Combination therapy for melanoma with BRAF/MEK inhibitor and immune checkpoint inhibitor: a mathematical model

Mathematical modeling and analysis of cancer treatment with radiation and anti-PD-L1

In cancer treatment, radiation therapy (RT) induces direct tumor cell death due to DNA damage, but it also enhances the deaths of radiosensitive immune cells and is followed by local relapse and up-regulation of immune checkpoint ligand PD-L1. Since the binding between PD-1 and PD-L1 curtails anti-tumor immunities, combining RT and PD-L1 inhibitor, anti-PD-L1, is a potential method to improve the treatment efficacy by RT. Some experiments support this hypothesis by showing that the combination of ionizing irradiation (IR) and anti-PD-L1 improves tumor reduction comparing to the monotherapy of IR or anti-PD-L1. In this work, we create a simplified ODE model to study the order of tumor growths under treatments of IR and anti-PD-L1. Our synergy analysis indicates that both IR and anti-PD-L1 improve the tumor reduction of each other, when IR and anti-PD-L1 are given simultaneously. When giving IR and anti-PD-L1 separately, a high dosage of IR should be given first to efficiently reduce tumor load and then followed by anti-PD-L1 with strong efficacy to maintain the tumor reduction and slow down the relapse. Increasing the duration of anti-PD-L1 improves the tumor reduction, but it cannot prolong the duration that tumor relapses to the level of the control case. Under some simplification, we also prove that the model has an unstable tumor free equilibrium and a locally asymptotically stable tumor persistent equilibrium. Our bifurcation diagram reveals a transition from tumor elimination to tumor persistence, as the tumor growth rate increases. In the tumor persistent case, both anti-PD-L1 and IR can reduce tumor amount in the long term.

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.

IL-27 in combination with anti-PD-1 can be anti-cancer or pro-cancer

Interleukin-27 (IL-27) is known to play opposing roles in immunology. The present paper considers, specifically, the role IL-27 plays in cancer immunotherapy when combined with immune checkpoint inhibitor anti-PD-1. We first develop a mathematical model for this combination therapy, by a system of Partial Differential Equations, and show agreement with experimental results in mice injected with melanoma cells. We then proceed to simulate tumor volume with IL-27 injection at a variable dose F and anti-PD-1 at a variable dose g. We show that in some range of "small" values of g, as f increases tumor volume decreases as long as fFc(g), where Fc(g) is a monotone increasing function of g. This demonstrates that IL-27 can be both anti-cancer and pro-cancer, depending on the ranges of both anti-PD-1 and IL-27.

Different mechanisms of CD200-CD200R induce diverse outcomes in cancer treatment

The CD200 is a cell membrane protein expressed by tumor cells, and its receptor CD200 receptor (CD200R) is expressed by immune cells including macrophages and dendritic cells. The formation of CD200-CD200R inhibits the cellular functions of the targeted immune cells, so CD200 is one type of the immune checkpoint and blockade CD200-CD200R formation is a potential cancer treatment. However, the CD200 blockade has opposite treatment outcomes in different types of cancers. For instance, the CD200R deficient mice have a higher tumor load than the wild type (WT) mice in melanoma suggesting that CD200-CD200R inhibits melanoma. On the other hand, the antibody anti-CD200 treatment in pancreatic ductal adenocarcinoma (PDAC) and head and neck squamous cell carcinoma (HNSCC) significantly reduces the tumor load indicating that CD200-CD200R promotes PDAC and HNSCC. In this work, we hypothesize that different mechanisms of CD200-CD200R in tumor microenvironment could be one of the reasons for the diverse treatment outcomes of CD200 blockade in different types of cancers. We create one Ordinary Differential Equations (ODEs) model for melanoma including the inhibition of CCL8 and regulatory T cells and the switching from M2 to M1 macrophages by CD200-CD200R to capture the tumor inhibition by CD200-CD200R. We also create another ODEs model for PDAC and HNSCC including the promotion of the polarization and suppressive activities of M2 macrophages by CD200-CD200R to generate the tumor promotion by CD200-CD200R. Furthermore, we use these two models to investigate the treatment efficacy of the combination treatment between the CD200-CD200R blockade and the other immune checkpoint inhibitor, anti-PD-1. Our result shows that different mechanisms of CD200-CD200R can induce different treatment outcomes in combination treatments, namely, only the CD200-CD200R blockade reduces tumor load in melanoma and only the anti-PD-1 and CD200 knockout decrease tumor load in PDAC and HNSCC. Moreover, in melanoma, the CD200-CD200R mainly utilizes the inhibitions on M1 macrophages and dendritic cells to inhibit tumor growth, instead of M2 macrophages.

