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In this opinion, we highlight agent-based modeling as a key tool for exploration of cell-cell and cell-environment interactions that drive cancer progression, therapeutic resistance, and metastasis. These biological phenomena are particularly suited to be captured at the cell-scale resolution possible only within agent-based or individual-based mathematical models. These modeling approaches complement experimental work (in vitro and in vivo systems) through parameterization and data extrapolation but also feed forward to drive new experiments that test model-generated predictions.

Adaptive therapy, as per the dose modulation, dose-skipping, or intermittent treatment protocol works well for treatment using a single cytotoxic drug, under a wide range of scenarios and parameter settings. In contrast, adaptive therapy works well only under a limited number of scenarios and parameter settings when using a single cytostatic drug. In general, adaptive therapy works best under conditions of higher fitness cost, higher replacement rate, higher turnover. Adaptive therapy works best when drug dosages are changed as soon as a change in tumor burden is detected. In general, it is better to pause treatment sooner than later, when the tumor is shrinking If the amount of drug used is too low, it is unable to control the sensitive cells and the tumor grows. However, if the drug dose is too high, it quickly selects for resistant cells and eventually the tumor grows out of control. However, there appears to be intermediate levels of dosing, which we call the minimum effective dose, which is able to control the sensitive cells but is not high enough to select for the resistant cells to grow out of control.

While the dose modulation (DM) protocols (DM Cocktail Tandem, DM Ping-Pong Alternate Every Cycle, DM Ping-Pong on Progression) involves adjusting drug dosages when the tumor burden changes, the fixed-dose (FD) protocols involves administering a specific, constant dosage of the drug only when the tumor is growing (Dose-Skipping) or when the absolute tumor burden is above the baseline level until it reduces to a certain percentage of the baseline (Intermittent). Moreover, two different drugs can be administered simultaneously (cocktail), or the drugs can be switched such that only one drug is applied at a given time (ping-pong), either every cycle (ping-pong alternate every cycle) or when the tumor grows (ping-pong on progression). The dose modulation protocols work well when treated with two cytotoxic drugs, however, the ping-pong protocols (DM Ping-Pong Alternate Every Cycle, DM Ping-Pong on Progression, FD Ping-Pong Intermittent) work well when treated with two cytostatic drugs. In general, adaptive therapy, using either two cytotoxic or two cytostatic drugs works best under conditions of high competition, such as high fitness cost, high replacement rates, and high turnover, although treatment using two cytostatic drugs works best under low turnover in many cases. Adaptive therapy works best when drug dosages are changed as soon as a change in tumor burden is detected, and it is best to pause treatment sooner rather than later when the tumor is shrinking. Adaptive therapy works best when an intermediate level of drug dosage is used, and both treatment with too little or too much drug leads to poor survival outcome.

Molecular clocks that record cell ancestry mutate too slowly to measure the short-timescale dynamics of cell renewal in adult tissues. Here, we show that fluctuating DNA methylation marks can be used as clocks in cells where ongoing methylation and demethylation cause repeated ‘flip–flops’ between methylated and unmethylated states. We identify endogenous fluctuating CpG (fCpG) sites using standard methylation arrays and develop a mathematical model to quantitatively measure human adult stem cell dynamics from these data. Small intestinal crypts were inferred to contain slightly more stem cells than the colon, with slower stem cell replacement in the small intestine. Germline APC mutation increased the number of replacements per crypt. In blood, we measured rapid expansion of acute leukemia and slower growth of chronic disease. Thus, the patterns of human somatic cell birth and death are measurable with fluctuating methylation clocks (FMCs).

