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

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.

Unraveling the role of exercise in cancer suppression: insights from a mathematical model

Recent experimental studies have shown that physical exercise has the potential to suppress tumor progression. Such suppression has been reported to be mediated by the exercise-induced activation of natural killer (NK) cells through the release of IL-6, a cytokine. Aimed at shedding light on how exercise-induced NK cell activation helps in the suppression of cancer, we developed a coarse-grained mathematical model based on a system of ordinary differential equations describing the interaction between IL-6, NK-cells, and tumor cells. The model is then used to study how exercise duration and exercise intensity affect tumor suppression. Our results show that increasing exercise intensity or increasing exercise duration leads to greater and sustained tumor suppression. Furthermore, multi-bout exercise patterns hold promise for improving cancer treatment strategies by adjusting exercise intensity and frequency. Thus, the proposed mathematical model provides insights into the role of exercise in tumor suppression and can be instrumental in guiding future experimental studies, potentially leading to more effective exercise interventions.

A modelling framework for cancer ecology and evolution

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

Threshold-awareness in adaptive cancer therapy

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

Mathematical modeling of the evolution of resistance and aggressiveness of high-grade serous ovarian cancer from patient CA-125 time series

A time-series analysis of serum Cancer Antigen 125 (CA-125) levels was performed in 791 patients with high-grade serous ovarian cancer (HGSOC) from the Australian Ovarian Cancer Study to evaluate the development of chemoresistance and response to therapy. To investigate chemoresistance and better predict the treatment effectiveness, we examined two traits: resistance (defined as the rate of CA-125 change when patients were treated with therapy) and aggressiveness (defined as the rate of CA-125 change when patients were not treated). We found that as the number of treatment lines increases, the data-based resistance increases (a decreased rate of CA-125 decay). We use mathematical models of two distinct cancer cell types, treatment-sensitive cells and treatment-resistant cells, to estimate the values and evolution of the two traits in individual patients. By fitting to individual patient HGSOC data, our models successfully capture the dynamics of the CA-125 level. The parameters estimated from the mathematical models show that patients with inferred low growth rates of treatment-sensitive cells and treatment-resistant cells (low model-estimated aggressiveness) and a high death rate of treatment-resistant cells (low model-estimated resistance) have longer survival time after completing their second-line of therapy. These findings show that mathematical models can characterize the degree of resistance and aggressiveness in individual patients, which improves our understanding of chemoresistance development and could predict treatment effectiveness in HGSOC patients.

Mathematical modeling of combined therapies for treating tumor drug resistance

Drug resistance is one of the most intractable issues to the targeted therapy for cancer diseases. To explore effective combination therapy schemes, we propose a mathematical model to study the effects of different treatment schemes on the dynamics of cancer cells. Then we characterize the dynamical behavior of the model by finding the equilibrium points and exploring their local stability. Lyapunov functions are constructed to investigate the global asymptotic stability of the model equilibria. Numerical simulations are carried out to verify the stability of equilibria and treatment outcomes using a set of collected model parameters and experimental data on murine colon carcinoma. Simulation results suggest that immunotherapy combined with chemotherapy contributes significantly to the control of tumor growth compared to monotherapy. Sensitivity analysis is performed to identify the importance of model parameters on the variations of model outcomes.

Phenotype-structured model of intra-clonal heterogeneity and drug resistance in multiple myeloma

Multiple myeloma (MM) is a genetically complex hematological cancer characterized by the abnormal proliferation of malignant plasma cells in the bone marrow. This disease progresses from a premalignant condition known as monoclonal gammopathy of unknown significance (MGUS) through sequential genetic alterations involving various genes. These genetic changes contribute to the uncontrolled growth of multiple clones of plasma cells. In this study, we present a phenotype-structured model that captures the intra-clonal heterogeneity and drug resistance in multiple myeloma (MM). The model accurately reproduces the branching evolutionary pattern observed in MM progression, aligning with a previously developed multiscale model. Numerical simulations reveal that higher mutation rates enhance tumor phenotype diversity, while access to growth factors accelerates tumor evolution and increases its final size. Interestingly, the model suggests that further increasing growth factor access primarily amplifies tumor size rather than altering clonal dynamics. Additionally, the model emphasizes that higher mutation frequencies and growth factor availability elevate the chances of drug resistance and relapse. It indicates that the timing of the treatment could trajectory of tumor evolution and clonal emergence in the case of branching evolutionary pattern. Given its low computational cost, our model is well-suited for quantitative studies on MM clonal heterogeneity and its interaction with chemotherapeutic treatments.