Immune-checkpoint inhibitor therapy response evaluation using oncophysics-based mathematical models

The field of oncology has transformed with the advent of immunotherapies. The standard of care for multiple cancers now includes novel drugs that target key checkpoints that function to modulate immune responses, enabling the patient's immune system to elicit an effective anti-tumor response. While these immune-based approaches can have dramatic effects in terms of significantly reducing tumor burden and prolonging survival for patients, the therapeutic approach remains active only in a minority of patients and is often not durable. Multiple biological investigations have identified key markers that predict response to the most common form of immunotherapy-immune checkpoint inhibitors (ICI). These biomarkers help enrich patients for ICI but are not 100% predictive. Understanding the complex interactions of these biomarkers with other pathways and factors that lead to ICI resistance remains a major goal. Principles of oncophysics-the idea that cancer can be described as a multiscale physical aberration-have shown promise in recent years in terms of capturing the essence of the complexities of ICI interactions. Here, we review the biological knowledge of mechanisms of ICI action and how these are incorporated into modern oncophysics-based mathematical models. Building on the success of oncophysics-based mathematical models may help to discover new, rational methods to engineer immunotherapy for patients in the future. This article is categorized under: Therapeutic Approaches and Drug Discovery > Nanomedicine for Oncologic Disease.

Cancer therapy with immune checkpoint inhibitor and CSF-1 blockade: A mathematical model

Immune checkpoint inhibitors (ICIs) introduced in recent years have revolutionized the treatment of many metastatic cancers. However, data suggest that treatment has benefits only in a limited percentage of patients, and that this is due to immune suppression of the tumor microenvironment (TME). Anti-tumor inflammatory macrophages (M1), which are attracted to the TME, are converted by tumor secreted cytokines, such as CSF-1, to pro-tumor anti-inflammatory macrophages (M2), or tumor associated macrophages (TAMs), which block the anti-tumor T cells. In the present paper we develop a mathematical model that represents the interactions among the immune cells and cancer in terms of differential equations. The model can be used to assess treatments of combination therapy of anti-PD-1 with anti-CSF-1. Examples are given in comparing the efficacy among different strategies for anti-CSF-1 dosing in a setup of clinical trials.

Melanoma 2.0. Skin cancer as a paradigm for emerging diagnostic technologies, computational modelling and artificial intelligence

We live in an unprecedented time in oncology. We have accumulated samples and cases in cohorts larger and more complex than ever before. New technologies are available for quantifying solid or liquid samples at the molecular level. At the same time, we are now equipped with the computational power necessary to handle this enormous amount of quantitative data. Computational models are widely used helping us to substantiate and interpret data. Under the label of systems and precision medicine, we are putting all these developments together to improve and personalize the therapy of cancer. In this review, we use melanoma as a paradigm to present the successful application of these technologies but also to discuss possible future developments in patient care linked to them. Melanoma is a paradigmatic case for disruptive improvements in therapies, with a considerable number of metastatic melanoma patients benefiting from novel therapies. Nevertheless, a large proportion of patients does not respond to therapy or suffers from adverse events. Melanoma is an ideal case study to deploy advanced technologies not only due to the medical need but also to some intrinsic features of melanoma as a disease and the skin as an organ. From the perspective of data acquisition, the skin is the ideal organ due to its accessibility and suitability for many kinds of advanced imaging techniques. We put special emphasis on the necessity of computational strategies to integrate multiple sources of quantitative data describing the tumour at different scales and levels.

