Mathematical Modeling of Therapy-induced Cancer Drug Resistance: Connecting Cancer Mechanisms to Population Survival Rates

A Role of Effector CD 8 + T Cells Against Circulating Tumor Cells Cloaked with Platelets: Insights from a Mathematical Model

Cancer metastasis accounts for a majority of cancer-related deaths worldwide. Metastasis occurs when the primary tumor sheds cells into the blood and lymphatic circulation, thereby becoming circulating tumor cells (CTCs) that transverse through the circulatory system, extravasate the circulation and establish a secondary distant tumor. Accumulating evidence suggests that circulating effector CD 8 + T cells are able to recognize and attack arrested or extravasating CTCs, but this important antitumoral effect remains largely undefined. Recent studies highlighted the supporting role of activated platelets in CTCs's extravasation from the bloodstream, contributing to metastatic progression. In this work, a simple mathematical model describes how the primary tumor, CTCs, activated platelets and effector CD 8 + T cells participate in metastasis. The stability analysis reveals that for early dissemination of CTCs, effector CD 8 + T cells can present or keep secondary metastatic tumor burden at low equilibrium state. In contrast, for late dissemination of CTCs, effector CD 8 + T cells are unlikely to inhibit secondary tumor growth. Moreover, global sensitivity analysis demonstrates that the rate of the primary tumor growth, intravascular CTC proliferation, as well as the CD 8 + T cell proliferation, strongly affects the number of the secondary tumor cells. Additionally, model simulations indicate that an increase in CTC proliferation greatly contributes to tumor metastasis. Our simulations further illustrate that the higher the number of activated platelets on CTCs, the higher the probability of secondary tumor establishment. Intriguingly, from a mathematical immunology perspective, our simulations indicate that if the rate of effector CD 8 + T cell proliferation is high, then the secondary tumor formation can be considerably delayed, providing a window for adjuvant tumor control strategies. Collectively, our results suggest that the earlier the effector CD 8 + T cell response is enhanced the higher is the probability of preventing or delaying secondary tumor metastases.

Simulating BRAFV600E-MEK-ERK signalling dynamics in response to vertical inhibition treatment strategies

In vertical inhibition treatment strategies, multiple components of an intracellular pathway are simultaneously inhibited. Vertical inhibition of the BRAFV600E-MEK-ERK signalling pathway is a standard of care for treating BRAFV600E-mutated melanoma where two targeted cancer drugs, a BRAFV600E-inhibitor, and a MEK inhibitor, are administered in combination. Targeted therapies have been linked to early onsets of drug resistance, and thus treatment strategies of higher complexities and lower doses have been proposed as alternatives to current clinical strategies. However, finding optimal complex, low-dose treatment strategies is a challenge, as it is possible to design more treatment strategies than are feasibly testable in experimental settings. To quantitatively address this challenge, we develop a mathematical model of BRAFV600E-MEK-ERK signalling dynamics in response to combinations of the BRAFV600E-inhibitor dabrafenib (DBF), the MEK inhibitor trametinib (TMT), and the ERK-inhibitor SCH772984 (SCH). From a model of the BRAFV600E-MEK-ERK pathway, and a set of molecular-level drug-protein interactions, we extract a system of chemical reactions that is parameterised by in vitro data and converted to a system of ordinary differential equations (ODEs) using the law of mass action. The ODEs are solved numerically to produce simulations of how pathway-component concentrations change over time in response to different treatment strategies, i.e., inhibitor combinations and doses. The model can thus be used to limit the search space for effective treatment strategies that target the BRAFV600E-MEK-ERK pathway and warrant further experimental investigation. The results demonstrate that DBF and DBF-TMT-SCH therapies show marked sensitivity to BRAFV600E concentrations in silico, whilst TMT and SCH monotherapies do not.

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.

The deformation of cancer cells through narrow micropores holds the potential to regulate genes that impact cancer malignancy

Surgery, radiation, hormonal therapy, chemotherapy, and immunotherapy are standard treatment strategies for metastatic breast cancer. However, the heterogeneous nature of the disease poses challenges and continues to make it life-threatening. It is crucial to elucidate further the underlying signaling pathways to improve treatment efficacy. Our study established two triple-negative breast cancer cell lines (TW-1 and TW-2) that were physically deformed using 3 μm pores to investigate the relationship between cancer cell deformation and metastasis within a heterogeneous population. The physical transformation of TW-1 and TW-2 cells significantly affected their growth and migration speed, as evidenced by wound healing assays for collective cell migration and microchannel assays for single-cell migration. We conducted bulk RNA sequencing to gain insights into the genes influenced by physical deformation. Additionally, we evaluated the effects of trametinib resistance on breast cancer cell metastasis by assessing cell viability and migration rates. Interestingly, TW-1 and TW-2 cells exhibited resistance to trametinib treatment. We observed a significant upregulation of GABRA-3, a protein commonly expressed in malignant breast cancer, and the critical transcription factor Myc in TW-1 and TW-2 cells compared to the control group (Ori). However, we did not observe a significant difference in Myc expression between TW-1 and TW-2 cells. In contrast, in the trametinib-resistant cell lines (TW-1-Tra and TW-2-Tra), we found increased expression of OCT4 and SOX2 rather than GABRA-3 or Myc. These findings highlight the differential expression patterns of these genes in our study, suggesting their potential role in cancer cell deformation and drug resistance. Our study presents a potential in vitro model for metastatic and drug-resistant breast cancer cells. By investigating the correlation between cancer cell deformation and metastasis, we contribute to understanding breast cancer heterogeneity and lay the groundwork for developing improved treatment strategies.

Mathematical model combined with microdosimetric kinetic model for tumor volume calculation in stereotactic body radiation therapy

We proposed a new mathematical model that combines an ordinary differential equation (ODE) and microdosimetric kinetic model (MKM) to predict the tumor-cell lethal effect of Stereotactic body radiation therapy (SBRT) applied to non-small cell lung cancer (NSCLC). The tumor growth volume was calculated by the ODE in the multi-component mathematical model (MCM) for the cell lines NSCLC A549 and NCI-H460 (H460). The prescription doses 48 Gy/4 fr and 54 Gy/3 fr were used in the SBRT, and the effect of the SBRT on tumor cells was evaluated by the MKM. We also evaluated the effects of (1) linear quadratic model (LQM) and the MKM, (2) varying the ratio of active and quiescent tumors for the total tumor volume, and (3) the length of the dose-delivery time per fractionated dose (tinter) on the initial tumor volume. We used the ratio of the tumor volume at 1 day after the end of irradiation to the tumor volume before irradiation to define the radiation effectiveness value (REV). The combination of MKM and MCM significantly reduced REV at 48 Gy/4 fr compared to the combination of LQM and MCM. The ratio of active tumors and the prolonging of tinter affected the decrease in the REV for A549 and H460 cells. We evaluated the tumor volume considering a large fractionated dose and the dose-delivery time by combining the MKM with a mathematical model of tumor growth using an ODE in lung SBRT for NSCLC A549 and H460 cells.

