Ever since the war on cancer was declared in 1971, there has been an explosion in our understanding of this diverse group of diseases. The application of molecular genetics and molecular biology technologies have enabled a deep understanding of the genetic, epigenetic, signaling cascades, survival pathways, and invasive mechanisms that underlie the cancer phenotype. Concomitantly this has translated in the development of ever more effective and safe medications that work through different mechanisms of action and target fundamental aspects of the biology of the tumor. The paradigm has been chronic myeloid leukemia where the discovery of the Philadelphia chromosome, ultimately led to the identification of the BCR-ABL oncogene and the development of tyrosine kinase inhibitors such as imatinib, nilotinib, dasatinib and others and lead to rapid, deep and long-lasting remissions in this disease. Another success story has been acute promyelocytic leukemia with the vast majority of patients now being cured of the disease without the need for any classical chemotherapy.

Biological systems across various length and time scales are noisy, including tissues. Why are biological tissues inherently chaotic? Does heterogeneity play a role in determining the physiology and pathology of tissues? How do physical and biochemical heterogeneity crosstalk to dictate tissue function? In this review, we begin with a brief primer on heterogeneity in biological tissues. Then, we take examples from recent literature indicating functional relevance of biochemical and physical heterogeneity and discuss the impact of heterogeneity on tissue function and pathology. We take specific examples from studies on epithelial tissues to discuss the potential role of inherent tissue heterogeneity in tumorigenesis.

Cancer cell plasticity is the ability of tumor cells to switch phenotypes and is one of the predominant requisites of cancer cells capable of undergoing metastasis. Cancer cell plasticity is also recognised as one of the major contributors to intra-tumoral heterogeneity, a critical factor underlying the progression of malignant tumors which is known to modify tumor response and induce resistance against various modes of therapy thus posing a barrier to efficient cancer management. Cancer cell plasticity is acquired by the subversion of cell signaling pathways like MAPK, PI3K, STAT3, Wnt, Hedgehog and Notch as well as cellular programs such as epithelial to mesenchymal transition (EMT) and phenotypic plasticity. This complex phenomenon has been studied in many cancer types like pancreatic cancer, colon cancer and breast cancer. Some cancers like breast cancer are known to exhibit a hierarchical organization with cancer stem cells (CSCs) at the pinnacle of the pyramid due to their ability to promote tumorigenesis, metastasis and therapy resistance. CSCs which can undergo phenotypic changes resulting in heterogenous cell populations with differing potential to develop programs necessary for the metastatic process lies at the core of the cancer cell plasticity hypothesis. Our expanding knowledge of this field can lead to the development of more therapeutic strategies that can be used in cancer and other solid tumors that exhibit similar mechanisms of plasticity. This review will explore the current understanding we have of breast cancer on the intrinsic molecular mechanisms of cancer cell plasticity and the resistance to various types of cancer therapy that arise as a result of plasticity. We conclude by exploring the potential novel therapies that specifically target the pathways leading to plasticity and can be leveraged to treat patients living with the disease. Keywords: Cancer cell plasticity, Epithelial to Mesenchymal Transition (EMT), therapy resistance, targeted therapy.

Introduction: The use of prostate-specific antigen (PSA) as a prognostic indicator for prostate cancer (PCa) patients is controversial, especially since it has been shown to correlate poorly with tumor burden. The poor quality of PSA as a biomarker could be explained by current guidelines not accounting for the mechanism by which it enters circulation. Given that mature blood vessels are relatively impermeable to it, we hypothesize that immature and leaky blood vessels, formed under angiogenic cues in a hypoxic tumor, facilitate PSA extravasation into circulation. Methods: To explore our hypotheses, we develop a nonlinear dynamical systems model describing the vascular growth of PCa, that explicitly links PSA leakage into circulation with changes in intra-tumoral oxygen tension and vessel permeability. The model is calibrated versus serum PSA and tumor burden time-courses from a mouse xenograft model of castration resistant PCa response to androgen deprivation. Results: The model recapitulates the experimentally observed – and counter-intuitive – phenomenon of increasing tumor burden despite decreasing serum PSA levels. The validated model is then extended to the human scale by incorporating patient-specific parameters and fitting individual PSA time-courses from patients with biochemically failing PCa. Our results highlight the limitations of using time to PSA failure as a clinical indicator of androgen deprivation efficacy. We propose an alternative indicator, namely a treatment efficacy index, for patients with castration resistant disease, to identify who would benefit most from enhanced androgen deprivation. Conclusions: A critical challenge in prostate cancer therapeutics is quantifying the relationship between serum PSA and tumor burden. Our results underscore the potential of mathematical modeling in understanding the limitations of serum PSA as a prognostic indicator. Finally, we provide a means of augmenting PSA time-courses in the diagnostic process, with changes in intra-tumoral vascularity and vascular architecture .