Distinct Dynamics of Migratory Response to PD-1 and CTLA-4 Blockade Reveals New Mechanistic Insights for Potential T-Cell Reinvigoration following Immune Checkpoint Blockade

Cytotoxic T-lymphocyte-associated antigen 4 (CTLA-4) and programmed cell death protein 1 (PD-1), two clinically relevant targets for the immunotherapy of cancer, are negative regulators of T-cell activation and migration. Optimizing the therapeutic response to CTLA-4 and PD-1 blockade calls for a more comprehensive insight into the coordinated function of these immune regulators. Mathematical modeling can be used to elucidate nonlinear tumor-immune interactions and highlight the underlying mechanisms to tackle the problem. Here, we investigated and statistically characterized the dynamics of T-cell migration as a measure of the functional response to these pathways. We used a previously developed three-dimensional organotypic culture of patient-derived tumor spheroids treated with anti-CTLA-4 and anti-PD-1 antibodies for this purpose. Experiment-based dynamical modeling revealed the delayed kinetics of PD-1 activation, which originates from the distinct characteristics of PD-1 and CTLA-4 regulation, and followed through with the modification of their contributions to immune modulation. The simulation results show good agreement with the tumor cell reduction and active immune cell count in each experiment. Our findings demonstrate that while PD-1 activation provokes a more exhaustive intracellular cascade within a mature tumor environment, the time-delayed kinetics of PD-1 activation outweighs its preeminence at the individual cell level and consequently confers a functional dominance to the CTLA-4 checkpoint. The proposed model explains the distinct immunostimulatory pattern of PD-1 and CTLA-4 blockade based on mechanisms involved in the regulation of their expression and may be useful for planning effective treatment schemes targeting PD-1 and CTLA-4 functions.

Mathematical modeling for the combination treatment of IFN- γ and anti-PD-1 in cancer immunotherapy

When the immune-checkpoint programmed death-1 (PD-1) binds to its ligand programmed death ligand 1 (PD-L1) to form the complex PD-1-PD-L1, this complex inactivates immune cells resulting in cell apoptosis, downregulation of immune reaction, and tumor evasion. The antibody, anti-PD-1 or anti-PD-L1, blocks the PD-1-PD-L1 complex formation to restore the functions of T cells. Combination of anti-PD-1 with other treatment shows promising in different types of cancer treatments. Interferon-gamma (IFN-γ) plays an important role in immune responses. It is mainly regarded as a pro-inflammatory cytokine that promotes the proliferation of CD8⁺ T cell and cytotoxic T cell, enhances the activation of Th1 cells and CD8⁺ T cells, and enhances tumor elimination. However, recent studies have been discovering many anti-inflammatory functions of IFN-γ, such as promotion of the PD-L1 expression, T cell apoptosis, and tumor metastasis, as well as inhibition of the immune recognition and the killing rates by T cells. In this work, we construct a mathematical model incorporating pro-inflammatory and anti-inflammatory functions of IFN-γ to capture tumor growth under anti-PD-1 treatment in the wild type and IFN-γ null mutant melanoma. Our simulation results qualitatively fit experimental data that IFN-γ null mutant with anti-PD-1 obtains the highest tumor reduction comparing to IFN-γ null mutant without anti-PD-1 and wild type tumor with anti-PD-1 therapy. Moreover, our synergy analysis indicates that, in the combination treatment, the tumor volume decreases as either the dosage of anti-PD-1 increases or the IFN-γ production efficiency decreases. Thus, the combination of anti-PD-1 and IFN-γ blockade improves the tumor reduction comparing to the monotherapy of anti-PD-1 or the monotherapy of IFN-γ blockade. We also find a threshold curve of the minimal dosage of anti-PD-1 corresponding to the IFN-γ production efficiency to ensure the tumor reduction under the presence of IFN-γ.

