Optimal control strategies of eradicating invisible glioblastoma cells after conventional surgery

Bistable dynamics of TAN-NK cells in tumor growth and control of radiotherapy-induced neutropenia in lung cancer treatment

Neutrophils play a crucial role in the innate immune response as a first line of defense in many diseases, including cancer. Tumor-associated neutrophils (TANs) can either promote or inhibit tumor growth in various steps of cancer progression via mutual interactions with cancer cells in a complex tumor microenvironment (TME). In this study, we developed and analyzed mathematical models to investigate the role of natural killer cells (NK cells) and the dynamic transition between N1 and N2 TAN phenotypes in killing cancer cells through key signaling networks and how adjuvant therapy with radiation can be used in combination to increase anti-tumor efficacy. We examined the complex immune-tumor dynamics among N1/N2 TANs, NK cells, and tumor cells, communicating through key extracellular mediators (Transforming growth factor (TGF-$ \beta $), Interferon gamma (IFN-$ \gamma $)) and intracellular regulation in the apoptosis signaling network. We developed several tumor prevention strategies to eradicate tumors, including combination (IFN-$ \gamma $, exogenous NK, TGF-$ \beta $ inhibitor) therapy and optimally-controlled ionizing radiation in a complex TME. Using this model, we investigated the fundamental mechanism of radiation-induced changes in the TME and the impact of internal and external immune composition on the tumor cell fate and their response to different treatment schedules.

Optimal strategies of oncolytic virus-bortezomib therapy via the apoptotic, necroptotic, and oncolysis signaling network

Bortezomib and oncolytic virotherapy are two emerging targeted cancer therapies. Bortezomib, a proteasome inhibitor, disrupts protein degradation in cells, leading to the accumulation of unfolded proteins that induce apoptosis. On the other hand, virotherapy uses genetically modified oncolytic viruses (OVs) to infect cancer cells, trigger cell lysis, and activate anti-tumor response. Despite progress in cancer treatment, identifying administration protocols for therapeutic agents remains a significant concern, aiming to strike a balance between efficacy, minimizing toxicity, and administrative costs. In this work, optimal control theory was employed to design a cost-effective and efficient co-administration protocols for bortezomib and OVs that could significantly diminish the population of cancer cells via the cell death program with the NF$ \kappa $B-BAX-RIP1 signaling network. Both linear and quadratic control strategies were explored to obtain practical treatment approaches by adapting necroptosis protocols to efficient cell death programs. Our findings demonstrated that a combination therapy commencing with the administration of OVs followed by bortezomib infusions yields an effective tumor-killing outcome. These results could provide valuable guidance for the development of clinical administration protocols in cancer treatment.

Optimal regulation of tumour-associated neutrophils in cancer progression

In a tumour microenvironment, tumour-associated neutrophils could display two opposing differential phenotypes: anti-tumour (N1) and pro-tumour (N2) effector cells. Converting N2 to N1 neutrophils provides innovative therapies for cancer treatment. In this study, a mathematical model for N1-N2 dynamics describing the cancer survival and immune inhibition in response to TGF-β and IFN-β is considered. The effects of exogenous intervention of TGF-β inhibitor and IFN-β are examined in order to enhance N1 recruitment to combat tumour progression. Our approach employs optimal control theory to determine drug infusion protocols that could minimize tumour volume with least administration cost possible. Four optimal control scenarios corresponding to different therapeutic strategies are explored, namely, TGF-β inhibitor control only, IFN-β control only, concomitant TGF-β inhibitor and IFN-β controls, and alternating TGF-β inhibitor and IFN-β controls. For each scheme, different initial conditions are varied to depict different pathophysiological condition of a cancer patient, leading to adaptive treatment schedule. TGF-β inhibitor and IFN-β drug dosages, total drug amount, infusion times and relative cost of drug administrations are obtained under various circumstances. The control strategies achieved could guide in designing individualized therapeutic protocols.

Atorvastatin-mediated rescue of cancer-related cognitive changes in combined anticancer therapies

Acute administration of trastuzumab (TZB) may induce various forms of cognitive impairment. These cancer-related cognitive changes (CRCC) are regulated by an adverse biological process involving cancer stem cells (CSCs) and IL-6. Recent studies have reported that atorvastatin (ATV) may change the dynamic of cognitive impairment in a combination (TZB+ATV) therapy. In this study, we investigate the mutual interactions between cancer stem cells and the tumor cells that facilitate cognitive impairment during long term TZB therapy by developing a mathematical model that involves IL-6 and the key apoptotic regulation. These include the densities of tumor cells and CSCs, and the concentrations of intracellular signaling molecules (NFκB, Bcl-2, BAX). We apply the mathematical model to a single or combination (ATV+TZB) therapy used in the experiments to demonstrate that the CSCs can enhance CRCC by secreting IL-6 and ATV may interfere the whole regulation. We show that the model can both reproduce the major experimental observation on onset and prevention of CRCC, and suggest several important predictions to guide future experiments with the goal of the development of new anti-tumor and anti-CRCC strategies. Moreover, using this model, we investigate the fundamental mechanism of onset of cognitive impairment in TZB-treated patients and the impact of alternating therapies on the anti-tumor efficacy and intracellular response to different treatment schedules.

