Towards Multidrug Adaptive Therapy

The theory of tumor ecosystem

Cancer cells can be conceived as “living organisms” interacting with cellular or non‐cellular components in the host internal environment, not only the local tumor microenvironment but also the distant organ niches, as well as the immune, nervous and endocrine systems, to construct a self‐sustainable tumor ecosystem. With increasing evidence for the systemic tumor‐host interplay, we predict that a new era of cancer therapy targeting the ecosystemic vulnerability of human malignancies has come. Revolving around the tumor ecosystem scoped as different hierarchies of primary, regional, distal and systemic onco‐spheres, we comprehensively review the tumor‐host interaction among cancer cells and their local microenvironment, distant organ niches, immune, nervous and endocrine systems, highlighting material and energy flow with tumor ecological homeostasis as an internal driving force. We also substantiate the knowledge of visualizing, modelling and subtyping this dynamically intertwined network with recent technological advances, and discuss ecologically rational strategies for more effective cancer therapies.

In Silico Investigations of Multi-Drug Adaptive Therapy Protocols

The standard of care for cancer patients aims to eradicate the tumor by killing the maximum number of cancer cells using the maximum tolerated dose (MTD) of a drug. MTD causes significant toxicity and selects for resistant cells, eventually making the tumor refractory to treatment. Adaptive therapy aims to maximize time to progression (TTP), by maintaining sensitive cells to compete with resistant cells. We explored both dose modulation (DM) protocols and fixed dose (FD) interspersed with drug holiday protocols. In contrast to previous single drug protocols, we explored the determinants of success of two-drug adaptive therapy protocols, using an agent-based model. In almost all cases, DM protocols (but not FD protocols) increased TTP relative to MTD. DM protocols worked well when there was more competition, with a higher cost of resistance, greater cell turnover, and when crowded proliferating cells could replace their neighbors. The amount that the drug dose was changed, mattered less. The more sensitive the protocol was to tumor burden changes, the better. In general, protocols that used as little drug as possible, worked best. Preclinical experiments should test these predictions, especially dose modulation protocols, with the goal of generating successful clinical trials for greater cancer control.

Drug-Resistant Cancer Treatment Strategies Based on the Dynamics of Clonal Evolution and PKPD Modeling of Drug Combinations

A method for determining a dosage strategy is proposed to combat drug resistance in tumor progression. The method is based on a dynamic model for the clonal evolution of cancerous cells and considers the Pharmacokinetic/Pharmacodynamic (PKPD) modeling of combination therapy. The proposed mathematical representation models the dynamic and kinetic effects of multiple drugs on the number of cells while considering potential mutations and assuming that no cross-resistance arises. An optimization problem is then proposed to minimize the total number of cancerous cells in a finite treatment period given a limited number of treatments. The dosage schedule, including the amount of each drug to be administered and the timing, is found by solving the optimization problem. This treatment schedule is constrained to achieve a target minimum effectiveness, while also ensuring that the concentration of the drugs, individually and totally, does not exceed a prescribed toxicity threshold. The proposed optimization problem is represented as a Complementary Geometric Programming (CGP) problem. The results show that the solution of the optimization problem for combination therapy is the dosing schedule that leads to tumor eradication at the end of the treatment period. The results also investigate the tumor dynamics for all mutation types when undergoing treatment, showing that single drug therapies can fail to combat the emergence of resistance, while optimized combination therapies can reduce the amount of all mutation types during the course of treatment, thereby combating resistance.

Spatial structure impacts adaptive therapy by shaping intra-tumoral competition

Background

Adaptive therapy aims to tackle cancer drug resistance by leveraging resource competition between drug-sensitive and resistant cells. Here, we present a theoretical study of intra-tumoral competition during adaptive therapy, to investigate under which circumstances it will be superior to aggressive treatment.

Methods

We develop and analyse a simple, 2-D, on-lattice, agent-based tumour model in which cells are classified as fully drug-sensitive or resistant. Subsequently, we compare this model to its corresponding non-spatial ordinary differential equation model, and fit it to longitudinal prostate-specific antigen data from 65 prostate cancer patients undergoing intermittent androgen deprivation therapy following biochemical recurrence.

Results

Leveraging the individual-based nature of our model, we explicitly demonstrate competitive suppression of resistance during adaptive therapy, and examine how different factors, such as the initial resistance fraction or resistance costs, alter competition. This not only corroborates our theoretical understanding of adaptive therapy, but also reveals that competition of resistant cells with each other may play a more important role in adaptive therapy in solid tumours than was previously thought. To conclude, we present two case studies, which demonstrate the implications of our work for: (i) mathematical modelling of adaptive therapy, and (ii) the intra-tumoral dynamics in prostate cancer patients during intermittent androgen deprivation treatment, a precursor of adaptive therapy.

Conclusion

Our work shows that the tumour’s spatial architecture is an important factor in adaptive therapy and provides insights into how adaptive therapy leverages both inter- and intra-specific competition to control resistance.

Cancer therapy traditionally focuses on maximising tumour cell kill with the aim of achieving a cure, but such aggressive treatment can open up space for drug-resistant cells to grow. In contrast, adaptive therapy aims to leverage competition between drug-sensitive and resistant cells by adjusting treatment to maintain the tumour at a tolerable size, whilst preserving drug-sensitive cells. This approach is being tested in trials but is not yet widely used as deeper understanding of cell-cell competition is required. Here, we used a mathematical model to investigate how strongly, and with whom, resistant cells compete during continuous and adaptive therapy, and applied our insights to hormone therapy in prostate cancer where adaptive therapy has recently been successfully trialed. Our results provide new insights into how adaptive therapy works and show that, by shaping cell competition, the tumour’s spatial architecture is important in determining therapy response.

Strobl et al. develop an agent-based spatial model of drug resistance in tumour cells under adaptive therapy. Using this model, they investigate how the tumour’s spatial architecture impacts intratumoural competitive dynamics of drug-sensitive vs. -resistant clones in response to therapy.

TUMOR CELL MALIGNANCY: A COMPLEX TRAIT BUILT THROUGH RECIPROCAL INTERACTIONS BETWEEN TUMORS AND TISSUE-BODY SYSTEM

Since the discovery of oncogenes and tumor suppressor genes in the late past century, cancer research has been overwhelmingly focused on the genetics and biology of tumor cells and hence has addressed mostly cell-autonomous processes with emphasis on traditional driver/passenger genetic models. Nevertheless, over that same period, multiple seminal observations have accumulated highlighting the role of non-cell autonomous effectors in tumor growth and metastasis. However, given that cell autonomous and non-autonomous events are observed together at the time of diagnosis, it is in fact impossible to know whether the malignant transformation is initiated by cell autonomous oncogenic events or by non-cell autonomous conditions generated by alterations of the tissue-body ecosystem. This review aims at addressing this issue by taking the option of defining malignancy as a complex genetic trait incorporating genetically determined reciprocal interactions between tumor cells and tissue-body ecosystem.

