Computational and Mathematical Biology Centre
Research Theme 1
Developing mathematical models to study disease dynamics
Studying cancer through mathematical models
Studying glucose dynamics through mathematical model
Studying the existence of bistability in biological systems through mathematical model
Studying Tuberculosis through mathematical models
According to a WHO report, cancer is the second leading cause of death globally and, thus, one of the major interests in the research community. Through mathematical and computational models, we aimed to understand cellular modulation in cancer, which might lead to possible therapeutic development.
The first model was developed to study the interplay between DNA damage and autophagy in lung cancer. p53 plays an unequivocal role in the DNA repair process and has an abiding presence at the crossroads of the pathways linking DNA damage and cancer. p53 also dually regulates autophagy based on its cellular localization. The association of p53 and autophagic cell death is vital as the former acts whenever any threat comes to DNA, while the latter may play a role in getting rid of the culprit cell. So, we proposed a seven-dimensional mathematical model connecting p53, DNA damage, and autophagy in lung cancer. Both local and global sensitivity analyses were performed, along with parameter recalibration analyses, to understand the system dynamics. We hypothesized, by modulation of beclin1 level, that the regulation of AMPK and BCL2 could be a possible strategy to mitigate lung cancer progression (Biosystems, 206, 10443 (2021)).
The second model was built to understand Doxorubicin-associated calcium remodelling during triple-negative breast cancer treatment (TNBC). It is the most malignant subtype of breast cancer with high heterogeneity, rapid progression, and paucity of treatment options. The most effective chemotherapeutic drug for TNBC is doxorubicin (Doxo), an anthracycline antibiotic. However, Doxo treatment alters cytosolic calcium dynamics, leading to the drug-resistance condition. We developed a mathematical model to capture the alterations in the activity of various calcium channels and pumps during Doxo treatment. The model predicts the potential combination therapy for Doxo that can overcome Doxo-associated drug resistance. It was also observed that the indispensability of calcium influx rate is paramount in Doxo drug resistance. Finally, three drugs were identified from existing literature that could be used as a combination therapy with Doxo. The investigation highlights the importance of integrating the calcium signaling of various calcium regulating compounds for their effective anti-tumor effects deliverance along with chemotherapeutic agents (Explore Target Antitumor Ther; 2, 208-26, (2021)).
We have also developed a mathematical model to study low-dose metronomic scheduling for chemotherapy. Metronomic chemotherapy refers to the frequent administration of chemotherapeutic agents at a lower dose and presents an attractive alternative to conventional chemotherapy with encouraging response rates. The confounding effects of tumor-endothelial-immune interactions during metronomic administration of drugs have not yet been explored in detail, resulting in an incomplete assessment of drug dose and frequency evaluations. We aimed to gain a mechanistic understanding of different actions of metronomic chemotherapy using a mathematical model. We have established an analytical condition for determining the dosage and frequency of the drug depending on its clearance rate for complete tumor elimination. The results from the global sensitivity analysis showed an increase in the sensitivity of drug and immune-mediated killing factors toward the tumor population during metronomic scheduling. Our results emphasize metronomic scheduling over the maximum tolerated dose (MTD) and define a model-based approach for approximating the optimal schedule of drug administration to eliminate tumors while minimizing harm to the immune cells and the patient’s body (Mathematical Biosciences, 372, 109186 (2024)).
Diabetes is a noncommunicable disease associated with high plasma glucose level (PGL) and is the fifth leading cause of death worldwide. Diabetes is frequently associated with cardiovascular diseases, including heart failure. To study diabetes and its association with cardiovascular diseases, we built models to understand the glucose dynamics in pancreatic beta cells and cardiomyocytes (the work on cardiomyocytes were supported through the SERB project).
Any dysfunction in the secretion of insulin and/or in its use is critical in the development of type 2 diabetes (T2D). Calcium plays an important role in the insulin secretion mechanism from beta-cells. We built a four-dimensional system of nonlinear delay differential equations (DDEs) to give insights into possible mechanisms for maintaining plasma glucose homeostasis through calcium-induced insulin secretion. The time duration between ATP formation and subsequent calcium influx through the cell membrane was found to be critical in maintaining insulin homeostasis. The new potential drug therapies were also discussed through parameter recalibration (Applied Mathematical Modelling, 84, 202–221, (2020)).
Impaired glucose-stimulated insulin secretion (GSIS) is responsible for beta-cell failure and one of the major causes of developing T2D in the presence of insulin resistance (IR). The mechanisms underlying the progressive failure of beta-cells in insulin resistance-induced prolonged hyperglycemic conditions remain unresolved. We proposed and analyzed the GSIS process through a six-dimensional model incorporating calcium and ATP. The model was established by simulating normal and insulin resistance-induced hyperglycemic conditions. Our analysis revealed the possible factors responsible for the impaired GSIS process in IR, whose dysfunction can lead to T2D. The parameter recalibration was again used to propose the potential therapeutic strategies (Applied Mathematical Modelling, 108, 408–426, (2022)).
Next, we studied insulin synthesis and secretion processes through a minimal mathematical model incorporating insulin mRNA, proinsulin pool, and insulin granules. Defects in the insulin granule trafficking and exocytosis processes hamper first- and second-phase insulin secretion and might be one of the main reasons for β-cell dysfunction in type 2 diabetes. The long-term effect of abnormal insulin synthesis could hamper insulin secretion and make the scenario more critical, causing complete insulin loss inside the β-cells. Besides, uncontrolled insulin synthesis could increase basal insulin secretion and drive toward fasting hypoglycemia. We hypothesize that regulation of insulin synthesis through targeting transcription and translation is a potential therapeutic strategy for controlling impaired insulin secretion. (Applied Mathematical Modelling, 122, 456–476, (2023)).
