nipalsMCIA: Flexible Multi-Block Dimensionality Reduction in R via Non-linear Iterative Partial Least Squares.

Motivation: With the increased reliance on multi-omics data for bulk and single cell analyses, the availability of robust approaches to perform unsupervised analysis for clustering, visualization, and feature selection is imperative. Joint dimensionality reduction methods can be applied to multi-omics datasets to derive a global sample embedding analogous to single-omic techniques such as Principal Components Analysis (PCA). Multiple co-inertia analysis (MCIA) is a method for joint dimensionality reduction that maximizes the covariance between block- and global-level embeddings. Current implementations for MCIA are not optimized for large datasets such such as those arising from single cell studies, and lack capabilities with respect to embedding new data. Results: We introduce nipalsMCIA, an MCIA implementation that solves the objective function using an extension to Non-linear Iterative Partial Least Squares (NIPALS), and shows significant speed-up over earlier implementations that rely on eigendecompositions for single cell multi-omics data. It also removes the dependence on an eigendecomposition for calculating the variance explained, and allows users to perform out-of-sample embedding for new data. nipalsMCIA provides users with a variety of pre-processing and parameter options, as well as ease of functionality for down-stream analysis of single-omic and global-embedding factors. Availability: nipalsMCIA is available as a BioConductor package at https://bioconductor.org/packages/release/bioc/html/nipalsMCIA.html, and includes detailed documentation and application vignettes. Supplementary Materials are available online.

Integrated longitudinal multiomics study identifies immune programs associated with acute COVID-19 severity and mortality.

BACKGROUNDPatients hospitalized for COVID-19 exhibit diverse clinical outcomes, with outcomes for some individuals diverging over time even though their initial disease severity appears similar to that of other patients. A systematic evaluation of molecular and cellular profiles over the full disease course can link immune programs and their coordination with progression heterogeneity.METHODSWe performed deep immunophenotyping and conducted longitudinal multiomics modeling, integrating 10 assays for 1,152 Immunophenotyping Assessment in a COVID-19 Cohort (IMPACC) study participants and identifying several immune cascades that were significant drivers of differential clinical outcomes.RESULTSIncreasing disease severity was driven by a temporal pattern that began with the early upregulation of immunosuppressive metabolites and then elevated levels of inflammatory cytokines, signatures of coagulation, formation of neutrophil extracellular traps, and T cell functional dysregulation. A second immune cascade, predictive of 28-day mortality among critically ill patients, was characterized by reduced total plasma Igs and B cells and dysregulated IFN responsiveness. We demonstrated that the balance disruption between IFN-stimulated genes and IFN inhibitors is a crucial biomarker of COVID-19 mortality, potentially contributing to failure of viral clearance in patients with fatal illness.CONCLUSIONOur longitudinal multiomics profiling study revealed temporal coordination across diverse omics that potentially explain the disease progression, providing insights that can inform the targeted development of therapies for patients hospitalized with COVID-19, especially those who are critically ill.TRIAL REGISTRATIONClinicalTrials.gov NCT04378777.FUNDINGNIH (5R01AI135803-03, 5U19AI118608-04, 5U19AI128910-04, 4U19AI090023-11, 4U19AI118610-06, R01AI145835-01A1S1, 5U19AI062629-17, 5U19AI057229-17, 5U19AI125357-05, 5U19AI128913-03, 3U19AI077439-13, 5U54AI142766-03, 5R01AI104870-07, 3U19AI089992-09, 3U19AI128913-03, and 5T32DA018926-18); NIAID, NIH (3U19AI1289130, U19AI128913-04S1, and R01AI122220); and National Science Foundation (DMS2310836).

Integrating Diversity, Equity, and Inclusion into Preclinical, Clinical, and Public Health Mathematical Models.

