Cancer treatment scheduling and dynamic heterogeneity in social dilemmas of tumour acidity and vasculature

Threshold-awareness in adaptive cancer therapy

Although adaptive cancer therapy shows promise in integrating evolutionary dynamics into treatment scheduling, the stochastic nature of cancer evolution has seldom been taken into account. Various sources of random perturbations can impact the evolution of heterogeneous tumors, making performance metrics of any treatment policy random as well. In this paper, we propose an efficient method for selecting optimal adaptive treatment policies under randomly evolving tumor dynamics. The goal is to improve the cumulative "cost" of treatment, a combination of the total amount of drugs used and the total treatment time. As this cost also becomes random in any stochastic setting, we maximize the probability of reaching the treatment goals (tumor stabilization or eradication) without exceeding a pre-specified cost threshold (or a "budget"). We use a novel Stochastic Optimal Control formulation and Dynamic Programming to find such "threshold-aware" optimal treatment policies. Our approach enables an efficient algorithm to compute these policies for a range of threshold values simultaneously. Compared to treatment plans shown to be optimal in a deterministic setting, the new "threshold-aware" policies significantly improve the chances of the therapy succeeding under the budget, which is correlated with a lower general drug usage. We illustrate this method using two specific examples, but our approach is far more general and provides a new tool for optimizing adaptive therapies based on a broad range of stochastic cancer models.

Studying mixed-species biofilms of Candida albicans and Staphylococcus aureus using evolutionary game theory

Mixed-species biofilms of Candida albicans and Staphylococcus aureus pose a significant clinical challenge due to their resistance to the human immune system and antimicrobial therapy. Using evolutionary game theory and nonlinear dynamics, we analyse the complex interactions between these organisms to understand their coexistence in the human host. We determine the Nash equilibria and evolutionary stable strategies of the game between C. albicans and S. aureus and point out different states of the mixed-species biofilm. Using replicator equations we study the fungal-bacterial interactions on a population level. Our focus is on the influence of available nutrients and the quorum sensing molecule farnesol, including the potential therapeutic use of artificially added farnesol. We also investigate the impact of the suggested scavenging of C. albicans hyphae by S. aureus. Contrary to common assumptions, we confirm the hypothesis that under certain conditions, mixed-species biofilms are not universally beneficial. Instead, different Nash equilibria occur depending on encountered conditions (i.e. varying farnesol levels, either produced by C. albicans or artificially added), including antagonism. We further show that the suggested scavenging of C. albicans' hyphae by S. aureus does not influence the overall outcome of the game. Moreover, artificially added farnesol strongly affects the dynamics of the game, although its use as a medical adjuvant (add-on medication) may pose challenges.

Digitize your Biology! Modeling multicellular systems through interpretable cell behavior

Cells are fundamental units of life, constantly interacting and evolving as dynamical systems. While recent spatial multi-omics can quantitate individual cells' characteristics and regulatory programs, forecasting their evolution ultimately requires mathematical modeling. We develop a conceptual framework-a cell behavior hypothesis grammar-that uses natural language statements (cell rules) to create mathematical models. This allows us to systematically integrate biological knowledge and multi-omics data to make them computable. We can then perform virtual "thought experiments" that challenge and extend our understanding of multicellular systems, and ultimately generate new testable hypotheses. In this paper, we motivate and describe the grammar, provide a reference implementation, and demonstrate its potential through a series of examples in tumor biology and immunotherapy. Altogether, this approach provides a bridge between biological, clinical, and systems biology researchers for mathematical modeling of biological systems at scale, allowing the community to extrapolate from single-cell characterization to emergent multicellular behavior.

