Optimal Therapy Scheduling Based on a Pair of Collaterally Sensitive Drugs

Reinforcement learning informs optimal treatment strategies to limit antibiotic resistance

Antimicrobial resistance was estimated to be associated with 4.95 million deaths worldwide in 2019. It is possible to frame the antimicrobial resistance problem as a feedback-control problem. If we could optimize this feedback-control problem and translate our findings to the clinic, we could slow, prevent, or reverse the development of high-level drug resistance. Prior work on this topic has relied on systems where the exact dynamics and parameters were known a priori. In this study, we extend this work using a reinforcement learning (RL) approach capable of learning effective drug cycling policies in a system defined by empirically measured fitness landscapes. Crucially, we show that it is possible to learn effective drug cycling policies despite the problems of noisy, limited, or delayed measurement. Given access to a panel of 15 [Formula: see text]-lactam antibiotics with which to treat the simulated Escherichia coli population, we demonstrate that RL agents outperform two naive treatment paradigms at minimizing the population fitness over time. We also show that RL agents approach the performance of the optimal drug cycling policy. Even when stochastic noise is introduced to the measurements of population fitness, we show that RL agents are capable of maintaining evolving populations at lower growth rates compared to controls. We further tested our approach in arbitrary fitness landscapes of up to 1,024 genotypes. We show that minimization of population fitness using drug cycles is not limited by increasing genome size. Our work represents a proof-of-concept for using AI to control complex evolutionary processes.

Reinforcement Learning informs optimal treatment strategies to limit antibiotic resistance

Antimicrobial resistance was estimated to be associated with 4.95 million deaths worldwide in 2019. It is possible to frame the antimicrobial resistance problem as a feedback-control problem. If we could optimize this feedback-control problem and translate our findings to the clinic, we could slow, prevent or reverse the development of high-level drug resistance. Prior work on this topic has relied on systems where the exact dynamics and parameters were known a priori. In this study, we extend this work using a reinforcement learning (RL) approach capable of learning effective drug cycling policies in a system defined by empirically measured fitness landscapes. Crucially, we show that is possible to learn effective drug cycling policies despite the problems of noisy, limited, or delayed measurement. Given access to a panel of 15 β-lactam antibiotics with which to treat the simulated E. coli population, we demonstrate that RL agents outperform two naive treatment paradigms at minimizing the population fitness over time. We also show that RL agents approach the performance of the optimal drug cycling policy. Even when stochastic noise is introduced to the measurements of population fitness, we show that RL agents are capable of maintaining evolving populations at lower growth rates compared to controls. We further tested our approach in arbitrary fitness landscapes of up to 1024 genotypes. We show that minimization of population fitness using drug cycles is not limited by increasing genome size. Our work represents a proof-of-concept for using AI to control complex evolutionary processes.

Treatment of evolving cancers will require dynamic decision support

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

Evolution-Informed Strategies for Combating Drug Resistance in Cancer

The ever-changing nature of cancer poses the most difficult challenge oncologists face today. Cancer's remarkable adaptability has inspired many to work toward understanding the evolutionary dynamics that underlie this disease in hopes of learning new ways to fight it. Eco-evolutionary dynamics of a tumor are not accounted for in most standard treatment regimens, but exploiting them would help us combat treatment-resistant effectively. Here, we outline several notable efforts to exploit these dynamics and circumvent drug resistance in cancer.

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.

Inferring density-dependent population dynamics mechanisms through rate disambiguation for logistic birth-death processes

Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can manifest in birth processes, death processes, or both. Therefore, we utilize the mean and variance of cell number fluctuations to separately identify birth and death rates from time series that follow stochastic birth-death processes with logistic growth. Our nonparametric method provides a novel perspective on stochastic parameter identifiability, which we validate by analyzing the accuracy in terms of the discretization bin size. We apply our method to the scenario where a homogeneous cell population goes through three stages: (1) grows naturally to its carrying capacity, (2) is treated with a drug that reduces its carrying capacity, and (3) overcomes the drug effect to restore its original carrying capacity. In each stage, we disambiguate whether the dynamics occur through the birth process, death process, or some combination of the two, which contributes to understanding drug resistance mechanisms. In the case of limited sample sizes, we provide an alternative method based on maximum likelihood and solve a constrained nonlinear optimization problem to identify the most likely density dependence parameter for a given cell number time series. Our methods can be applied to other biological systems at different scales to disambiguate density-dependent mechanisms underlying the same net growth rate.

