Bioelectrical model of head-tail patterning based on cell ion channels and intercellular gap junctions

Robust control of anterior-posterior axial patterning during regeneration is mediated by bioelectric signaling. However, a number of systems-level properties of bioelectrochemical circuits, including stochastic outcomes such as seen in permanently de-stabilized "cryptic" flatworms, are not completely understood. We present a bioelectrical model for head-tail patterning that combines single-cell characteristics such as membrane ion channels with multicellular community effects via voltage-gated gap junctions. It complements the biochemically-focused models by describing the effects of intercellular electrochemical coupling, cutting plane, and gap junction blocking of the multicellular ensemble. We provide qualitative insights into recent experiments concerning planarian anterior/posterior polarity by showing that: (i) bioelectrical signals can help separated cell domains to know their relative position after injury and contribute to the transitions between the abnormal double-head state and the normal head-tail state; (ii) the bioelectrical phase-space of the system shows a bi-stability region that can be interpreted as the cryptic system state; and (iii) context-dependent responses are obtained depending on the cutting plane position, the initial bioelectrical state of the multicellular system, and the intercellular connectivity. The model reveals how simple bioelectric circuits can exhibit complex tissue-level patterning and suggests strategies for regenerative control in vivo and in synthetic biology contexts.