Mathematical Modeling and Analysis of CD200-CD200R in Cancer Treatment

CD200 is a cell membrane protein that binds to its receptor, CD200 receptor (CD200R). The CD200 positive tumor cells inhibit the cellular functions of M1 and M2 macrophages and dendritic cells (DCs) through the CD200-CD200R complex, resulting in downregulation of Interleukin-10 and Interleukin-12 productions and affecting the activation of cytotoxic T lymphocytes. In this work, we provide two ordinary differential equation models, one complete model and one simplified model, to investigate how the binding affinities of CD200R and the populations of M1 and M2 macrophages affect the functions of the CD200-CD200R complex in tumor growth. Our simulations demonstrate that (i) the impact of the CD200-CD200R complex on tumor promotion or inhibition highly depends on the binding affinity of the CD200R on M2 macrophages and DCs to the CD200 on tumor cells, and (ii) a stronger binding affinity of the CD200R on M1 macrophages or DCs to the CD200 on tumor cells induces a higher tumor cell density in the CD200 positive tumor. Thus, the CD200 blockade would be an efficient treatment method in this case. Moreover, the simplified model shows that the binding affinity of CD200R on macrophages is the major factor to determine the treatment efficacy of CD200 blockade when the binding affinities of CD200R on M1 and M2 macrophages are significantly different to each other. On the other hand, both the binding affinity of CD200R and the population of macrophages are the major factors to determine the treatment efficacy of CD200 blockade when the binding affinities of CD200R on M1 and M2 macrophages are close to each other. We also analyze the simplified model to investigate the dynamics of the positive and trivial equilibria of the CD200 positive tumor case and the CD200 deficient tumor case. The bifurcation diagrams show that when M1 macrophages dominate the population, the tumor cell density of the CD200 positive tumor is higher than the one of CD200 deficient tumor. Moreover, the dynamics of tumor cell density change from tumor elimination to tumor persistence to oscillation, as the maximal proliferation rate of tumor cells increases.

Combination Therapy in Alzheimer’s Disease: Is It Time?

Alzheimer’s disease (AD) is the most common cause of dementia globally. There is increasing evidence showing AD has no single pathogenic mechanism, and thus treatment approaches focusing only on one mechanism are unlikely to be meaningfully effective. With only one potentially disease modifying treatment approved, targeting amyloid-β (Aβ), AD is underserved regarding effective drug treatments. Combining multiple drugs or designing treatments that target multiple pathways could be an effective therapeutic approach. Considering the distinction between added and combination therapies, one can conclude that most trials fall under the category of added therapies. For combination therapy to have an actual impact on the course of AD, it is likely necessary to target multiple mechanisms including but not limited to Aβ and tau pathology. Several challenges have to be addressed regarding combination therapy, including choosing the correct agents, the best time and stage of AD to intervene, designing and providing proper protocols for clinical trials. This can be achieved by a cooperation between the pharmaceutical industry, academia, private research centers, philanthropic institutions, and the regulatory bodies. Based on all the available information, the success of combination therapy to tackle complicated disorders such as cancer, and the blueprint already laid out on how to implement combination therapy and overcome its challenges, an argument can be made that the field has to move cautiously but quickly toward designing new clinical trials, further exploring the pathological mechanisms of AD, and re-examining the previous studies with combination therapies so that effective treatments for AD may be finally found.

