Mathematical modelling approaches have become increasingly abundant in cancer research. The complexity of cancer is well suited to quantitative approaches as it provides challenges and opportunities for new developments. In turn, mathematical modelling contributes to cancer research by helping to elucidate mechanisms and by providing quantitative predictions that can be validated. The recent expansion of quantitative models addresses many questions regarding tumour initiation, progression and metastases as well as intra-tumour heterogeneity, treatment responses and resistance. Mathematical models can complement experimental and clinical studies, but also challenge current paradigms, redefine our understanding of mechanisms driving tumorigenesis and shape future research in cancer biology.

To investigate immune escape during breast tumor progression, we analyzed the composition of leukocytes in normal breast tissues, ductal carcinoma in situ (DCIS), and invasive ductal carcinomas (IDC). We found significant tissue and tumor subtype-specific differences in multiple cell types including T cells and neutrophils. Gene expression profiling of CD45+CD3+ T cells demonstrated a decrease in CD8+ signatures in IDCs. Immunofluorescence analysis showed fewer activated GZMB+CD8+ T cells in IDC than in DCIS, including in matched DCIS recurrent IDC. TCR clonotype diversity was significantly higher in DCIS than in IDCs. Immune checkpoint protein TIGIT expressing T cells were more frequent in DCIS whereas high PD-L1 expression and amplification of CD274 (encoding PD-L1) was only detected in triple negative IDCs. Co-amplification of 17q12 chemokine cluster with ERBB2 subdivided HER2+ breast tumors into immunologically and clinically distinct subtypes. Our results show co-evolution of cancer cells and the immune microenvironment during tumor progression.

While agents that inhibit specific oncogenic kinases have been successful in a subset of cancers, there are currently few treatment options for malignancies that lack a targetable oncogenic driver. Nevertheless, during tumor evolution cancers engage a variety of protective pathways, which may provide alternative actionable dependencies. Here we identify a promising combination therapy that kills NF1-mutant tumors by triggering catastrophic oxidative stress. Specifically, we show that mTOR and HDAC inhibitors kill aggressive nervous system malignancies and shrink tumors in vivo by converging on the TXNIP/thioredoxin anti-oxidant pathway, through cooperative effects on chromatin and transcription. Accordingly, TXNIP triggers cell death by inhibiting thioredoxin and activating Apoptosis Signal-regulating Kinase 1 (ASK1). Moreover, this drug combination also kills NF1-mutant and KRAS-mutant non-small cell lung cancers. Together these studies identify a promising therapeutic combination for several currently untreatable malignancies, and reveal a protective nodal point of convergence between these important epigenetic and oncogenic enzymes.

BackgroundThe advent of targeted therapy for cancer treatment has brought about a paradigm shift in the clinical management of human malignancies. Agents such as erlotinib used for EGFR-mutant non-small cell lung cancer or imatinib for chronic myeloid leukemia, for instance, lead to rapid tumor responses. Unfortunately, however, resistance often emerges and renders these agents ineffective after a variable amount of time. The FDA-approved dosing schedules for these drugs were not designed to optimally prevent the emergence of resistance. To this end, we have previously utilized evolutionary mathematical modeling of treatment responses to elucidate the dosing schedules best able to prevent or delay the onset of resistance. Here we expand on our approaches by taking into account dose-dependent mutation rates at which resistant cells emerge. The relationship between the serum drug concentration and the rate at which resistance mutations arise can lead to non-intuitive results about the best dose administration strategies to prevent or delay the emergence of resistance.MethodsWe used mathematical modeling, available clinical trial data, and different considerations of the relationship between mutation rate and drug concentration to predict the effectiveness of different dosing strategies.ResultsWe designed several distinct measures to interrogate the effects of different treatment dosing strategies and found that a low-dose continuous strategy coupled with high-dose pulses leads to the maximal delay until clinically observable resistance. Furthermore, the response to treatment is robust against different assumptions of the mutation rate as a function of drug concentration.ConclusionsFor new and existing targeted drugs, our methodology can be employed to compare the effectiveness of different dose administration schedules and investigate the influence of changing mutation rates on outcomes.

