The role of cell density and intratumoral heterogeneity in multidrug resistance

The development of drug resistance in metastatic tumours under chemotherapy: An evolutionary perspective

We present a mathematical model of the evolutionary dynamics of a metastatic tumour under chemotherapy, comprising non-local partial differential equations for the phenotype-structured cell populations in the primary tumour and its metastasis. These equations are coupled with a physiologically-based pharmacokinetic model of drug administration and distribution, implementing a realistic delivery schedule. The model is carefully calibrated from the literature, focusing on BRAF-mutated melanoma treated with Dabrafenib as a case study. By means of long-time asymptotic and global sensitivity analyses, as well as numerical simulations, we explore the impact of cell migration from the primary to the metastatic site, physiological aspects of the tumour tissues and drug dose on the development of chemoresistance and treatment efficacy. Our findings provide a possible explanation for empirical evidence indicating that chemotherapy may foster metastatic spread and that metastases may be less impacted by the chemotherapeutic agent.

Time-dependent proteomics and drug response in expanding cancer cells

Cancer cell line is commonly used for discovery and development of anti-cancer drugs. It is generally considered that drug response remains constant for a certain cell line due to the identity of genetics thus protein patterns. Here, we demonstrated that cancer cells continued dividing even after reaching confluence, in that the proteomics was changed continuously and dramatically with strong relevance to cell division, cell adhesion and cell metabolism, indicating time-dependent intrinsically reprogramming of cells during expansion. Of note, the inhibition effect of most anti-cancer drugs was strikingly attenuated in culture cells along with cell expansion, with the strongest change at the third day when cells were still expanding. Profiling of an FDA-approved drug library revealed that attenuation of response with cell expansion is common for most drugs, an exception was TAK165 that was a selective inhibitor of mitochondrial respiratory chain complex I. Finally, we screened a panel of natural products and identified four pentacyclic triterpenes as selective inhibitors of cancer cells under prolonged growth. Taken together, our findings underscore that caution should be taken in evaluation of anti-cancer drugs using culture cells, and provide agents selectively targeting overgrowth cancer cells.

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.

The Increase in the Drug Resistance of Acute Myeloid Leukemia THP-1 Cells in High-Density Cell Culture Is Associated with Inflammatory-like Activation and Anti-Apoptotic Bcl-2 Proteins

It is known that cell culture density can modulate the drug resistance of acute myeloid leukemia (AML) cells. In this work, we studied the drug sensitivity of AML cells in high-density cell cultures (cell lines THP-1, HL-60, MV4-11, and U937). It was shown that the AML cells in high-density cell cultures in vitro were significantly more resistant to DNA-damaging drugs and recombinant ligand izTRAIL than those in low-density cell cultures. To elucidate the mechanism of the increased drug resistance of AML cells in high-density cell cultures, we studied the activation of Bcl-2, Hif-1alpha, and NF-kB proteins, as well as cytokine secretion, the inflammatory immunophenotype, and the transcriptome for THP-1 cells in the low-density and high-density cultures. The results indicated that the increase in the drug resistance of proliferating THP-1 cells in high-density cell cultures was associated with the accumulation of inflammatory cytokines in extracellular medium, and the formation of NF-kB-dependent inflammatory-like cell activation with the anti-apoptotic proteins Bcl-2 and Bcl-xl. The increased drug resistance of THP-1 cells in high-density cultures can be reduced by ABT-737, an inhibitor of Bcl-2 family proteins, and by inhibitors of NF-kB. The results suggest a mechanism for increasing the drug resistance of AML cells in the bone marrow and are of interest for developing a strategy to suppress this resistance.

Modeling the effects of EMT-immune dynamics on carcinoma disease progression

During progression from carcinoma in situ to an invasive tumor, the immune system is engaged in complex sets of interactions with various tumor cells. Tumor cell plasticity alters disease trajectories via epithelial-to-mesenchymal transition (EMT). Several of the same pathways that regulate EMT are involved in tumor-immune interactions, yet little is known about the mechanisms and consequences of crosstalk between these regulatory processes. Here we introduce a multiscale evolutionary model to describe tumor-immune-EMT interactions and their impact on epithelial cancer progression from in situ to invasive disease. Through simulation of patient cohorts in silico, the model predicts that a controllable region maximizes invasion-free survival. This controllable region depends on properties of the mesenchymal tumor cell phenotype: its growth rate and its immune-evasiveness. In light of the model predictions, we analyze EMT-inflammation-associated data from The Cancer Genome Atlas, and find that association with EMT worsens invasion-free survival probabilities. This result supports the predictions of the model, and leads to the identification of genes that influence outcomes in bladder and uterine cancer, including FGF pathway members. These results suggest new means to delay disease progression, and demonstrate the importance of studying cancer-immune interactions in light of EMT.