Mathematical modelling applied to preclinical, clinical, and public health research is critical for our understanding of a multitude of biological principles. Biology is fundamentally heterogeneous, and mathematical modelling must meet the challenge of variability head on to ensure the principles of diversity, equity, and inclusion (DEI) are integrated into quantitative analyses. Here we provide a follow-up perspective on the DEI plenary session held at the 2023 Society for Mathematical Biology Annual Meeting to discuss key issues for the increased integration of DEI in mathematical modelling in biology.

A supervised Bayesian factor model for the identification of multi-omics signatures.

MOTIVATION: Predictive biological signatures provide utility as biomarkers for disease diagnosis and prognosis, as well as prediction of responses to vaccination or therapy. These signatures are identified from high-throughput profiling assays through a combination of dimensionality reduction and machine learning techniques. The genes, proteins, metabolites, and other biological analytes that compose signatures also generate hypotheses on the underlying mechanisms driving biological responses, thus improving biological understanding. Dimensionality reduction is a critical step in signature discovery to address the large number of analytes in omics datasets, especially for multi-omics profiling studies with tens of thousands of measurements. Latent factor models, which can account for the structural heterogeneity across diverse assays, effectively integrate multi-omics data and reduce dimensionality to a small number of factors that capture correlations and associations among measurements. These factors provide biologically interpretable features for predictive modeling. However, multi-omics integration and predictive modeling are generally performed independently in sequential steps, leading to suboptimal factor construction. Combining these steps can yield better multi-omics signatures that are more predictive while still being biologically meaningful. RESULTS: We developed a supervised variational Bayesian factor model that extracts multi-omics signatures from high-throughput profiling datasets that can span multiple data types. Signature-based multiPle-omics intEgration via lAtent factoRs (SPEAR) adaptively determines factor rank, emphasis on factor structure, data relevance and feature sparsity. The method improves the reconstruction of underlying factors in synthetic examples and prediction accuracy of coronavirus disease 2019 severity and breast cancer tumor subtypes. AVAILABILITY AND IMPLEMENTATION: SPEAR is a publicly available R-package hosted at https://bitbucket.org/kleinstein/SPEAR.

A multi-omics systems vaccinology resource to develop and test computational models of immunity.

Systems vaccinology studies have identified factors affecting individual vaccine responses, but comparing these findings is challenging due to varying study designs. To address this lack of reproducibility, we established a community resource for comparing Bordetella pertussis booster responses and to host annual contests for predicting patients' vaccination outcomes. We report here on our experiences with the "dry-run" prediction contest. We found that, among 20+ models adopted from the literature, the most successful model predicting vaccination outcome was based on age alone. This confirms our concerns about the reproducibility of conclusions between different vaccinology studies. Further, we found that, for newly trained models, handling of baseline information on the target variables was crucial. Overall, multiple co-inertia analysis gave the best results of the tested modeling approaches. Our goal is to engage community in these prediction challenges by making data and models available and opening a public contest in August 2024.

Integrated longitudinal multi-omics study identifies immune programs associated with COVID-19 severity and mortality in 1152 hospitalized participants.

Hospitalized COVID-19 patients exhibit diverse clinical outcomes, with some individuals diverging over time even though their initial disease severity appears similar. A systematic evaluation of molecular and cellular profiles over the full disease course can link immune programs and their coordination with progression heterogeneity. In this study, we carried out deep immunophenotyping and conducted longitudinal multi-omics modeling integrating ten distinct assays on a total of 1,152 IMPACC participants and identified several immune cascades that were significant drivers of differential clinical outcomes. Increasing disease severity was driven by a temporal pattern that began with the early upregulation of immunosuppressive metabolites and then elevated levels of inflammatory cytokines, signatures of coagulation, NETosis, and T-cell functional dysregulation. A second immune cascade, predictive of 28-day mortality among critically ill patients, was characterized by reduced total plasma immunoglobulins and B cells, as well as dysregulated IFN responsiveness. We demonstrated that the balance disruption between IFN-stimulated genes and IFN inhibitors is a crucial biomarker of COVID-19 mortality, potentially contributing to the failure of viral clearance in patients with fatal illness. Our longitudinal multi-omics profiling study revealed novel temporal coordination across diverse omics that potentially explain disease progression, providing insights that inform the targeted development of therapies for hospitalized COVID-19 patients, especially those critically ill.