Camptothecin-based prodrug nanomedicines for cancer therapy

Camptothecin (CPT) is a cytotoxic alkaloid that attenuates the replication of cancer cells via blocking DNA topoisomerase 1. Despite its encouraging and wide-spectrum antitumour activity, its application is significantly restricted owing to its instability, low solubility, significant toxicity, and acquired tumour cell resistance. This has resulted in the development of many CPT-based therapeutic agents, especially CPT-based nanomedicines, with improved pharmacokinetic and pharmacodynamic profiles. Specifically, smart CPT-based prodrug nanomedicines with stimuli-responsive release capacity have been extensively explored owing to the advantages such as high drug loading, improved stability, and decreased potential toxicity caused by the carrier materials in comparison with normal nanodrugs and traditional delivery systems. In this review, the potential strategies and applications of CPT-based nanoprodrugs for enhanced CPT delivery toward cancer cells are summarized. We appraise in detail the chemical structures and release mechanisms of these nanoprodrugs and guide materials chemists to develop more powerful nanomedicines that have real clinical therapeutic capacities.

Patterning of nonlocal transport models in biology: The impact of spatial dimension

Throughout developmental biology and ecology, transport can be driven by nonlocal interactions. Examples include cells that migrate based on contact with pseudopodia extended from other cells, and animals that move based on their awareness of other animals. Nonlocal integro-PDE models have been used to investigate contact attraction and repulsion in cell populations in 1D. In this paper, we generalise the analysis of pattern formation in such a model from 1D to higher spatial dimensions. Numerical simulations in 2D demonstrate complex behaviour in the model, including spatio-temporal patterns, multi-stability, and patterns with wavelength and shape that differ significantly depending on whether interactions are attractive or repulsive. Through linear stability analysis in N dimensions, we demonstrate how, unlike in local Turing reaction-diffusion models, the capacity for pattern formation fundamentally changes with dimensionality for this nonlocal model. Most notably, pattern formation is possible only in higher than one spatial dimension for both the single species system with repulsive interactions, and the two species system with 'run-and-chase' interactions. The latter case may be relevant to zebrafish stripe formation, which has been shown to be driven by run-and-chase dynamics between melanophore and xanthophore pigment cells.

DDQN-based optimal targeted therapy with reversible inhibitors to combat the Warburg effect

We cover the Warburg effect with a three-component evolutionary model, where each component represents a different metabolic strategy. In this context, a scenario involving cells expressing three different phenotypes is presented. One tumour phenotype exhibits glycolytic metabolism through glucose uptake and lactate secretion. Lactate is used by a second malignant phenotype to proliferate. The third phenotype represents healthy cells, which performs oxidative phosphorylation. The purpose of this model is to gain a better understanding of the metabolic alterations associated with the Warburg effect. It is suitable to reproduce some of the clinical trials obtained in colorectal cancer and other even more aggressive tumours. It shows that lactate is an indicator of poor prognosis, since it favours the setting of polymorphic tumour equilibria that complicates its treatment. This model is also used to train a reinforcement learning algorithm, known as Double Deep Q-networks, in order to provide the first optimal targeted therapy based on experimental tumour growth inhibitors as genistein and AR-C155858. Our in silico solution includes the optimal therapy for all the tumour state space and also ensures the best possible quality of life for the patients, by considering the duration of treatment, the use of low-dose medications and the existence of possible contraindications. Optimal therapies obtained with Double Deep Q-networks are validated with the solutions of the Hamilton-Jacobi-Bellman equation.

A critical review on the dissemination of PH and stimuli-responsive polymeric nanoparticular systems to improve drug delivery in cancer therapy

Stimuli-responsive nanocarriers have the potential to revolutionize cancer treatment by allowing precise delivery of drugs to the site of disease. The use of polymeric nanocarriers with surfaces that respond to triggers such as pH, light, temperature, and redox potential enables targeted drug distribution. pH is a particularly useful tool, as the lower pH in tumour microenvironments can trigger changes in drug release. Recent advances in the development of pH-responsive polymer nanoparticles have shown great promise for improved in vivo drug delivery, reduced negative drug responses, and more precise drug distribution. A deeper understanding of these nanocarriers will allow us to overcome the challenges of targeted cancer treatment and create a better drug delivery system.

Spatio-temporal modelling of phenotypic heterogeneity in tumour tissues and its impact on radiotherapy treatment

We present a mathematical model that describes how tumour heterogeneity evolves in a tissue slice that is oxygenated by a single blood vessel. Phenotype is identified with the stemness level of a cell and determines its proliferative capacity, apoptosis propensity and response to treatment. Our study is based on numerical bifurcation analysis and dynamical simulations of a system of coupled, non-local (in phenotypic "space") partial differential equations that link the phenotypic evolution of the tumour cells to local tissue oxygen levels. In our formulation, we consider a 1D geometry where oxygen is supplied by a blood vessel located on the domain boundary and consumed by the tumour cells as it diffuses through the tissue. For biologically relevant parameter values, the system exhibits multiple steady states; in particular, depending on the initial conditions, the tumour is either eliminated ("tumour-extinction") or it persists ("tumour-invasion"). We conclude by using the model to investigate tumour responses to radiotherapy, and focus on identifying radiotherapy strategies which can eliminate the tumour. Numerical simulations reveal how phenotypic heterogeneity evolves during treatment and highlight the critical role of tissue oxygen levels on the efficacy of radiation protocols that are commonly used in the clinic.

