Cancer recurrence times from a branching process model

A Role of Effector CD 8 + T Cells Against Circulating Tumor Cells Cloaked with Platelets: Insights from a Mathematical Model

Cancer metastasis accounts for a majority of cancer-related deaths worldwide. Metastasis occurs when the primary tumor sheds cells into the blood and lymphatic circulation, thereby becoming circulating tumor cells (CTCs) that transverse through the circulatory system, extravasate the circulation and establish a secondary distant tumor. Accumulating evidence suggests that circulating effector CD 8 + T cells are able to recognize and attack arrested or extravasating CTCs, but this important antitumoral effect remains largely undefined. Recent studies highlighted the supporting role of activated platelets in CTCs's extravasation from the bloodstream, contributing to metastatic progression. In this work, a simple mathematical model describes how the primary tumor, CTCs, activated platelets and effector CD 8 + T cells participate in metastasis. The stability analysis reveals that for early dissemination of CTCs, effector CD 8 + T cells can present or keep secondary metastatic tumor burden at low equilibrium state. In contrast, for late dissemination of CTCs, effector CD 8 + T cells are unlikely to inhibit secondary tumor growth. Moreover, global sensitivity analysis demonstrates that the rate of the primary tumor growth, intravascular CTC proliferation, as well as the CD 8 + T cell proliferation, strongly affects the number of the secondary tumor cells. Additionally, model simulations indicate that an increase in CTC proliferation greatly contributes to tumor metastasis. Our simulations further illustrate that the higher the number of activated platelets on CTCs, the higher the probability of secondary tumor establishment. Intriguingly, from a mathematical immunology perspective, our simulations indicate that if the rate of effector CD 8 + T cell proliferation is high, then the secondary tumor formation can be considerably delayed, providing a window for adjuvant tumor control strategies. Collectively, our results suggest that the earlier the effector CD 8 + T cell response is enhanced the higher is the probability of preventing or delaying secondary tumor metastases.

Mathematical Model of Intrinsic Drug Resistance in Lung Cancer

Drug resistance is a bottleneck in cancer treatment. Commonly, a molecular treatment for cancer leads to the emergence of drug resistance in the long term. Thus, some drugs, despite their initial excellent response, are withdrawn from the market. Lung cancer is one of the most mutated cancers, leading to dozens of targeted therapeutics available against it. Here, we have developed a mechanistic mathematical model describing sensitization to nine groups of targeted therapeutics and the emergence of intrinsic drug resistance. As we focus only on intrinsic drug resistance, we perform the computer simulations of the model only until clinical diagnosis. We have utilized, for model calibration, the whole-exome sequencing data combined with clinical information from over 1000 non-small-cell lung cancer patients. Next, the model has been applied to find an answer to the following questions: When does intrinsic drug resistance emerge? And how long does it take for early-stage lung cancer to grow to an advanced stage? The results show that drug resistance is inevitable at diagnosis but not always detectable and that the time interval between early and advanced-stage tumors depends on the selection advantage of cancer cells.

Intermetastatic and Intrametastatic Heterogeneity Shapes Adaptive Therapy Cycling Dynamics

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.

Sequential mutations in exponentially growing populations

Stochastic models of sequential mutation acquisition are widely used to quantify cancer and bacterial evolution. Across manifold scenarios, recurrent research questions are: how many cells are there with n alterations, and how long will it take for these cells to appear. For exponentially growing populations, these questions have been tackled only in special cases so far. Here, within a multitype branching process framework, we consider a general mutational path where mutations may be advantageous, neutral or deleterious. In the biologically relevant limiting regimes of large times and small mutation rates, we derive probability distributions for the number, and arrival time, of cells with n mutations. Surprisingly, the two quantities respectively follow Mittag-Leffler and logistic distributions regardless of n or the mutations' selective effects. Our results provide a rapid method to assess how altering the fundamental division, death, and mutation rates impacts the arrival time, and number, of mutant cells. We highlight consequences for mutation rate inference in fluctuation assays.

Waiting times in a branching process model of colorectal cancer initiation

We study a multi-stage model for the development of colorectal cancer from initially healthy tissue. The model incorporates a complex sequence of driver gene alterations, some of which result in immediate growth advantage, while others have initially neutral effects. We derive analytic estimates for the sizes of premalignant subpopulations, and use these results to compute the waiting times to premalignant and malignant genotypes. This work contributes to the quantitative understanding of colorectal tumor evolution and the lifetime risk of colorectal cancer.

