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.

Breast Cancer Exosomal microRNAs Facilitate Pre-Metastatic Niche Formation in the Bone: A Mathematical Model.

Pre-metastatic niche is a location where cancer cells, separating from a primary tumor, find "fertile soil" for growth and proliferation, ensuring successful metastasis. Exosomal miRNAs of breast cancer are known to enter the bone and degrade it, which facilitates cancer cells invasion into the bone interior and ensures its successful colonization. In this paper, we use a mathematical model to first describe, in health, the continuous remodeling of the bone by bone-forming osteoblasts, bone-resorbing osteoclasts and the RANKL-OPG-RANK signaling system, which keeps the balance between bone formation and bone resorption. We next demonstrate how breast cancer exosomal miRNAs disrupt this balance, either by increasing or by decreasing the ratio of osteoclasts/osteoblasts, which results in abnormal high bone resorption or abnormal high bone forming, respectively, and in bone weakening in both cases. Finally we consider the case of abnormally high resorption and evaluate the effect of drugs, which may increase bone density to normal level, thus protecting the bone from invasion by cancer cells.

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.

Optimal timing of steroid initiation in response to CTLA-4 antibody in metastatic cancer: A mathematical model.

Immune checkpoint inhibitors, introduced in recent years, have revolutionized the treatment of many cancers. However, the toxicity associated with this therapy may cause severe adverse events. In the case of advanced lung cancer or metastatic melanoma, a significant number (10%) of patients treated with CTLA-4 inhibitor incur damage to the pituitary gland. In order to reduce the risk of hypophysitis and other severe adverse events, steroids may be combined with CTLA-4 inhibitor; they reduce toxicity, but they also diminish the anti-cancer effect of the immunotherapy. This trade-off between tumor reduction and the risk of severe adverse events poses the following question: What is the optimal time to initiate treatment with steroid. We address this question with a mathematical model from which we can also evaluate the comparative benefits of each schedule of steroid administration. In particular, we conclude that treatment with steroid should not begin too early, but also not very late, after immunotherapy began; more precisely, it should start as soon as tumor volume, under the effect of CTLA-4 inhibitor alone, begins to decrease. We can also compare the benefits of short term treatment of steroid at high doses to a longer term treatment with lower doses.

A cancer model with nonlocal free boundary dynamics.

Cancer cells at the tumor boundary move in the direction of the oxygen gradient, while cancer cells far within the tumor are in a necrotic state. This paper introduces a simple mathematical model that accounts for these facts. The model consists of cancer cells, cytotoxic T cells, and oxygen satisfying a system of partial differential equations. Some of the model parameters represent the effect of anti-cancer drugs. The tumor boundary is a free boundary whose dynamics is determined by the movement of cancer cells at the boundary. The model is simulated for radially symmetric and axially symmetric tumors, and it is shown that the tumor may increase or decrease in size, depending on the "strength" of the drugs. Existence theorems are proved, global in-time in the radially symmetric case, and local in-time for any shape of tumor. In the radially symmetric case, it is proved, under different conditions, that the tumor may shrink monotonically, or expand monotonically.

A mathematical model of immunomodulatory treatment in myocardial infarction.

A heart attack, or acute myocardial infarction (MI) is caused by the acute occlusion of a coronary artery. MI is associated with 30% mortality; approximately half of the deaths occur prior to arrival at the hospital. Reperfusion therapy in the hospital is a medical treatment to restore blood flow through the blocked artery; treatment includes drugs and surgery. However, the damage to the heart muscles through the infarct area is permanent and there is additional damage around the infarct area due to inflammation or insufficient oxygen supply. Approximately half of the patients who survive MI are hospitalized again within one year after reperfusion treatment. In this paper we develop a mathematical model of MI and use it to assess the efficacy of drugs used, post reperfusion, to reduce the damage caused by inflammation in a region of the left ventricular wall surrounding the infarct area. The mathematical model, represented by a system of partial differential equations. The model variables include myocytes, endothelial cells, neutrophils, macrophages, fibroblasts and cytokines that play a role in the interactions among these cells. The drugs used to in the model include IL-1, TNF-α and TGF-ß inhibitors, and the delivery of VEGF. The model is based on mice data. In particular, we find that immunomodulatory treatment with TNF-α and IL-1 inhibitors can significantly increase the low density of myocytes bordering the infarct area by 50-60% and decrease the abnormally high density of ECM in a region surrounding the infarct area.

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.

TGF-ß inhibition can overcome cancer primary resistance to PD-1 blockade: A mathematical model.