Multicomponent mathematical model for tumor volume calculation with setup error using single-isocenter stereotactic radiotherapy for multiple brain metastases

We evaluated the tumor residual volumes considering six degrees-of-freedom (6DoF) patient setup errors in stereotactic radiotherapy (SRT) with multicomponent mathematical model using single-isocenter irradiation for brain metastases. Simulated spherical gross tumor volumes (GTVs) with 1.0 (GTV 1), 2.0 (GTV 2), and 3.0 (GTV 3)-cm diameters were used. The distance between the GTV center and isocenter (d) was set at 0-10 cm. The GTV was simultaneously translated within 0-1.0 mm (T) and rotated within 0°-1.0° (R) in the three axis directions using affine transformation. We optimized the tumor growth model parameters using measurements of non-small cell lung cancer cell lines' (A549 and NCI-H460) growth. We calculated the GTV residual volume at the irradiation's end using the physical dose to the GTV when the GTV size, d, and 6DoF setup error varied. The d-values that satisfy tolerance values (10%, 35%, and 50%) of the GTV residual volume rate based on the pre-irradiation GTV volume were determined. The larger the tolerance value set for both cell lines, the longer the distance to satisfy the tolerance value. In GTV residual volume evaluations based on the multicomponent mathematical model on SRT with single-isocenter irradiation, the smaller the GTV size and the larger the distance and 6DoF setup error, the shorter the distance that satisfies the tolerance value might need to be.

Bioinformatics toolbox for exploring target mutation-induced drug resistance

Drug resistance is increasingly among the main issues affecting human health and threatening agriculture and food security. In particular, developing approaches to overcome target mutation-induced drug resistance has long been an essential part of biological research. During the past decade, many bioinformatics tools have been developed to explore this type of drug resistance, and they have become popular for elucidating drug resistance mechanisms in a low cost, fast and effective way. However, these resources are scattered and underutilized, and their strengths and limitations have not been systematically analyzed and compared. Here, we systematically surveyed 59 freely available bioinformatics tools for exploring target mutation-induced drug resistance. We analyzed and summarized these resources based on their functionality, data volume, data source, operating principle, performance, etc. And we concisely discussed the strengths, limitations and application examples of these tools. Specifically, we tested some predictive tools and offered some thoughts from the clinician's perspective. Hopefully, this work will provide a useful toolbox for researchers working in the biomedical, pesticide, bioinformatics and pharmaceutical engineering fields, and a good platform for non-specialists to quickly understand drug resistance prediction.

Tumor organoid biobank-new platform for medical research

Organoids are a new type of 3D model for tumor research, which makes up for the shortcomings of cell lines and xenograft models, and promotes the development of personalized precision medicine. Long-term culture, expansion and storage of organoids provide the necessary conditions for the establishment of biobanks. Biobanks standardize the collection and preservation of normal or pathological specimens, as well as related clinical information. The tumor organoid biobank has a good quality control system, which is conducive to the clinical transformation and large-scale application of tumor organoids, such as disease modeling, new drug development and high-throughput drug screening. This article summarized the common tumor types of patient-derived organoid (PDO) biobanks and the necessary information for biobank construction, such as the number of organoids, morphology, success rate of culture and resuscitation, pathological types. In our results, we found that patient-derived tumor organoid (PDTO) biobanks were being established more and more, with the Netherlands, the United States, and China establishing the most. Biobanks of colorectal, pancreas, breast, glioma, and bladder cancers were established more, which reflected the relative maturity of culture techniques for these tumors. In addition, we provided insights on the precautions and future development direction of PDTO biobank building.

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

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

Identification of solamargine as a cisplatin sensitizer through phenotypical screening in cisplatin-resistant NSCLC organoids

Although Cisplatin (DDP) is a widely used first-line chemotherapy medication, DDP resistance is one of the main causes of treatment failure in advanced lung cancer. Therefore, it is urgent to identify DDP sensitizers and investigate the underlying molecular mechanisms. Here we utilized DDP-resistant organoids established from tumor biopsies of patients with relapsed lung cancers. In this study, we identified Solamargine as a potential DDP sensitizer through screening a natural product library. Mechanically, Solamargine induced G0/G1-phase arrest and apoptosis in DDP-resistant lung cancer cell lines. Gene expression analysis and KEGG pathway analysis indicated that the hedgehog pathway was suppressed by Solamargine. Moreover, Gli responsive element (GRE) reporter gene assay and BODIPY-cyclopamine binding assay showed that Solamargine inhibited the hedgehog pathway via direct binding to SMO protein. Interestingly, Solamargine and DDP showed a synergetic effect in inhibiting DDP-resistant lung cancer cell lines. Taken together, our work herein revealed Solamargine as a hedgehog pathway inhibitor and DDP-sensitizer, which might provide a new direction for further treatment of advanced DDP-resistant lung cancer patients.

Modeling the effect of gut microbiome on therapeutic efficacy of immune checkpoint inhibitors against cancer

Immune checkpoint inhibitors have been shown to be highly successful against some solid metastatic malignancies, but only for a subset of patients who show durable clinical responses. The overall patient response rate is limited due to the interpatient heterogeneity. Preclinical and clinical studies have recently shown that the therapeutic responses can be improved through the modulation of gut microbiome. However, the underlying mechanisms are not fully understood. In this paper, we explored the effect of favorable and unfavorable gut bacteria on the therapeutic efficacy of anti-PD-1 against cancer by modeling the tumor-immune-gut microbiome interactions, and further examined the predictive markers of responders and non-responders to anti-PD-1. The dynamics of the gut bacteria was fitted to the clinical data of melanoma patients, and virtual patients data were generated based on the clinical patient survival data. Our simulation results show that low initial growth rate and low level of favorable bacteria at the initiation of anti-PD-1 therapy are predictive of non-responders, while high level of favorable bacteria at the initiation of anti-PD-1 therapy is predictive of responders. Simulation results also confirmed that it is possible to promote patients' response rate to anti-PD-1 by manipulating the gut bacteria composition of non-responders, whereby achieving long-term progression-free survival.