Coupled Source-Sink Habitats Produce Spatial and Temporal Variation of Cancer Cell Molecular Properties as an Alternative to Branched Clonal Evolution and Stem Cell Paradigms

Intratumoral molecular cancer cell heterogeneity is conventionally ascribed to the accumulation of random mutations that occasionally generate fitter phenotypes. This model is built upon the “mutation-selection” paradigm in which mutations drive ever-fitter cancer cells independent of environmental circumstances. An alternative model posits spatio-temporal variation (e.g., blood flow heterogeneity) drives speciation by selecting for cancer cells adapted to each different environment. Here, spatial genetic variation is the consequence rather than the cause of intratumoral evolution. In nature, spatially heterogenous environments are frequently coupled through migration. Drawing from ecological models, we investigate adjacent well-perfused and poorly-perfused tumor regions as “source” and “sink” habitats, respectively. The source habitat has a high carrying capacity resulting in more emigration than immigration. Sink habitats may support a small (“soft-sink”) or no (“hard-sink”) local population. Ecologically, sink habitats can reduce the population size of the source habitat so that, for example, the density of cancer cells directly around blood vessels may be lower than expected. Evolutionarily, sink habitats can exert a selective pressure favoring traits different from those in the source habitat so that, for example, cancer cells adjacent to blood vessels may be suboptimally adapted for that habitat. Soft sinks favor a generalist cancer cell type that moves between the environment but can, under some circumstances, produce speciation events forming source and sink habitat specialists resulting in significant molecular variation in cancer cells separated by small distances. Finally, sink habitats, with limited blood supply, may receive reduced concentrations of systemic drug treatments; and local hypoxia and acidosis may further decrease drug efficacy allowing cells to survive treatment and evolve resistance. In such cases, the sink transforms into the source habitat for resistant cancer cells, leading to treatment failure and tumor progression. We note these dynamics will result in spatial variations in molecular properties as an alternative to the conventional branched evolution model and will result in cellular migration as well as variation in cancer cell phenotype and proliferation currently described by the stem cell paradigm.

Evaluating cell viability heterogeneity based on information fusion of multiple adhesion strengths

Cell viability evaluation is significantly meaningful for cellular assays. Some cells with weak viability are easily killed in the detection of anticancer drugs, while others with strong viability survive and proliferate, ultimately leading to the treatment failure or the inaccuracy of biological assays. Accurately evaluating cell viability heterogeneity still remains difficult. This article proposed a multiphysical property information fusion method for evaluating cell viability heterogeneity based on polynomial regression in a single-channel integrated microfluidic chip. In this method, adhesion strengths τ_N , that are defined as the magnitude of shear stress needed to detach (100 - N) % of cell population, were extracted as the independent variables of polynomial regression model by calculating the nonlinear fitting of the impedance-response curves for shear stress (cell detachment assay). Besides, by calculating the nonlinear fitting of the drug dose-response curves for cancer cells (IC₅₀ assay), the half-maximal inhibitory concentration (IC₅₀ ) was extracted as the dependent variables of polynomial regression model. The results show that the mean relative error of our fusion method averagely reduces by 6.04% and 62.79% compared with the multiple linear regression method and the cell counting method. Moreover, a simplified theoretical model used to describe the quantitative relationship between cell viability and its adhesion strengths was built to provide a theoretical basis for our fusion method.

miRNAs mediated drug resistance in hematological malignancies

Despite improvements in the therapeutic approaches for hematological malignancies in the last decades, refractory disease still occurs, and cancer drug resistance still remains a major hurdle in the clinical management of these cancer patients. The investigation of this problem has been extensive and different mechanism and molecules have been associated with drug resistance. MicroRNAs (miRNAs) have been described as having an important action in the emergence of cancer, including hematological tumors, and as being major players in their progression, aggressiveness and response to treatments. Moreover, miRNAs have been strongly associated with cancer drug resistance and with the modulation of the sensitivity of cancer cells to a wide array of anticancer drugs. Furthermore, this role has also been reported for miRNAs packaged into extracellular vesicles (EVs-miRNAs), which in turn have been described as essential for the horizontal transfer of drug resistance to sensitive cells. Several studies have been suggesting the use of miRNAs as biomarkers for drug response and clinical outcome prediction, as well as promising therapeutic tools in hematological diseases. Indeed, the combination of miRNA-based therapeutic tools with conventional drugs contributes to overcome drug resistance. This review addresses the role of miRNAs in the pathogenesis of hematological malignances, namely multiple myeloma, leukemias and lymphomas, highlighting their important action (either in their cell-free circulating form or within circulating EVs) in drug resistance and their potential clinical applications.

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

Purpose

Drug resistance is a major impediment to the success of cancer treatment. Resistance is typically thought to arise from random genetic mutations, after which mutated cells expand via Darwinian selection. However, recent experimental evidence suggests that progression to drug resistance need not occur randomly, but instead may be induced by the treatment itself via either genetic changes or epigenetic alterations. This relatively novel notion of resistance complicates the already challenging task of designing effective treatment protocols.

Materials and Methods

To better understand resistance, we have developed a mathematical modeling framework that incorporates both spontaneous and drug-induced resistance.

