Exploiting ecological principles to better understand cancer progression and treatment

Softness or Stiffness What Contributes to Cancer and Cancer Metastasis?

Beyond the genomic and proteomic analysis of bulk and single cancer cells, a new focus of cancer research is emerging that is based on the mechanical analysis of cancer cells. Therefore, several biophysical techniques have been developed and adapted. The characterization of cancer cells, like human cancer cell lines, started with their mechanical characterization at mostly a single timepoint. A universal hypothesis has been proposed that cancer cells need to be softer to migrate and invade tissues and subsequently metastasize in targeted organs. Thus, the softness of cancer cells has been suggested to serve as a universal physical marker for the malignancy of cancer types. However, it has turned out that there exists the opposite phenomenon, namely that stiffer cancer cells are more migratory and invasive and therefore lead to more metastases. These contradictory results question the universality of the role of softness of cancer cells in the malignant progression of cancers. Another problem is that the various biophysical techniques used can affect the mechanical properties of cancer cells, making it even more difficult to compare the results of different studies. Apart from the instrumentation, the culture and measurement conditions of the cancer cells can influence the mechanical measurements. The review highlights the main advances of the mechanical characterization of cancer cells, discusses the strength and weaknesses of the approaches, and questions whether the passive mechanical characterization of cancer cells is still state-of-the art. Besides the cell models, conditions and biophysical setups, the role of the microenvironment on the mechanical characteristics of cancer cells is presented and debated. Finally, combinatorial approaches to determine the malignant potential of tumors, such as the involvement of the ECM, the cells in a homogeneous or heterogeneous association, or biological multi-omics analyses, together with the dynamic-mechanical analysis of cancer cells, are highlighted as new frontiers of research.

Inverse Game Theory Characterizes Frequency-Dependent Selection Driven by Karyotypic Diversity in Triple Negative Breast Cancer

Chromosomal instability (CIN), characterized by pervasive copy number alterations (CNAs), significantly contributes to cancer progression and therapeutic resistance. CNAs drive intratumoral genetic heterogeneity, creating distinct subpopulations whose interactions shape tumor evolution through frequency-dependent selection. Here, we introduce, ECO-K (Ecological-Karyotypes), an inverse game theory framework that infers subpopulation interactions from longitudinal single-cell whole genome sequencing data. Applying this approach to serially-passaged, triple-negative breast cancer (TNBC) cell lines and patient-derived xenografts (PDXs), we systematically identified frequency-dependent selection dynamics governed by karyotypic diversity. Notably, in one PDX lineage, we found consistent evidence of karyotypically defined subpopulations acting as interaction hubs, associated specifically with chromosome 1 loss and chromosome 14p gain. Our framework provides testable predictions of intratumoral ecological dynamics, highlighting opportunities to strategically target key subpopulations to disrupt tumor evolution.

The Hallmarks of Cancer as Eco-Evolutionary Processes

SIGNIFICANCE

Viewing the hallmarks as a sequence of adaptations captures the "why" behind the "how" of the molecular changes driving cancer. This eco-evolutionary view distils the complexity of cancer progression into logical steps, providing a framework for understanding all existing and emerging hallmarks of cancer and developing therapeutic interventions.

Modeling tumors as complex ecosystems

Many cancers resist therapeutic intervention. This is fundamentally related to intratumor heterogeneity: multiple cell populations, each with different phenotypic signatures, coexist within a tumor and its metastases. Like species in an ecosystem, cancer populations are intertwined in a complex network of ecological interactions. Most mathematical models of tumor ecology, however, cannot account for such phenotypic diversity or predict its consequences. Here, we propose that the generalized Lotka-Volterra model (GLV), a standard tool to describe species-rich ecological communities, provides a suitable framework to model the ecology of heterogeneous tumors. We develop a GLV model of tumor growth and discuss how its emerging properties provide a new understanding of the disease. We discuss potential extensions of the model and their application to phenotypic plasticity, cancer-immune interactions, and metastatic growth. Our work outlines a set of questions and a road map for further research in cancer ecology.

An evolutionary differential game for regulating the role of monoclonal antibodies in treating signalling pathways in oesophageal cancer

This work presents a new framework for a competitive evolutionary game between monoclonal antibodies and signalling pathways in oesophageal cancer. The framework is based on a novel dynamical model that takes into account the dynamic progression of signalling pathways, resistance mechanisms and monoclonal antibody therapies. This game involves a scenario in which signalling pathways and monoclonal antibodies are the players competing against each other, where monoclonal antibodies use Brentuximab and Pembrolizumab dosages as strategies to counter the evolutionary resistance strategy implemented by the signalling pathways. Their interactions are described by the dynamical model, which serves as the game's playground. The analysis and computation of two game-theoretic strategies, Stackelberg and Nash equilibria, are conducted within this framework to ascertain the most favourable outcome for the patient. By comparing Stackelberg equilibria with Nash equilibria, numerical experiments show that the Stackelberg equilibria are superior for treating signalling pathways and are critical for the success of monoclonal antibodies in improving oesophageal cancer patient outcomes.

A modelling framework for cancer ecology and evolution

Cancer incidence increases rapidly with age, typically as a polynomial. The somatic mutation theory explains this increase through the waiting time for enough mutations to build up to generate cells with the full set of traits needed to grow without control. However, lines of evidence ranging from tumour reversion and dormancy to the prevalence of presumed cancer mutations in non-cancerous tissues argue that this is not the whole story, and that cancer is also an ecological process, and that mutations only lead to cancer when the systems of control within and across cells have broken down. Aging thus has two effects: the build-up of mutations and the breakdown of control. This paper presents a mathematical modelling framework to unify these theories with novel approaches to model the mutation and diversification of cell lineages and of the breakdown of the layers of control both within and between cells. These models correctly predict the polynomial increase of cancer with age, show how germline defects in control accelerate cancer initiation, and compute how the positive feedback between cell replication, ecology and layers of control leads to a doubly exponential growth of cell populations.

Modeling tumors as species-rich ecological communities

Many advanced cancers resist therapeutic intervention. This process is fundamentally related to intra-tumor heterogeneity: multiple cell populations, each with different mutational and phenotypic signatures, coexist within a tumor and its metastatic nodes. Like species in an ecosystem, many cancer cell populations are intertwined in a complex network of ecological interactions. Most mathematical models of tumor ecology, however, cannot account for such phenotypic diversity nor are able to predict its consequences. Here we propose that the Generalized Lotka-Volterra model (GLV), a standard tool to describe complex, species-rich ecological communities, provides a suitable framework to describe the ecology of heterogeneous tumors. We develop a GLV model of tumor growth and discuss how its emerging properties, such as outgrowth and multistability, provide a new understanding of the disease. Additionally, we discuss potential extensions of the model and their application to three active areas of cancer research, namely phenotypic plasticity, the cancer-immune interplay and the resistance of metastatic tumors to treatment. Our work outlines a set of questions and a tentative road map for further research in cancer ecology.