Analyzing the relationship between the vitamin D deficiency and COVID-19 mortality rate and modeling the time-delay interactions between body's immune healthy cells, infected cells, and virus particles with the effect of vitamin D levels

This paper presents some recent views on the aspects of vitamin D levels in relation to the COVID-19 infections and analyzes the relationship between the prevalence rates of vitamin D deficiency and COVID-19 death rates per million of various countries in Europe and Asia using the data from the PubMed database. The paper also discusses a new mathematical model of time-delay interactions between the body's immune healthy cells, infected cells, and virus particles with the effect of vitamin D levels. The model can be used to monitor the timely progression of healthy immune cells with the effects of the levels of vitamin D and probiotics supplement. It also can help to predict when the infected cells and virus particles free state can ever be reached as time progresses. The consideration of the time delay in the modeling due to effects of the infected cells or virus particles and the growth of healthy cells is also an important factor that can significantly change the outcomes of the body's immune cells as well as the infections.

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

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

Functional stratification of cancer drugs through integrated network similarity

Drugs not only perturb their immediate protein targets but also modulate multiple signaling pathways. In this study, we explored networks modulated by several drugs across multiple cancer cell lines by integrating their targets with transcriptomic and phosphoproteomic data. As a result, we obtained 236 reconstructed networks covering five cell lines and 70 drugs. A rigorous topological and pathway analysis showed that chemically and functionally different drugs may modulate overlapping networks. Additionally, we revealed a set of tumor-specific hidden pathways with the help of drug network models that are not detectable from the initial data. The difference in the target selectivity of the drugs leads to disjoint networks despite sharing a similar mechanism of action, e.g., HDAC inhibitors. We also used the reconstructed network models to study potential drug combinations based on the topological separation and found literature evidence for a set of drug pairs. Overall, network-level exploration of drug-modulated pathways and their deep comparison may potentially help optimize treatment strategies and suggest new drug combinations.

Optimizing Dosage-Specific Treatments in a Multi-Scale Model of a Tumor Growth

The emergence of cell resistance in cancer treatment is a complex phenomenon that emerges from the interplay of processes that occur at different scales. For instance, molecular mechanisms and population-level dynamics such as competition and cell–cell variability have been described as playing a key role in the emergence and evolution of cell resistances. Multi-scale models are a useful tool for studying biology at very different times and spatial scales, as they can integrate different processes occurring at the molecular, cellular, and intercellular levels. In the present work, we use an extended hybrid multi-scale model of 3T3 fibroblast spheroid to perform a deep exploration of the parameter space of effective treatment strategies based on TNF pulses. To explore the parameter space of effective treatments in different scenarios and conditions, we have developed an HPC-optimized model exploration workflow based on EMEWS. We first studied the effect of the cells’ spatial distribution in the values of the treatment parameters by optimizing the supply strategies in 2D monolayers and 3D spheroids of different sizes. We later study the robustness of the effective treatments when heterogeneous populations of cells are considered. We found that our model exploration workflow can find effective treatments in all the studied conditions. Our results show that cells’ spatial geometry and population variability should be considered when optimizing treatment strategies in order to find robust parameter sets.

Mathematical Modeling the Time-Delay Interactions between Tumor Viruses and the Immune System with the Effects of Chemotherapy and Autoimmune Diseases

The immune system is the body’s defense against pathogens, which are complex living organisms found in many parts in the body including organs, tissues, cells, molecules, and proteins. When the immune system works properly, it can recognize and kill the abnormal cells and the infected cells. Otherwise, it can attack the body’s healthy cells even if there is no invader. Many researchers have developed immunotherapy (or cancer vaccines) and have used chemotherapy for cancer treatment that can kill fast-growing cancer cells or at least slow down tumor growth. However, chemotherapy drugs travel throughout the body and tend to kill both healthy cells and cancer cells. In this study, we consider the fact that chemotherapy can kill tumor cells and that the loss of the immune cells may at the same time stir up cancer growth. We present a dynamic time-delay tumor-immune model with the effects of chemotherapy drugs and autoimmune disease. The modeling results can be used to determine the progression of tumor cells in the human body with the effect of chemotherapy, autoimmune diseases, and time delays based on partial differential equations. It can also be used to predict when the tumor viruses’ free state can be reached as time progresses, as well as the state of the body’s healthy cells as time progresses. We also present a few numerical cases that illustrate that the model can be used to monitor the effects of chemotherapy drug treatment and the growth rate of tumor virus-infected cells and the autoimmune disease.

Optimal chemotherapy counteracts cancer adaptive resistance in a cell-based, spatially-extended, evolutionary model

Most aggressive cancers are incurable due to their fast evolution of drug resistance. We model cancer growth and adaptive response in a simplified cell-based (CB) setting, assuming a genetic resistance to two chemotherapeutic drugs. We show that optimal administration protocols can steer cells resistance and turned it into a weakness for the disease. Our work extends the population-based (PB) model proposed by Orlando et al. (Physical Biology, 2012), in which a homogeneous population of cancer cells evolves according to a fitness landscape. The landscape models three types of trade-offs, differing on whether the cells are more, less, or equal effective when generalizing resistance to two drugs as opposed to specializing to a single one. The CB framework allows us to include genetic heterogeneity, spatial competition, and drugs diffusion, as well as realistic administration protocols. By calibrating our model on Orlando et al.'s assumptions, we show that dynamical protocols that alternate the two drugs minimize the cancer size at the end of (or at mid-points during) treatment. These results significantly differ from those obtained with the homogeneous model---suggesting static protocols under the pro-generalizing and neutral allocation trade-offs---highlighting the important role of spatial and genetic heterogeneities. Our work is the first attempt to search for optimal treatments in a CB setting, a step forward toward realistic clinical applications.

A Dynamic Model of Multiple Time-Delay Interactions between the Virus-Infected Cells and Body’s Immune System with Autoimmune Diseases

The immune system is a complex interconnected network consisting of many parts including organs, tissues, cells, molecules and proteins that work together to protect the body from illness when germs enter the body. An autoimmune disease is a disease in which the body’s immune system attacks healthy cells. It is known that when the immune system is working properly, it can clearly recognize and kill the abnormal cells and virus-infected cells. But when it doesn’t work properly, the human body will not be able to recognize the virus-infected cells and, therefore, it can attack the body’s healthy cells when there is no invader or does not stop an attack after the invader has been killed, resulting in autoimmune disease.; This paper presents a mathematical modeling of the virus-infected development in the body’s immune system considering the multiple time-delay interactions between the immune cells and virus-infected cells with autoimmune disease. The proposed model aims to determine the dynamic progression of virus-infected cell growth in the immune system. The patterns of how the virus-infected cells spread and the development of the body’s immune cells with respect to time delays will be derived in the form of a system of delay partial differential equations. The model can be used to determine whether the virus-infected free state can be reached or not as time progresses. It also can be used to predict the number of the body’s immune cells at any given time. Several numerical examples are discussed to illustrate the proposed model. The model can provide a real understanding of the transmission dynamics and other significant factors of the virus-infected disease and the body’s immune system subject to the time delay, including approaches to reduce the growth rate of virus-infected cell and the autoimmune disease as well as to enhance the immune effector cells.

