Stochastic modeling of tumor progression and immune evasion

How modulation of the tumor microenvironment drives cancer immune escape dynamics

Metastatic disease is the leading cause of cancer-related death, despite recent advances in therapeutic interventions. Prior modeling approaches have accounted for the adaptive immune system's role in combating tumors, which has led to the development of stochastic models that explain cancer immunoediting and tumor-immune co-evolution. However, cancer immune-mediated dormancy, wherein the adaptive immune system maintains a micrometastatic population by keeping its growth in check, remains poorly understood. Immune-mediated dormancy can significantly delay the emergence (and therefore detection) of metastasis. An improved quantitative understanding of this process will thereby improve our ability to identify and treat cancer during the micrometastatic period. Here, we introduce a generalized stochastic model that incorporates the dynamic effects of immunomodulation within the tumor microenvironment on T cell-mediated cancer killing. This broad class of nonlinear birth-death model can account for a variety of cytotoxic T cell immunosuppressive effects, including regulatory T cells, cancer-associated fibroblasts, and myeloid-derived suppressor cells. We develop analytic expressions for the likelihood and mean time of immune escape. We also develop a method for identifying a corresponding diffusion approximation applicable to estimating population dynamics across a wide range of nonlinear birth-death processes. Lastly, we apply our model to estimate the nature and extent of immunomodulation that best explains the timing of disease recurrence in bladder and breast cancer patients. Our findings quantify the effects that stochastic tumor-immune interaction dynamics can play in the timing and likelihood of disease progression. Our analytical approximations provide a method of studying population escape in other ecological contexts involving nonlinear transition rates.

Understanding the interplay between extracellular matrix topology and tumor-immune interactions: Challenges and opportunities

Modern cancer management comprises a variety of treatment strategies. Immunotherapy, while successful at treating many cancer subtypes, is often hindered by tumor immune evasion and T cell exhaustion as a result of an immunosuppressive tumor microenvironment (TME). In solid malignancies, the extracellular matrix (ECM) embedded within the TME plays a central role in T cell recognition and cancer growth by providing structural support and regulating cell behavior. Relative to healthy tissues, tumor associated ECM signatures include increased fiber density and alignment. These and other differentiating features contributed to variation in clinically observed tumor-specific ECM configurations, collectively referred to as Tumor-Associated Collagen Signatures (TACS) 1-3. TACS is associated with disease progression and immune evasion. This review explores our current understanding of how ECM geometry influences the behaviors of both immune cells and tumor cells, which in turn impacts treatment efficacy and cancer evolutionary progression. We discuss the effects of ECM remodeling on cancer cells and T cell behavior and review recent in silico models of cancer-immune interactions.

A stochastic framework for evaluating CAR T cell therapy efficacy and variability

Based on a deterministic and stochastic process hybrid model, we use white noises to account for patient variabilities in treatment outcomes, use a hyperparameter to represent patient heterogeneity in a cohort, and construct a stochastic model in terms of Ito stochastic differential equations for testing the efficacy of three different treatment protocols in CAR T cell therapy. The stochastic model has three ergodic invariant measures which correspond to three unstable equilibrium solutions of the deterministic system, while the ergodic invariant measures are attractors under some conditions for tumor growth. As the stable dynamics of the stochastic system reflects long-term outcomes of the therapy, the transient dynamics provide chances of cure in short-term. Two stopping times, the time to cure and time to progress, allow us to conduct numerical simulations with three different protocols of CAR T cell treatment through the transient dynamics of the stochastic model. The probability distributions of the time to cure and time to progress present outcome details of different protocols, which are significant for current clinical study of CAR T cell therapy.

The novel dynamic nomogram and risk classification system constructed for predicting post-surgical overall survival and mortality risk in primary chondrosarcoma: a population study based on SEER database

BACKGROUND

Surgery is the predominant method to improve the prognosis of primary chondrosarcoma patients. We aimed to construct the first reliable nomogram to predict the post-surgical overall survival (OS) of primary chondrosarcoma patients.

