Comparison of the local and hybrid methods.

Compare to Fig 2. (TIF)</p

Comparison of wall times between the two methods when solving the intracellular signaling with MATLAB’s ode45 and every other differential equation as described in Table 2.

Simulations were ran until t = 2 min. One sample was run for each method. (TIF)</p

Oxygen concentrations in simulations relating to Fig 2.

Shaded areas represents ±1 SD from the mean. A. Average internalized oxygen concentration in proliferating cells. B. Average internalized oxygen concentration in quiescent cells. C-D. Percent difference between the two methods in A-B above, respectively. E. Average oxygen concentration throughout the microenvironment. F. Percent difference between the two methods in E. (TIF)</p

The global method agrees with the local method when quiescent cells chemotax along the oxygen gradient.

Eight samples of each method are shown. Direct Euler was used to solve the intracellular signaling ODE. A-F. See caption for Fig 2. G-H. Distribution of all proportions of moves that are along the oxygen gradient by type in the local (G) and global (H) method. Specifically, for each sequence of moves an agent performs while in a single state, the proportion of those moves along the gradient is computed. These proportions are concatenated across all eight samples. Note: spikes in the quiescent histograms correspond to rational numbers with small denominators, e.g., 2/3 and 3/4. I-J. Snapshots of the local (I) and global (J) methods at t = 5 d. Snapshots are given at a later time point to show the effect of chemotaxis. Proliferating cells are in blue, quiescent cells are in orange.</p

Extended results of simulations related to Fig 4.

A. Wall time distributions for the two methods. B. Comparison of movements downward (along oxygen gradient) against all movement for both cell types across both methods. Each point represents all movements within one continuous time window in which a agent is in a constant state. C. Heat maps of the four scatter plots shown in B. (TIF)</p

Parameter values.

Values are calibrated within biological ranges to produce both normoxic and hypoxic regions within the microenvironment.</p

Molecular dynamics in the local method.

: set of all lattice sites. : set of all agents interacting with the molecule. (PDF)</p

Comparison of the intra-regional heterogeneity in the local and global methods.

Each panel shows a heatmap of the composition of all regions throughout the simulation and across all samples. The x-axis indicates how many proliferating cells are in the region. The y-axis indicates how many quiescent cells are in the region. The heatmap is restricted to only regions that contained at least one of both cell types, otherwise the values along the axes would dominate the values shown here. Top row: quiescence is determined based on a threshold value for the internalized oxygen. Bottom row: quiescence is an event that cells can stochastically undergo based on internalized oxygen. (TIF)</p

The global method agrees with the local method.

Eight samples of each method are shown. Shaded area in A-F represents ±1 SD from the mean. A. Proliferating cell population in both methods. B. Quiescent cell population. C-D. Percent difference from the average population in the local method. E-F. Mean distance of proliferating (E) and quiescent (F) cells from the vasculature at the bottom of the microenvironment. G. Wall time of each method when using direct Euler to solve the intracellular signaling ODEs. H. Wall time of each method when using a Runge-Kutta method to solve the intracellular signaling ODEs for only 2 minutes. I-J. Snapshots of the local (I) and global (J) methods at t = 2 d. Proliferating cells are in blue, quiescent cells are in orange.</p

Molecular dynamics in the global method.

: set of all regions. (PDF)</p