A systems vaccinology resource to develop and test computational models of immunity.

Computational models that predict an individual's response to a vaccine offer the potential for mechanistic insights and personalized vaccination strategies. These models are increasingly derived from systems vaccinology studies that generate immune profiles from human cohorts pre- and post-vaccination. Most of these studies involve relatively small cohorts and profile the response to a single vaccine. The ability to assess the performance of the resulting models would be improved by comparing their performance on independent datasets, as has been done with great success in other areas of biology such as protein structure predictions. To transfer this approach to system vaccinology studies, we established a prototype platform that focuses on the evaluation of Computational Models of Immunity to Pertussis Booster vaccinations (CMI-PB). A community resource, CMI-PB generates experimental data for the explicit purpose of model evaluation, which is performed through a series of annual data releases and associated contests. We here report on our experience with the first such 'dry run' for a contest where the goal was to predict individual immune responses based on pre-vaccination multi-omic profiles. Over 30 models adopted from the literature were tested, but only one was predictive, and was based on age alone. The performance of new models built using CMI-PB training data was much better, but varied significantly based on the choice of pre-vaccination features used and the model building strategy. This suggests that previously published models developed for other vaccines do not generalize well to Pertussis Booster vaccination. Overall, these results reinforced the need for comparative analysis across models and datasets that CMI-PB aims to achieve. We are seeking wider community engagement for our first public prediction contest, which will open in early 2024.

Multi-omic longitudinal study reveals immune correlates of clinical course among hospitalized COVID-19 patients.

The IMPACC cohort, composed of >1,000 hospitalized COVID-19 participants, contains five illness trajectory groups (TGs) during acute infection (first 28 days), ranging from milder (TG1-3) to more severe disease course (TG4) and death (TG5). Here, we report deep immunophenotyping, profiling of >15,000 longitudinal blood and nasal samples from 540 participants of the IMPACC cohort, using 14 distinct assays. These unbiased analyses identify cellular and molecular signatures present within 72 h of hospital admission that distinguish moderate from severe and fatal COVID-19 disease. Importantly, cellular and molecular states also distinguish participants with more severe disease that recover or stabilize within 28 days from those that progress to fatal outcomes (TG4 vs. TG5). Furthermore, our longitudinal design reveals that these biologic states display distinct temporal patterns associated with clinical outcomes. Characterizing host immune responses in relation to heterogeneity in disease course may inform clinical prognosis and opportunities for intervention.

A supervised Bayesian factor model for the identification of multi-omics signatures.

MOTIVATION: Predictive biological signatures provide utility as biomarkers for disease diagnosis and prognosis, as well as prediction of responses to vaccination or therapy. These signatures are iden-tified from high-throughput profiling assays through a combination of dimensionality reduction and machine learning techniques. The genes, proteins, metabolites, and other biological analytes that compose signatures also generate hypotheses on the underlying mechanisms driving biological responses, thus improving biological understanding. Dimensionality reduction is a critical step in signature discovery to address the large number of analytes in omics datasets, especially for multi-omics profiling studies with tens of thousands of measurements. Latent factor models, which can account for the structural heterogeneity across diverse assays, effectively integrate multi-omics data and reduce dimensionality to a small number of factors that capture correlations and associations among measurements. These factors provide biologically interpretable features for predictive model-ing. However, multi-omics integration and predictive modeling are generally performed independent-ly in sequential steps, leading to suboptimal factor construction. Combining these steps can yield better multi-omics signatures that are more predictive while still being biologically meaningful. RESULTS: We developed a supervised variational Bayesian factor model that extracts multi-omics signatures from high-throughput profiling datasets that can span multiple data types. Signature-based multiPle-omics intEgration via lAtent factoRs (SPEAR) adaptively determines factor rank, emphasis on factor structure, data relevance and feature sparsity. The method improves the recon-struction of underlying factors in synthetic examples and prediction accuracy of COVID-19 severity and breast cancer tumor subtypes. AVAILABILITY: SPEAR is a publicly available R-package hosted at https://bitbucket.org/kleinstein/SPEAR.