Scales of Cancer Evolution: Selfish Genome or Cooperating Cells?

Simple Summary

Cancer continuously evolves its ability to survive in time-varying microenvironment, which results, regarding the therapeutic context, in its therapeutic resistance. As it is accepted that the development of resistance is the direct consequence of intratumour heterogeneity, its evolutionary etiology is intensively studied. Models of carinogenesis are often assessed accordingly to how well they fit into the evolutionary scenario. In the paper, the relevant observations and concepts in cancer research, such as intratumour heterogeneity, cell plasticity, and Markov cell state dynamics, are reviewed and integrated into an evolutionary model. The possibility that the interaction between cancer cells can be interpreted as cooperation is proposed.

Abstract

The exploitation of the evolutionary modus operandi of cancer to steer its progression towards drug sensitive cancer cells is a challenging research topic. Integrating evolutionary principles into cancer therapy requires properly identified selection level, the relevant timescale, and the respective fitness of the principal selection unit on that timescale. Interpretation of some features of cancer progression, such as increased heterogeneity of isogenic cancer cells, is difficult from the most straightforward evolutionary view with the cancer cell as the principal selection unit. In the paper, the relation between the two levels of intratumour heterogeneity, genetic, due to genetic instability, and non-genetic, due to phenotypic plasticity, is reviewed and the evolutionary role of the latter is outlined. In analogy to the evolutionary optimization in a changing environment, the cell state dynamics in cancer clones are interpreted as the risk diversifying strategy bet hedging, optimizing the balance between the exploitation and exploration of the cell state space.

Identifying cell-to-cell variability in internalization using flow cytometry

Biological heterogeneity is a primary contributor to the variation observed in experiments that probe dynamical processes, such as the internalization of material by cells. Given that internalization is a critical process by which many therapeutics and viruses reach their intracellular site of action, quantifying cell-to-cell variability in internalization is of high biological interest. Yet, it is common for studies of internalization to neglect cell-to-cell variability. We develop a simple mathematical model of internalization that captures the dynamical behaviour, cell-to-cell variation, and extrinsic noise introduced by flow cytometry. We calibrate our model through a novel distribution-matching approximate Bayesian computation algorithm to flow cytometry data of internalization of anti-transferrin receptor antibody in a human B-cell lymphoblastoid cell line. This approach provides information relating to the region of the parameter space, and consequentially the nature of cell-to-cell variability, that produces model realizations consistent with the experimental data. Given that our approach is agnostic to sample size and signal-to-noise ratio, our modelling framework is broadly applicable to identify biological variability in single-cell data from internalization assays and similar experiments that probe cellular dynamical processes.

Experimental Determination of Cancer Drug Targets with Independent Mechanisms of Resistance

Mathematical modelling of tumour mutation dynamics has suggested that cancer drug targets that have different resistance mechanisms should be good candidates for combination treatment. This is because the development of mutations that cause resistance to all drugs at once should arise relatively infrequently. However, it is difficult to identify drug targets fulfilling this requirement for particular cancers. Here we present four experimental criteria that we argue are necessary (but not sufficient) conditions that drug combinations should meet in order to be considered for combination drug treatment aimed at delaying or overcoming cancer drug resistance. We present the results of our own experiments - guided by these criteria - using anaplastic lymphoma kinase mutated lung cancer cells. Each set of experiments demonstrate results for different drug combinations. We conclude that the combination of ALK and MEK inhibitors come closest to meeting all our criteria.

Improving cancer treatments via dynamical biophysical models

Despite significant advances in oncological research, cancer nowadays remains one of the main causes of mortality and morbidity worldwide. New treatment techniques, as a rule, have limited efficacy, target only a narrow range of oncological diseases, and have limited availability to the general public due their high cost. An important goal in oncology is thus the modification of the types of antitumor therapy and their combinations, that are already introduced into clinical practice, with the goal of increasing the overall treatment efficacy. One option to achieve this goal is optimization of the schedules of drugs administration or performing other medical actions. Several factors complicate such tasks: the adverse effects of treatments on healthy cell populations, which must be kept tolerable; the emergence of drug resistance due to the intrinsic plasticity of heterogeneous cancer cell populations; the interplay between different types of therapies administered simultaneously. Mathematical modeling, in which a tumor and its microenvironment are considered as a single complex system, can address this complexity and can indicate potentially effective protocols, that would require experimental verification. In this review, we consider classical methods, current trends and future prospects in the field of mathematical modeling of tumor growth and treatment. In particular, methods of treatment optimization are discussed with several examples of specific problems related to different types of treatment.