Results

Our model demonstrates that the ability of a drug to induce resistance can result in qualitatively different responses to the same drug dose and delivery schedule. We have also proven that the induction parameter in our model is theoretically identifiable and propose an in vitro protocol that could be used to determine a treatment’s propensity to induce resistance.

A Review of Mathematical Models for Tumor Dynamics and Treatment Resistance Evolution of Solid Tumors

Increasing knowledge of intertumor heterogeneity, intratumor heterogeneity, and cancer evolution has improved the understanding of anticancer treatment resistance. A better characterization of cancer evolution and subsequent use of this knowledge for personalized treatment would increase the chance to overcome cancer treatment resistance. Model‐based approaches may help achieve this goal. In this review, we comprehensively summarized mathematical models of tumor dynamics for solid tumors and of drug resistance evolution. Models displayed by ordinary differential equations, algebraic equations, and partial differential equations for characterizing tumor burden dynamics are introduced and discussed. As for tumor resistance evolution, stochastic and deterministic models are introduced and discussed. The results may facilitate a novel model‐based analysis on anticancer treatment response and the occurrence of resistance, which incorporates both tumor dynamics and resistance evolution. The opportunities of a model‐based approach as discussed in this review can be of great benefit for future optimizing and personalizing anticancer treatment.

Interplay of Darwinian Selection, Lamarckian Induction and Microvesicle Transfer on Drug Resistance in Cancer

Development of drug resistance in cancer has major implications for patients’ outcome. It is related to processes involved in the decrease of drug efficacy, which are strongly influenced by intratumor heterogeneity and changes in the microenvironment. Heterogeneity arises, to a large extent, from genetic mutations analogously to Darwinian evolution, when selection of tumor cells results from the adaptation to the microenvironment, but could also emerge as a consequence of epigenetic mutations driven by stochastic events. An important exogenous source of alterations is the action of chemotherapeutic agents, which not only affects the signalling pathways but also the interactions among cells. In this work we provide experimental evidence from in vitro assays and put forward a mathematical kinetic transport model to describe the dynamics displayed by a system of non-small-cell lung carcinoma cells (NCI-H460) which, depending on the effect of a chemotherapeutic agent (doxorubicin), exhibits a complex interplay between Darwinian selection, Lamarckian induction and the nonlocal transfer of extracellular microvesicles. The role played by all of these processes to multidrug resistance in cancer is elucidated and quantified.

Nanogel-mediated delivery of a cocktail of epigenetic drugs plus doxorubicin overcomes drug resistance in breast cancer cells

Epigenetic modifications (e.g., DNA methylation or histone deacetylation) are commonly implicated in cancer chemoresistance. We previously showed that pretreating resistant MCF-7/ADR breast cancer cells with a demethylating agent (5-aza-2'-deoxycytidine (DAC)) or with an inhibitor of histone deacetylase (suberoylanilide hydroxamic acid (SAHA)) sensitized resistant cells to doxorubicin (DOX) treatment. However, even with increasing doses of DOX, a fraction of resistant cells remained nonresponsive to this pretreatment (~ 25% pretreated with DAC, ~ 45% with SAHA). We hypothesized that pretreating resistant cells with a combination of epigenetic drugs (DAC + SAHA) could more effectively overcome drug resistance. We postulated that delivery of epigenetic drugs encapsulated in biodegradable nanogels (NGs) would further enhance their efficacy. MCF-7/ADR cells were first treated with a single drug vs. a combination of epigenetic drugs, either as solutions or encapsulated in NGs, then subjected to DOX, either in solution or in NGs. Antiproliferative data showed that pretreatment with epigenetic drugs in NGs, then with DOX in NGs, was most effective in overcoming resistance; this treatment inhibited cell growth by > 90%, even at low doses of DOX. Cell cycle analysis showed that a major fraction of cells treated with a cocktail of epigenetic drugs + DOX, all in NG formulations, remained in the G2/M cell cycle arrest phase for a prolonged period. The mechanism of better efficacy of epigenetic drugs in NGs could be attributed to their sustained effect. A similar strategy could be developed for other cancer cells in which drug resistance is due to epigenetic modifications.

A multi-state model of chemoresistance to characterize phenotypic dynamics in breast cancer

The development of resistance to chemotherapy is a major cause of treatment failure in breast cancer. While mathematical models describing the dynamics of resistant cancer cell subpopulations have been proposed, experimental validation has been difficult due to the complex nature of resistance that limits the ability of a single phenotypic marker to sufficiently identify the drug resistant subpopulations. We address this problem with a coupled experimental/modeling approach to reveal the composition of drug resistant subpopulations changing in time following drug exposure. We calibrate time-resolved drug sensitivity assays to three mathematical models to interrogate the models' ability to capture drug response dynamics. The Akaike information criterion was employed to evaluate the three models, and it identified a multi-state model incorporating the role of population heterogeneity and cellular plasticity as the optimal model. To validate the model's ability to identify subpopulation composition, we mixed different proportions of wild-type MCF-7 and MCF-7/ADR resistant cells and evaluated the corresponding model output. Our blinded two-state model was able to estimate the proportions of cell types with an R-squared value of 0.857. To the best of our knowledge, this is the first work to combine experimental time-resolved drug sensitivity data with a mathematical model of resistance development.

