Mathematical Approach to Differentiate Spontaneous and Induced Evolution to Drug Resistance During Cancer Treatment

A mathematical framework for comparison of intermittent versus continuous adaptive chemotherapy dosing in cancer

Chemotherapy resistance in cancer remains a barrier to curative therapy in advanced disease. Dosing of chemotherapy is often chosen based on the maximum tolerated dosing principle; drugs that are more toxic to normal tissue are typically given in on-off cycles, whereas those with little toxicity are dosed daily. When intratumoral cell-cell competition between sensitive and resistant cells drives chemotherapy resistance development, it has been proposed that adaptive chemotherapy dosing regimens, whereby a drug is given intermittently at a fixed-dose or continuously at a variable dose based on tumor size, may lengthen progression-free survival over traditional dosing. Indeed, in mathematical models using modified Lotka-Volterra systems to study dose timing, rapid competitive release of the resistant population and tumor outgrowth is apparent when cytotoxic chemotherapy is maximally dosed. This effect is ameliorated with continuous (dose modulation) or intermittent (dose skipping) adaptive therapy in mathematical models and experimentally, however, direct comparison between these two modalities has been limited. Here, we develop a mathematical framework to formally analyze intermittent adaptive therapy in the context of bang-bang control theory. We prove that continuous adaptive therapy is superior to intermittent adaptive therapy in its robustness to uncertainty in initial conditions, time to disease progression, and cumulative toxicity. We additionally show that under certain conditions, resistant population extinction is possible under adaptive therapy or fixed-dose continuous therapy. Here, continuous fixed-dose therapy is more robust to uncertainty in initial conditions than adaptive therapy, suggesting an advantage of traditional dosing paradigms.

Understanding tumour growth variability in breast cancer xenograft models identifies PARP inhibition resistance biomarkers

Understanding the mechanisms of resistance to PARP inhibitors (PARPi) is a clinical priority, especially in breast cancer. We developed a novel mathematical framework accounting for intrinsic resistance to olaparib, identified by fitting the model to tumour growth metrics from breast cancer patient-derived xenograft (PDX) data. Pre-treatment transcriptomic profiles were used with the calculated resistance to identify baseline biomarkers of resistance, including potential combination targets. The model provided both a classification of responses, as well as a continuous description of resistance, allowing for more robust biomarker associations and capturing the observed variability. Thirty-six resistance gene markers were identified, including multiple homologous recombination repair (HRR) pathway genes. High WEE1 expression was also linked to resistance, highlighting an opportunity for combining PARP and WEE1 inhibitors. This framework facilitates a fully automated way of capturing intrinsic resistance, and accounts for the pharmacological response variability captured within PDX studies and hence provides a precision medicine approach.

Modelling glioblastoma resistance to temozolomide. A mathematical model to simulate cellular adaptation in vitro

Drug resistance is one of the biggest challenges in the fight against cancer. In particular, in the case of glioblastoma, the most lethal brain tumour, resistance to temozolomide (the standard of care drug for chemotherapy in this tumour) is one of the main reasons behind treatment failure and hence responsible for the poor prognosis of patients diagnosed with this disease. In this work, we combine the power of three-dimensional in vitro experiments of treated glioblastoma spheroids with mathematical models of tumour evolution and adaptation. We use a novel approach based on internal variables for modelling the acquisition of resistance to temozolomide that was observed in experiments for a group of treated spheroids. These internal variables describe the cell's phenotypic state, which depends on the history of drug exposure and affects cell behaviour. We use model selection to determine the most parsimonious model and calibrate it to reproduce the experimental data, obtaining a high level of agreement between the in vitro and in silico outcomes. A sensitivity analysis is carried out to investigate the impact of each model parameter in the predictions. More importantly, we show how the model is useful for answering biological questions, such as what is the intrinsic adaptation mechanism, or for separating the sensitive and resistant populations. We conclude that the proposed in silico framework, in combination with experiments, can be useful to improve our understanding of the mechanisms behind drug resistance in glioblastoma and to eventually set some guidelines for the design of new treatment schemes.

