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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.
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Evolución Clonal , Epidermis , Homeostasis , Queratinocitos , Carcinogénesis/genética , Evolución Clonal/genética , Epidermis/metabolismo , Humanos , Queratinocitos/citología , Queratinocitos/fisiología , Mutación , Receptor Notch1/genética , Proteína p53 Supresora de Tumor/genéticaRESUMEN
Drug dose response curves are ubiquitous in cancer biology, but these curves are often used to measure differential response in first-order effects: the effectiveness of increasing the cumulative dose delivered. In contrast, second-order effects (the variance of drug dose) are often ignored. Knowledge of second-order effects may improve the design of chemotherapy scheduling protocols, leading to improvements in tumor response without changing the total dose delivered. By considering treatment schedules with identical cumulative dose delivered, we characterize differential treatment outcomes resulting from high variance schedules (e.g. high dose, low dose) and low variance schedules (constant dose). We extend a previous framework used to quantify second-order effects, known as antifragility theory, to investigate the role of drug pharmacokinetics. Using a simple one-compartment model, we find that high variance schedules are effective for a wide range of cumulative dose values. Next, using a mouse-parameterized two-compartment model of 5-fluorouracil, we show that schedule viability depends on initial tumor volume. Finally, we illustrate the trade-off between tumor response and lean mass preservation. Mathematical modeling indicates that high variance dose schedules provide a potential path forward in mitigating the risk of chemotherapy-associated cachexia by preserving lean mass without sacrificing tumor response.
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Caquexia , Conceptos Matemáticos , Animales , Caquexia/tratamiento farmacológico , Caquexia/etiología , Protocolos de Quimioterapia Combinada Antineoplásica , Biología , Modelos Animales de EnfermedadRESUMEN
The harsh microenvironment of ductal carcinoma in situ (DCIS) exerts strong evolutionary selection pressures on cancer cells. We hypothesize that the poor metabolic conditions near the ductal center foment the emergence of a Warburg Effect (WE) phenotype, wherein cells rapidly ferment glucose to lactic acid, even in normoxia. To test this hypothesis, we subjected low-glycolytic breast cancer cells to different microenvironmental selection pressures using combinations of hypoxia, acidosis, low glucose, and starvation for many months and isolated single clones for metabolic and transcriptomic profiling. The two harshest conditions selected for constitutively expressed WE phenotypes. RNA sequencing analysis of WE clones identified the transcription factor KLF4 as potential inducer of the WE phenotype. In stained DCIS samples, KLF4 expression was enriched in the area with the harshest microenvironmental conditions. We simulated in vivo DCIS phenotypic evolution using a mathematical model calibrated from the in vitro results. The WE phenotype emerged in the poor metabolic conditions near the necrotic core. We propose that harsh microenvironments within DCIS select for a WE phenotype through constitutive transcriptional reprogramming, thus conferring a survival advantage and facilitating further growth and invasion.
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Neoplasias de la Mama/genética , Carcinoma Intraductal no Infiltrante/genética , Factores de Transcripción de Tipo Kruppel/genética , Efecto Warburg en Oncología , Neoplasias de la Mama/metabolismo , Neoplasias de la Mama/patología , Carcinoma Intraductal no Infiltrante/metabolismo , Carcinoma Intraductal no Infiltrante/patología , Femenino , Regulación Neoplásica de la Expresión Génica/genética , Glucólisis/genética , Humanos , Factor 4 Similar a Kruppel , Células MCF-7 , Estadificación de Neoplasias , Hipoxia Tumoral/genética , Microambiente Tumoral/genéticaRESUMEN
Research over the past two decades has made substantial inroads into our understanding of somatic mutations. Recently, these studies have focused on understanding their presence in homeostatic tissue. In parallel, agent-based mechanistic models have emerged as an important tool for understanding somatic mutation in tissue; yet no common methodology currently exists to provide base-pair resolution data for these models. Here, we present Gattaca as the first method for introducing and tracking somatic mutations at the base-pair resolution within agent-based models that typically lack nuclei. With nuclei that incorporate human reference genomes, mutational context, and sequence coverage/error information, Gattaca is able to realistically evolve sequence data, facilitating comparisons between in silico cell tissue modeling with experimental human somatic mutation data. This user-friendly method, incorporated into each in silico cell, allows us to fully capture somatic mutation spectra and evolution.