"Patchiness" in mechanical stiffness across a tumor as an early-stage marker for malignancy

Mechanical phenotyping of tumors, either at an individual cell level or tumor cell population level is gaining traction as a diagnostic tool. However, the extent of diagnostic and prognostic information that can be gained through these measurements is still unclear. In this work, we focus on the heterogeneity in mechanical properties of cells obtained from a single source such as a tissue or tumor as a potential novel biomarker. We believe that this heterogeneity is a conventionally overlooked source of information in mechanical phenotyping data. We use mechanics-based in-silico models of cell-cell interactions and cell population dynamics within 3D environments to probe how heterogeneity in cell mechanics drives tissue and tumor dynamics. Our simulations show that the initial heterogeneity in the mechanical properties of individual cells and the arrangement of these heterogenous sub-populations within the environment can dictate overall cell population dynamics and cause a shift towards the growth of malignant cell phenotypes within healthy tissue environments. The overall heterogeneity in the cellular mechanotype and their spatial distributions is quantified by a "patchiness" index, which is the ratio of the global to local heterogeneity in cell populations. We observe that there exists a threshold value of the patchiness index beyond which an overall healthy population of cells will show a steady shift towards a more malignant phenotype. Based on these results, we propose that the "patchiness" of a tumor or tissue sample, can be an early indicator for malignant transformation and cancer occurrence in benign tumors or healthy tissues. Additionally, we suggest that tissue patchiness, measured either by biochemical or biophysical markers, can become an important metric in predicting tissue health and disease likelihood just as landscape patchiness is an important metric in ecology.

Adaptive therapy: a tumor therapy strategy based on Darwinian evolution theory

Cancer progression is a dynamic process of continuous evolution, in which genetic diversity and heterogeneity are generated by clonal and subclonal amplification based on random mutations. Traditional cancer treatment strategies have a great challenge, which often leads to treatment failure due to drug resistance. Integrating evolutionary dynamics into treatment regimens may be an effective way to overcome the problem of drug resistance. In particular, a potential treatment is adaptive therapy, which strategy advocates containment strategies that adjust the treatment cycles according to tumor evolution to control the growth of treatment-resistant cells. In this review, we first summarize the shortcomings of traditional tumor treatment methods in evolution and then introduce the theoretical basis and research status of adaptive therapy. By analyzing the limitations of adaptive therapy and exploring possible solutions, we can broaden people's understanding of adaptive therapy and provide new insights and strategies for tumor treatment.

Bayesian inference on the Allee effect in cancer cell line populations using time-lapse microscopy images

The Allee effect describes the phenomenon that the per capita reproduction rate increases along with the population density at low densities. Allee effects have been observed at all scales, including in microscopic environments where individual cells are taken into account. This is great interest to cancer research, as understanding critical tumour density thresholds can inform treatment plans for patients. In this paper, we introduce a simple model for cell division in the case where the cancer cell population is modelled as an interacting particle system. The rate of the cell division is dependent on the local cell density, introducing an Allee effect. We perform parameter inference of the key model parameters through Markov Chain Monte Carlo, and apply our procedure to two image sequences from a cervical cancer cell line. The inference method is verified on in silico data to accurately identify the key parameters, and results on the in vitro data strongly suggest an Allee effect.

Understanding and leveraging phenotypic plasticity during metastasis formation

Cancer metastasis is the process of detrimental systemic spread and the primary cause of cancer-related fatalities. Successful metastasis formation requires tumor cells to be proliferative and invasive; however, cells cannot be effective at both tasks simultaneously. Tumor cells compensate for this trade-off by changing their phenotype during metastasis formation through phenotypic plasticity. Given the changing selection pressures and competitive interactions that tumor cells face, it is poorly understood how plasticity shapes the process of metastasis formation. Here, we develop an ecology-inspired mathematical model with phenotypic plasticity and resource competition between phenotypes to address this knowledge gap. We find that phenotypically plastic tumor cell populations attain a stable phenotype equilibrium that maintains tumor cell heterogeneity. Considering treatment types inspired by chemo- and immunotherapy, we highlight that plasticity can protect tumors against interventions. Turning this strength into a weakness, we corroborate current clinical practices to use plasticity as a target for adjuvant therapy. We present a parsimonious view of tumor plasticity-driven metastasis that is quantitative and experimentally testable, and thus potentially improving the mechanistic understanding of metastasis at the cell population level, and its treatment consequences.

Treatment of evolving cancers will require dynamic decision support

Cancer research has traditionally focused on developing new agents, but an underexplored question is that of the dose and frequency of existing drugs. Based on the modus operandi established in the early days of chemotherapies, most drugs are administered according to predetermined schedules that seek to deliver the maximum tolerated dose and are only adjusted for toxicity. However, we believe that the complex, evolving nature of cancer requires a more dynamic and personalized approach. Chronicling the milestones of the field, we show that the impact of schedule choice crucially depends on processes driving treatment response and failure. As such, cancer heterogeneity and evolution dictate that a one-size-fits-all solution is unlikely-instead, each patient should be mapped to the strategy that best matches their current disease characteristics and treatment objectives (i.e. their 'tumorscape'). To achieve this level of personalization, we need mathematical modeling. In this perspective, we propose a five-step 'Adaptive Dosing Adjusted for Personalized Tumorscapes (ADAPT)' paradigm to integrate data and understanding across scales and derive dynamic and personalized schedules. We conclude with promising examples of model-guided schedule personalization and a call to action to address key outstanding challenges surrounding data collection, model development, and integration.

Evolutionary Dynamics and Intermittent Therapy for Metastatic Cancers

Mathematical models show that the induction period of intermittent cancer therapy drives cancer toward resistance

Adaptive therapy achieves long-term control of chemotherapy resistance in high grade ovarian cancer

Drug resistance results in poor outcomes for most patients with metastatic cancer. Adaptive Therapy (AT) proposes to address this by exploiting presumed fitness costs incurred by drug-resistant cells when drug is absent, and prescribing dose reductions to allow fitter, sensitive cells to re-grow and re-sensitise the tumour. However, empirical evidence for treatment-induced fitness change is lacking. We show that fitness costs in chemotherapy-resistant ovarian cancer cause selective decline and apoptosis of resistant populations in low-resource conditions. Moreover, carboplatin AT caused fluctuations in sensitive/resistant tumour population size in vitro and significantly extended survival of tumour-bearing mice. In sequential blood-derived cell-free DNA and tumour samples obtained longitudinally from ovarian cancer patients during treatment, we inferred resistant cancer cell population size through therapy and observed it correlated strongly with disease burden. These data have enabled us to launch a multicentre, phase 2 randomised controlled trial (ACTOv) to evaluate AT in ovarian cancer.