Platelet response to influenza vaccination reflects effects of aging.

Platelets are uniquely positioned as mediators of not only hemostasis but also innate immunity. However, how age and geriatric conditions such as frailty influence platelet function during an immune response remains unclear. We assessed the platelet transcriptome at baseline and following influenza vaccination in Younger (age 21-35) and Older (age ≥65) adults (including community-dwelling individuals who were largely non-frail and skilled nursing facility (SNF)-resident adults who nearly all met criteria for frailty). Prior to vaccination, we observed an age-associated increase in the expression of platelet activation and mitochondrial RNAs and decrease in RNAs encoding proteins mediating translation. Age-associated differences were also identified in post-vaccination response trajectories over 28 days. Using tensor decomposition analysis, we found increasing RNA expression of genes in platelet activation pathways in young participants, but decreasing levels in (SNF)-resident adults. Translation RNA trajectories were inversely correlated with these activation pathways. Enhanced platelet activation was found in community-dwelling older adults at the protein level, compared to young individuals both prior to and post-vaccination; whereas SNF residents showed decreased platelet activation compared to community-dwelling older adults that could reflect the influence of decreased translation RNA expression. Our results reveal alterations in the platelet transcriptome and activation responses that may contribute to age-associated chronic inflammation and the increased incidence of thrombotic and pro-inflammatory diseases in older adults.

Systems biology of ferroptosis: A modeling approach.

Ferroptosis is a recently discovered form of iron-dependent regulated cell death (RCD) that occurs via peroxidation of phospholipids containing polyunsaturated fatty acid (PUFA) moieties. Activating this form of cell death is an emerging strategy in cancer treatment. Because multiple pathways and molecular species contribute to the ferroptotic process, predicting which tumors will be sensitive to ferroptosis is a challenge. We thus develop a mathematical model of several critical pathways to ferroptosis in order to perform a systems-level analysis of the process. We show that sensitivity to ferroptosis depends on the activity of multiple upstream cascades, including PUFA incorporation into the phospholipid membrane, and the balance between levels of pro-oxidant factors (reactive oxygen species, lipoxogynases) and antioxidant factors (GPX4). We perform a systems-level analysis of ferroptosis sensitivity as an outcome of five input variables (ACSL4, SCD1, ferroportin, transferrin receptor, and p53) and organize the resulting simulations into 'high' and 'low' ferroptosis sensitivity groups. We make a novel prediction corresponding to the combinatorial requirements of ferroptosis sensitivity to SCD1 and ACSL4 activity. To validate our prediction, we model the ferroptotic response of an ovarian cancer stem cell line following single- and double-knockdown of SCD1 and ACSL4. We find that the experimental outcomes are consistent with our simulated predictions. This work suggests that a systems-level approach is beneficial for understanding the complex combined effects of ferroptotic input, and in predicting cancer susceptibility to ferroptosis.

A mathematical model of combined CD8 T cell costimulation by 4-1BB (CD137) and OX40 (CD134) receptors.

Combined agonist stimulation of the TNFR costimulatory receptors 4-1BB (CD137) and OX40(CD134) has been shown to generate supereffector CD8 T cells that clonally expand to greater levels, survive longer, and produce a greater quantity of cytokines compared to T cells stimulated with an agonist of either costimulatory receptor individually. In order to understand the mechanisms for this effect, we have created a mathematical model for the activation of the CD8 T cell intracellular signaling network by mono- or dual-costimulation. We show that supereffector status is generated via downstream interacting pathways that are activated upon engagement of both receptors, and in silico simulations of the model are supported by published experimental results. The model can thus be used to identify critical molecular targets of T cell dual-costimulation in the context of cancer immunotherapy.