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Genoma Humano , Neoplasias , Evolución Clonal , Humanos , Mutación , Neoplasias/genéticaRESUMEN
We extend techniques and learnings about the stochastic properties of nonlinear responses from finance to medicine, particularly oncology, where it can inform dosing and intervention. We define antifragility. We propose uses of risk analysis for medical problems, through the properties of nonlinear responses (convex or concave). We (1) link the convexity/concavity of the dose-response function to the statistical properties of the results; (2) define "antifragility" as a mathematical property for local beneficial convex responses and the generalization of "fragility" as its opposite, locally concave in the tails of the statistical distribution; (3) propose mathematically tractable relations between dosage, severity of conditions, and iatrogenics. In short, we propose a framework to integrate the necessary consequences of nonlinearities in evidence-based oncology and more general clinical risk management.
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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.
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A tumor is made up of a heterogeneous collection of cell types, all competing on a fitness landscape mediated by microenvironmental conditions that dictate their interactions. Despite the fact that much is known about cell signaling, cellular cooperation, and the functional constraints that affect cellular behavior, the specifics of how these constraints (and the range over which they act) affect the macroscopic tumor growth laws that govern total volume, mass, and carrying capacity remain poorly understood. We develop a statistical mechanics approach that focuses on the total number of possible states each cell can occupy and show how different assumptions on correlations of these states give rise to the many different macroscopic tumor growth laws used in the literature. Although it is widely understood that molecular and cellular heterogeneity within a tumor is a driver of growth, here we emphasize that focusing on the functional coupling of states at the cellular level is what determines macroscopic growth characteristics.
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Comunicación Celular/fisiología , Aumento de la Célula , Modelos Biológicos , Neoplasias , Biodiversidad , Humanos , Neoplasias/patología , Neoplasias/terapia , Transducción de Señal/fisiología , Microambiente Tumoral/fisiologíaRESUMEN
The Hybrid Automata Library (HAL) is a Java Library developed for use in mathematical oncology modeling. It is made of simple, efficient, generic components that can be used to model complex spatial systems. HAL's components can broadly be classified into: on- and off-lattice agent containers, finite difference diffusion fields, a GUI building system, and additional tools and utilities for computation and data collection. These components are designed to operate independently and are standardized to make them easy to interface with one another. As a demonstration of how modeling can be simplified using our approach, we have included a complete example of a hybrid model (a spatial model with interacting agent-based and PDE components). HAL is a useful asset for researchers who wish to build performant 1D, 2D and 3D hybrid models in Java, while not starting entirely from scratch. It is available on GitHub at https://github.com/MathOnco/HAL under the MIT License. HAL requires the Java JDK version 1.8 or later to compile and run the source code.
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Biología Computacional/métodos , Algoritmos , Computadores , Biblioteca de Genes , Modelos Biológicos , Modelos Teóricos , Programas Informáticos , Interfaz Usuario-ComputadorRESUMEN
The development of chemotherapeutic resistance resulting in tumor relapse is largely the consequence of the mechanism of competitive release of pre-existing resistant tumor cells selected for regrowth after chemotherapeutic agents attack the previously dominant chemo-sensitive population. We introduce a prisoner's dilemma game theoretic mathematical model based on the replicator of three competing cell populations: healthy (cooperators), sensitive (defectors), and resistant (defectors) cells. The model is shown to recapitulate prostate-specific antigen measurement data from three clinical trials for metastatic castration-resistant prostate cancer patients treated with 1) prednisone, 2) mitoxantrone and prednisone and 3) docetaxel and prednisone. Continuous maximum tolerated dose schedules reduce the sensitive cell population, initially shrinking tumor burden, but subsequently "release" the resistant cells from competition to re-populate and re-grow the tumor in a resistant form. The evolutionary model allows us to quantify responses to conventional (continuous) therapeutic strategies as well as to design adaptive strategies.These novel adaptive strategies are robust to small perturbations in timing and extend simulated time to relapse from continuous therapy administration.