Cysteine allows ovarian cancer cells to adapt to hypoxia and to escape from carboplatin cytotoxicity

Ovarian cancer is the second most common gynaecologic malignancy and the main cause of death from gynaecologic cancer, due to late diagnosis and chemoresistance. Studies have reported the role of cysteine in cancer, by contributing for hydrogen sulphide (H2S) generation and as a precursor of glutathione (GSH). However, the role of cysteine in the adaptation to hypoxia and therapy response remains unclear. We used several ovarian cancer cell lines, ES2, OVCAR3, OVCAR8, A2780 and A2780cisR, to clarify cysteine relevance in ovarian cancer cells survival upon hypoxia and carboplatin. Results show that ES2 and OVCAR8 cells presented a stronger dependence on cysteine availability upon hypoxia and carboplatin exposure than OVCAR3 cells. Interestingly, the A2780 cisR, but not A2780 parental cells, benefits from cysteine upon carboplatin exposure, showing that cysteine is crucial for chemoresistance. Moreover, GSH degradation and subsequent cysteine recycling pathway is associated with ovarian cancer as seen in peripheral blood serum from patients. Higher levels of total free cysteine (Cys) and homocysteine (HCys) were found in ovarian cancer patients in comparison with benign tumours and lower levels of GSH were found in ovarian neoplasms patients in comparison with healthy individuals. Importantly, the total and S-Homocysteinylated levels distinguished blood donors from patients with neoplasms as well as patients with benign from patients with malignant tumours. The levels of S-cysteinylated proteins distinguish blood donors from patients with neoplasms and the free levels of Cys in serum distinguish blood from patients with benign tumours from patients with malignant tumours. Herein we disclosed that cysteine contributes for a worse disease prognosis, allowing faster adaptation to hypoxia and protecting cells from carboplatin. The measurement of serum cysteine levels can be an effective tool for early diagnosis, for outcome prediction and follow up of disease progression.

The role of spatial variations of abiotic factors in mediating intratumour phenotypic heterogeneity

We present here a space- and phenotype-structured model of selection dynamics between cancer cells within a solid tumour. In the framework of this model, we combine formal analyses with numerical simulations to investigate in silico the role played by the spatial distribution of abiotic components of the tumour microenvironment in mediating phenotypic selection of cancer cells. Numerical simulations are performed both on the 3D geometry of an in silico multicellular tumour spheroid and on the 3D geometry of an in vivo human hepatic tumour, which was imaged using computerised tomography. The results obtained show that inhomogeneities in the spatial distribution of oxygen, currently observed in solid tumours, can promote the creation of distinct local niches and lead to the selection of different phenotypic variants within the same tumour. This process fosters the emergence of stable phenotypic heterogeneity and supports the presence of hypoxic cells resistant to cytotoxic therapy prior to treatment. Our theoretical results demonstrate the importance of integrating spatial data with ecological principles when evaluating the therapeutic response of solid tumours to cytotoxic therapy.

Prevention of hepatocellular carcinoma by targeting MYCN-positive liver cancer stem cells with acyclic retinoid

Hepatocellular carcinoma (HCC) is a highly lethal cancer, partly because of its high rate of recurrence, which is caused by the presence of liver cancer stem cells (CSCs). Here, using a selective chemopreventive agent, acyclic retinoid (ACR), as a bioprobe, we identified MYCN, which is mostly recognized as an oncogene in neuroblastoma, as a therapeutic target of ACR for HCC through a selective deletion of MYCN⁺ liver CSCs. We also demonstrated that the expression of MYCN in HCC served as a prognostic biomarker and positively correlated with recurrence of de novo HCC after curative treatment. Our study highlighted MYCN as a biomarker and therapeutic target in drug discovery for screening chemopreventive agents against the recurrence of HCC.

Hepatocellular carcinoma (HCC) is a highly lethal cancer that has a high rate of recurrence, in part because of cancer stem cell (CSC)-dependent field cancerization. Acyclic retinoid (ACR) is a synthetic vitamin A-like compound capable of preventing the recurrence of HCC. Here, we performed a genome-wide transcriptome screen and showed that ACR selectively suppressed the expression of MYCN, a member of the MYC family of basic helix–loop–helix–zipper transcription factors, in HCC cell cultures, animal models, and liver biopsies obtained from HCC patients. MYCN expression in human HCC was correlated positively with both CSC and Wnt/β-catenin signaling markers but negatively with mature hepatocyte markers. Functional analysis showed repressed cell-cycle progression, proliferation, and colony formation, activated caspase-8, and induced cell death in HCC cells following silencing of MYCN expression. High-content single-cell imaging analysis and flow cytometric analysis identified a MYCN⁺ CSC subpopulation in the heterogeneous HCC cell cultures and showed that these cells were selectively killed by ACR. Particularly, EpCAM⁺ cells isolated using a cell-sorting system showed increased MYCN expression and sensitivity to ACR compared with EpCAM⁻ cells. In a long-term (>10 y) follow-up study of 102 patients with HCC, MYCN was expressed at higher levels in the HCC tumor region than in nontumor regions, and there was a positive correlation between MYCN expression and recurrence of de novo HCC but not metastatic HCC after curative treatment. In summary, these results suggest that MYCN serves as a prognostic biomarker and therapeutic target of ACR for liver CSCs in de novo HCC.