Using Parallel Coordinates in Optimization of Nano-Particle Drug Delivery

Nanoparticle drug delivery better targets neoplastic lesions than free drugs and thus has emerged as a safer form of cancer therapy. Nanoparticle design variables are important determinants of efficacy as they influence the drug biodistribution and pharmacokinetics. Previously, we determined optimal designs through mechanistic modeling and optimization. However, the numerical nature of the tumor model and numerous candidate nanoparticle designs hinder hypothesis generation and treatment personalization. In this paper, we utilize the parallel coordinates technique to visualize high-dimensional optimal solutions and extract correlations between nanoparticle design and treatment outcomes. We found that at optimality, two major design variables are dependent, and thus the optimization problem can be reduced. In addition, we obtained an analytical relationship between optimal nanoparticle sizes and optimal distribution, which could facilitate the utilization of tumors models in preclinical studies. Our approach has simplified the results of the previously integrated modeling and optimization framework developed for nanotherapy and enhanced the interpretation and utilization of findings. Integrated mathematical frameworks are increasing in the medical field, and our method can be applied outside nanotherapy to facilitate the clinical translation of computational methods.

Can artificial intelligence improve cancer treatments?

Artificial intelligence (AI) powered by the accumulating clinical and molecular data about cancer has fueled the expectation that a transformation in cancer treatments towards significant improvement of patient outcomes is at hand. However, such transformation has been so far elusive. The opacity of AI algorithms and the lack of quality annotated data being available at population scale are among the challenges to the application of AI in oncology. Fundamentally however, the heterogeneity of cancer and its evolutionary dynamics make every tumor response to therapy sufficiently different from the population, machine-learned statistical models, challenging hence the capacity of these models to yield reliable inferences about treatment recommendations that can improve patient outcomes. This article reviews the nominal elements of clinical decision-making for precision oncology and frames the utility of AI to cancer treatment improvements in light of cancer unique challenges.

Intermittent treatment of BRAFV600E melanoma cells delays resistance by adaptive resensitization to drug rechallenge

Preclinical studies of metastatic melanoma treated with targeted therapeutics have suggested that alternating periods of treatment and withdrawal might delay the onset of resistance. This has been attributed to drug addiction, where cells lose fitness upon drug removal due to the resulting hyperactivation of mitogen-activated protein (MAP) kinase signaling. This study presents evidence that the intermittent treatment response can also be explained by the resensitization of cells following drug removal and enhanced cell loss upon drug rechallenge. Resensitization is accompanied by adaptive transcriptomic switching and occurs despite the sustained expression of resistance genes throughout the intermittent treatment.

Patients with melanoma receiving drugs targeting BRAF^V600E and mitogen-activated protein (MAP) kinase kinases 1 and 2 (MEK1/2) invariably develop resistance and face continued progression. Based on preclinical studies, intermittent treatment involving alternating periods of drug withdrawal and rechallenge has been proposed as a method to delay the onset of resistance. The beneficial effect of intermittent treatment has been attributed to drug addiction, where drug withdrawal reduces the viability of resistant cells due to MAP kinase pathway hyperactivation. However, the mechanistic basis of the intermittent effect is incompletely understood. We show that intermittent treatment with the BRAF^V600E inhibitor, LGX818/encorafenib, suppresses growth compared with continuous treatment in human melanoma cells engineered to express BRAF^V600E, p61-BRAF^V600E, or MEK2^C125 oncogenes. Analysis of the BRAF^V600E-overexpressing cells shows that, while drug addiction clearly occurs, it fails to account for the advantageous effect of intermittent treatment. Instead, growth suppression is best explained by resensitization during periods of drug removal, followed by cell death after drug readdition. Continuous treatment leads to transcriptional responses prominently associated with chemoresistance in melanoma. By contrast, cells treated intermittently reveal a subset of transcripts that reverse expression between successive cycles of drug removal and rechallenge and include mediators of cell invasiveness and the epithelial-to-mesenchymal transition. These transcripts change during periods of drug removal by adaptive switching, rather than selection pressure. Resensitization occurs against a background of sustained expression of melanoma resistance genes, producing a transcriptome distinct from that of the initial drug-naive cell state. We conclude that phenotypic plasticity leading to drug resensitization can underlie the beneficial effect of intermittent treatment.

Deciphering Tumour Heterogeneity: From Tissue to Liquid Biopsy

Simple Summary

Most malignant tumours are highly heterogeneous at molecular and phenotypic levels. Tumour variability poses challenges for the management of patients, as it arises between patients and even evolves in space and time within a single patient. Currently, treatment-decision making usually relies on the molecular characteristics of a limited tumour tissue sample at the time of diagnosis or disease progression but does not take into account the complexity of the bulk tumours and their constant evolution over time. In this review, we explore the extent of tumour heterogeneity and report the mechanisms that promote and sustain this diversity in cancers. We summarise the clinical strikes of tumour diversity in the management of patients with cancer. Finally, we discuss the current material and technological approaches that are relevant to adequately appreciate tumour heterogeneity.

Abstract

Human solid malignancies harbour a heterogeneous set of cells with distinct genotypes and phenotypes. This heterogeneity is installed at multiple levels. A biological diversity is commonly observed between tumours from different patients (inter-tumour heterogeneity) and cannot be fully captured by the current consensus molecular classifications for specific cancers. To extend the complexity in cancer, there are substantial differences from cell to cell within an individual tumour (intra-tumour heterogeneity, ITH) and the features of cancer cells evolve in space and time. Currently, treatment-decision making usually relies on the molecular characteristics of a limited tumour tissue sample at the time of diagnosis or disease progression but does not take into account the complexity of the bulk tumours and their constant evolution over time. In this review, we explore the extent of tumour heterogeneity with an emphasis on ITH and report the mechanisms that promote and sustain this diversity in cancers. We summarise the clinical strikes of ITH in the management of patients with cancer. Finally, we discuss the current material and technological approaches that are relevant to adequately appreciate ITH.