Interlocked feedback loops balance the adaptive immune response

Adaptive immune responses can be activated by harmful stimuli. Upon activation, a cascade of biochemical events ensues the proliferation and the differentiation of T cells, which can remove the stimuli and undergo cell death to maintain immune cell homeostasis. However, normal immune processes can be disrupted by certain dysregulations, leading to pathological responses, such as cytokine storms and immune escape. In this paper, a qualitative mathematical model, composed of key feedback loops within the immune system, was developed to study the dynamics of various response behaviors. First, simulation results of the model well reproduce the results of several immune response processes, particularly pathological immune responses. Next, we demonstrated how the interaction of positive and negative feedback loops leads to irreversible bistable, reversible bistable and monostable, which characterize different immune response processes: cytokine storm, normal immune response, immune escape. The stability analyses suggest that the switch-like behavior is the basis of rapid activation of the immune system, and a balance between positive and negative regulation loops is necessary to prevent pathological responses. Furthermore, we have shown how the treatment moves the system back to a healthy state from the pathological immune response. The bistable mechanism that revealed in this work is helpful to understand the dynamics of different immune response processes.

Combination therapy for mCRPC with immune checkpoint inhibitors, ADT and vaccine: A mathematical model

Metastatic castration resistant prostate cancer (mCRPC) is commonly treated by androgen deprivation therapy (ADT) in combination with chemotherapy. Immune therapy by checkpoint inhibitors, has become a powerful new tool in the treatment of melanoma and lung cancer, and it is currently being used in clinical trials in other cancers, including mCRPC. However, so far, clinical trials with PD-1 and CTLA-4 inhibitors have been disappointing. In the present paper we develop a mathematical model to assess the efficacy of any combination of ADT with cancer vaccine, PD-1 inhibitor, and CTLA-4 inhibitor. The model is represented by a system of partial differential equations (PDEs) for cells, cytokines and drugs whose density/concentration evolves in time within the tumor. Efficacy of treatment is determined by the reduction in tumor volume at the endpoint of treatment. In mice experiments with ADT and various combinations of PD-1 and CTLA-4 inhibitors, tumor volume at day 30 was always larger than the initial tumor. Our model, however, shows that we can decrease tumor volume with large enough dose; for example, with 10 fold increase in the dose of anti-PD-1, initial tumor volume will decrease by 60%. Although the treatment with ADT in combination with PD-1 inhibitor or CTLA-4 inhibitor has been disappointing in clinical trials, our simulations suggest that, disregarding negative effects, combinations of ADT with checkpoint inhibitors can be effective in reducing tumor volume if larger doses are used. This points to the need for determining the optimal combination and amounts of dose for individual patients.

Intratumoral VEGF nanotrapper reduces gliobastoma vascularization and tumor cell mass

Glioblastoma multiforme (GBM) is the most aggressive and invasive malignant brain cancer. GBM is characterized by a dramatic metabolic imbalance leading to increased secretion of the pro-angiogenic factor VEGF and subsequent abnormal tumor vascularization. In 2009, FDA approved the intravenous administration of bevacizumab, an anti-VEGF monoclonal antibody, as a therapeutic agent for patients with GBM. However, the number of systemic side effects and reduced accessibility of bevacizumab to the central nervous system and consequently to the GBM tumor mass limited its effectiveness in improving patient survival. In this study, we combined experimental and computational modelling to quantitatively characterize the dynamics of VEGF secretion and turnover in GBM and in normal brain cells and simultaneous monitoring of vessel growth. We showed that sequestration of VEGF inside GBM cells, can be used as a novel target for improved bevacizumab-based therapy. We have engineered the VEGF nanotrapper, a cargo system that allows cellular uptake of bevacizumab and inhibits VEGF secretion required for angiogenesis activation and development. Here, we show the therapeutic efficacy of this nanocargo in reducing vascularization and tumor cell mass of GBM in vitro and in vivo cancer models.

