Figure 1

A diagrammatic derivation of Eqns 1 to 6 (details given in Additional file 1 ). a) In the most general case, we consider stem cells (S), a series of Multipotent Progenitor Cells (MPP), a Common Lymphoid Progenitor (CLP) and a Common Myeloid Progenitor (CMP). CLPs give rise to B, NK, and T cells; CMPs give rise to Erythrocytes (E), Granulocytes (G), and Platelets (P). We denote the total numbers of lymphoid and myeloid cells by L and M respectively, rates of differentiation by r _·(with subscript indicating the cell type involved), rates of development of MPP cells by λ _·, feedback from fully differentiated cells on those rates by Φ _·, and rates of cell death by μ _·. The feedback functions have the property that they are 1 when stem cell or fully differentiated cell numbers are low and decline as stem cells or fully differentiated cells increase. Thus, for example, stem cells renew (one stem cell becomes two) at rate r _s Φ _s (l,m)when the concentrations of lymphoid and myeloid cells are l and m respectively, asymmetrically differentiate (one stem cell becomes two stage-0 progenitors) at rate $2r_{p^{\prime }}{\Phi }_{p^{\prime }}(l,m){\Phi }_s(l,m)$, symmetrically differentiate (one stem cell becomes a stem cell and a stage-0 progenitor) at rate r _p Φ _s (l,m), and die at rate μ _s . Similar interpretations hold for other transitions. The Multipotent Commitment Response (MPCR), denoted by ρ(l,m), is the probability that a MPP in its final stage commits to the lymphoid route. b) To focus on the MPCR, we combine all of the fully differentiated cells into lymphoid and myeloid classes (L and M) and use Michaelis-Menten-like arguments to compress the MPP class into a single stage, assuming that steady states of intermediate stages are rapidly reached, characterized by combination of rate constants Ω _N .