Modeling multi-mutation and drug resistance: analysis of some case studies

A survey of open questions in adaptive therapy: Bridging mathematics and clinical translation

Adaptive therapy is a dynamic cancer treatment protocol that updates (or 'adapts') treatment decisions in anticipation of evolving tumor dynamics. This broad term encompasses many possible dynamic treatment protocols of patient-specific dose modulation or dose timing. Adaptive therapy maintains high levels of tumor burden to benefit from the competitive suppression of treatment-sensitive subpopulations on treatment-resistant subpopulations. This evolution-based approach to cancer treatment has been integrated into several ongoing or planned clinical trials, including treatment of metastatic castrate resistant prostate cancer, ovarian cancer, and BRAF-mutant melanoma. In the previous few decades, experimental and clinical investigation of adaptive therapy has progressed synergistically with mathematical and computational modeling. In this work, we discuss 11 open questions in cancer adaptive therapy mathematical modeling. The questions are split into three sections: (1) integrating the appropriate components into mathematical models (2) design and validation of dosing protocols, and (3) challenges and opportunities in clinical translation.

Model-informed experimental design recommendations for distinguishing intrinsic and acquired targeted therapeutic resistance in head and neck cancer

The promise of precision medicine has been limited by the pervasive resistance to many targeted therapies for cancer. Inferring the timing (i.e., pre-existing or acquired) and mechanism (i.e., drug-induced) of such resistance is crucial for designing effective new therapeutics. This paper studies cetuximab resistance in head and neck squamous cell carcinoma (HNSCC) using tumor volume data obtained from patient-derived tumor xenografts. We ask if resistance mechanisms can be determined from this data alone, and if not, what data would be needed to deduce the underlying mode(s) of resistance. To answer these questions, we propose a family of mathematical models, with each member of the family assuming a different timing and mechanism of resistance. We present a method for fitting these models to individual volumetric data, and utilize model selection and parameter sensitivity analyses to ask: which member(s) of the family of models best describes HNSCC response to cetuximab, and what does that tell us about the timing and mechanisms driving resistance? We find that along with time-course volumetric data to a single dose of cetuximab, the initial resistance fraction and, in some instances, dose escalation volumetric data are required to distinguish among the family of models and thereby infer the mechanisms of resistance. These findings can inform future experimental design so that we can best leverage the synergy of wet laboratory experimentation and mathematical modeling in the study of novel targeted cancer therapeutics.

Precision Anti-Cancer Medicines by Oligonucleotide Therapeutics in Clinical Research Targeting Undruggable Proteins and Non-Coding RNAs

Cancer incidence and mortality continue to increase, while the conventional chemotherapeutic drugs confer limited efficacy and relevant toxic side effects. Novel strategies are urgently needed for more effective and safe therapeutics in oncology. However, a large number of proteins are considered undruggable by conventional drugs, such as the small molecules. Moreover, the mRNA itself retains oncological functions, and its targeting offers the double advantage of blocking the tumorigenic activities of the mRNA and the translation into protein. Finally, a large family of non-coding RNAs (ncRNAs) has recently emerged that are also dysregulated in cancer, but they could not be targeted by drugs directed against the proteins. In this context, this review describes how the oligonucleotide therapeutics targeting RNA or DNA sequences, are emerging as a new class of drugs, able to tackle the limitations described above. Numerous clinical trials are evaluating oligonucleotides for tumor treatment, and in the next few years some of them are expected to reach the market. We describe the oligonucleotide therapeutics targeting undruggable proteins (focusing on the most relevant, such as those originating from the MYC and RAS gene families), and for ncRNAs, in particular on those that are under clinical trial evaluation in oncology. We highlight the challenges and solutions for the clinical success of oligonucleotide therapeutics, with particular emphasis on the peculiar challenges that render it arduous to treat tumors, such as heterogeneity and the high mutation rate. In the review are presented these and other advantages offered by the oligonucleotide as an emerging class of biotherapeutics for a new era of precision anti-cancer medicine.