Darwinian Approaches for Cancer Treatment: Benefits of Mathematical Modeling

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

Single-Cell RNA Sequencing Reveals Cellular Heterogeneity and Stage Transition under Temperature Stress in Synchronized Plasmodium falciparum Cells

The malaria parasite has a complex life cycle exhibiting phenotypic and morphogenic variations in two different hosts by existing in heterogeneous developmental states. To investigate this cellular heterogeneity of the parasite within the human host, we performed single-cell RNA sequencing of synchronized Plasmodium cells under control and temperature treatment conditions. Using the Malaria Cell Atlas (https://www.sanger.ac.uk/science/tools/mca) as a guide, we identified 9 subtypes of the parasite distributed across known intraerythrocytic stages. Interestingly, temperature treatment results in the upregulation of the AP2-G gene, the master regulator of sexual development in a small subpopulation of the parasites. Moreover, we identified a heterogeneous stress-responsive subpopulation (clusters 5, 6, and 7 [∼10% of the total population]) that exhibits upregulation of stress response pathways under normal growth conditions. We also developed an online exploratory tool that will provide new insights into gene function under normal and temperature stress conditions. Thus, our study reveals important insights into cell-to-cell heterogeneity in the parasite population under temperature treatment that will be instrumental toward a mechanistic understanding of cellular adaptation and population dynamics in Plasmodium falciparum. IMPORTANCE The malaria parasite has a complex life cycle exhibiting phenotypic variations in two different hosts accompanied by cell-to-cell variability that is important for stress tolerance, immune evasion, and drug resistance. To investigate cellular heterogeneity determined by gene expression, we performed single-cell RNA sequencing (scRNA-seq) of about 12,000 synchronized Plasmodium cells under physiologically relevant normal (37°C) and temperature stress (40°C) conditions phenocopying the cyclic bouts of fever experienced during malarial infection. In this study, we found that parasites exhibit transcriptional heterogeneity in an otherwise morphologically synchronized culture. Also, a subset of parasites is continually committed to gametocytogenesis and stress-responsive pathways. These observations have important implications for understanding the mechanisms of drug resistance generation and vaccine development against the malaria parasite.

On Systems of Active Particles Perturbed by Symmetric Bounded Noises: A Multiscale Kinetic Approach

We consider an ensemble of active particles, i.e., of agents endowed by internal variables u(t). Namely, we assume that the nonlinear dynamics of u is perturbed by realistic bounded symmetric stochastic perturbations acting nonlinearly or linearly. In the absence of birth, death and interactions of the agents (BDIA) the system evolution is ruled by a multidimensional Hypo-Elliptical Fokker–Plank Equation (HEFPE). In presence of nonlocal BDIA, the resulting family of models is thus a Partial Integro-differential Equation with hypo-elliptical terms. In the numerical simulations we focus on a simple case where the unperturbed dynamics of the agents is of logistic type and the bounded perturbations are of the Doering–Cai–Lin noise or the Arctan bounded noise. We then find the evolution and the steady state of the HEFPE. The steady state density is, in some cases, multimodal due to noise-induced transitions. Then we assume the steady state density as the initial condition for the full system evolution. Namely we modeled the vital dynamics of the agents as logistic nonlocal, as it depends on the whole size of the population. Our simulations suggest that both the steady states density and the total population size strongly depends on the type of bounded noise. Phenomena as transitions to bimodality and to asymmetry also occur.

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

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

Cancer recurrence and lethality are enabled by enhanced survival and reversible cell cycle arrest of polyaneuploid cells

We present a unifying theory to explain cancer recurrence, therapeutic resistance, and lethality. The basis of this theory is the formation of simultaneously polyploid and aneuploid cancer cells, polyaneuploid cancer cells (PACCs), that avoid the toxic effects of systemic therapy by entering a state of cell cycle arrest. The theory is independent of which of the classically associated oncogenic mutations have already occurred. PACCs have been generally disregarded as senescent or dying cells. Our theory states that therapeutic resistance is driven by PACC formation that is enabled by accessing a polyploid program that allows an aneuploid cancer cell to double its genomic content, followed by entry into a nondividing cell state to protect DNA integrity and ensure cell survival. Upon removal of stress, e.g., chemotherapy, PACCs undergo depolyploidization and generate resistant progeny that make up the bulk of cancer cells within a tumor.

A Mathematical Study of the Influence of Hypoxia and Acidity on the Evolutionary Dynamics of Cancer

Hypoxia and acidity act as environmental stressors promoting selection for cancer cells with a more aggressive phenotype. As a result, a deeper theoretical understanding of the spatio-temporal processes that drive the adaptation of tumour cells to hypoxic and acidic microenvironments may open up new avenues of research in oncology and cancer treatment. We present a mathematical model to study the influence of hypoxia and acidity on the evolutionary dynamics of cancer cells in vascularised tumours. The model is formulated as a system of partial integro-differential equations that describe the phenotypic evolution of cancer cells in response to dynamic variations in the spatial distribution of three abiotic factors that are key players in tumour metabolism: oxygen, glucose and lactate. The results of numerical simulations of a calibrated version of the model based on real data recapitulate the eco-evolutionary spatial dynamics of tumour cells and their adaptation to hypoxic and acidic microenvironments. Moreover, such results demonstrate how nonlinear interactions between tumour cells and abiotic factors can lead to the formation of environmental gradients which select for cells with phenotypic characteristics that vary with distance from intra-tumour blood vessels, thus promoting the emergence of intra-tumour phenotypic heterogeneity. Finally, our theoretical findings reconcile the conclusions of earlier studies by showing that the order in which resistance to hypoxia and resistance to acidity arise in tumours depend on the ways in which oxygen and lactate act as environmental stressors in the evolutionary dynamics of cancer cells.