Optimal control design for drug delivery of immunotherapy in chemoimmunotherapy treatment

BACKGROUND AND OBJECTIVE

There are various approaches to control a mathematical dynamic of cancer, each of which is suitable for a special goal. Optimal control is considered as an applicable method to calculate the minimum necessary drug delivery in such systems.

METHODS

In this paper, a mathematical dynamic of cancer is proposed considering tumor cells, natural killer cells, CD8+T cells, circulating lymphocytes, IL-2 cytokine and Regulatory T cells as the system states, and chemotherapy, IL-2 and activated CD8+T cells injection rate as the control signals. After verifying the proposed mathematical model, the importance of the drug delivery timing and the effect of cancer cells initial condition are discussed. Afterwards, an optimal control is designed by defining a proper cost function with the goal of minimizing the number of tumor cells, and two immunotherapy drug amounts during treatment CONCLUSIONS: Results show that inappropriate injection of immunotherapy time schedule and the number of initial conditions of cancer cells might result in chemoimmunotherapy failure and auxiliary treatment must be prescribed to decrease tumor size before any treatment takes place. The obtained optimal control signals show that with lower amount of drug delivery and a suitable drug injection time schedule, tumor cells can be eliminated while a fixed immunotherapy time schedule protocol fails with larger amount of drug injection. This conclusion can be utilized with the aim of personalizing drug delivery and designing more accurate clinical trials based on the improved model simulations in order to save cost and time.

In Vitro/In Vivo Translation of Synergistic Combination of MDM2 and MEK Inhibitors in Melanoma Using PBPK/PD Modelling: Part III

The development of in vitro/in vivo translational methods and a clinical trial framework for synergistically acting drug combinations are needed to identify optimal therapeutic conditions with the most effective therapeutic strategies. We performed physiologically based pharmacokinetic-pharmacodynamic (PBPK/PD) modelling and virtual clinical trial simulations for siremadlin, trametinib, and their combination in a virtual representation of melanoma patients. In this study, we built PBPK/PD models based on data from in vitro absorption, distribution, metabolism, and excretion (ADME), and in vivo animals' pharmacokinetic-pharmacodynamic (PK/PD) and clinical data determined from the literature or estimated by the Simcyp simulator (version V21). The developed PBPK/PD models account for interactions between siremadlin and trametinib at the PK and PD levels. Interaction at the PK level was predicted at the absorption level based on findings from animal studies, whereas PD interaction was based on the in vitro cytotoxicity results. This approach, combined with virtual clinical trials, allowed for the estimation of PK/PD profiles, as well as melanoma patient characteristics in which this therapy may be noninferior to the dabrafenib and trametinib drug combination. PBPK/PD modelling, combined with virtual clinical trial simulation, can be a powerful tool that allows for proper estimation of the clinical effect of the above-mentioned anticancer drug combination based on the results of in vitro studies. This approach based on in vitro/in vivo extrapolation may help in the design of potential clinical trials using siremadlin and trametinib and provide a rationale for their use in patients with melanoma.

In Vitro/In Vivo Translation of Synergistic Combination of MDM2 and MEK Inhibitors in Melanoma Using PBPK/PD Modelling: Part I

Translation of the synergy between the Siremadlin (MDM2 inhibitor) and Trametinib (MEK inhibitor) combination observed in vitro into in vivo synergistic efficacy in melanoma requires estimation of the interaction between these molecules at the pharmacokinetic (PK) and pharmacodynamic (PD) levels. The cytotoxicity of the Siremadlin and Trametinib combination was evaluated in vitro in melanoma A375 cells with MTS and RealTime-Glo assays. Analysis of the drug combination matrix was performed using Synergy and Synergyfinder packages. Calculated drug interaction metrics showed high synergy between Siremadlin and Trametinib: 23.12%, or a 7.48% increase of combined drug efficacy (concentration-independent parameter β from Synergy package analysis and concentration-dependent δ parameter from Synergyfinder analysis, respectively). In order to select the optimal PD interaction parameter which may translate observed in vitro synergy metrics into the in vivo setting, further PK/PD studies on cancer xenograft animal models coupled with PBPK/PD modelling are needed.