A conventional drug, trastuzumab (TZB), was shown to be an effective weapon in killing cancer cells in brain. However, long term treatment of TZB increases the proportion of cancer stem cells (CSCs) in the tumour microenvironment (TME) and induces up-regulation of pro-tumoral molecules such as IL-6 in TME. These cancer cells then become more resistant to this chemotherapy through the IL-mediated up-regulation of NFκB and CSCs. More importantly, these changes in TME result in a serious side effect, cognitive impairment called cancer-related cognitive changes (CRCC). The detailed mechanism of CRCC is still poorly understood. However, cancer patients with chemotherapy-induced cognitive impairment can have long-term or delayed mental changes. In this study, we investigated the fundamental mechanism of CRCC in cancer patients based on experiments and a mathematical model that describes how tumor cells interact with CSCs in response to chemo drugs. In particular, we investigate how TZB-induced CSCs with modified IL-6 landscapes shape the cognitive functions in cancer patients. We showed that the combination treatment with another drug, atorvastatin (ATV), can abrogate the TZB-induced CRCC and enhance the survival probability of cancer patients by synergistic anti-tumor effect. We demonstrate that the cognitive functions and survival rates in cancer patients depend on the apoptotic signaling pathways via the critical communication and IL-6 landscapes of stimulated CTCs.

Mathematical model of STAT signalling pathways in cancer development and optimal control approaches

In various diseases, the STAT family display various cellular controls over various challenges faced by the immune system and cell death programs. In this study, we investigate how an intracellular signalling network (STAT1, STAT3, Bcl-2 and BAX) regulates important cellular states, either anti-apoptosis or apoptosis of cancer cells. We adapt a mathematical framework to illustrate how the signalling network can generate a bi-stability condition so that it will induce either apoptosis or anti-apoptosis status of tumour cells. Then, we use this model to develop several anti-tumour strategies including IFN-β infusion. The roles of JAK-STATs signalling in regulation of the cell death program in cancer cells and tumour growth are poorly understood. The mathematical model unveils the structure and functions of the intracellular signalling and cellular outcomes of the anti-tumour drugs in the presence of IFN-β and JAK stimuli. We identify the best injection order of IFN-β and DDP among many possible combinations, which may suggest better infusion strategies of multiple anti-cancer agents at clinics. We finally use an optimal control theory in order to maximize anti-tumour efficacy and minimize administrative costs. In particular, we minimize tumour volume and maximize the apoptotic potential by minimizing the Bcl-2 concentration and maximizing the BAX level while minimizing total injection amount of both IFN-β and JAK2 inhibitors (DDP).

Glioblastoma and MiRNAs

Glioblastoma (GB) is one of the most common types of lethal brain tumors. Although several treatment options are available including surgery, along with adjuvant chemo and radiotherapy, the disease has a poor prognosis and patients generally die within 14 months of diagnosis. GB is chemo and radio resistant. Thus, there is a critical need for new insights into GB treatment to increase the chance of therapeutic success. This is why microRNA (miRNA) is being potentially considered in the diagnosis and treatment of glioblastoma. The objective of our review is to provide a holistic picture of GB up-regulated and down-regulated miRNA, in relationship with the expression of other genes, cell signaling pathways, and their role in GB diagnosis and treatment. MiRNA treatment is being considered to be used against GB together with radiotherapy and chemotherapy. Moreover, the use of miRNA as a diagnostic tool has also begun. Knowing that miRNAs are isolated in almost all human body fluids and that there are more than 3000 miRNAs in the human genome, plus the fact that each miRNA controls hundreds of different mRNAs, there is still much study needed to explore how miRNAs relate to GB for its proliferation, progression, and inhibition.

