 by the invertase secreted by other Saccharomyces species. Greig and Travisano [10] 40 studied wild-type cells of S. cerevisiae and cells in which the gene SUC2 had been 41 42 deleted. They observed coexistence between both cell types (although the 43 44 subpopulations were generated artificially in that case). Another example is provided by 45 46 Candida albicans. The activity of extracellular enzymes such as proteinase and 47 phospholipase differs significantly among three different genotypic strains [11, 12] and 48 49 among karyotypes of that fungus [13]. 50 51 Secretion of exoenzymes and partial or complete failure to do so can be regarded as 52 53 different strategies of cells in an evolutionary “game” on fitness (growth rates). The 54 55 strategies correspond to genetic or epigenetic states, and switches between them can 56 occur, for example, by mutations or gene silencing, respectively. Evolutionary game 57 58 theory [14 −18] can be used to determine equilibrium states of the population (i.e. 59 60 mixtures of strategies) when the fitness of an organism depends not only on its own Wiley-VCH Biotechnology Journal Page 4 of 23 4 1 2 3 4 5 strategy but also on the strategies of others. That theory has been used for analyzing 6 many properties of living organisms such as sex ratios [14]), the evolution of 7 8 cooperation [16, 18-20], biofilms [21], and the selection of biochemical pathways [22, 9 10 23]. Moreover, it can be used for classification in data analysis [24]. Game theory is 11 12 also a well-suited tool for analyzing and optimizing biotechnological setups in which 13 the balance between competition and cooperation determines productivity. Here we 14 15 present a mathematical framework for modelling exoenzyme production based on 16 17 evolutionary game theory. We analyze the difference in fitness of cooperating and 18 19 cheating cells in dependence on total cell density and on the costs of enzyme production 20 For Peer Review 21 and secretion. 22 In game theory, a number of typical games can be distinguished. Probably the most 23 24 famous is the Prisoner’s Dilemma [25]. In the traditional Prisoner’s Dilemma, defection 25 26 (cheating) is the only stable strategy. Thus, much work has been done on how 27 28 cooperation can evolve in a Prisoner’s Dilemma setting, for example, by stochastic or 29 spatial effects or iteration of the game [15, 16, 26, 27]. Another game is the snowdrift 30 31 game, also known as game of chicken or hawk-dove game [14, 15, 18, 20]. The name 32 33 snowdrift originates from a cover story in which two car drivers got stuck in a blizzard, 34 35 and shoveling snow by one of them is sufficient for both to move on.
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