tl;dw (others can jump in if they'd like):
- Organism morphology seem to be highly dependent upon large-scale electrical potential differentials between cells
- These electrical networks are primarily regulated by cell-to-cell gated ion channels; simple chemical pumps (the same types of membrane proteins that control faster-acting electric potentials that enable muscle contraction, neural activity)
- These networks and patterns of bioelectric signalling have stable memory (once a pattern between cells is induced, it remains stable) and are responsible for driving "subroutines" of large groups of cells -- morphological gene, protein expression downstream of this
Michael Levin mentions a few times how they manipulate these bioelectric fields towards desired morphological outcomes ("we don't apply electrodes", etc.)... but I have a feeling the CS-y people might still get a little lost, so, I'll try to summarize as best I can. (Some nuance will be lost, apologies in advance.)
The gated ion channels (mentioned above) are simply protein complexes that transfer ions (K+, etc.) across cells (and thus regulate the overall bioelectric signature: charge of specific tissues, regions). As protein complexes these gates themselves can be altered either in the way they're built (genetically) or with a "cocktail of chemicals", this cocktail being one that interferes to some degree with the rate at which ions are transferred between cells.
To make an analogy to human society to help you understand: imagine individual cells (or cell types, tissues) are like countries, and imagine ions are engineers. Gated ion channels are border crossings, complete with Visa requirements and regulations. To stably get more engineers from [Head Country] to [Tail Country] to build a head, you'd try to find a way to prioritize skilled immigration acceptance in [Tail Country]. This means you modify [Visa requirements] slightly, but not enough to relax immigration requirements completely and throw the country's economy into chaos.
Modifying [Visa requirements] (gated ion channel behavior) is a much more nuanced and stable way to change organism morphology, and it appears to be as elegant as it sounds re: regulating downstream effects. Really exciting stuff. If I had remained in academia I would be extremely interested in pursuing this field of research, definitely having a moment of rose-tinted glasses here :).
To opine on my own: what I'm really interested in, personally, is the applications to individual organ regrowth that isn't just restricted to [whole organism morphology]. The immediately obvious benefit of this work, to me, is the prospect of eliminating transplant lists altogether.