METHODS

We downloaded all primary chondrosarcoma patients treated with surgery between 2004 and 2015 from the Surveillance, Epidemiology, and End Results (SEER) database, and randomized them into training set (60%) and validation set (40%). Cox proportional regression analysis was applied to the training set to identify independent prognostic variables, and then constructed a nomogram for predicting 3-, 5-, and 8-year OS. The Harrell's concordance index (C-index), receiver operating characteristic curve (ROC), the area under curve (AUC), calibration curve and decision curve analysis (DCA) was used to assess the predictive efficacy and clinical applicability of the nomogram. The nomogram was also compared with The American Joint Committee on Cancer (AJCC) staging system.

RESULTS

A total of 1005 post-surgical primary chondrosarcoma patients were included in this study. We finally identified five independent prognostic variables to construct the nomogram, being age, grade, tumor size, disease stage and histological type. The C-index results showed that the prediction performance of the nomogram was significantly better than the AJCC staging system. In the training set, (C-index: 0.805, 95% CI 0.879-0.730 vs 0.686, 95% CI 0.606-0.766); in the validation set, (C-index: 0.811, 95% CI 0.895-0.727 vs 0.697, 95% CI 0.647-0.799). Additionally, the AUC values generated by the ROC were all greater than 0.8, which also indicated the excellent predictive performance of the nomogram. The calibration curves showed that the predicted survival rate was highly similar to the actual. Time-dependent ROC and DCA showed that the nomogram has better predictive performance and net clinical benefits than the AJCC staging system. Finally, a risk stratification system based on nomogram was constructed.

CONCLUSION

We successfully constructed and validated the first nomogram that could reliably predict 3-, 5-, and 8-year post-surgical OS in primary chondrosarcoma patients. Furthermore, the web-based dynamic nomogram could be more conveniently applied to clinic, providing assistance to surgeons and patients.

Optimal cancer evasion in a dynamic immune microenvironment generates diverse post-escape tumor antigenicity profiles

The failure of cancer treatments, including immunotherapy, continues to be a major obstacle in preventing durable remission. This failure often results from tumor evolution, both genotypic and phenotypic, away from sensitive cell states. Here, we propose a mathematical framework for studying the dynamics of adaptive immune evasion that tracks the number of tumor-associated antigens available for immune targeting. We solve for the unique optimal cancer evasion strategy using stochastic dynamic programming and demonstrate that this policy results in increased cancer evasion rates compared to a passive, fixed strategy. Our foundational model relates the likelihood and temporal dynamics of cancer evasion to features of the immune microenvironment, where tumor immunogenicity reflects a balance between cancer adaptation and host recognition. In contrast with a passive strategy, optimally adaptive evaders navigating varying selective environments result in substantially heterogeneous post-escape tumor antigenicity, giving rise to immunogenically hot and cold tumors.

Analysis of tumor-immune functional responses in a mathematical model of neoantigen cancer vaccines

Cancer neoantigen vaccines have emerged as a promising approach to stimulating the immune system to fight cancer. We propose a simple model including key elements of cancer-immune interactions and conduct a phase plane analysis to understand the immunological mechanisms of cancer neoantigen vaccines. Analytical results are obtained for two widely used functional forms that represent the killing rate of tumor cells by immune cells: the law of mass action (LMA) and the dePillis-Radunskaya Law (LPR). Using the LMA, our results reveal that a slowly growing tumor can escape the immune surveillance and that there is a unique periodic solution. The LPR offers richer dynamics, in which tumor elimination and uncontrolled tumor growth are both present. We show that tumor elimination requires sufficient number of initial activated T cells in relationship to the malignant cells, which lends support to using the neoantigen cancer vaccine as an adjuvant therapy after the primary tumor is surgically removed or treated using radiotherapy. We also derive a sufficient condition for uncontrolled tumor growth under the assumption of the LPR. The juxtaposition of analyses with these two different choices for the killing rate function highlights their importance on model behavior and biological implications, by which we hope to spur further theoretical and experimental work to understand mechanisms underlying different functional forms for the killing rate.