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Protocolos de Quimioterapia Combinada Antineoplásica/administración & dosificación , Modelos Biológicos , Neoplasias de la Próstata Resistentes a la Castración , Docetaxel/administración & dosificación , Humanos , Masculino , Mitoxantrona/administración & dosificación , Prednisona/administración & dosificación , Neoplasias de la Próstata Resistentes a la Castración/tratamiento farmacológico , Neoplasias de la Próstata Resistentes a la Castración/metabolismo , Neoplasias de la Próstata Resistentes a la Castración/patologíaRESUMEN
Primary neuroendocrine tumors of the liver are exceedingly rare, and unlike metastatic neuroendocrine tumors, rarely cause carcinoid syndrome. There are fewer than 150 cases reported in the current literature. We report two cases of primary hepatic neuroendocrine carcinomas of the liver. Both patients remain healthy without any recurrence to date. A review of the current literature regarding diagnosis, pathology, and management of this disease is included.
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Carcinoma Neuroendocrino , Hepatectomía/métodos , Neoplasias Hepáticas , Hígado/patología , Anciano , Carcinoma Neuroendocrino/patología , Carcinoma Neuroendocrino/cirugía , Femenino , Humanos , Inmunohistoquímica , Hallazgos Incidentales , Neoplasias Hepáticas/patología , Neoplasias Hepáticas/cirugía , Masculino , Persona de Mediana Edad , Invasividad Neoplásica , Estadificación de Neoplasias , Tomografía Computarizada por Rayos X/métodos , Resultado del TratamientoRESUMEN
Direct observation of immune cell trafficking patterns and tumor-immune interactions is unlikely in human tumors with currently available technology, but computational simulations based on clinical data can provide insight to test hypotheses. It is hypothesized that patterns of collagen formation evolve as a mechanism of immune escape, but the exact nature of the interaction between immune cells and collagen is poorly understood. Spatial data quantifying the degree of collagen fiber alignment in squamous cell carcinomas indicates that late stage disease is associated with highly aligned fibers. Here, we introduce a computational modeling framework (called Lenia) to discriminate between two hypotheses: immune cell migration that moves 1) parallel or 2) perpendicular to collagen fiber orientation. The modeling recapitulates immune-ECM interactions where collagen patterns provide immune protection, leading to an emergent inverse relationship between disease stage and immune coverage. We also illustrate the capabilities of Lenia to model the evolution of tumor progression and immune predation. Lenia provides a flexible framework for considering a spectrum of local (cell-scale) to global (tumor-scale) dynamics by defining a kernel cell-cell interaction function that governs tumor growth dynamics under immune predation with immune cell migration. Mathematical modeling provides important mechanistic insights into cell interactions. Short-range interaction kernels provide a mechanism for tumor cell survival under conditions with strong Allee effects, while asymmetric tumor-immune interaction kernels lead to poor immune response. Thus, the length scale of tumor-immune interactions drives tumor growth and infiltration.
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Introduction: 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. Methods: Here, 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. The model explores several immune escape mechanisms such as i) acid inactivation of immune cells, ii) competition for glucose, and iii) inhibitory immune checkpoint receptor expression (PD-L1). We also explore the efficacy of anti-PD-L1 and sodium bicarbonate buffer agents for treatment. 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. Results: Fomenting a stronger immune response leads to initial benefits (additional cytotoxicity), but this advantage is offset by increased cell turnover that leads to accelerated evolution and the emergence of aggressive phenotypes. This creates a bimodal therapy landscape: either the immune system should be maximized for complete cure, or kept in check to avoid rapid evolution of invasive cells. These constraints are dependent on heterogeneity in vascular context, microenvironmental acidification, and the strength of immune response. Discussion: 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.
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Antígeno B7-H1 , Neoplasias , Humanos , Antígeno B7-H1/metabolismo , Neoplasias/genética , Neoplasias/patología , GlucosaRESUMEN
Lenia, a cellular automata framework used in artificial life, provides a natural setting to implement mathematical models of cancer incorporating features such as morphogenesis, homeostasis, motility, reproduction, growth, stimuli response, evolvability, and adaptation. Historically, agent-based models of cancer progression have been constructed with rules that govern birth, death and migration, with attempts to map local rules to emergent global growth dynamics. In contrast, Lenia provides a flexible framework for considering a spectrum of local (cell-scale) to global (tumor-scale) dynamics by defining an interaction kernel governing density-dependent growth dynamics. Lenia can recapitulate a range of cancer model classifications including local or global, deterministic or stochastic, non-spatial or spatial, single or multi-population, and off or on-lattice. Lenia is subsequently used to develop data-informed models of 1) single-population growth dynamics, 2) multi-population cell-cell competition models, and 3) cell migration or chemotaxis. Mathematical modeling provides important mechanistic insights. First, short-range interaction kernels provide a mechanism for tumor cell survival under conditions with strong Allee effects. Next, we find that asymmetric interaction tumor-immune kernels lead to poor immune response. Finally, modeling recapitulates immune-ECM interactions where patterns of collagen formation provide immune protection, indicated by an emergent inverse relationship between disease stage and immune coverage.
