Game-theoretical description of the go-or-grow dichotomy in tumor development for various settings and parameter constellations.

A medically important feature of several types of tumors is their ability to "decide" between staying at a primary site in the body or leaving it and forming metastases. The present theoretical study aims to provide a better understanding of the ultimate reasons for this so-called "go-or-grow" dichotomy. To that end, we use game theory, which has proven to be useful in analyzing the competition between tumors and healthy tissues or among different tumor cells. We begin by determining the game types in the Basanta-Hatzikirou-Deutsch model, depending on the parameter values. Thereafter, we suggest and analyze five modified variants of the model. For example, in the basic model, the deadlock game, Prisoner's Dilemma, and hawk-dove game can occur. The modified versions lead to several additional game types, such as battle of the sexes, route-choice, and stag-hunt games. For some game types, all cells are predicted to stay on their original site ("grow phenotype"), while for other types, only a certain fraction stay and the other cells migrate away ("go phenotype"). If the nutrient supply at a distant site is high, all the cells are predicted to go. We discuss our predictions in terms of the pros and cons of caloric restriction and limitations of the supply of vitamins or methionine. Our results may help devise treatments to prevent metastasis.

Molecular crypsis by pathogenic fungi using human factor H. A numerical model.

Molecular mimicry is the formation of specific molecules by microbial pathogens to avoid recognition and attack by the immune system of the host. Several pathogenic Ascomycota and Zygomycota show such a behaviour by utilizing human complement factor H to hide in the blood stream. We call this type of mimicry molecular crypsis. Such a crypsis can reach a point where the immune system can no longer clearly distinguish between self and non-self cells. Thus, a trade-off between attacking disguised pathogens and erroneously attacking host cells has to be made. Based on signalling theory and protein-interaction modelling, we here present a mathematical model of molecular crypsis of pathogenic fungi using the example of Candida albicans. We tackle the question whether perfect crypsis is feasible, which would imply that protection of human cells by complement factors would be useless. The model identifies pathogen abundance relative to host cell abundance as the predominant factor influencing successful or unsuccessful molecular crypsis. If pathogen cells gain a (locally) quantitative advantage over host cells, even autoreactivity may occur. Our new model enables insights into the mechanisms of candidiasis-induced sepsis and complement-associated autoimmune diseases.

Decision-making of the benthic diatom Seminavis robusta searching for inorganic nutrients and pheromones.

Microorganisms encounter a diversity of chemical stimuli that trigger individual responses and influence population dynamics. However, microbial behavior under the influence of different incentives and microbial decision-making is poorly understood. Benthic marine diatoms that react to sexual attractants as well as to nutrient gradients face such multiple constraints. Here, we document and model behavioral complexity and context-sensitive responses of these motile unicellular algae to sex pheromones and the nutrient silicate. Throughout the life cycle of the model diatom Seminavis robusta nutrient-starved cells localize sources of silicate by combined chemokinetic and chemotactic motility. However, with an increasing need for sex to restore the initial cell size, a change in behavior favoring the attraction-pheromone-guided search for a mating partner takes place. When sex becomes inevitable to prevent cell death, safeguard mechanisms are abandoned, and cells prioritize the search for mating partners. Such selection processes help to explain biofilm organization and to understand species interactions in complex communities.

Playing 'hide-and-seek' with factor H: game-theoretical analysis of a single nucleotide polymorphism.

As a part of the complement system, factor H regulates phagocytosis and helps differentiate between a body's own and foreign cells. Owing to mimicry efforts, some pathogenic microorganisms such as Candida albicans are able to bind factor H on their cell surfaces and, thus, become similar to host cells. This implies that the decision between self and foreign is not clear-cut, which leads to a classification problem for the immune system. Here, two different alleles determining the binding affinity of factor H are relevant. Those alleles differ in the SNP Y402H; they are known to be associated with susceptibility to certain diseases. Interestingly, the fraction of both alleles differs in ethnic groups. The game-theoretical model proposed in this article explains the coexistence of both alleles by a battle of the sexes game and investigates the trade-off between pathogen detection and protection of host cells. Further, we discuss the ethnicity-dependent frequencies of the alleles. Moreover, the model elucidates the mimicry efforts by pathogenic microorganisms.

Computational Investigation of Environment-Noise Interaction in Single-Cell Organisms: The Merit of Expression Stochasticity Depends on the Quality of Environmental Fluctuations.