A circuit for secretion-coupled cellular autonomy in multicellular eukaryotic cells

Cancers represent complex autonomous systems, displaying self-sufficiency in growth signaling. Autonomous growth is fueled by a cancer cell's ability to "secrete-and-sense" growth factors (GFs): a poorly understood phenomenon. Using an integrated computational and experimental approach, here we dissect the impact of a feedback-coupled GTPase circuit within the secretory pathway that imparts secretion-coupled autonomy. The circuit is assembled when the Ras-superfamily monomeric GTPase Arf1, and the heterotrimeric GTPase Giαβγ and their corresponding GAPs and GEFs are coupled by GIV/Girdin, a protein that is known to fuel aggressive traits in diverse cancers. One forward and two key negative feedback loops within the circuit create closed-loop control, allow the two GTPases to coregulate each other, and convert the expected switch-like behavior of Arf1-dependent secretion into an unexpected dose-response alignment behavior of sensing and secretion. Such behavior translates into cell survival that is self-sustained by stimulus-proportionate secretion. Proteomic studies and protein-protein interaction network analyses pinpoint GFs (e.g., the epidermal GF) as key stimuli for such self-sustenance. Findings highlight how the enhanced coupling of two biological switches in cancer cells is critical for multiscale feedback control to achieve secretion-coupled autonomy of growth factors.

A survey of open questions in adaptive therapy: Bridging mathematics and clinical translation

Adaptive therapy is a dynamic cancer treatment protocol that updates (or 'adapts') treatment decisions in anticipation of evolving tumor dynamics. This broad term encompasses many possible dynamic treatment protocols of patient-specific dose modulation or dose timing. Adaptive therapy maintains high levels of tumor burden to benefit from the competitive suppression of treatment-sensitive subpopulations on treatment-resistant subpopulations. This evolution-based approach to cancer treatment has been integrated into several ongoing or planned clinical trials, including treatment of metastatic castrate resistant prostate cancer, ovarian cancer, and BRAF-mutant melanoma. In the previous few decades, experimental and clinical investigation of adaptive therapy has progressed synergistically with mathematical and computational modeling. In this work, we discuss 11 open questions in cancer adaptive therapy mathematical modeling. The questions are split into three sections: (1) integrating the appropriate components into mathematical models (2) design and validation of dosing protocols, and (3) challenges and opportunities in clinical translation.

Nasopharyngeal carcinoma ecology theory: cancer as multidimensional spatiotemporal "unity of ecology and evolution" pathological ecosystem

Nasopharyngeal carcinoma (NPC) is a particular entity of head neck cancer that is generally regarded as a genetic disease with diverse intertumor and intratumor heterogeneity. This perspective review mainly outlines the up-to-date knowledge of cancer ecology and NPC progression, and presents a number of conceptual stepping-stones. At the beginning, I explicitly advocate that the nature of NPC (cancer) is not a genetic disease but an ecological disease: a multidimensional spatiotemporal "unity of ecology and evolution" pathological ecosystem. The hallmarks of cancer is proposed to act as ecological factors of population fitness. Subsequently, NPC cells are described as invasive species and its metastasis as a multidirectional ecological dispersal. The foundational ecological principles include intraspecific relationship (e.g. communication) and interspecific relationship (e.g. competition, predation, parasitism and mutualism) are interpreted to understand NPC progression. "Mulberry-fish-ponds" model can well illustrate the dynamic reciprocity of cancer ecosystem. Tumor-host interface is the ecological transition zone of cancer, and tumor buddings should be recognized as ecological islands separated from the mainland. It should be noted that tumor-host interface has a significantly molecular and functional edge effect because of its curvature and irregularity. Selection driving factors and ecological therapy including hyperthermia for NPC patients, and future perspectives in such field as "ecological pathology", "multidimensional tumoriecology" are also discussed. I advance that "nothing in cancer evolution or ecology makes sense except in the light of the other". The cancer ecology tree is constructed to comprehensively point out the future research direction. Taken together, the establishment of NPC ecology theory and cancer ecology tree might provide a novel conceptual framework and paradigm for our understanding of cancer complex causal process and potential preventive and therapeutic applications for patients.

An oncospace for human cancers

Human cancers comprise an heterogeneous array of diseases with different progression patterns and responses to therapy. However, they all develop within a host context that constrains their natural history. Since it occurs across the diversity of organisms, one can conjecture that there is order in the cancer multiverse. Is there a way to capture the broad range of tumor types within a space of the possible? Here we define the oncospace, a coordinate system that integrates the ecological, evolutionary and developmental components of cancer complexity. The spatial position of a tumor results from its departure from the healthy tissue along these three axes, and progression trajectories inform about the components driving malignancy across cancer subtypes. We postulate that the oncospace topology encodes new information regarding tumorigenic pathways, subtype prognosis, and therapeutic opportunities: treatment design could benefit from considering how to nudge tumors toward empty evolutionary dead ends in the oncospace.

Integration of quantitative methods and mathematical approaches for the modeling of cancer cell proliferation dynamics

Physiological processes rely on the control of cell proliferation, and the dysregulation of these processes underlies various pathological conditions, including cancer. Mathematical modeling can provide new insights into the complex regulation of cell proliferation dynamics. In this review, we first examine quantitative experimental approaches for measuring cell proliferation dynamics in vitro and compare the various types of data that can be obtained in these settings. We then explore the toolbox of common mathematical modeling frameworks that can describe cell behavior, dynamics, and interactions of proliferation. We discuss how these wet-laboratory studies may be integrated with different mathematical modeling approaches to aid the interpretation of the results and to enable the prediction of cell behaviors, specifically in the context of cancer.

Measuring competitive exclusion in non-small cell lung cancer

In this study, we experimentally measure the frequency-dependent interactions between a gefitinib-resistant non-small cell lung cancer population and its sensitive ancestor via the evolutionary game assay. We show that cost of resistance is insufficient to accurately predict competitive exclusion and that frequency-dependent growth rate measurements are required. Using frequency-dependent growth rate data, we then show that gefitinib treatment results in competitive exclusion of the ancestor, while the absence of treatment results in a likely, but not guaranteed, exclusion of the resistant strain. Then, using simulations, we demonstrate that incorporating ecological growth effects can influence the predicted extinction time. In addition, we show that higher drug concentrations may not lead to the optimal reduction in tumor burden. Together, these results highlight the potential importance of frequency-dependent growth rate data for understanding competing populations, both in the laboratory and as we translate adaptive therapy regimens to the clinic.