Stearoyl-CoA Desaturase 1 Protects Ovarian Cancer Cells from Ferroptotic Cell Death.

Activation of ferroptosis, a recently described mechanism of regulated cell death, dramatically inhibits growth of ovarian cancer cells. Given the importance of lipid metabolism in ferroptosis and the key role of lipids in ovarian cancer, we examined the contribution to ferroptosis of stearoyl-CoA desaturase (SCD1, SCD), an enzyme that catalyzes the rate-limiting step in monounsaturated fatty acid synthesis in ovarian cancer cells. SCD1 was highly expressed in ovarian cancer tissue, cell lines, and a genetic model of ovarian cancer stem cells. Inhibition of SCD1 induced lipid oxidation and cell death. Conversely, overexpression of SCD or exogenous administration of its C16:1 and C18:1 products, palmitoleic acid or oleate, protected cells from death. Inhibition of SCD1 induced both ferroptosis and apoptosis. Inhibition of SCD1 decreased CoQ10, an endogenous membrane antioxidant whose depletion has been linked to ferroptosis, while concomitantly decreasing unsaturated fatty acyl chains in membrane phospholipids and increasing long-chain saturated ceramides, changes previously linked to apoptosis. Simultaneous triggering of two death pathways suggests SCD1 inhibition may be an effective component of antitumor therapy, because overcoming this dual mechanism of cell death may present a significant barrier to the emergence of drug resistance. Supporting this concept, we observed that inhibition of SCD1 significantly potentiated the antitumor effect of ferroptosis inducers in both ovarian cancer cell lines and a mouse orthotopic xenograft model. Our results suggest that the use of combined treatment with SCD1 inhibitors and ferroptosis inducers may provide a new therapeutic strategy for patients with ovarian cancer. SIGNIFICANCE: The combination of SCD1 inhibitors and ferroptosis inducers may provide a new therapeutic strategy for the treatment of ovarian cancer patients.See related commentary by Carbone and Melino, p. 5149.

Neoantigens retention in patient derived xenograft models mediates autologous T cells activation in ovarian cancer.

Ovarian cancer (OC) has an overall modest number of mutations that facilitate a functional immune infiltrate able to recognize tumor mutated antigens, or neoantigens. Although patient-derived xenografts (PDXs) can partially model the tumor mutational load and mimic response to chemotherapy, no study profiled a neoantigen-driven response in OC PDXs. Here we demonstrate that the genomic status of the primary tumor from an OC patient can be recapitulated in vivo in a PDX model, with the goal of defining autologous T cells activation by neoantigens using in silico, in vitro and in vivo approaches. By profiling the PDX mutanome we discovered three main clusters of mutations defining the expansion, retraction or conservation of tumor clones based on their variant allele frequencies (VAF). RNASeq analyses revealed a strong functional conservation between the primary tumor and PDXs, highlighted by the upregulation of antigen presenting pathways. We tested in vitro a set of 30 neoantigens for recognition by autologous T cells and identified a core of six neoantigens that define a potent T cell activation able to slow tumor growth in vivo. The pattern of recognition of these six neoantigens indicates the pre-existence of anti-tumor immunity in the patient. To evaluate the breadth of T cell activation, we performed single cell sequencing profiling the TCR repertoire upon stimulation with neoantigenic moieties and identified sequence motifs that define an oligoclonal and autologous T cell response. Overall, these results indicate that OC PDXs can be a valid tool to model OC response to immunotherapy.

A Systems Biology Approach to Understanding the Pathophysiology of High-Grade Serous Ovarian Cancer: Focus on Iron and Fatty Acid Metabolism.