The role of non-genetic information in evolutionary frameworks

The evolution of organisms has been a subject of paramount debate for hundreds of years and though major advances in the field have been made, the precise mechanisms underlying evolutionary processes remain fragmentary. Strikingly, the majority of the core principles accepted across the many fields of biology only consider genetic information as the major - if not exclusive - biological information carrier and thus consider it as the main evolutionary avatar. However, the real picture appears far more complex than originally anticipated, as compelling data suggest that nongenetic information steps up when highly dynamic evolutionary frameworks are explored. In light of recent evidence, we discuss herein the dynamic nature and complexity of nongenetic information carriers, and their emerging relevance in the evolutionary process. We argue that it is possible to overcome the historical arguments which dismissed these carriers, and instead consider that they are indeed core to life itself as they support a sustainable, continuous source of rapid adaptation in ever-changing environments. Ultimately, we will address the intricacies of genetic and non-genetic networks underlying evolutionary models to build a framework where both core biological information concepts are considered non-negligible and equally fundamental.

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.

In silico trials predict that combination strategies for enhancing vesicular stomatitis oncolytic virus are determined by tumor aggressivity

Background

Immunotherapies, driven by immune-mediated antitumorigenicity, offer the potential for significant improvements to the treatment of multiple cancer types. Identifying therapeutic strategies that bolster antitumor immunity while limiting immune suppression is critical to selecting treatment combinations and schedules that offer durable therapeutic benefits. Combination oncolytic virus (OV) therapy, wherein complementary OVs are administered in succession, offer such promise, yet their translation from preclinical studies to clinical implementation is a major challenge. Overcoming this obstacle requires answering fundamental questions about how to effectively design and tailor schedules to provide the most benefit to patients.

Methods

We developed a computational biology model of combined oncolytic vaccinia (an enhancer virus) and vesicular stomatitis virus (VSV) calibrated to and validated against multiple data sources. We then optimized protocols in a cohort of heterogeneous virtual individuals by leveraging this model and our previously established in silico clinical trial platform.

Results

Enhancer multiplicity was shown to have little to no impact on the average response to therapy. However, the duration of the VSV injection lag was found to be determinant for survival outcomes. Importantly, through treatment individualization, we found that optimal combination schedules are closely linked to tumor aggressivity. We predicted that patients with aggressively growing tumors required a single enhancer followed by a VSV injection 1 day later, whereas a small subset of patients with the slowest growing tumors needed multiple enhancers followed by a longer VSV delay of 15 days, suggesting that intrinsic tumor growth rates could inform the segregation of patients into clinical trials and ultimately determine patient survival. These results were validated in entirely new cohorts of virtual individuals with aggressive or non-aggressive subtypes.

Conclusions

Based on our results, improved therapeutic schedules for combinations with enhancer OVs can be studied and implemented. Our results further underline the impact of interdisciplinary approaches to preclinical planning and the importance of computational approaches to drug discovery and development.

Cancer cells employ an evolutionarily conserved polyploidization program to resist therapy

Unusually large cancer cells with abnormal nuclei have been documented in the cancer literature since 1858. For more than 100 years, they have been generally disregarded as irreversibly senescent or dying cells, too morphologically misshapen and chromatin too disorganized to be functional. Cell enlargement, accompanied by whole genome doubling or more, is observed across organisms, often associated with mitigation strategies against environmental change, severe stress, or the lack of nutrients. Our comparison of the mechanisms for polyploidization in other organisms and non-transformed tissues suggest that cancer cells draw from a conserved program for their survival, utilizing whole genome doubling and pausing proliferation to survive stress. These polyaneuploid cancer cells (PACCs) are the source of therapeutic resistance, responsible for cancer recurrence and, ultimately, cancer lethality.

Establishing patient-tailored variability-based paradigms for anti-cancer therapy: Using the inherent trajectories which underlie cancer for overcoming drug resistance

Drug resistance is a major obstacle for successful therapy of many malignancies and is affecting the loss of response to chemotherapy and immunotherapy. Tumor-related compensatory adaptation mechanisms contribute to the development of drug resistance. Variability is inherent to biological systems and altered patterns of variability are associated with disease conditions. The marked intra and inter patient tumor heterogeneity, and the diverse mechanism contributing to drug resistance in different subjects, which may change over time even in the same patient, necessitate the development of personalized dynamic approaches for overcoming drug resistance. Altered dosing regimens, the potential role of chronotherapy, and drug holidays are effective in cancer therapy and immunotherapy. In the present review we describe the difficulty of overcoming drug resistance in a dynamic system and present the use of the inherent trajectories which underlie cancer development for building therapeutic regimens which can overcome resistance. The establishment of a platform wherein patient-tailored variability signatures are used for overcoming resistance for ensuing long term sustainable improved responses is presented.