DDQN-based optimal targeted therapy with reversible inhibitors to combat the Warburg effect

We cover the Warburg effect with a three-component evolutionary model, where each component represents a different metabolic strategy. In this context, a scenario involving cells expressing three different phenotypes is presented. One tumour phenotype exhibits glycolytic metabolism through glucose uptake and lactate secretion. Lactate is used by a second malignant phenotype to proliferate. The third phenotype represents healthy cells, which performs oxidative phosphorylation. The purpose of this model is to gain a better understanding of the metabolic alterations associated with the Warburg effect. It is suitable to reproduce some of the clinical trials obtained in colorectal cancer and other even more aggressive tumours. It shows that lactate is an indicator of poor prognosis, since it favours the setting of polymorphic tumour equilibria that complicates its treatment. This model is also used to train a reinforcement learning algorithm, known as Double Deep Q-networks, in order to provide the first optimal targeted therapy based on experimental tumour growth inhibitors as genistein and AR-C155858. Our in silico solution includes the optimal therapy for all the tumour state space and also ensures the best possible quality of life for the patients, by considering the duration of treatment, the use of low-dose medications and the existence of possible contraindications. Optimal therapies obtained with Double Deep Q-networks are validated with the solutions of the Hamilton-Jacobi-Bellman equation.

A Systems Biology Approach for Addressing Cisplatin Resistance in Non-Small Cell Lung Cancer

Translational research in medicine, defined as the transfer of knowledge and discovery from the basic sciences to the clinic, is typically achieved through interactions between members across scientific disciplines to overcome the traditional silos within the community. Thus, translational medicine underscores 'Team Medicine', the partnership between basic science researchers and clinicians focused on addressing a specific goal in medicine. Here, we highlight this concept from a City of Hope perspective. Using cisplatin resistance in non-small cell lung cancer (NSCLC) as a paradigm, we describe how basic research scientists, clinical research scientists, and medical oncologists, in true 'Team Science' spirit, addressed cisplatin resistance in NSCLC and identified a previously approved compound that is able to alleviate cisplatin resistance in NSCLC. Furthermore, we discuss how a 'Team Medicine' approach can help to elucidate the mechanisms of innate and acquired resistance in NSCLC and develop alternative strategies to overcome drug resistance.

The role of evolutionary game theory in spatial and non-spatial models of the survival of cooperation in cancer: a review

Evolutionary game theory (EGT) is a branch of mathematics which considers populations of individuals interacting with each other to receive pay-offs. An individual’s pay-off is dependent on the strategy of its opponent(s) as well as on its own, and the higher its pay-off, the higher its reproductive fitness. Its offspring generally inherit its interaction strategy, subject to random mutation. Over time, the composition of the population shifts as different strategies spread or are driven extinct. In the last 25 years there has been a flood of interest in applying EGT to cancer modelling, with the aim of explaining how cancerous mutations spread through healthy tissue and how intercellular cooperation persists in tumour-cell populations. This review traces this body of work from theoretical analyses of well-mixed infinite populations through to more realistic spatial models of the development of cooperation between epithelial cells. We also consider work in which EGT has been used to make experimental predictions about the evolution of cancer, and discuss work that remains to be done before EGT can make large-scale contributions to clinical treatment and patient outcomes.

Long-time behavior of a PDE replicator equation for multilevel selection in group-structured populations

In many biological systems, natural selection acts simultaneously on multiple levels of organization. This scenario typically presents an evolutionary conflict between the incentive of individuals to cheat and the collective incentive to establish cooperation within a group. Generalizing previous work on multilevel selection in evolutionary game theory, we consider a hyperbolic PDE model of a group-structured population, in which members within a single group compete with each other for individual-level replication; while the group also competes against other groups for group-level replication. We derive a threshold level of the relative strength of between-group competition such that defectors take over the population below the threshold while cooperation persists in the long-time population above the threshold. Under stronger assumptions on the initial distribution of group compositions, we further prove that the population converges to a steady state density supporting cooperation for between-group selection strength above the threshold. We further establish long-time bounds on the time-average of the collective payoff of the population, showing that the long-run population cannot outperform the payoff of a full-cooperator group even in the limit of infinitely-strong between-group competition. When the group replication rate is maximized by an intermediate level of within-group cooperation, individual-level selection casts a long shadow on the dynamics of multilevel selection: no level of between-group competition can erase the effects of the individual incentive to defect. We further extend our model to study the case of multiple types of groups, showing how the games that groups play can coevolve with the level of cooperation.