The current paradigm of clinical trials treating patients until disease progression using maximum tolerated dose does not account for the dynamic tumor-host-drug interactions that result in acquired resistance. Here, we present the concept of an Evolutionary Tumor Board (ETB) and report interim results from a prospective, non-interventional pilot study in which novel therapeutic strategies based on evolutionary principles were developed under the ETB framework. The ETB approach relies on an interdisciplinary team that integrates clinical, preclinical, and theoretical knowledge and the application of mathematical modeling to predict patient responses to different therapies, including novel approaches derived from eco-evolutionary first principles. We have previously proposed several evolutionary therapies that aim to enhance the efficacy of an overall treatment regimen, using existing agents for a given disease. Key among these evolutionary therapies is the idea of “first-strike second-strike”, where different agents are administered in sequence, and new strikes are applied as soon as the efficacy of the previous strike is nearing a minimum, as opposed to waiting until progression is identified on periodic imaging. This approach requires careful analysis of longitudinal patient data coupled with predictive dynamics generated by mathematical models. Here we describe the ETB process and the interim results from 15 patients enrolled in the feasibility trial. In addition, we describe the challenges faced as well as the solutions that can be implemented via improved modeling approaches, better patient data collection, and a reassessment of how we understand tumor dynamics in the light of evolutionary principles.

The emergence of SARS-CoV-2 variants of concern (VOC) requires adequate coverage of vaccine protection. We evaluated whether a SARS-CoV-2 spike ferritin nanoparticle vaccine (SpFN), adjuvanted with the Army Liposomal Formulation QS21 (ALFQ), conferred protection against the Alpha (B.1.1.7), and Beta (B.1.351) VOCs in Syrian golden hamsters. SpFN-ALFQ was administered as either single or double-vaccination (0 and 4 week) regimens, using a high (10 μg) or low (0.2 μg) dose. Animals were intranasally challenged at week 11. Binding antibody responses were comparable between high- and low-dose groups. Neutralizing antibody titers were equivalent against WA1, B.1.1.7, and B.1.351 variants following two high dose vaccinations. Dose-dependent SpFN-ALFQ vaccination protected against SARS-CoV-2-induced disease and viral replication following intranasal B.1.1.7 or B.1.351 challenge, as evidenced by reduced weight loss, lung pathology, and lung and nasal turbinate viral burden. These data support the development of SpFN-ALFQ as a broadly protective, next-generation SARS-CoV-2 vaccine.

1.AbstractLung cancer is the leading cause of cancer death worldwide with 1.76 million people die as a result of the disease yearly. Analyzing high-throughput multiplexed images of tissues has recently emerged as a routine clinical procedure for early detection, clinical cancer diagnosis, treatment planning and prognosis for many cancer types including non-small cell lung cancer (NSCLC). Multiplexed images enable the precise interpretation of spatial distribution of cells and cellular states and the characterization of tumor-immune interactions in situ and at the single-cell level. Through two cornerstone image processing techniques - cell segmentation and image tiling generating quadrats - we perform an in-depth analysis of multiplexed images based on the frequency, phenotype, and spatial distribution of immune and tumor cells within the immune landscape of NSCLC. Multiplexed images were obtained from nine patients with advanced/metastatic NSCLC with progression who were treated with an oral HDAC inhibitor (vorinostat) combined with a PD-1 inhibitor (pembrolizumab). Images were collected from all patients both pre- and on-treatment (days 15-21). We profile ∼100K cells and ∼10K quadrats from tumor and adjacent tissues to characterize cellular composition and spatial neighborhoods and elucidate that distinct spatial cellular ecologies exist across progressive disease (PD) and stable disease (SD) patients where tumors of PD patients are characterized by a highly suppressed immune environment prior to treatment enabling higher chances of disease progression during treatment. These fundamentally distinct architectures across PD and SD patients enable disease progression prediction and clinical biomarker identification. Our results also provide a potential companion biomarker for PD-L1 in NSCLC. Validating the biomarker and its feasibility will require further in-depth investigation.

