Impact of metabolic heterogeneity on tumor growth, invasion, and treatment outcomes

Abstract

Histopathologic knowledge that extensive heterogeneity exists between and within tumors has been confirmed and deepened recently by molecular studies. However, the impact of tumor heterogeneity on prognosis and treatment remains as poorly understood as ever. Using a hybrid multiscale mathematical model of tumor growth in vascularized tissue, we investigated the selection pressures exerted by spatial and temporal variations in tumor microenvironment and the resulting phenotypic adaptations. A key component of this model is normal and tumor metabolism and its interaction with microenvironmental factors. The metabolic phenotype of tumor cells is plastic, and microenvironmental selection leads to increased tumor glycolysis and decreased pH. Once this phenotype emerges, the tumor dramatically changes its behavior due to acid-mediated invasion, an effect that depends on both variations in the tumor cell phenotypes and their spatial distribution within the tumor. In early stages of growth, tumors are stratified, with the most aggressive cells developing within the interior of the tumor. These cells then grow to the edge of the tumor and invade into the normal tissue using acidosis. Simulations suggest that diffusible cytotoxic treatments, such as chemotherapy, may increase the metabolic aggressiveness of a tumor due to drug-mediated selection. Chemotherapy removes the metabolic stratification of the tumor and allows more aggressive cells to grow toward blood vessels and normal tissue. Antiangiogenic therapy also selects for aggressive phenotypes due to degradation of the tumor microenvironment, ultimately resulting in a more invasive tumor. In contrast, pH buffer therapy slows down the development of aggressive tumors, but only if administered when the tumor is still stratified. Overall, findings from this model highlight the risks of cytotoxic and antiangiogenic treatments in the context of tumor heterogeneity resulting from a selection for more aggressive behaviors.

Figure 1

CA decision process for each cell, with diamonds representing decisions, green arrows meaning the condition is satisfied, and red meaning the condition is not met. Therapies are shown in yellow.

Figure 2

(a) Model interaction network for diffusible molecules (yellow), vasculature (light gray) , normal tissue (dark gray), and variable tumor phenotypes (colors). Red lines show negative or inhibitory interactions and green lines show positive or productive interactions. (b) A flow map of tumor phenotype space. The horizontal axis is the constitutively activated log-glycolytic capacity (log p_G), and vertical axis is the change in acid resistance (−Δβ_T) from normal, with higher resistance to acidic conditions being higher on the plot. The normal metabolic phenotype is at the origin (magenta circle), while the arrows represent two possible routes to reach the aggressive state of high glycolysis and high acid-resistance, as discussed in section 3.1. The white line shows the equal maximal variation, such that a cell acquiring maximal positive changes in glycolytic capacity and acid-resistance on each division would move along this line in phenotype space.

Figure 3

(a–h) Representative simulation of tumor growth with time points (in days): (a/b)=1270, (c/d)=1392, (e/f)=1610, and (g/h)=1912. Scale bar is 400 microns. Video available on the online supplemental section (Video 1). (Left column): The 2D CA model output with vasculature (white), empty space (black), necrosis (dark gray), normal tissue (medium gray) and tumor cells labeled with colors corresponding with the cell position on the phenotype flow diagram of the right column. (Right column): Distribution of tumor cells along two phenotype axes, as described in Fig. 2, with starting (yellow) and median (cyan) tumor phenotype. (i) Growth curve for the simulation. (j) Radial pH_e and tumor growth from a murine dorsal window chamber [4]. The pH at the tumor edge was measured at multiples of 22.5 degrees and compared to the tumor growth at the same angular positions over 10 days. (k) Radial pH_e and tumor growth from the simulation by sampling the pH around the tumor edge and measuring the radial growth rate.

Figure 4

Comparison of three pH buffering simulations with identical initial conditions at two different time points. The left column is an untreated simulation; the central column is continuously treated with sodium bicarbonate starting at t_rel=0 days; the right column starts treatment at t_rel=75 days. The top panels (a–f) show the state of the three simulations at t_rel=78 days, i.e. shortly after the tumor in the right column has started the buffer therapy. The bottom set of panels (g–l) shows the state of the tumors at t_rel=142 days. Scale bar is 400 microns. Video available on the online supplemental section (Video 2).

Figure 5

Comparison of untreated and anti-angiogenic therapy simulations with identical initial conditions at two different time points. The left column is untreated; the right column has anti-angiogenic treatment at t_rel=0 days. The top panels (a – d) show the state at t_rel=141 days, i.e. 141 days after the start of therapy in the right panel. The bottom set of panels (e – h) is at t_rel=285 days. Scale bar is 400 microns. Video available on the online supplemental section (Video 3).

Figure 6

(a–f) Comparison of untreated and chemotherapy simulations with identical initial conditions at two different time points. The left column is an untreated simulation; the central column was pulsed with cytotoxic therapy starting at t_rel=0; the right column starts the identical treatment at t_rel=105. The top panels (a–c) show the state of the three simulations at t_rel=264, i.e. shortly after the tumor in the right column has finished the therapy. The bottom set of panels (d – f) shows the state of the tumors at t_rel=380. Scale bar is 400 microns. Video available on the online supplemental section (Video 4). (g) Growth curves for untreated (solid), early (dashed), and late (dotted) chemotherapy from (a–f). Tumor size on the vertical axis is the diameter in microns.