Cancer's second genome: Microbial cancer diagnostics and redefining clonal evolution as a multispecies process: Humans and their tumors are not aseptic, and the multispecies nature of cancer modulates clinical care and clonal evolution: Humans and their tumors are not aseptic, and the multispecies nature of cancer modulates clinical care and clonal evolution

The presence and role of microbes in human cancers has come full circle in the last century. Tumors are no longer considered aseptic, but implications for cancer biology and oncology remain underappreciated. Opportunities to identify and build translational diagnostics, prognostics, and therapeutics that exploit cancer's second genome-the metagenome-are manifold, but require careful consideration of microbial experimental idiosyncrasies that are distinct from host-centric methods. Furthermore, the discoveries of intracellular and intra-metastatic cancer bacteria necessitate fundamental changes in describing clonal evolution and selection, reflecting bidirectional interactions with non-human residents. Reconsidering cancer clonality as a multispecies process similarly holds key implications for understanding metastasis and prognosing therapeutic resistance while providing rational guidance for the next generation of bacterial cancer therapies. Guided by these new findings and challenges, this Review describes opportunities to exploit cancer's metagenome in oncology and proposes an evolutionary framework as a first step towards modeling multispecies cancer clonality. Also see the video abstract here: https://youtu.be/-WDtIRJYZSs.

Theoretical modeling of collaterally sensitive drug cycles: shaping heterogeneity to allow adaptive therapy

In previous work, we focused on the optimal therapeutic strategy with a pair of drugs which are collaterally sensitive to each other, that is, a situation in which evolution of resistance to one drug induces sensitivity to the other, and vice versa. Yoona (Bull Math Biol 8:1-34,Yoon et al. 2018) Here, we have extended this exploration to the optimal strategy with a collaterally sensitive drug sequence of an arbitrary length, N. To explore this, we have developed a dynamical model of sequential drug therapies with N drugs. In this model, tumor cells are classified as one of N subpopulations represented as [Formula: see text]. Each subpopulation, [Formula: see text], is resistant to '[Formula: see text]' and each subpopulation, [Formula: see text] (or [Formula: see text], if [Formula: see text]), is sensitive to it, so that [Formula: see text] increases under '[Formula: see text]' as it is resistant to it, and after drug-switching, decreases under '[Formula: see text]' as it is sensitive to that drug(s). Similar to our previous work examining optimal therapy with two drugs, we found that there is an initial period of time in which the tumor is 'shaped' into a specific makeup of each subpopulation, at which time all the drugs are equally effective ([Formula: see text]). After this shaping period, all the drugs are quickly switched with duration relative to their efficacy in order to maintain each subpopulation, consistent with the ideas underlying adaptive therapy. West(Canver Res 80(7):578-589Gatenby et al. 2009) and Gatenby (Cancer Res 67(11):4894-4903West et al. 2020). Additionally, we have developed methodologies to administer the optimal regimen under clinical or experimental situations in which no drug parameters and limited information of trackable populations data (all the subpopulations or only total population) are known. The therapy simulation based on these methodologies showed consistency with the theoretical effect of optimal therapy .

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.

Cooperative success in epithelial public goods games

Cancer cells obtain mutations which rely on the production of diffusible growth factors to confer a fitness benefit. These mutations can be considered cooperative, and studied as public goods games within the framework of evolutionary game theory. The population structure, benefit function and update rule all influence the evolutionary success of cooperators. We model the evolution of cooperation in epithelial cells using the Voronoi tessellation model. Unlike traditional evolutionary graph theory, this allows us to implement global updating, for which birth and death events are spatially decoupled. We compare, for a sigmoid benefit function, the conditions for cooperation to be favoured and/or beneficial for well-mixed and structured populations. We find that when population structure is combined with global updating, cooperation is more successful than if there were local updating or the population were well-mixed. Interestingly, the qualitative behaviour for the well-mixed population and the Voronoi tessellation model is remarkably similar, but the latter case requires significantly lower incentives to ensure cooperation.

