Use of game-theoretical methods in biochemistry and biophysics

Game-Theoretic Flux Balance Analysis Model for Predicting Stable Community Composition

Models for microbial interactions attempt to understand and predict the steady state network of inter-species relationships in a community, e.g. competition for shared metabolites, and cooperation through cross-feeding. Flux balance analysis (FBA) is an approach that was introduced to model the interaction of a particular microbial species with its environment. This approach has been extended to analyzing interactions in a community of microbes; however, these approaches have two important drawbacks: first, one has to numerically solve a differential equation to identify the steady state, and second, there are no methods available to analyze the stability of the steady state. We propose a game theory based community FBA model wherein species compete to maximize their individual growth rate, and the state of the community is given by the resulting Nash equilibrium. We develop a computationally efficient method for directly computing the steady state biomasses and fluxes without solving a differential equation. We also develop a method to determine the stability of a steady state to perturbations in the biomasses and to invasion by new species. We report the results of applying our proposed framework to a small community of four E. coli mutants that compete for externally supplied glucose, as well as cooperate since the mutants are auxotrophic for metabolites exported by other mutants, and a more realistic model for a gut microbiome consisting of nine species.

Evolutionary Game-Theoretic Approach to the Population Dynamics of Early Replicators

The population dynamics of early replicators has revealed numerous puzzles, highlighting the difficulty of transitioning from simple template-directed replicating molecules to complex biological systems. The resolution of these puzzles has set the research agenda on prebiotic evolution since the seminal works of Manfred Eigen in the 1970s. Here, we study the effects of demographic noise on the population dynamics of template-directed (non-enzymatic) and protein-mediated (enzymatic) replicators. We borrow stochastic algorithms from evolutionary game theory to simulate finite populations of two types of replicators. These algorithms recover the replicator equation framework in the infinite population limit. For large but finite populations, we use finite-size scaling to determine the probability of fixation and the mean time to fixation near a threshold that delimits the regions of dominance of each replicator type. Since enzyme-producing replicators cannot evolve in a well-mixed population containing replicators that benefit from the enzyme but do not encode it, we study the evolution of enzyme-producing replicators in a finite population structured in temporarily formed random groups of fixed size n. We argue that this problem is identical to the weak-altruism version of the n-player prisoner's dilemma, and show that the threshold is given by the condition that the reward for altruistic behavior is equal to its cost.

Diffusion and pattern formation in spatial games

Diffusion plays an important role in a wide variety of phenomena, from bacterial quorum sensing to the dynamics of traffic flow. While it generally tends to level out gradients and inhomogeneities, diffusion has nonetheless been shown to promote pattern formation in certain classes of systems. Formation of stable structures often serves as a key factor in promoting the emergence and persistence of cooperative behavior in otherwise competitive environments, however, an in-depth analysis on the impact of diffusion on such systems is lacking. We therefore investigate the effects of diffusion on cooperative behavior using a cellular automaton (CA) model of the noisy spatial iterated prisoner's dilemma (IPD), physical extension, and stochasticity being unavoidable characteristics of several natural phenomena. We further derive a mean-field (MF) model that captures the three-species predation dynamics from the CA model and highlight how pattern formation arises in this new model, then characterize how including diffusion by interchange similarly enables the emergence of large scale structures in the CA model as well. We investigate how these emerging patterns favors cooperative behavior for parameter space regions where IPD error rates classically forbid such dynamics. We thus demonstrate how the coupling of diffusion with nonlinear dynamics can, counterintuitively, promote large-scale structure formation and in return establish new grounds for cooperation to take hold in stochastic spatial systems.

Shifts in evolutionary balance of phenotypes under environmental changes

Environments shape communities by driving individual interactions and the evolutionary outcome of competition. In static, homogeneous environments a robust, evolutionary stable, outcome is sometimes reachable. However, inherently stochastic, this evolutionary process need not stabilize, resulting in a dynamic ecological state, often observed in microbial communities. We use evolutionary games to study the evolution of phenotypic competition in dynamic environments. Under the assumption that phenotypic expression depends on the environmental shifts, existing periodic relationships may break or result in formation of new periodicity in phenotypic interactions. The exact outcome depends on the environmental shift itself, indicating the importance of understanding how environments influence affected systems. Under periodic environmental fluctuations, a stable state preserving dominant phenotypes may exist. However, rapid environmental shifts can lead to critical shifts in the phenotypic evolutionary balance. This might lead to environmentally favoured phenotypes dominating making the system vulnerable. We suggest that understanding of the robustness of the system's current state is necessary to anticipate when it will shift to a new equilibrium via understanding what level of perturbations the system can take before its equilibrium changes. Our results provide insights in how microbial communities can be steered to states where they are dominated by desired phenotypes.