A fractional model of cancer-immune system with Caputo and Caputo-Fabrizio derivatives

Recently, it is important to try to understand diseases with large mortality rates worldwide, such as infectious disease and cancer. For this reason, mathematical modeling can be used to comment on diseases that adversely affect all people. So, this paper discuss mathematical model presented for the first time that examines the interaction between immune system and cancer cells by adding IL-12 cytokine and anti-PD-L1 inhibitor. The proposed ordinary differential new mathematical model is studied by considering in term of Caputo and Caputo-Fabrizio (CF) derivative. Stability analysis, existence, and uniqueness of the solution is examined for Caputo fractional derivative. Then numerical simulations of ordinary and fractional differential new mathematical model are given. It is obtained that a reduction (20%-80%) of the number of cancer cells for Caputo derivative and ( 100 % ) of the number of cancer cells for CF derivative. The reduction is one of the most important aspects of the new fractional model for the order discussed especially obtained for CF derivative.

Computational modelling of modern cancer immunotherapy

Modern cancer immunotherapy has revolutionised oncology and carries the potential to radically change the approach to cancer treatment. However, numerous questions remain to be answered to understand immunotherapy response better and further improve the benefit for future cancer patients. Computational models are promising tools that can contribute to accelerated immunotherapy research by providing new clues and hypotheses that could be tested in future trials, based on preceding simulations in addition to the empirical rationale. In this topical review, we briefly summarise the history of cancer immunotherapy, including computational modelling of traditional cancer immunotherapy, and comprehensively review computational models of modern cancer immunotherapy, such as immune checkpoint inhibitors (as monotherapy and combination treatment), co-stimulatory agonistic antibodies, bispecific antibodies, and chimeric antigen receptor T cells. The modelling approaches are classified into one of the following categories: data-driven top-down vs mechanistic bottom-up, simplistic vs detailed, continuous vs discrete, and hybrid. Several common modelling approaches are summarised, such as pharmacokinetic/pharmacodynamic models, Lotka-Volterra models, evolutionary game theory models, quantitative systems pharmacology models, spatio-temporal models, agent-based models, and logic-based models. Pros and cons of each modelling approach are critically discussed, particularly with the focus on the potential for successful translation into immuno-oncology research and routine clinical practice. Specific attention is paid to calibration and validation of each model, which is a necessary prerequisite for any successful model, and at the same time, one of the main obstacles. Lastly, we provide guidelines and suggestions for the future development of the field.

Metabolism and Distribution of Novel Tumor Targeting Drugs In Vivo

BACKGROUND

As a new tumor therapy, targeted therapy is becoming a hot topic due to its high efficiency and low toxicity. Drug effects of targeted tumor drugs are closely related to pharmacokinetics, so it is important to understand their distribution and metabolism in vivo.

METHODS

A systematic review of the literature on the metabolism and distribution of targeted drugs over the past 20 years was conducted, and the pharmacokinetic parameters of approved targeted drugs were summarized in combination with the FDA's drug instructions. Targeting drugs are divided into two categories: small molecule inhibitors and monoclonal antibodies. Novel targeting drugs and their mechanisms of action, which have been developed in recent years, are summarized. The distribution and metabolic processes of each drug in the human body are reviewed.

RESULTS

In this review, we found that the distribution and metabolism of small molecule kinase inhibitors (TKI) and monoclonal antibodies (mAb) showed different characteristics based on the differences of action mechanism and molecular characteristics. TKI absorbed rapidly (Tmax ≈ 1-4 h) and distributed in large amounts (Vd > 100 L). It was mainly oxidized and reduced by cytochrome P450 CYP3A4. However, due to the large molecular diameter, mAb was distributed to tissues slowly, and the volume of distribution was usually very low (Vd < 10 L). It was mainly hydrolyzed and metabolized into peptides and amino acids by protease hydrolysis. In addition, some of the latest drugs are still in clinical trials, and the in vivo process still needs further study.