Threshold-awareness in adaptive cancer therapy

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

On minimising tumoural growth under treatment resistance

Drug resistance is a major challenge for curative cancer treatment, representing the main reason of death in patients. Evolutionary biology suggests pauses between treatment rounds as a way to delay or even avoid resistance emergence. Indeed, this approach has already shown promising preclinical and early clinical results, and stimulated the development of mathematical models for finding optimal treatment protocols. Due to their complexity, however, these models do not lend themself to a rigorous mathematical analysis, hence so far clinical recommendations generally relied on numerical simulations and ad-hoc heuristics. Here, we derive two mathematical models describing tumour growth under genetic and epigenetic treatment resistance, respectively, which are simple enough for a complete analytical investigation. First, we find key differences in response to treatment protocols between the two modes of resistance. Second, we identify the optimal treatment protocol which leads to the largest possible tumour shrinkage rate. Third, we fit the "epigenetic model" to previously published xenograft experiment data, finding excellent agreement, underscoring the biological validity of our approach. Finally, we use the fitted model to calculate the optimal treatment protocol for this specific experiment, which we demonstrate to cause curative treatment, making it superior to previous approaches which generally aimed at stabilising tumour burden. Overall, our approach underscores the usefulness of simple mathematical models and their analytical examination, and we anticipate our findings to guide future preclinical and, ultimately, clinical research in optimising treatment regimes.

Modelling cell adaptation using internal variables: Accounting for cell plasticity in continuum mathematical biology

Cellular adaptation is the ability of cells to change in response to different stimuli and environmental conditions. It occurs via phenotypic plasticity, that is, changes in gene expression derived from changes in the physiological environment. This phenomenon is important in many biological processes, in particular in cancer evolution and its treatment. Therefore, it is crucial to understand the mechanisms behind it. Specifically, the emergence of the cancer stem cell phenotype, showing enhanced proliferation and invasion rates, is an essential process in tumour progression. We present a mathematical framework to simulate phenotypic heterogeneity in different cell populations as a result of their interaction with chemical species in their microenvironment, through a continuum model using the well-known concept of internal variables to model cell phenotype. The resulting model, derived from conservation laws, incorporates the relationship between the phenotype and the history of the stimuli to which cells have been subjected, together with the inheritance of that phenotype. To illustrate the model capabilities, it is particularised for glioblastoma adaptation to hypoxia. A parametric analysis is carried out to investigate the impact of each model parameter regulating cellular adaptation, showing that it permits reproducing different trends reported in the scientific literature. The framework can be easily adapted to any particular problem of cell plasticity, with the main limitation of having enough cells to allow working with continuum variables. With appropriate calibration and validation, it could be useful for exploring the underlying processes of cellular adaptation, as well as for proposing favourable/unfavourable conditions or treatments.

Modeling the effect of acquired resistance on cancer therapy outcomes

Adaptive therapy (AT) is an evolution-based treatment strategy that exploits cell-cell competition. Acquired resistance can change the competitive nature of cancer cells in a tumor, impacting AT outcomes. We aimed to determine if adaptive therapy can still be effective with cell's acquiring resistance. We developed an agent-based model for spatial tumor growth considering three different types of acquired resistance: random genetic mutations during cell division, drug-induced reversible (plastic) phenotypic changes, and drug-induced irreversible phenotypic changes. These three resistance mechanisms lead to different spatial distributions of resistant cells. To quantify the spatial distribution, we propose an extension of Ripley's K-function, Sampled Ripley's K-function (SRKF), which calculates the non-randomness of the resistance distribution over the tumor domain. Our model predicts that the emergent spatial distribution of resistance can determine the time to progression under both adaptive and continuous therapy (CT). Notably, a high rate of random genetic mutations leads to quicker progression under AT than CT due to the emergence of many small clumps of resistant cells. Drug-induced phenotypic changes accelerate tumor progression irrespective of the treatment strategy. Low-rate switching to a sensitive state reduces the benefits of AT compared to CT. Furthermore, we also demonstrated that drug-induced resistance necessitates aggressive treatment under CT, regardless of the presence of cancer-associated fibroblasts. However, there is an optimal dose that can most effectively delay tumor relapse under AT by suppressing resistance. In conclusion, this study demonstrates that diverse resistance mechanisms can shape the distribution of resistance and thus determine the efficacy of adaptive therapy.