Optimizing the future: how mathematical models inform treatment schedules for cancer

For decades, mathematical models have influenced how we schedule chemotherapeutics. More recently, mathematical models have leveraged lessons from ecology, evolution, and game theory to advance predictions of optimal treatment schedules, often in a personalized medicine manner. We discuss both established and emerging therapeutic strategies that deviate from canonical standard-of-care regimens, and how mathematical models have contributed to the design of such schedules. We first examine scheduling options for single therapies and review the advantages and disadvantages of various treatment plans. We then consider the challenge of scheduling multiple therapies, and review the mathematical and clinical support for various conflicting treatment schedules. Finally, we propose how a consilience of mathematical and clinical knowledge can best determine the optimal treatment schedules for patients.

The impact of the spatial heterogeneity of resistant cells and fibroblasts on treatment response

A long-standing practice in the treatment of cancer is that of hitting hard with the maximum tolerated dose to eradicate tumors. This continuous therapy, however, selects for resistant cells, leading to the failure of the treatment. A different type of treatment strategy, adaptive therapy, has recently been shown to have a degree of success in both preclinical xenograft experiments and clinical trials. Adaptive therapy is used to maintain a tumor's volume by exploiting the competition between drug-sensitive and drug-resistant cells with minimum effective drug doses or timed drug holidays. To further understand the role of competition in the outcomes of adaptive therapy, we developed a 2D on-lattice agent-based model. Our simulations show that the superiority of the adaptive strategy over continuous therapy depends on the local competition shaped by the spatial distribution of resistant cells. Intratumor competition can also be affected by fibroblasts, which produce microenvironmental factors that promote cancer cell growth. To this end, we simulated the impact of different fibroblast distributions on treatment outcomes. As a proof of principle, we focused on five types of distribution of fibroblasts characterized by different locations, shapes, and orientations of the fibroblast region with respect to the resistant cells. Our simulation shows that the spatial architecture of fibroblasts modulates tumor progression in both continuous and adaptive therapy. Finally, as a proof of concept, we simulated the outcomes of adaptive therapy of a virtual patient with four metastatic sites composed of different spatial distributions of fibroblasts and drug-resistant cell populations. Our simulation highlights the importance of undetected metastatic lesions on adaptive therapy outcomes.

Regulation of Tumor Invasion by the Physical Microenvironment: Lessons from Breast and Brain Cancer

The success of anticancer therapies is often limited by heterogeneity within and between tumors. While much attention has been devoted to understanding the intrinsic molecular diversity of tumor cells, the surrounding tissue microenvironment is also highly complex and coevolves with tumor cells to drive clinical outcomes. Here, we propose that diverse types of solid tumors share common physical motifs that change in time and space, serving as universal regulators of malignancy. We use breast cancer and glioblastoma as instructive examples and highlight how invasion in both diseases is driven by the appropriation of structural guidance cues, contact-dependent heterotypic interactions with stromal cells, and elevated interstitial fluid pressure and flow. We discuss how engineering strategies show increasing value for measuring and modeling these physical properties for mechanistic studies. Moreover, engineered systems offer great promise for developing and testing novel therapies that improve patient prognosis by normalizing the physical tumor microenvironment. Expected final online publication date for the Annual Review of Biomedical Engineering, Volume 24 is June 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Optimal dynamic incentive scheduling for Hawk-Dove evolutionary games

The Hawk-Dove evolutionary game offers a paradigm of the trade-offs associated with aggressive and passive behaviors. When two (or more) populations of players compete, their success or failure is measured by their frequency in the population, and the system is governed by the replicator dynamics. We develop a time-dependent optimal-adaptive control theory for this dynamical system in which the entries of the payoff matrix are dynamically altered to produce control schedules that minimize and maximize the aggressive population through a finite-time cycle. These schedules provide upper and lower bounds on the outcomes for all possible strategies since they represent two extremizers of the cost function. We then adaptively extend the optimal control schedules over multiple cycles to produce absolute maximizers and minimizers for the system.

Dimensionless parameter predicts bacterial prodrug success

Understanding mechanisms of antibiotic failure is foundational to combating the growing threat of multidrug-resistant bacteria. Prodrugs-which are converted into a pharmacologically active compound after administration-represent a growing class of therapeutics for treating bacterial infections but are understudied in the context of antibiotic failure. We hypothesize that strategies that rely on pathogen-specific pathways for prodrug conversion are susceptible to competing rates of prodrug activation and bacterial replication, which could lead to treatment escape and failure. Here, we construct a mathematical model of prodrug kinetics to predict rate-dependent conditions under which bacteria escape prodrug treatment. From this model, we derive a dimensionless parameter we call the Bacterial Advantage Heuristic (BAH) that predicts the transition between prodrug escape and successful treatment across a range of time scales (1-104  h), bacterial carrying capacities (5 × 104 -105  CFU/µl), and Michaelis constants (KM  = 0.747-7.47 mM). To verify these predictions in vitro, we use two models of bacteria-prodrug competition: (i) an antimicrobial peptide hairpin that is enzymatically activated by bacterial surface proteases and (ii) a thiomaltose-conjugated trimethoprim that is internalized by bacterial maltodextrin transporters and hydrolyzed by free thiols. We observe that prodrug failure occurs at BAH values above the same critical threshold predicted by the model. Furthermore, we demonstrate two examples of how failing prodrugs can be rescued by decreasing the BAH below the critical threshold via (i) substrate design and (ii) nutrient control. We envision such dimensionless parameters serving as supportive pharmacokinetic quantities that guide the design and administration of prodrug therapeutics.

Systemic Triple Therapy in Metastatic Hormone-Sensitive Prostate Cancer (mHSPC): Ready for Prime Time or Still to Be Explored?

For decades, mono androgen deprivation therapy (ADT) has been the gold standard for metastatic hormone-sensitive prostate cancer (mHSPC) treatment. Several studies have been published within the last seven years demonstrating a significant survival advantage by combination treatment with standard ADT plus docetaxel or androgen receptor-axis-targeted therapy (ARAT) compared to ADT monotherapy. As a result, overall survival can be prolonged by at least 18 months. Recently published congress data of the PEACE-1 study suggests that in the future, triple therapy might be the new gold standard. In addition to this study, which has shown that triple treatment with standard ADT plus docetaxel plus abiraterone is superior to standard ADT plus docetaxel, several other phase III triple therapy studies are currently ongoing. The different modes of action that are investigated reach from AR-targeting over mitotic inhibition and immunotherapy to PARP and AKT inhibition. In this review we will explore if triple therapy has the potential to be the new standard for mHSPC treatment in the near future.