A multispecies framework for modeling adaptive immunity and immunotherapy in cancer

Predator-prey theory is commonly used to describe tumor growth in the presence of selective pressure from the adaptive immune system. These interactions are mediated by the tumor immunopeptidome (what the tumor "shows" the body) and the T-cell receptor (TCR) repertoire (how well the body "sees" cancer cells). The tumor immunopeptidome comprises neoantigens which can be gained and lost throughout tumorigenesis and treatment. Heterogeneity in the immunopeptidome is predictive of poor response to immunotherapy in some tumor types, suggesting that the TCR repertoire is unable to support a fully polyclonal response against every neoantigen. Importantly, while tumor and T-cell populations are known to compete with each other for intratumoral resources, whether between-lineage competition among peripheral T cells influences the TCR repertoire is unknown and difficult to interrogate experimentally. Computational models may offer a way to investigate these phenomena and deepen our understanding of the tumor-immune axis. Here, we construct a predator-prey-like model and calibrate it to preclinical and clinical data to describe tumor growth and immunopeptidome diversification. Simultaneously, we model the expansion of antigen-specific T-cell lineages and their consumption of both lineage-specific antigenic resources and lineage-agnostic, shared resources. This predator-prey-like framework accurately described clinically observed immunopeptidomes; recapitulated response-associated effects of immunotherapy, including immunoediting; and allowed exploration of treatment of tumors with varying growth and mutation rates.

Animal Models and Their Role in Imaging-Assisted Co-Clinical Trials

The availability of high-fidelity animal models for oncology research has grown enormously in recent years, enabling preclinical studies relevant to prevention, diagnosis, and treatment of cancer to be undertaken. This has led to increased opportunities to conduct co-clinical trials, which are studies on patients that are carried out parallel to or sequentially with animal models of cancer that mirror the biology of the patients' tumors. Patient-derived xenografts (PDX) and genetically engineered mouse models (GEMM) are considered to be the models that best represent human disease and have high translational value. Notably, one element of co-clinical trials that still needs significant optimization is quantitative imaging. The National Cancer Institute has organized a Co-Clinical Imaging Resource Program (CIRP) network to establish best practices for co-clinical imaging and to optimize translational quantitative imaging methodologies. This overview describes the ten co-clinical trials of investigators from eleven institutions who are currently supported by the CIRP initiative and are members of the Animal Models and Co-clinical Trials (AMCT) Working Group. Each team describes their corresponding clinical trial, type of cancer targeted, rationale for choice of animal models, therapy, and imaging modalities. The strengths and weaknesses of the co-clinical trial design and the challenges encountered are considered. The rich research resources generated by the members of the AMCT Working Group will benefit the broad research community and improve the quality and translational impact of imaging in co-clinical trials.

Cancer's second genome: Microbial cancer diagnostics and redefining clonal evolution as a multispecies process: Humans and their tumors are not aseptic, and the multispecies nature of cancer modulates clinical care and clonal evolution: Humans and their tumors are not aseptic, and the multispecies nature of cancer modulates clinical care and clonal evolution

The presence and role of microbes in human cancers has come full circle in the last century. Tumors are no longer considered aseptic, but implications for cancer biology and oncology remain underappreciated. Opportunities to identify and build translational diagnostics, prognostics, and therapeutics that exploit cancer's second genome-the metagenome-are manifold, but require careful consideration of microbial experimental idiosyncrasies that are distinct from host-centric methods. Furthermore, the discoveries of intracellular and intra-metastatic cancer bacteria necessitate fundamental changes in describing clonal evolution and selection, reflecting bidirectional interactions with non-human residents. Reconsidering cancer clonality as a multispecies process similarly holds key implications for understanding metastasis and prognosing therapeutic resistance while providing rational guidance for the next generation of bacterial cancer therapies. Guided by these new findings and challenges, this Review describes opportunities to exploit cancer's metagenome in oncology and proposes an evolutionary framework as a first step towards modeling multispecies cancer clonality. Also see the video abstract here: https://youtu.be/-WDtIRJYZSs.