Recent studies have revealed that normal human tissues accumulate many somatic mutations. In particular, human skin is riddled with mutations, with multiple subclones of variable sizes. Driver mutations are frequent and tend to have larger subclone sizes, suggesting selection. To begin to understand the histories encoded by these complex somatic mutations, we incorporated genomes into a simple agent-based skin-cell model whose prime directive is homeostasis. In this model, stem-cell survival is random and dependent on proximity to the basement membrane. This simple homeostatic skin model recapitulates the observed log-linear distributions of somatic mutations, where most mutations are found in increasingly smaller subclones that are typically lost with time. Hence, neutral mutations are “passengers” whose fates depend on the random survival of their stem cells, where a rarer larger subclone reflects the survival and spread of mutations acquired earlier in life. The model can also maintain homeostasis and accumulate more frequent and larger driver subclones if these mutations (NOTCH1 and TP53) confer relatively higher persistence in normal skin or during tissue damage (sunlight). Therefore, a relatively simple model of epithelial turnover indicates how observed passenger and driver somatic mutations could accumulate without violating the prime directive of homeostasis in normal human tissues.

Metabolism plays a complex role in the evolution of cancerous tumors, including inducing a multifaceted effect on the immune system to aid immune escape. Immune escape is, by definition, a collective phenomenon by requiring the presence of two cell types interacting in close proximity: tumor and immune. The microenvironmental context of these interactions is influenced by the dynamic process of blood vessel growth and remodelling, creating heterogeneous patches of well-vascularized tumor or acidic niches. We present a multiscale mathematical model that captures the phenotypic, vascular, microenvironmental, and spatial heterogeneity which shapes acid-mediated invasion and immune escape over a biologically-realistic time scale. We model immune escape mechanisms such as i) acid inactivation of immune cells, ii) competition for glucose, and iii) inhibitory immune checkpoint receptor expression (PD-L1) under anti-PD-L1 and sodium bicarbonate buffer therapies. To aid in understanding immune escape as a collective cellular phenomenon, we define immune escape in the context of six collective phenotypes (termed “meta-phenotypes”):Self-Acidify, Mooch Acid, PD-L1 Attack, Mooch PD-L1, Proliferate Fast, and Starve Glucose. Fomenting a stronger immune response leads to initial benefits but this advantage is offset by increased cell turnover that accelerates the emergence of aggressive phenotypes by inducing an evolutionary bottleneck. This model helps to untangle the key constraints on evolutionary costs and benefits of three key phenotypic axes on tumor invasion and treatment: acid-resistance, glycolysis, and PD-L1 expression. The benefits of concomitant anti-PD-L1 and buffer treatments is a promising treatment strategy to limit the adverse effects of immune escape.

Cancer growth can be described as a caricature of the renewal process of the tissue of origin, where the tissue architecture has a strong influence on the evolutionary dynamics within the tumor. Using a classic, well-studied model of tumor evolution (a passenger-driver mutation model) we systematically alter spatial constraints and cell mixing rates to show how tissue structure influences functional (driver) mutations and genetic heterogeneity over time. This approach explores a key mechanism behind both inter-patient and intratumoral tumor heterogeneity: competition for space. Time-varying competition leads to an emergent transition from Darwinian premalignant growth to subsequent invasive neutral tumor growth. Initial spatial constraints determine the emergent mode of evolution (Darwinian to neutral) without a change in cell-specific mutation rate or fitness effects. Driver acquisition during the Darwinian precancerous stage may be modulated en route to neutral evolution by the combination of two factors: spatial constraints and limited cellular mixing. These two factors occur naturally in ductal carcinomas, where the branching topology of the ductal network dictates spatial constraints and mixing rates., Some cancers occur in spatially constrained tissues such as the mammary gland, and how the morphological features influence the evolution of the cancer is unclear. Here, the authors use mathematical modeling to study the question of competition for space and provide inferences on the mode of evolution of cancers in such tissues.