Cancer cell heterogeneity and plasticity: A paradigm shift in glioblastoma

Phenotypic plasticity has emerged as a major contributor to intra-tumoral heterogeneity and treatment resistance in cancer. Increasing evidence shows that glioblastoma (GBM) cells display prominent intrinsic plasticity and reversibly adapt to dynamic microenvironmental conditions. Limited genetic evolution at recurrence further suggests that resistance mechanisms also largely operate at the phenotypic level. Here we review recent literature underpinning the role of GBM plasticity in creating gradients of heterogeneous cells including those that carry cancer stem cell (CSC) properties. A historical perspective from the hierarchical to the nonhierarchical concept of CSCs towards the recent appreciation of GBM plasticity is provided. Cellular states interact dynamically with each other and with the surrounding brain to shape a flexible tumor ecosystem, which enables swift adaptation to external pressure including treatment. We present the key components regulating intra-tumoral phenotypic heterogeneity and the equilibrium of phenotypic states, including genetic, epigenetic, and microenvironmental factors. We further discuss plasticity in the context of intrinsic tumor resistance, where a variable balance between preexisting resistant cells and adaptive persisters leads to reversible adaptation upon treatment. Innovative efforts targeting regulators of plasticity and mechanisms of state transitions towards treatment-resistant states are needed to restrict the adaptive capacities of GBM.

Is the Fixed Periodic Treatment Effective for the Tumor System without Complete Information?

Objective

The treatment plans designed with the guidance of the mathematical model and adaptive strategy can trap tumor subpopulations in a periodic and controllable loop. But this process requires detailed information about the tumor system, which is difficult to obtain. Therefore, we wondered whether the fixed periodic treatment plans designed with the typical values of population parameters could be applied to a similar tumor system without complete information.

Methods

A binary tumor system constructed by an EGFR-mutant and a KRAS-mutant cell line was used to explore the applicability of the fixed periodic treatment plans. The dynamics of this system were described by combining the Lotka-Volterra model with the framework of the nonlinear mixed-effects model. The typical values of population parameters were used to design the plans, and the robust plans were screened through parameter variation. These screened plans were examined their applicability in animal experiments and simulations.

Results

In animal experiments where system parameters vary from -30% to 30%, the "osimertinib administration, withdrawal, FK866 administration and withdrawal" plan can trap subpopulations of the system in periodic cycles. In simulation, when there was an unknown resistant subpopulation, the screened fixed periodic treatment plans can still delay the evolution of resistance. The median outcomes of screened plans were better than conventional sequential treatment in most cases. There was no significant difference between the outcomes of the screened plan with median stability and the optimal therapy. The evolutionary trajectories of these two plans were similar.

Conclusion

According to the results, these fixed periodic plans should be tried in treatment even the information of the tumor system was incomplete.

Tumor Heterogeneity and Consequences for Bladder Cancer Treatment

Simple Summary

Bladder cancer is a heterogeneous disease that is composed of epithelia with varying transcriptional, mutational and lineage signatures. The epithelia of bladder tumors can also undergo pronounced changes in transcriptional and phenotypical qualities in response to progression, treatment related stresses and cues from the tumor microenvironment (TME). We hypothesize that changes in epithelial tumor heterogeneity (EpTH) occur due to the evolving content of epithelial subpopulations through both Darwinian and Lamarckian-like natural selection processes. We further conjecture that lineage-defined subpopulations can change through nongenomic and genomic cellular mechanisms that include cellular plasticity and acquired driver mutations, respectively. We propose that such processes are dynamic and contribute towards clinical treatment challenges including progression to drug resistance. In this article, we assess mechanisms that may support dynamic tumor heterogeneity with the overall goal of emphasizing the application of these concepts to the clinical setting.

Abstract

Acquired therapeutic resistance remains a major challenge in cancer management and associates with poor oncological outcomes in most solid tumor types. A major contributor is tumor heterogeneity (TH) which can be influenced by the stromal; immune and epithelial tumor compartments. We hypothesize that heterogeneity in tumor epithelial subpopulations—whether de novo or newly acquired—closely regulate the clinical course of bladder cancer. Changes in these subpopulations impact the tumor microenvironment including the extent of immune cell infiltration and response to immunotherapeutics. Mechanisms driving epithelial tumor heterogeneity (EpTH) can be broadly categorized as mutational and non-mutational. Mechanisms regulating lineage plasticity; acquired cellular mutations and changes in lineage-defined subpopulations regulate stress responses to clinical therapies. If tumor heterogeneity is a dynamic process; an increased understanding of how EpTH is regulated is critical in order for clinical therapies to be more sustained and durable. In this review and analysis, we assess the importance and regulatory mechanisms governing EpTH in bladder cancer and the impact on treatment response.

Optimizing Adaptive Therapy Based on the Reachability to Tumor Resistant Subpopulation

Simple Summary

The intra-competition among tumor subpopulations is a promising target to modify and control the outgrowth of the resistant subpopulation. Adaptive therapy lives up to this principle well, but the gain of tumors with an aggressive resistant subpopulation is not superior to maximum tolerated dose therapy (MTD). How to integrate these two therapies to maximize the outcome? According to the model and system reachability, the ‘restore index’ is proposed to evaluate the timing of the transition from the treatment cycle of adaptive therapy to high-frequency administration, and to juggle the benefits of intra-competition and killing of the sensitive subpopulation. Based on the simulation and animal experiment, the effectiveness of this method in treating tumors with an aggressive resistant subpopulation has been confirmed.

Abstract

Adaptive therapy exploits the self-organization of tumor cells to delay the outgrowth of resistant subpopulations successfully. When the tumor has aggressive resistant subpopulations, the outcome of adaptive therapy was not superior to maximum tolerated dose therapy (MTD). To explore methods to improve the adaptive therapy’s performance of this case, the tumor system was constructed by osimertinib-sensitive and resistant cell lines and illustrated by the Lotka-Volterra model in this study. Restore index proposed to assess the system reachability can predict the duration of each treatment cycle. Then the threshold of the restore index was estimated to evaluate the timing of interrupting the treatment cycle and switching to high-frequency administration. The introduced reachability-based adaptive therapy and classic adaptive therapy were compared through simulation and animal experiments. The results suggested that reachability-based adaptive therapy showed advantages when the tumor has an aggressive resistant subpopulation. This study provides a feasible method for evaluating whether to continue the adaptive therapy treatment cycle or switch to high-frequency administration. This method improves the gain of adaptive therapy by taking into account the benefits of tumor intra-competition and the tumor control of killing sensitive subpopulation.

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

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

A narrative review of tumor heterogeneity and challenges to tumor drug therapy

Objective

To accurately evaluate tumor heterogeneity, make multidimensional diagnosis according to the causes and phenotypes of tumor heterogeneity, and assist in the individualized treatment of tumors.

