Fine-grained simulations of the microenvironment of vascularized tumours

Incorporating temporal information during feature engineering bolsters emulation of spatio-temporal emergence

MOTIVATION

Emergent biological dynamics derive from the evolution of lower-level spatial and temporal processes. A long-standing challenge for scientists and engineers is identifying simple low-level rules that give rise to complex higher-level dynamics. High-resolution biological data acquisition enables this identification and has evolved at a rapid pace for both experimental and computational approaches. Simultaneously harnessing the resolution and managing the expense of emerging technologies-e.g. live cell imaging, scRNAseq, agent-based models-requires a deeper understanding of how spatial and temporal axes impact biological systems. Effective emulation is a promising solution to manage the expense of increasingly complex high-resolution computational models. In this research, we focus on the emulation of a tumor microenvironment agent-based model to examine the relationship between spatial and temporal environment features, and emergent tumor properties.

RESULTS

Despite significant feature engineering, we find limited predictive capacity of tumor properties from initial system representations. However, incorporating temporal information derived from intermediate simulation states dramatically improves the predictive performance of machine learning models. We train a deep-learning emulator on intermediate simulation states and observe promising enhancements over emulators trained solely on initial conditions. Our results underscore the importance of incorporating temporal information in the evaluation of spatio-temporal emergent behavior. Nevertheless, the emulators exhibit inconsistent performance, suggesting that the underlying model characterizes unique cell populations dynamics that are not easily replaced.

AVAILABILITY AND IMPLEMENTATION

All source codes for the agent-based model, emulation, and analyses are publicly available at the corresponding DOIs: 10.5281/zenodo.10622155, 10.5281/zenodo.10611675, 10.5281/zenodo.10621244, respectively.

The role of physics in multiomics and cancer evolution

Complex interactions between the physical environment and phenotype of a tumour, and genomics, transcriptomics, proteomics and epigenomics, are increasingly known to have a significant influence on cancer development, progression and evolution. For example, mechanical stress can alter both genome maintenance and histone modifications, which consequently affect transcription and the epigenome. Increased stiffness has been linked to genetic heterogeneity and is responsible for heterochromatin accumulations. Stiffness thereby leads to deregulation in gene expression, disrupts the proteome and can impact angiogenesis. Several studies have shown how the physics of cancer can influence diverse cancer hallmarks such as resistance to cell death, angiogenesis and evasion from immune destruction. In this review, we will explain the role that physics of cancer plays in cancer evolution and explore how multiomics are being used to elucidate the mechanisms underpinning them.

The control of acidity in tumor cells: a biophysical model

Acidosis of the tumor microenvironment leads to cancer invasion, progression and resistance to therapies. We present a biophysical model that describes how tumor cells regulate intracellular and extracellular acidity while they grow in a microenvironment characterized by increasing acidity and hypoxia. The model takes into account the dynamic interplay between glucose and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {O}_2$$\end{document}O2 consumption with lactate and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {CO}_2$$\end{document}CO2 production and connects these processes to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {H}^+$$\end{document}H+ and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {HCO}_3^-$$\end{document}HCO3- fluxes inside and outside cells. We have validated the model with independent experimental data and used it to investigate how and to which extent tumor cells can survive in adverse micro-environments characterized by acidity and hypoxia. The simulations show a dominance of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {H}^+$$\end{document}H+ exchanges in well-oxygenated regions, and of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {HCO}_3^-$$\end{document}HCO3- exchanges in the inner hypoxic regions where tumor cells are known to acquire malignant phenotypes. The model also includes the activity of the enzyme Carbonic Anhydrase 9 (CA9), a known marker of tumor aggressiveness, and the simulations demonstrate that CA9 acts as a nonlinear \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {pH}_i$$\end{document}pHi equalizer at any \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {O}_2$$\end{document}O2 level in cells that grow in acidic extracellular environments.

Oxygen in the Tumor Microenvironment: Mathematical and Numerical Modeling

There are many reasons to try to achieve a good grasp of the distribution of oxygen in the tumor microenvironment. The lack of oxygen - hypoxia - is a main actor in the evolution of tumors and in their growth and appears to be just as important in tumor invasion and metastasis. Mathematical models of the distribution of oxygen in tumors which are based on reaction-diffusion equations provide partial but qualitatively significant descriptions of the measured oxygen concentrations in the tumor microenvironment, especially when they incorporate important elements of the blood vessel network such as the blood vessel size and spatial distribution and the pulsation of local pressure due to blood circulation. Here, we review our mathematical and numerical approaches to the distribution of oxygen that yield insights both on the role of the distribution of blood vessel density and size and on the fluctuations of blood pressure.