Aggregation Effects and Population-Based Dynamics as a Source of Therapy Resistance in Cancer

Spatial interactions modulate tumor growth and immune infiltration

Lenia, a cellular automata framework used in artificial life, provides a natural setting to implement mathematical models of cancer incorporating features such as morphogenesis, homeostasis, motility, reproduction, growth, stimuli response, evolvability, and adaptation. Historically, agent-based models of cancer progression have been constructed with rules that govern birth, death and migration, with attempts to map local rules to emergent global growth dynamics. In contrast, Lenia provides a flexible framework for considering a spectrum of local (cell-scale) to global (tumor-scale) dynamics by defining an interaction kernel governing density-dependent growth dynamics. Lenia can recapitulate a range of cancer model classifications including local or global, deterministic or stochastic, non-spatial or spatial, single or multi-population, and off or on-lattice. Lenia is subsequently used to develop data-informed models of 1) single-population growth dynamics, 2) multi-population cell-cell competition models, and 3) cell migration or chemotaxis. Mathematical modeling provides important mechanistic insights. First, short-range interaction kernels provide a mechanism for tumor cell survival under conditions with strong Allee effects. Next, we find that asymmetric interaction tumor-immune kernels lead to poor immune response. Finally, modeling recapitulates immune-ECM interactions where patterns of collagen formation provide immune protection, indicated by an emergent inverse relationship between disease stage and immune coverage.

A Phase 1b Adaptive Androgen Deprivation Therapy Trial in Metastatic Castration Sensitive Prostate Cancer

Background: We hypothesize that cancer survival can be improved through adapting treatment strategies to cancer evolutionary dynamics and conducted a phase 1b study in metastatic castration sensitive prostate cancer (mCSPC). Methods: Men with asymptomatic mCSPC were enrolled and proceeded with a treatment break after achieving > 75% PSA decline with LHRH analog plus an NHA. ADT was restarted at the time of PSA or radiographic progression and held again after achieving >50% PSA decline. This on-off cycling of ADT continued until on treatment imaging progression. Results: At data cut off in August 2022, only 2 of the 16 evaluable patients were off study due to imaging progression at 28 months from first dose of LHRH analog for mCSPC. Two additional patients showed PSA progression at 12.4 and 20.5 months and remain on trial. Since none of the 16 patients developed imaging progression at 12 months, the study succeeded in its primary objective of feasibility. The secondary endpoints of median time to PSA progression and median time to radiographic progression have not been reached at a median follow up of 26 months. Conclusions: It is feasible to use an individual’s PSA response and testosterone levels to guide intermittent ADT in mCSPC.

Evolutionary Dynamics of Treatment-Induced Resistance in Cancer Informs Understanding of Rapid Evolution in Natural Systems

Rapid evolution is ubiquitous in nature. We briefly review some of this quite broadly, particularly in the context of response to anthropogenic disturbances. Nowhere is this more evident, replicated and accessible to study than in cancer. Curiously cancer has been late - relative to fisheries, antibiotic resistance, pest management and evolution in human dominated landscapes - in recognizing the need for evolutionarily informed management strategies. The speed of evolution matters. Here, we employ game-theoretic modeling to compare time to progression with continuous maximum tolerable dose to that of adaptive therapy where treatment is discontinued when the population of cancer cells gets below half of its initial size and re-administered when the cancer cells recover, forming cycles with and without treatment. We show that the success of adaptive therapy relative to continuous maximum tolerable dose therapy is much higher if the population of cancer cells is defined by two cell types (sensitive vs. resistant in a polymorphic population). Additionally, the relative increase in time to progression increases with the speed of evolution. These results hold with and without a cost of resistance in cancer cells. On the other hand, treatment-induced resistance can be modeled as a quantitative trait in a monomorphic population of cancer cells. In that case, when evolution is rapid, there is no advantage to adaptive therapy. Initial responses to therapy are blunted by the cancer cells evolving too quickly. Our study emphasizes how cancer provides a unique system for studying rapid evolutionary changes within tumor ecosystems in response to human interventions; and allows us to contrast and compare this system to other human managed or dominated systems in nature.