GLUT1 production in cancer cells: a tragedy of the commons

The tragedy of the commons occurs when competition among individual members of a group leads to overexploitation of a shared resource to the detriment of the overall population. We hypothesize that cancer cells may engage in a tragedy of the commons when competing for a shared resource such as glucose. To formalize this notion, we create a game theoretic model of glucose uptake based on a cell’s investment in transporters relative to that of its neighboring cells. We show that production of transporters per cell increases as the number of competing cells in a microenvironment increases and nutrient uptake per cell decreases. Furthermore, the greater the resource availability, the more intense the tragedy of the commons at the ESS. Based on our simulations, cancer cells produce 2.2–2.7 times more glucose transporters than would produce optimal fitness for all group members. A tragedy of the commons affords novel therapeutic strategies. By simulating GLUT1 inhibitor and glucose deprivation treatments, we demonstrate a synergistic combination with standard-of-care therapies, while also displaying the existence of a trade-off between competition among cancer cells and depression of their gain function. Assuming cancer cell transporter production is heritable, we then show the potential for a sucker’s gambit therapy by exploiting this trade-off. By strategically changing environmental conditions, we can take advantage of cellular competition and gain function depression.

Transition Therapy: Tackling the Ecology of Tumor Phenotypic Plasticity

Phenotypic switching in cancer cells has been found to be present across tumor types. Recent studies on Glioblastoma report a remarkably common architecture of four well-defined phenotypes coexisting within high levels of intra-tumor genetic heterogeneity. Similar dynamics have been shown to occur in breast cancer and melanoma and are likely to be found across cancer types. Given the adaptive potential of phenotypic switching (PHS) strategies, understanding how it drives tumor evolution and therapy resistance is a major priority. Here we present a mathematical framework uncovering the ecological dynamics behind PHS. The model is able to reproduce experimental results, and mathematical conditions for cancer progression reveal PHS-specific features of tumors with direct consequences on therapy resistance. In particular, our model reveals a threshold for the resistant-to-sensitive phenotype transition rate, below which any cytotoxic or switch-inhibition therapy is likely to fail. The model is able to capture therapeutic success thresholds for cancers where nonlinear growth dynamics or larger PHS architectures are in place, such as glioblastoma or melanoma. By doing so, the model presents a novel set of conditions for the success of combination therapies able to target replication and phenotypic transitions at once. Following our results, we discuss transition therapy as a novel scheme to target not only combined cytotoxicity but also the rates of phenotypic switching.

Theoretical Evaluation of the Impact of Hyperthermia in Combination with Radiation Therapy in an Artificial Immune-Tumor-Ecosystem

Simple Summary

Radio-sensitizing effects of moderate or mild hyperthermia (heating up tumor cells up to 41–43 °C) in combination with radiotherapy (thermoradiotherapy) have been evaluated for decades. However, how this combination might modulate an anti-tumor immune response is not well known. To investigate the dynamic behavior of immune–tumor ecosystems in different scenarios, a model representing an artificial adaptive immune system in silico is used. Such a model may be far removed from the real situation in the patient, but it could serve as a laboratory to investigate fundamental principles of dynamics in such systems under well-controlled conditions and it could be used to generate and refine hypothesis supporting the design of clinical trials. Regarding the results of the presented computer simulations, the main effect is governed by the cellular radio-sensitization. In addition, the application of hyperthermia during the first radiotherapy fractions seems to be more effective.

Abstract

There is some evidence that radiotherapy (RT) can trigger anti-tumor immune responses. In addition, hyperthermia (HT) is known to be a tumor cell radio-sensitizer. How HT could enhance the anti-tumor immune response produced by RT is still an open question. The aim of this study is the evaluation of potential dynamic effects regarding the adaptive immune response induced by different combinations of RT fractions with HT. The adaptive immune system is considered as a trainable unit (perceptron) which compares danger signals released by necrotic or apoptotic cell death with the presence of tumor- and host tissue cell population-specific molecular patterns (antigens). To mimic the changes produced by HT such as cell radio-sensitization or increase of the blood perfusion after hyperthermia, simplistic biophysical models were included. To study the effectiveness of the different RT+HT treatments, the Tumor Control Probability (TCP) was calculated. In the considered scenarios, the major effect of HT is related to the enhancement of the cell radio-sensitivity while perfusion or heat-based effects on the immune system seem to contribute less. Moreover, no tumor vaccination effect has been observed. In the presented scenarios, HT boosts the RT cell killing but it does not fundamentally change the anti-tumor immune response.

Forecasting Individual Patient Response to Radiation Therapy in Head and Neck Cancer With a Dynamic Carrying Capacity Model

Purpose:

To model and predict individual patient responses to radiation therapy.

Methods and Materials:

We modeled tumor dynamics as logistic growth and the effect of radiation as a reduction in the tumor carrying capacity, motivated by the effect of radiation on the tumor microenvironment. The model was assessed on weekly tumor volume data collected for 2 independent cohorts of patients with head and neck cancer from the H. Lee Moffitt Cancer Center (MCC) and the MD Anderson Cancer Center (MDACC) who received 66 to 70 Gy in standard daily fractions or with accelerated fractionation. To predict response to radiation therapy for individual patients, we developed a new forecasting framework that combined the learned tumor growth rate and carrying capacity reduction fraction (δ) distribution with weekly measurements of tumor volume reduction for a given test patient to estimate δ, which was used to predict patient-specific outcomes.

Results:

The model fit data from MCC with high accuracy with patient-specific δ and a fixed tumor growth rate across all patients. The model fit data from an independent cohort from MDACC with comparable accuracy using the tumor growth rate learned from the MCC cohort, showing transferability of the growth rate. The forecasting framework predicted patient-specific outcomes with 76% sensitivity and 83% specificity for locoregional control and 68% sensitivity and 85% specificity for disease-free survival with the inclusion of 4 on-treatment tumor volume measurements.

Conclusions:

These results demonstrate that our simple mathematical model can describe a variety of tumor volume dynamics. Furthermore, combining historically observed patient responses with a few patient-specific tumor volume measurements allowed for the accurate prediction of patient outcomes, which may inform treatment adaptation and personalization.

