Patient-derived glioblastoma organoids reflect tumor heterogeneity and treatment sensitivity.

Background: Treatment resistance and tumor relapse are the primary causes of mortality in glioblastoma (GBM), with intratumoral heterogeneity playing a significant role. Patient-derived cancer organoids have emerged as a promising model capable of recapitulating tumor heterogeneity. Our objective was to develop patient-derived GBM organoids (PGO) to investigate treatment response and resistance. Methods: GBM samples were used to generate PGOs and analyzed using whole-exome sequencing (WES) and single-cell karyotype sequencing. PGOs were subjected to temozolomide (TMZ) to assess viability. Bulk RNA sequencing was performed before and after TMZ. Results: WES analysis on individual PGOs cultured for 3 time points (1-3 months) showed a high inter-organoid correlation and retention of genetic variants (range 92.3%-97.7%). Most variants were retained in the PGO compared to the tumor (range 58%-90%) and exhibited similar copy number variations. Single-cell karyotype sequencing demonstrated preservation of genetic heterogeneity. Single-cell multiplex immunofluorescence showed maintenance of cellular states. TMZ treatment of PGOs showed a differential response, which largely corresponded with MGMT promoter methylation. Differentially expressed genes before and after TMZ revealed an upregulation of the JNK kinase pathway. Notably, the combination treatment of a JNK kinase inhibitor and TMZ demonstrated a synergistic effect. Conclusions: Overall, these findings demonstrate the robustness of PGOs in retaining the genetic and phenotypic heterogeneity in culture and the application of measuring clinically relevant drug responses. These data show that PGOs have the potential to be further developed into avatars for personalized adaptive treatment selection and actionable drug target discovery and as a platform to study GBM biology.

Stackelberg evolutionary game theory: how to manage evolving systems.

Stackelberg evolutionary game (SEG) theory combines classical and evolutionary game theory to frame interactions between a rational leader and evolving followers. In some of these interactions, the leader wants to preserve the evolving system (e.g. fisheries management), while in others, they try to drive the system to extinction (e.g. pest control). Often the worst strategy for the leader is to adopt a constant aggressive strategy (e.g. overfishing in fisheries management or maximum tolerable dose in cancer treatment). Taking into account the ecological dynamics typically leads to better outcomes for the leader and corresponds to the Nash equilibria in game-theoretic terms. However, the leader's most profitable strategy is to anticipate and steer the eco-evolutionary dynamics, leading to the Stackelberg equilibrium of the game. We show how our results have the potential to help in fields where humans try to bring an evolutionary system into the desired outcome, such as, among others, fisheries management, pest management and cancer treatment. Finally, we discuss limitations and opportunities for applying SEGs to improve the management of evolving biological systems. This article is part of the theme issue 'Half a century of evolutionary games: a synthesis of theory, application and future directions'.

The Contribution of Evolutionary Game Theory to Understanding and Treating Cancer.

Evolutionary game theory mathematically conceptualizes and analyzes biological interactions where one's fitness not only depends on one's own traits, but also on the traits of others. Typically, the individuals are not overtly rational and do not select, but rather inherit their traits. Cancer can be framed as such an evolutionary game, as it is composed of cells of heterogeneous types undergoing frequency-dependent selection. In this article, we first summarize existing works where evolutionary game theory has been employed in modeling cancer and improving its treatment. Some of these game-theoretic models suggest how one could anticipate and steer cancer's eco-evolutionary dynamics into states more desirable for the patient via evolutionary therapies. Such therapies offer great promise for increasing patient survival and decreasing drug toxicity, as demonstrated by some recent studies and clinical trials. We discuss clinical relevance of the existing game-theoretic models of cancer and its treatment, and opportunities for future applications. Moreover, we discuss the developments in cancer biology that are needed to better utilize the full potential of game-theoretic models. Ultimately, we demonstrate that viewing tumors with evolutionary game theory has medically useful implications that can inform and create a lockstep between empirical findings and mathematical modeling. We suggest that cancer progression is an evolutionary competition between different cell types and therefore needs to be viewed as an evolutionary game.

Classical mathematical models for prediction of response to chemotherapy and immunotherapy.