Treatment-induced evolutionary dynamics in nonmetastatic locally advanced rectal adenocarcinoma

Multi-modal treatment of non-metastatic locally advanced rectal adenocarcinoma (LARC) includes chemotherapy, radiation, and life-altering surgery. Although highly effective for local cancer control, metastatic failure remains significant and drives rectal cancer-related mortality. A consistent observation of this tri-modality treatment paradigm is that histologic response of the primary tumor to neoadjuvant treatment(s), which varies across patients, predicts overall oncologic outcome. In this chapter, we will examine this treatment response heterogeneity in the context of evolutionary dynamics. We hypothesize that improved understanding of eco-evolutionary pressures rendering small cancer cell populations vulnerable to extinction may influence treatment strategies and improve patient outcomes. Applying effective treatment(s) to cancer populations causes a "race to extinction." We explore principles of eco-evolutionary extinction in the context of these small cancer cell populations, evaluating how treatment(s) aim to eradicate the cancer populations to ultimately result in cure. In this chapter, we provide an evolutionary rationale for limiting continuous treatment(s) with the same agent or combination of agents to avoid selection of resistant cancer subpopulation phenotypes, allowing "evolutionary rescue." We draw upon evidence from nature demonstrating species extinction rarely occurring as a single event phenomenon, but rather a series of events in the slide to extinction. We posit that eradicating small cancer populations, similar to small populations in natural extinctions, will usually require a sequence of different external perturbations that produce negative, synergistic dynamics termed the "extinction vortex." By exploiting these unique extinction vulnerabilities of small cancer populations, the optimal therapeutic sequences may be informed by evolution-informed strategies for patients with LARC.

Superlinear growth reveals the Allee effect in tumors

Integrating experimental data into ecological models plays a central role in understanding biological mechanisms that drive tumor progression where such knowledge can be used to develop new therapeutic strategies. While the current studies emphasize the role of competition among tumor cells, they fail to explain recently observed superlinear growth dynamics across human tumors. Here we study tumor growth dynamics by developing a model that incorporates evolutionary dynamics inside tumors with tumor-microenvironment interactions. Our results reveal that tumor cells' ability to manipulate the environment and induce angiogenesis drives superlinear growth-a process compatible with the Allee effect. In light of this understanding, our model suggests that, for high-risk tumors that have a higher growth rate, suppressing angiogenesis can be the appropriate therapeutic intervention.

Novel evolutionary dynamics of small populations in breast cancer adjuvant and neoadjuvant therapy

Disseminated cancer cells (DCCs) are detected in the circulation and bone marrow of up to 40% of breast cancer (BC) patients with clinically localized disease. The formation of metastases is governed by eco-evolutionary interactions of DCCs with the tissue during the transition from microscopic populations to macroscopic disease. Here, we view BC adjuvant and neoadjuvant treatments in the context of small population extinction dynamics observed in the Anthropocene era. Specifically, the unique eco-evolutionary dynamics of small asexually reproducing cancer populations render them highly vulnerable to: (1) environmental and demographic fluctuations, (2) Allee effects, (3) genetic drift and (4) population fragmentation. Furthermore, these typically interact, producing self-reinforcing, destructive dynamics—termed the Extinction Vortex—eradicating the population even when none of the perturbations is individually capable of causing extinction. We propose that developing BC adjuvant and neoadjuvant protocols may exploit these dynamics to prevent recovery and proliferation of small cancer populations during and after treatment—termed “Eco-evolutionary rescue” in natural extinctions. We hypothesize more strategic application of currently available agents based on the extinction vulnerabilities of small populations could improve clinical outcomes.

The Evolution and Ecology of Resistance in Cancer Therapy

Despite the continuous deployment of new treatment strategies and agents over many decades, most disseminated cancers remain fatal. Cancer cells, through their access to the vast information of the human genome, have a remarkable capacity to deploy adaptive strategies for even the most effective treatments. We note there are two critical steps in the clinical manifestation of treatment resistance. The first, which is widely investigated, requires molecular machinery necessary to eliminate the cytotoxic effect of the treatment. However, the emergence of a resistant phenotype is not in itself clinically significant. That is, resistant cells affect patient outcomes only when they succeed in the second step of resistance by proliferating into a sufficiently large population to allow tumor progression and treatment failure. Importantly, proliferation of the resistant phenotype is by no means certain and, in fact, depends on complex Darwinian dynamics governed by the costs and benefits of the resistance mechanisms in the context of the local environment and competing populations. Attempts to target the molecular machinery of resistance have had little clinical success largely because of the diversity within the human genome-therapeutic interruption of one mechanism simply results in its replacement by an alternative. Here we explore evolutionarily informed strategies (adaptive, double-bind, and extinction therapies) for overcoming treatment resistance that seek to understand and exploit the critical evolutionary dynamics that govern proliferation of the resistant phenotypes. In general, this approach has demonstrated that, while emergence of resistance mechanisms in cancer cells to every current therapy is inevitable, proliferation of the resistant phenotypes is not and can be delayed and even prevented with sufficient understanding of the underlying eco-evolutionary dynamics.