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Toxicity and emerging drug resistance pose important challenges in poly-adenosine ribose polymerase inhibitor (PARPi) maintenance therapy of ovarian cancer. We propose that adaptive therapy, which dynamically reduces treatment based on the tumor dynamics, might alleviate both issues. Utilizing in vitro time-lapse microscopy and stepwise model selection, we calibrate and validate a differential equation mathematical model, which we leverage to test different plausible adaptive treatment schedules. Our model indicates that adjusting the dosage, rather than skipping treatments, is more effective at reducing drug use while maintaining efficacy due to a delay in cell kill and a diminishing dose-response relationship. In vivo pilot experiments confirm this conclusion. Although our focus is toxicity mitigation, reducing drug use may also delay resistance. This study enhances our understanding of PARPi treatment scheduling and illustrates the first steps in developing adaptive therapies for new treatment settings. A record of this paper's transparent peer review process is included in the supplemental information.
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Neoplasias Ováricas , Inhibidores de Poli(ADP-Ribosa) Polimerasas , Femenino , Inhibidores de Poli(ADP-Ribosa) Polimerasas/farmacología , Inhibidores de Poli(ADP-Ribosa) Polimerasas/uso terapéutico , Neoplasias Ováricas/tratamiento farmacológico , Humanos , Línea Celular Tumoral , Animales , Resistencia a Antineoplásicos , RatonesRESUMEN
For many patients, the cancer continuum includes a syndrome known as cancer-associated cachexia (CAC), which encompasses the unintended loss of body weight and muscle mass, and is often associated with fat loss, decreased appetite, lower tolerance and poorer response to treatment, poor quality of life, and reduced survival. Unfortunately, there are no effective therapeutic interventions to completely reverse cancer cachexia and no FDA-approved pharmacologic agents; hence, new approaches are urgently needed. In May of 2022, researchers and clinicians from Moffitt Cancer Center held an inaugural retreat on CAC that aimed to review the state of the science, identify knowledge gaps and research priorities, and foster transdisciplinary collaborative research projects. This review summarizes research priorities that emerged from the retreat, examples of ongoing collaborations, and opportunities to move science forward. The highest priorities identified include the need to (1) evaluate patient-reported outcome (PRO) measures obtained in clinical practice and assess their use in improving CAC-related outcomes; (2) identify biomarkers (imaging, molecular, and/or behavioral) and novel analytic approaches to accurately predict the early onset of CAC and its progression; and (3) develop and test interventions (pharmacologic, nutritional, exercise-based, and through mathematical modeling) to prevent CAC progression and improve associated symptoms and outcomes.
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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.
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Modelos Biológicos , Neoplasias , Humanos , Neoplasias/patologíaRESUMEN
Antifragility characterizes the benefit of a dynamical system derived from the variability in environmental perturbations. Antifragility carries a precise definition that quantifies a system's output response to input variability. Systems may respond poorly to perturbations (fragile) or benefit from perturbations (antifragile). In this manuscript, we review a range of applications of antifragility theory in technical systems (e.g., traffic control, robotics) and natural systems (e.g., cancer therapy, antibiotics). While there is a broad overlap in methods used to quantify and apply antifragility across disciplines, there is a need for precisely defining the scales at which antifragility operates. Thus, we provide a brief general introduction to the properties of antifragility in applied systems and review relevant literature for both natural and technical systems' antifragility. We frame this review within three scales common to technical systems: intrinsic (input-output nonlinearity), inherited (extrinsic environmental signals), and interventional (feedback control), with associated counterparts in biological systems: ecological (homogeneous systems), evolutionary (heterogeneous systems), and interventional (control). We use the common noun in designing systems that exhibit antifragile behavior across scales and guide the reader along the spectrum of fragility-adaptiveness-resilience-robustness-antifragility, the principles behind it, and its practical implications.
