A theoretical model of neural maturation in the developing spinal cord

Cellular differentiation is a tightly regulated process under the control of intricate signaling and transcription factors networks working in coordination. Due to their complexity, these networks are studied and modelled independently despite their codependence: signals instruct transcription factors to drive cellular responses, and transcription factors provide the context for the cells to respond to signals. These reciprocal interactions make the systems dynamic, robust and stable but also difficult to dissect. Differential equation based mathematical models provide an important theoretical tool to understand the behavior of these intricate networks. In the spinal cord, recent work has shown that a network of FGF, Wnt and Retinoic Acid (RA) signaling factors regulate neural maturation by directing the activity of a transcription factor network that contains CDX at its core. Here we have used differential equation based models to understand the spatiotemporal dynamics of the FGF/Wnt/RA and the CDX regulated networks, alone and in combination. We show that in both networks, the strength of interaction among network partners impacts the dynamics, behavior and output of the system. In the signaling network, small changes in the strength of the interactions among networking partners can result in a signal overriding, balancing or oscillating with another signal. We also show that the signaling network conveys the spatiotemporal information to the transcription network, whose interpretation produces a transition zone to separate regions of high cell potency from regions of cell differentiation. This analysis provides a model for the interaction conditions underlying spinal cord cell maturation during embryonic axial elongation.