Organisms need to adapt to changing environments and they do so by using a broad spectrum of strategies. These strategies include finding the right balance between expressing genes before or when they are needed, and adjusting the degree of noise inherent in gene expression. We investigated the interplay between different nutritional environments and the inhabiting organisms' metabolic and genetic adaptations by applying an evolutionary algorithm to an agent-based model of a concise bacterial metabolism. Our results show that constant environments and rapidly fluctuating environments produce similar adaptations in the organisms, making the predictability of the environment a major factor in determining optimal adaptation. We show that exploitation of expression noise occurs only in some types of fluctuating environment and is strongly dependent on the quality and availability of nutrients: stochasticity is generally detrimental in fluctuating environments and beneficial only at equal periods of nutrient availability and above a threshold environmental richness. Moreover, depending on the availability and nutritional value of nutrients, nutrient-dependent and stochastic expression are both strategies used to deal with environmental changes. Overall, we comprehensively characterize the interplay between the quality and periodicity of an environment and the resulting optimal deterministic and stochastic regulation strategies of nutrient-catabolizing pathways.

Modelling the host-pathogen interactions of macrophages and Candida albicans using Game Theory and dynamic optimization.

The release of fungal cells following macrophage phagocytosis, called non-lytic expulsion, is reported for several fungal pathogens. On one hand, non-lytic expulsion may benefit the fungus in escaping the microbicidal environment of the phagosome. On the other hand, the macrophage could profit in terms of avoiding its own lysis and being able to undergo proliferation. To analyse the causes of non-lytic expulsion and the relevance of macrophage proliferation in the macrophage-Candida albicans interaction, we employ Evolutionary Game Theory and dynamic optimization in a sequential manner. We establish a game-theoretical model describing the different strategies of the two players after phagocytosis. Depending on the parameter values, we find four different Nash equilibria and determine the influence of the systems state of the host upon the game. As our Nash equilibria are a direct consequence of the model parameterization, we can depict several biological scenarios. A parameter region, where the host response is robust against the fungal infection, is determined. We further apply dynamic optimization to analyse whether macrophage mitosis is relevant in the host-pathogen interaction of macrophages and C. albicans For this, we study the population dynamics of the macrophage-C. albicans interactions and the corresponding optimal controls for the macrophages, indicating the best macrophage strategy of switching from proliferation to attacking fungal cells.

Pervasive Selection for Cooperative Cross-Feeding in Bacterial Communities.

Bacterial communities are taxonomically highly diverse, yet the mechanisms that maintain this diversity remain poorly understood. We hypothesized that an obligate and mutual exchange of metabolites, as is very common among bacterial cells, could stabilize different genotypes within microbial communities. To test this, we developed a cellular automaton to model interactions among six empirically characterized genotypes that differ in their ability and propensity to produce amino acids. By systematically varying intrinsic (i.e. benefit-to-cost ratio) and extrinsic parameters (i.e. metabolite diffusion level, environmental amino acid availability), we show that obligate cross-feeding of essential metabolites is selected for under a broad range of conditions. In spatially structured environments, positive assortment among cross-feeders resulted in the formation of cooperative clusters, which limited exploitation by non-producing auxotrophs, yet allowed them to persist at the clusters' periphery. Strikingly, cross-feeding helped to maintain genotypic diversity within populations, while amino acid supplementation to the environment decoupled obligate interactions and favored auxotrophic cells that saved amino acid production costs over metabolically autonomous prototrophs. Together, our results suggest that spatially structured environments and limited nutrient availabilities should facilitate the evolution of metabolic interactions, which can help to maintain genotypic diversity within natural microbial populations.

Privatization of cooperative benefits stabilizes mutualistic cross-feeding interactions in spatially structured environments.

Metabolic cross-feeding interactions are ubiquitous in natural microbial communities. However, it remains generally unclear whether the production and exchange of metabolites incurs fitness costs to the producing cells and if so, which ecological mechanisms can facilitate a cooperative exchange of metabolites among unrelated individuals. We hypothesized that positive assortment within structured environments can maintain mutualistic cross-feeding. To test this, we engineered Acinetobacter baylyi and Escherichia coli to reciprocally exchange essential amino acids. Interspecific coculture experiments confirmed that non-cooperating types were selectively favoured in spatially unstructured (liquid culture), yet disfavoured in spatially structured environments (agar plates). Both an individual-based model and experiments with engineered genotypes indicated that a segregation of cross-feeders and non-cooperating auxotrophs stabilized cooperative cross-feeding in spatially structured environments. Chemical imaging confirmed that auxotrophs were spatially excluded from cooperative benefits. Together, these results demonstrate that cooperative cross-feeding between different bacterial species is favoured in structured environments such as bacterial biofilms, suggesting this type of interactions might be common in natural bacterial communities.