Thermodynamic selection: mechanisms and scenarios

Thermodynamic selection is an indirect competition between agents feeding on the same energy resource and obeying the laws of thermodynamics. We examine scenarios of this selection, where the agent is modeled as a heat-engine coupled to two thermal baths and extracting work from the high-temperature bath. The agents can apply different work-extracting, game-theoretical strategies, e.g. the maximum power or the maximum efficiency. They can also have a fixed structure or be adaptive. Depending on whether the resource (i.e. the high-temperature bath) is infinite or finite, the fitness of the agent relates to the work-power or the total extracted work. These two selection scenarios lead to increasing or decreasing efficiencies of the work-extraction, respectively. The scenarios are illustrated via plant competition for sunlight, and the competition between different ATP production pathways. We also show that certain general concepts of game-theory and ecology-the prisoner's dilemma and the maximal power principle-emerge from the thermodynamics of competing agents. We emphasize the role of adaptation in developing efficient work-extraction mechanisms.

Emerging spatiotemporal patterns in cyclic predator-prey systems with habitats

Three-species cyclic predator-prey systems are known to establish spiral waves that allow species to coexist. In this study, we analyze a structured heterogeneous system which gives one species an advantage to escape predation in an area that we refer to as a habitat and study the effect on species coexistence and emerging spatiotemporal patterns. Counterintuitively, the predator of the advantaged species emerges as dominant species with the highest average density inside the habitat. The species given the advantage in the form of an escape rate has the lowest average density until some threshold value for the escape rate is exceeded, after which the density of the species with the advantage overtakes that of its prey. Numerical analysis of the spatial density of each species as well as of the spatial two-point correlation function for both inside and outside the habitats allow a detailed quantitative discussion. Our analysis is extended to a six-species game that exhibits spontaneous spiral waves, which displays similar but more complicated results.

A Mutation Threshold for Cooperative Takeover

One of the leading theories for the origin of life includes the hypothesis according to which life would have evolved as cooperative networks of molecules. Explaining cooperation—and particularly, its emergence in favoring the evolution of life-bearing molecules—is thus a key element in describing the transition from nonlife to life. Using agent-based modeling of the iterated prisoner’s dilemma, we investigate the emergence of cooperative behavior in a stochastic and spatially extended setting and characterize the effects of inheritance and variability. We demonstrate that there is a mutation threshold above which cooperation is—counterintuitively—selected, which drives a dramatic and robust cooperative takeover of the whole system sustained consistently up to the error catastrophe, in a manner reminiscent of typical phase transition phenomena in statistical physics. Moreover, our results also imply that one of the simplest conditional cooperative strategies, “Tit-for-Tat”, plays a key role in the emergence of cooperative behavior required for the origin of life.

Predicting Nash equilibria for microbial metabolic interactions

MOTIVATION

Microbial metabolic interactions impact ecosystems, human health and biotechnology profoundly. However, their determination remains elusive, invoking an urgent need for predictive models seamlessly integrating metabolism with evolutionary principles that shape community interactions.

RESULTS

Inspired by the evolutionary game theory, we formulated a bi-level optimization framework termed NECom for which any feasible solutions are Nash equilibria of microbial community metabolic models with/without an outer-level (community) objective function. Distinct from discrete matrix games, NECom models the continuous interdependent strategy space of metabolic fluxes. We showed that NECom successfully predicted several classical games in the context of metabolic interactions that were falsely or incompletely predicted by existing methods, including prisoner's dilemma, snowdrift and cooperation. The improved capability originates from the novel formulation to prevent 'forced altruism' hidden in previous static algorithms while allowing for sensing all potential metabolite exchanges to determine evolutionarily favorable interactions between members, a feature missing in dynamic methods. The results provided insights into why mutualism is favorable despite seemingly costly cross-feeding metabolites and demonstrated similarities and differences between games in the continuous metabolic flux space and matrix games. NECom was then applied to a reported algae-yeast co-culture system that shares typical cross-feeding features of lichen, a model system of mutualism. 488 growth conditions corresponding to 3,221 experimental data points were simulated. Without training any parameters using the data, NECom is more predictive of species' growth rates given uptake rates compared with flux balance analysis with an overall 63.5% and 81.7% reduction in root-mean-square error for the two species.