Epigenetic instability may alter cell state transitions and anticancer drug resistance

Drug resistance is a significant obstacle to successful and durable anti-cancer therapy. Targeted therapy is often effective during early phases of treatment; however, eventually cancer cells adapt and transition to drug-resistant cells states rendering the treatment ineffective. It is proposed that cell state can be a determinant of drug efficacy and manipulated to affect the development of anticancer drug resistance. In this work, we developed two stochastic cell state models and an integrated stochastic-deterministic model referenced to brain tumors. The stochastic cell state models included transcriptionally-permissive and -restrictive states based on the underlying hypothesis that epigenetic instability mitigates lock-in of drug-resistant states. When moderate epigenetic instability was implemented the drug-resistant cell populations were reduced, on average, by 60%, whereas a high level of epigenetic disruption reduced them by about 90%. The stochastic-deterministic model utilized the stochastic cell state model to drive the dynamics of the DNA repair enzyme, methylguanine-methyltransferase (MGMT), that repairs temozolomide (TMZ)-induced O6-methylguanine (O6mG) adducts. In the presence of epigenetic instability, the production of MGMT decreased that coincided with an increase of O6mG adducts following a multiple-dose regimen of TMZ. Generation of epigenetic instability via epigenetic modifier therapy could be a viable strategy to mitigate anticancer drug resistance.

Evolutionary Dynamics of Treatment-Induced Resistance in Cancer Informs Understanding of Rapid Evolution in Natural Systems

Rapid evolution is ubiquitous in nature. We briefly review some of this quite broadly, particularly in the context of response to anthropogenic disturbances. Nowhere is this more evident, replicated and accessible to study than in cancer. Curiously cancer has been late - relative to fisheries, antibiotic resistance, pest management and evolution in human dominated landscapes - in recognizing the need for evolutionarily informed management strategies. The speed of evolution matters. Here, we employ game-theoretic modeling to compare time to progression with continuous maximum tolerable dose to that of adaptive therapy where treatment is discontinued when the population of cancer cells gets below half of its initial size and re-administered when the cancer cells recover, forming cycles with and without treatment. We show that the success of adaptive therapy relative to continuous maximum tolerable dose therapy is much higher if the population of cancer cells is defined by two cell types (sensitive vs. resistant in a polymorphic population). Additionally, the relative increase in time to progression increases with the speed of evolution. These results hold with and without a cost of resistance in cancer cells. On the other hand, treatment-induced resistance can be modeled as a quantitative trait in a monomorphic population of cancer cells. In that case, when evolution is rapid, there is no advantage to adaptive therapy. Initial responses to therapy are blunted by the cancer cells evolving too quickly. Our study emphasizes how cancer provides a unique system for studying rapid evolutionary changes within tumor ecosystems in response to human interventions; and allows us to contrast and compare this system to other human managed or dominated systems in nature.

Strategies for the treatment of breast cancer: from classical drugs to mathematical models

Breast cancer is one of the most common cancers and generally affects women. It is a heterogeneous disease that presents different entities, different biological characteristics, and differentiated clinical behaviors. With this in mind, this literature review had as its main objective to analyze the path taken from the simple use of classical drugs to the application of mathematical models, which through the many ongoing studies, have been considered as one of the reliable strategies, explaining the reasons why chemotherapy is not always successful. Besides, the most commonly mentioned strategies are immunotherapy, which includes techniques and therapies such as the use of antibodies, cytokines, antitumor vaccines, oncolytic and genomic viruses, among others, and nanoparticles, including metallic, magnetic, polymeric, liposome, dendrimer, micelle, and others, as well as drug reuse, which is a process by which new therapeutic indications are found for existing and approved drugs. The most commonly used pharmacological categories are cardiac, antiparasitic, anthelmintic, antiviral, antibiotic, and others. For the efficient development of reused drugs, there must be a process of exchange of purposes, methods, and information already available, and for their better understanding, computational mathematical models are then used, of which the methods of blind search or screening, based on the target, knowledge, signature, pathway or network and the mechanism to which it is directed, stand out. To conclude it should be noted that these different strategies can be applied alone or in combination with each other always to improve breast cancer treatment.

A tipping point in cancer-immune dynamics leads to divergent immunotherapy responses and hampers biomarker discovery

BACKGROUND

Predicting treatment response or survival of cancer patients remains challenging in immuno-oncology. Efforts to overcome these challenges focus, among others, on the discovery of new biomarkers. Despite advances in cellular and molecular approaches, only a limited number of candidate biomarkers eventually enter clinical practice.

METHODS

A computational modeling approach based on ordinary differential equations was used to simulate the fundamental mechanisms that dictate tumor-immune dynamics and to investigate its implications on responses to immune checkpoint inhibition (ICI) and patient survival. Using in silico biomarker discovery trials, we revealed fundamental principles that explain the diverging success rates of biomarker discovery programs.

RESULTS

Our model shows that a tipping point-a sharp state transition between immune control and immune evasion-induces a strongly non-linear relationship between patient survival and both immunological and tumor-related parameters. In patients close to the tipping point, ICI therapy may lead to long-lasting survival benefits, whereas patients far from the tipping point may fail to benefit from these potent treatments.

CONCLUSION

These findings have two important implications for clinical oncology. First, the apparent conundrum that ICI induces substantial benefits in some patients yet completely fails in others could be, to a large extent, explained by the presence of a tipping point. Second, predictive biomarkers for immunotherapy should ideally combine both immunological and tumor-related markers, as a patient's distance from the tipping point can typically not be reliably determined from solely one of these. The notion of a tipping point in cancer-immune dynamics helps to devise more accurate strategies to select appropriate treatments for patients with cancer.

Treatment scheduling effects on the evolution of drug resistance in heterogeneous cancer cell populations

The effect of scheduling of targeted therapy combinations on drug resistance is underexplored in triple-negative breast cancer (TNBC). TNBC constitutes heterogeneous cancer cell populations the composition of which can change dynamically during treatment resulting in the selection of resistant clones with a fitness advantage. We evaluated crizotinib (ALK/MET inhibitor) and navitoclax (ABT-263; Bcl-2/Bcl-xL inhibitor) combinations in a large design consisting of 696 two-cycle sequential and concomitant treatment regimens with varying treatment dose, duration, and drug holiday length over a 26-day period in MDA-MB-231 TNBC cells and found that patterns of resistance depend on the schedule and sequence in which the drugs are given. Further, we tracked the clonal dynamics and mechanisms of resistance using DNA-integrated barcodes and single-cell RNA sequencing. Our study suggests that longer formats of treatment schedules in vitro screening assays are required to understand the effects of resistance and guide more realistically in vivo and clinical studies.

