Parallel arrangements of positive feedback loops limit cell-to-cell variability in differentiation

Cellular differentiations are often regulated by bistable switches resulting from specific arrangements of multiple positive feedback loops (PFL) fused to one another. Although bistability generates digital responses at the cellular level, stochasticity in chemical reactions causes population heterogeneity in terms of its differentiated states. We hypothesized that the specific arrangements of PFLs may have evolved to minimize the cellular heterogeneity in differentiation. In order to test this we investigated variability in cellular differentiation controlled either by parallel or serial arrangements of multiple PFLs having similar average properties under extrinsic and intrinsic noises. We find that motifs with PFLs fused in parallel to one another around a central regulator are less susceptible to noise as compared to the motifs with PFLs arranged serially. Our calculations suggest that the increased resistance to noise in parallel motifs originate from the less sensitivity of bifurcation points to the extrinsic noise. Whereas estimation of mean residence times indicate that stable branches of bifurcations are robust to intrinsic noise in parallel motifs as compared to serial motifs. Model conclusions are consistent both in AND- and OR-gate input signal configurations and also with two different modeling strategies. Our investigations provide some insight into recent findings that differentiation of preadipocyte to mature adipocyte is controlled by network of parallel PFLs.细胞分化通常由双稳态开关（bistable switches）调控，这类开关源自多个正向反馈环（positive feedback loops, PFL）彼此耦联形成的特定拓扑排布。尽管双稳态可在细胞层面产生数字化响应，但化学反应的随机性会导致细胞群体在分化状态上出现异质性。我们提出假说：正向反馈环的特定排布或许在演化过程中被优化，以最小化细胞分化中的群体异质性。为验证该假说，我们针对受并行或串行排布的多PFL系统调控的细胞分化，在外源噪声（extrinsic noise）与内源噪声（intrinsic noise）条件下，探究了具有相似平均特性的分化过程的变异程度。研究发现，围绕中央调控因子彼此并行耦联的PFL所构成的网络基序（motifs），相较于串行排布的PFL基序，对噪声的敏感性更低。我们的计算表明，并行基序对噪声的抗性提升，源于其分岔点（bifurcation points）对外源噪声的敏感性更低。而平均驻留时间的估算结果显示，相较于串行基序，并行基序中的分岔稳定分支对内源噪声更具鲁棒性。模型结论在与门（AND-gate）和或门（OR-gate）两种输入信号配置下，以及两种不同的建模策略中均保持一致。我们的研究为近期一项发现提供了理论支撑：前脂肪细胞（preadipocyte）向成熟脂肪细胞（mature adipocyte）的分化过程，正是由并行排布的正向反馈环网络所调控的。