Interdependence theory of tissue failure: bulk and boundary effects

The mortality rate of many complex multicellular organisms increases with age, which suggests that net ageing damage is accumulative, despite remodelling processes. But how exactly do these little mishaps in the cellular level accumulate and spread to become a systemic catastrophe? To address this question we present experiments with synthetic tissues, an analytical model consistent with experiments, and a number of implications that follow the analytical model. Our theoretical framework describes how shape, curvature and density influences the propagation of failure in a tissue subjected to oxidative damage. We propose that ageing is an emergent property governed by interaction between cells, and that intercellular processes play a role that is at least as important as intracellular ones.

Modeling the Transfer of Drug Resistance in Solid Tumors

ABC efflux transporters are a key factor leading to multidrug resistance in cancer. Overexpression of these transporters significantly decreases the efficacy of anti-cancer drugs. Along with selection and induction, drug resistance may be transferred between cells, which is the focus of this paper. Specifically, we consider the intercellular transfer of P-glycoprotein (P-gp), a well-known ABC transporter that was shown to confer resistance to many common chemotherapeutic drugs. In a recent paper, Durán et al. (Bull Math Biol 78(6):1218-1237, 2016) studied the dynamics of mixed cultures of resistant and sensitive NCI-H460 (human non-small lung cancer) cell lines. As expected, the experimental data showed a gradual increase in the percentage of resistance cells and a decrease in the percentage of sensitive cells. The experimental work was accompanied with a mathematical model that assumed P-gp transfer from resistant cells to sensitive cells, rendering them temporarily resistant. The mathematical model provided a reasonable fit to the experimental data. In this paper, we develop a new mathematical model for the transfer of drug resistance between cancer cells. Our model is based on incorporating a resistance phenotype into a model of cancer growth (Greene et al. in J Theor Biol 367:262-277, 2015). The resulting model for P-gp transfer, written as a system of integro-differential equations, follows the dynamics of proliferating, quiescent, and apoptotic cells, with a varying resistance phenotype. We show that this model provides a good match to the dynamics of the experimental data of Durán et al. (2016). The mathematical model shows a better fit when resistant cancer cells have a slower division rate than the sensitive cells.

Pharmacokinetics and Drug Interactions Determine Optimum Combination Strategies in Computational Models of Cancer Evolution

The identification of optimal drug administration schedules to battle the emergence of resistance is a major challenge in cancer research. The existence of a multitude of resistance mechanisms necessitates administering drugs in combination, significantly complicating the endeavor of predicting the evolutionary dynamics of cancers and optimal intervention strategies. A thorough understanding of the important determinants of cancer evolution under combination therapies is therefore crucial for correctly predicting treatment outcomes. Here we developed the first computational strategy to explore pharmacokinetic and drug interaction effects in evolutionary models of cancer progression, a crucial step towards making clinically relevant predictions. We found that incorporating these phenomena into our multiscale stochastic modeling framework significantly changes the optimum drug administration schedules identified, often predicting nonintuitive strategies for combination therapies. We applied our approach to an ongoing phase Ib clinical trial (TATTON) administering AZD9291 and selumetinib to EGFR-mutant lung cancer patients. Our results suggest that the schedules used in the three trial arms have almost identical efficacies, but slight modifications in the dosing frequencies of the two drugs can significantly increase tumor cell eradication. Interestingly, we also predict that drug concentrations lower than the MTD are as efficacious, suggesting that lowering the total amount of drug administered could lower toxicities while not compromising on the effectiveness of the drugs. Our approach highlights the fact that quantitative knowledge of pharmacokinetic, drug interaction, and evolutionary processes is essential for identifying best intervention strategies. Our method is applicable to diverse cancer and treatment types and allows for a rational design of clinical trials. Cancer Res; 77(14); 3908-21. ©2017 AACR.

Application of mathematical models to metronomic chemotherapy: What can be inferred from minimal parameterized models?

Metronomic chemotherapy refers to the frequent administration of chemotherapy at relatively low, minimally toxic doses without prolonged treatment interruptions. Different from conventional or maximum-tolerated-dose chemotherapy which aims at an eradication of all malignant cells, in a metronomic dosing the goal often lies in the long-term management of the disease when eradication proves elusive. Mathematical modeling and subsequent analysis (theoretical as well as numerical) have become an increasingly more valuable tool (in silico) both for determining conditions under which specific treatment strategies should be preferred and for numerically optimizing treatment regimens. While elaborate, computationally-driven patient specific schemes that would optimize the timing and drug dose levels are still a part of the future, such procedures may become instrumental in making chemotherapy effective in situations where it currently fails. Ideally, mathematical modeling and analysis will develop into an additional decision making tool in the complicated process that is the determination of efficient chemotherapy regimens. In this article, we review some of the results that have been obtained about metronomic chemotherapy from mathematical models and what they infer about the structure of optimal treatment regimens.