Ovarian cancer (OVC) is the most lethal of the gynecological malignancies, with diagnosis often occurring during advanced stages of the disease. Moreover, a majority of cases become refractory to chemotherapeutic approaches. Therefore, it is important to improve our understanding of the molecular dependencies underlying the disease to identify novel diagnostic and precision therapeutics for OVC. Cancer cells are known to sequester iron, which can potentiate cancer progression through mechanisms that have not yet been completely elucidated. We developed an algorithm to identify novel links between iron and pathways implicated in high-grade serous ovarian cancer (HGSOC), the most common and deadliest subtype of OVC, using microarray gene expression data from both clinical sources and an experimental model. Using our approach, we identified several links between fatty acid (FA) and iron metabolism, and subsequently developed a network for iron involvement in FA metabolism in HGSOC. FA import and synthesis pathways are upregulated in HGSOC and other cancers, but a link between these processes and iron-related genes has not yet been identified. We used the network to derive hypotheses of specific mechanisms by which iron and iron-related genes impact and interact with FA metabolic pathways to promote tumorigenesis. These results suggest a novel mechanism by which iron sequestration by cancer cells can potentiate cancer progression, and may provide novel targets for use in diagnosis and/or treatment of HGSOC.

Contribution of three-dimensional architecture and tumor-associated fibroblasts to hepcidin regulation in breast cancer.

Hepcidin is a peptide hormone that negatively regulates iron efflux and plays an important role in controlling the growth of breast tumors. In patients with breast cancer, the combined expression of hepcidin and its membrane target, ferroportin, predict disease outcome. However, mechanisms that control hepcidin expression in breast cancer cells remain largely unknown. Here, we use three-dimensional breast cancer spheroids derived from cell lines and breast cancer patients to probe mechanisms of hepcidin regulation in breast cancer. We observe that the extent of hepcidin induction and pathways of its regulation are markedly changed in breast cancer cells grown in three dimensions. In monolayer culture, BMPs, particularly BMP6, regulate hepcidin transcription. When breast cancer cells are grown as spheroids, there is a >10-fold induction in hepcidin transcripts. Microarray analysis combined with knockdown experiments reveal that GDF-15 is the primary mediator of this change. The increase in hepcidin as breast cells develop a three-dimensional architecture increases intracellular iron, as indicated by an increase in the iron storage protein ferritin. Immunohistochemical staining of human breast tumors confirms that both GDF-15 and hepcidin are expressed in breast cancer specimens. Further, levels of GDF-15 are significantly correlated with levels of hepcidin at both the mRNA and protein level in patient samples, consistent with a role for GDF-15 in control of hepcidin in human breast tumors. Inclusion of tumor-associated fibroblasts in breast cancer spheroids further induces hepcidin. This induction is mediated by fibroblast-dependent secretion of IL-6. Breast cancer cells grown as spheroids are uniquely receptive to IL-6-dependent induction of hepcidin by tumor-associated fibroblasts, since IL-6 does not induce hepcidin in cells grown as monolayers. Collectively, our results suggest a new paradigm for tumor-mediated control of iron through the control of hepcidin by tumor architecture and the breast tumor microenvironment.

Activation of the HGF/c-Met axis in the tumor microenvironment: A multispecies model.

The tumor microenvironment is an integral component in promoting tumor development. Cancer-associated fibroblasts (CAFs), which reside in the tumor stroma, produce Hepatocyte Growth Factor (HGF), an important trigger for invasive and metastatic tumor behavior. HGF contributes to a pro-tumorigenic environment by activating its cognate receptor, c-Met, on tumor cells. Tumor cells, in turn, secrete growth factors that upregulate HGF production in CAFs, thereby establishing a dynamic tumor-host signaling program. Using a spatiotemporal multispecies model of tumor growth, we investigate how the development and spread of a tumor is impacted by the initiation of a dynamic interaction between tumor-derived growth factors and CAF-derived HGF. We show that establishment of such an interaction results in increased tumor growth and morphological instability, the latter due in part to increased cell species heterogeneity at the tumor-host boundary. Invasive behavior is further increased if the tumor lowers responsiveness to paracrine pro-differentiation signals, which is a hallmark of neoplastic development. By modeling anti-HGF and anti-c-Met therapy, we show how disruption of the HGF/c-Met axis can reduce tumor invasiveness and growth, thereby providing theoretical evidence that targeting tumor-microenvironment interactions is a promising avenue for therapeutic development.