Statistical inference of the rates of cell proliferation and phenotypic switching in cancer

Recent evidence suggests that nongenetic (epigenetic) mechanisms play an important role at all stages of cancer evolution. In many cancers, these mechanisms have been observed to induce dynamic switching between two or more cell states, which commonly show differential responses to drug treatments. To understand how these cancers evolve over time, and how they respond to treatment, we need to understand the state-dependent rates of cell proliferation and phenotypic switching. In this work, we propose a rigorous statistical framework for estimating these parameters, using data from commonly performed cell line experiments, where phenotypes are sorted and expanded in culture. The framework explicitly models the stochastic dynamics of cell division, cell death and phenotypic switching, and it provides likelihood-based confidence intervals for the model parameters. The input data can be either the fraction of cells or the number of cells in each state at one or more time points. Through a combination of theoretical analysis and numerical simulations, we show that when cell fraction data is used, the rates of switching may be the only parameters that can be estimated accurately. On the other hand, using cell number data enables accurate estimation of the net division rate for each phenotype, and it can even enable estimation of the state-dependent rates of cell division and cell death. We conclude by applying our framework to a publicly available dataset.

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.

Designing experimental conditions to use the Lotka-Volterra model to infer tumor cell line interaction types

The Lotka-Volterra model is widely used to model interactions between two species. Here, we generate synthetic data mimicking competitive, mutualistic and antagonistic interactions between two tumor cell lines, and then use the Lotka-Volterra model to infer the interaction type. Structural identifiability of the Lotka-Volterra model is confirmed, and practical identifiability is assessed for three experimental designs: (a) use of a single data set, with a mixture of both cell lines observed over time, (b) a sequential design where growth rates and carrying capacities are estimated using data from experiments in which each cell line is grown in isolation, and then interaction parameters are estimated from an experiment involving a mixture of both cell lines, and (c) a parallel experimental design where all model parameters are fitted to data from two mixtures (containing both cell lines but with different initial ratios) simultaneously. Each design is tested on data generated from the Lotka-Volterra model with noise added, to determine efficacy in an ideal sense. In addition to assessing each design for practical identifiability, we investigate how the predictive power of the model - i.e., its ability to fit data for initial ratios other than those to which it was calibrated - is affected by the choice of experimental design. The parallel calibration procedure is found to be optimal and is further tested on in silico data generated from a spatially-resolved cellular automaton model, which accounts for oxygen consumption and allows for variation in the intensity level of the interaction between the two cell lines. We use this study to highlight the care that must be taken when interpreting parameter estimates for the spatially-averaged Lotka-Volterra model when it is calibrated against data produced by the spatially-resolved cellular automaton model, since baseline competition for space and resources in the CA model may contribute to a discrepancy between the type of interaction used to generate the CA data and the type of interaction inferred by the LV model.

Mathematical characterization of population dynamics in breast cancer cells treated with doxorubicin

The development of chemoresistance remains a significant cause of treatment failure in breast cancer. We posit that a mathematical understanding of chemoresistance could assist in developing successful treatment strategies. Towards that end, we have developed a model that describes the cytotoxic effects of the standard chemotherapeutic drug doxorubicin on the MCF-7 breast cancer cell line. We assume that treatment with doxorubicin induces a compartmentalization of the breast cancer cell population into surviving cells, which continue proliferating after treatment, and irreversibly damaged cells, which gradually transition from proliferating to treatment-induced death. The model is fit to experimental data including variations in drug concentration, inter-treatment interval, and number of doses. Our model recapitulates tumor cell dynamics in all these scenarios (as quantified by the concordance correlation coefficient, CCC > 0.95). In particular, superior tumor control is observed with higher doxorubicin concentrations, shorter inter-treatment intervals, and a higher number of doses (p < 0.05). Longer inter-treatment intervals require adapting the model parameterization after each doxorubicin dose, suggesting the promotion of chemoresistance. Additionally, we propose promising empirical formulas to describe the variation of model parameters as functions of doxorubicin concentration (CCC > 0.78). Thus, we conclude that our mathematical model could deepen our understanding of the cytotoxic effects of doxorubicin and could be used to explore practical drug regimens achieving optimal tumor control.