Most ovarian cancers are infiltrated by prognostically relevant activated T cells1–3, yet exhibit low response rates to immune checkpoint inhibitors4. Memory B cell and plasma cell infiltrates have previously been associated with better outcomes in ovarian cancer5,6, but the nature and functional relevance of these responses are controversial. Here, using 3 independent cohorts that in total comprise 534 patients with high-grade serous ovarian cancer, we show that robust, protective humoral responses are dominated by the production of polyclonal IgA, which binds to polymeric IgA receptors that are universally expressed on ovarian cancer cells. Notably, tumour B-cell-derived IgA redirects myeloid cells against extracellular oncogenic drivers, which causes tumour cell death. In addition, IgA transcytosis through malignant epithelial cells elicits transcriptional changes that antagonize the RAS pathway and sensitize tumour cells to cytolytic killing by T cells, which also contributes to hindering malignant progression. Thus, tumour-antigen-specific and -antigen-independent IgA responses antagonize the growth of ovarian cancer by governing coordinated tumour cell, T cell and B cell responses. These findings provide a platform for identifying targets that are spontaneously recognized by intratumoural B-cell-derived antibodies, and suggest that immunotherapies that augment B cell responses may be more effective than approaches that focus on T cells, particularly for malignancies that are resistant to checkpoint inhibitors. In patients with high-grade serous ovarian cancer, robust and protective humoral responses are dominated by B-cell-derived polyclonal IgA that binds to polymeric IgA receptors that are universally expressed on ovarian cancer cells.

The influence of biological sex differences on human health and disease, while being increasingly recognized, has long been underappreciated and underexplored. While humans of all sexes are more alike than different, there is evidence for sex differences in the most basic aspects of human biology and these differences have consequences for the etiology and pathophysiology of many diseases. In a disease like cancer, these consequences manifest in the sex biases in incidence and outcome of many cancer types. The ability to deliver precise, targeted therapies to complex cancer cases is limited by our current understanding of the underlying sex differences. Gaining a better understanding of the implications and interplay of sex differences in diseases like cancer will thus be informative for clinical practice and biological research. Here we review the evidence for a broad array of biological sex differences in humans and discuss how these differences may relate to observed sex differences in various diseases, including many cancers and specifically glioblastoma. We focus on areas of human biology that play vital roles in healthy and disease states, including metabolism, development, hormones, and the immune system, and emphasize that the intersection of sex differences in these areas should not go overlooked. We further propose that mathematical approaches can be useful for exploring the extent to which sex differences affect disease outcomes and accounting for those in the development of therapeutic strategies.

The purpose of this study is to use the dynamics of commonly collected biomarker levels for prostate cancer to identify the underlying cancer cell subtype composition and help predict response to treatment. In castrate-sensitive prostate cancer, the current standard of care is continuous maximum-tolerated dose (MTD) of anti-androgen compounds, which successfully reduces the tumor burden. However, continuous use often leads to treatment resistance. Alternatively, adaptive therapy approaches have been used clinically to delay or prevent resistant outgrowth. In adaptive therapy, a drug is given to maintain a tumor size by killing enough treatment-sensitive cells to shrink the burden but keep enough sensitive cells to suppress the outgrowth of resistant cells. Clinical trials using adaptive therapy approaches have shown longer tumor control compared to MTD for castrate-resistant disease and, more recently, shown feasibility for control in castrate-sensitive disease. This approach relies on using prostate-specific antigen (PSA) as a systemic biomarker as a surrogate for total tumor burden. Because PSA is a product of testosterone metabolism by androgen receptors (AR) in cells, and both testosterone and AR can vary over time and amongst cells, we can use a mathematical model to couple PSA, testosterone, and AR-dependency to dissociate systemic biomarkers from tumor burden and uncover potential mechanisms of resistance. We build a system of ordinary differential equations to investigate the emergence of different resistance mechanisms for metastatic castrate-sensitive prostate cancer patients. We first fit the equations to testosterone dynamics alone. Then, fixing those parameters, we fit to the dynamics of PSA assuming cell subtypes consisting of testosterone-dependent cells, testosterone producers, and AR-overexpressing cells. From the best fits, we can estimate the tumor cell subtype compositions for each patient and test different treatment strategies. We find that patients with tightly correlated testosterone and PSA levels tend to have mostly testosterone-dependent cells and continued robust responses to each round of treatment. Less correlated testosterone and PSA dynamics was usually associated with changes in PSA nadirs, peaks, or rates of return after stopping treatment over subsequent rounds of adaptive therapy. By fitting to both PSA and testosterone dynamics, we can distinguish between tumors that maintain testosterone-dependent cells from those with increasing resistant cell types. This allows for better quantification of the underlying tumor composition to help optimize therapies that target those cell types and better maintain tumor control. Citation Format: Jill Gallaher, Maximilian Strobl, Jeffrey West, Mark Robertson-Tessi, Robert Gatenby, Jingsong Zhang, Alexander R. A. Anderson. Predicting progression in metastatic castrate-sensitive prostate cancer by coupling PSA and testosterone dynamics to a mechanistic mathematical model [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 1 (Regular and Invited Abstracts); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(7_Suppl):Abstract nr 852.