Integrating evolutionary dynamics into cancer therapy

Many effective drugs for metastatic and/or advanced-stage cancers have been developed over the past decade, although the evolution of resistance remains the major barrier to disease control or cure. In large, diverse populations such as the cells that compose metastatic cancers, the emergence of cells that are resistant or that can quickly develop resistance is virtually inevitable and most likely cannot be prevented. However, clinically significant resistance occurs only when the pre-existing resistant phenotypes are able to proliferate extensively, a process governed by eco-evolutionary dynamics. Attempts to disrupt the molecular mechanisms of resistance have generally been unsuccessful in clinical practice. In this Review, we focus on the Darwinian processes driving the eco-evolutionary dynamics of treatment-resistant cancer populations. We describe a variety of evolutionarily informed strategies designed to increase the probability of disease control or cure by anticipating and steering the evolutionary dynamics of acquired resistance.

Transcompp: understanding phenotypic plasticity by estimating Markov transition rates for cell state transitions

MOTIVATION

Gradual population-level changes in tissues can be driven by stochastic plasticity, meaning rare stochastic transitions of single-cell phenotype. Quantifying the rates of these stochastic transitions requires time-intensive experiments, and analysis is generally confounded by simultaneous bidirectional transitions and asymmetric proliferation kinetics. To quantify cellular plasticity, we developed Transcompp (Transition Rate ANalysis of Single Cells to Observe and Measure Phenotypic Plasticity), a Markov modeling algorithm that uses optimization and resampling to compute best-fit rates and statistical intervals for stochastic cell-state transitions.

RESULTS

We applied Transcompp to time-series datasets in which purified subpopulations of stem-like or non-stem cancer cells were exposed to various cell culture environments, and allowed to re-equilibrate spontaneously over time. Results revealed that commonly used cell culture reagents hydrocortisone and cholera toxin shifted the cell population equilibrium toward stem-like or non-stem states, respectively, in the basal-like breast cancer cell line MCF10CA1a. In addition, applying Transcompp to patient-derived cells showed that transition rates computed from short-term experiments could predict long-term trajectories and equilibrium convergence of the cultured cell population.

AVAILABILITY AND IMPLEMENTATION

Freely available for download at http://github.com/nsuhasj/Transcompp.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Eradicating Metastatic Cancer and the Eco-Evolutionary Dynamics of Anthropocene Extinctions

Curative therapy for metastatic cancers is equivalent to causing extinction of a large, heterogeneous, and geographically dispersed population. Although eradication of dinosaurs is a dramatic example of extinction dynamics, similar application of massive eco-evolutionary force in cancer treatment is typically limited by host toxicity. Here, we investigate the evolutionary dynamics of Anthropocene species extinctions as an alternative model for curative cancer therapy. Human activities can produce extinctions of large, diverse, and geographically distributed populations. The extinction of a species typically follows a pattern in which initial demographic and ecological insults reduce the size and heterogeneity of the population. The surviving individuals, with decreased genetic diversity and often fragmented ecology, are then vulnerable to small stochastic perturbations that further reduce the population until extinction is inevitable. We hypothesize large, diverse, and disseminated cancer populations can be eradicated using similar evolutionary dynamics. Initial therapy is applied to reduce population size and diversity and followed by new treatments to exploit the eco-evolutionary vulnerability of small and/or declining populations. Mathematical models and computer simulations demonstrate initial reductive treatment followed immediately by demographic and ecological perturbations, similar to the empirically derived treatment of pediatric acute lymphocytic leukemia, can consistently achieve curative outcomes in nonpediatric cancers. SIGNIFICANCE: Anthropocene extinctions suggest a strategy for eradicating metastatic cancers in which initial therapy, by reducing the size and diversity of the population, renders it vulnerable to extinction by rapidly applied additional perturbations.