Senescence-Induced Chemoresistance in Triple Negative Breast Cancer and Evolution-Based Treatment Strategies

Triple negative breast cancer (TNBC) is classically treated with combination chemotherapies. Although, initially responsive to chemotherapies, TNBC patients frequently develop drug-resistant, metastatic disease. Chemotherapy resistance can develop through many mechanisms, including induction of a transient growth-arrested state, known as the therapy-induced senescence (TIS). In this paper, we will focus on chemoresistance in TNBC due to TIS. One of the key characteristics of senescent cells is a complex secretory phenotype, known as the senescence-associated secretory proteome (SASP), which by prompting immune-mediated clearance of senescent cells maintains tissue homeostasis and suppresses tumorigenesis. However, in cancer, particularly with TIS, senescent cells themselves as well as SASP promote cellular reprograming into a stem-like state responsible for the emergence of drug-resistant, aggressive clones. In addition to chemotherapies, outcomes of recently approved immune and DNA damage-response (DDR)-directed therapies are also affected by TIS, implying that this a common strategy used by cancer cells for evading treatment. Although there has been an explosion of scientific research for manipulating TIS for prevention of drug resistance, much of it is still at the pre-clinical stage. From an evolutionary perspective, cancer is driven by natural selection, wherein the fittest tumor cells survive and proliferate while the tumor microenvironment influences tumor cell fitness. As TIS seems to be preferred for increasing the fitness of drug-challenged cancer cells, we will propose a few tactics to control it by using the principles of evolutionary biology. We hope that with appropriate therapeutic intervention, this detrimental cellular fate could be diverted in favor of TNBC patients.

Group Behavior and Emergence of Cancer Drug Resistance

Drug resistance is a major impediment in cancer. Although it is generally thought that acquired drug resistance is due to genetic mutations, emerging evidence indicates that nongenetic mechanisms also play an important role. Resistance emerges through a complex interplay of clonal groups within a heterogeneous tumor and the surrounding microenvironment. Traits such as phenotypic plasticity, intercellular communication, and adaptive stress response, act in concert to ensure survival of intermediate reversible phenotypes, until permanent, resistant clones can emerge. Understanding the role of group behavior, and the underlying nongenetic mechanisms, can lead to more efficacious treatment designs and minimize or delay emergence of resistance.

What Is the Storage Effect, Why Should It Occur in Cancers, and How Can It Inform Cancer Therapy?

Intratumor heterogeneity is a feature of cancer that is associated with progression, treatment resistance, and recurrence. However, the mechanisms that allow diverse cancer cell lineages to coexist remain poorly understood. The storage effect is a coexistence mechanism that has been proposed to explain the diversity of a variety of ecological communities, including coral reef fish, plankton, and desert annual plants. Three ingredients are required for there to be a storage effect: (1) temporal variability in the environment, (2) buffered population growth, and (3) species-specific environmental responses. In this article, we argue that these conditions are observed in cancers and that it is likely that the storage effect contributes to intratumor diversity. Data that show the temporal variation within the tumor microenvironment are needed to quantify how cancer cells respond to fluctuations in the tumor microenvironment and what impact this has on interactions among cancer cell types. The presence of a storage effect within a patient’s tumors could have a substantial impact on how we understand and treat cancer.

Roles of phenotypic heterogeneity and microenvironment feedback in early tumor development

The local microenvironment of a tumor plays an important and commonly observed role in cancer development and progression. Dynamic changes in the tissue microenvironment are thought to epigenetically disrupt healthy cellular phenotypes and drive cancer incidence. Despite the experimental work in this area there are no conceptual models to understand the interplay between the epigenetic dysregulation in the microenvironment of early tumors and the appearance of cancer driver mutations. Here, we develop a minimal model of the tissue microenvironment which considers three interacting subpopulations: healthy, phenotypically dysregulated, and mutated cancer cells. Healthy cells can epigenetically (reversibly) transition to the dysregulated phenotype, and from there to the cancer state. The epigenetic transition rates of noncancer cells can be influenced by the number of cancer cells in the microenvironment (termed microenvironment feedback). Our model delineates the regime in which microenvironment feedback accelerates the rate of cancer initiation. In addition, the model shows when and how microenvironment feedback may inhibit cancer progression. We discuss how our framework may provide resolution to some of the puzzling experimental observations of slow cancer progression.