Immune checkpoint inhibitors have demonstrated, over the recent years, impressive clinical response in cancer patients, but some patients do not respond at all to checkpoint blockade, exhibiting primary resistance. Primary resistance to PD-1 blockade is reported to occur under conditions of immunosuppressive tumor environment, a condition caused by myeloid derived suppressor cells (MDSCs), and by T cells exclusion, due to increased level of T regulatory cells (Tregs). Since TGF-ß activates Tregs, TGF-ß inhibitor may overcome primary resistance to anti-PD-1. Indeed, recent mice experiments show that combining anti-PD-1 with anti-TGF-ß yields significant therapeutic improvements compared to anti-TGF-ß alone. The present paper introduces two cancer-specific parameters and, correspondingly, develops a mathematical model which explains how primary resistance to PD-1 blockade occurs, in terms of the two cancer-specific parameters, and how, in combination with anti-TGF-ß, anti-PD-1 provides significant benefits. The model is represented by a system of partial differential equations and the simulations are in agreement with the recent mice experiments. In some cancer patients, treatment with anti-PD-1 results in rapid progression of the disease, known as hyperprogression disease (HPD). The mathematical model can also explain how this situation arises, and it predicts that HPD may be reversed by combining anti-TGF-ß to anti-PD-1. The model is used to demonstrate how the two cancer-specific parameters may serve as biomarkers in predicting the efficacy of combination therapy with PD-1 and TGF-ß inhibitors.

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

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

Overcoming Drug Resistance to BRAF Inhibitor.

One of the most frequently found mutations in human melanomas is in the B-raf gene, making its protein BRAF a key target for therapy. However, in patients treated with BRAF inhibitor (BRAFi), although the response is very good at first, relapse occurs within 6 months, on the average. In order to overcome this drug resistance to BRAFi, various combinations of BRAFi with other drugs have been explored, and some are being applied clinically, such as a combination of BRAF and MEK inhibitors. Experimental data for melanoma in mice show that under continuous treatment with BRAFi, the pro-cancer MDSCs and chemokine CCL2 initially decrease but eventually increase to above their original level, while the anticancer T cells continuously decrease. In this paper, we develop a mathematical model that explains these experimental results. The model is used to explore the efficacy of combinations of BRAFi with anti-CCL2, anti-PD-1 and anti-CTLA-4, with the aim of eliminating or reducing drug resistance to BRAFi.

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.

Mathematical modeling in scheduling cancer treatment with combination of VEGF inhibitor and chemotherapy drugs.

The present paper considers a treatment of cancer with a combination of anti-VEGF (bevacizumab) and a chemotherapy drug (docetaxel). Since anti-VEGF reduces the perfusion of chemotherapy drugs, the question arises whether it is more effective to administer the two drugs at the same time, or non-overlapping, in order to reduce tumor volume more effectively. To address this question we develop a mathematical model and use it to simulate different schedules. We find that the treatment of cancer would be far more effective if the two drugs are given non-overlappingly, with the chemotherapy drug at day 0 and anti-VEGF at day 7 in cycles of 21 days.

Modeling combination therapy for breast cancer with BET and immune checkpoint inhibitors.

CTLA-4 is an immune checkpoint expressed on active anticancer T cells. When it combines with its ligand B7 on dendritic cells, it inhibits the activity of the T cells. The Bromo- and Extra-Terminal (BET) protein family includes proteins that regulate the expression of key oncogenes and antiapoptotic proteins. BET inhibitor (BETi) has been shown to reduce the expression of MYC by suppressing its transcription factors and to down-regulate the hypoxic transcriptome response to VEGF-A. This paper develops a mathematical model of the treatment of cancer by combination therapy of BETi and CTLA-4 inhibitor. The model shows that the two drugs are positively correlated in the sense that the tumor volume decreases as the dose of each of the drugs is increased. The model also considers the effect of the combined therapy on levels of myeloid-derived suppressor cells (MDSCs) and the overexpression of TNF-α, which may predict gastrointestinal side effects of the combination.

Chronic hepatitis B virus and liver fibrosis: A mathematical model.

Hepatitis B virus (HBV) infection is a liver disorder that can result in cirrhosis, liver failure and hepatocellular carcinoma. HBV infection remains a major global health problem, as it affects more 350 million people chronically and kills roughly 600,000 people annually. Drugs currently used against HBV include IFN-α that decreases viremia, inflammation and the growth of liver fibrosis, and adefovir that decreases the viral load. Each of these drugs can have severe side-effects. In the present paper, we consider the treatment of chronic HBV by a combination of IFN-α and adefovir, and raise the following question: What should be the optimal ratio between IFN-α and adefovir in order to achieve the best 'efficacy' under constraints on the total amount of the drugs; here the efficacy is measured by the reduction of the levels of inflammation and of fibrosis? We develop a mathematical model of HBV pathogenesis by a system of partial differential equations (PDEs) and use the model to simulate a 'synergy map' which addresses the above question.

Complex role of NK cells in regulation of oncolytic virus-bortezomib therapy.

In the present work, we investigated the role of natural killer (NK) cells in combination therapy with oncolytic virus (OV) and bortezomib, a proteasome inhibitor. NK cells display rapid and potent immunity to metastatic and hematological cancers, and they overcome immunosuppressive effects of tumor microenvironment. We developed a mathematical model to address the question of how the density of NK cells affects the growth of the tumor. We found that the antitumor efficacy increases when the endogenous NKs are depleted and also when exogenous NK cells are injected into the tumor. These predictions were validated by our in vivo and in vitro experiments.