In Vitro/In Vivo Translation of Synergistic Combination of MDM2 and MEK Inhibitors in Melanoma Using PBPK/PD Modelling: Part II

The development of in vitro/in vivo translational methods for synergistically acting drug combinations is needed to identify the most effective therapeutic strategies. We performed PBPK/PD modelling for siremadlin, trametinib, and their combination at various dose levels and dosing schedules in an A375 xenografted mouse model (melanoma cells). In this study, we built models based on in vitro ADME and in vivo PK/PD data determined from the literature or estimated by the Simcyp Animal simulator (V21). The developed PBPK/PD models allowed us to account for the interactions between siremadlin and trametinib at PK and PD levels. The interaction at the PK level was described by an interplay between absorption and tumour disposition levels, whereas the PD interaction was based on the in vitro results. This approach allowed us to reasonably estimate the most synergistic and efficacious dosing schedules and dose levels for combinations of siremadlin and trametinib in mice. PBPK/PD modelling is a powerful tool that allows researchers to properly estimate the in vivo efficacy of the anticancer drug combination based on the results of in vitro studies. Such an approach based on in vitro and in vivo extrapolation may help researchers determine the most efficacious dosing strategies and will allow for the extrapolation of animal PBPK/PD models into clinical settings.

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.

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.

Quantification of long-term doxorubicin response dynamics in breast cancer cell lines to direct treatment schedules

While acquired chemoresistance is recognized as a key challenge to treating many types of cancer, the dynamics with which drug sensitivity changes after exposure are poorly characterized. Most chemotherapeutic regimens call for repeated dosing at regular intervals, and if drug sensitivity changes on a similar time scale then the treatment interval could be optimized to improve treatment performance. Theoretical work suggests that such optimal schedules exist, but experimental confirmation has been obstructed by the difficulty of deconvolving the simultaneous processes of death, adaptation, and regrowth taking place in cancer cell populations. Here we present a method of optimizing drug schedules in vitro through iterative application of experimentally calibrated models, and demonstrate its ability to characterize dynamic changes in sensitivity to the chemotherapeutic doxorubicin in three breast cancer cell lines subjected to treatment schedules varying in concentration, interval between pulse treatments, and number of sequential pulse treatments. Cell populations are monitored longitudinally through automated imaging for 600–800 hours, and this data is used to calibrate a family of cancer growth models, each consisting of a system of ordinary differential equations, derived from the bi-exponential model which characterizes resistant and sensitive subpopulations. We identify a model incorporating both a period of growth arrest in surviving cells and a delay in the death of chemosensitive cells which outperforms the original bi-exponential growth model in Akaike Information Criterion based model selection, and use the calibrated model to quantify the performance of each drug schedule. We find that the inter-treatment interval is a key variable in determining the performance of sequential dosing schedules and identify an optimal retreatment time for each cell line which extends regrowth time by 40%-239%, demonstrating that the time scale of changes in chemosensitivity following doxorubicin exposure allows optimization of drug scheduling by varying this inter-treatment interval.

Acquired chemoresistance is a common cause of treatment failure in cancer. The scheduling of a multi-dose course of chemotherapeutic treatment may influence the dynamics of acquired chemoresistance, and drug schedule optimization may increase the duration of effectiveness of a particular chemotherapeutic agent for a particular patient. Here we present a method for experimentally optimizing an in vitro drug schedule through iterative rounds of experimentation and computational analysis, and demonstrate the method’s ability to improve the performance of doxorubicin treatment in three breast carcinoma cell lines. Specifically, we find that the interval between drug exposures can be optimized while holding drug concentration and number of treatments constant, suggesting that this may be a key variable to explore in future drug schedule optimization efforts. We further use this method’s model calibration and selection process to extract information about the underlying biology of the doxorubicin response, and find that the incorporation of delays on both cell death and regrowth are necessary for accurate parameterization of cell growth data.