AN ADAPTIVE PHARMACOKINETIC OPTIMAL CONTROL APPROACH IN CHEMOTHERAPY FOR HETEROGENEOUS TUMOR

The mathematical study of cancer received great attention in recent years. The theoretical and numerical investigations of models employed for studying the growth of cancer cells and treatment of cancer can help the clinical practitioners in adapting new strategies to face the challenges posed by the deadly disease. Chemotherapy is the most common method of treatment for cancer. The resistance of tumor cells toward the administered drug and the toxic effect of anti-cancer agents on healthy cells are major hurdles to the success of therapy. In this paper, we study this as an optimal control problem in which the amount of drug injected is taken as control. The evolution of different types of cells — sensitive tumor cells, resistant tumor cells and normal cells — under treatment are analyzed. The pharmacokinetics of the drug is also incorporated into the mathematical model. We propose a treatment protocol that assures the death of a maximum number of tumor cells but also manages to keep the normal cells at a sufficient level. We also validated our theoretical results numerically.

Molecular Mechanisms Involving the Sonic Hedgehog Pathway in Lung Cancer Therapy: Recent Advances

According to the latest statistics from the International Agency for Research on Cancer (IARC), lung cancer is one of the most lethal malignancies in the world, accounting for approximately 18% of all cancer-associated deaths. Yet, even with aggressive interventions for advanced lung cancer, the five-year survival rate remains low, at around 15%. The hedgehog signaling pathway is highly conserved during embryonic development and is involved in tissue homeostasis as well as organ development. However, studies have documented an increasing prevalence of aberrant activation of HH signaling in lung cancer patients, promoting malignant lung cancer progression with poor prognostic outcomes. Inhibitors targeting the HH pathway have been widely used in tumor therapy, however, they still cannot avoid the occurrence of drug resistance. Interestingly, natural products, either alone or in combination with chemotherapy, have greatly improved overall survival outcomes for lung cancer patients by acting on the HH signaling pathway because of its unique and excellent pharmacological properties. In this review, we elucidate on the underlying molecular mechanisms through which the HH pathway promotes malignant biological behaviors in lung cancer, as well as the potential of inhibitors or natural compounds in targeting HH signaling for clinical applications in lung cancer therapy.

Mathematical Modeling and Analysis of Tumor Chemotherapy

Cancer diseases lead to the second-highest death rate all over the world. For treating tumors, one of the most common schemes is chemotherapy, which can decrease the tumor size and control the progression of cancer diseases. To better understand the mechanisms of chemotherapy, we developed a mathematical model of tumor growth under chemotherapy. This model includes both immune system response and drug therapy. We characterize the symmetrical properties and dynamics of this differential equation model by finding the equilibrium points and exploring the stability and symmetry properties in a range of model parameters. Sensitivity analyses suggest that the chemotherapy drug-induced tumor mortality rate and the drug decay rate contribute significantly to the determination of treatment outcomes. Numerical simulations highlight the importance of CTL activation in tumor chemotherapy.

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

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

A New ODE-Based Model for Tumor Cells and Immune System Competition

Changes in diet are heavily associated with high mortality rates in several types of cancer. In this paper, a new mathematical model of tumor cells growth is established to dynamically demonstrate the effects of abnormal cell progression on the cells affected by the tumor in terms of the immune system’s functionality and normal cells’ dynamic growth. This model is called the normal-tumor-immune-unhealthy diet model (NTIUNHDM) and governed by a system of ordinary differential equations. In the NTIUNHDM, there are three main populations normal cells, tumor cell and immune cells. The model is discussed analytically and numerically by utilizing a fourth-order Runge–Kutta method. The dynamic behavior of the NTIUNHDM is discussed by analyzing the stability of the system at various equilibrium points and the Mathematica software is used to simulate the model. From analysis and simulation of the NTIUNHDM, it can be deduced that instability of the response stage, due to a weak immune system, is classified as one of the main reasons for the coexistence of abnormal cells and normal cells. Additionally, it is obvious that the NTIUNHDM has only one stable case when abnormal cells begin progressing into early stages of tumor cells such that the immune cells are generated once. Thus, early boosting of the immune system might contribute to reducing the risk of cancer.

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.

TNF-α inhibitor reduces drug-resistance to anti-PD-1: A mathematical model

Drug resistance is a primary obstacle in cancer treatment. In many patients who at first respond well to treatment, relapse occurs later on. Various mechanisms have been explored to explain drug resistance in specific cancers and for specific drugs. In this paper, we consider resistance to anti-PD-1, a drug that enhances the activity of anti-cancer T cells. Based on results in experimental melanoma, it is shown, by a mathematical model, that resistances to anti-PD-1 can be significantly reduced by combining it with anti-TNF-α. The model is used to simulate the efficacy of the combined therapy with different range of doses, different initial tumor volume, and different schedules. In particular, it is shown that under a course of treatment with 3-week cycles where each drug is injected in the first day of either week 1 or week 2, injecting anti-TNF-α one week after anti-PD-1 is the most effective schedule in reducing tumor volume.