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.

The Role of Exosomes in Pancreatic Cancer Microenvironment.

Exosomes are nanovesicles shed by cells as a means of communication with other cells. Exosomes contain mRNAs, microRNAs (miRs) and functional proteins. In the present paper, we develop a mathematical model of tumor-immune interaction by means of exosomes shed by pancreatic cancer cells and dendritic cells. Cancer cells' exosomes contain miRs that promote their proliferation and that inhibit immune response by dendritic cells, and by CD4+ and CD8+ T cells. Dendritic cells release exosomes with proteins that induce apoptosis of cancer cells and that block regulatory T cells. Simulations of the model show how the size of the pancreatic cancer can be determined by measurement of specific miRs (miR-21 and miR-203 in the case of pancreatic cancer), suggesting these miRs as biomarkers for cancer.

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

BACKGROUND: The B-raf gene is mutated in up to 66% of human malignant melanomas, and its protein product, BRAF kinase, is a key part of RAS-RAF-MEK-ERK (MAPK) pathway of cancer cell proliferation. BRAF-targeted therapy induces significant responses in the majority of patients, and the combination BRAF/MEK inhibitor enhances clinical efficacy, but the response to BRAF inhibitor and to BRAF/MEK inhibitor is short lived. On the other hand, treatment of melanoma with an immune checkpoint inhibitor, such as anti-PD-1, has lower response rate but the response is much more durable, lasting for years. For this reason, it was suggested that combination of BRAF/MEK and PD-1 inhibitors will significantly improve overall survival time. RESULTS: This paper develops a mathematical model to address the question of the correlation between BRAF/MEK inhibitor and PD-1 inhibitor in melanoma therapy. The model includes dendritic and cancer cells, CD 4+ and CD 8+ T cells, MDSC cells, interleukins IL-12, IL-2, IL-6, IL-10 and TGF- ß, PD-1 and PD-L1, and the two drugs: BRAF/MEK inhibitor (with concentration γ B ) and PD-1 inhibitor (with concentration γ A ). The model is represented by a system of partial differential equations, and is used to develop an efficacy map for the combined concentrations (γ B ,γ A ). It is shown that the two drugs are positively correlated if γ B and γ A are at low doses, that is, the growth of the tumor volume decreases if either γ B or γ A is increased. On the other hand, the two drugs are antagonistic at some high doses, that is, there are zones of (γ B ,γ A ) where an increase in one of the two drugs will increase the tumor volume growth, rather than decrease it. CONCLUSIONS: It will be important to identify, by animal experiments or by early clinical trials, the zones of (γ B ,γ A ) where antagonism occurs, in order to avoid these zones in more advanced clinical trials.

Combination therapy of cancer with cancer vaccine and immune checkpoint inhibitors: A mathematical model.

In this paper we consider a combination therapy of cancer. One drug is a vaccine which activates dendritic cells so that they induce more T cells to infiltrate the tumor. The other drug is a checkpoint inhibitor, which enables the T cells to remain active against the cancer cells. The two drugs are positively correlated in the sense that an increase in the amount of each drug results in a reduction in the tumor volume. We consider the question whether a treatment with combination of the two drugs at certain levels is preferable to a treatment by one of the drugs alone at 'roughly' twice the dosage level; if that is the case, then we say that there is a positive 'synergy' for this combination of dosages. To address this question, we develop a mathematical model using a system of partial differential equations. The variables include dendritic and cancer cells, CD4+ and CD8+ T cells, IL-12 and IL-2, GM-CSF produced by the vaccine, and a T cell checkpoint inhibitor associated with PD-1. We use the model to explore the efficacy of the two drugs, separately and in combination, and compare the simulations with data from mouse experiments. We next introduce the concept of synergy between the drugs and develop a synergy map which suggests in what proportion to administer the drugs in order to achieve the maximum reduction of tumor volume under the constraint of maximum tolerated dose.

Mathematical model of chronic pancreatitis.

Chronic pancreatitis (CP) is a progressive inflammatory disease of the pancreas, leading to its fibrotic destruction. There are currently no drugs that can stop or slow the progression of the disease. The etiology of the disease is multifactorial, whereas recurrent attacks of acute pancreatitis are thought to precede the development of CP. A better understanding of the pathology of CP is needed to facilitate improved diagnosis and treatment strategies for this disease. The present paper develops a mathematical model of CP based on a dynamic network that includes macrophages, pancreatic stellate cells, and prominent cytokines that are present at high levels in the CP microenvironment. The model is represented by a system of partial differential equations. The model is used to explore in silico potential drugs that could slow the progression of the disease, for example infliximab (anti-TNF-[Formula: see text]) and tocilizumab or siltuximab (anti-IL-6/IL-6R).