The Individual Effects of Cyclin-Dependent Kinase Inhibitors on Head and Neck Cancer Cells-A Systematic Analysis

Cyclin-dependent kinase inhibitors (CDKi´s) display cytotoxic activity against different malignancies, including head and neck squamous cell carcinomas (HNSCC). By coordinating the DNA damage response, these substances may be combined with cytostatics to enhance cytotoxicity. Here, we investigated the influence of different CDKi´s (palbociclib, dinaciclib, THZ1) on two HNSCC cell lines in monotherapy and combination therapy with clinically-approved drugs (5-FU, Cisplatin, cetuximab). Apoptosis/necrosis, cell cycle, invasiveness, senescence, radiation-induced γ-H2AX DNA double-strand breaks, and effects on the actin filament were studied. Furthermore, the potential to increase tumor immunogenicity was assessed by analyzing Calreticulin translocation and immune relevant surface markers. Finally, an in vivo mouse model was used to analyze the effect of dinaciclib and Cisplatin combination therapy. Dinaciclib, palbociclib, and THZ1 displayed anti-neoplastic activity after low-dose treatment, while the two latter substances slightly enhanced radiosensitivity. Dinaciclib decelerated wound healing, decreased invasiveness, and induced MHC-I, accompanied by high amounts of surface-bound Calreticulin. Numbers of early and late apoptotic cells increased initially (24 h), while necrosis dominated afterward. Antitumoral effects of the selective CDKi palbociclib were weaker, but combinations with 5-FU potentiated effects of the monotherapy. Additionally, CDKi and CDKi/chemotherapy combinations induced MHC I, indicative of enhanced immunogenicity. The in vivo studies revealed a cell line-specific response with best tumor growth control in the combination approach. Global acting CDKi's should be further investigated as targeting agents for HNSCC, either individually or in combination with selected drugs. The ability of dinaciclib to increase the immunogenicity of tumor cells renders this substance a particularly interesting candidate for immune-based oncological treatment regimens.

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.

Optimal control to reach eco-evolutionary stability in metastatic castrate-resistant prostate cancer

In the absence of curative therapies, treatment of metastatic castrate-resistant prostate cancer (mCRPC) using currently available drugs can be improved by integrating evolutionary principles that govern proliferation of resistant subpopulations into current treatment protocols. Here we develop what is coined as an 'evolutionary stable therapy', within the context of the mathematical model that has been used to inform the first adaptive therapy clinical trial of mCRPC. The objective of this therapy is to maintain a stable polymorphic tumor heterogeneity of sensitive and resistant cells to therapy in order to prolong treatment efficacy and progression free survival. Optimal control analysis shows that an increasing dose titration protocol, a very common clinical dosing process, can achieve tumor stabilization for a wide range of potential initial tumor compositions and volumes. Furthermore, larger tumor volumes may counter intuitively be more likely to be stabilized if sensitive cells dominate the tumor composition at time of initial treatment, suggesting a delay of initial treatment could prove beneficial. While it remains uncertain if metastatic disease in humans has the properties that allow it to be truly stabilized, the benefits of a dose titration protocol warrant additional pre-clinical and clinical investigations.

Modeling Resistance and Recurrence Patterns of Combined Targeted-Chemoradiotherapy Predicts Benefit of Shorter Induction Period