NETISCE: a network-based tool for cell fate reprogramming

The search for effective therapeutic targets in fields like regenerative medicine and cancer research has generated interest in cell fate reprogramming. This cellular reprogramming paradigm can drive cells to a desired target state from any initial state. However, methods for identifying reprogramming targets remain limited for biological systems that lack large sets of experimental data or a dynamical characterization. We present NETISCE, a novel computational tool for identifying cell fate reprogramming targets in static networks. In combination with machine learning algorithms, NETISCE estimates the attractor landscape and predicts reprogramming targets using signal flow analysis and feedback vertex set control, respectively. Through validations in studies of cell fate reprogramming from developmental, stem cell, and cancer biology, we show that NETISCE can predict previously identified cell fate reprogramming targets and identify potentially novel combinations of targets. NETISCE extends cell fate reprogramming studies to larger-scale biological networks without the need for full model parameterization and can be implemented by experimental and computational biologists to identify parts of a biological system relevant to the desired reprogramming task.

Optimal Strategy and Benefit of Pulsed Therapy Depend On Tumor Heterogeneity and Aggressiveness at Time of Treatment Initiation

Therapeutic resistance is a fundamental obstacle in cancer treatment. Tumors that initially respond to treatment may have a preexisting resistant subclone or acquire resistance during treatment, making relapse theoretically inevitable. Here, we investigate treatment strategies that may delay relapse using mathematical modeling. We find that for a single-drug therapy, pulse treatment-short, elevated doses followed by a complete break from treatment-delays relapse compared with continuous treatment with the same total dose over a length of time. For tumors treated with more than one drug, continuous combination treatment is only sometimes better than sequential treatment, while pulsed combination treatment or simply alternating between the two therapies at defined intervals delays relapse the longest. These results are independent of the fitness cost or benefit of resistance, and are robust to noise. Machine-learning analysis of simulations shows that the initial tumor response and heterogeneity at the start of treatment suffice to determine the benefit of pulsed or alternating treatment strategies over continuous treatment. Analysis of eight tumor burden trajectories of breast cancer patients treated at Memorial Sloan Kettering Cancer Center shows the model can predict time to resistance using initial responses to treatment and estimated preexisting resistant populations. The model calculated that pulse treatment would delay relapse in all eight cases. Overall, our results support that pulsed treatments optimized by mathematical models could delay therapeutic resistance.

Roadmap on plasticity and epigenetics in cancer

The role of plasticity and epigenetics in shaping cancer evolution and response to therapy has taken center stage with recent technological advances including single cell sequencing. This roadmap article is focused on state-of-the-art mathematical and experimental approaches to interrogate plasticity in cancer, and addresses the following themes and questions: is there a formal overarching framework that encompasses both non-genetic plasticity and mutation-driven somatic evolution? How do we measure and model the role of the microenvironment in influencing/controlling non-genetic plasticity? How can we experimentally study non-genetic plasticity? Which mathematical techniques are required or best suited? What are the clinical and practical applications and implications of these concepts?

Drug-induced resistance evolution necessitates less aggressive treatment

Increasing body of experimental evidence suggests that anticancer and antimicrobial therapies may themselves promote the acquisition of drug resistance by increasing mutability. The successful control of evolving populations requires that such biological costs of control are identified, quantified and included to the evolutionarily informed treatment protocol. Here we identify, characterise and exploit a trade-off between decreasing the target population size and generating a surplus of treatment-induced rescue mutations. We show that the probability of cure is maximized at an intermediate dosage, below the drug concentration yielding maximal population decay, suggesting that treatment outcomes may in some cases be substantially improved by less aggressive treatment strategies. We also provide a general analytical relationship that implicitly links growth rate, pharmacodynamics and dose-dependent mutation rate to an optimal control law. Our results highlight the important, but often neglected, role of fundamental eco-evolutionary costs of control. These costs can often lead to situations, where decreasing the cumulative drug dosage may be preferable even when the objective of the treatment is elimination, and not containment. Taken together, our results thus add to the ongoing criticism of the standard practice of administering aggressive, high-dose therapies and motivate further experimental and clinical investigation of the mutagenicity and other hidden collateral costs of therapies.