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

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

Chitosan based pH-responsive polymeric prodrug vector for enhanced tumor targeted co-delivery of doxorubicin and siRNA

The co-delivery of chemotherapeutic drugs and siRNA has gained increasing attentions owing to the enhanced antitumor efficacy over single administration. In this work, a chitosan-based pH-responsive prodrug vector was developed for the co-delivery of doxorubicin (DOX) and Bcl-2 siRNA. The accumulation of fabricated nanoparticles in hepatoma cells was enhanced by glycyrrhetinic acid receptor-mediated endocytosis. The cumulative release amount of the encapsulated DOX and siRNA reached 90.2 % and 81.3 % in 10 h, respectively. More strikingly, this nanoplatform can efficiently integrate gene- and chemo-therapies with a dramatically enhanced tumor inhibitory rate (88.0 %) in vivo. This co-delivery system may provide the latest strategy to meet the needs of combination therapies for tumors, offering safe and efficient improvements to the synergistic antitumor efficacy of gene-chemotherapies.

Synergisms of genome and metabolism stabilizing antitumor therapy (GMSAT) in human breast and colon cancer cell lines: a novel approach to screen for synergism

BACKGROUND

Despite an improvement of prognosis in breast and colon cancer, the outcome of the metastatic disease is still severe. Microevolution of cancer cells often leads to drug resistance and tumor-recurrence. To target the driving forces of the tumor microevolution, we focused on synergistic drug combinations of selected compounds. The aim is to prevent the tumor from evolving in order to stabilize disease remission. To identify synergisms in a high number of compounds, we propose here a three-step concept that is cost efficient, independent of high-throughput machines and reliable in its predictions.

METHODS

We created dose response curves using MTT- and SRB-assays with 14 different compounds in MCF-7, HT-29 and MDA-MB-231 cells. In order to efficiently screen for synergies, we developed a screening tool in which 14 drugs were combined (91 combinations) in MCF-7 and HT-29 using EC25 or less. The most promising combinations were verified by the method of Chou and Talalay.

RESULTS

All 14 compounds exhibit antitumor effects on each of the three cell lines. The screening tool resulted in 19 potential synergisms detected in HT-29 (20.9%) and 27 in MCF-7 (29.7%). Seven of the top combinations were further verified over the whole dose response curve, and for five combinations a significant synergy could be confirmed. The combination Nutlin-3 (inhibition of MDM2) and PX-478 (inhibition of HIF-1α) could be confirmed for all three cell lines. The same accounts for the combination of Dichloroacetate (PDH activation) and NHI-2 (LDH-A inhibition). Our screening method proved to be an efficient tool that is reliable in its projections.

CONCLUSIONS

The presented three-step concept proved to be cost- and time-efficient with respect to the resulting data. The newly found combinations show promising results in MCF-7, HT-29 and MDA-MB231 cancer cells.

Cell plasticity in cancer cell populations

In this review, we propose a recension of biological observations on plasticity in cancer cell populations and discuss theoretical considerations about their mechanisms.

Convergent Evolution, Evolving Evolvability, and the Origins of Lethal Cancer

Advances in curative treatment to remove the primary tumor have increased survival of localized cancers for most solid tumor types, yet cancers that have spread are typically incurable and account for >90% of cancer-related deaths. Metastatic disease remains incurable because, somehow, tumors evolve resistance to all known compounds, including therapies. In all of these incurable patients, de novo lethal cancer evolves capacities for both metastasis and resistance. Therefore, cancers in different patients appear to follow the same eco-evolutionary path that independently manifests in affected patients. This convergent outcome, that always includes the ability to metastasize and exhibit resistance, demands an explanation beyond the slow and steady accrual of stochastic mutations. The common denominator may be that cancer starts as a speciation event when a unicellular protist breaks away from its multicellular host and initiates a cancer clade within the patient. As the cancer cells speciate and diversify further, some evolve the capacity to evolve: evolvability. Evolvability becomes a heritable trait that influences the available variation of other phenotypes that can then be acted upon by natural selection. Evolving evolvability may be an adaptation for cancer cells. By generating and maintaining considerable heritable variation, the cancer clade can, with high certainty, serendipitously produce cells resistant to therapy and cells capable of metastasizing. Understanding that cancer cells can swiftly evolve responses to novel and varied stressors create opportunities for adaptive therapy, double-bind therapies, and extinction therapies; all involving strategic decision making that steers and anticipates the convergent coevolutionary responses of the cancers.