Once cancer is initiated, with normal cells mutated into malignant ones, a solid tumour grows, develops and spreads within its microenvironment invading the local tissue; the disease progresses and the cancer cells migrate around the body leading to metastasis, the formation of distant secondary tumours. Interactions between the tumour and its microenvironment drive this cascade of events which have devastating, if not fatal, consequences for the human host/patient. Among these interactions, biomechanical interactions are a vital component. In this paper, key biomechanical relationships are discussed through a review of modelling efforts by the mathematical and computational oncology community. The main focus is directed, naturally, towards lattice-free agent-based, force-based models of solid tumour growth and development. In such models interactions between pairs of cancer cells (as well as between cells and other structures of the tumour microenvironment) are governed by forces. These forces are ones of repulsion and adhesion, and are typically modelled via either an extended Hertz model of contact mechanics or using Johnson-Kendal-Roberts theory, both of which are discussed here. The role of the extracellular matrix in determining disease progression is outlined along with important cell-vessel interactions which combined together account for a great proportion of Hanahan and Weinberg’s “Hallmarks of Cancer”.

MicroRNAs (miRNAs) are short (~22 nucleotides) non-coding RNAs that are often intricately integrated into the regulatory networks of various cellular processes and govern the cell fate decision making events associated with oncogenesis by regulating the gene expression through post-transcriptional modifications. miRNAs repress the target genes by either degrading the target mRNA or by inhibiting the process of translation. However, mathematical and computational modeling of miRNA-mediated target gene regulation in various cellular network motifs suggests that miRNAs play a much more complex role in cellular decision-making events. In this review, we give an overview of the quantitative insights obtained from such kind of mathematical modeling of miRNA mediated gene regulation by highlighting the various factors associated with miRNA regulation that are pivotal in diversifying the cell fate decisions related to oncogenesis. Intriguingly, recent experiments suggest that miRNAs can even upregulate the translation of the target protein under certain circumstances, which may lead to more complexities in miRNA-mediated gene regulations. We discussed possible avenues to explore such unusual biological observations related to miRNA’s that can be modeled to get a detailed understanding of the influence of miRNAs in the context of oncogenesis.

Bladder cancer is a common malignancy with over 80,000 estimated new cases and nearly 18,000 deaths per year in the United States alone. Therapeutic options for metastatic bladder cancer had not evolved much for nearly four decades, until recently, when five immune checkpoint inhibitors were approved by the FDA. Despite the activity of these drugs in some patients, the objective response rate for each is less than 25%. At the same time, fibroblast growth factor receptors (FGFRs) have been attractive drug targets for a variety of cancers, and in 2019 the FDA approved the first therapy targeted against FGFR3 for bladder cancer. Given the excitement around these new receptor tyrosine kinase and immune checkpoint targeted strategies, and the challenges they each may face on their own, emerging data suggest that combining these treatment options could lead to improved therapeutic outcomes. In this paper, we develop a mathematical model for FGFR3-mediated tumor growth and use it to investigate the impact of the combined administration of a small molecule inhibitor of FGFR3 and a monoclonal antibody against the PD-1/PD-L1 immune checkpoint. The model is carefully calibrated and validated with experimental data before survival benefits and dosing schedules are explored. Predictions of the model suggest that FGFR3 mutation reduces the effectiveness of anti-PD-L1 therapy, that there are regions of parameter space where each monotherapy can outperform the other, and that pretreatment with anti-PD-L1 therapy always results in greater tumor reduction even when anti-FGFR3 therapy is the more effective monotherapy.