Alternative strategies for optimizing treatment of chronic lymphocytic leukemia with complex clonal architecture

In silico simulation of pre-clinical and clinical data may accelerate pre-clinical and clinical trial advances, leading to benefits for therapeutic outcomes, toxicity and cost savings. Combining this with clonal architecture data may permit truly personalized therapy. Chronic lymphocytic leukemia (CLL) exhibits clonal diversity, evolution and selection, spontaneously and under treatment pressure. We apply a dynamic simulation model to published CLL clonal architecture data to explore alternative therapeutic strategies, focusing on BTK inhibition. By deriving parameters of clonal growth and death behavior we model continuous vs time-limited ibrutinib therapy, and find that, despite persistence of disease, time to clinical progression may not differ. This is a testable hypothesis. We model IgVH-mutated CLL vs unmutated CLL by varying proliferation and find, based on the limited available data about clonal dynamics after such therapy, that there are differences predicted in response to anti-CD20 efficacy. These models can suggest potential clinical trials, and also indicate what additional data are needed to improve predictions. Ongoing work will expand modeling to agents such as venetoclax and to T cell therapies.

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.

Integrating transcriptomics and bulk time course data into a mathematical framework to describe and predict therapeutic resistance in cancer

A significant challenge in the field of biomedicine is the development of methods to integrate the multitude of dispersed data sets into comprehensive frameworks to be used to generate optimal clinical decisions. Recent technological advances in single cell analysis allow for high-dimensional molecular characterization of cells and populations, but to date, few mathematical models have attempted to integrate measurements from the single cell scale with other types of longitudinal data. Here, we present a framework that actionizes static outputs from a machine learning model and leverages these as measurements of state variables in a dynamic model of treatment response. We apply this framework to breast cancer cells to integrate single cell transcriptomic data with longitudinal bulk cell population (bulk time course) data. We demonstrate that the explicit inclusion of the phenotypic composition estimate, derived from single cell RNA-sequencing data (scRNA-seq), improves accuracy in the prediction of new treatments with a concordance correlation coefficient (CCC) of 0.92 compared to a prediction accuracy of CCC = 0.64 when fitting on longitudinal bulk cell population data alone. To our knowledge, this is the first work that explicitly integrates single cell clonally-resolved transcriptome datasets with bulk time-course data to jointly calibrate a mathematical model of drug resistance dynamics. We anticipate this approach to be a first step that demonstrates the feasibility of incorporating multiple data types into mathematical models to develop optimized treatment regimens from data.

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.

Challenges and Opportunities in Cancer Drug Resistance

There has been huge progress in the discovery of targeted cancer therapies in recent years. However, even for the most successful and impactful cancer drugs which have been approved, both innate and acquired mechanisms of resistance are commonplace. These emerging mechanisms of resistance have been studied intensively, which has enabled drug discovery scientists to learn how it may be possible to overcome such resistance in subsequent generations of treatments. In some cases, novel drug candidates have been able to supersede previously approved agents; in other cases they have been used sequentially or in combinations with existing treatments. This review summarizes the current field in terms of the challenges and opportunities that cancer resistance presents to drug discovery scientists, with a focus on small molecule therapeutics. As part of this review, common themes and approaches have been identified which have been utilized to successfully target emerging mechanisms of resistance. This includes the increase in target potency and selectivity, alternative chemical scaffolds, change of mechanism of action (covalents, PROTACs), increases in blood-brain barrier permeability (BBBP), and the targeting of allosteric pockets. Finally, wider approaches are covered such as monoclonal antibodies (mAbs), bispecific antibodies, antibody drug conjugates (ADCs), and combination therapies.