Modeling the Th17 and Tregs Paradigm: Implications for Cancer Immunotherapy

CD4 + T cell differentiation is governed by gene regulatory and metabolic networks, with both networks being highly interconnected and able to adapt to external stimuli. Th17 and Tregs differentiation networks play a critical role in cancer, and their balance is affected by the tumor microenvironment (TME). Factors from the TME mediate recruitment and expansion of Th17 cells, but these cells can act with pro or anti-tumor immunity. Tregs cells are also involved in tumor development and progression by inhibiting antitumor immunity and promoting immunoevasion. Due to the complexity of the underlying molecular pathways, the modeling of biological systems has emerged as a promising solution for better understanding both CD4 + T cell differentiation and cancer cell behavior. In this review, we present a context-dependent vision of CD4 + T cell transcriptomic and metabolic network adaptability. We then discuss CD4 + T cell knowledge-based models to extract the regulatory elements of Th17 and Tregs differentiation in multiple CD4 + T cell levels. We highlight the importance of complementing these models with data from omics technologies such as transcriptomics and metabolomics, in order to better delineate existing Th17 and Tregs bifurcation mechanisms. We were able to recompilate promising regulatory components and mechanisms of Th17 and Tregs differentiation under normal conditions, which we then connected with biological evidence in the context of the TME to better understand CD4 + T cell behavior in cancer. From the integration of mechanistic models with omics data, the transcriptomic and metabolomic reprograming of Th17 and Tregs cells can be predicted in new models with potential clinical applications, with special relevance to cancer immunotherapy.

Polymeric Nanoparticle Delivery of Combination Therapy with Synergistic Effects in Ovarian Cancer

Treatment of ovarian cancer is challenging due to late stage diagnosis, acquired drug resistance mechanisms, and systemic toxicity of chemotherapeutic agents. Combination chemotherapy has the potential to enhance treatment efficacy by activation of multiple downstream pathways to overcome drug resistance and reducing required dosages. Sequence of delivery and the dosing schedule can further enhance treatment efficacy. Formulation of drug combinations into nanoparticles can further enhance treatment efficacy. Due to their versatility, polymer-based nanoparticles are an especially promising tool for clinical translation of combination therapies with tunable dosing schedules. We review polymer nanoparticle (e.g., micelles, dendrimers, and lipid nanoparticles) carriers of drug combinations formulated to treat ovarian cancer. In particular, the focus on this review is combinations of platinum and taxane agents (commonly used first line treatments for ovarian cancer) combined with other small molecule therapeutic agents. In vitro and in vivo drug potency are discussed with a focus on quantifiable synergistic effects. The effect of drug sequence and dosing schedule is examined. Computational approaches as a tool to predict synergistic drug combinations and dosing schedules as a tool for future nanoparticle design are also briefly discussed.

Adaptive Therapy for Metastatic Melanoma: Predictions from Patient Calibrated Mathematical Models

Adaptive therapy is an evolution-based treatment approach that aims to maintain tumor volume by employing minimum effective drug doses or timed drug holidays. For successful adaptive therapy outcomes, it is critical to find the optimal timing of treatment switch points in a patient-specific manner. Here we develop a combination of mathematical models that examine interactions between drug-sensitive and resistant cells to facilitate melanoma adaptive therapy dosing and switch time points. The first model assumes genetically fixed drug-sensitive and -resistant popul tions that compete for limited resources. The second model considers phenotypic switching between drug-sensitive and -resistant cells. We calibrated each model to fit melanoma patient biomarker changes over time and predicted patient-specific adaptive therapy schedules. Overall, the models predict that adaptive therapy would have delayed time to progression by 6-25 months compared to continuous therapy with dose rates of 6-74% relative to continuous therapy. We identified predictive factors driving the clinical time gained by adaptive therapy, such as the number of initial sensitive cells, competitive effect, switching rate from resistant to sensitive cells, and sensitive cell growth rate. This study highlights that there is a range of potential patient-specific benefits of adaptive therapy and identifies parameters that modulate this benefit.

Network-based survival analysis to discover target genes for developing cancer immunotherapies and predicting patient survival

Recently, cancer immunotherapies have been life-savers, however, only a fraction of treated patients have durable responses. Consequently, statistical methods that enable the discovery of target genes for developing new treatments and predicting patient survival are of importance. This paper introduced a network-based survival analysis method and applied it to identify candidate genes as possible targets for developing new treatments. RNA-seq data from a mouse study was used to select differentially expressed genes, which were then translated to those in humans. We constructed a gene network and identified gene clusters using a training set of 310 human gliomas. Then we conducted gene set enrichment analysis to select the gene clusters with significant biological function. A penalized Cox model was built to identify a small set of candidate genes to predict survival. An independent set of 690 human glioma samples was used to evaluate predictive accuracy of the survival model. The areas under time-dependent ROC curves in both the training and validation sets are more than 90%, indicating strong association between selected genes and patient survival. Consequently, potential biomedical interventions targeting these genes might be able to alter their expressions and prolong patient survival.

An elementary mathematical modeling of drug resistance in cancer

Targeted therapy is one of the promising strategies for the treatment of cancer. However, resistance to anticancer drug strongly limits the long-term effectiveness of treatment, which is a major obstacle for successfully treating cancer. In this paper, we analyze a linear system of ordinary differential equations for cancer multi-drug resistance induced mainly by random genetic point mutation. We investigate that the resistance generated before the beginning of the treatment is greater than that developed during-treatment. This result depends on the concentration of the drug, which holds only when the concentration of the drug reaches a lower limit. Moreover, no matter how many drugs are used in the treatment, the amount of resistance (generated at the beginning of the treatment and within a certain period of time after the treatment) always depends on the turnover rate. Using numerical simulations, we also evaluate the response of the mutant cancer cell population as a function of time under different treatment strategies. At appropriate dosages, combination therapy produces significant effects for the treatment with low-turnover rate cancer. For cancer with very high-turnover rate (close to 1), combination therapy can not significantly reduce the amount of resistant mutants compared to monotherapy, so in this case, combination therapy would not have advantage over monotherapy.

Challenges and Opportunities in Cancer Drug Resistance

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

Computational models of melanoma

Genes, proteins, or cells influence each other and consequently create patterns, which can be increasingly better observed by experimental biology and medicine. Thereby, descriptive methods of statistics and bioinformatics sharpen and structure our perception. However, additionally considering the interconnectivity between biological elements promises a deeper and more coherent understanding of melanoma. For instance, integrative network-based tools and well-grounded inductive in silico research reveal disease mechanisms, stratify patients, and support treatment individualization. This review gives an overview of different modeling techniques beyond statistics, shows how different strategies align with the respective medical biology, and identifies possible areas of new computational melanoma research.