AVAILABILITY

Simulation code and data are available at https://github.com/Jingyi-Cai/NECom.git.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Origin of biomolecular games: deception and molecular evolution

Biological macromolecules encode information: some of it to endow the molecule with structural flexibility, some of it to enable molecular actions as a catalyst or a substrate, but a residual part can be used to communicate with other macromolecules. Thus, macromolecules do not need to possess information only to survive in an environment, but also to strategically interact with others by sending signals to a receiving macromolecule that can properly interpret the signal and act suitably. These sender-receiver signalling games are sustained by the information asymmetry that exists among the macromolecules. In both biochemistry and molecular evolution, the important role of information asymmetry remains largely unaddressed. Here, we provide a new unifying perspective on the impact of information symmetry between macromolecules on molecular evolutionary processes, while focusing on molecular deception. Biomolecular games arise from the ability of biological macromolecules to exert precise recognition, and their role as units of selection, meaning that they are subject to competition and cooperation with other macromolecules. Thus, signalling game theory can be used to better understand fundamental features of living systems such as molecular recognition, molecular mimicry, selfish elements and 'junk' DNA. We show how deceptive behaviour at the molecular level indicates a conflict of interest, and so provides evidence of genetic conflict. This model proposes that molecular deception is diagnostic of selfish behaviour, helping to explain the evasive behaviour of transposable elements in 'junk' DNA, for example. Additionally, in this broad review, a range of major evolutionary transitions are shown to be associated with the establishment of signalling conventions, many of which are susceptible to molecular deception. These perspectives allow us to assign rudimentary behaviour to macromolecules, and show how participation in signalling games differentiates biochemistry from abiotic chemistry.

Game Theory in Molecular Nanosensing System for Rapid Detection of Hg2+ in Aqueous Solutions

Game theory—the scientific study of interactive, rational decision making—describes the interaction of two or more players from macroscopic organisms to microscopic cellular and subcellular levels. Life based on molecules is the highest and most complex expression of molecular interactions. However, using simple molecules to expand game theory for molecular decision-making remains challenging. Herein, we demonstrate a proof-of-concept molecular game-theoretical system (molecular prisoner’s dilemma) that relies on formation of the thymine–Hg2+–thymine hairpin structure specifically induced by Hg2+ and fluorescence quenching and molecular adsorption capacities of cobalt oxyhydroxide (CoOOH) nanosheets, resulting in fluorescence intensity and distribution change of polythymine oligonucleotide 33-repeat thymines (T33). The “bait” molecule, T33, interacted with two molecular players, CoOOH and Hg2+, in different states (absence = silence and presence = betrayal), regarded as strategies. We created conflicts (sharing or self-interest) of fluorescence distribution of T33, quantifiable in a 2 × 2 payoff matrix. In addition, the molecular game-theoretical-system based on T33 and CoOOH was used for sensing Hg2+ over the range of 20 to 600 nM with the detection limit of 7.94 nM (3σ) and for determination of Hg2+ in pond water. Inspired by the proof-of-concept for molecular game theory, various molecular decision-making systems could be developed, which would help promote molecular information processing and generating novel molecular intelligent decision systems for environmental monitoring and molecular diagnosis and therapy.

A game theory appraisal of the insurance hypothesis: Specific polymorphisms in the energy homeostasis network as imprints of a successful minimax strategy

The existence of specific polymorphisms in genes of key hormones of the energy homeostasis network that have been shown to predispose to obesity and the so-called metabolic syndrome provides further biological support for the proposed insurance hypothesis. In a broader sense, such polymorphisms can be understood as biological imprints of an evolutionarily successful minimax strategy employed by ancient Homo sapiens subpopulations in a one-player game against nature.