Delicate Balances in Cancer Chemotherapy: Modeling Immune Recruitment and Emergence of Systemic Drug Resistance

Metronomic chemotherapy can drastically enhance immunogenic tumor cell death. However, the mechanisms responsible are still incompletely understood. Here, we develop a mathematical model to elucidate the underlying complex interactions between tumor growth, immune system activation, and therapy-mediated immunogenic cell death. Our model is conceptually simple, yet it provides a surprisingly excellent fit to empirical data obtained from a GL261 SCID mouse glioma model treated with cyclophosphamide on a metronomic schedule. The model includes terms representing immune recruitment as well as the emergence of drug resistance during prolonged metronomic treatments. Strikingly, a single fixed set of parameters, adjusted neither for individuals nor for drug schedule, recapitulates experimental data across various drug regimens remarkably well, including treatments administered at intervals ranging from 6 to 12 days. Additionally, the model predicts peak immune activation times, rediscovering experimental data that had not been used in parameter fitting or in model construction. Notably, the validated model suggests that immunostimulatory and immunosuppressive intermediates are responsible for the observed phenomena of resistance and immune cell recruitment, and thus for variation of responses with respect to different schedules of drug administration.

Mathematical Details on a Cancer Resistance Model

One of the most important factors limiting the success of chemotherapy in cancer treatment is the phenomenon of drug resistance. We have recently introduced a framework for quantifying the effects of induced and non-induced resistance to cancer chemotherapy (Greene et al., 2018a, 2019). In this work, we expound on the details relating to an optimal control problem outlined in Greene et al. (2018a). The control structure is precisely characterized as a concatenation of bang-bang and path-constrained arcs via the Pontryagin Maximum Principle and differential Lie algebraic techniques. A structural identifiability analysis is also presented, demonstrating that patient-specific parameters may be measured and thus utilized in the design of optimal therapies prior to the commencement of therapy. For completeness, a detailed analysis of existence results is also included.

Drug-Induced Resistance in Micrometastases: Analysis of Spatio-Temporal Cell Lineages

Resistance to anti-cancer drugs is a major cause of treatment failure. While several intracellular mechanisms of resistance have been postulated, the role of extrinsic factors in the development of resistance in individual tumor cells is still not fully understood. Here we used a hybrid agent-based model to investigate how sensitive tumor cells develop drug resistance in the heterogeneous tumor microenvironment. We characterized the spatio-temporal evolution of lineages of the resistant cells and examined how resistance at the single-cell level contributes to the overall tumor resistance. We also developed new methods to track tumor cell adaptation, to trace cell viability trajectories and to examine the three-dimensional spatio-temporal lineage trees. Our findings indicate that drug-induced resistance can result from cells adaptation to the changes in drug distribution. Two modes of cell adaptation were identified that coincide with microenvironmental niches—areas sheltered by cell micro-communities (protectorates) or regions with limited drug penetration (refuga or sanctuaries). We also recognized that certain cells gave rise to lineages of resistant cells (precursors of resistance) and pinpointed three temporal periods and spatial locations at which such cells emerged. This supports the hypothesis that tumor micrometastases do not need to harbor cell populations with pre-existing resistance, but that individual tumor cells can adapt and develop resistance induced by the drug during the treatment.

Molecular Mechanisms Underlying Autophagy-Mediated Treatment Resistance in Cancer

Despite advances in diagnostic tools and therapeutic options, treatment resistance remains a challenge for many cancer patients. Recent studies have found evidence that autophagy, a cellular pathway that delivers cytoplasmic components to lysosomes for degradation and recycling, contributes to treatment resistance in different cancer types. A role for autophagy in resistance to chemotherapies and targeted therapies has been described based largely on associations with various signaling pathways, including MAPK and PI3K/AKT signaling. However, our current understanding of the molecular mechanisms underlying the role of autophagy in facilitating treatment resistance remains limited. Here we provide a comprehensive summary of the evidence linking autophagy to major signaling pathways in the context of treatment resistance and tumor progression, and then highlight recently emerged molecular mechanisms underlying autophagy and the p62/KEAP1/NRF2 and FOXO3A/PUMA axes in chemoresistance.