Phenotypic Heterogeneity in Tumor Progression, and Its Possible Role in the Onset of Cancer

Heterogeneity among isogenic cells/individuals has been known for at least 150 years. Even Mendel, working on pea plants, realized that not all tall plants were identical. However, Mendel was more interested in the discontinuous variation between genetically distinct individuals. The concept of environment dictating distinct phenotypes among isogenic individuals has since been shown to impact the evolution of populations in numerous examples at different scales of life. In this review, we discuss how phenotypic heterogeneity and its evolutionary implications exist at all levels of life, from viruses to mammals. In particular, we discuss how a particular disease condition (cancer) is impacted by heterogeneity among isogenic cells, and propose a potential role that phenotypic heterogeneity might play toward the onset of the disease.

IsoMaTrix: a framework to visualize the isoclines of matrix games and quantify uncertainty in structured populations

 

Evolutionary game theory describes frequency-dependent selection for fixed, heritable strategies in a population of competing individuals using a payoff matrix. We present a software package to aid in the construction, analysis, and visualization of three-strategy matrix games. The IsoMaTrix package computes the isoclines (lines of zero growth) of matrix games, and facilitates direct comparison of well-mixed dynamics to structured populations on a lattice grid. IsoMaTrix computes fixed points, phase flow, trajectories, (sub)velocities, and uncertainty quantification for stochastic effects in spatial matrix games. We describe a result obtained via IsoMaTrix's spatial games functionality, which shows that the timing of competitive release in a cancer model (under continuous treatment) critically depends on the initial spatial configuration of the tumor.

AVAILABILITY

The code is available at: https://github.com/mathonco/isomatrix.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Can Environmental Manipulation Help Suppress Cancer? Non-Linear Competition Among Tumor Cells in Periodically Changing Conditions

It has been shown that the tumor population growth dynamics in a periodically varying environment can drastically differ from the one in a fixed environment. Thus, the environment of a tumor can potentially be manipulated to suppress cancer progression. Diverse evolutionary processes play vital roles in cancer progression and accordingly, understanding the interplay between these processes is essential in optimizing the treatment strategy. Somatic evolution and genetic instability result in intra-tumor cell heterogeneity. Various models have been developed to analyze the interactions between different types of tumor cells. Here, models of density-dependent interaction between different types of tumor cells under fast periodical environmental changes are examined. It is illustrated that tumor population densities, which vary on a slow time scale, are affected by fast environmental variations. Finally, the intriguing density-dependent interactions in metastatic castration-resistant prostate cancer (mCRPC) in which the different types of tumor cells are defined with respect to the production of and dependence on testosterone are discussed.

Optimizing adaptive cancer therapy: dynamic programming and evolutionary game theory

Recent clinical trials have shown that adaptive drug therapies can be more efficient than a standard cancer treatment based on a continuous use of maximum tolerated doses (MTD). The adaptive therapy paradigm is not based on a preset schedule; instead, the doses are administered based on the current state of tumour. But the adaptive treatment policies examined so far have been largely ad hoc. We propose a method for systematically optimizing adaptive policies based on an evolutionary game theory model of cancer dynamics. Given a set of treatment objectives, we use the framework of dynamic programming to find the optimal treatment strategies. In particular, we optimize the total drug usage and time to recovery by solving a Hamilton-Jacobi-Bellman equation. We compare MTD-based treatment strategy with optimal adaptive treatment policies and show that the latter can significantly decrease the total amount of drugs prescribed while also increasing the fraction of initial tumour states from which the recovery is possible. We conclude that the use of optimal control theory to improve adaptive policies is a promising concept in cancer treatment and should be integrated into clinical trial design.