Classical mathematical models of tumor growth have shaped our understanding of cancer and have broad practical implications for treatment scheduling and dosage. However, even the simplest textbook models have been barely validated in real world-data of human patients. In this study, we fitted a range of differential equation models to tumor volume measurements of patients undergoing chemotherapy or cancer immunotherapy for solid tumors. We used a large dataset of 1472 patients with three or more measurements per target lesion, of which 652 patients had six or more data points. We show that the early treatment response shows only moderate correlation with the final treatment response, demonstrating the need for nuanced models. We then perform a head-to-head comparison of six classical models which are widely used in the field: the Exponential, Logistic, Classic Bertalanffy, General Bertalanffy, Classic Gompertz and General Gompertz model. Several models provide a good fit to tumor volume measurements, with the Gompertz model providing the best balance between goodness of fit and number of parameters. Similarly, when fitting to early treatment data, the general Bertalanffy and Gompertz models yield the lowest mean absolute error to forecasted data, indicating that these models could potentially be effective at predicting treatment outcome. In summary, we provide a quantitative benchmark for classical textbook models and state-of-the art models of human tumor growth. We publicly release an anonymized version of our original data, providing the first benchmark set of human tumor growth data for evaluation of mathematical models.

Coordination games in cancer.

We propose a model of cancer initiation and progression where tumor growth is modulated by an evolutionary coordination game. Evolutionary games of cancer are widely used to model frequency-dependent cell interactions with the most studied games being the Prisoner's Dilemma and public goods games. Coordination games, by their more obscure and less evocative nature, are left understudied, despite the fact that, as we argue, they offer great potential in understanding and treating cancer. In this paper we present the conditions under which coordination games between cancer cells evolve, we propose aspects of cancer that can be modeled as results of coordination games, and explore the ways through which coordination games of cancer can be exploited for therapy.

Exploring the influence of cytosolic and membrane FAK activation on YAP/TAZ nuclear translocation.

Membrane binding and unbinding dynamics play a crucial role in the biological activity of several nonintegral membrane proteins, which have to be recruited to the membrane to perform their functions. By localizing to the membrane, these proteins are able to induce downstream signal amplification in their respective signaling pathways. Here, we present a 3D computational approach using reaction-diffusion equations to investigate the relation between membrane localization of focal adhesion kinase (FAK), Ras homolog family member A (RhoA), and signal amplification of the YAP/TAZ signaling pathway. Our results show that the theoretical scenarios in which FAK is membrane bound yield robust and amplified YAP/TAZ nuclear translocation signals. Moreover, we predict that the amount of YAP/TAZ nuclear translocation increases with cell spreading, confirming the experimental findings in the literature. In summary, our in silico predictions show that when the cell membrane interaction area with the underlying substrate increases, for example, through cell spreading, this leads to more encounters between membrane-bound signaling partners and downstream signal amplification. Because membrane activation is a motif common to many signaling pathways, this study has important implications for understanding the design principles of signaling networks.

Identifying key questions in the ecology and evolution of cancer.

The application of evolutionary and ecological principles to cancer prevention and treatment, as well as recognizing cancer as a selection force in nature, has gained impetus over the last 50 years. Following the initial theoretical approaches that combined knowledge from interdisciplinary fields, it became clear that using the eco-evolutionary framework is of key importance to understand cancer. We are now at a pivotal point where accumulating evidence starts to steer the future directions of the discipline and allows us to underpin the key challenges that remain to be addressed. Here, we aim to assess current advancements in the field and to suggest future directions for research. First, we summarize cancer research areas that, so far, have assimilated ecological and evolutionary principles into their approaches and illustrate their key importance. Then, we assembled 33 experts and identified 84 key questions, organized around nine major themes, to pave the foundations for research to come. We highlight the urgent need for broadening the portfolio of research directions to stimulate novel approaches at the interface of oncology and ecological and evolutionary sciences. We conclude that progressive and efficient cross-disciplinary collaborations that draw on the expertise of the fields of ecology, evolution and cancer are essential in order to efficiently address current and future questions about cancer.

Fisheries management as a Stackelberg Evolutionary Game: Finding an evolutionarily enlightened strategy.

Fish populations subject to heavy exploitation are expected to evolve over time smaller average body sizes. We introduce Stackelberg evolutionary game theory to show how fisheries management should be adjusted to mitigate the potential negative effects of such evolutionary changes. We present the game of a fisheries manager versus a fish population, where the former adjusts the harvesting rate and the net size to maximize profit, while the latter responds by evolving the size at maturation to maximize the fitness. We analyze three strategies: i) ecologically enlightened (leading to a Nash equilibrium in game-theoretic terms); ii) evolutionarily enlightened (leading to a Stackelberg equilibrium) and iii) domestication (leading to team optimum) and the corresponding outcomes for both the fisheries manager and the fish. Domestication results in the largest size for the fish and the highest profit for the manager. With the Nash approach the manager tends to adopt a high harvesting rate and a small net size that eventually leads to smaller fish. With the Stackelberg approach the manager selects a bigger net size and scales back the harvesting rate, which lead to a bigger fish size and a higher profit. Overall, our results encourage managers to take the fish evolutionary dynamics into account. Moreover, we advocate for the use of Stackelberg evolutionary game theory as a tool for providing insights into the eco-evolutionary consequences of exploiting evolving resources.