Nuclear organization of genomic DNA affects DNA damage and repair processes, and yet its impact on mutational landscapes in cancer genomes remains unclear. Here we analyzed genome-wide somatic mutations from 366 samples of 6 cancer types. We found that lamina-associated regions, which are typically localized at the nuclear periphery, displayed higher somatic mutation frequencies compared to the inter-lamina regions at the nuclear core. This effect remained even after adjusting for features such as GC%, chromatin, and replication timing. Furthermore, mutational signatures differed between the nuclear core and periphery, indicating differences in the patterns of DNA damage and/or DNA repair processes. For instance, smoking and UV-related signatures were more enriched in the nuclear periphery. Substitutions at certain motifs were also more common in the nuclear periphery. Taken together, we found that the nuclear architecture influences mutational landscapes in cancer genomes beyond the effects already captured by chromatin and replication timing.

The traditional view of cancer as a genetic disease that can successfully be treated with drugs targeting mutant onco-proteins has motivated whole-genome sequencing efforts in many human cancer types. However, only a subset of mutations found within the genomic landscape of cancer is likely to provide a fitness advantage to the cell. Distinguishing such “driver” mutations from innocuous “passenger” events is critical for prioritizing the validation of candidate mutations in disease-relevant models. We design a novel statistical index, called the Hitchhiking Index, which reflects the probability that any observed candidate gene is a passenger alteration, given the frequency of alterations in a cross-sectional cancer sample set, and apply it to a mutational data set in colorectal cancer. Our methodology is based upon a population dynamics model of mutation accumulation and selection in colorectal tissue prior to cancer initiation as well as during tumorigenesis. This methodology can be used to aid in the prioritization of candidate mutations for functional validation and contributes to the process of drug discovery.

Reprogramming of somatic cells to induced pluripotent stem cells (iPSCs) is typically an inefficient and asynchronous process. A variety of technological efforts have been made to accelerate and/or synchronize this process. In order to define a unified framework to study and compare the dynamics of reprogramming under different conditions, we developed an in silico analysis platform based on mathematical modeling. Our approach takes into account the variability in experimental results stemming from probabilistic growth and death of cells and potentially heterogeneous reprogramming rates. We suggested that reprogramming driven by the Yamanaka factors alone is a more heterogeneous process possibly due to cell-specific reprogramming rates, which could be homogenized by the addition of additional factors. We validated our approach using publicly available reprogramming data sets, including data on early reprogramming dynamics as well as cell count data, and thus demonstrated the general utility and predictive power of our methodology for investigating reprogramming and other cell fate change systems.

Pancreatic ductal adenocarcinoma (PDAC) exhibits a variety of phenotypes with regard to disease progression and treatment response. This variability complicates clinical decision-making despite the improvement of survival due to the recent introduction of FOLFIRINOX (FFX) and nab-paclitaxel. Questions remain as to the timing and sequence of therapies and the role of radiotherapy for unresectable PDAC. Here we developed a computational analysis platform to investigate the dynamics of growth, metastasis and treatment response to FFX, gemcitabine (GEM), and GEM+nab-paclitaxel. Our approach was informed using data of 1,089 patients treated at the Massachusetts General Hospital and validated using an independent cohort from Osaka Medical College. Our framework establishes a logistic growth pattern of PDAC and defines the Local Advancement Index (LAI), which determines the eventual primary tumor size and predicts the number of metastases. We found that a smaller LAI leads to a larger metastatic burden. Furthermore, our analyses ascertain that i) radiotherapy after induction chemotherapy improves survival in cases receiving induction FFX or with larger LAI, ii) neoadjuvant chemotherapy improves survival in cases with resectable PDAC, and iii) temporary cessations of chemotherapies do not impact overall survival, which supports the feasibility of treatment holidays for patients with FFX-associated adverse effects. Our findings inform clinical decision-making for PDAC patients and allow for the rational design of clinical strategies using FFX, GEM, GEM+nab-paclitaxel, neoadjuvant chemotherapy, and radiation.