Applications of personalised signalling network models in precision oncology

As our ability to provide in-depth, patient-specific characterisation of the molecular alterations within tumours rapidly improves, it is becoming apparent that new approaches will be required to leverage the power of this data and derive the full benefit for each individual patient. Systems biology approaches are beginning to emerge within this field as a potential method of incorporating large volumes of network level data and distilling a coherent, clinically-relevant prediction of drug response. However, the initial promise of this developing field is yet to be realised. Here we argue that in order to develop these precise models of individual drug response and tailor treatment accordingly, we will need to develop mathematical models capable of capturing both the dynamic nature of drug-response signalling networks and key patient-specific information such as mutation status or expression profiles. We also review the modelling approaches commonly utilised within this field, and outline recent examples of their use in furthering the application of systems biology for a precision medicine approach to cancer treatment.

Acquired Resistance in Lung Cancer

The last decade has witnessed a transformation in the treatment of advanced-stage lung cancer from a largely palliative approach to one where long-term durable remissions and even cures might be within reach. In this review, we discuss the current state of oncogene-directed precision medicine therapies in lung cancer and focus on the major cause of mortality for lung cancer patients: acquired resistance. We consider the multifaceted resistance mechanisms tumors utilize, often simultaneously. We then present areas for future scientific and clinical investigation with an emphasis on population dynamics, early detection, combinatorial therapies targeting resistance mechanisms, and understanding the drug-tolerant persister state.

Circulating tumor DNA as an early cancer detection tool

Circulating tumor DNA holds substantial promise as an early detection biomarker, particularly for cancers that do not have currently accepted screening methodologies, such as ovarian, pancreatic, and gastric cancers. Many features intrinsic to ctDNA analysis may be leveraged to enhance its use as an early cancer detection biomarker: including ctDNA fragment lengths, DNA copy number variations, and associated patient phenotypic information. Furthermore, ctDNA testing may be synergistically used with other multi-omic biomarkers to enhance early detection. For instance, assays may incorporate early detection proteins (i.e., CA-125), epigenetic markers, circulating tumor RNA, nucleosomes, exosomes, and associated immune markers. Many companies are currently competing to develop a marketable early cancer detection test that leverages ctDNA. Although some hurdles (like early stage disease assay accuracy, high implementation costs, confounding from clonal hematopoiesis, and lack of clinical utility studies) need to be addressed before integration into healthcare, ctDNA assays hold substantial potential as an early cancer screening test.

Modeling Acquired Resistance to the Second-Generation Androgen Receptor Antagonist Enzalutamide in the TRAMP Model of Prostate Cancer

Enzalutamide (MDV3100) is a potent second-generation androgen receptor antagonist approved for the treatment of castration-resistant prostate cancer (CRPC) in chemotherapy-naïve as well as in patients previously exposed to chemotherapy. However, resistance to enzalutamide and enzalutamide withdrawal syndrome have been reported. Thus, reliable and integrated preclinical models are required to elucidate the mechanisms of resistance and to assess therapeutic settings that may delay or prevent the onset of resistance. In this study, the prostate cancer multistage murine model TRAMP and TRAMP-derived cells have been used to extensively characterize in vitro and in vivo the response and resistance to enzalutamide. The therapeutic profile as well as the resistance onset were characterized and a multiscale stochastic mathematical model was proposed to link the in vitro and in vivo evolution of prostate cancer. The model showed that all therapeutic strategies that use enzalutamide result in the onset of resistance. The model also showed that combination therapies can delay the onset of resistance to enzalutamide, and in the best scenario, can eliminate the disease. These results set the basis for the exploitation of this "TRAMP-based platform" to test novel therapeutic approaches and build further mathematical models of combination therapies to treat prostate cancer and CRPC.Significance: Merging mathematical modeling with experimental data, this study presents the "TRAMP-based platform" as a novel experimental tool to study the in vitro and in vivo evolution of prostate cancer resistance to enzalutamide.

Cell death and survival due to cytotoxic exposure modelled as a two-state Ising system

Cancer chemotherapy agents are assessed for their therapeutic utility primarily by their ability to cause apoptosis of cancer cells and their potency is given by an IC50 value. Chemotherapy uses both target-specific and systemic-action drugs and drug combinations to treat cancer. It is important to judiciously choose a drug type, its dosage and schedule for optimized drug selection and administration. Consequently, the precise mathematical formulation of cancer cells' response to chemotherapy may assist in the selection process. In this paper, we propose a mathematical description of the cancer cell response to chemotherapeutic agent exposure based on a time-tested physical model of two-state multiple-component systems near criticality. We describe the Ising model methodology and apply it to a diverse panel of cytotoxic drugs administered against numerous cancer cell lines in a dose-response manner. The analysed dataset was generated by the Netherlands Translational Research Center B.V. (Oncolines). This approach allows for an accurate and consistent analysis of cytotoxic agents' effects on cancer cell lines and reveals the presence or absence of the bystander effect through the interaction constant. By calculating the susceptibility function, we see the value of IC50 coinciding with the peak of this measure of the system's sensitivity to external perturbations.

Differential regulatory network-based quantification and prioritization of key genes underlying cancer drug resistance based on time-course RNA-seq data

Drug resistance is a major cause for the failure of cancer chemotherapy or targeted therapy. However, the molecular regulatory mechanisms controlling the dynamic evolvement of drug resistance remain poorly understood. Thus, it is important to develop methods for identifying key gene regulatory mechanisms of the resistance to specific drugs. In this study, we developed a data-driven computational framework, DryNetMC, using a differential regulatory network-based modeling and characterization strategy to quantify and prioritize key genes underlying cancer drug resistance. The DryNetMC does not only infer gene regulatory networks (GRNs) via an integrated approach, but also characterizes and quantifies dynamical network properties for measuring node importance. We used time-course RNA-seq data from glioma cells treated with dbcAMP (a cAMP activator) as a realistic case to reconstruct the GRNs for sensitive and resistant cells. Based on a novel node importance index that comprehensively quantifies network topology, network entropy and expression dynamics, the top ranked genes were verified to be predictive of the drug sensitivities of different glioma cell lines, in comparison with other existing methods. The proposed method provides a quantitative approach to gain insights into the dynamic adaptation and regulatory mechanisms of cancer drug resistance and sheds light on the design of novel biomarkers or targets for predicting or overcoming drug resistance.