Polytherapeutic strategies with oncolytic virus-bortezomib and adjuvant NK cells in cancer treatment

Proteasome inhibition and oncolytic virotherapy are two emerging targeted cancer therapies. Bortezomib, a proteasome inhibitor, disrupts the degradation of proteins in the cell leading to accumulation of unfolded proteins inducing apoptosis. On the other hand, oncolytic virotherapy uses genetically modified oncolytic viruses (OV) to infect cancer cells, induce cell lysis, and activate an antitumour response. In this work, optimal control theory is used to minimize the cancer cell population by identifying strategic infusion protocols of bortezomib, OV and natural killer (NK) cells. Three different therapeutic protocols are explored: (i) periodic bortezomib and single administrations of both OV and NK cells therapy; (ii) alternating sequential combination therapy; and (iii) NK cell depletion and infusion therapy. In the first treatment scheme, early OV administration followed by well-timed adjuvant NK cell infusion maximizes antitumour efficacy. The second strategy supports timely OV infusion. The last treatment scheme indicates that transient NK cell depletion followed by appropriate NK cell adjuvant therapy yields the maximal benefits. Relative doses and administrative costs of the three anticancer agents for each approach are qualitatively presented. This study provides potential polytherapeutic strategies in cancer treatment.

Collective invasion of glioma cells through OCT1 signalling and interaction with reactive astrocytes after surgery

Glioblastoma multiforme (GBM) is the most aggressive form of brain cancer with a short median survival time. GBM is characterized by the hallmarks of aggressive proliferation and cellular infiltration of normal brain tissue. miR-451 and its downstream molecules are known to play a pivotal role in regulation of the balance of proliferation and aggressive invasion in response to metabolic stress in the tumour microenvironment (TME). Surgery-induced transition in reactive astrocyte populations can play a significant role in tumour dynamics. In this work, we develop a multi-scale mathematical model of miR-451-LKB1-AMPK-OCT1-mTOR pathway signalling and individual cell dynamics of the tumour and reactive astrocytes after surgery. We show how the effects of fluctuating glucose on tumour cells need to be reprogrammed by taking into account the recent history of glucose variations and an AMPK/miR-451 reciprocal feedback loop. The model shows how variations in glucose availability significantly affect the activity of signalling molecules and, in turn, lead to critical cell migration. The model also predicts that microsurgery of a primary tumour induces phenotypical changes in reactive astrocytes and stem cell-like astrocytes promoting tumour cell proliferation and migration by Cxcl5. Finally, we investigated a new anti-tumour strategy by Cxcl5-targeting drugs. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.

Radiation protraction schedules for low-grade gliomas: a comparison between different mathematical models

We optimize radiotherapy (RT) administration strategies for treating low-grade gliomas. Specifically, we consider different tumour growth laws, both with and without spatial effects. In each scenario, we find the optimal treatment in the sense of maximizing the overall survival time of a virtual low-grade glioma patient, whose tumour progresses according to the examined growth laws. We discover that an extreme protraction therapeutic strategy, which amounts to substantially extending the time interval between RT sessions, may lead to better tumour control. The clinical implications of our results are also presented.

Strategies in regulating glioblastoma signaling pathways and anti-invasion therapy

Glioblastoma multiforme is one of the most invasive type of glial tumors, which rapidly grows and commonly spreads into nearby brain tissue. It is a devastating brain cancer that often results in death within approximately 12 to 15 months after diagnosis. In this work, optimal control theory was applied to regulate intracellular signaling pathways of miR-451–AMPK–mTOR–cell cycle dynamics via glucose and drug intravenous administration infusions. Glucose level is controlled to activate miR-451 in the up-stream pathway of the model. A potential drug blocking the inhibitory pathway of mTOR by AMPK complex is incorporated to explore regulation of the down-stream pathway to the cell cycle. Both miR-451 and mTOR levels are up-regulated inducing cell proliferation and reducing invasion in the neighboring tissues. Concomitant and alternating glucose and drug infusions are explored under various circumstances to predict best clinical outcomes with least administration costs.

MicroRNA-451 Inhibits Migration of Glioblastoma while Making It More Susceptible to Conventional Therapy

Malignant glioblastoma (GBM, glioma) is the most common and aggressive primary adult brain tumor. The prognosis of GBM patients remains poor, despite surgery, radiation and chemotherapy. The major obstacles for successful remedy are invasiveness and therapy resistance of GBM cells. Invasive glioma cells leave primary tumor core and infiltrate surrounding normal brain leading to inevitable recurrence, even after surgical resection, radiation and chemotherapy. Therapy resistance allowing for selection of more aggressive and resistant sub-populations including GBM stem-like cells (GSCs) upon treatment is another serious impediment to successful treatment. Through their regulation of multiple genes, microRNAs can orchestrate complex programs of gene expression and act as master regulators of cellular processes. MicroRNA-based therapeutics could thus impact broad cellular programs, leading to inhibition of invasion and sensitization to radio/chemotherapy. Our data show that miR-451 attenuates glioma cell migration in vitro and invasion in vivo. In addition, we have found that miR-451 sensitizes glioma cells to conventional chemo- and radio-therapy. Our data also show that miR-451 is regulated in vivo by AMPK pathway and that AMPK/miR-451 loop has the ability to switch between proliferative and migratory pattern of glioma cells behavior. We therefore postulate that AMPK/miR-451 negative reciprocal feedback loop allows GBM cells/GSCs to adapt to tumor “ecosystem” by metabolic and behavioral flexibility, and that disruption of such a loop reduces invasiveness and diminishes therapy resistance.