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Adaptive therapies that alternate between drug applications and drug-free vacations can exploit competition between sensitive and resistant cells to maximize the time to progression. However, optimal dosing schedules depend on the properties of metastases, which are often not directly measurable in clinical practice. Here, we proposed a framework for estimating features of metastases through tumor response dynamics during the first adaptive therapy treatment cycle. Longitudinal prostate-specific antigen (PSA) levels in 16 patients with metastatic castration-resistant prostate cancer undergoing adaptive androgen deprivation treatment were analyzed to investigate relationships between cycle dynamics and clinical variables such as Gleason score, the change in the number of metastases over a cycle, and the total number of cycles over the course of treatment. The first cycle of adaptive therapy, which consists of a response period (applying therapy until 50% PSA reduction), and a regrowth period (removing treatment until reaching initial PSA levels), delineated several features of the computational metastatic system: larger metastases had longer cycles; a higher proportion of drug-resistant cells slowed the cycles; and a faster cell turnover rate sped up drug response time and slowed regrowth time. The number of metastases did not affect cycle times, as response dynamics were dominated by the largest tumors rather than the aggregate. In addition, systems with higher intermetastasis heterogeneity responded better to continuous therapy and correlated with dynamics from patients with high or low Gleason scores. Conversely, systems with higher intrametastasis heterogeneity responded better to adaptive therapy and correlated with dynamics from patients with intermediate Gleason scores. SIGNIFICANCE: Multiscale mathematical modeling combined with biomarker dynamics during adaptive therapy helps identify underlying features of metastatic cancer to inform treatment decisions.
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Neoplasias de la Próstata Resistentes a la Castración , Neoplasias de la Próstata , Masculino , Humanos , Neoplasias de la Próstata/tratamiento farmacológico , Neoplasias de la Próstata/patología , Antígeno Prostático Específico , Antagonistas de Andrógenos/uso terapéutico , Biomarcadores , Neoplasias de la Próstata Resistentes a la Castración/tratamiento farmacológico , Neoplasias de la Próstata Resistentes a la Castración/patología , Resultado del TratamientoRESUMEN
Toxicity and emerging drug resistance are important challenges in PARP inhibitor (PARPi) treatment of ovarian cancer. Recent research has shown that evolutionary-inspired treatment algorithms which adapt treatment to the tumor's treatment response (adaptive therapy) can help to mitigate both. Here, we present a first step in developing an adaptive therapy protocol for PARPi treatment by combining mathematical modelling and wet-lab experiments to characterize the cell population dynamics under different PARPi schedules. Using data from in vitro Incucyte Zoom time-lapse microscopy experiments and a step-wise model selection process we derive a calibrated and validated ordinary differential equation model, which we then use to test different plausible adaptive treatment schedules. Our model can accurately predict the in vitro treatment dynamics, even to new schedules, and suggests that treatment modifications need to be carefully timed, or one risks losing control over tumour growth, even in the absence of any resistance. This is because our model predicts that multiple rounds of cell division are required for cells to acquire sufficient DNA damage to induce apoptosis. As a result, adaptive therapy algorithms that modulate treatment but never completely withdraw it are predicted to perform better in this setting than strategies based on treatment interruptions. Pilot experiments in vivo confirm this conclusion. Overall, this study contributes to a better understanding of the impact of scheduling on treatment outcome for PARPis and showcases some of the challenges involved in developing adaptive therapies for new treatment settings.
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Adaptive therapy is a dynamic cancer treatment protocol that updates (or 'adapts') treatment decisions in anticipation of evolving tumor dynamics. This broad term encompasses many possible dynamic treatment protocols of patient-specific dose modulation or dose timing. Adaptive therapy maintains high levels of tumor burden to benefit from the competitive suppression of treatment-sensitive subpopulations on treatment-resistant subpopulations. This evolution-based approach to cancer treatment has been integrated into several ongoing or planned clinical trials, including treatment of metastatic castrate resistant prostate cancer, ovarian cancer, and BRAF-mutant melanoma. In the previous few decades, experimental and clinical investigation of adaptive therapy has progressed synergistically with mathematical and computational modeling. In this work, we discuss 11 open questions in cancer adaptive therapy mathematical modeling. The questions are split into three sections: (1) integrating the appropriate components into mathematical models (2) design and validation of dosing protocols, and (3) challenges and opportunities in clinical translation.