A mathematical model to study the impact of intra-tumour heterogeneity on anti-tumour CD8+ T cell immune response

Multicellular ecotypes shape progression of lung adenocarcinoma from ground-glass opacity toward advanced stages

Lung adenocarcinoma is a type of cancer that exhibits a wide range of clinical radiological manifestations, from ground-glass opacity (GGO) to pure solid nodules, which vary greatly in terms of their biological characteristics. Our current understanding of this heterogeneity is limited. To address this gap, we analyze 58 lung adenocarcinoma patients via machine learning, single-cell RNA sequencing (scRNA-seq), and whole-exome sequencing, and we identify six lung multicellular ecotypes (LMEs) correlating with distinct radiological patterns and cancer cell states. Notably, GGO-associated neoantigens in early-stage cancers are recognized by CD8+ T cells, indicating an immune-active environment, while solid nodules feature an immune-suppressive LME with exhausted CD8+ T cells, driven by specific stromal cells such as CTHCR1+ fibroblasts. This study also highlights EGFR(L858R) neoantigens in GGO samples, suggesting potential CD8+ T cell activation. Our findings offer valuable insights into lung adenocarcinoma heterogeneity, suggesting avenues for targeted therapies in early-stage disease.

An individual-based model to explore the impact of psychological stress on immune infiltration into tumour spheroids

In recentin vitroexperiments on co-culture between breast tumour spheroids and activated immune cells, it was observed that the introduction of the stress hormone cortisol resulted in a decreased immune cell infiltration into the spheroids. Moreover, the presence of cortisol deregulated the normal levels of the pro- and anti-inflammatory cytokines IFN-γand IL-10. We present an individual-based model to explore the interaction dynamics between tumour and immune cells under psychological stress conditions. With our model, we explore the processes underlying the emergence of different levels of immune infiltration, with particular focus on the biological mechanisms regulated by IFN-γand IL-10. The set-up of numerical simulations is defined to mimic the scenarios considered in the experimental study. Similarly to the experimental quantitative analysis, we compute a score that quantifies the level of immune cell infiltration into the tumour. The results of numerical simulations indicate that the motility of immune cells, their capability to infiltrate through tumour cells, their growth rate and the interplay between these cell parameters can affect the level of immune cell infiltration in different ways. Ultimately, numerical simulations of this model support a deeper understanding of the impact of biological stress-induced mechanisms on immune infiltration.

A new treatment for breast cancer using a combination of two drugs: AZD9496 and palbociclib

In this study, we examined a mathematical model of breast cancer (BC) treatment that combines an oral oestrogen receptor inhibitor, AZD9496 with Palbociclib, a selective inhibitor of cyclin- dependent kinases CDK4 and CDK6. Treatment is described by analytical functions that enable us to control the dosage and time interval of the treatment, thus personalising the treatment for each patient. Initially, we investigated the effect of each treatment separately, and finally, we investigated the combination of both treatments. By applying numerical simulations, we confirmed that the combination of AZD9496 with palbociclib was the optimal treatment for BC. The dosage of AZD9496 increased and decreased throughout the treatment period, while the intervals were constant between treatments. Palbociclib changed almost cyclically, whereas the time intervals remained constant. To investigate the mathematical model, we applied the singularly perturbed homotopy analysis method, which is a numerical algorithm. The significant advantage of this method is that the mathematical model does not have to contain a small parameter (as is standard in perturbation theory). However, it is possible to artificially introduce a small parameter into the system of equations, making it possible to study the model using asymptotic methods.

Comparison of the Predictive Value of Inflammatory Biomarkers for the Risk of Stroke-Associated Pneumonia in Patients with Acute Ischemic Stroke

Purpose

To investigate the predictive value of various inflammatory biomarkers in patients with acute ischemic stroke (AIS) and evaluate the relationship between stroke-associated pneumonia (SAP) and the best predictive index.

Patients and Methods

We calculated the neutrophil-to-lymphocyte ratio (NLR), platelet-to-lymphocyte ratio (PLR), monocyte-to-lymphocyte ratio (MLR), prognostic nutritional index (PNI), systemic inflammation response index (SIRI), systemic immune inflammation index (SII), Glasgow prognostic score (GPS), modified Glasgow prognostic score (mGPS), and prognostic index (PI). Variables were selectively included in the logistic regression analysis to explore the associations of NLR, PLR, MLR, PNI, SIRI, SII, GPS, mGPS, and PI with SAP. We assessed the predictive performance of biomarkers by analyzing receiver operating characteristic (ROC) curves. We further used restricted cubic splines (RCS) to investigate the association. Next, we conducted subgroup analyses to investigate whether specific populations were more susceptible to NLR.

Results

NLR, PLR, MLR, SIRI, SII, GPS, mGPS, and PI increased significantly in SAP patients, and PNI was significantly decreased. After adjustment for potential confounders, the association of inflammatory biomarkers with SAP persisted. NLR showed the most favorable discriminative performance and was an independent risk factor predicting SAP. The RCS showed an increasing nonlinear trend of SAP risk with increasing NLR. The AUC of the combined indicator of NLR and C-reactive protein (CRP) was significantly higher than those of NLR and CRP alone (DeLong test, P<0.001). Subgroup analyses suggested good generalizability of the predictive effect.