A Secure Occupational Therapy Framework for Monitoring Cancer Patients' Quality of Life

Once diagnosed with cancer, a patient goes through a series of diagnosis and tests, which are referred to as "after cancer treatment". Due to the nature of the treatment and side effects, maintaining quality of life (QoL) in the home environment is a challenging task. Sometimes, a cancer patient's situation changes abruptly as the functionality of certain organs deteriorates, which affects their QoL. One way of knowing the physiological functional status of a cancer patient is to design an occupational therapy. In this paper, we propose a blockchain and off-chain-based framework, which will allow multiple medical and ambient intelligent Internet of Things sensors to capture the QoL information from one's home environment and securely share it with their community of interest. Using our proposed framework, both transactional records and multimedia big data can be shared with an oncologist or palliative care unit for real-time decision support. We have also developed blockchain-based data analytics, which will allow a clinician to visualize the immutable history of the patient's data available from an in-home secure monitoring system for a better understanding of a patient's current or historical states. Finally, we will present our current implementation status, which provides significant encouragement for further development.

Modeling heterogeneous tumor growth dynamics and cell-cell interactions at single-cell and cell-population resolution

Cancer is a complex, dynamic disease that despite recent advances remains mostly incurable. Inter- and intratumoral heterogeneity are generally considered major drivers of therapy resistance, metastasis, and treatment failure. Recent advances in high-throughput experimentation have produced a wealth of data on tumor heterogeneity and researchers are increasingly turning to mathematical modeling to aid in the interpretation of these complex datasets. In this mini-review, we discuss three important classes of approaches for modeling cellular dynamics within heterogeneous tumors: agent-based models, population dynamics, and multiscale models. An important new focus, for which we provide an example, is the role of intratumoral cell-cell interactions.

Time scales and wave formation in non-linear spatial public goods games

The co-evolutionary dynamics of competing populations can be strongly affected by frequency-dependent selection and spatial population structure. As co-evolving populations grow into a spatial domain, their initial spatial arrangement and their growth rate differences are important factors that determine the long-term outcome. We here model producer and free-rider co-evolution in the context of a diffusive public good (PG) that is produced by the producers at a cost but evokes local concentration-dependent growth benefits to all. The benefit of the PG can be non-linearly dependent on public good concentration. We consider the spatial growth dynamics of producers and free-riders in one, two and three dimensions by modeling producer cell, free-rider cell and public good densities in space, driven by the processes of birth, death and diffusion (cell movement and public good distribution). Typically, one population goes extinct, but the time-scale of this process varies with initial conditions and the growth rate functions. We establish that spatial variation is transient regardless of dimensionality, and that structured initial conditions lead to increasing times to get close to an extinction state, called ε-extinction time. Further, we find that uncorrelated initial spatial structures do not influence this ε-extinction time in comparison to a corresponding well-mixed (non-spatial) system. In order to estimate the ε-extinction time of either free-riders or producers we derive a slow manifold solution. For invading populations, i.e. for populations that are initially highly segregated, we observe a traveling wave, whose speed can be calculated. Our results provide quantitative predictions for the transient spatial dynamics of cooperative traits under pressure of extinction.

Evolutionary public good (PG) games capture the essence of production of growth-beneficial factors that are vulnerable to exploitation by free-riders who do not carry the cost of production. PGs emerge in cellular populations, for example in growing bacteria and cancer cells. We study the eco-evolutionary dynamics of a PG in populations that grow in space. In our model, PG-producer cells and free-rider cells can grow according to their own birth and death rates. Co-evolution occurs due to public good-driven surplus in the intrinsic growth rates at a cost to producers. A net growth rate-benefit to free-riders leads to the well-known tragedy of the commons in which producers go extinct. What is often omitted from discussions is the time scale on which this extinction can occur, especially in spatial populations. Here, we derive analytical estimates of the ε-extinction time in different spatial settings. As we do not consider a stochastic process, the ε-extinction time captures the time needed to approach an extinction state. We identify spatial scenarios in which extinction takes long enough such that the tragedy of the commons never occurs within a meaningful lifetime of the system. Using numerical simulations we analyze the deviations from our analytical predictions.