Optimal integration of molecularly targeted therapies, such as tyrosine kinase inhibitors (TKI), with concurrent chemotherapy and radiation (CRT) to improve outcomes in genotype-defined cancers remains a current challenge in clinical settings. Important questions regarding optimal scheduling and length of induction period for neoadjuvant use of targeted agents remain unsolved and vary among clinical trial protocols. Here, we develop and validate a biomathematical framework encompassing drug resistance and radiobiology to simulate patterns of local versus distant recurrences in a non-small cell lung cancer (NSCLC) population with mutated EGFR receiving TKIs and CRT. Our model predicted that targeted induction before CRT, an approach currently being tested in clinical trials, may render adjuvant targeted therapy less effective due to proliferation of drug-resistant cancer cells when using very long induction periods. Furthermore, simulations not only demonstrated the competing effects of drug-resistant cell expansion versus overall tumor regression as a function of induction length, but also directly estimated the probability of observing an improvement in progression-free survival at a given cohort size. We thus demonstrate that such stochastic biological simulations have the potential to quantitatively inform the design of multimodality clinical trials in genotype-defined cancers. SIGNIFICANCE: A biomathematical framework based on fundamental principles of evolution and radiobiology for in silico clinical trial design allows clinicians to optimize administration of TKIs before chemoradiotherapy in oncogene-driven NSCLC.

An Optimal Control Framework for the Automated Design of Personalized Cancer Treatments

One of the key challenges in current cancer research is the development of computational strategies to support clinicians in the identification of successful personalized treatments. Control theory might be an effective approach to this end, as proven by the long-established application to therapy design and testing. In this respect, we here introduce the Control Theory for Therapy Design (CT4TD) framework, which employs optimal control theory on patient-specific pharmacokinetics (PK) and pharmacodynamics (PD) models, to deliver optimized therapeutic strategies. The definition of personalized PK/PD models allows to explicitly consider the physiological heterogeneity of individuals and to adapt the therapy accordingly, as opposed to standard clinical practices. CT4TD can be used in two distinct scenarios. At the time of the diagnosis, CT4TD allows to set optimized personalized administration strategies, aimed at reaching selected target drug concentrations, while minimizing the costs in terms of toxicity and adverse effects. Moreover, if longitudinal data on patients under treatment are available, our approach allows to adjust the ongoing therapy, by relying on simplified models of cancer population dynamics, with the goal of minimizing or controlling the tumor burden. CT4TD is highly scalable, as it employs the efficient dCRAB/RedCRAB optimization algorithm, and the results are robust, as proven by extensive tests on synthetic data. Furthermore, the theoretical framework is general, and it might be applied to any therapy for which a PK/PD model can be estimated, and for any kind of administration and cost. As a proof of principle, we present the application of CT4TD to Imatinib administration in Chronic Myeloid leukemia, in which we adopt a simplified model of cancer population dynamics. In particular, we show that the optimized therapeutic strategies are diversified among patients, and display improvements with respect to the current standard regime.

Resistance to targeted therapies as a multifactorial, gradual adaptation to inhibitor specific selective pressures

Despite high initial efficacy, targeted therapies eventually fail in advanced cancers, as tumors develop resistance and relapse. In contrast to the substantial body of research on the molecular mechanisms of resistance, understanding of how resistance evolves remains limited. Using an experimental model of ALK positive NSCLC, we explored the evolution of resistance to different clinical ALK inhibitors. We found that resistance can originate from heterogeneous, weakly resistant subpopulations with variable sensitivity to different ALK inhibitors. Instead of the commonly assumed stochastic single hit (epi) mutational transition, or drug-induced reprogramming, we found evidence for a hybrid scenario involving the gradual, multifactorial adaptation to the inhibitors through acquisition of multiple cooperating genetic and epigenetic adaptive changes. Additionally, we found that during this adaptation tumor cells might present unique, temporally restricted collateral sensitivities, absent in therapy naïve or fully resistant cells, suggesting the potential for new therapeutic interventions, directed against evolving resistance.

Acquired resistance to cancer therapies reflects the ability of cancers to adapt to therapy-imposed selective pressures. Here, the authors elucidate the dynamics of developing resistance to ALK inhibitors in an ALK+ lung cancer cell line showing that resistance originates from drug-specific tolerant cancer cells and it develops as a gradual adaptation.