Tumor microenvironment as a metapopulation model: the effects of angiogenesis, emigration and treatment modalities

Tumors consist of heterogeneous cell subpopulations that may develop differing phenotypes, such as increased cell growth, metastatic potential and treatment sensitivity or resistance. To study the dynamics of cancer development at a single-cell level, we model the tumor microenvironment as a metapopulation, in which habitat patches correspond to possible sites for cell subpopulations. Cancer cells may emigrate into dispersal pool (e.g. circulation system) and spread to new sites (i.e. metastatic disease). In the patches, cells divide and new variants may arise, possibly leading into an invasion provided the aberration promotes the cell growth. To study such adaptive landscape of cancer ecosystem, we consider various evolutionary strategies (phenotypes), such as emigration and angiogenesis, which are important determinants during early stages of tumor development. We use the metapopulation fitness of new variants to investigate how these strategies evolve through natural selection and disease progression. We further study various treatment effects and investigate how different therapy regimens affect the evolution of the cell populations. These aspects are relevant, for example, when examining the dynamic process of a benign tumor becoming cancerous, and what is the best treatment strategy during the early stages of cancer development. It is shown that positive angiogenesis promotes cancer cell growth in the absence of anti-angiogenic treatment, and that the anti-angiogenic treatment reduces the need of cytotoxic treatment when used in a combination. Interestingly, the model predicts that treatment resistance might become a favorable quality to cancer cells when the anti-angiogenic treatment is intensive enough. Thus, the optimal treatment dosage should remain below a patient-specific level to avoid treatment resistance.

AIM2 inhibits the proliferation, invasion and migration, and promotes the apoptosis of osteosarcoma cells by inactivating the PI3K/AKT/mTOR signaling pathway

Osteosarcoma is a primary bone tumor that mainly occurs in children and adolescents. Absent in melanoma 2 (AIM2) has been demonstrated to be involved in regulating the occurrence and development of cancer, exerting oncogenic and pro-cancer effects; however, its role in osteosarcoma is poorly understood. The present study aimed to explore the function and molecular mechanism of AIM2 in the progression of osteosarcoma. In the present study, AIM2 expression was predicted using the Cancer Cell Line Encyclopedia database and examined in several osteosarcoma cell lines using reverse transcription-quantitative PCR and western blotting. Following AIM2 overexpression, cell proliferation and apoptosis were examined using Cell Counting Kit-8, colony formation and TUNEL staining assays. The expression levels of proteins related to apoptosis, epithelial-mesenchymal transition (EMT) and the PI3K/AKT/mTOR signaling pathway were determined by western blotting. Additionally, cell invasion and migration were assessed using Transwell and wound healing assays. After addition of the PI3K/AKT/mTOR signaling pathway inhibitor LY294002 or activator 740Y-P, cell function analysis was performed. The results demonstrated that AIM2 was expressed at low levels in osteosarcoma cell lines. AIM2 overexpression inhibited proliferation, invasion, migration and EMT, and promoted apoptosis in osteosarcoma cells. Furthermore, the levels of phosphorylated (p)-PI3K, p-AKT and p-mTOR were markedly downregulated following AIM2 overexpression. Furthermore, LY294002 treatment had the same effects as AIM2 upregulation on osteosarcoma cell proliferation, apoptosis, invasion, migration and EMT. By contrast, 740Y-P reversed the effects of AIM2 overexpression on the behavior of osteosarcoma cells. Overall, the findings of the present study demonstrated that AIM2 may inhibit the progression of osteosarcoma by inactivating the PI3K/AKT/mTOR signaling pathway, and suggested that AIM2 may be a promising marker for the treatment of osteosarcoma.

Dynamics of Acquired Resistance to Nivolumab Therapies Varies From Administration Strategies

PURPOSE

The identification of optimal drug administration schedules to overcome the emergence of resistance that causes treatment failure is a major challenge in cancer research. We report the outcomes of a computational strategy to assess the dynamics of tumor progression as a function of time under different treatment regimens.

METHODS

We developed an evolutionary game theory model that combined Lotka-Volterra equations and pharmacokinetic properties with 2 competing cancer species: nivolumab-response cells and Janus kinase (JAK1/2) mutation cells. We selected 3 therapeutic schemes that have been tested in the clinical trials: 3 mg/kg Q2w, 10 mg/kg Q2w, and 480 mg Q4w. The simulation was performed under the intervals of 75, 125, and 175 days, respectively, for each regimen. The data sources of the pharmacokinetic parameters used in this study were collected from previous published clinical trials. Other parameters in the evolutionary model come from the existing references.

FINDINGS

Predictions under various dose schedules indicated a strong selection for nivolumab-independent cells. Under the 3 mg/kg dose strategy, the reproduction rate of JAK mutation cells was highest, with strongest tumor elimination ability at a 75-day interval between treatments. Prolonged drug intervals to 125 or 175 days delayed tumor evolution but accelerated tumor recurrence. Although 10 mg/kg Q2w had an obvious clinical effect in a short time, it further promotes the progress of resistant population compared with the 3 mg/kg dose. Our model suggests that 480 mg Q4w would be more valuable in terms of clinical efficacy, but complete resistant occurs earlier regardless the interval.