The first model for cardiomyocytes mimics the cross-talk among plasma glucose, plasma insulin, intracellular glucose and cytoplasmic calcium of a cardiomyocyte. We analyzed the delay-induced model and deciphered conditions for stability and bifurcation. It was also observed that the time taken to transport extracellular glucose into the cell through GLUT4 plays an important role in maintaining physiological oscillations of the state variables. Parameter recalibration exercise showed that a reduced input rate of glucose in the blood plasma or an alteration in transportation delay may be used for therapeutic targets in diabetic-like conditions for maintaining normal cardiac function. (Journal of Biological Physics, 46, 253–281, (2020)).
The second model for cardiomyocytes was developed to study the effect of random translocation of GLUT4 on calcium oscillations. The defect in excitation-contraction coupling (ECC) is mainly caused by the dysregulation of the calcium homeostasis in normal cardiomyocytes due to prolonged elevated blood glucose levels. We examined the effect of the random movement of GLUT4 on the entry of glucose in the cardiomyocytes. By altering system parameters, we induced insulin resistance in cardiomyocytes to mimic diabetic conditions and proposed potential restoration strategies to restore normal calcium dynamics. Early bifurcation was observed with the introduction of randomness in the system. (Applied Mathematical Modelling, 125, 599–616 (2024)).
A subgroup of T cells called T-regulatory cells (Tregs) regulates the body’s immune responses to maintain homeostasis and self-tolerance. Tregs are crucial for preventing illnesses like cancer and autoimmunity. However, contrasting patterns of Treg frequency are observed in different autoimmune diseases. The commonality of tumour necrosis factor receptor 2 (TNFR2) defects and decrease in Treg frequency on the onset of autoimmunity demands an in-depth study of the TNFR2 pathway. To unravel this mystery, we studied the cell survival mechanism and death in Tregs through an ordinary differential equation (ODE)-based model. The sensitivity analysis reveals that the input stimulus, the concentration of tumour necrosis factor (TNF), is the most sensitive parameter for the model system. The model shows that the cell goes into survival or apoptosis via bistable switching. Through hysteretic switching, the system tries to cope with the changing stimuli. We compute bifurcation diagrams and obtain cell fate maps to understand how stimulus strength and feedback strength influence cell survival and death. Our results indicate that the elevated TNF concentration and increased c-Jun N-terminal kinase (JNK) phosphorylation are the major contributors to the death of T-regulatory cells. Biological evidence cements our hypothesis and can be controlled by reducing the TNF concentration. Finally, the system was studied under stochastic perturbation to see the effect of noise on the system’s dynamics. We observed that introducing random perturbations disrupts the bistability, reducing the system’s bistable region, which can affect the system’s normal functioning (Journal of Biological Physics, 49, 95–119, (2023)).
Mycobacterium tuberculosis (Mtb) has evolved with diverse strategies to evade killing by host macrophages, enabling it to establish persistent infection within the host, including manipulating apoptosis. Studies have established bistability as an obvious appeal in apoptosis. However, the underlying mechanisms behind the bistability in the apoptosis pathway under Mtb infection conditions remain a research topic. In this study, we explored how Mtb influences host proteins’ bistable behaviour, dictating apoptotic or non-apoptotic outcomes. We studied this complex host-pathogen interaction during mycobacterial pathogenesis through a mathematical model of the apoptosis pathway. The most significant finding of the current study involves the existence and disappearance of bistability, which is required for normal cellular functioning. We demonstrated that Mtb disrupts the bistability of caspase-3 by secreting virulence factors, facilitating its survival within the host cell. We proposed restoration strategies to reinstate bistability and promote host cell apoptosis to counteract Mtb virulence. Our investigation delved into comparing the efficacy of various restoration strategies to identify the most promising targets for host-directed therapy (HDT) against TB, preserving bistability in the system (Communicated for publication).
We have also constructed a population-level model to study the spread of Tuberculosis (TB) in the human population and the significance of Latent tuberculosis infection (LTBI). TB caused by Mycobacterium tuberculosis (Mtb) is a devastating and rapidly spreading disease. Despite years of scientific research and numerous efforts, it is still a major and resurgent health problem worldwide, with high mortality rates. Added to the concern is that TB persists as a latent infection, an occult face of TB, that becomes a potential reservoir for active tuberculosis. Since latent TB-infected patients may eventually advance to the active form of TB, an accurate diagnosis and effective treatment of latent tuberculosis are essential for TB control. LTBI treatment is a prominent component of TB control in low-prevalence countries like the United States; however, its implication in high-incidence countries like India is still challenging. So, we aimed to evaluate the impact of implementing diagnosis and treatment of LTBI in high-incidence countries using a mathematical model-based approach. Through our model, we predicted the incidence rate based on the current treatment regimen in India for the year 2035, which is one of the milestones of WHO for a substantial reduction in TB incidence. We observed demographic variability in the effects of various parameters on the TB incidence rate. Finally, we formulated the putative treatment strategies to reduce the TB burden in high-incidence scenarios. Further, we estimated the impact of these proposed treatment strategies on the drug-resistant population in high-incidence scenarios. The model predictions suggested molding the current treatment strategies and focused implementation of LTBI diagnosis and treatment in high-incidence scenarios (Mathematical Methods in the Applied Sciences, (Published online) (2024), 1-15. DOI 10.1002/mma.10532).