Using Selection by Nonantibiotic Stressors to Sensitize Bacteria to Antibiotics

Evolutionary adaptation of bacteria to nonantibiotic selective forces, such as osmotic stress, has been previously associated with increased antibiotic resistance, but much less is known about potentially sensitizing effects of nonantibiotic stressors. In this study, we use laboratory evolution to investigate adaptation of Enterococcus faecalis, an opportunistic bacterial pathogen, to a broad collection of environmental agents, ranging from antibiotics and biocides to extreme pH and osmotic stress. We find that nonantibiotic selection frequently leads to increased sensitivity to other conditions, including multiple antibiotics. Using population sequencing and whole-genome sequencing of single isolates from the evolved populations, we identify multiple mutations in genes previously linked with resistance to the selecting conditions, including genes corresponding to known drug targets or multidrug efflux systems previously tied to collateral sensitivity. Finally, we hypothesized based on the measured sensitivity profiles that sequential rounds of antibiotic and nonantibiotic selection may lead to hypersensitive populations by harnessing the orthogonal collateral effects of particular pairs of selective forces. To test this hypothesis, we show experimentally that populations evolved to a sequence of linezolid (an oxazolidinone antibiotic) and sodium benzoate (a common preservative) exhibit increased sensitivity to more stressors than adaptation to either condition alone. The results demonstrate how sequential adaptation to drug and nondrug environments can be used to sensitize bacteria to antibiotics and highlight new potential strategies for exploiting shared constraints governing adaptation to diverse environmental challenges.

Optimizing adaptive cancer therapy: dynamic programming and evolutionary game theory

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

Evolving generalists in switching rugged landscapes

Evolving systems, be it an antibody repertoire in the face of mutating pathogens or a microbial population exposed to varied antibiotics, constantly search for adaptive solutions in time-varying fitness landscapes. Generalists refer to genotypes that remain fit across diverse selective pressures; while multi-drug resistant microbes are undesired yet prevalent, broadly-neutralizing antibodies are much wanted but rare. However, little is known about under what conditions such generalists with a high capacity to adapt can be efficiently discovered by evolution. In addition, can epistasis-the source of landscape ruggedness and path constraints-play a different role, if the environment varies in a non-random way? We present a generative model to estimate the propensity of evolving generalists in rugged landscapes that are tunably related and alternating relatively slowly. We find that environmental cycling can substantially facilitate the search for fit generalists by dynamically enlarging their effective basins of attraction. Importantly, these high performers are most likely to emerge at intermediate levels of ruggedness and environmental relatedness. Our approach allows one to estimate correlations across environments from the topography of experimental fitness landscapes. Our work provides a conceptual framework to study evolution in time-correlated complex environments, and offers statistical understanding that suggests general strategies for eliciting broadly neutralizing antibodies or preventing microbes from evolving multi-drug resistance.

Cooperative adaptation to therapy (CAT) confers resistance in heterogeneous non-small cell lung cancer

Understanding intrinsic and acquired resistance is crucial to overcoming cancer chemotherapy failure. While it is well-established that intratumor, subclonal genetic and phenotypic heterogeneity significantly contribute to resistance, it is not fully understood how tumor sub-clones interact with each other to withstand therapy pressure. Here, we report a previously unrecognized behavior in heterogeneous tumors: cooperative adaptation to therapy (CAT), in which cancer cells induce co-resistant phenotypes in neighboring cancer cells when exposed to cancer therapy. Using a CRISPR/Cas9 toolkit we engineered phenotypically diverse non-small cell lung cancer (NSCLC) cells by conferring mutations in Dicer1, a type III cytoplasmic endoribonuclease involved in small non-coding RNA genesis. We monitored three-dimensional growth dynamics of fluorescently-labeled mutant and/or wild-type cells individually or in co-culture using a substrate-free NanoCulture system under unstimulated or drug pressure conditions. By integrating mathematical modeling with flow cytometry, we characterized the growth patterns of mono- and co-cultures using a mathematical model of intra- and interspecies competition. Leveraging the flow cytometry data, we estimated the model’s parameters to reveal that the combination of WT and mutants in co-cultures allowed for beneficial growth in previously drug sensitive cells despite drug pressure via induction of cell state transitions described by a cooperative game theoretic change in the fitness values. Finally, we used an ex vivo human tumor model that predicts clinical response through drug sensitivity analyses and determined that cellular and morphologic heterogeneity correlates to prognostic failure of multiple clinically-approved and off-label drugs in individual NSCLC patient samples. Together, these findings present a new paradox in drug resistance implicating non-genetic cooperation among tumor cells to thwart drug pressure, suggesting that profiling for druggable targets (i.e. mutations) alone may be insufficient to assign effective therapy.