CONCLUSION

According to the summary of the research progress of the existing targeting drugs, it is found that they have high specificity, but there are still deficiencies in drug resistance and safety. Therefore, the development of safer and more effective targeted drugs is the future research direction. Meanwhile, this study also provides a theoretical basis for clinical accurate drug delivery.

Quantitative Mechanistic Modeling in Support of Pharmacological Therapeutics Development in Immuno-Oncology

Following the approval, in recent years, of the first immune checkpoint inhibitor, there has been an explosion in the development of immuno-modulating pharmacological modalities for the treatment of various cancers. From the discovery phase to late-stage clinical testing and regulatory approval, challenges in the development of immuno-oncology (IO) drugs are multi-fold and complex. In the preclinical setting, the multiplicity of potential drug targets around immune checkpoints, the growing list of immuno-modulatory molecular and cellular forces in the tumor microenvironment-with additional opportunities for IO drug targets, the emergence of exploratory biomarkers, and the unleashed potential of modality combinations all have necessitated the development of quantitative, mechanistically-oriented systems models which incorporate key biology and patho-physiology aspects of immuno-oncology and the pharmacokinetics of IO-modulating agents. In the clinical setting, the qualification of surrogate biomarkers predictive of IO treatment efficacy or outcome, and the corresponding optimization of IO trial design have become major challenges. This mini-review focuses on the evolution and state-of-the-art of quantitative systems models describing the tumor vs. immune system interplay, and their merging with quantitative pharmacology models of IO-modulating agents, as companion tools to support the addressing of these challenges.

How to schedule VEGF and PD-1 inhibitors in combination cancer therapy?

Background

One of the questions in the design of cancer clinical trials with combination of two drugs is in which order to administer the drugs. This is an important question, especially in the case where one agent may interfere with the effectiveness of the other agent.

Results

In the present paper we develop a mathematical model to address this scheduling question in a specific case where one of the drugs is anti-VEGF, which is known to affect the perfusion of other drugs. As a second drug we take anti-PD-1. Both drugs are known to increase the activation of anticancer T cells. Our simulations show that in the case where anti-VEGF reduces the perfusion, a non-overlapping schedule is significantly more effective than a simultaneous injection of the two drugs, and it is somewhat more beneficial to inject anti-PD-1 first.

Conclusion

The method and results of the paper can be extended to other combinations, and they could play an important role in the design of clinical trials with combination therapy, where scheduling strategies may significantly affect the outcome.

A structural methodology for modeling immune-tumor interactions including pro- and anti-tumor factors for clinical applications

The immune system turns out to have both stimulatory and inhibitory factors influencing on tumor growth. In recent years, the pro-tumor role of immunity factors such as regulatory T cells and TGF-β cytokines has specially been considered in mathematical modeling of tumor-immune interactions. This paper presents a novel structural methodology for reviewing these models and classifies them into five subgroups on the basis of immune factors included. By using our experimental data due to immunotherapy experimentation in mice, these five modeling groups are evaluated and scored. The results show that a model with a small number of variables and coefficients performs efficiently in predicting the tumor-immune system interactions. Though immunology theorems suggest to employ a larger number of variables and coefficients, more complicated models are here shown to be inefficient due to redundant parallel pathways. So, these models are trapped in local minima and restricted in prediction capability. This paper investigates the mathematical models that were previously developed and proposes variables and pathways that are essential for modeling tumor-immune. Using these variables and pathways, a minimal structure for modeling tumor-immune interactions is proposed for future studies.

Personalized Medicine in Malignant Melanoma: Towards Patient Tailored Treatment

Despite enormous international efforts, skin melanoma is still a major clinical challenge. Melanoma takes a top place among the most common cancer types and it has one of the most rapidly increasing incidences in many countries around the world. Until recent years, there have been limited options for effective systemic treatment of disseminated melanoma. However, lately, we have experienced a rapid advancement in the understanding of the biology and molecular background of the disease. This has led to new molecular classifications and the development of more effective targeted therapies adapted to distinct melanoma subtypes. Not only are these treatments more effective but they can be rationally prescribed to the patients standing to benefit. As such, melanoma management has now become one of the most developed for personalized medicine. The aim of the present paper is to summarize the current knowledge on melanoma molecular classification, predictive markers, combination therapies, as well as emerging new treatments.