Three-Dimensional Spatiotemporal Modeling of Colon Cancer Organoids Reveals that Multimodal Control of Stem Cell Self-Renewal is a Critical Determinant of Size and Shape in Early Stages of Tumor Growth.

We develop a three-dimensional multispecies mathematical model to simulate the growth of colon cancer organoids containing stem, progenitor and terminally differentiated cells, as a model of early (prevascular) tumor growth. Stem cells (SCs) secrete short-range self-renewal promoters (e.g., Wnt) and their long-range inhibitors (e.g., Dkk) and proliferate slowly. Committed progenitor (CP) cells proliferate more rapidly and differentiate to produce post-mitotic terminally differentiated cells that release differentiation promoters, forming negative feedback loops on SC and CP self-renewal. We demonstrate that SCs play a central role in normal and cancer colon organoids. Spatial patterning of the SC self-renewal promoter gives rise to SC clusters, which mimic stem cell niches, around the organoid surface, and drive the development of invasive fingers. We also study the effects of externally applied signaling factors. Applying bone morphogenic proteins, which inhibit SC and CP self-renewal, reduces invasiveness and organoid size. Applying hepatocyte growth factor, which enhances SC self-renewal, produces larger sizes and enhances finger development at low concentrations but suppresses fingers at high concentrations. These results are consistent with recent experiments on colon organoids. Because many cancers are hierarchically organized and are subject to feedback regulation similar to that in normal tissues, our results suggest that in cancer, control of cancer stem cell self-renewal should influence the size and shape in similar ways, thereby opening the door to novel therapies.

Addressing current challenges in cancer immunotherapy with mathematical and computational modelling.

The goal of cancer immunotherapy is to boost a patient's immune response to a tumour. Yet, the design of an effective immunotherapy is complicated by various factors, including a potentially immunosuppressive tumour microenvironment, immune-modulating effects of conventional treatments and therapy-related toxicities. These complexities can be incorporated into mathematical and computational models of cancer immunotherapy that can then be used to aid in rational therapy design. In this review, we survey modelling approaches under the umbrella of the major challenges facing immunotherapy development, which encompass tumour classification, optimal treatment scheduling and combination therapy design. Although overlapping, each challenge has presented unique opportunities for modellers to make contributions using analytical and numerical analysis of model outcomes, as well as optimization algorithms. We discuss several examples of models that have grown in complexity as more biological information has become available, showcasing how model development is a dynamic process interlinked with the rapid advances in tumour-immune biology. We conclude the review with recommendations for modellers both with respect to methodology and biological direction that might help keep modellers at the forefront of cancer immunotherapy development.

Feedback Regulation in a Cancer Stem Cell Model can Cause an Allee Effect.

The exact mechanisms of spontaneous tumor remission or complete response to treatment are phenomena in oncology that are not completely understood. We use a concept from ecology, the Allee effect, to help explain tumor extinction in a model of tumor growth that incorporates feedback regulation of stem cell dynamics, which occurs in many tumor types where certain signaling molecules, such as Wnts, are upregulated. Due to feedback and the Allee effect, a tumor may become extinct spontaneously or after therapy even when the entire tumor has not been eradicated by the end of therapy. We quantify the Allee effect using an 'Allee index' that approximates the area of the basin of attraction for tumor extinction. We show that effectiveness of combination therapy in cancer treatment may occur due to the increased probability that the system will be in the Allee region after combination treatment versus monotherapy. We identify therapies that can attenuate stem cell self-renewal, alter the Allee region and increase its size. We also show that decreased response of tumor cells to growth inhibitors can reduce the size of the Allee region and increase stem cell densities, which may help to explain why this phenomenon is a hallmark of cancer.