Here, we provide mathematical and empirical evidence to support a potentially new paradigm in drug resistance, which we have termed “cooperative adaptation to therapy” (CAT). CAT is defined by a phenomenon wherein drug-sensitive cancer cells with different genetic and phenotypic features within a 3-dimensional heterogeneous tumor induce non-mutational resistance in their neighboring cells under pressure of cancer therapy. To develop this novel conclusion we deployed an interdisciplinary effort including an ex vivo human tumor model, a CRISPR/Cas9 platform with 3-dimensional in vitro experiments, and high throughput flow cytometry. Importantly, we wove these data together using a mathematical model of intra- and interspecies competition to understand how tumor heterogeneity influenced our observations. By estimating the model’s parameters, we determined that the combination of genetic clonal variants in co-cultures allowed for previously drug-sensitive cells to continue to grow despite drug pressure. We were thus able to characterize distinct growth regimens in mono- and co-cultures without and with drug pressure.

Hybrid modeling frameworks of tumor development and treatment

Tumors are complex multicellular heterogeneous systems comprised of components that interact with and modify one another. Tumor development depends on multiple factors: intrinsic, such as genetic mutations, altered signaling pathways, or variable receptor expression; and extrinsic, such as differences in nutrient supply, crosstalk with stromal or immune cells, or variable composition of the surrounding extracellular matrix. Tumors are also characterized by high cellular heterogeneity and dynamically changing tumor microenvironments. The complexity increases when this multiscale, multicomponent system is perturbed by anticancer treatments. Modeling such complex systems and predicting how tumors will respond to therapies require mathematical models that can handle various types of information and combine diverse theoretical methods on multiple temporal and spatial scales, that is, hybrid models. In this update, we discuss the progress that has been achieved during the last 10 years in the area of the hybrid modeling of tumors. The classical definition of hybrid models refers to the coupling of discrete descriptions of cells with continuous descriptions of microenvironmental factors. To reflect on the direction that the modeling field has taken, we propose extending the definition of hybrid models to include of coupling two or more different mathematical frameworks. Thus, in addition to discussing recent advances in discrete/continuous modeling, we also discuss how these two mathematical descriptions can be coupled with theoretical frameworks of optimal control, optimization, fluid dynamics, game theory, and machine learning. All these methods will be illustrated with applications to tumor development and various anticancer treatments.

This article is characterized under:

Analytical and Computational Methods > Computational Methods

Translational, Genomic, and Systems Medicine > Therapeutic Methods

Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models

Nonlinear adaptive control of competitive release and chemotherapeutic resistance

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

Antibiotic collateral sensitivity is contingent on the repeatability of evolution

Antibiotic resistance represents a growing health crisis that necessitates the immediate discovery of novel treatment strategies. One such strategy is the identification of collateral sensitivities, wherein evolution under a first drug induces susceptibility to a second. Here, we report that sequential drug regimens derived from in vitro evolution experiments may have overstated therapeutic benefit, predicting a collaterally sensitive response where cross-resistance ultimately occurs. We quantify the likelihood of this phenomenon by use of a mathematical model parametrised with combinatorially complete fitness landscapes for Escherichia coli. Through experimental evolution we then verify that a second drug can indeed stochastically exhibit either increased susceptibility or increased resistance when following a first. Genetic divergence is confirmed as the driver of this differential response through targeted and whole genome sequencing. Taken together, these results highlight that the success of evolutionarily-informed therapies is predicated on a rigorous probabilistic understanding of the contingencies that arise during the evolution of drug resistance.

The evolution of resistance to an antibiotic can render bacteria more susceptible, or more resistant, to a second antibiotic. Here, Nichol et al. provide evidence that the final outcome can be fairly stochastic and depends on the shape of the evolutionary fitness landscape.