Synergistic Effects of Bortezomib-OV Therapy and Anti-Invasive Strategies in Glioblastoma: A Mathematical Model

It is well-known that the tumor microenvironment (TME) plays an important role in the regulation of tumor growth and the efficacy of anti-tumor therapies. Recent studies have demonstrated the potential of combination therapies, using oncolytic viruses (OVs) in conjunction with proteosome inhibitors for the treatment of glioblastoma, but the role of the TME in such therapies has not been studied. In this paper, we develop a mathematical model for combination therapies based on the proteosome inhibitor bortezomib and the oncolytic herpes simplex virus (oHSV), with the goal of understanding their roles in bortezomib-induced endoplasmic reticulum (ER) stress, and how the balance between apoptosis and necroptosis is affected by the treatment protocol. We show that the TME plays a significant role in anti-tumor efficacy in OV combination therapy, and illustrate the effect of different spatial patterns of OV injection. The results illustrate a possible phenotypic switch within tumor populations in a given microenvironment, and suggest new anti-invasion therapies.

Role of extracellular matrix and microenvironment in regulation of tumor growth and LAR-mediated invasion in glioblastoma

The cellular dispersion and therapeutic control of glioblastoma, the most aggressive type of primary brain cancer, depends critically on the migration patterns after surgery and intracellular responses of the individual cancer cells in response to external biochemical cues in the microenvironment. Recent studies have shown that miR-451 regulates downstream molecules including AMPK/CAB39/MARK and mTOR to determine the balance between rapid proliferation and invasion in response to metabolic stress in the harsh tumor microenvironment. Surgical removal of the main tumor is inevitably followed by recurrence of the tumor due to inaccessibility of dispersed tumor cells in normal brain tissue. In order to address this complex process of cell proliferation and invasion and its response to conventional treatment, we propose a mathematical model that analyzes the intracellular dynamics of the miR-451-AMPK- mTOR-cell cycle signaling pathway within a cell. The model identifies a key mechanism underlying the molecular switches between proliferative phase and migratory phase in response to metabolic stress in response to fluctuating glucose levels. We show how up- or down-regulation of components in these pathways affects the key cellular decision to infiltrate or proliferate in a complex microenvironment in the absence and presence of time delays and stochastic noise. Glycosylated chondroitin sulfate proteoglycans (CSPGs), a major component of the extracellular matrix (ECM) in the brain, contribute to the physical structure of the local brain microenvironment but also induce or inhibit glioma invasion by regulating the dynamics of the CSPG receptor LAR as well as the spatiotemporal activation status of resident astrocytes and tumor-associated microglia. Using a multi-scale mathematical model, we investigate a CSPG-induced switch between invasive and non-invasive tumors through the coordination of ECM-cell adhesion and dynamic changes in stromal cells. We show that the CSPG-rich microenvironment is associated with non-invasive tumor lesions through LAR-CSGAG binding while the absence of glycosylated CSPGs induce the critical glioma invasion. We illustrate how high molecular weight CSPGs can regulate the exodus of local reactive astrocytes from the main tumor lesion, leading to encapsulation of non-invasive tumor and inhibition of tumor invasion. These different CSPG conditions also change the spatial profiles of ramified and activated microglia. The complex distribution of CSPGs in the tumor microenvironment can determine the nonlinear invasion behaviors of glioma cells, which suggests the need for careful therapeutic strategies.

The role of myosin II in glioma invasion: A mathematical model

Gliomas are malignant tumors that are commonly observed in primary brain cancer. Glioma cells migrate through a dense network of normal cells in microenvironment and spread long distances within brain. In this paper we present a two-dimensional multiscale model in which a glioma cell is surrounded by normal cells and its migration is controlled by cell-mechanical components in the microenvironment via the regulation of myosin II in response to chemoattractants. Our simulation results show that the myosin II plays a key role in the deformation of the cell nucleus as the glioma cell passes through the narrow intercellular space smaller than its nuclear diameter. We also demonstrate that the coordination of biochemical and mechanical components within the cell enables a glioma cell to take the mode of amoeboid migration. This study sheds lights on the understanding of glioma infiltration through the narrow intercellular spaces and may provide a potential approach for the development of anti-invasion strategies via the injection of chemoattractants for localization.