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

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

Recent Progress in Characterizing Long Noncoding RNAs in Cancer Drug Resistance

Drug resistance is an important cause of failure in cancer chemotherapies. A large number of long noncoding RNAs (lncRNAs) have been found to be related to drug resistance in cancers. Therefore, lncRNAs provide potential targets for cancer therapies. The lncRNAs involved in cancer drug resistance are attracting interest from an increasing number of researchers. This review summarizes the latest research on the mechanisms and functions of lncRNAs in cancer drug resistance and envisages their future developments and therapeutic applications. This research suggests that lncRNAs regulate drug resistance through multiple mechanisms. LncRNAs do not affect drug resistance directly; usually, they do so by regulating the expression of some intermediate regulatory factors. In addition, lncRNAs exhibit a diversity of functions in cancer drug resistance. The overexpression of most lncRNAs promotes drug resistance, while a few lncRNAs have inhibitory effects.

Computational modelling of resistance and associated treatment response heterogeneity in metastatic cancers

Metastatic cancer patients invariably develop treatment resistance. Different levels of resistance lead to observed heterogeneity in treatment response. The main goal was to evaluate treatment response heterogeneity with a computation model simulating the dynamics of drug-sensitive and drug-resistant cells. Model parameters included proliferation, drug-induced death, transition and proportion of intrinsically resistant cells. The model was benchmarked with imaging metrics extracted from 39 metastatic prostate cancer patients who had ¹⁸F-NaF-PET/CT scans performed at baseline and at three cycles into chemotherapy or hormonal therapy. Two initial model assumptions were evaluated: considering only inter-patient heterogeneity and both inter-patient and intra-patient heterogeneity in the proportion of intrinsically resistant cells. The correlation between the median proportion of intrinsically resistant cells and baseline patient-level imaging metrics was assessed with Spearman's rank correlation coefficient. The impact of model parameters on simulated treatment response was evaluated with a sensitivity study. Treatment response after periods of six, nine, and 12 months was predicted with the model. The median predicted range of response for patients treated with both therapies was compared with a Wilcoxon rank sum test. For each patient, the time was calculated when the proportion of disease with a non-favourable response outperformed a favourable response. By taking into account inter-patient and intra-patient heterogeneity in the proportion of intrinsically resistant cells, the model performed significantly better ([Formula: see text]) than by taking into account only inter-patient heterogeneity ([Formula: see text]). The median proportion of intrinsically resistant cells showed a moderate correlation (ρ  =  0.55) with mean patient-level uptake, and a low correlation (ρ  =  0.36) with the dispersion of mean metastasis-level uptake in a patient. The sensitivity study showed a strong impact of the proportion of intrinsically resistant cells on model behaviour after three cycles of therapy. The difference in the median range of response (MRR) was not significant between cohorts at any time point (p   >  0.15). The median time when the proportion of disease with a non-favourable response outperformed the favourable response was eight months, for both cohorts. The model provides an insight into inter-patient and intra-patient heterogeneity in the evolution of treatment resistance.

Adefovir dipivoxil sensitizes colon cancer cells to vemurafenib by disrupting the KCTD12-CDK1 interaction

Vemurafenib is a B-Raf V600E inhibitor that exerts significant inhibitory effects in melanoma but not in colon cancer, and the mechanism of vemurafenib resistance remains unclear. In this study, bioinformatics analysis of gene profiles in cancer cells treated with vemurafenib or its analog revealed that cell cycle progression is significantly affected by vemurafenib. We found that CDK1 is stably activated in the vemurafenib-resistant (VR) colon cancer sublines that we established, indicating that CDK1 activation is responsible for vemurafenib resistance. As the KCTD12-CDK1 interaction is necessary for CDK1 activation, we screened an FDA-approved drug library consisting of 616 compounds and identified that adefovir dipivoxil (AD), a nucleoside analog for treatment of HBV infections, disrupts the CDK1-KCTD12 interaction and induces G2 phase arrest in the cell cycle. Functional assays demonstrated that AD significantly inhibited colon cancer cell proliferation and tumorigenesis both in vitro and in vivo with no observed side effects. Furthermore, AD sensitized vemurafenib-resistant colon cancer cells and tumor xenografts to vemurafenib. This study reveals that CDK1 activation induces vemurafenib resistance and that AD is a promising therapeutic strategy for colon cancer both as a single agent and in combination with vemurafenib.