Golden Gait: An Optimization Theory Perspective on Human and Humanoid Walking

Human walking is a complex task which includes hundreds of muscles, bones and joints working together to deliver harmonic movements with the need of finding equilibrium between moving forward and maintaining stability. Many different computational approaches have been used to explain human walking mechanisms, from pendular model to fractal approaches. A new perspective can be gained from using the principles developed in the field of Optimization theory and in particularly the branch of Game Theory. In particular we provide a new insight into human walking showing as the trade-off between advancement and equilibrium managed during walking has the same solution of the Ultimatum game, one of the most famous paradigms of game theory, and this solution is the golden ratio. The golden ratio is an irrational number that was found in many biological and natural systems self-organized in a harmonic, asymmetric, and fractal structure. Recently, the golden ratio has also been found as the equilibrium point between two players involved into the Ultimatum Game. It has been suggested that this result can be due to the fact that the golden ratio is perceived as the fairest asymmetric solution by the two players. The golden ratio is also the most common proportion between stance and swing phase of human walking. This approach may explain the importance of harmony in human walking, and provide new perspectives for developing quantitative assessment of human walking, efficient humanoid robotic walkers, and effective neurorobots for rehabilitation.

The prisoner's dilemma as a cancer model

Tumor development is an evolutionary process in which a heterogeneous population of cells with different growth capabilities compete for resources in order to gain a proliferative advantage. What are the minimal ingredients needed to recreate some of the emergent features of such a developing complex ecosystem? What is a tumor doing before we can detect it? We outline a mathematical model, driven by a stochastic Moran process, in which cancer cells and healthy cells compete for dominance in the population. Each are assigned payoffs according to a Prisoner's Dilemma evolutionary game where the healthy cells are the cooperators and the cancer cells are the defectors. With point mutational dynamics, heredity, and a fitness landscape controlling birth and death rates, natural selection acts on the cell population and simulated 'cancer-like' features emerge, such as Gompertzian tumor growth driven by heterogeneity, the log-kill law which (linearly) relates therapeutic dose density to the (log) probability of cancer cell survival, and the Norton-Simon hypothesis which (linearly) relates tumor regression rates to tumor growth rates. We highlight the utility, clarity, and power that such models provide, despite (and because of) their simplicity and built-in assumptions.

Synthetic Ecology of Microbes: Mathematical Models and Applications

As the indispensable role of natural microbial communities in many aspects of life on Earth is uncovered, the bottom-up engineering of synthetic microbial consortia with novel functions is becoming an attractive alternative to engineering single-species systems. Here, we summarize recent work on synthetic microbial communities with a particular emphasis on open challenges and opportunities in environmental sustainability and human health. We next provide a critical overview of mathematical approaches, ranging from phenomenological to mechanistic, to decipher the principles that govern the function, dynamics and evolution of microbial ecosystems. Finally, we present our outlook on key aspects of microbial ecosystems and synthetic ecology that require further developments, including the need for more efficient computational algorithms, a better integration of empirical methods and model-driven analysis, the importance of improving gene function annotation, and the value of a standardized library of well-characterized organisms to be used as building blocks of synthetic communities.

Causes of upregulation of glycolysis in lymphocytes upon stimulation. A comparison with other cell types

In this review, we revisit the metabolic shift from respiration to glycolysis in lymphocytes upon activation, which is known as the Warburg effect in tumour cells. We compare the situation in lymphocytes with those in several other cell types, such as muscle cells, Kupffer cells, microglia cells, astrocytes, stem cells, tumour cells and various unicellular organisms (e.g. yeasts). We critically discuss and compare several explanations put forward in the literature for the observation that proliferating cells adopt this apparently less efficient pathway: hypoxia, poisoning of competitors by end products, higher ATP production rate, higher precursor supply, regulatory effects, and avoiding harmful effects (e.g. by reactive oxygen species). We conclude that in the case of lymphocytes, increased ATP production rate and precursor supply are the main advantages of upregulating glycolysis.

Evolutionary game theory: cells as players

In two papers we review game theory applications in biology below the level of cognitive living beings. It can be seen that evolution and natural selection replace the rationality of the actors appropriately. Even in these micro worlds, competing situations and cooperative relationships can be found and modeled by evolutionary game theory. Also those units of the lowest levels of life show different strategies for different environmental situations or different partners. We give a wide overview of evolutionary game theory applications to microscopic units. In this first review situations on the cellular level are tackled. In particular metabolic problems are discussed, such as ATP-producing pathways, secretion of public goods and cross-feeding. Further topics are cyclic competition among more than two partners, intra- and inter-cellular signalling, the struggle between pathogens and the immune system, and the interactions of cancer cells. Moreover, we introduce the theoretical basics to encourage scientists to investigate problems in cell biology and molecular biology by evolutionary game theory.