Three-dimensional experiments and individual based simulations show that cell proliferation drives melanoma nest formation in human skin tissue

Background

Melanoma can be diagnosed by identifying nests of cells on the skin surface. Understanding the processes that drive nest formation is important as these processes could be potential targets for new cancer drugs. Cell proliferation and cell migration are two potential mechanisms that could conceivably drive melanoma nest formation. However, it is unclear which one of these two putative mechanisms plays a dominant role in driving nest formation.

Results

We use a suite of three-dimensional (3D) experiments in human skin tissue and a parallel series of 3D individual-based simulations to explore whether cell migration or cell proliferation plays a dominant role in nest formation. In the experiments we measure nest formation in populations of irradiated (non-proliferative) and non-irradiated (proliferative) melanoma cells, cultured together with primary keratinocyte and fibroblast cells on a 3D experimental human skin model. Results show that nest size depends on initial cell number and is driven primarily by cell proliferation rather than cell migration.

Conclusions

Nest size depends on cell number, and is driven primarily by cell proliferation rather than cell migration. All experimental results are consistent with simulation data from a 3D individual based model (IBM) of cell migration and cell proliferation.

Electronic supplementary material

The online version of this article (10.1186/s12918-018-0559-9) contains supplementary material, which is available to authorized users.

Endocytosis as a stabilizing mechanism for tissue homeostasis

Cells in tissues communicate by secreted growth factors (GF) and other signals. An important function of cell circuits is tissue homeostasis: maintaining proper balance between the amounts of different cell types. Homeostasis requires negative feedback on the GFs, to avoid a runaway situation in which cells stimulate each other and grow without control. Feedback can be obtained in at least two ways: endocytosis in which a cell removes its cognate GF by internalization and cross-inhibition in which a GF down-regulates the production of another GF. Here we ask whether there are design principles for cell circuits to achieve tissue homeostasis. We develop an analytically solvable framework for circuits with multiple cell types and find that feedback by endocytosis is far more robust to parameter variation and has faster responses than cross-inhibition. Endocytosis, which is found ubiquitously across tissues, can even provide homeostasis to three and four communicating cell types. These design principles form a conceptual basis for how tissues maintain a healthy balance of cell types and how balance may be disrupted in diseases such as degeneration and fibrosis.

Combination therapy for cancer with oncolytic virus and checkpoint inhibitor: A mathematical model

Oncolytic virus (OV) is a replication competent virus that selectively invades cancer cells; as these cells die under the viral burden, the released virus particles proceed to infect other cancer cells. Oncolytic viruses are designed to also be able to stimulate the anticancer immune response. Thus, one may represent an OV by two parameters: its replication potential and its immunogenicity. In this paper we consider a combination therapy with OV and a checkpoint inhibitor, anti-PD-1. We evaluate the efficacy of the combination therapy in terms of the tumor volume at some later time, for example, 6 months from initial treatment. Since T cells kill not only virus-free cancer cells but also virus-infected cancer cells, the following question arises: Does increasing the amount of the checkpoint inhibitor always improve the efficacy? We address this question, by a mathematical model consisting of a system of partial differential equations. We use the model to construct, by simulations, an efficacy map in terms of the doses of the checkpoint inhibitor and the OV injection. We show that there are regions in the map where an increase in the checkpoint inhibitor actually decreases the efficacy of the treatment. We also construct efficacy maps with checkpoint inhibitor vs. the replication potential of the virus that show the same antagonism, namely, an increase in the checkpoint inhibitor may actually decrease the efficacy. These results have implications for clinical trials.