Clinical Characteristics, Prognostic Factor and a Novel Dynamic Prediction Model for Overall Survival of Elderly Patients With Chondrosarcoma: A Population-Based Study

Background

Chondrosarcoma is the most common primary bone sarcoma among elderly population. This study aims to explore independent prognostic factors and develop prediction model in elderly patients with CHS.

Methods

This study retrospectively analyzed the clinical data of elderly patients diagnosed as CHS between 2004 and 2018 from the Surveillance, Epidemiology, and End Results (SEER) database. We randomly divided enrolled patients into training and validation group, univariate and multivariate Cox regression analyses were used to determine independent prognostic factors. Based on the identified variables, the nomogram was developed and verified to predict the 12-, 24-, and 36-month overall survival (OS) of elderly patients with CHS. A k-fold cross-validation method (k=10) was performed to validate the newly proposed model. The discrimination, calibration and clinical utility of the nomogram were assessed using the Harrells concordance index (C-index), receiver operating characteristic (ROC) curve and the area under the curve (AUC), calibration curve, decision curve analysis (DCA), the integrated discrimination improvement (IDI) and net reclassification index (NRI). Furthermore, a web-based survival calculator was developed based on the nomogram.

Results

The study finally included 595 elderly patients with CHS and randomized them into the training group (419 cases) and validation group (176 cases) at a ratio of 7:3. Age, sex, grade, histology, M stage, surgery and tumor size were identified as independent prognostic factors of this population. The novel nomogram displayed excellent predictive performance, which can be accessible by https://nomoresearch.shinyapps.io/elderlywithCHS/, with a C-index of 0.800 for the training group and 0.789 for the validation group. The value AUC values at 12-, 24-, and 36-month of 0.866, 0.855, and 0.860 in the training group and of 0.839, 0.856, and 0.840 in the validation group, respectively. The calibration curves exhibited good concordance from the predicted survival probabilities to actual observation. The ROC curves, IDI, NRI, and DCA showed the nomogram was superior to the existing AJCC staging system.

Conclusion

This study developed a novel web-based nomogram for accurately predicting probabilities of OS in elderly patients with CHS, which will contribute to personalized survival assessment and clinical management for elderly patients with CHS.

Construction and validation of prognostic nomograms for elderly patients with metastatic non-small cell lung cancer

BACKGROUND

Metastatic non-small cell lung cancer (NSCLC) is mostly seen in older patients and is associated with poor prognosis. There is no reliable method to predict the prognosis of elderly patients (≥60 years old) with metastatic NSCLC. The aim of our study was to develop and validate nomograms which accurately predict survival in this group of patients.

METHODS

NSCLC patients diagnosed between 2010 and 2015 were all identified from the Surveillance, Epidemiology, and End Results (SEER) database. Nomograms were constructed by significant clinicopathological variables (p < 0.05) selected in multivariate Cox analysis regression.

RESULTS

A total of 9584 patients met the inclusion criteria and were randomly allocated in the training (n = 6712) and validation (n = 2872) cohorts. In training cohort, independent prognostic factors included age, gender, race, grade, tumor site, pathology, T stage, N stage, radiotherapy, surgery, chemotherapy, and metastatic site (p < 0.05) for lung cancer-specific survival (LCSS) and overall survival (OS) were identified by the Cox regression. Nomograms for predicting 1-, 2-, and 3-years LCSS and OS were established and showed excellent predictive performance with a higher C-index than that of the 7th TNM staging system (LCSS: training cohort: 0.712 vs. 0.534; p < 0.001; validation cohort: 0.707 vs. 0.528; p < 0.001; OS: training cohort: 0.713 vs. 0.531; p < 0.001; validation cohort: 0.710 vs. 0.528; p < 0.001). The calibration plots showed good consistency from the predicted to actual survival probabilities both in training cohort and validation cohort. Moreover, the decision curve analysis (DCA) achieved better net clinical benefit compared with TNM staging models.