Different perceptions of social dilemmas: evolutionary multigames in structured populations

Motivated by the fact that the same social dilemma can be perceived differently by different players, we here study evolutionary multigames in structured populations. While the core game is the weak prisoner's dilemma, a fraction of the population adopts either a positive or a negative value of the sucker's payoff, thus playing either the traditional prisoner's dilemma or the snowdrift game. We show that the higher the fraction of the population adopting a different payoff matrix the more the evolution of cooperation is promoted. The microscopic mechanism responsible for this outcome is unique to structured populations, and it is due to the payoff heterogeneity, which spontaneously introduces strong cooperative leaders that give rise to an asymmetric strategy imitation flow in favor of cooperation. We demonstrate that the reported evolutionary outcomes are robust against variations of the interaction network, and they also remain valid if players are allowed to vary which game they play over time. These results corroborate existing evidence in favor of heterogeneity-enhanced network reciprocity, and they reveal how different perceptions of social dilemmas may contribute to their resolution.

Critical transitions in a game theoretic model of tumour metabolism

Tumour proliferation is promoted by an intratumoral metabolic symbiosis in which lactate from stromal cells fuels energy generation in the oxygenated domain of the tumour. Furthermore, empirical data show that tumour cells adopt an intermediate metabolic state between lactate respiration and glycolysis. This study models the metabolic symbiosis in the tumour through the formalism of evolutionary game theory. Our game model of metabolic symbiosis in cancer considers two types of tumour cells, hypoxic and oxygenated, while glucose and lactate are considered as the two main sources of energy within the tumour. The model confirms the presence of multiple intermediate stable states and hybrid energy strategies in the tumour. It predicts that nonlinear interaction between two subpopulations leads to tumour metabolic critical transitions and that tumours can obtain different intermediate states between glycolysis and respiration which can be regulated by the genomic mutation rate. The model can apply in the epithelial-stromal metabolic decoupling therapy.

Defection and extortion as unexpected catalysts of unconditional cooperation in structured populations

We study the evolution of cooperation in the spatial prisoner's dilemma game, where besides unconditional cooperation and defection, tit-for-tat, win-stay-lose-shift and extortion are the five competing strategies. While pairwise imitation fails to sustain unconditional cooperation and extortion regardless of game parametrization, myopic updating gives rise to the coexistence of all five strategies if the temptation to defect is sufficiently large or if the degree distribution of the interaction network is heterogeneous. This counterintuitive evolutionary outcome emerges as a result of an unexpected chain of strategy invasions. Firstly, defectors emerge and coarsen spontaneously among players adopting win-stay-lose-shift. Secondly, extortioners and players adopting tit-for-tat emerge and spread via neutral drift among the emerged defectors. And lastly, among the extortioners, cooperators become viable too. These recurrent evolutionary invasions yield a five-strategy phase that is stable irrespective of the system size and the structure of the interaction network, and they reveal the most unexpected mechanism that stabilizes extortion and cooperation in an evolutionary setting.

Evolutionary game theory: molecules as players

In many situations macromolecules, such as proteins, DNA and RNA, can be considered as players in the sense of game theory. In this review we discuss the usefulness of game theory in describing macromolecular processes.

Nodes having a major influence to break cooperation define a novel centrality measure: game centrality

Cooperation played a significant role in the self-organization and evolution of living organisms. Both network topology and the initial position of cooperators heavily affect the cooperation of social dilemma games. We developed a novel simulation program package, called ‘NetworGame’, which is able to simulate any type of social dilemma games on any model, or real world networks with any assignment of initial cooperation or defection strategies to network nodes. The ability of initially defecting single nodes to break overall cooperation was called as ‘game centrality’. The efficiency of this measure was verified on well-known social networks, and was extended to ‘protein games’, i.e. the simulation of cooperation between proteins, or their amino acids. Hubs and in particular, party hubs of yeast protein-protein interaction networks had a large influence to convert the cooperation of other nodes to defection. Simulations on methionyl-tRNA synthetase protein structure network indicated an increased influence of nodes belonging to intra-protein signaling pathways on breaking cooperation. The efficiency of single, initially defecting nodes to convert the cooperation of other nodes to defection in social dilemma games may be an important measure to predict the importance of nodes in the integration and regulation of complex systems. Game centrality may help to design more efficient interventions to cellular networks (in forms of drugs), to ecosystems and social networks.