Background

Tumor heterogeneity is one of the most essential characteristics of malignant tumors. In tumor recurrence, development, and evolution, tumor heterogeneity can lead to the formation of different cell groups with other molecular characteristics. Tumor heterogeneity can be characterized by the uneven distribution of tumor cell subsets of other genes between and within the disease site (spatial heterogeneity) or the time change of cancer cell molecular composition (temporal heterogeneity). The discovery of tumor targeting drugs has dramatically promoted tumor therapy. However, the existence of heterogeneity seriously affects the effect of tumor treatment and the prognosis of patients.

Methods

The literature discussing tumor heterogeneity and its resistance to tumor therapy was broadly searched to analyze tumor heterogeneity as well as the challenges and solutions for gene detection and tumor drug therapy.

Conclusions

Tumor heterogeneity is affected by many factors consist of internal cell factors and cell microenvironment. Tumor heterogeneity greatly hinders effective and individualized tumor treatment. Understanding the fickle of tumors in multiple dimensions and flexibly using a variety of detection methods to capture the changes of tumors can help to improve the design of diagnosis and treatment plans for cancer and benefit millions of patients.

Clonal Evolution of Multiple Myeloma-Clinical and Diagnostic Implications

Plasma cell dyscrasias are a heterogeneous group of diseases characterized by the expansion of bone marrow plasma cells. Malignant transformation of plasma cells depends on the continuity of events resulting in a sequence of well-defined disease stages, from monoclonal gammopathy of undetermined significance (MGUS) through smoldering myeloma (SMM) to symptomatic multiple myeloma (MM). Evolution of a pre-malignant cell into a malignant cell, as well as further tumor progression, dissemination, and relapse, require development of multiple driver lesions conferring selective advantage of the dominant clone and allowing subsequent evolution under selective pressure of microenvironment and treatment. This process of natural selection facilitates tumor plasticity leading to the formation of genetically complex and heterogenous tumors that are notoriously difficult to treat. Better understanding of the mechanisms underlying tumor evolution in MM and identification of lesions driving the evolution from the premalignant clone is therefore a key to development of effective treatment and long-term disease control. Here, we review recent advances in clonal evolution patterns and genomic landscape dynamics of MM, focusing on their clinical implications.

The somatic molecular evolution of cancer: Mutation, selection, and epistasis

Cancer progression has been attributed to somatic changes in single-nucleotide variants, copy-number aberrations, loss of heterozygosity, chromosomal instability, epistatic interactions, and the tumor microenvironment. It is not entirely clear which of these changes are essential and which are ancillary to cancer. The dynamic nature of cancer evolution in a patient can be illuminated using several concepts and tools from classical evolutionary biology. Neutral mutation rates in cancer cells are calculable from genomic data such as synonymous mutations, and selective pressures are calculable from rates of fixation occurring beyond the expectation by neutral mutation and drift. However, these cancer effect sizes of mutations are complicated by epistatic interactions that can determine the likely sequence of gene mutations. In turn, longitudinal phylogenetic analyses of somatic cancer progression offer an opportunity to identify key moments in cancer evolution, relating the timing of driver mutations to corresponding landmarks in the clinical timeline. These analyses reveal temporal aspects of genetic and phenotypic change during tumorigenesis and across clinical timescales. Using a related framework, clonal deconvolution, physical locations of clones, and their phylogenetic relations can be used to infer tumor migration histories. Additionally, genetic interactions with the tumor microenvironment can be analyzed with longstanding approaches applied to organismal genotype-by-environment interactions. Fitness landscapes for cancer evolution relating to genotype, phenotype, and environment could enable more accurate, personalized therapeutic strategies. An understanding of the trajectories underlying the evolution of neoplasms, primary, and metastatic tumors promises fundamental advances toward accurate and personalized predictions of therapeutic response.

The role of memory in non-genetic inheritance and its impact on cancer treatment resistance

Intra-tumour heterogeneity is a leading cause of treatment failure and disease progression in cancer. While genetic mutations have long been accepted as a primary mechanism of generating this heterogeneity, the role of phenotypic plasticity is becoming increasingly apparent as a driver of intra-tumour heterogeneity. Consequently, understanding the role of this plasticity in treatment resistance and failure is a key component of improving cancer therapy. We develop a mathematical model of stochastic phenotype switching that tracks the evolution of drug-sensitive and drug-tolerant subpopulations to clarify the role of phenotype switching on population growth rates and tumour persistence. By including cytotoxic therapy in the model, we show that, depending on the strategy of the drug-tolerant subpopulation, stochastic phenotype switching can lead to either transient or permanent drug resistance. We study the role of phenotypic heterogeneity in a drug-resistant, genetically homogeneous population of non-small cell lung cancer cells to derive a rational treatment schedule that drives population extinction and avoids competitive release of the drug-tolerant sub-population. This model-informed therapeutic schedule results in increased treatment efficacy when compared against periodic therapy, and, most importantly, sustained tumour decay without the development of resistance.

Do mechanisms matter? Comparing cancer treatment strategies across mathematical models and outcome objectives

When eradication is impossible, cancer treatment aims to delay the emergence of resistance while minimizing cancer burden and treatment. Adaptive therapies may achieve these aims, with success based on three assumptions: resistance is costly, sensitive cells compete with resistant cells, and therapy reduces the population of sensitive cells. We use a range of mathematical models and treatment strategies to investigate the tradeoff between controlling cell populations and delaying the emergence of resistance. These models extend game theoretic and competition models with four additional components: 1) an Allee effect where cell populations grow more slowly at low population sizes, 2) healthy cells that compete with cancer cells, 3) immune cells that suppress cancer cells, and 4) resource competition for a growth factor like androgen. In comparing maximum tolerable dose, intermittent treatment, and adaptive therapy strategies, no therapeutic choice robustly breaks the three-way tradeoff among the three therapeutic aims. Almost all models show a tight tradeoff between time to emergence of resistant cells and cancer cell burden, with intermittent and adaptive therapies following identical curves. For most models, some adaptive therapies delay overall tumor growth more than intermittent therapies, but at the cost of higher cell populations. The Allee effect breaks these relationships, with some adaptive therapies performing poorly due to their failure to treat sufficiently to drive populations below the threshold. When eradication is impossible, no treatment can simultaneously delay emergence of resistance, limit total cancer cell numbers, and minimize treatment. Simple mathematical models can play a role in designing the next generation of therapies that balance these competing objectives.