On drug resistance and metronomic chemotherapy: A mathematical modeling and optimal control approach

Effects that tumor heterogeneity and drug resistance have on the structure of chemotherapy protocols are discussed from a mathematical modeling and optimal control point of view. In the case when two compartments consisting of sensitive and resistant cells are considered, optimal protocols consist of full dose chemotherapy as long as the relative proportion of sensitive cells is high. When resistant cells become more dominant, optimal controls switch to lower dose regimens defined by so-called singular controls. The role that singular controls play in the structure of optimal therapy protocols for cell populations with a large number of traits is explored in mathematical models.

Optimal control of a mathematical model for cancer chemotherapy under tumor heterogeneity

We consider cancer chemotherapy as an optimal control problem with the aim to minimize a combination of the tumor volume and side effects over an a priori specified therapy horizon when the tumor consists of a heterogeneous agglomeration of many subpopulations. The mathematical model, which accounts for different growth and apoptosis rates in the presence of cell densities, is a finite-dimensional approximation of a model originally formulated by Lorz et al. [18,19] and Greene et al. [10,11] with a continuum of possible traits. In spite of an arbitrarily high dimension, for this problem singular controls (which correspond to time-varying administration schedules at less than maximum doses) can be computed explicitly in feedback form. Interestingly, these controls have the property to keep the entire tumor population constant. Numerical computations and simulations that explore the optimality of bang-bang and singular controls are given. These point to the optimality of protocols that combine a full dose therapy segment with a period of lower dose drug administration.

Limiting the development of anti-cancer drug resistance in a spatial model of micrometastases

While chemoresistance in primary tumors is well-studied, much less is known about the influence of systemic chemotherapy on the development of drug resistance at metastatic sites. In this work, we use a hybrid spatial model of tumor response to a DNA damaging drug to study how the development of chemoresistance in micrometastases depends on the drug dosing schedule. We separately consider cell populations that harbor pre-existing resistance to the drug, and those that acquire resistance during the course of treatment. For each of these independent scenarios, we consider one hypothetical cell line that is responsive to metronomic chemotherapy, and another that with high probability cannot be eradicated by a metronomic protocol. Motivated by experimental work on ovarian cancer xenografts, we consider all possible combinations of a one week treatment protocol, repeated for three weeks, and constrained by the total weekly drug dose. Simulations reveal a small number of fractionated-dose protocols that are at least as effective as metronomic therapy in eradicating micrometastases with acquired resistance (weak or strong), while also being at least as effective on those that harbor weakly pre-existing resistant cells. Given the responsiveness of very different theoretical cell lines to these few fractionated-dose protocols, these may represent more effective ways to schedule chemotherapy with the goal of limiting metastatic tumor progression.

Tracking the evolution of cancer cell populations through the mathematical lens of phenotype-structured equations

Background

A thorough understanding of the ecological and evolutionary mechanisms that drive the phenotypic evolution of neoplastic cells is a timely and key challenge for the cancer research community. In this respect, mathematical modelling can complement experimental cancer research by offering alternative means of understanding the results of in vitro and in vivo experiments, and by allowing for a quick and easy exploration of a variety of biological scenarios through in silico studies.

Results

To elucidate the roles of phenotypic plasticity and selection pressures in tumour relapse, we present here a phenotype-structured model of evolutionary dynamics in a cancer cell population which is exposed to the action of a cytotoxic drug. The analytical tractability of our model allows us to investigate how the phenotype distribution, the level of phenotypic heterogeneity, and the size of the cell population are shaped by the strength of natural selection, the rate of random epimutations, the intensity of the competition for limited resources between cells, and the drug dose in use.

Conclusions

Our analytical results clarify the conditions for the successful adaptation of cancer cells faced with environmental changes. Furthermore, the results of our analyses demonstrate that the same cell population exposed to different concentrations of the same cytotoxic drug can take different evolutionary trajectories, which culminate in the selection of phenotypic variants characterised by different levels of drug tolerance. This suggests that the response of cancer cells to cytotoxic agents is more complex than a simple binary outcome, i.e., extinction of sensitive cells and selection of highly resistant cells. Also, our mathematical results formalise the idea that the use of cytotoxic agents at high doses can act as a double-edged sword by promoting the outgrowth of drug resistant cellular clones. Overall, our theoretical work offers a formal basis for the development of anti-cancer therapeutic protocols that go beyond the ‘maximum-tolerated-dose paradigm’, as they may be more effective than traditional protocols at keeping the size of cancer cell populations under control while avoiding the expansion of drug tolerant clones.