Darwinian Approaches for Cancer Treatment: Benefits of Mathematical Modeling

One of the major problems of traditional anti-cancer treatments is that they lead to the emergence of treatment-resistant cells, which results in treatment failure. To avoid or delay this phenomenon, it is relevant to take into account the eco-evolutionary dynamics of tumors. Designing evolution-based treatment strategies may help overcoming the problem of drug resistance. In particular, a promising candidate is adaptive therapy, a containment strategy which adjusts treatment cycles to the evolution of the tumors in order to keep the population of treatment-resistant cells under control. Mathematical modeling is a crucial tool to understand the dynamics of cancer in response to treatments, and to make predictions about the outcomes of these treatments. In this review, we highlight the benefits of in silico modeling to design adaptive therapy strategies, and to assess whether they could effectively improve treatment outcomes. Specifically, we review how two main types of models (i.e., mathematical models based on Lotka-Volterra equations and agent-based models) have been used to model tumor dynamics in response to adaptive therapy. We give examples of the advances they permitted in the field of adaptive therapy and discuss about how these models can be integrated in experimental approaches and clinical trial design.

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.

A Circuit for Secretion-coupled Cellular Autonomy in Multicellular Eukaryotes.. [DOI: 10.1101/2021.03.18.436048]

Cancers represent complex autonomous systems, displaying self-sufficiency in growth signaling. Autonomous growth is fueled by a cancer cell’s ability to ‘secrete-and-sense’ growth factors: a poorly understood phenomenon. Using an integrated systems and experimental approach, here we dissect the impact of a feedback-coupled GTPase circuit within the secretory pathway that imparts secretion-coupled autonomy. The circuit is assembled when the Ras-superfamily monomeric GTPase Arf1, and the heterotrimeric GTPase Giαβγ and their corresponding GAPs and GEFs are coupled by GIV/Girdin, a protein that is known to fuel aggressive traits in diverse cancers. One forward and two key negative feedback loops within the circuit create closed-loop control (CLC), allow the two GTPases to coregulate each other, and convert the expected switch-like behavior of Arf1-dependent secretion into an unexpected dose response alignment behavior of sensing and secretion. Such behavior translates into cell survival that is self-sustained by stimulus-proportionate secretion. Proteomic studies and protein-protein interaction network analyses pinpoint growth factors (e.g., the epidermal growth factor; EGF) as a key stimuli for such self-sustenance. Findings highlight how enhanced coupling of two biological switches in cancer cells is critical for multiscale feedback control to achieve secretion-coupled autonomy of growth factors.

SYNOPSIS IMAGE

STANDFIRST TEXT

This work defines the inner workings of a Golgi-localized molecular circuitry comprised of coupled GTPases, which empowers cells to achieve self-sufficiency in growth factor signaling by creating a secrete-and-sense autocrine loop.

HIGHLIGHTS/MAIN FINDINGS

Modeling and experimental approaches were used to dissect a coupled GTPase circuit.

Coupling enables closed loop feedback and mutual control of GTPases.

Coupling generates dose response alignment behavior of sensing and secretion of growth factors.

Coupling is critical for multiscale feedback control to achieve secretion-coupled autonomy.

Role of synergy and antagonism in designing multidrug adaptive chemotherapy schedules

Chemotherapeutic resistance via the mechanism of competitive release of resistant tumor cell subpopulations is a major problem associated with cancer treatments and one of the main causes of tumor recurrence. Often, chemoresistance is mitigated by using multidrug schedules (two or more combination therapies) that can act synergistically, additively, or antagonistically on the heterogeneous population of cells as they evolve. In this paper, we develop a three-component evolutionary game theory model to design two-drug adaptive schedules that mitigate chemoresistance and delay tumor recurrence in an evolving collection of tumor cells with two resistant subpopulations and one chemosensitive population that has a higher baseline fitness but is not resistant to either drug. Using the nonlinear replicator dynamical system with a payoff matrix of Prisoner's Dilemma (PD) type (enforcing a cost to resistance), we investigate the nonlinear dynamics of this three-component system along with an additional tumor growth model whose growth rate is a function of the fitness landscape of the tumor cell populations. A key parameter determines whether the two drugs interact synergistically, additively, or antagonistically. We show that antagonistic drug interactions generally result in slower rates of adaptation of the resistant cells than synergistic ones, making them more effective in combating the evolution of resistance. We then design evolutionary cycles (closed loops) in the three-component phase space by shaping the fitness landscape of the cell populations (i.e., altering the evolutionary stable states of the game) using appropriately designed time-dependent schedules (adaptive therapy), altering the dosages and timing of the two drugs. We describe two key bifurcations associated with our drug interaction parameter which help explain why antagonistic interactions are more effective at controlling competitive release of the resistant population than synergistic interactions in the context of an evolving tumor.

Variation in the life history strategy underlies functional diversity of tumors

Classical r- vs. K-selection theory describes the trade-offs between high reproductive output and competitiveness and guides research in evolutionary ecology. While its impact has waned in the recent past, cancer evolution may rekindle it. Herein, we impose r- or K-selection on cancer cell lines to obtain strongly proliferative r cells and highly competitive K cells to test ideas on life-history strategy evolution. RNA-seq indicates that the trade-offs are associated with distinct expression of genes involved in the cell cycle, adhesion, apoptosis, and contact inhibition. Both empirical observations and simulations based on an ecological competition model show that the trade-off between cell proliferation and competitiveness can evolve adaptively. When the r and K cells are mixed, they exhibit strikingly different spatial and temporal distributions. Due to this niche separation, the fitness of the entire tumor increases. The contrasting selective pressure may operate in a realistic ecological setting of actual tumors.

Selection-driven tumor evolution with public goods leads to patterns of clonal expansion consistent with neutral growth

Cancers are the result of eco-evolutionary processes fueled by heritable phenotypic diversification and driven by environmentally dependent selection. Space represents a key growth-limiting ecological resource, the ability to explore this resource is likely under strong selection. Using agent-based modeling, we explored the interplay between phenotypic strategies centered on gaining access to new space through cell-extrinsic degradation of extracellular matrix barriers and the exploitation of this resource through maximizing cell proliferation. While cell proliferation is a cell-intrinsic property, newly accessed space represents a public good, which can benefit both producers and non-producers. We found that this interplay results in ecological succession, enabling emergence of large, heterogeneous, and highly proliferative populations. Even though in our simulations both remodeling and proliferation strategies were under strong positive selection, their interplay led to sub-clonal architecture that could be interpreted as evidence for neutral evolution, warranting cautious interpretation of inferences from sequencing of cancer genomes.