Structure and dynamics of molecular networks: a novel paradigm of drug discovery: a comprehensive review

Despite considerable progress in genome- and proteome-based high-throughput screening methods and in rational drug design, the increase in approved drugs in the past decade did not match the increase of drug development costs. Network description and analysis not only give a systems-level understanding of drug action and disease complexity, but can also help to improve the efficiency of drug design. We give a comprehensive assessment of the analytical tools of network topology and dynamics. The state-of-the-art use of chemical similarity, protein structure, protein-protein interaction, signaling, genetic interaction and metabolic networks in the discovery of drug targets is summarized. We propose that network targeting follows two basic strategies. The "central hit strategy" selectively targets central nodes/edges of the flexible networks of infectious agents or cancer cells to kill them. The "network influence strategy" works against other diseases, where an efficient reconfiguration of rigid networks needs to be achieved by targeting the neighbors of central nodes/edges. It is shown how network techniques can help in the identification of single-target, edgetic, multi-target and allo-network drug target candidates. We review the recent boom in network methods helping hit identification, lead selection optimizing drug efficacy, as well as minimizing side-effects and drug toxicity. Successful network-based drug development strategies are shown through the examples of infections, cancer, metabolic diseases, neurodegenerative diseases and aging. Summarizing >1200 references we suggest an optimized protocol of network-aided drug development, and provide a list of systems-level hallmarks of drug quality. Finally, we highlight network-related drug development trends helping to achieve these hallmarks by a cohesive, global approach.

Evolution of emotions on networks leads to the evolution of cooperation in social dilemmas

We show that the resolution of social dilemmas in random graphs and scale-free networks is facilitated by imitating not the strategy of better-performing players but, rather, their emotions. We assume sympathy and envy to be the two emotions that determine the strategy of each player in any given interaction, and we define them as the probabilities of cooperating with players having a lower and a higher payoff, respectively. Starting with a population where all possible combinations of the two emotions are available, the evolutionary process leads to a spontaneous fixation to a single emotional profile that is eventually adopted by all players. However, this emotional profile depends not only on the payoffs but also on the heterogeneity of the interaction network. Homogeneous networks, such as lattices and regular random graphs, lead to fixations that are characterized by high sympathy and high envy, while heterogeneous networks lead to low or modest sympathy but also low envy. Our results thus suggest that public emotions and the propensity to cooperate at large depend, and are in fact determined by, the properties of the interaction network.

Activated lymphocytes as a metabolic model for carcinogenesis

Metabolic reprogramming is a key event in tumorigenesis to support cell growth, and cancer cells frequently become both highly glycolytic and glutamine dependent. Similarly, T lymphocytes (T cells) modify their metabolism after activation by foreign antigens to shift from an energetically efficient oxidative metabolism to a highly glycolytic and glutamine-dependent metabolic program. This metabolic transition enables T cell growth, proliferation, and differentiation. In both activated T cells and cancer cells metabolic reprogramming is achieved by similar mechanisms and offers similar survival and cell growth advantages. Activated T cells thus present a useful model with which to study the development of tumor metabolism. Here, we review the metabolic similarities and distinctions between activated T cells and cancer cells, and discuss both the common signaling pathways and master metabolic regulators that lead to metabolic rewiring. Ultimately, understanding how and why T cells adopt a cancer cell-like metabolic profile may identify new therapeutic strategies to selectively target tumor metabolism or inflammatory immune responses.

Beyond pairwise strategy updating in the prisoner's dilemma game

In spatial games players typically alter their strategy by imitating the most successful or one randomly selected neighbor. Since a single neighbor is taken as reference, the information stemming from other neighbors is neglected, which begets the consideration of alternative, possibly more realistic approaches. Here we show that strategy changes inspired not only by the performance of individual neighbors but rather by entire neighborhoods introduce a qualitatively different evolutionary dynamics that is able to support the stable existence of very small cooperative clusters. This leads to phase diagrams that differ significantly from those obtained by means of pairwise strategy updating. In particular, the survivability of cooperators is possible even by high temptations to defect and over a much wider uncertainty range. We support the simulation results by means of pair approximations and analysis of spatial patterns, which jointly highlight the importance of local information for the resolution of social dilemmas.