Modeling heterogeneous tumor growth dynamics and cell-cell interactions at single-cell and cell-population resolution

Cancer is a complex, dynamic disease that despite recent advances remains mostly incurable. Inter- and intratumoral heterogeneity are generally considered major drivers of therapy resistance, metastasis, and treatment failure. Recent advances in high-throughput experimentation have produced a wealth of data on tumor heterogeneity and researchers are increasingly turning to mathematical modeling to aid in the interpretation of these complex datasets. In this mini-review, we discuss three important classes of approaches for modeling cellular dynamics within heterogeneous tumors: agent-based models, population dynamics, and multiscale models. An important new focus, for which we provide an example, is the role of intratumoral cell-cell interactions.

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.

Mathematical modeling and computational prediction of cancer drug resistance

Diverse forms of resistance to anticancer drugs can lead to the failure of chemotherapy. Drug resistance is one of the most intractable issues for successfully treating cancer in current clinical practice. Effective clinical approaches that could counter drug resistance by restoring the sensitivity of tumors to the targeted agents are urgently needed. As numerous experimental results on resistance mechanisms have been obtained and a mass of high-throughput data has been accumulated, mathematical modeling and computational predictions using systematic and quantitative approaches have become increasingly important, as they can potentially provide deeper insights into resistance mechanisms, generate novel hypotheses or suggest promising treatment strategies for future testing. In this review, we first briefly summarize the current progress of experimentally revealed resistance mechanisms of targeted therapy, including genetic mechanisms, epigenetic mechanisms, posttranslational mechanisms, cellular mechanisms, microenvironmental mechanisms and pharmacokinetic mechanisms. Subsequently, we list several currently available databases and Web-based tools related to drug sensitivity and resistance. Then, we focus primarily on introducing some state-of-the-art computational methods used in drug resistance studies, including mechanism-based mathematical modeling approaches (e.g. molecular dynamics simulation, kinetic model of molecular networks, ordinary differential equation model of cellular dynamics, stochastic model, partial differential equation model, agent-based model, pharmacokinetic–pharmacodynamic model, etc.) and data-driven prediction methods (e.g. omics data-based conventional screening approach for node biomarkers, static network approach for edge biomarkers and module biomarkers, dynamic network approach for dynamic network biomarkers and dynamic module network biomarkers, etc.). Finally, we discuss several further questions and future directions for the use of computational methods for studying drug resistance, including inferring drug-induced signaling networks, multiscale modeling, drug combinations and precision medicine.

Optimizing drug development in oncology by clinical trial simulation: Why and how?

In therapeutic research, the safety and efficacy of pharmaceutical products are necessarily tested on humans via clinical trials after an extensive and expensive preclinical development period. Methodologies such as computer modeling and clinical trial simulation (CTS) might represent a valuable option to reduce animal and human assays. The relevance of these methods is well recognized in pharmacokinetics and pharmacodynamics from the preclinical phase to postmarketing. However, they are barely used and are poorly regarded for drug approval, despite Food and Drug Administration and European Medicines Agency recommendations. The generalization of CTS could be greatly facilitated by the availability of software for modeling biological systems, by clinical trial studies and hospital databases. Data sharing and data merging raise legal, policy and technical issues that will need to be addressed. Development of future molecules will have to use CTS for faster development and thus enable better patient management. Drug activity modeling coupled with disease modeling, optimal use of medical data and increased computing speed should allow this leap forward. The realization of CTS requires not only bioinformatics tools to allow interconnection and global integration of all clinical data but also a universal legal framework to protect the privacy of every patient. While recognizing that CTS can never replace 'real-life' trials, they should be implemented in future drug development schemes to provide quantitative support for decision-making. This in silico medicine opens the way to the P4 medicine: predictive, preventive, personalized and participatory.

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.

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.

Multicellular gene network analysis identifies a macrophage-related gene signature predictive of therapeutic response and prognosis of gliomas

BACKGROUND

The tumor-associated microenvironment plays important roles in tumor progression and drug resistance. However, systematic investigations of macrophage-tumor cell interactions to identify novel macrophage-related gene signatures in gliomas for predicting patient prognoses and responses to targeted therapies are lacking.

METHODS

We developed a multicellular gene network approach to investigating the prognostic role of macrophage-tumor cell interactions in tumor progression and drug resistance in gliomas. Multicellular gene networks connecting macrophages and tumor cells were constructed from re-grouped drug-sensitive and drug-resistant samples of RNA-seq data in mice gliomas treated with BLZ945 (a CSF1R inhibitor). Subsequently, a differential network-based COX regression model was built to identify the risk signature using a cohort of 310 glioma samples from the Chinese Glioma Genome Atlas database. A large independent validation set of 690 glioma samples from The Cancer Genome Atlas database was used to test the prognostic significance and accuracy of the gene signature in predicting prognosis and targeted therapeutic response of glioma patients.

RESULTS

A macrophage-related gene signature was developed consisting of twelve genes (ANPEP, DPP4, PRRG1, GPNMB, TMEM26, PXDN, CDH6, SCN3A, SEMA6B, CCDC37, FANCA, NETO2), which was tested in the independent validation set to examine its prognostic significance and accuracy. The generation of 1000 random gene signatures by a bootstrapping scheme justified the non-random nature of the macrophage-related gene signature. Moreover, the discovered gene signature was verified to be predictive of the sensitivity or resistance of glioma patients to molecularly targeted therapeutics and outperformed other existing gene signatures. Additionally, the macrophage-related gene signature was an independent and the strongest prognostic factor when adjusted for clinicopathologic risk factors and other existing gene signatures.

CONCLUSION

The multicellular gene network approach developed herein indicates profound roles of the macrophage-mediated tumor microenvironment in the progression and drug resistance of gliomas. The identified macrophage-related gene signature has good prognostic value for predicting resistance to targeted therapeutics and survival of glioma patients, implying that combining current targeted therapies with new macrophage-targeted therapy may be beneficial for the long-term treatment outcomes of glioma patients.

Multiscale modeling reveals angiogenesis-induced drug resistance in brain tumors and predicts a synergistic drug combination targeting EGFR and VEGFR pathways

BACKGROUND

Experimental studies have demonstrated that both the extracellular vasculature or microenvironment and intracellular molecular network (e.g., epidermal growth factor receptor (EGFR) signaling pathway) are important for brain tumor growth. Additionally, some drugs have been developed to inhibit EGFR signaling pathways. However, how angiogenesis affects the response of tumor cells to drug treatment has rarely been mechanistically studied. Therefore, a multiscale model is required to investigate such complex biological systems that contain interactions and feedback among multiple levels.