Prostate cancer (PCa) progression is a complex eco-evolutionary process driven by the feedback between evolving tumour cell phenotypes and microenvironmentally driven selection. To better understand this relationship, we used a multiscale mathematical model that integrates data from biology and pathology on the microenvironmental regulation of PCa cell behaviour. Our data indicate that the interactions between tumour cells and their environment shape the evolutionary dynamics of PCa cells and explain overall tumour aggressiveness. A key environmental determinant of this aggressiveness is the stromal ecology, which can be either inhibitory, highly reactive (supportive) or non-reactive (neutral). Our results show that stromal ecology correlates directly with tumour growth but inversely modulates tumour evolution. This suggests that aggressive, environmentally independent PCa may be a result of poor stromal ecology, supporting the concept that purely tumour epithelium-centric metrics of aggressiveness may be incomplete and that incorporating markers of stromal ecology would improve prognosis.

Gattaca provides the first base-pair resolution artificial genomes for tracking somatic mutations within agent based modeling. Through the incorporation of human reference genomes, mutational context, sequence coverage/error information Gattaca is able to realistically provide comparable sequence data for in-silico comparative evolution studies with human somatic evolution studies. This user-friendly method, incorporated into each in-silico cell, allows us to fully capture somatic mutation spectra and evolution.

Spatial analyses can reveal important interactions between and among cells and their microenvironment. However, most existing staining methods are limited to a handful of markers per slice, thereby limiting the number of interactions that can be studied. This limitation is frequently overcome by registering multiple images to create a single composite image containing many markers. While there are several existing image registration methods for whole slide images (WSI), most have specific use cases. Here, we present the Virtual Alignment of pathoLogy Image Series (VALIS), a fully automated pipeline that opens, registers (rigid and/or non-rigid), and saves aligned slides in the ome.tiff format. VALIS has been tested with 273 immunohistochemistry (IHC) samples and 340 immunofluorescence (IF) samples, each of which contained between 2-69 images per sample. The registered WSI tend to have low error and are completed within a matter of minutes. In addition to registering slides, VALIS can also using the registration parameters to warp point data, such as cell centroids previously determined via cell segmentation and phenotyping. VALIS is written in Python and requires only few lines of code for execution. VALIS therefore provides a free, opensource, flexible, and simple pipeline for rigid and non-rigid registration of IF and/or IHC that can facilitate spatial analyses of WSI from novel and existing datasets.

Understanding the complex ecology of a tumor tissue and the spatio-temporal relationships between its cellular and microenvironment components is becoming a key component of translational research, especially in immune-oncology. The generation and analysis of multiplexed images from patient samples is of paramount importance to facilitate this understanding. In this work, we present Mistic, an open-source multiplexed image t-SNE viewer that enables the simultaneous viewing of multiple 2D images rendered using multiple layout options to provide an overall visual preview of the entire dataset. In particular, the positions of the images can be taken from t-SNE or UMAP coordinates. This grouped view of all the images further aids an exploratory understanding of the specific expression pattern of a given biomarker or collection of biomarkers across all images, helps to identify images expressing a particular phenotype or to select images for subsequent downstream analysis. Currently there is no freely available tool to generate such image t-SNEs. Mistic is open-source and can be downloaded at: https://github.com/MathOnco/Mistic.

