Interactions and tradeoffs between cell recruitment, proliferation, and differentiation affect CNS regeneration

Abstract

Regeneration of central nervous system (CNS) lesions requires movement of progenitor cells and production of their differentiated progeny. Although damage to the CNS clearly promotes these two processes, the interplay between these complex events and how it affects a response remains elusive. Here, we use spatial stochastic modeling to show that tradeoffs arise between production and recruitment during regeneration. Proper spatial control of cell cycle timing can mitigate these tradeoffs, maximizing recruitment, improving infiltration into the lesion, and reducing wasteful production outside of it. Feedback regulation of cell lineage dynamics alone however leads to spatial defects in cell recruitment, suggesting a novel, to our knowledge, hypothesis for the aggregation of cells to the periphery of a lesion in multiple sclerosis. Interestingly, stronger chemotaxis does not correct this aggregation and instead, substantial random cell motions near the site of the lesion are required to improve CNS regeneration.

Figure 1

Schematic depiction of spatiotemporal progenitor dynamics during regeneration. (Panel a) Depiction of the multistage lineage dynamics involving self-renewing stem cells (S) that give rise to transiently amplifying progenitor cells (P), which in turn differentiate to form terminally differentiated cells (D). τ is an intrinsic cell cycle length, whereas q is a probability of dividing versus differentiating. (Panel b) A breakdown of one cycle of lineage progression (red box in panel a, for example). Each initially quiescent progenitor is assumed to exit quiescence with time constant τ_q, and then make the choice to either divide or differentiate, which we assume take the same amount of time for simplicity. (Panel c) Schematic of chemotactic recruitment scenarios with different proliferative control. To see this figure in color, go online.

Figure 2

Optimal lineage dynamics for the recruitment response depend on n and T. Heat map representing the number of TD cells drawn to an in silico lesion in two spatial dimensions under different parametric conditions. Each panel quantifies the number of cells recruited to the lesion (depicted in Fig. 1c) as a function of q, τ. Each column indicates the cumulative number of cells recruited by a specific time (T = 3, 14, 28), whereas each row indicates results for different values of the proliferative restriction (n = 4, 8, 12). Base 10 logarithm of cell numbers R_t (computed using Eq. 7) is reported. Purple stars depict the state of progenitors (e.g., the values of q^h, τ^h) in the healthy CNS (see Results and Supporting Material text, section 2). The domain is the 2D plane with a r₀ = 5 mm radius circular lesion (initially devoid of TD and progenitor cells) surrounded by a region of healthy tissue (see Fig. 1c for schematic). The range of influence of the damage extends to a radius r_M = 15 mm and the initial cell density is 5 cells/mm² (this lower density is used to reduce computational time in simulations later). The chemotactic velocity is w = 0.02 mm/h. To see this figure in color, go online.

Figure 3

Intertemporal tradeoff between early and late time responses. The number of cells recruited to the lesion at times T = 3, 14, 28 for n = 4 and q = 1. T = 3 data is scaled by a factor of 10 for visual purposes. All other parameters are the same as in Fig. 2. There is an intertemporal tradeoff, a different cell cycle time is required for efficient recruitment at different times post injury. To see this figure in color, go online.

Figure 4

Local confinement of cell cycle speedup improves performance and mitigates recruitment tradeoffs. (Panels a and b) Time course simulation under five conditions showing cumulative cell recruitment and rate of recruitment. Black curve: q = 1 and τ = 1 are independent of chemokine concentration in the chemotactic region A. Gray curve: same as black but with τ = 2. Blue curve: τ has a critical distance of r_crit = 1 mm with τ^w = 1 to τ^h with the range of q extending to r_M. Red curve: q transitions from q^w = 1 to q^h at R_crit = 1 with the range of τ extending to r_M. Green curve: both transition at R_crit = 1. (Panel c) Density of TD cells as a function of space at T = 28 days with q independent of chemokine concentration and τ transitioning to τ = 1 at R_crit = 1 mm. (Panels d, e, and f). Delivery efficiency for the three concentration dependent strategies as a function of the critical radius R_crit. The number of TDs delivered to the inner core (d) of the lesion (defined as the circle of radius 2.5 mm), the periphery (e) (the annular region between 2.5 and 5 mm), and outside of the lesion (f) (beyond the 5 mm radius lesion) are counted at time T = 28. Mean and standard deviation over an ensemble of 50 simulations is reported for each data point. In all cases w = 0.02 mm/h is used with σ = w/4 mm²/hr, τ^h = 9 days, and q^h = 0.25. To see this figure in color, go online.

Figure 5

Randomness of cell motility improves cell infiltration. Density of TD cells at time T = 28 for three values of the diffusion constant σ. It assumed that τ varies between τ^h = 9 and τ^w = 1 days according to (6) with R_crit = 1 mm. For other parameter, q^h = 0.25, q^w = 1, n = 8, and w = 0.02 mm/h. To see this figure in color, go online.