IMPLICATIONS

The results of this study emphasize that increasing the dose or shortening the interval between doses accelerates the evolution of heterogeneous populations, although the short-term effect is significant. In practice, the therapeutic regimen should be balanced according to the evolutionary principle.

Integrating single cell sequencing with a spatial quantitative systems pharmacology model spQSP for personalized prediction of triple-negative breast cancer immunotherapy response

Response to cancer immunotherapies depends on the complex and dynamic interactions between T cell recognition and killing of cancer cells that are counteracted through immunosuppressive pathways in the tumor microenvironment. Therefore, while measurements such as tumor mutational burden provide biomarkers to select patients for immunotherapy, they neither universally predict patient response nor implicate the mechanisms that underlie immunotherapy resistance. Recent advances in single-cell RNA sequencing technology measure cellular heterogeneity within cells of an individual tumor but have yet to realize the promise of predictive oncology. In addition to data, mechanistic multiscale computational models are developed to predict treatment response. Incorporating single-cell data from tumors to parameterize these computational models provides deeper insights into prediction of clinical outcome in individual patients. Here, we integrate whole-exome sequencing and scRNA-seq data from Triple-Negative Breast Cancer patients to model neoantigen burden in tumor cells as input to a spatial Quantitative System Pharmacology model. The model comprises a four-compartmental Quantitative System Pharmacology sub-model to represent a whole patient and a spatial agent-based sub-model to represent tumor volumes at the cellular scale. We use the high-throughput single-cell data to model the role of antigen burden and heterogeneity relative to the tumor microenvironment composition on predicted immunotherapy response. We demonstrate how this integrated modeling and single-cell analysis framework can be used to relate neoantigen heterogeneity to immunotherapy treatment outcomes. Our results demonstrate feasibility of merging single-cell data to initialize cell states in multiscale computational models such as the spQSP for personalized prediction of clinical outcomes to immunotherapy.

Epigenetic instability may alter cell state transitions and anticancer drug resistance

Drug resistance is a significant obstacle to successful and durable anti-cancer therapy. Targeted therapy is often effective during early phases of treatment; however, eventually cancer cells adapt and transition to drug-resistant cells states rendering the treatment ineffective. It is proposed that cell state can be a determinant of drug efficacy and manipulated to affect the development of anticancer drug resistance. In this work, we developed two stochastic cell state models and an integrated stochastic-deterministic model referenced to brain tumors. The stochastic cell state models included transcriptionally-permissive and -restrictive states based on the underlying hypothesis that epigenetic instability mitigates lock-in of drug-resistant states. When moderate epigenetic instability was implemented the drug-resistant cell populations were reduced, on average, by 60%, whereas a high level of epigenetic disruption reduced them by about 90%. The stochastic-deterministic model utilized the stochastic cell state model to drive the dynamics of the DNA repair enzyme, methylguanine-methyltransferase (MGMT), that repairs temozolomide (TMZ)-induced O6-methylguanine (O6mG) adducts. In the presence of epigenetic instability, the production of MGMT decreased that coincided with an increase of O6mG adducts following a multiple-dose regimen of TMZ. Generation of epigenetic instability via epigenetic modifier therapy could be a viable strategy to mitigate anticancer drug resistance.

Overcoming Chemoresistance via Extracellular Vesicle Inhibition

With the ever-growing number of cancer deaths worldwide, researchers have been working hard to identify the key reasons behind the failure of cancer therapies so the efficacy of those therapies may be improved. Based on extensive research activities and observations done by researchers, chemoresistance has been identified as a major contributor to the drastic number of deaths among cancer patients. Several factors have been linked to formation of chemoresistance, such as chemotherapy drug efflux, immunosuppression, and epithelial-mesenchymal transition (EMT). Lately, increasing evidence has shed light on the role of extracellular vesicles (EVs) in the regulation of chemoresistance. However, there is limited research into the possibility that inhibiting EV release or uptake in cancer cells may curb chemoresistance, allowing chemotherapy drugs to target cancer cells without restriction. Prominent inhibitors of EV uptake and release in cancer cells have been compiled and contrasted in this review. This is in the hope of sparking greater interest in the field of EV-mediated chemoresistance, as well as to provide an overview of the field for fundamental and clinical research communities, particularly in the field of cancer resistance research. In-depth studies of EV-mediated chemoresistance and EV inhibitors in cancer cells would spur significant improvement in cancer treatments which are currently available.