The ecology of cancer differentiation therapy

A promising, yet still under development approach to cancer treatment is based on the idea of differentiation therapy (DTH). Most tumours are characterized by poorly differentiated cell populations exhibiting a marked loss of traits associated to communication and tissue homeostasis. DTH has been suggested as an alternative (or complement) to cytotoxic-based approaches, and has proven successful in some specific types of cancer such as acute promyelocytic leukemia (APL). While novel drugs favouring the activation of differentiation therapies are being tested, several open problems emerge in relation to its effectiveness on solid tumors. Here we present a mathematical framework to DTH based on a well-known ecological model used to describe habitat loss. The models presented here account for some of the observed clinical and in vitro outcomes of DTH, providing relevant insight into potential therapy design. Furthermore, the same ecological approach is tested in a hierarchical model that accounts for cancer stem cells, highlighting the role of niche specificity in CSC therapy resistance. We show that the lessons learnt from metapopulation ecology can help guide future developments and potential difficulties of DTH.

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.

Evidence for hypoxia increasing the tempo of evolution in glioblastoma

BACKGROUND

Tumour hypoxia is associated with metastatic disease, and while there have been many mechanisms proposed for why tumour hypoxia is associated with metastatic disease, it remains unclear whether one precise mechanism is the key reason or several in concert. Somatic evolution drives cancer progression and treatment resistance, fuelled not only by genetic and epigenetic mutation but also by selection from interactions between tumour cells, normal cells and physical micro-environment. Ecological habitats influence evolutionary dynamics, but the impact on tempo of evolution is less clear.

METHODS

We explored this complex dialogue with a combined clinical-theoretical approach by simulating a proliferative hierarchy under heterogeneous oxygen availability with an agent-based model. Predictions were compared against histology samples taken from glioblastoma patients, stained to elucidate areas of necrosis and TP53 expression heterogeneity.

RESULTS

Results indicate that cell division in hypoxic environments is effectively upregulated, with low-oxygen niches providing avenues for tumour cells to spread. Analysis of human data indicates that cell division is not decreased under hypoxia, consistent with our results.

CONCLUSIONS

Our results suggest that hypoxia could be a crucible that effectively warps evolutionary velocity, making key mutations more likely. Thus, key tumour ecological niches such as hypoxic regions may alter the evolutionary tempo, driving mutations fuelling tumour heterogeneity.

Eco-oncology: Applying ecological principles to understand and manage cancer

Cancer is a disease of single cells that expresses itself at the population level. The striking similarities between initiation and growth of tumors and dynamics of biological populations, and between metastasis and ecological invasion and community dynamics suggest that oncology can benefit from an ecological perspective to improve our understanding of cancer biology. Tumors can be viewed as complex, adaptive, and evolving systems as they are spatially and temporally heterogeneous, continually interacting with each other and with the microenvironment and evolving to increase the fitness of the cancer cells. We argue that an eco-evolutionary perspective is essential to understand cancer biology better. Furthermore, we suggest that ecologically informed therapeutic approaches that combine standard of care treatments with strategies aimed at decreasing the evolutionary potential and fitness of neoplastic cells, such as disrupting cell-to-cell communication and cooperation, and preventing successful colonization of distant organs by migrating cancer cells, may be effective in managing cancer as a chronic condition.

High School Internship Program in Integrated Mathematical Oncology (HIP IMO): Five-Year Experience at Moffitt Cancer Center

Modern cancer research, and the wealth of data across multiple spatial and temporal scales, has created the need for researchers that are well versed in the life sciences (cancer biology, developmental biology, immunology), medical sciences (oncology) and natural sciences (mathematics, physics, engineering, computer sciences). College undergraduate education traditionally occurs in disciplinary silos, which creates a steep learning curve at the graduate and postdoctoral levels that increasingly bridge multiple disciplines. Numerous colleges have begun to embrace interdisciplinary curricula, but students who double major in mathematics (or other quantitative sciences) and biology (or medicine) remain scarce. We identified the need to educate junior and senior high school students about integrating mathematical and biological skills, through the lens of mathematical oncology, to better prepare students for future careers at the interdisciplinary interface. The High school Internship Program in Integrated Mathematical Oncology (HIP IMO) at Moffitt Cancer Center has so far trained 59 students between 2015 and 2019. We report here on the program structure, training deliverables, curriculum and outcomes. We hope to promote interdisciplinary educational activities early in a student's career.

Histoecology: Applying Ecological Principles and Approaches to Describe and Predict Tumor Ecosystem Dynamics Across Space and Time

Cancer cells exist within a complex spatially structured ecosystem composed of resources and different cell types. As the selective pressures imposed by this environment determine the fate of cancer cells, an improved understanding of how this ecosystem evolves will better elucidate how tumors grow and respond to therapy. State of the art imaging methods can now provide highly resolved descriptions of the microenvironment, yielding the data required for a thorough study of its role in tumor growth and treatment resistance. The field of landscape ecology has been studying such species-environment relationship for decades, and offers many tools and perspectives that cancer researchers could greatly benefit from. Here, we discuss one such tool, species distribution modeling (SDM), that has the potential to, among other things, identify critical environmental factors that drive tumor evolution and predict response to therapy. SDMs only scratch the surface of how ecological theory and methods can be applied to cancer, and we believe further integration will take cancer research in exciting new and productive directions. Significance: Here we describe how species distribution modeling can be used to quantitatively describe the complex relationship between tumor cells and their microenvironment. Such a description facilitates a deeper understanding of cancers eco-evolutionary dynamics, which in turn sheds light on the factors that drive tumor growth and response to treatment.

Mix and Match: Phenotypic Coexistence as a Key Facilitator of Cancer Invasion

Invasion of healthy tissue is a defining feature of malignant tumours. Traditionally, invasion is thought to be driven by cells that have acquired all the necessary traits to overcome the range of biological and physical defences employed by the body. However, in light of the ever-increasing evidence for geno- and phenotypic intra-tumour heterogeneity, an alternative hypothesis presents itself: could invasion be driven by a collection of cells with distinct traits that together facilitate the invasion process? In this paper, we use a mathematical model to assess the feasibility of this hypothesis in the context of acid-mediated invasion. We assume tumour expansion is obstructed by stroma which inhibits growth and extra-cellular matrix (ECM) which blocks cancer cell movement. Further, we assume that there are two types of cancer cells: (i) a glycolytic phenotype which produces acid that kills stromal cells and (ii) a matrix-degrading phenotype that locally remodels the ECM. We extend the Gatenby-Gawlinski reaction-diffusion model to derive a system of five coupled reaction-diffusion equations to describe the resulting invasion process. We characterise the spatially homogeneous steady states and carry out a simulation study in one spatial dimension to determine how the tumour develops as we vary the strength of competition between the two phenotypes. We find that overall tumour growth is most extensive when both cell types can stably coexist, since this allows the cells to locally mix and benefit most from the combination of traits. In contrast, when inter-species competition exceeds intra-species competition the populations spatially separate and invasion arrests either: (i) rapidly (matrix-degraders dominate) or (ii) slowly (acid-producers dominate). Overall, our work demonstrates that the spatial and ecological relationship between a heterogeneous population of tumour cells is a key factor in determining their ability to cooperate. Specifically, we predict that tumours in which different phenotypes coexist stably are more invasive than tumours in which phenotypes are spatially separated.