Risk-driven migration and the collective-risk social dilemma

A collective-risk social dilemma implies that personal endowments will be lost if contributions to the common pool within a group are too small. Failure to reach the collective target thus has dire consequences for all group members, independently of their strategies. Wanting to move away from unfavorable locations is therefore anything but surprising. Inspired by these observations, we here propose and study a collective-risk social dilemma where players are allowed to move if the collective failure becomes too probable. More precisely, this so-called risk-driven migration is launched depending on the difference between the actual contributions and the declared target. Mobility therefore becomes an inherent property that is utilized in an entirely self-organizing manner. We show that under these assumptions cooperation is promoted much more effectively than under the action of manually determined migration rates. For the latter, we in fact identify parameter regions where the evolution of cooperation is greatly inhibited. Moreover, we find unexpected spatial patterns where cooperators that do not form compact clusters outperform those that do, and where defectors are able to utilize strikingly different ways of invasion. The presented results support the recently revealed importance of percolation for the successful evolution of public cooperation, while at the same time revealing surprisingly simple methods of self-organization towards socially desirable states.

Wisdom of groups promotes cooperation in evolutionary social dilemmas

Whether or not to change strategy depends not only on the personal success of each individual, but also on the success of others. Using this as motivation, we study the evolution of cooperation in games that describe social dilemmas, where the propensity to adopt a different strategy depends both on individual fitness as well as on the strategies of neighbors. Regardless of whether the evolutionary process is governed by pairwise or group interactions, we show that plugging into the “wisdom of groups” strongly promotes cooperative behavior. The more the wider knowledge is taken into account the more the evolution of defectors is impaired. We explain this by revealing a dynamically decelerated invasion process, by means of which interfaces separating different domains remain smooth and defectors therefore become unable to efficiently invade cooperators. This in turn invigorates spatial reciprocity and establishes decentralized decision making as very beneficial for resolving social dilemmas.

Conditional strategies and the evolution of cooperation in spatial public goods games

The fact that individuals will most likely behave differently in different situations begets the introduction of conditional strategies. Inspired by this, we study the evolution of cooperation in the spatial public goods game, where, besides unconditional cooperators and defectors, also different types of conditional cooperators compete for space. Conditional cooperators will contribute to the public good only if other players within the group are likely to cooperate as well but will withhold their contribution otherwise. Depending on the number of other cooperators that are required to elicit cooperation of a conditional cooperator, the latter can be classified in as many types as there are players within each group. We find that the most cautious cooperators, who require all other players within a group to be conditional cooperators, are the undisputed victors of the evolutionary process, even at very low synergy factors. We show that the remarkable promotion of cooperation is due primarily to the spontaneous emergence of quarantining of defectors, who become surrounded by conditional cooperators and are forced into isolated convex "bubbles" from which they are unable to exploit the public good. This phenomenon can be observed only in structured populations, thus adding to the relevance of pattern formation for the successful evolution of cooperation.

Evolution of interactions and cooperation in the spatial prisoner's dilemma game

We study the evolution of cooperation in the spatial prisoner's dilemma game where players are allowed to establish new interactions with others. By employing a simple coevolutionary rule entailing only two crucial parameters, we find that different selection criteria for the new interaction partners as well as their number vitally affect the outcome of the game. The resolution of the social dilemma is most probable if the selection favors more successful players and if their maximally attainable number is restricted. While the preferential selection of the best players promotes cooperation irrespective of game parametrization, the optimal number of new interactions depends somewhat on the temptation to defect. Our findings reveal that the "making of new friends" may be an important activity for the successful evolution of cooperation, but also that partners must be selected carefully and their number limited.