Reviewers

This article was reviewed by Angela Pisco, Sébastien Benzekry and Heiko Enderling.

Electronic supplementary material

The online version of this article (doi:10.1186/s13062-016-0143-4) contains supplementary material, which is available to authorized users.

Cell population heterogeneity and evolution towards drug resistance in cancer: Biological and mathematical assessment, theoretical treatment optimisation

BACKGROUND

Drug-induced drug resistance in cancer has been attributed to diverse biological mechanisms at the individual cell or cell population scale, relying on stochastically or epigenetically varying expression of phenotypes at the single cell level, and on the adaptability of tumours at the cell population level.

SCOPE OF REVIEW

We focus on intra-tumour heterogeneity, namely between-cell variability within cancer cell populations, to account for drug resistance. To shed light on such heterogeneity, we review evolutionary mechanisms that encompass the great evolution that has designed multicellular organisms, as well as smaller windows of evolution on the time scale of human disease. We also present mathematical models used to predict drug resistance in cancer and optimal control methods that can circumvent it in combined therapeutic strategies.

MAJOR CONCLUSIONS

Plasticity in cancer cells, i.e., partial reversal to a stem-like status in individual cells and resulting adaptability of cancer cell populations, may be viewed as backward evolution making cancer cell populations resistant to drug insult. This reversible plasticity is captured by mathematical models that incorporate between-cell heterogeneity through continuous phenotypic variables. Such models have the benefit of being compatible with optimal control methods for the design of optimised therapeutic protocols involving combinations of cytotoxic and cytostatic treatments with epigenetic drugs and immunotherapies.

GENERAL SIGNIFICANCE

Gathering knowledge from cancer and evolutionary biology with physiologically based mathematical models of cell population dynamics should provide oncologists with a rationale to design optimised therapeutic strategies to circumvent drug resistance, that still remains a major pitfall of cancer therapeutics. This article is part of a Special Issue entitled "System Genetics" Guest Editor: Dr. Yudong Cai and Dr. Tao Huang.

Microenvironmental Niches and Sanctuaries: A Route to Acquired Resistance

A tumor vasculature that is functionally abnormal results in irregular gradients of metabolites and drugs within the tumor tissue. Recently, significant efforts have been committed to experimentally examine how cellular response to anti-cancer treatments varies based on the environment in which the cells are grown. In vitro studies point to specific conditions in which tumor cells can remain dormant and survive the treatment. In vivo results suggest that cells can escape the effects of drug therapy in tissue regions that are poorly penetrated by the drugs. Better understanding how the tumor microenvironments influence the emergence of drug resistance in both primary and metastatic tumors may improve drug development and the design of more effective therapeutic protocols. This chapter presents a hybrid agent-based model of the growth of tumor micrometastases and explores how microenvironmental factors can contribute to the development of acquired resistance in response to a DNA damaging drug. The specific microenvironments of interest in this work are tumor hypoxic niches and tumor normoxic sanctuaries with poor drug penetration. We aim to quantify how spatial constraints of limited drug transport and quiescent cell survival contribute to the development of drug resistant tumors.

Toward a Better Understanding of the Complexity of Cancer Drug Resistance

Resistance to anticancer drugs is a complex process that results from alterations in drug targets; development of alternative pathways for growth activation; changes in cellular pharmacology, including increased drug efflux; regulatory changes that alter differentiation pathways or pathways for response to environmental adversity; and/or changes in the local physiology of the cancer, such as blood supply, tissue hydrodynamics, behavior of neighboring cells, and immune system response. All of these specific mechanisms are facilitated by the intrinsic hallmarks of cancer, such as tumor cell heterogeneity, redundancy of growth-promoting pathways, increased mutation rate and/or epigenetic alterations, and the dynamic variation of tumor behavior in time and space. Understanding the relative contribution of each of these factors is further complicated by the lack of adequate in vitro models that mimic clinical cancers. Several strategies to use current knowledge of drug resistance to improve treatment of cancer are suggested.

Emergence of drug tolerance in cancer cell populations: an evolutionary outcome of selection, nongenetic instability, and stress-induced adaptation

In recent experiments on isogenetic cancer cell lines, it was observed that exposure to high doses of anticancer drugs can induce the emergence of a subpopulation of weakly proliferative and drug-tolerant cells, which display markers associated with stem cell-like cancer cells. After a period of time, some of the surviving cells were observed to change their phenotype to resume normal proliferation and eventually repopulate the sample. Furthermore, the drug-tolerant cells could be drug resensitized following drug washout. Here, we propose a theoretical mechanism for the transient emergence of such drug tolerance. In this framework, we formulate an individual-based model and an integro-differential equation model of reversible phenotypic evolution in a cell population exposed to cytotoxic drugs. The outcomes of both models suggest that nongenetic instability, stress-induced adaptation, selection, and the interplay between these mechanisms can push an actively proliferating cell population to transition into a weakly proliferative and drug-tolerant state. Hence, the cell population experiences much less stress in the presence of the drugs and, in the long run, reacquires a proliferative phenotype, due to phenotypic fluctuations and selection pressure. These mechanisms can also reverse epigenetic drug tolerance following drug washout. Our study highlights how the transient appearance of the weakly proliferative and drug-tolerant cells is related to the use of high-dose therapy. Furthermore, we show how stem-like characteristics can act to stabilize the transient, weakly proliferative, and drug-tolerant subpopulation for a longer time window. Finally, using our models as in silico laboratories, we propose new testable hypotheses that could help uncover general principles underlying the emergence of cancer drug tolerance.