Tepoxalin increases chemotherapy efficacy in drug-resistant breast cancer cells overexpressing the multidrug transporter gene ABCB1

•

The COX-2 encoding gene PTGS2 is up-regulated upon ABCB1 overexpression in mammary epithelial cells.

•

The 5-LOX, COX-1/2 inhibitor tepoxalin plus chemotherapy improves treatment efficacy in ABCB1-expressing cells.

•

Tepoxalin reduces chemotherapy-induced selection for drug-resistant ABCB1-expressing cells.

Effective cancer chemotherapy treatment requires both therapy delivery and retention by malignant cells. Cancer cell overexpression of the multidrug transmembrane transporter gene ABCB1 (MDR1, multi-drug resistance protein 1) thwarts therapy retention, leading to a drug-resistant phenotype. We explored the phenotypic impact of ABCB1 overexpression in normal human mammary epithelial cells (HMECs) via acute adenoviral delivery and in breast cancer cell lines with stable integration of inducible ABCB1 expression. One hundred sixty-two genes were differentially expressed between ABCB1-expressing and GFP-expressing HMECs, including the gene encoding the cyclooxygenase-2 protein, PTGS2. Several breast cancer cell lines with inducible ABCB1 expression demonstrated sensitivity to the 5-lipoxygenase, cyclooxygenase-1/2 inhibitor tepoxalin in two-dimensional drug response assays, and combination treatment of tepoxalin either with chemotherapies or with histone deacetylase (HDAC) inhibitors improved therapeutic efficacy in these lines. Moreover, selection for the ABCB1-expressing cell population was reduced in three-dimensional co-cultures of ABCB1-expressing and GFP-expressing cells when chemotherapy was given in combination with tepoxalin. Further study is warranted to ascertain the clinical potential of tepoxalin, an FDA-approved therapeutic for use in domesticated mammals, to restore chemosensitivity and improve drug response in patients with ABCB1-overexpressing drug-resistant breast cancers.

Interdisciplinary research: shaping the healthcare of the future

The hospitals of the future will be shaped by scientific and technical advances made across a wide range of disciplines because complex problems in healthcare cannot be addressed successfully by a single discipline. This paper considers how interdisciplinary research is being promoted and the prospects for developing stronger and deeper collaborations between medicine, health and other disciplines, drawing on case studies from mathematics, physics and engineering. The anticipated impact of greater interdisciplinarity on clinical training and the provision of care is also reviewed. While the role and training of clinicians in the provision of care will continue to evolve, they will remain leading members of a much broader and more diverse interdisciplinary team, alert to the value of deep and sustained interdisciplinary research.

Are Adaptive Chemotherapy Schedules Robust? A Three-Strategy Stochastic Evolutionary Game Theory Model

We investigate the robustness of adaptive chemotherapy schedules over repeated cycles and a wide range of tumor sizes. Using a non-stationary stochastic three-component fitness-dependent Moran process model (to track frequencies), we quantify the variance of the response to treatment associated with multidrug adaptive schedules that are designed to mitigate chemotherapeutic resistance in an idealized (well-mixed) setting. The finite cell (N tumor cells) stochastic process consists of populations of chemosensitive cells, chemoresistant cells to drug 1, and chemoresistant cells to drug 2, and the drug interactions can be synergistic, additive, or antagonistic. Tumor growth rates in this model are proportional to the average fitness of the tumor as measured by the three populations of cancer cells compared to a background microenvironment average value. An adaptive chemoschedule is determined by using the N→∞ limit of the finite-cell process (i.e., the adjusted replicator equations) which is constructed by finding closed treatment response loops (which we call evolutionary cycles) in the three component phase-space. The schedules that give rise to these cycles are designed to manage chemoresistance by avoiding competitive release of the resistant cell populations. To address the question of how these cycles perform in practice over large patient populations with tumors across a range of sizes, we consider the variances associated with the approximate stochastic cycles for finite N, repeating the idealized adaptive schedule over multiple periods. For finite cell populations, the distributions remain approximately multi-Gaussian in the principal component coordinates through the first three cycles, with variances increasing exponentially with each cycle. As the number of cycles increases, the multi-Gaussian nature of the distribution breaks down due to the fact that one of the three sub-populations typically saturates the tumor (competitive release) resulting in treatment failure. This suggests that to design an effective and repeatable adaptive chemoschedule in practice will require a highly accurate tumor model and accurate measurements of the sub-population frequencies or the errors will quickly (exponentially) degrade its effectiveness, particularly when the drug interactions are synergistic. Possible ways to extend the efficacy of the stochastic cycles in light of the computational simulations are discussed.

Cancer as a form of life: Musings of the cancer and evolution symposium

Advanced cancer is one of the major problems in oncology as currently, despite the recent technological and scientific advancements, the mortality of metastatic disease remains very high at 70-90%. The field of oncology is in urgent need of novel ideas in order to improve quality of life and prognostic of cancer patients. The Cancer and Evolution Symposium organized online October 14-16, 2020 brought together a group of specialists from different fields that presented innovative strategies for better understanding, preventing, diagnosing, and treating cancer. Today still, the main reasons behind the high incidence and mortality of advanced cancer are, on one hand, the paucity of funding and effort directed to cancer prevention and early detection, and, on the other hand, the lack of understanding of the cancer process itself. I argue that besides being a disease, cancer is also a form of life, and, this frame of reference may provide a fresh look on this complex process. Here, I provide a different angle to several contemporary cancer theories discussing them from the perspective of "cancer-forms of life" (i.e. bionts) point of view. The perspectives and the several "bionts" introduced here, by no means exclusive or comprehensive, are just a shorthand that will hopefully encourage the readers, to further explore the contemporary oncology theoretical landscape.

Resistance to second-generation androgen receptor antagonists in prostate cancer

The introduction of second-generation androgen receptor antagonists (SG-ARAs) has greatly impacted the treatment of metastatic prostate cancer, providing tolerable and efficacious alternatives to chemotherapy. SG-ARAs provide similar therapeutic benefit to abiraterone, a potent CYP17 inhibitor, and do not require the co-administration of prednisone. Despite considerable improvements in clinical outcomes in the settings of both castration sensitivity and castration resistance, the durability of clinical response to the SG-ARAs enzalutamide, apalutamide and darolutamide, similar to abiraterone, is limited by inevitable acquired resistance. Genomic aberrations that confer resistance to SG-ARAs or provide potential alternative treatment modalities have been identified in numerous studies, including alterations of the androgen receptor, DNA repair, cell cycle, PI3K-AKT-mTOR and Wnt-β-catenin pathways. To combat resistance, researchers have explored approaches to optimizing the utility of available treatments, as well as the use of alternative agents with a variety of targets, including AR-V7, AKT, EZH2 and HIF1α. Ongoing research to establish predictive biomarkers for the treatment of tumours with resistance to SG-ARAs led to the approval of the PARP inhibitors olaparib and rucaparib in pre-treated metastatic castration-resistant prostate cancer. The results of ongoing studies will help to shape precision medicine in prostate cancer and further optimize treatment paradigms to maximize clinical outcomes.