Towards Multidrug Adaptive Therapy

A new ecologically inspired paradigm in cancer treatment known as "adaptive therapy" capitalizes on competitive interactions between drug-sensitive and drug-resistant subclones. The goal of adaptive therapy is to maintain a controllable stable tumor burden by allowing a significant population of treatment-sensitive cells to survive. These, in turn, suppress proliferation of the less-fit resistant populations. However, there remain several open challenges in designing adaptive therapies, particularly in extending these therapeutic concepts to multiple treatments. We present a cancer treatment case study (metastatic castrate-resistant prostate cancer) as a point of departure to illustrate three novel concepts to aid the design of multidrug adaptive therapies. First, frequency-dependent "cycles" of tumor evolution can trap tumor evolution in a periodic, controllable loop. Second, the availability and selection of treatments may limit the evolutionary "absorbing region" reachable by the tumor. Third, the velocity of evolution significantly influences the optimal timing of drug sequences. These three conceptual advances provide a path forward for multidrug adaptive therapy. SIGNIFICANCE: Driving tumor evolution into periodic, repeatable treatment cycles provides a path forward for multidrug adaptive therapy.

Cancer Ecology and Evolution: Positive interactions and system vulnerability

Parallels of cancer with ecology and evolution have provided new insights into the initiation and spread of cancer, and new approaches to therapy. This review describes those parallels while emphasizing some key contrasts. We argue that cancers are less like invasive species than like native species or even crops that have escaped control, and that ecological control and homeo-static control differ fundamentally through both their ends and their means. From our focus on the role of positive interactions in control processes, we introduce a novel mathematical modeling framework that tracks how individual cell lineages arise, and how the many layers of control break down in the emergence of cancer. The next generation of therapies must continue to look beyond cancers as being created by individual renegade cells and address not only the network of interactions those cells inhabit, but the evolutionary logic that created those interactions and their intrinsic vulnerability.

Cancer cell population growth kinetics at low densities deviate from the exponential growth model and suggest an Allee effect

Most models of cancer cell population expansion assume exponential growth kinetics at low cell densities, with deviations to account for observed slowing of growth rate only at higher densities due to limited resources such as space and nutrients. However, recent preclinical and clinical observations of tumor initiation or recurrence indicate the presence of tumor growth kinetics in which growth rates scale positively with cell numbers. These observations are analogous to the cooperative behavior of species in an ecosystem described by the ecological principle of the Allee effect. In preclinical and clinical models, however, tumor growth data are limited by the lower limit of detection (i.e., a measurable lesion) and confounding variables, such as tumor microenvironment, and immune responses may cause and mask deviations from exponential growth models. In this work, we present alternative growth models to investigate the presence of an Allee effect in cancer cells seeded at low cell densities in a controlled in vitro setting. We propose a stochastic modeling framework to disentangle expected deviations due to small population size stochastic effects from cooperative growth and use the moment approach for stochastic parameter estimation to calibrate the observed growth trajectories. We validate the framework on simulated data and apply this approach to longitudinal cell proliferation data of BT-474 luminal B breast cancer cells. We find that cell population growth kinetics are best described by a model structure that considers the Allee effect, in that the birth rate of tumor cells increases with cell number in the regime of small population size. This indicates a potentially critical role of cooperative behavior among tumor cells at low cell densities with relevance to early stage growth patterns of emerging and relapsed tumors.

Practically scheduling hormone therapy for prostate cancer using a mathematical model

Hormone therapy is one of the popular therapeutic methods for prostate cancer. Intermittent androgen suppression (IAS) is the method which stops and resumes hormone therapy repeatedly. The efficacy of IAS differs depending on patients; both the cases have been reported where the relapse of cancer happened and did not happen, for the patients who had undergone IAS. For the patients who cannot avoid the relapse of cancer by IAS, we should delay the relapse of cancer as later as possible. Here we compared some practical methods of determining when to stop and restart hormone therapy for IAS using an existing mathematical model of prostate cancer. The method we suggest is to determine the ratio of on-treatment period and off-treatment period sparsely for each cycle, namely the "sparse search." We also compared the performance of the sparse search with the exhaustive search and the model predictive control. We found that the sparse search can find a good treatment schedule without failure, and the computational cost is not so high compared to the exhaustive method. In addition, we focus on the model predictive control (MPC) method which has been applied to the scheduling of IAS in some existing studies. The MPC is computationary efficient, although it does not always find an optimal schedule in the numerical experiments here. We believe that the MPC method might be also promising because of its reasonable computational costs and its possibility of expanding of the model.

Simulated ablation for detection of cells impacting paracrine signalling in histology analysis

Intra-tumour phenotypic heterogeneity limits accuracy of clinical diagnostics and hampers the efficiency of anti-cancer therapies. Dealing with this cellular heterogeneity requires adequate understanding of its sources, which is extremely difficult, as phenotypes of tumour cells integrate hardwired (epi)mutational differences with the dynamic responses to microenvironmental cues. The later comes in form of both direct physical interactions, as well as inputs from gradients of secreted signalling molecules. Furthermore, tumour cells can not only receive microenvironmental cues, but also produce them. Despite high biological and clinical importance of understanding spatial aspects of paracrine signaling, adequate research tools are largely lacking. Here, a partial differential equation (PDE)-based mathematical model is developed that mimics the process of cell ablation. This model suggests how each cell might contribute to the microenvironment by either absorbing or secreting diffusible factors, and quantifies the extent to which observed intensities can be explained via diffusion-mediated signalling. The model allows for the separation of phenotypic responses to signalling gradients within tumour microenvironments from the combined influence of responses mediated by direct physical contact and hardwired (epi)genetic differences. The method is applied to a multi-channel immunofluorescence in situ hybridisation (iFISH)-stained breast cancer histological specimen, and correlations are investigated between: HER2 gene amplification, HER2 protein expression and cell interaction with the diffusible microenvironment. This approach allows partial deconvolution of the complex inputs that shape phenotypic heterogeneity of tumour cells and identifies cells that significantly impact gradients of signalling molecules.