Background Adaptive therapy aims to tackle cancer drug resistance by leveraging resource competition between drug-sensitive and resistant cells. Here, we present a theoretical study of intra-tumoral competition during adaptive therapy, to investigate under which circumstances it will be superior to aggressive treatment. Methods We develop and analyse a simple, 2-D, on-lattice, agent-based tumour model in which cells are classified as fully drug-sensitive or resistant. Subsequently, we compare this model to its corresponding non-spatial ordinary differential equation model, and fit it to longitudinal prostate-specific antigen data from 65 prostate cancer patients undergoing intermittent androgen deprivation therapy following biochemical recurrence. Results Leveraging the individual-based nature of our model, we explicitly demonstrate competitive suppression of resistance during adaptive therapy, and examine how different factors, such as the initial resistance fraction or resistance costs, alter competition. This not only corroborates our theoretical understanding of adaptive therapy, but also reveals that competition of resistant cells with each other may play a more important role in adaptive therapy in solid tumours than was previously thought. To conclude, we present two case studies, which demonstrate the implications of our work for: (i) mathematical modelling of adaptive therapy, and (ii) the intra-tumoral dynamics in prostate cancer patients during intermittent androgen deprivation treatment, a precursor of adaptive therapy. Conclusion Our work shows that the tumour’s spatial architecture is an important factor in adaptive therapy and provides insights into how adaptive therapy leverages both inter- and intra-specific competition to control resistance.

The role of plasticity and epigenetics in shaping cancer evolution and response to therapy has taken center stage with recent technological advances including single cell sequencing. This roadmap article is focused on state-of-the-art mathematical and experimental approaches to interrogate plasticity in cancer, and addresses the following themes and questions: is there a formal overarching framework that encompasses both non-genetic plasticity and mutation-driven somatic evolution? How do we measure and model the role of the microenvironment in influencing/controlling non-genetic plasticity? How can we experimentally study non-genetic plasticity? Which mathematical techniques are required or best suited? What are the clinical and practical applications and implications of these concepts?

The evolutionary dynamics of tumor initiation remain undetermined, and the interplay between neoplastic cells and the immune system is hypothesized to be critical in transformation. Colorectal cancer (CRC) presents a unique opportunity to study the transition to malignancy as pre-cancers (adenomas) and early stage cancers are frequently detected and surgically removed. Here, we demonstrate a key role for the immune response in tumor initiation by studying tumor-immune eco-evolutionary dynamics from pre-cancer to carcinoma using a computational model, ecological analysis of digital pathology data, and multi-region exome sequencing and neoantigen prediction in a total of 62 patient samples. Modelling indicates there are several potential routes to malignancy, each of which uniquely sculpts tumor ecology and intra-tumor antigenic heterogeneity (aITH). In patient samples, the immune microenvironment was characterized using the spatial distribution of 17 markers across registered whole-slide images, and patterns of intra-lesion aITH measured using multi-region exome sequencing and neoantigen prediction. The patient data were best described by a model whereby immunogenic adenomas do not progress to CRC because they are under immune control, and progression initially proceeds in adenomas with low immunogenicity followed by the gradual construction of an immunosuppressive niche depleted in CD8+ cytotoxic T cells. There was little evidence for immune blockade (PD-L1 expression) in tumor initiation or progression. These results suggest that re-engineering the immunosuppressive niche may prove to be an effective immunotherapy in CRC.

Summary Evolutionary game theory describes frequency-dependent selection for fixed, heritable strategies in a population of competing individuals using a payoff matrix. We present a software package to aid in the construction, analysis and visualization of three-strategy matrix games. The IsoMaTrix package computes the isoclines (lines of zero growth) of matrix games, and facilitates direct comparison of well-mixed dynamics to structured populations on a lattice grid. IsoMaTrix computes fixed points, phase flow, trajectories, (sub)velocities and uncertainty quantification for stochastic effects in spatial matrix games. We describe a result obtained via IsoMaTrix’s spatial games functionality, which shows that the timing of competitive release in a cancer model (under continuous treatment) critically depends on the initial spatial configuration of the tumor. Availability and implementation The code is available at: https://github.com/mathonco/isomatrix. Supplementary information Supplementary data are available at Bioinformatics online.