Intro: Long-term treatment with interferon-alfa (IFN) can reduce the disease burden of patients diagnosed with myeloproliferative neoplasms (MPN). Determining individual patient-responses to IFN-therapy may allow for efficient personalized treatment, reducing both drop out and disease burden. Methods: A mathematical model describing hematopoietic stem cells and the immune system is suggested. Considering the bone marrow and the blood allows for modelling disease dynamics both in the absence and presence of treatment. Through comprehensive modelling of the effects of IFN, the model was related to individualized patient-data consisting of longitudinal hematologic and molecular measurements. Treatment responses are modelled on a population-level, allowing for personalized predictions from a single pre-treatment data point. Results: Personalized fits were found to agree well with data. This allowed for a quantitative description of the treatment-response, yielding a mechanistic interpretation of differences between individual patients. Population-level treatment-responses were simulated. Based on pre-treatment data and the actual treatment scheduling, the population-level response was found to predict the treatment-response of particular patients accurately over a five-year period. Conclusion: Mechanism-based modelling of treatment effects demonstrates that hematologic and molecular observables can be predicted on the level of individual patients. Personalized patient-fits suggest that the effect of IFN-treatment can be quantified and interpreted through mathematical modelling, despite variation in hematologic and molecular response for different patients. Modelling suggests that both hematologic and molecular markers must be considered to avoid immediate relapse. Furthermore, personalized model-fits provides quantitative measures of the hematologic and molecular response, determining when treatment-cessation is appropriate. Proof-of-concept population-level modelling of treatment-responses from pre-treatment data successfully predicted clinical measures for a five-year period. This approach could have direct clinical relevance, offering expert guidance for clinical decisions about IFN-treatment of MPN-patients.

Ovarian cancer is commonly diagnosed in its late stages, and new treatment modalities are needed to improve patient outcomes and survival. We have recently established the synergistic effects of combination tumour necrosis factor-related apoptosis-inducing ligand (TRAIL) and procaspase activating compound (PAC-1) therapies in granulosa cell tumours (GCT) of the ovary, a rare form of ovarian cancer, using a mathematical model of the effects of both drugs in a GCT cell line. Here, to understand the mechanisms of combined TRAIL and PAC-1 therapy, study the viability of this treatment strategy, and accelerate preclinical translation, we leveraged our mathematical model in combination with population pharmacokinetics (PopPK) models of both TRAIL and PAC-1 to expand a realistic heterogeneous cohort of virtual patients and optimize treatment schedules. Using this approach, we investigated treatment responses in this virtual cohort and determined optimal therapeutic schedules based on patient-specific pharmacokinetic characteristics. Our results showed that schedules with high initial doses of PAC-1 were required for therapeutic efficacy. Further analysis of individualized regimens revealed two distinct groups of virtual patients within our cohort: one with high PAC-1 elimination, and one with normal PAC-1 elimination. In the high elimination group, high weekly doses of both PAC-1 and TRAIL were necessary for therapeutic efficacy, however virtual patients in this group were predicted to have a worse prognosis when compared to those in the normal elimination group. Thus, PAC-1 pharmacokinetic characteristics, particularly clearance, can be used to identify patients most likely to respond to combined PAC-1 and TRAIL therapy. This work underlines the importance of quantitative approaches in preclinical oncology.

Hypoxia Inducible Factor (HIF), the main actor in the cell response to hypoxia, represents a potential target in cancer therapy. HIF is involved in many biological processes such as cell proliferation, survival, apoptosis, angiogenesis, iron metabolism and glucose metabolism. This protein regulates the expressions of Lactate Dehydrogenase (LDH) and Pyruvate Dehydrogenase (PDH), both essential for the conversion of pyruvate to be used in aerobic and anaerobic pathways. HIF upregulates LDH, increasing the conversion of pyruvate into lactate which leads to higher secretion of lactic acid by the cell and reduced pH in the microenvironment. HIF indirectly downregulates PDH, decreasing the conversion of pyruvate into Acetyl Coenzyme A which leads to reduced usage of the Tricarboxylic Acid (TCA) cycle in aerobic pathways. Upregulation of HIF may promote the use of anaerobic pathways for energy production even in normal extracellular oxygen conditions. Higher use of glycolysis even in normal oxygen conditions is called the Warburg effect. In this paper, we focus on HIF variations during tumour growth and study, through a mathematical model, its impact on the two metabolic key genes PDH and LDH, to investigate its role in the emergence of the Warburg effect. Mathematical equations describing the enzymes regulation pathways were solved for each cell of the tumour represented in an agent-based model to best capture the spatio-temporal oxygen variations during tumour development caused by cell consumption and reduced diffusion inside the tumour. Simulation results show that reduced HIF degradation in normoxia can induce higher lactic acid production. The emergence of the Warburg effect appears after the first period of hypoxia before oxygen conditions return to a normal level. The results also show that targeting the upregulation of LDH and the downregulation of PDH could be relevant in therapy.