Genome-scale metabolic modeling elucidates the role of proliferative adaptation in causing the Warburg effect

The Warburg effect--a classical hallmark of cancer metabolism--is a counter-intuitive phenomenon in which rapidly proliferating cancer cells resort to inefficient ATP production via glycolysis leading to lactate secretion, instead of relying primarily on more efficient energy production through mitochondrial oxidative phosphorylation, as most normal cells do. The causes for the Warburg effect have remained a subject of considerable controversy since its discovery over 80 years ago, with several competing hypotheses. Here, utilizing a genome-scale human metabolic network model accounting for stoichiometric and enzyme solvent capacity considerations, we show that the Warburg effect is a direct consequence of the metabolic adaptation of cancer cells to increase biomass production rate. The analysis is shown to accurately capture a three phase metabolic behavior that is observed experimentally during oncogenic progression, as well as a prominent characteristic of cancer cells involving their preference for glutamine uptake over other amino acids.

Heterogeneous aspirations promote cooperation in the prisoner's dilemma game

To be the fittest is central to proliferation in evolutionary games. Individuals thus adopt the strategies of better performing players in the hope of successful reproduction. In structured populations the array of those that are eligible to act as strategy sources is bounded to the immediate neighbors of each individual. But which one of these strategy sources should potentially be copied? Previous research dealt with this question either by selecting the fittest or by selecting one player uniformly at random. Here we introduce a parameter u that interpolates between these two extreme options. Setting u equal to zero returns the random selection of the opponent, while positive u favor the fitter players. In addition, we divide the population into two groups. Players from group A select their opponents as dictated by the parameter u, while players from group B do so randomly irrespective of u. We denote the fraction of players contained in groups A and B by v and 1 - v, respectively. The two parameters u and v allow us to analyze in detail how aspirations in the context of the prisoner’s dilemma game influence the evolution of cooperation. We find that for sufficiently positive values of u there exist a robust intermediate v ≈ 0.5 for which cooperation thrives best. The robustness of this observation is tested against different levels of uncertainty in the strategy adoption process K and for different interaction networks. We also provide complete phase diagrams depicting the dependence of the impact of u and v for different values of K, and contrast the validity of our conclusions by means of an alternative model where individual aspiration levels are subject to evolution as well. Our study indicates that heterogeneity in aspirations may be key for the sustainability of cooperation in structured populations.

Cooperation and cheating in microbial exoenzyme production--theoretical analysis for biotechnological applications

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 exoenzyme production and benefit from the product provided by the "cooperating" cells. We present a game-theoretical model to analyze population structure and exoenzyme productivity in terms of 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 fraction of cooperating cells increases with decreasing cell density and reaches unity at a critical threshold. Our model provides an estimate of the cell density maximizing exoenzyme production.

Induced fit, conformational selection and independent dynamic segments: an extended view of binding events

Single molecule and NMR measurements of protein dynamics increasingly uncover the complexity of binding scenarios. Here, we describe an extended conformational selection model that embraces a repertoire of selection and adjustment processes. Induced fit can be viewed as a subset of this repertoire, whose contribution is affected by the bond types stabilizing the interaction and the differences between the interacting partners. We argue that protein segments whose dynamics are distinct from the rest of the protein ('discrete breathers') can govern conformational transitions and allosteric propagation that accompany binding processes and, as such, might be more sensitive to mutational events. Additionally, we highlight the dynamic complexity of binding scenarios as they relate to events such as aggregation and signalling, and the crowded cellular environment.

Coevolutionary games--a mini review

Prevalence of cooperation within groups of selfish individuals is puzzling in that it contradicts with the basic premise of natural selection. Favoring players with higher fitness, the latter is key for understanding the challenges faced by cooperators when competing with defectors. Evolutionary game theory provides a competent theoretical framework for addressing the subtleties of cooperation in such situations, which are known as social dilemmas. Recent advances point towards the fact that the evolution of strategies alone may be insufficient to fully exploit the benefits offered by cooperative behavior. Indeed, while spatial structure and heterogeneity, for example, have been recognized as potent promoters of cooperation, coevolutionary rules can extend the potentials of such entities further, and even more importantly, lead to the understanding of their emergence. The introduction of coevolutionary rules to evolutionary games implies, that besides the evolution of strategies, another property may simultaneously be subject to evolution as well. Coevolutionary rules may affect the interaction network, the reproduction capability of players, their reputation, mobility or age. Here we review recent works on evolutionary games incorporating coevolutionary rules, as well as give a didactic description of potential pitfalls and misconceptions associated with the subject. In addition, we briefly outline directions for future research that we feel are promising, thereby particularly focusing on dynamical effects of coevolutionary rules on the evolution of cooperation, which are still widely open to research and thus hold promise of exciting new discoveries.