Modelling Erythroblastic Islands: Using a Hybrid Model to Assess the Function of Central Macrophage

The production and regulation of red blood cells, erythropoiesis, occurs in the bone marrow where erythroid cells proliferate and differentiate within particular structures, called erythroblastic islands. A typical structure of these islands consists in a macrophage (white cell) surrounded by immature erythroid cells (progenitors), with more mature cells on the periphery of the island, ready to leave the bone marrow and enter the bloodstream. A hybrid model, coupling a continuous model (ordinary differential equations) describing intracellular regulation through competition of two key proteins, to a discrete spatial model describing cell-cell interactions, with growth factor diffusion in the medium described by a continuous model (partial differential equations), is proposed to investigate the role of the central macrophage in normal erythropoiesis. Intracellular competition of the two proteins leads the erythroid cell to either proliferation, differentiation, or death by apoptosis. This approach allows considering spatial aspects of erythropoiesis, involved for instance in the occurrence of cellular interactions or the access to external factors, as well as dynamics of intracellular and extracellular scales of this complex cellular process, accounting for stochasticity in cell cycle durations and orientation of the mitotic spindle. The analysis of the model shows a strong effect of the central macrophage on the stability of an erythroblastic island, when assuming the macrophage releases pro-survival cytokines. Even though it is not clear whether or not erythroblastic island stability must be required, investigation of the model concludes that stability improves responsiveness of the model, hence stressing out the potential relevance of the central macrophage in normal erythropoiesis.

💡 Research Summary

The manuscript presents a multiscale hybrid computational framework designed to capture the spatial and intracellular dynamics of erythropoiesis within the bone‑marrow micro‑environment known as the erythroblastic island. An erythroblastic island consists of a central macrophage surrounded by a cohort of erythroid progenitors that mature as they move outward. The authors integrate three modelling layers: (i) intracellular regulatory networks, (ii) discrete cell‑based agents, and (iii) extracellular diffusion of growth factors and cytokines.

At the intracellular level, the fate of each erythroid progenitor (self‑renewal, differentiation, or apoptosis) is governed by the antagonistic interaction between two proteins, Erk and Fas. Their normalized concentrations, E and F, evolve according to a pair of nonlinear ordinary differential equations (ODEs):

 dE/dt = (α(Epo, GF) + β E) (1 − E) − a E − b E F,
 dF/dt = γ(FL) (1 − F) − c E F − d F.

Here α represents activation by erythropoietin (Epo) and other growth factors (GF), β captures Erk self‑activation, γ encodes Fas activation by Fas‑ligand (FL) released from mature reticulocytes, while a, b, c, d are degradation or cross‑inhibition rates. The ODE system admits up to three steady states, each corresponding to a distinct cell fate. Linear stability analysis (Jacobian eigenvalues) identifies parameter regimes where the high‑Erk/low‑Fas state (self‑renewal) is locally stable.

The second layer treats each cell as an off‑lattice particle with a defined radius and position. Cells interact mechanically (volume exclusion) and biologically (exchange of signals) with neighbours. Cell cycle length and mitotic spindle orientation are drawn from stochastic distributions, reproducing the observed variability in division timing and daughter placement. Upon division, daughter cells inherit the intracellular ODE state of the mother and are placed according to the sampled spindle orientation.

The third layer models the extracellular milieu using partial differential equations (PDEs) for diffusion and reaction of soluble factors: Epo, generic growth factors (GF), Fas‑ligand (FL), and a macrophage‑derived pro‑survival cytokine (e.g., IL‑6, TGF‑β). The macrophage is fixed at the island centre and continuously secretes the cytokine, creating a spatial gradient that decays with distance. At each time step, the local concentrations sampled at a cell’s location feed back into the ODE parameters α and γ, thereby coupling the extracellular field to intracellular decision making. Conversely, cells contribute source terms to the PDEs when they secrete or consume factors, closing the feedback loop.

The authors explore two contrasting configurations: (1) islands lacking a central macrophage, and (2) islands with a macrophage that releases the pro‑survival cytokine. In the macrophage‑absent case, the model predicts rapid depletion of the progenitor pool: Fas activation dominates, leading to differentiation and apoptosis, and the spatial structure collapses after only a few cell‑cycle iterations. In the macrophage‑present case, the cytokine field sustains high Erk levels in nearby progenitors, enlarging the basin of attraction of the self‑renewal steady state. Consequently, the island can persist indefinitely, maintaining a steady flux of mature erythrocytes. Moreover, the presence of the macrophage sharpens the system’s responsiveness to systemic Epo fluctuations; the island’s output adjusts more quickly and with reduced overshoot compared with the macrophage‑free scenario.

Mathematical analysis confirms that the cytokine gradient expands the parameter region where the high‑Erk equilibrium is stable. Sensitivity analyses reveal that the cross‑inhibition coefficients (b, c) and the cytokine secretion rate are the most influential parameters for island stability. The authors calibrate model parameters using literature values and experimental data on erythroid progenitor dynamics, and they demonstrate that modest changes in macrophage activity can shift the system from a stable to an unstable regime, suggesting a mechanistic basis for certain anemias where macrophage function is impaired.

Overall, the study provides the first quantitative, spatially explicit model of erythroblastic islands that simultaneously captures intracellular protein competition, stochastic cell‑level events, and extracellular diffusion. It highlights the central macrophage as a pivotal niche component that confers structural stability and robust regulation of erythropoiesis. The framework can be extended to test pharmacological interventions (e.g., cytokine therapy) or genetic perturbations affecting Erk/Fas signaling, offering a valuable tool for both basic hematology research and the design of therapeutic strategies targeting bone‑marrow niches.