Rising horizon in circumventing multidrug resistance in chemotherapy with nanotechnology

Multidrug resistance (MDR) is one of the key barriers in chemotherapy, leading to the generation of insensitive cancer cells towards administered therapy. Genetic and epigenetic alterations of the cells are the consequences of MDR, resulted in drug resistivity, which reflects in impaired delivery of cytotoxic agents to the cancer site. Nanotechnology-based nanocarriers have shown immense shreds of evidence in overcoming these problems, where these promising tools handle desired dosage load of hydrophobic chemotherapeutics to facilitate designing of safe, controlled and effective delivery to specifically at tumor microenvironment. Therefore, encapsulating drugs within the nano-architecture have shown to enhance solubility, bioavailability, drug targeting, where co-administered P-gp inhibitors have additionally combat against developed MDR. Moreover, recent advancement in the stimuli-sensitive delivery of nanocarriers facilitates a tumor-targeted release of the chemotherapeutics to reduce the associated toxicities of chemotherapeutic agents in normal cells. The present article is focused on MDR development strategies in the cancer cell and different nanocarrier-based approaches in circumventing this hurdle to establish an effective therapy against deadliest cancer disease.

Fibroblasts and alectinib switch the evolutionary games played by non-small cell lung cancer

Heterogeneity in strategies for survival and proliferation among the cells which constitute a tumour is a driving force behind the evolution of resistance to cancer therapy. The rules mapping the tumour’s strategy distribution to the fitness of individual strategies can be represented as an evolutionary game. We develop a game assay to measure effective evolutionary games in co-cultures of non-small cell lung cancer cells which are sensitive and resistant to the anaplastic lymphoma kinase inhibitor Alectinib. The games are not only quantitatively different between different environments, but targeted therapy and cancer associated fibroblasts qualitatively switch the type of game being played by the in-vitro population from Leader to Deadlock. This observation provides empirical confirmation of a central theoretical postulate of evolutionary game theory in oncology: we can treat not only the player, but also the game. Although we concentrate on measuring games played by cancer cells, the measurement methodology we develop can be used to advance the study of games in other microscopic systems by providing a quantitative description of non-cell-autonomous effects.

Cooperation among cancer cells: applying game theory to cancer

Cell cooperation promotes many of the hallmarks of cancer via the secretion of diffusible factors that can affect cancer cells or stromal cells in the tumour microenvironment. This cooperation cannot be explained simply as the collective action of cells for the benefit of the tumour because non-cooperative subclones can constantly invade and free-ride on the diffusible factors produced by the cooperative cells. A full understanding of cooperation among the cells of a tumour requires methods and concepts from evolutionary game theory, which has been used successfully in other areas of biology to understand similar problems but has been underutilized in cancer research. Game theory can provide insights into the stability of cooperation among cells in a tumour and into the design of potentially evolution-proof therapies that disrupt this cooperation.

An extended Moran process that captures the struggle for fitness

When a new type of individual appears in a stable population, the newcomer is typically not advantageous. Due to stochasticity, the new type can grow in numbers, but the newcomers can only become advantageous if they manage to change the environment in such a way that they increase their fitness. This dynamics is observed in several situations in which a relatively stable population is invaded by an alternative strategy, for instance the evolution of cooperation among bacteria, the invasion of cancer in a multicellular organism and the evolution of ideas that contradict social norms. These examples also show that, by generating different versions of itself, the new type increases the probability of winning the struggle for fitness. Our model captures the imposed cooperation whereby the first generation of newcomers dies while changing the environment such that the next generations become more advantageous.