Guizhi Fuling Decoction inhibiting the PI3K and MAPK pathways in breast cancer cells revealed by HTS2 technology and systems pharmacology

As one of the classical traditional Chinese medicine (TCM) prescriptions in treating gynecological tumors, Guizhi Fuling Decoction (GFD) has been used to treat breast cancer (BRCA). Nonetheless, the potential molecular mechanism remains unclear so far. Therefore, systems pharmacology was used in combination with high throughput sequencing-based high throughput screening (HTS2) assay and bioinformatic technologies in this study to investigate the molecular mechanisms of GFD in treating BRCA. By computationally analyzing 76 active ingredients in GFD, 38 potential therapeutic targets were predicted and significantly enriched in the "pathways in cancer". Meanwhile, experimental analysis was carried out to examine changes in the expression levels of 308 genes involved in the "pathways in cancer" in BRCA cells treated by five herbs of GFD utilizing HTS2 platform, and 5 key therapeutic targets, including HRAS, EGFR, PTK2, SOS1, and ITGB1, were identified. The binding mode of active compounds to these five targets was analyzed by molecular docking and molecular dynamics simulation. It was found after integrating the computational and experimental data that, GFD possessed the anti-proliferation, pro-apoptosis, and anti-angiogenesis activities mainly through regulating the PI3K and the MAPK signaling pathways to inhibit BRCA. Besides, consistent with the TCM theory about the synergy of Cinnamomi Ramulus (Guizhi) by Cortex Moutan (Mudanpi) in GFD, both of these two herbs acted on the same targets and pathways. Taken together, the combined application of computational systems pharmacology techniques and experimental HTS2 platform provides a practical research strategy to investigate the functional and biological mechanisms of the complicated TCM prescriptions.

Transcompp: understanding phenotypic plasticity by estimating Markov transition rates for cell state transitions

MOTIVATION

Gradual population-level changes in tissues can be driven by stochastic plasticity, meaning rare stochastic transitions of single-cell phenotype. Quantifying the rates of these stochastic transitions requires time-intensive experiments, and analysis is generally confounded by simultaneous bidirectional transitions and asymmetric proliferation kinetics. To quantify cellular plasticity, we developed Transcompp (Transition Rate ANalysis of Single Cells to Observe and Measure Phenotypic Plasticity), a Markov modeling algorithm that uses optimization and resampling to compute best-fit rates and statistical intervals for stochastic cell-state transitions.

RESULTS

We applied Transcompp to time-series datasets in which purified subpopulations of stem-like or non-stem cancer cells were exposed to various cell culture environments, and allowed to re-equilibrate spontaneously over time. Results revealed that commonly used cell culture reagents hydrocortisone and cholera toxin shifted the cell population equilibrium toward stem-like or non-stem states, respectively, in the basal-like breast cancer cell line MCF10CA1a. In addition, applying Transcompp to patient-derived cells showed that transition rates computed from short-term experiments could predict long-term trajectories and equilibrium convergence of the cultured cell population.

AVAILABILITY AND IMPLEMENTATION

Freely available for download at http://github.com/nsuhasj/Transcompp.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

In Silico implementation of evolutionary paradigm in therapy design: Towards anti-cancer therapy as Darwinian process

In here presented in silico study we suggest a way how to implement the evolutionary principles into anti-cancer therapy design. We hypothesize that instead of its ongoing supervised adaptation, the therapy may be constructed as a self-sustaining evolutionary process in a dynamic fitness landscape established implicitly by evolving cancer cells, microenvironment and the therapy itself. For these purposes, we replace a unified therapy with the 'therapy species', which is a population of heterogeneous elementary therapies, and propose a way how to turn the toxicity of the elementary therapy into its fitness in a way conforming to evolutionary causation. As a result, not only the therapies govern the evolution of different cell phenotypes, but the cells' resistances govern the evolution of the therapies as well. We illustrate the approach by the minimalistic ad hoc evolutionary model. Its results indicate that the resistant cells could bias the evolution towards more toxic elementary therapies by inhibiting the less toxic ones. As the evolutionary causation of cancer drug resistance has been intensively studied for a few decades, we refer to cancer as a special case to illustrate purely theoretical analysis.

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.

Stochastic modeling of phenotypic switching and chemoresistance in cancer cell populations

Phenotypic heterogeneity in cancer cells is widely observed and is often linked to drug resistance. In several cases, such heterogeneity in drug sensitivity of tumors is driven by stochastic and reversible acquisition of a drug tolerant phenotype by individual cells even in an isogenic population. Accumulating evidence further suggests that cell-fate transitions such as the epithelial to mesenchymal transition (EMT) are associated with drug resistance. In this study, we analyze stochastic models of phenotypic switching to provide a framework for analyzing cell-fate transitions such as EMT as a source of phenotypic variability in drug sensitivity. Motivated by our cell-culture based experimental observations connecting phenotypic switching in EMT and drug resistance, we analyze a coarse-grained model of phenotypic switching between two states in the presence of cytotoxic stress from chemotherapy. We derive analytical results for time-dependent probability distributions that provide insights into the rates of phenotypic switching and characterize initial phenotypic heterogeneity of cancer cells. The results obtained can also shed light on fundamental questions relating to adaptation and selection scenarios in tumor response to cytotoxic therapy.