Optimal control to reach eco-evolutionary stability in metastatic castrate-resistant prostate cancer.

In the absence of curative therapies, treatment of metastatic castrate-resistant prostate cancer (mCRPC) using currently available drugs can be improved by integrating evolutionary principles that govern proliferation of resistant subpopulations into current treatment protocols. Here we develop what is coined as an 'evolutionary stable therapy', within the context of the mathematical model that has been used to inform the first adaptive therapy clinical trial of mCRPC. The objective of this therapy is to maintain a stable polymorphic tumor heterogeneity of sensitive and resistant cells to therapy in order to prolong treatment efficacy and progression free survival. Optimal control analysis shows that an increasing dose titration protocol, a very common clinical dosing process, can achieve tumor stabilization for a wide range of potential initial tumor compositions and volumes. Furthermore, larger tumor volumes may counter intuitively be more likely to be stabilized if sensitive cells dominate the tumor composition at time of initial treatment, suggesting a delay of initial treatment could prove beneficial. While it remains uncertain if metastatic disease in humans has the properties that allow it to be truly stabilized, the benefits of a dose titration protocol warrant additional pre-clinical and clinical investigations.

The activity of Saccharomyces cerevisiae Na+, K+/H+ antiporter Nha1 is negatively regulated by 14-3-3 protein binding at serine 481.

Na+/H+ antiporters are involved in ensuring optimal intracellular concentrations of alkali-metal cations and protons in most organisms. In Saccharomyces cerevisiae, the plasma-membrane Na+, K+/H+ antiporter Nha1 mediates Na+ and K+ efflux, which is important for cell growth in the presence of salts. Nha1 belongs among housekeeping proteins and, due to its ability to export K+, it has many physiological functions. The Nha1 transport activity is regulated through its long, hydrophilic and unstructured C-terminus (554 of 985 aa). Although Nha1 has been previously shown to interact with the yeast 14-3-3 isoform (Bmh2), the binding site remains unknown. In this work, we identified the residues through which Nha1 interacts with the 14-3-3 protein. Biophysical characterization of the interaction between the C-terminal polypeptide of Nha1 and Bmh proteins in vitro revealed that the 14-3-3 protein binds to phosphorylated Ser481 of Nha1, and the crystal structure of the phosphopeptide containing Ser481 bound to Bmh1 provided the structural basis of this interaction. Our data indicate that 14-3-3 binding induces a disorder-to-order transition of the C-terminus of Nha1, and in vivo experiments showed that the mutation of Ser481 to Ala significantly increases cation efflux activity via Nha1, which renders cells sensitive to low K+ concentrations. Hence, 14-3-3 binding is apparently essential for the negative regulation of Nha1 activity, which should be low under standard growth conditions, when low amounts of toxic salts are present and yeast cells need to accumulate high amounts of K+.

Optimizing Cancer Treatment Using Game Theory: A Review.

Importance: While systemic therapy for disseminated cancer is often initially successful, malignant cells, using diverse adaptive strategies encoded in the human genome, almost invariably evolve resistance, leading to treatment failure. Thus, the Darwinian dynamics of resistance are formidable barriers to all forms of systemic cancer treatment but rarely integrated into clinical trial design or included within precision oncology initiatives. Observations: We investigate cancer treatment as a game theoretic contest between the physician's therapy and the cancer cells' resistance strategies. This game has 2 critical asymmetries: (1) Only the physician can play rationally. Cancer cells, like all evolving organisms, can only adapt to current conditions; they can neither anticipate nor evolve adaptations for treatments that the physician has not yet applied. (2) It has a distinctive leader-follower (or "Stackelberg") dynamics; the "leader" oncologist plays first and the "follower" cancer cells then respond and adapt to therapy. Current treatment protocols for metastatic cancer typically exploit neither asymmetry. By repeatedly administering the same drug(s) until disease progression, the physician "plays" a fixed strategy even as the opposing cancer cells continuously evolve successful adaptive responses. Furthermore, by changing treatment only when the tumor progresses, the physician cedes leadership to the cancer cells and treatment failure becomes nearly inevitable. Without fundamental changes in strategy, standard-of-care cancer therapy typically results in "Nash solutions" in which no unilateral change in treatment can favorably alter the outcome. Conclusions and Relevance: Physicians can exploit the advantages inherent in the asymmetries of the cancer treatment game, and likely improve outcomes, by adopting more dynamic treatment protocols that integrate eco-evolutionary dynamics and modulate therapy accordingly. Implementing this approach will require new metrics of tumor response that incorporate both ecological (ie, size) and evolutionary (ie, molecular mechanisms of resistance and relative size of resistant population) changes.