Conclusion

NLR, PLR, MLR, PNI, SIRI, SII, GPS, mGPS, and PI can predict the occurrence of SAP. Among the indices, the NLR was the best predictor of SAP occurrence. It can therefore be used for the early identification of SAP.

Modelling of chemotactic sprouting endothelial cells through an extracellular matrix

Sprouting angiogenesis is a core biological process critical to vascular development. Its accurate simulation, relevant to multiple facets of human health, is of broad, interdisciplinary appeal. This study presents an in-silico model replicating a microfluidic assay where endothelial cells sprout into a biomimetic extracellular matrix, specifically, a large-pore, low-concentration fibrin-based porous hydrogel, influenced by chemotactic factors. We introduce a novel approach by incorporating the extracellular matrix and chemotactic factor effects into a unified term using a single parameter, primarily focusing on modelling sprouting dynamics and morphology. This continuous model naturally describes chemotactic-induced sprouting with no need for additional rules. In addition, we extended our base model to account for matrix sensing and degradation, crucial aspects of angiogenesis. We validate our model via a hybrid in-silico experimental method, comparing the model predictions with experimental results derived from the microfluidic setup. Our results underscore the intricate relationship between the extracellular matrix structure and angiogenic sprouting, proposing a promising method for predicting the influence of the extracellular matrix on angiogenesis.

Computational Modeling to Determine the Effect of Phenotypic Heterogeneity in Tumors on the Collective Tumor-Immune Interactions

Tumor immunotherapy aims to maintain or enhance the killing capability of CD8+ T cells to clear tumor cells. The tumor-immune interactions affect the function of CD8+ T cells. However, the effect of phenotype heterogeneity of a tumor mass on the collective tumor-immune interactions is insufficiently investigated. We developed the cellular-level computational model based on the principle of cellular Potts model to solve the case mentioned above. We considered how asymmetric division and glucose distribution jointly regulated the transient changes in the proportion of proliferating/quiescent tumor cells in a solid tumor mass. The evolution of a tumor mass in contact with T cells was explored and validated by comparing it with previous studies. Our modeling exhibited that proliferating/quiescent tumor cells, exhibiting distinct anti-apoptotic and suppressive behaviors, redistributed within the domain accompanied by the evolution of a tumor mass. Collectively, a tumor mass prone to a quiescent state weakened the collective suppressive functions of a tumor mass on cytotoxic T cells and triggered a decline of apoptosis of tumor cells. Although quiescent tumor cells did not sufficiently do their inhibitory functions, the possibility of long-term survival was improved due to their interior location within a mass. Overall, the proposed model provides a useful framework to investigate collective-targeted strategies for improving the efficiency of immunotherapy.

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.

Quantification of spatial and phenotypic heterogeneity in an agent-based model of tumour-macrophage interactions

We introduce a new spatial statistic, the weighted pair correlation function (wPCF). The wPCF extends the existing pair correlation function (PCF) and cross-PCF to describe spatial relationships between points marked with combinations of discrete and continuous labels. We validate its use through application to a new agent-based model (ABM) which simulates interactions between macrophages and tumour cells. These interactions are influenced by the spatial positions of the cells and by macrophage phenotype, a continuous variable that ranges from anti-tumour to pro-tumour. By varying model parameters that regulate macrophage phenotype, we show that the ABM exhibits behaviours which resemble the 'three Es of cancer immunoediting': Equilibrium, Escape, and Elimination. We use the wPCF to analyse synthetic images generated by the ABM. We show that the wPCF generates a 'human readable' statistical summary of where macrophages with different phenotypes are located relative to both blood vessels and tumour cells. We also define a distinct 'PCF signature' that characterises each of the three Es of immunoediting, by combining wPCF measurements with the cross-PCF describing interactions between vessels and tumour cells. By applying dimension reduction techniques to this signature, we identify its key features and train a support vector machine classifier to distinguish between simulation outputs based on their PCF signature. This proof-of-concept study shows how multiple spatial statistics can be combined to analyse the complex spatial features that the ABM generates, and to partition them into interpretable groups. The intricate spatial features produced by the ABM are similar to those generated by state-of-the-art multiplex imaging techniques which distinguish the spatial distribution and intensity of multiple biomarkers in biological tissue regions. Applying methods such as the wPCF to multiplex imaging data would exploit the continuous variation in biomarker intensities and generate more detailed characterisation of the spatial and phenotypic heterogeneity in tissue samples.

Modeling tumour heterogeneity of PD-L1 expression in tumour progression and adaptive therapy

Although PD-1/PD-L1 inhibitors show potent and durable anti-tumour effects in some refractory tumours, the response rate in overall patients is unsatisfactory, which in part due to the inherent heterogeneity of PD-L1. In order to establish an approach for predicting and estimating the dynamic alternation of PD-L1 heterogeneity during cancer progression and treatment, this study establishes a comprehensive modelling and computational framework based on a mathematical model of cancer cell evolution in the tumour-immune microenvironment, and in combination with epigenetic data and overall survival data of clinical patients from The Cancer Genome Atlas. Through PD-L1 heterogeneous virtual patients obtained by the computational framework, we explore the adaptive therapy of administering anti-PD-L1 according to the dynamic of PD-L1 state among cancer cells. Our results show that in contrast to the continuous maximum tolerated dose treatment, adaptive therapy is more effective for PD-L1 positive patients, in that it prolongs the survival of patients by administration of drugs at lower dosage.