KDM5 Histone Demethylase Activity Links Cellular Transcriptomic Heterogeneity to Therapeutic Resistance

Members of the KDM5 histone H3 lysine 4 demethylase family are associated with therapeutic resistance, including endocrine resistance in breast cancer, but the underlying mechanism is poorly defined. Here we show that genetic deletion of KDM5A/B or inhibition of KDM5 activity increases sensitivity to anti-estrogens by modulating estrogen receptor (ER) signaling and by decreasing cellular transcriptomic heterogeneity. Higher KDM5B expression levels are associated with higher transcriptomic heterogeneity and poor prognosis in ER⁺ breast tumors. Single-cell RNA sequencing, cellular barcoding, and mathematical modeling demonstrate that endocrine resistance is due to selection for pre-existing genetically distinct cells, while KDM5 inhibitor resistance is acquired. Our findings highlight the importance of cellular phenotypic heterogeneity in therapeutic resistance and identify KDM5A/B as key regulators of this process.

Global stability with selection in integro-differential Lotka-Volterra systems modelling trait-structured populations

We analyse the asymptotic behaviour of integro-differential equations modelling N populations in interaction, all structured by different traits. Interactions are modelled by non-local terms involving linear combinations of the total number of individuals in each population. These models have already been shown to be suitable for the modelling of drug resistance in cancer, and they generalize the usual Lotka-Volterra ordinary differential equations. Our aim is to give conditions under which there is persistence of all species. Through the analysis of a Lyapunov function, our first main result gives a simple and general condition on the matrix of interactions, together with a convergence rate. The second main result establishes another type of condition in the specific case of mutualistic interactions. When either of these conditions is met, we describe which traits are asymptotically selected.

A Dynamic-Shape-Prior Guided Snake Model with Application in Visually Tracking Dense Cell Populations

This work proposes a dynamic-shape-prior guided snake model (DSP G-snake) that is designed to improve the overall stability of the point-based snake model. The dynamic shape prior is first proposed for snakes, that efficiently unifies different types of high-level priors into a new force term. To be specific, a global-topology regularity is first introduced that settles the inherent self-intersection problem with snakes. The problem that a snake's snaxels tend to unevenly distribute along the contour is also handled, leading to good parameterization. Unlike existing methods that employ learning templates or commonly enforce hard priors, the dynamic-template scheme strongly respects the deformation flexibility of the model, while retaining a decent global topology for the snake. It is verified by experiments that the proposed algorithm can effectively prevent snakes from self-crossing, or automatically untie an already selfintersected contour. In addition, the proposed model is combined with existing forces and applied to the very challenging task of tracking dense biological cell populations. The DSP G-snake model has enabled an improvement of up to 30% in tracking accuracy with respect to regular model-based approaches. Through experiments on real cellular datasets, with highly dense populations and relatively large displacements, it is confirmed that the proposed approach has enabled superior performance, in comparison to modern active-contour competitors as well as state-of-the-art cell tracking frameworks.

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.

A multiscale modelling approach for the regulation of the cell cycle by the circadian clock

We present a multiscale mathematical model for the regulation of the cell cycle by the circadian clock. Biologically, the model describes the proliferation of a population of heterogeneous cells connected to each other. The model consists of a high dimensional transport equation structured by molecular contents of the cell cycle-circadian clock coupled oscillator. We propose a computational method for resolution adapted from the concept of particle methods. We study the impact of molecular dynamics on cell proliferation and show an example where discordance of division rhythms between population and single cell levels is observed. This highlights the importance of multiscale modeling where such results cannot be inferred from considering solely one biological level.

The flashlights on a distinct role of protein kinase C δ: Phosphorylation of regulatory and catalytic domain upon oxidative stress in glioma cells

Glioblastoma multiforme are considered to be aggressive high-grade tumors with poor prognosis for patient survival. Photodynamic therapy is one of the adjuvant therapies which has been used for glioblastoma multiforme during last decade. Hypericin, a photosensitizer, can be employed in this treatment. We have studied the effect of hypericin on PKCδ phosphorylation in U87 MG cells before and after light application. Hypericin increased PKCδ phosphorylation at tyrosine 155 in the regulatory domain and serine 645 in the catalytic domain. However, use of the light resulted in apoptosis, decreased phosphorylation of tyrosine 155 and enhanced serine 645. The PKCδ localization and phosphorylation of regulatory and catalytic domains were shown to play a distinct role in the anti-apoptotic response of glioma cells. We hypothesized that PKCδ phosphorylated at the regulatory domain is primarily present in the cytoplasm and in mitochondria before irradiation, and it may participate in Bcl-2 phosphorylation. After hypericin and light application, PKCδ phosphorylated at a regulatory domain which is in the nucleus. In contrast, PKCδ phosphorylated at the catalytic domain may be mostly active in the nucleus before irradiation, but active in the cytoplasm after the irradiation. In summary, light-induced oxidative stress significantly regulates PKCδ pro-survival and pro-apoptotic activity in glioma cells by its phosphorylation at serine 645 and tyrosine 155.

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.