RESULTS

In this study, we developed a single cell-based multiscale spatiotemporal model to simulate vascular tumor growth and the drug response based on the vascular endothelial growth factor receptor (VEGFR) signaling pathway, the EGFR signaling pathway and the cell cycle as well as several microenvironmental factors that determine cell fate switches in a temporal and spatial context. By incorporating the EGFRI treatment effect, the model showed an interesting phenomenon in which the survival rate of tumor cells decreased in the early stage but rebounded in a later stage, revealing the emergence of drug resistance. Moreover, we revealed the critical role of angiogenesis in acquired drug resistance, since inhibiting blood vessel growth using a VEGFR inhibitor prevented the recovery of the survival rate of tumor cells in the later stage. We further investigated the optimal timing of combining VEGFR inhibition with EGFR inhibition and predicted that the drug combination targeting both the EGFR pathway and VEGFR pathway has a synergistic effect. The experimental data validated the prediction of drug synergy, confirming the effectiveness of our model. In addition, the combination of EGFR and VEGFR genes showed clinical relevance in glioma patients.

CONCLUSIONS

The developed multiscale model revealed angiogenesis-induced drug resistance mechanisms of brain tumors to EGFRI treatment and predicted a synergistic drug combination targeting both EGFR and VEGFR pathways with optimal combination timing. This study explored the mechanistic and functional mechanisms of the angiogenesis underlying tumor growth and drug resistance, which advances our understanding of novel mechanisms of drug resistance and provides implications for designing more effective cancer therapies.

Concordance measure and discriminatory accuracy in transformation cure models

Many populations of early-stage cancer patients have non-negligible latent cure fractions that can be modeled using transformation cure models. However, there is a lack of statistical metrics to evaluate prognostic utility of biomarkers in this context due to the challenges associated with unknown cure status and heavy censorship. In this article, we develop general concordance measures as evaluation metrics for the discriminatory accuracy of transformation cure models including the so-called promotion time cure models and mixture cure models. We introduce explicit formulas for the consistent estimates of the concordance measures, and show that their asymptotically normal distributions do not depend on the unknown censoring distribution. The estimates work for both parametric and semiparametric transformation models as well as transformation cure models. Numerical feasibility of the estimates and their robustness to the censoring distributions are illustrated via simulation studies and demonstrated using a melanoma data set.

Computational Approaches in Theranostics: Mining and Predicting Cancer Data

The ability to understand the complexity of cancer-related data has been prompted by the applications of (1) computer and data sciences, including data mining, predictive analytics, machine learning, and artificial intelligence, and (2) advances in imaging technology and probe development. Computational modelling and simulation are systematic and cost-effective tools able to identify important temporal/spatial patterns (and relationships), characterize distinct molecular features of cancer states, and address other relevant aspects, including tumor detection and heterogeneity, progression and metastasis, and drug resistance. These approaches have provided invaluable insights for improving the experimental design of therapeutic delivery systems and for increasing the translational value of the results obtained from early and preclinical studies. The big question is: Could cancer theranostics be determined and controlled in silico? This review describes the recent progress in the development of computational models and methods used to facilitate research on the molecular basis of cancer and on the respective diagnosis and optimized treatment, with particular emphasis on the design and optimization of theranostic systems. The current role of computational approaches is providing innovative, incremental, and complementary data-driven solutions for the prediction, simplification, and characterization of cancer and intrinsic mechanisms, and to promote new data-intensive, accurate diagnostics and therapeutics.

Glioma stem cells reconstruct similar immunoinflammatory microenvironment in different transplant sites and induce malignant transformation of tumor microenvironment cells

PURPOSE

This study aimed to examine whether the different tumor-transplanted sites could construct a similar immunoinflammatory microenvironment and to investigate the interactions between tumor microenvironment cells.

METHODS

The red fluorescent protein-SU3 (SU3-RFP) or SU3 glioma stem cells (GSC) were inoculated into the brain, liver, abdominal cavity, and subcutis of green fluorescent protein (GFP)-nude mice. The tumor tissues were taken to observe the tissue cell distribution. The single cell suspension of tumor tissues was prepared and cultured, while the SU3-RFP cells were co-cultured with the cells from GFP-transgenic mice. The RFP+, GFP+, and RFP+/GFP+ cells were traced by fluorescence microscope, and their protein expressions were determined by Western blot analysis. The markers of immunoinflammatory cells, including F4/80, CD11b, CD11c, CD80, CD47, and SIRP-α, were determined by RT-PCR and immunocytochemistry assays, respectively.

RESULTS

The xenograft models of all transplant sites were inducible, and the red tumor cells of tumor tissues were encircled by a great quantity of host-derived green cells, including immunoinflammatory cells with CD80, F4/80, CD11b, and CD11c expressions, which might generate the cell colonies and possess the pseudopodia. Additionally, the interactions between red tumor cells and green immunoinflammatory cells, including cell fusion process and yellow fusion cell formation, were observed in cultured cells. The fusion cells-derived B4 cells with expressions of CD47 and SIRP-α proteins had the strong proliferation ability and tumorigenic effect.

CONCLUSIONS

The similar tumor immunoinflammatory microenvironment was constructed by GSC in different transplant sites, and the cell fusion indicated a malignant transformation of the tumor microenvironment cells.

Cyclical Treatment of Colorectal Tumor Spheroids Induces Resistance to MEK Inhibitors

Adaptive drug resistance is a major obstacle to successful treatment of colorectal cancers. Physiologic tumor models of drug resistance are crucial to understand mechanisms of treatment failure and improve therapy by developing new therapeutics and treatment strategies. Using our aqueous two-phase system microtechnology, we developed colorectal tumor spheroids and periodically treated them with sub-lethal concentrations of three Mitogen Activated Kinase inhibitors (MEKi) used in clinical trials. We used long-term, periodic treatment and recovery of spheroids to mimic cycles of clinical chemotherapy and implemented a growth rate metric to quantitatively assess efficacy of the MEKi during treatment. Our results showed that efficacy of the MEKi significantly reduced with increased treatment cycles. Using a comprehensive molecular analysis, we established that resistance of colorectal tumor spheroids to the MEKi developed through activation of the PI3K/AKT/mTOR pathway. We also showed that other potential feedback mechanisms, such as STAT3 activation or amplified B-RAF, did not account for resistance to the MEKi. We combined each of the three MEKi with a PI3K/mTOR inhibitor and showed that the combination treatments synergistically blocked resistance to the MEKi. Importantly, and unlike the individual inhibitors, we demonstrated that synergistic concentrations of combinations of MEK and PI3K/mTOR inhibitors effectively inhibited growth of colorectal tumor spheroids in long-term treatments. This proof-of-concept study to model treatment-induced drug resistance of cancer cells using 3D cultures offers a unique approach to identify underlying molecular mechanisms and develop effective treatments.