Nonlinear adaptive control of competitive release and chemotherapeutic resistance

We use a three-component replicator system with healthy cells, sensitive cells, and resistant cells, with a prisoner's dilemma payoff matrix from evolutionary game theory, to model and control the nonlinear dynamical system governing the ecological mechanism of competitive release by which tumors develop chemotherapeutic resistance. The control method we describe is based on nonlinear trajectory design and energy transfer methods first introduced in the orbital mechanics literature for Hamiltonian systems. For continuous therapy, the basin boundaries of attraction associated with the chemo-sensitive population and the chemo-resistant population for increasing values of chemo-concentrations have an intertwined spiral structure with extreme sensitivity to changes in chemo-concentration level as well as sensitivity with respect to resistant mutations. For time-dependent therapies, we introduce an orbit transfer method to construct continuous families of periodic (closed) orbits by switching the chemo-dose at carefully chosen times and appropriate levels to design schedules that are superior to both maximum tolerated dose (MTD) schedules and low-dose metronomic (LDM) schedules, both of which ultimately lead to fixation of sensitive cells or resistant cells. By keeping the three subpopulations of cells in competition with each other indefinitely, we avoid fixation of the cancer cell population and regrowth of a resistant tumor. The method can be viewed as a way to dynamically shape the average population fitness landscape of a tumor to steer the chemotherapeutic response curve. We show that the method is remarkably insensitive to initial conditions and small changes in chemo-dosages, an important criterion for turning the method into an actionable strategy.

An ecosystem framework for understanding and treating disease

Pathogens and cancers are pervasive health risks in the human population. I argue that if we are to better understand disease and its treatment, then we need to take an ecological perspective of disease itself. I generalize and extend an emerging framework that views disease as an ecosystem and many of its components as interacting in a community. I develop the framework for biological etiological agents (BEAs) that multiply within humans—focusing on bacterial pathogens and cancers—but the framework could be extended to include other host and parasite species. I begin by describing why we need an ecosystem framework to understand disease, and the main components and interactions in bacterial and cancer disease ecosystems. Focus is then given to the BEA and how it may proceed through characteristic states, including emergence, growth, spread and regression. The framework is then applied to therapeutic interventions. Central to success is preventing BEA evasion, the best known being antibiotic resistance and chemotherapeutic resistance in cancers. With risks of evasion in mind, I propose six measures that either introduce new components into the disease ecosystem or manipulate existing ones. An ecosystem framework promises to enhance our understanding of disease, BEA and host (co)evolution, and how we can improve therapeutic outcomes.

Competition and niche construction in a model of cancer metastasis

Niche construction theory states that not only does the environment act on populations to generate Darwinian selection, but organisms reciprocally modify the environment and the sources of natural selection. Cancer cells participate in niche construction as they alter their microenvironments and create pre-metastatic niches; in fact, metastasis is a product of niche construction. Here, we present a mathematical model of niche construction and metastasis. Our model contains producers, which pay a cost to contribute to niche construction that benefits all tumor cells, and cheaters, which reap the benefits without paying the cost. We derive expressions for the conditions necessary for metastasis, showing that the establishment of a mutant lineage that promotes metastasis depends on niche construction specificity and strength of interclonal competition. We identify a tension between the arrival and invasion of metastasis-promoting mutants, where tumors composed only of cheaters remain small but are susceptible to invasion whereas larger tumors containing producers may be unable to facilitate metastasis depending on the level of niche construction specificity. Our results indicate that even if metastatic subclones arise through mutation, metastasis may be hindered by interclonal competition, providing a potential explanation for recent surprising findings that most metastases are derived from early mutants in primary tumors.

The complex ecosystem in non small cell lung cancer invasion

Many tumors are characterized by genetic instability, producing an assortment of genetic variants of tumor cells called subclones. These tumors and their surrounding environments form complex multi-cellular ecosystems, where subclones compete for resources and cooperate to perform multiple tasks, including cancer invasion. Our recent empirical studies revealed existence of such distinct phenotypes of cancer cells, leaders and followers, in lung cancer. These two cellular subclones exchange a complex array of extracellular signals demonstrating a symbiotic relationship at the cellular level. Here, we develop a computational model of the microenvironment of the lung cancer ecosystem to explore how the interactions between subclones can advance or inhibit invasion. We found that, due to the complexity of the ecosystem, invasion may have very different dynamics characterized by the different levels of aggressiveness. By altering the signaling environment, we could alter the ecological relationship between the cell types and the overall ecosystem development. Competition between leader and follower cell populations (defined by the limited amount of resources), positive feedback within the leader cell population (controlled by the focal adhesion kinase and fibronectin signaling), and impact of the follower cells to the leaders (represented by yet undetermined proliferation signal) all had major effects on the outcome of the collective dynamics. Specifically, our analysis revealed a class of tumors (defined by the strengths of fibronectin signaling and competition) that are particularly sensitive to manipulations of the signaling environment. These tumors can undergo irreversible changes to the tumor ecosystem that outlast the manipulations of feedbacks and have a profound impact on invasive potential. Our study predicts a complex division of labor between cancer cell subclones and suggests new treatment strategies targeting signaling within the tumor ecosystem.

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.

Similarity and diversity of the tumor microenvironment in multiple metastases: critical implications for overall and progression-free survival of high-grade serous ovarian cancer

The tumor microenvironment is pivotal in influencing cancer progression and metastasis. Different cells co-exist with high spatial diversity within a patient, yet their combinatorial effects are poorly understood. We investigate the similarity of the tumor microenvironment of 192 local metastatic lesions in 61 ovarian cancer patients. An ecologically inspired measure of microenvironmental diversity derived from multiple metastasis sites is correlated with clinicopathological characteristics and prognostic outcome. We demonstrate a high accuracy of our automated analysis across multiple sites. A low level of similarity in microenvironmental composition is observed between ovary tumor and corresponding local metastases (stromal ratio r = 0.30, lymphocyte ratio r = 0.37). We identify a new measure of microenvironmental diversity derived from Shannon entropy that is highly predictive of poor overall (p = 0.002, HR = 3.18, 95% CI = 1.51-6.68) and progression-free survival (p = 0.0036, HR = 2.83, 95% CI = 1.41-5.7), independent of and stronger than clinical variables, subtype stratifications based on single cell types alone and number of sites. Although stromal influence in ovary tumors is known to have significant clinical implications, our findings reveal an even stronger impact orchestrated by diverse cell types. Quantitative histology-based measures can further enable objective selection of patients who are in urgent need of new therapeutic strategies such as combinatorial treatments targeting heterogeneous tumor microenvironment.