Host-pathogen interactions between the human innate immune system and Candida albicans-understanding and modeling defense and evasion strategies.

The diploid, polymorphic yeast Candida albicans is one of the most important human pathogenic fungi. C. albicans can grow, proliferate and coexist as a commensal on or within the human host for a long time. However, alterations in the host environment can render C. albicans virulent. In this review, we describe the immunological cross-talk between C. albicans and the human innate immune system. We give an overview in form of pairs of human defense strategies including immunological mechanisms as well as general stressors such as nutrient limitation, pH, fever etc. and the corresponding fungal response and evasion mechanisms. Furthermore, Computational Systems Biology approaches to model and investigate these complex interactions are highlighted with a special focus on game-theoretical methods and agent-based models. An outlook on interesting questions to be tackled by Systems Biology regarding entangled defense and evasion mechanisms is given.

Discrimination between random and non-random processes in early bacterial colonization on biomaterial surfaces: application of point pattern analysis.

The dynamics of adhesion and growth of bacterial cells on biomaterial surfaces play an important role in the formation of biofilms. The surface properties of biomaterials have a major impact on cell adhesion processes, eg the random/non-cooperative adhesion of bacteria. In the present study, the spatial arrangement of Escherichia coli on different biomaterials is investigated in a time series during the first hours after exposure. The micrographs are analyzed via an image processing routine and the resulting point patterns are evaluated using second order statistics. Two main adhesion mechanisms can be identified: random adhesion and non-random processes. Comparison with an appropriate null-model quantifies the transition between the two processes with statistical significance. The fastest transition to non-random processes was found to occur after adhesion on PTFE for 2-3 h. Additionally, determination of cell and cluster parameters via image processing gives insight into surface influenced differences in bacterial micro-colony formation.

Quantification of the interaction between biomaterial surfaces and bacteria by 3-D modeling.

It is general knowledge that bacteria/surface interactions depend on the surface topography. However, this well-known dependence has so far not been included in the modeling efforts. We propose a model for calculating interaction energies between spherical bacteria and arbitrarily structured 3-D surfaces, combining the Derjaguin, Landau, Verwey, Overbeek theory and an extended surface element integration method. The influence of roughness on the interaction (for otherwise constant parameters, e.g. surface chemistry, bacterial hydrophobicity) is quantified, demonstrating that common experimental approaches which consider amplitude parameters of the surface topography but which ignore spacing parameters fail to adequately describe the influence of surface roughness on bacterial adhesion. The statistical roughness profile parameters arithmetic average height (representing an amplitude parameter) and peak density (representing a spacing parameter) both exert a distinct influence on the interaction energy. The influence of peak density on the interaction energy increases with decreasing arithmetic average height and contributes significantly to the total interaction energy with an arithmetic average height below 70 nm. With the aid of the proposed model, different sensitivity ranges of the interaction between rough surfaces and bacteria are identified. On the nanoscale, the spacing parameter of the surface dominates the interaction, whereas on the microscale the amplitude parameter adopts the governing role.

Agent-based modeling approach of immune defense against spores of opportunistic human pathogenic fungi.

Opportunistic human pathogenic fungi like the ubiquitous fungus Aspergillus fumigatus are a major threat to immunocompromised patients. An impaired immune system renders the body vulnerable to invasive mycoses that often lead to the death of the patient. While the number of immunocompromised patients is rising with medical progress, the process, and dynamics of defense against invaded and ready to germinate fungal conidia are still insufficiently understood. Besides macrophages, neutrophil granulocytes form an important line of defense in that they clear conidia. Live imaging shows the interaction of those phagocytes and conidia as a dynamic process of touching, dragging, and phagocytosis. To unravel strategies of phagocytes on the hunt for conidia an agent-based modeling approach is used, implemented in NetLogo. Different modes of movement of phagocytes are tested regarding their clearing efficiency: random walk, short-term persistence in their recent direction, chemotaxis of chemokines excreted by conidia, and communication between phagocytes. While the short-term persistence hunting strategy turned out to be superior to the simple random walk, following a gradient of chemokines released by conidial agents is even better. The advantage of communication between neutrophilic agents showed a strong dependency on the spatial scale of the focused area and the distribution of the pathogens.