Dosage strategies for delaying resistance emergence in heterogeneous tumors

Drug resistance in cancer treatments is a frequent problem that, when it arises, leads to failure in therapeutic efforts. Tumor heterogeneity is the primary reason for resistance emergence and a precise treatment design that takes heterogeneity into account is required to postpone the rise of resistant subpopulations in the tumor environment. In this paper, we present a mathematical framework involving clonal evolution modeling of drug-sensitive and drug-resistant clones. Using our framework, we examine delaying the rise of resistance in heterogeneous tumors during control phase of therapy in a containment treatment approach. We apply pharmacokinetic/pharmacodynamic (PKPD) modeling and show that dosage strategies can be designed to control the resistant subpopulation. Our results show that the drug dosage and schedule determine the relative dynamics of sensitive and resistant clones. We present an optimal control problem that finds the dosing strategy that maximizes the delay in resistance emergence for a given period of containment treatment.

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.

Adaptive Therapy for Metastatic Melanoma: Predictions from Patient Calibrated Mathematical Models

Adaptive therapy is an evolution-based treatment approach that aims to maintain tumor volume by employing minimum effective drug doses or timed drug holidays. For successful adaptive therapy outcomes, it is critical to find the optimal timing of treatment switch points in a patient-specific manner. Here we develop a combination of mathematical models that examine interactions between drug-sensitive and resistant cells to facilitate melanoma adaptive therapy dosing and switch time points. The first model assumes genetically fixed drug-sensitive and -resistant popul tions that compete for limited resources. The second model considers phenotypic switching between drug-sensitive and -resistant cells. We calibrated each model to fit melanoma patient biomarker changes over time and predicted patient-specific adaptive therapy schedules. Overall, the models predict that adaptive therapy would have delayed time to progression by 6-25 months compared to continuous therapy with dose rates of 6-74% relative to continuous therapy. We identified predictive factors driving the clinical time gained by adaptive therapy, such as the number of initial sensitive cells, competitive effect, switching rate from resistant to sensitive cells, and sensitive cell growth rate. This study highlights that there is a range of potential patient-specific benefits of adaptive therapy and identifies parameters that modulate this benefit.

Turnover Modulates the Need for a Cost of Resistance in Adaptive Therapy

Adaptive therapy seeks to exploit intratumoral competition to avoid, or at least delay, the emergence of therapy resistance in cancer. Motivated by promising results in prostate cancer, there is growing interest in extending this approach to other neoplasms. As such, it is urgent to understand the characteristics of a cancer that determine whether or not it will respond well to adaptive therapy. A plausible candidate for such a selection criterion is the fitness cost of resistance. In this article, we study a general, but simple, mathematical model to investigate whether the presence of a cost is necessary for adaptive therapy to extend the time to progression beyond that of a standard-of-care continuous therapy. Tumor cells were divided into sensitive and resistant populations and we model their competition using a system of two ordinary differential equations based on the Lotka-Volterra model. For tumors close to their environmental carrying capacity, a cost was not required. However, for tumors growing far from carrying capacity, a cost may be required to see meaningful gains. Notably, it is important to consider cell turnover in the tumor, and we discuss its role in modulating the impact of a resistance cost. To conclude, we present evidence for the predicted cost-turnover interplay in data from 67 patients with prostate cancer undergoing intermittent androgen deprivation therapy. Our work helps to clarify under which circumstances adaptive therapy may be beneficial and suggests that turnover may play an unexpectedly important role in the decision-making process. SIGNIFICANCE: Tumor cell turnover modulates the speed of selection against drug resistance by amplifying the effects of competition and resistance costs; as such, turnover is an important factor in resistance management via adaptive therapy.See related commentary by Strobl et al., p. 811.

Reconciling Non-Genetic Plasticity with Somatic Evolution in Cancer

Post-treatment progression of tumors is commonly explained by somatic Darwinian evolution (i.e., selection of cells carrying genetic mutations that create more aggressive cell traits). But cancer genome and transcriptome analyses now paint a picture far more complex, prompting us to see beyond the Darwinian scheme: non-genetic cell phenotype plasticity explained by alternative stable gene expression states ('attractors'), may also produce aggressive phenotypes that can be selected for, without mutations. Worse, treatment may even induce cell state transitions into more malignant attractors. We review recent evidence for non-genetic mechanisms of progression, explain the theoretical foundation of attractor transitions behind treatment-induced increase of aggressiveness, and provide a framework for unifying genetic and non-genetic dynamics in tumor progression.

Adriamycin-resistant cells are significantly less fit than adriamycin-sensitive cells in cervical cancer

Adriamycin (ADR) is an important chemotherapy agent in many advanced cancers, but the emergence of drug resistance during treatment is a major limitation to its successful use. Recent studies have suggested that drug-resistant cells become less fit and their growth could be inhibited by parental cells without cytotoxic treatment. In this study, we examined the fitness differences between HeLa and HeLa/ADR cells. Compared with the parental cell line, HeLa/ADR cells showed significantly lower growth rates, both in vitro and in vivo. There was no difference in the apoptosis rate between them, but G1 arrest and reduced DNA synthesis were found in HeLa/ADR cells. Further study indicated that HeLa/ADR cells failed to compete for space and nutrition against parental cells in vivo. Taken together, we demonstrate that HeLa/ADR cells are less fit and their growth can be inhibited by parental cells in the absence of ADR; therefore, the maintenance of a certain amount of ADR-sensitive cells during treatment may facilitate the control of the development of ADR resistance.