Mathematical Modeling of the Function of Warburg Effect in Tumor Microenvironment

Tumor cells are known for their increased glucose uptake rates even in the presence of abundant oxygen. This altered metabolic shift towards aerobic glycolysis is known as the Warburg effect. Despite an enormous number of studies conducted on the causes and consequences of this phenomenon, little is known about how the Warburg effect affects tumor growth and progression. We developed a multi-scale computational model to explore the detailed effects of glucose metabolism of cancer cells on tumorigenesis behavior in a tumor microenvironment. Despite glycolytic tumors, the growth of non-glycolytic tumor is dependent on a congruous morphology without markedly interfering with glucose and acid concentrations of the tumor microenvironment. Upregulated glucose metabolism helped to retain oxygen levels above the hypoxic limit during early tumor growth, and thus obviated the need for neo-vasculature recruitment. Importantly, simulating growth of tumors within a range of glucose uptake rates showed that there exists a spectrum of glucose uptake rates within which the tumor is most aggressive, i.e. it can exert maximal acidic stress on its microenvironment and most efficiently compete for glucose supplies. Moreover, within the same spectrum, the tumor could grow to invasive morphologies while its size did not markedly shrink.

Fractionated follow-up chemotherapy delays the onset of resistance in bone metastatic prostate cancer

Prostate cancer to bone metastases are almost always lethal. This results from the ability of metastatic prostate cancer cells to co-opt bone remodeling leading to what is known as the vicious cycle. Understanding how tumor cells can disrupt bone homeostasis through their interactions with the stroma and how metastatic tumors respond to treatment is key to the development of new treatments for what remains an incurable disease. Here we describe an evolutionary game theoretical model of both the homeostatic bone remodeling and its co-option by prostate cancer metastases. This model extends past the evolutionary aspects typically considered in game theoretical models by also including ecological factors such as the physical microenvironment of the bone. Our model recapitulates the current paradigm of the "vicious cycle" driving tumor growth and sheds light on the interactions of heterogeneous tumor cells with the bone microenvironment and treatment response. Our results show that resistant populations naturally become dominant in the metastases under conventional cytotoxic treatment and that novel schedules could be used to better control the tumor and the associated bone disease compared to the current standard of care. Specifically, we introduce fractionated follow up therapy - chemotherapy where dosage is administered initially in one solid block followed by alternating smaller doeses and holidays - and argue that it is better than either a continuous application or a periodic one. Furthermore, we also show that different regimens of chemotherapy can lead to different amounts of pathological bone that are known to correlate with poor quality of life for bone metastatic prostate cancer patients.

Optimal Therapy Scheduling Based on a Pair of Collaterally Sensitive Drugs

Despite major strides in the treatment of cancer, the development of drug resistance remains a major hurdle. One strategy which has been proposed to address this is the sequential application of drug therapies where resistance to one drug induces sensitivity to another drug, a concept called collateral sensitivity. The optimal timing of drug switching in these situations, however, remains unknown. To study this, we developed a dynamical model of sequential therapy on heterogeneous tumors comprised of resistant and sensitive cells. A pair of drugs (DrugA, DrugB) are utilized and are periodically switched during therapy. Assuming resistant cells to one drug are collaterally sensitive to the opposing drug, we classified cancer cells into two groups, [Formula: see text] and [Formula: see text], each of which is a subpopulation of cells resistant to the indicated drug and concurrently sensitive to the other, and we subsequently explored the resulting population dynamics. Specifically, based on a system of ordinary differential equations for [Formula: see text] and [Formula: see text], we determined that the optimal treatment strategy consists of two stages: an initial stage in which a chosen effective drug is utilized until a specific time point, T, and a second stage in which drugs are switched repeatedly, during which each drug is used for a relative duration (i.e., [Formula: see text]-long for DrugA and [Formula: see text]-long for DrugB with [Formula: see text] and [Formula: see text]). We prove that the optimal duration of the initial stage, in which the first drug is administered, T, is shorter than the period in which it remains effective in decreasing the total population, contrary to current clinical intuition. We further analyzed the relationship between population makeup, [Formula: see text], and the effect of each drug. We determine a critical ratio, which we term [Formula: see text], at which the two drugs are equally effective. As the first stage of the optimal strategy is applied, [Formula: see text] changes monotonically to [Formula: see text] and then, during the second stage, remains at [Formula: see text] thereafter. Beyond our analytic results, we explored an individual-based stochastic model and presented the distribution of extinction times for the classes of solutions found. Taken together, our results suggest opportunities to improve therapy scheduling in clinical oncology.