Extracellular ATP Mediates Cancer Cell Migration and Invasion Through Increased Expression of Cyclooxygenase 2

The tumor microenvironment plays a major role in the ability of the tumor cells to undergo metastasis. A major player of tumors gaining metastatic property is the inflammatory protein, cyclooxygenase 2 (COX-2). Several tumors show upregulation of this protein, which has been implicated in mediating metastasis in various cancer types such as of colon, breast and lung. In this report, we show that the concentration of extracellular ATP (eATP) is increased in response to cell death mediated by chemotherapeutic agents such as doxorubicin. By using three different cell-lines-HeLa (cervical), IMR-32 (neuronal) and MCF-7 (breast)-we show that this eATP goes on to act on purinergic (P2) receptors. Among the various P2 receptors expressed in these cells we identified P2X7, in IMR-32 and MCF-7 cells, and P2Y12, in HeLa cells, as important in modulating cell migration and invasion. Downstream of the P2 receptor activation, both p42/44 mitogen-activated protein kinase (MAPK) and the p38 MAPK are activated in these cells. These result in an increase in the expression of COX-2 mRNA and protein. We also observe an increase in the activity of matrix metalloproteinase 2 (MMP-2) enzyme in these cells. Blocking the P2 receptors not only blocks migration and invasion, but also COX-2 synthesis and MMP-2 activity. Our results show the link between purinergic receptors and COX-2 expression. Increased levels of ATP in the tumor microenvironment, therefore, leads to increased COX-2 expression, which, in turn, affords migratory and invasive properties to the tumor. This provides P2 receptor-based anti-inflammatory drugs (PBAIDs) a potential opportunity to be explored as cancer therapeutics.

A mathematical model of the metastatic bottleneck predicts patient outcome and response to cancer treatment

Metastases are the main reason for cancer-related deaths. Initiation of metastases, where newly seeded tumor cells expand into colonies, presents a tremendous bottleneck to metastasis formation. Despite its importance, a quantitative description of metastasis initiation and its clinical implications is lacking. Here, we set theoretical grounds for the metastatic bottleneck with a simple stochastic model. The model assumes that the proliferation-to-death rate ratio for the initiating metastatic cells increases when they are surrounded by more of their kind. For a total of 159,191 patients across 13 cancer types, we found that a single cell has an extremely low median probability of successful seeding of the order of 10-8. With increasing colony size, a sharp transition from very unlikely to very likely successful metastasis initiation occurs. The median metastatic bottleneck, defined as the critical colony size that marks this transition, was between 10 and 21 cells. We derived the probability of metastasis occurrence and patient outcome based on primary tumor size at diagnosis and tumor type. The model predicts that the efficacy of patient treatment depends on the primary tumor size but even more so on the severity of the metastatic bottleneck, which is estimated to largely vary between patients. We find that medical interventions aiming at tightening the bottleneck, such as immunotherapy, can be much more efficient than therapies that decrease overall tumor burden, such as chemotherapy.

Implications of immune-mediated metastatic growth on metastatic dormancy, blow-up, early detection, and treatment

Metastatic seeding of distant organs can occur in the very early stages of primary tumor development. Once seeded, these micrometastases may enter a dormant phase that can last decades. Curiously, the surgical removal of the primary tumor can stimulate the accelerated growth of distant metastases, a phenomenon known as metastatic blow-up. Recent clinical evidence has shown that the immune response can have strong tumor promoting effects. In this work, we investigate if the pro-tumor effects of the immune response can have a significant contribution to metastatic dormancy and metastatic blow-up. We develop an ordinary differential equation model of the immune-mediated theory of metastasis. We include both anti- and pro-tumor immune effects, in addition to the experimentally observed phenomenon of tumor-induced immune cell phenotypic plasticity. Using geometric singular perturbation analysis, we derive a rather simple model that captures the main processes and, at the same time, can be fully analyzed. Literature-derived parameter estimates are obtained, and model robustness is demonstrated through a time dependent sensitivity analysis. We determine conditions under which the parameterized model can successfully explain both metastatic dormancy and blow-up. The results confirm the significant active role of the immune system in the metastatic process. Numerical simulations suggest a novel measure to predict the occurrence of future metastatic blow-up in addition to new potential avenues for treatment of clinically undetectable micrometastases.