First Strike-Second Strike Strategies in Metastatic Cancer: Lessons from the Evolutionary Dynamics of Extinction

While clinical cancer research has produced many highly effective drugs, the diversity and evolutionary capacity of most cancer populations remain insurmountable barriers to cure. Here, we propose that curative outcomes may, nevertheless, be achieved by sequencing therapies that are individually effective but noncurative. Basic principles for such an approach are derived from the eco-evolutionary dynamics of background extinctions in which a "first strike" reduces the size and heterogeneity of the population. When followed immediately by demographic and ecological "second strikes," the population can be reduced below some minimum threshold, leading inevitably to extinction. This strategy bears strong similarity to the empirically-derived curative therapy in childhood acute lymphocytic leukemia.

Neighborhood size-effects shape growing population dynamics in evolutionary public goods games

An evolutionary game emerges when a subset of individuals incur costs to provide benefits to all individuals. Public goods games (PGG) cover the essence of such dilemmas in which cooperators are prone to exploitation by defectors. We model the population dynamics of a non-linear PGG and consider density-dependence on the global level, while the game occurs within local neighborhoods. At low cooperation, increases in the public good provide increasing returns. At high cooperation, increases provide diminishing returns. This mechanism leads to diverse evolutionarily stable strategies, including monomorphic and polymorphic populations, and neighborhood-size-driven state changes, resulting in hysteresis between equilibria. Stochastic or strategy-dependent variations in neighborhood sizes favor coexistence by destabilizing monomorphic states. We integrate our model with experiments of cancer cell growth and confirm that our framework describes PGG dynamics observed in cellular populations. Our findings advance the understanding of how neighborhood-size effects in PGG shape the dynamics of growing populations.

Multiscale Tumor Modeling With Drug Pharmacokinetic and Pharmacodynamic Profile Using Stochastic Hybrid System

Effective cancer treatment strategy requires an understanding of cancer behavior and development across multiple temporal and spatial scales. This has resulted into a growing interest in developing multiscale mathematical models that can simulate cancer growth, development, and response to drug treatments. This study thus investigates multiscale tumor modeling that integrates drug pharmacokinetic and pharmacodynamic (PK/PD) information using stochastic hybrid system modeling framework. Specifically, (1) pathways modeled by differential equations are adopted for gene regulations at the molecular level; (2) cellular automata (CA) model is proposed for the cellular and multicellular scales. Markov chains are used to model the cell behaviors by taking into account the gene expression levels, cell cycle, and the microenvironment. The proposed model enables the prediction of tumor growth under given molecular properties, microenvironment conditions, and drug PK/PD profile. Simulation results demonstrate the effectiveness of the proposed approach and the results agree with observed tumor behaviors.

Combination Therapy and the Evolution of Resistance: The Theoretical Merits of Synergism and Antagonism in Cancer

The search for effective combination therapies for cancer has focused heavily on synergistic combinations because they exhibit enhanced therapeutic efficacy at lower doses. Although synergism is intuitively attractive, therapeutic success often depends on whether drug resistance develops. The impact of synergistic combinations (vs. antagonistic or additive combinations) on the process of drug-resistance evolution has not been investigated. In this study, we use a simplified computational model of cancer cell numbers in a population of drug-sensitive, singly-resistant, and fully-resistant cells to simulate the dynamics of resistance evolution in the presence of two-drug combinations. When we compared combination therapies administered at the same combination of effective doses, simulations showed synergistic combinations most effective at delaying onset of resistance. Paradoxically, when the therapies were compared using dose combinations with equal initial efficacy, antagonistic combinations were most successful at suppressing expansion of resistant subclones. These findings suggest that, although synergistic combinations could suppress resistance through early decimation of cell numbers (making them "proefficacy" strategies), they are inherently fragile toward the development of single resistance. In contrast, antagonistic combinations suppressed the clonal expansion of singly-resistant cells, making them "antiresistance" strategies. The distinction between synergism and antagonism was intrinsically connected to the distinction between offensive and defensive strategies, where offensive strategies inflicted early casualties and defensive strategies established protection against anticipated future threats. Our findings question the exclusive focus on synergistic combinations and motivate further consideration of nonsynergistic combinations for cancer therapy.Significance: Computational simulations show that if different combination therapies have similar initial efficacy in cancers, then nonsynergistic drug combinations are more likely than synergistic drug combinations to provide a long-term defense against the evolution of therapeutic resistance. Cancer Res; 78(9); 2419-31. ©2018 AACR.