Modeling treatment-dependent glioma growth including a dormant tumor cell subpopulation

Background

Tumors comprise a variety of specialized cell phenotypes adapted to different ecological niches that massively influence the tumor growth and its response to treatment.

Methods

In the background of glioblastoma multiforme, a highly malignant brain tumor, we consider a rapid proliferating phenotype that appears susceptible to treatment, and a dormant phenotype which lacks this pronounced proliferative ability and is not affected by standard therapeutic strategies. To gain insight in the dynamically changing proportions of different tumor cell phenotypes under different treatment conditions, we develop a mathematical model and underline our assumptions with experimental data.

Results

We show that both cell phenotypes contribute to the distinct composition of the tumor, especially in cycling low and high dose treatment, and therefore may influence the tumor growth in a phenotype specific way.

Conclusion

Our model of the dynamic proportions of dormant and rapidly growing glioblastoma cells in different therapy settings suggests that phenotypically different cells should be considered to plan dose and duration of treatment schedules.

Extinction rates in tumour public goods games

Cancer evolution and progression are shaped by cellular interactions and Darwinian selection. Evolutionary game theory incorporates both of these principles, and has been proposed as a framework to understand tumour cell population dynamics. A cornerstone of evolutionary dynamics is the replicator equation, which describes changes in the relative abundance of different cell types, and is able to predict evolutionary equilibria. Typically, the replicator equation focuses on differences in relative fitness. We here show that this framework might not be sufficient under all circumstances, as it neglects important aspects of population growth. Standard replicator dynamics might miss critical differences in the time it takes to reach an equilibrium, as this time also depends on cellular turnover in growing but bounded populations. As the system reaches a stable manifold, the time to reach equilibrium depends on cellular death and birth rates. These rates shape the time scales, in particular, in coevolutionary dynamics of growth factor producers and free-riders. Replicator dynamics might be an appropriate framework only when birth and death rates are of similar magnitude. Otherwise, population growth effects cannot be neglected when predicting the time to reach an equilibrium, and cell-type-specific rates have to be accounted for explicitly.

Collateral sensitivity networks reveal evolutionary instability and novel treatment strategies in ALK mutated non-small cell lung cancer

Drug resistance remains an elusive problem in cancer therapy, particularly for novel targeted therapies. Much work is focused upon the development of an arsenal of targeted therapies, towards oncogenic driver genes such as ALK-EML4, to overcome the inevitable resistance that develops over time. Currently, after failure of first line ALK TKI therapy, another ALK TKI is administered, though collateral sensitivity is not considered. To address this, we evolved resistance in an ALK rearranged non-small cell lung cancer line (H3122) to a panel of 4 ALK TKIs, and performed a collateral sensitivity analysis. All ALK inhibitor resistant cell lines displayed significant cross-resistance to all other ALK inhibitors. We then evaluated ALK-inhibitor sensitivities after drug holidays of varying length (1-21 days), and observed dynamic patterns of resistance. This unpredictability led us to an expanded search for treatment options, where we tested 6 further anti-cancer agents for collateral sensitivity among resistant cells, uncovering possibilities for further treatment, including cross-sensitivity to standard cytotoxic therapies, as well as Hsp90 inhibitors. Taken together, these results imply that resistance to targeted therapy in non-small cell lung cancer is highly dynamic, and also one where there are many opportunities to re-establish sensitivities where there was once resistance. Drug resistance in cancer inevitably emerges during treatment; particularly with novel targeted therapies, designed to inhibit specific molecules. A clinically-relevant example of this phenomenon occurs in ALK-positive non-small cell lung cancer, where targeted therapies are used to inhibit the ALK-EML4 fusion protein. A potential solution to this may lie in finding drug sensitivities in the resistant population, termed collateral sensitivities, and then using these as second-line agents. This study shows how the evolution of resistance in ALK-positive lung cancer is a dynamic process through time, one in which patterns of drug resistance and collateral sensitivity change substantially, and therefore one where temporal regimens, such as drug cycling and drug holidays may have great benefit.