Mathematical Modeling of the Function of Warburg Effect in Tumor Microenvironment

Abstract

Tumor cells are known for their increased glucose uptake rates even in the presence of abundant oxygen. This altered metabolic shift towards aerobic glycolysis is known as the Warburg effect. Despite an enormous number of studies conducted on the causes and consequences of this phenomenon, little is known about how the Warburg effect affects tumor growth and progression. We developed a multi-scale computational model to explore the detailed effects of glucose metabolism of cancer cells on tumorigenesis behavior in a tumor microenvironment. Despite glycolytic tumors, the growth of non-glycolytic tumor is dependent on a congruous morphology without markedly interfering with glucose and acid concentrations of the tumor microenvironment. Upregulated glucose metabolism helped to retain oxygen levels above the hypoxic limit during early tumor growth, and thus obviated the need for neo-vasculature recruitment. Importantly, simulating growth of tumors within a range of glucose uptake rates showed that there exists a spectrum of glucose uptake rates within which the tumor is most aggressive, i.e. it can exert maximal acidic stress on its microenvironment and most efficiently compete for glucose supplies. Moreover, within the same spectrum, the tumor could grow to invasive morphologies while its size did not markedly shrink.

A multi-scale model for determining the effects of pathophysiology and metabolic disorders on tumor growth

“…The total number of cells linearly increases during ATG, plateaus during angiogenesis (ATG-to-VTG), and then exponentially increases during VTG. All these four tumor population dynamics agree with experimental observations and computational analyses 19,30,55,93 and are typical of solid tumors initiated far from primary-vessels 43,56 .…”

“…The literature is replete with models of avascular tumor growth (ATG) 29,41 , vascular tumor growth (VTG) 17,20 , and of the transition from avascular to vascular growth (ATG-to-VTG) 19,21,22,[42][43][44] , all of which can be useful for examining tumor growth and morphology. Governed by the coordinated cellular dynamics of tECs and sECs, tumor-induced angiogenesis involves sprouting, branching, anastomosis, rupturing, and remodeling of neo-vessels 32,45 .…”

“…Mathematical models that include angiogenesis can be divided into three classifications: (i) conventional, continuous models that calculate EC density without explicit representation of the structure of the neo-vessels or network 24,44,[46][47][48][49] , (ii) discrete models that predict EC migration and the creation of neo-vessels based on constant predefined, probabilistic motion 18,50,51 , and (iii) recent hybrid, continuous-discrete models that trace the EC pathways using variable agent-based motion probabilities 45,[52][53][54] . As such, the mathematical models of avascular tumor-growth (ATG) 29,41 , vascular tumor growth (VTG) 17,20 , and ATG-to-VTG 19,21,22,[42][43][44] utilize these three computational approaches to determine tumor morphology. The most comprehensive models for recapitulating the TME are ATG-to-VTG models with angiogenesis, which have been successfully developed for 2-D 21,42,43 and 3-D 19,22,55,56 domains.…”

“…As such, the mathematical models of avascular tumor-growth (ATG) 29,41 , vascular tumor growth (VTG) 17,20 , and ATG-to-VTG 19,21,22,[42][43][44] utilize these three computational approaches to determine tumor morphology. The most comprehensive models for recapitulating the TME are ATG-to-VTG models with angiogenesis, which have been successfully developed for 2-D 21,42,43 and 3-D 19,22,55,56 domains. Table 1 summarizes previous three-dimensional models of tumor growth and angiogenesis and the relevant aspects of the current work.…”

Metabolic Reprogramming of Fibroblasts as Therapeutic Target in Rheumatoid Arthritis and Cancer: Deciphering Key Mechanisms using Computational Systems Biology Approaches

“…In the same interest, a partial differential equation predictive model of metastatic spreading has been presented [131]. Interactions of cancer cells with the tumour microenvironment were also modelled using a four-compartment dynamic model [132] or an agent-based model [133]. However, the main focus of mathematical modelling in the cancer field has revolved around the study of tumour cells' metabolism.…”