Comparative sequencing analysis reveals high genomic concordance between matched primary and metastatic colorectal cancer lesions

Background

Colorectal cancer is the second leading cause of cancer death in the United States, with over 50,000 deaths estimated in 2014. Molecular profiling for somatic mutations that predict absence of response to anti-EGFR therapy has become standard practice in the treatment of metastatic colorectal cancer; however, the quantity and type of tissue available for testing is frequently limited. Further, the degree to which the primary tumor is a faithful representation of metastatic disease has been questioned. As next-generation sequencing technology becomes more widely available for clinical use and additional molecularly targeted agents are considered as treatment options in colorectal cancer, it is important to characterize the extent of tumor heterogeneity between primary and metastatic tumors.

Results

We performed deep coverage, targeted next-generation sequencing of 230 key cancer-associated genes for 69 matched primary and metastatic tumors and normal tissue. Mutation profiles were 100% concordant for KRAS, NRAS, and BRAF, and were highly concordant for recurrent alterations in colorectal cancer. Additionally, whole genome sequencing of four patient trios did not reveal any additional site-specific targetable alterations.

Conclusions

Colorectal cancer primary tumors and metastases exhibit high genomic concordance. As current clinical practices in colorectal cancer revolve around KRAS, NRAS, and BRAF mutation status, diagnostic sequencing of either primary or metastatic tissue as available is acceptable for most patients. Additionally, consistency between targeted sequencing and whole genome sequencing results suggests that targeted sequencing may be a suitable strategy for clinical diagnostic applications.

Electronic supplementary material

The online version of this article (doi:10.1186/s13059-014-0454-7) contains supplementary material, which is available to authorized users.

Combined therapeutic potential of nuclear receptors with receptor tyrosine kinase inhibitors in lung cancer

Cancer heterogeneity is a big hurdle in achieving complete cancer treatment, which has led to the emergence of combinational therapy. In this study, we investigated the potential use of nuclear receptor (NR) ligands for combinational therapy with other anti-cancer drugs. We first profiled all 48 NRs and 48 biological anti-cancer targets in four pairs of lung cell lines, where each pair was obtained from the same patient. Two sets of cell lines were normal and the corresponding tumor cell lines while the other two sets consisted of primary versus metastatic tumor cell lines. Analysis of the expression profile revealed 11 NRs and 15 cancer targets from the two pairs of normal versus tumor cell lines, and 9 NRs and 9 cancer targets from the primary versus metastatic tumor cell lines had distinct expression patterns in each category. Finally, the evaluation of nuclear receptor ligand T0901317 for liver X receptor (LXR) demonstrated its combined therapeutic potential with tyrosine kinase inhibitors. The combined treatment of cMET inhibitor PHA665752 or EGFR inhibitor gefitinib with T0901317 showed additive growth inhibition in both H2073 and H1993 cells. Mechanistically, the combined treatment suppressed cell cycle progression by inhibiting cyclinD1 and cyclinB expression. Taken together, this study provides insight into the potential use of NR ligands in combined therapeutics with other biological anti-cancer drugs.

The impact of cell density and mutations in a model of multidrug resistance in solid tumors

In this paper we develop a mathematical framework for describing multidrug resistance in cancer. To reflect the complexity of the underlying interplay between cancer cells and the therapeutic agent, we assume that the resistance level is a continuous parameter. Our model is written as a system of integro-differential equations that are parameterized by the resistance level. This model incorporates the cell density and mutation dependence. Analysis and simulations of the model demonstrate how the dynamics evolves to a selection of one or more traits corresponding to different levels of resistance. The emerging limit distribution with nonzero variance is the desirable modeling outcome as it represents tumor heterogeneity.

Simplifying the complexity of resistance heterogeneity in metastasis

The main goal of treatment regimens for metastasis is to control growth rates, not eradicate all cancer cells. Mathematical models offer methodologies that incorporate high-throughput data with dynamic effects on net growth. The ideal approach would simplify, but not over-simplify, a complex problem into meaningful and manageable estimators that predict the response of a patient to specific treatments. We explore here three fundamental approaches with different assumptions concerning resistance mechanisms in which the cells are categorized into either discrete compartments or described by a continuous range of resistance levels. We argue in favor of modeling resistance as a continuum, and demonstrate how integrating cellular growth rates, density-dependent versus exponential growth, and intratumoral heterogeneity improves predictions concerning the resistance heterogeneity of metastases.