Optimal control to develop therapeutic strategies for metastatic castrate resistant prostate cancer.

In metastatic castrate resistant prostate cancer (mCRPC), abiraterone is conventionally administered continuously at maximal tolerated dose until treatment failure. The majority of patients initially respond well to abiraterone but the cancer cells evolve resistance and the cancer progresses within a median time of 16 months. Incorporating techniques that attempt to delay or prevent the growth of the resistant cancer cell phenotype responsible for disease progression have only recently entered the clinical setting. Here we use evolutionary game theory to model the evolutionary dynamics of patients with mCRPC subject to abiraterone therapy. In evaluating therapy options, we adopt an optimal control theory approach and seek the best treatment schedule using nonlinear constrained optimization. We compare patient outcomes from standard clinical treatments to those with other treatment objectives, such as maintaining a constant total tumor volume or minimizing the fraction of resistant cancer cells within the tumor. Our model predicts that continuous high doses of abiraterone as well as other therapies aimed at curing the patient result in accelerated competitive release of the resistant phenotype and rapid subsequent tumor progression. We find that long term control is achievable using optimized therapy through the restrained and judicious application of abiraterone, maintaining its effectiveness while providing acceptable patient quality of life. Implementing this strategy will require overcoming psychological and emotional barriers in patients and physicians as well as acquisition of a new class of clinical data designed to accurately estimate intratumoral eco-evolutionary dynamics during therapy.

A two-phenotype model of immune evasion by cancer cells.

We propose a model with two types of cancer cells differentiated by their defense mechanisms against the immune system. "Selfish" cancer cells develop defense mechanisms that benefit the individual cell, whereas "cooperative" cells deploy countermeasures that increase the chance of survival of every cell. Our phenotypes capture the two main features of the tumor's efforts to avoid immune destruction, crypticity against immune cells for the selfish cells, and tumor-induced immunosuppression for the cooperative cells. We identify steady states of the system and show that only homogeneous tumors can be stable in both size and composition. We show that under generic parameter values, a tumor of selfish cells is more benign than a tumor of cooperative cells, and that a treatment against cancer crypticity may promote immunosuppression and increase cancer growth.

Spatial vs. non-spatial eco-evolutionary dynamics in a tumor growth model.

Metastatic prostate cancer is initially treated with androgen deprivation therapy (ADT). However, resistance typically develops in about 1 year - a clinical condition termed metastatic castrate-resistant prostate cancer (mCRPC). We develop and investigate a spatial game (agent based continuous space) of mCRPC that considers three distinct cancer cell types: (1) those dependent on exogenous testosterone (T+), (2) those with increased CYP17A expression that produce testosterone and provide it to the environment as a public good (TP), and (3) those independent of testosterone (T-). The interactions within and between cancer cell types can be represented by a 3 × 3 matrix. Based on the known biology of this cancer there are 22 potential matrices that give roughly three major outcomes depending upon the absence (good prognosis), near absence or high frequency (poor prognosis) of T- cells at the evolutionarily stable strategy (ESS). When just two cell types coexist the spatial game faithfully reproduces the ESS of the corresponding matrix game. With three cell types divergences occur, in some cases just two strategies coexist in the spatial game even as a non-spatial matrix game supports all three. Discrepancies between the spatial game and non-spatial ESS happen because different cell types become more or less clumped in the spatial game - leading to non-random assortative interactions between cell types. Three key spatial scales influence the distribution and abundance of cell types in the spatial game: i. Increasing the radius at which cells interact with each other can lead to higher clumping of each type, ii. Increasing the radius at which cells experience limits to population growth can cause densely packed tumor clusters in space, iii. Increasing the dispersal radius of daughter cells promotes increased mixing of cell types. To our knowledge the effects of these spatial scales on eco-evolutionary dynamics have not been explored in cancer models. The fact that cancer interactions are spatially explicit and that our spatial game of mCRPC provides in general different outcomes than the non-spatial game might suggest that non-spatial models are insufficient for capturing key elements of tumorigenesis.

Game theory as a conceptual framework for managing insect pests.