CONCLUSIONS

We established and validated novel nomograms for predicting LCSS and OS in elderly patients with metastatic NSCLC with desirable discrimination and calibration ability. These nomograms could provide personalized risk assessment for these patients and assist in clinical decision.

Rapid Assessment of T-Cell Receptor Specificity of the Immune Repertoire

Accurate assessment of TCR-antigen specificity at the whole immune repertoire level lies at the heart of improved cancer immunotherapy, but predictive models capable of high-throughput assessment of TCR-peptide pairs are lacking. Recent advances in deep sequencing and crystallography have enriched the data available for studying TCR-p-MHC systems. Here, we introduce a pairwise energy model, RACER, for rapid assessment of TCR-peptide affinity at the immune repertoire level. RACER applies supervised machine learning to efficiently and accurately resolve strong TCR-peptide binding pairs from weak ones. The trained parameters further enable a physical interpretation of interacting patterns encoded in each specific TCR-p-MHC system. When applied to simulate thymic selection of an MHC-restricted T-cell repertoire, RACER accurately estimates recognition rates for tumor-associated neoantigens and foreign peptides, thus demonstrating its utility in helping address the large computational challenge of reliably identifying the properties of tumor antigen-specific T-cells at the level of an individual patient's immune repertoire.

A Systematic Review of the Efforts and Hindrances of Modeling and Simulation of CAR T-cell Therapy

Chimeric antigen receptor (CAR) T-cell therapy is an immunotherapy that has recently become highly instrumental in the fight against life-threatening diseases. A variety of modeling and computational simulation efforts have addressed different aspects of CAR T-cell therapy, including T-cell activation, T- and malignant cell population dynamics, therapeutic cost-effectiveness strategies, and patient survival. In this article, we present a systematic review of those efforts, including mathematical, statistical, and stochastic models employing a wide range of algorithms, from differential equations to machine learning. To the best of our knowledge, this is the first review of all such models studying CAR T-cell therapy. In this review, we provide a detailed summary of the strengths, limitations, methodology, data used, and data gap in currently published models. This information may help in designing and building better models for enhanced prediction and assessment of the benefit-risk balance associated with novel CAR T-cell therapies, as well as with the data need for building such models.

Implications of Tumor-Immune Coevolution on Cancer Evasion and Optimized Immunotherapy

Cancer represents a diverse collection of diseases characterized by heterogeneous cell populations that dynamically evolve in their environment. As painfully evident in cases of treatment failure and recurrence, this general feature makes identifying long-term successful therapies difficult. It is now well-established that the adaptive immune system recognizes and eliminates cancer cells, and various immunotherapeutic strategies have emerged to augment this effect. These therapies, while promising, often fail as a result of immune-specific cancer evasion. Increasingly available empirical evidence details both cancer and immune system populations pre- and post-treatment, providing rich opportunity for mathematical models of the tumor-immune interaction and subsequent co-evolution. Integrated mathematical and experimental efforts bear immediate relevance for optimized therapies and will undoubtedly accelerate our understanding of this emergent field.

Sustained Coevolution in a Stochastic Model of Cancer-Immune Interaction

The dynamic interactions between an evolving malignancy and the adaptive immune system generate diverse evolutionary trajectories that ultimately result in tumor clearance or immune escape. Here, we create a simple mathematical model coupling T-cell recognition with an evolving cancer population that may randomly produce evasive subclones, imparting transient protection against the effector T cells. T-cell turnover declines and evasion rates together explained differences in early incidence data across almost all cancer types. Fitting the model to TRACERx evolutionary data argued in favor of substantial and sustained immune pressure exerted upon a developing tumor, suggesting that clinically observed incidence is a small proportion of all cancer initiation events. This dynamical model promises to increase our quantitative understanding of many immune escape contexts, including cancer progression and intracellular pathogenic infections. SIGNIFICANCE: The early cancer-immune interaction sculpts intratumor heterogeneity through the selection of immune-evasive clones. This study provides a mathematical framework for investigating the coevolution between an immune-evasive cancer population and the adaptive immune system.