Targeting of Evolutionarily Acquired Cancer Cell Phenotype by Exploiting pHi-Metabolic Vulnerabilities

Evolutionary dynamics can be used to control cancers when a cure is not clinically considered to be achievable. Understanding Darwinian intratumoral interactions of microenvironmental selection forces can be used to steer tumor progression towards a less invasive trajectory. Here, we approach intratumoral heterogeneity and evolution as a dynamic interaction among subpopulations through the application of small, but selective biological forces such as intracellular pH (pHi) and/or extracellular pH (pHe) vulnerabilities. Increased glycolysis is a prominent phenotype of cancer cells under hypoxia or normoxia (Warburg effect). Glycolysis leads to an important aspect of cancer metabolism: reduced pHe and higher pHi. We recently showed that decreasing pHi and targeting pHi sensitive enzymes can reverse the Warburg effect (WE) phenotype and inhibit tumor progression. Herein, we used diclofenac (DIC) repurposed to control MCT activity, and Koningic acid (KA) that is a GAPDH partial inhibitor, and observed that we can control the subpopulation of cancer cells with WE phenotype within a tumor in favor of a less aggressive phenotype without a WE to control progression and metastasis. In a 3D spheroid co-cultures, we showed that our strategy can control the growth of more aggressive MDA-MB-231 cells, while sparing the less aggressive MCF7 cells. In an animal model, we show that our approach can reduce tumor growth and metastasis. We thus propose that evolutionary dynamics can be used to control tumor cells' clonal or sub-clonal populations in favor of slower growth and less damage to patients. We propose that this can result in cancer control for tumors where cure is not an option.

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

 

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

AVAILABILITY

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

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Searching for Goldilocks: How Evolution and Ecology Can Help Uncover More Effective Patient-Specific Chemotherapies

Deaths from cancer are mostly due to metastatic disease that becomes resistant to therapy. A mainstay treatment for many cancers is chemotherapy, for which the dosing strategy is primarily limited by patient toxicity. While this MTD approach builds upon the intuitively appealing principle that maximum therapeutic benefit is achieved by killing the largest possible number of cancer cells, there is increasing evidence that moderation might allow host-specific features to contribute to success. We believe that a "Goldilocks Window" of submaximal chemotherapy will yield improved overall outcomes. This window combines the complex interplay of cancer cell death, immune activity, emergence of chemoresistance, and metastatic dissemination. These multiple activities driven by chemotherapy have tradeoffs that depend on the specific agents used as well as their dosing levels and schedule. Here we present evidence supporting the idea that MTD may not always be the best approach and offer suggestions toward a more personalized treatment regime that integrates insights into patient-specific eco-evolutionary dynamics.

Modifying Adaptive Therapy to Enhance Competitive Suppression

Adaptive therapy is a promising new approach to cancer treatment. It is designed to leverage competition between drug-sensitive and drug-resistant cells in order to suppress resistance and maintain tumor control for longer. Prompted by encouraging results from a recent pilot clinical trial, we evaluate the design of this initial test of adaptive therapy and identify three simple modifications that should improve performance. These modifications are designed to increase competition and are easy to implement. Using the mathematical model that supported the recent adaptive therapy trial, we show that the suggested modifications further delay time to tumor progression and also increase the range of patients who can benefit from adaptive therapy.

Cancer evolution: A means by which tumors evade treatment

Although various methods have been tried to study and treat cancer, the cancer remains a major challenge for human medicine today. One important reason for this is the presence of cancer evolution. Cancer evolution is a process in which tumor cells adapt to the external environment, which can suppress the human immune system's ability to recognize and attack tumors, and also reduce the reproducibility of cancer research. Among them, heterogeneity of the tumor provides intrinsic motivation for this process. Recently, with the development of related technologies such as liquid biopsy, more and more knowledge about cancer evolution has been gained and interest in this topic has also increased. Therefore, starting from the causes of tumorigenesis, this paper introduces several tumorigenesis processes and pathways, as well as treatment options for different targets.

Targeting the Deterministic Evolutionary Trajectories of Clear Cell Renal Cell Carcinoma

The emergence of clinical resistance to currently available systemic therapies forces us to rethink our approach to clear cell renal cell carcinoma (ccRCC). The ability to influence ccRCC evolution by inhibiting processes that propel it or manipulating its course may be an adequate strategy. There are seven deterministic evolutionary trajectories of ccRCC, which correlate with clinical phenotypes. We suspect that each trajectory has its own unique weaknesses that could be exploited. In this review, we have summarized recent advances in the treatment of ccRCC and demonstrated how to improve systemic therapies from the evolutionary perspective. Since there are only a few evolutionary trajectories in ccRCC, it appears feasible to use them as potential biomarkers for guiding intervention and surveillance. We believe that the presented patient stratification could help predict future steps of malignant progression, thereby informing optimal and personalized clinical decisions.

Engineering in Medicine To Address the Challenge of Cancer Drug Resistance: From Micro- and Nanotechnologies to Computational and Mathematical Modeling

Drug resistance has profoundly limited the success of cancer treatment, driving relapse, metastasis, and mortality. Nearly all anticancer drugs and even novel immunotherapies, which recalibrate the immune system for tumor recognition and destruction, have succumbed to resistance development. Engineers have emerged across mechanical, physical, chemical, mathematical, and biological disciplines to address the challenge of drug resistance using a combination of interdisciplinary tools and skill sets. This review explores the developing, complex, and under-recognized role of engineering in medicine to address the multitude of challenges in cancer drug resistance. Looking through the "lens" of intrinsic, extrinsic, and drug-induced resistance (also referred to as "tolerance"), we will discuss three specific areas where active innovation is driving novel treatment paradigms: (1) nanotechnology, which has revolutionized drug delivery in desmoplastic tissues, harnessing physiochemical characteristics to destroy tumors through photothermal therapy and rationally designed nanostructures to circumvent cancer immunotherapy failures, (2) bioengineered tumor models, which have benefitted from microfluidics and mechanical engineering, creating a paradigm shift in physiologically relevant environments to predict clinical refractoriness and enabling platforms for screening drug combinations to thwart resistance at the individual patient level, and (3) computational and mathematical modeling, which blends in silico simulations with molecular and evolutionary principles to map mutational patterns and model interactions between cells that promote resistance. On the basis that engineering in medicine has resulted in discoveries in resistance biology and successfully translated to clinical strategies that improve outcomes, we suggest the proliferation of multidisciplinary science that embraces engineering.

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.

The special issue on cancer and evolution: Lessons learned

This special issue of evolutionary applications focused on the evolution of cancer has provided a wealth of different viewpoints and results from leaders in the field. Together, these papers emphasize the importance of a broad perspective in order to understand why we and other animals get cancer, how it evolves within an individual, and what we can do about it. We can no longer take reductionist approaches that consider only the cancer cells and their genes. Instead, we need to understand how millions of years of evolution have guided strategies that shape cancer risk, why cancer risk varies across different animals, how cancer risk can vary in a population and be influenced by ecology (and influence this ecology), and of course how cancers evolve within us and the evolutionarily informed strategies to counter their impact. My goal here will be to "bring it all home," providing a refresher of lessons learned with added kibitzing.