For over 100 years it has been recognized that insect pests evolve resistance to chemical pesticides. More recently, managers have advocated restrained use of pesticides, crop rotation, the use of multiple pesticides, and pesticide-free sanctuaries as resistance management practices. Game theory provides a conceptual framework for combining the resistance strategies of the insects and the control strategies of the pest manager into a unified conceptual and modelling framework. Game theory can contrast an ecologically enlightened application of pesticides with an evolutionarily enlightened one. In the former case the manager only considers ecological consequences whereas the latter anticipates the evolutionary response of the pests. Broader applications of this game theory approach include anti-biotic resistance, fisheries management and therapy resistance in cancer.

The canonical equation of adaptive dynamics for life histories: from fitness-returns to selection gradients and Pontryagin's maximum principle.

This paper should be read as addendum to Dieckmann et al. (J Theor Biol 241:370-389, 2006) and Parvinen et al. (J Math Biol 67: 509-533, 2013). Our goal is, using little more than high-school calculus, to (1) exhibit the form of the canonical equation of adaptive dynamics for classical life history problems, where the examples in Dieckmann et al. (J Theor Biol 241:370-389, 2006) and Parvinen et al. (J Math Biol 67: 509-533, 2013) are chosen such that they avoid a number of the problems that one gets in this most relevant of applications, (2) derive the fitness gradient occurring in the CE from simple fitness return arguments, (3) show explicitly that setting said fitness gradient equal to zero results in the classical marginal value principle from evolutionary ecology, (4) show that the latter in turn is equivalent to Pontryagin's maximum principle, a well known equivalence that however in the literature is given either ex cathedra or is proven with more advanced tools, (5) connect the classical optimisation arguments of life history theory a little better to real biology (Mendelian populations with separate sexes subject to an environmental feedback loop), (6) make a minor improvement to the form of the CE for the examples in Dieckmann et al. and Parvinen et al.

Irreversible prey diapause as an optimal strategy of a physiologically extended Lotka-Volterra model.

We propose an optimal control framework to describe intra-seasonal predator-prey interactions, which are characterized by a continuous-time dynamical model comprising predator and prey density, as well as the energy budget of the prey over the length of a season. The model includes a time-dependent decision variable for the prey, representing the portion of the prey population in time that is active, as opposed to diapausing (a state of physiological rest). The predator follows autonomous dynamics and accordingly it remains active during the season. The proposed model is a generalization of the classical Lotka-Volterra predator-prey model towards non-autonomous dynamics that furthermore includes the effect of an energy variable. The model has been inspired by a specific biological system of predatory mites (Acari: Phytoseiidae) and prey mites (so-called fruit-tree red spider mites) (Acari: Tetranychidae) that feed on leaves of apple trees--its parameters have been instantiated based on laboratory and field studies. The goal of the work is to understand the decisions of the prey mites to enter diapause (a state of physiological rest) given the dynamics of the predatory mites: this is achieved by solving an optimization problem hinging on the maximization of the prey population contribution to the next season. The main features of the optimal strategy for the prey are shown to be that (1) once in diapause, the prey does not become active again within the same season and hence diapause is an irreversible process; (2) for the vast majority of parameter space, the portion of prey individuals entering diapause within the season does not decrease in time; (3) with an increased number of predators, the optimal population strategy for the prey is to start diapause earlier and to enter diapause more gradually. This optimal population strategy will be studied for its ESS properties in a sequel to the work presented in this article.

Joining or opting out of a Lotka-Volterra game between predators and prey: does the best strategy depend on modelling energy lost and gained?

Apart from interacting, prey and predators may also avoid each other by moving into refuges where they lack food, yet survive by switching to an energy-saving physiological state. Lotka-Volterra models of predator-prey interactions ignore this option. Therefore, we have modelled this game of 'joining versus opting out' by extending Lotka-Volterra models to include portions of populations not in interaction and with different energy dynamics. Given this setting, the prey's decisions to join or to opt out influence those of the predator and vice versa, causing the set of possible strategies to be complex and large. However, using game theory, we analysed and published two models showing (i) which strategies are best for the prey population given the predator's strategy, and (ii) which are best for prey and predator populations simultaneously. The predicted best strategies appear to match empirical observations on plant-inhabiting predator and prey mites. Here, we consider a plausible third model that does not take energy dynamics into account, but appears to yield contrasting predictions. This supports our assumption to extend Lotka-Volterra models with 'interaction-dependent' energy dynamics, but more work is required to prove that it is essential and that what is best for the population is also best for the individual.