The interplay between genetic and bioelectrical signaling permits a spatial regionalisation of membrane potentials in model multicellular ensembles

Figure 6a considers again the positive regulation of Fig. 4a but now we assume instead of , which leads to the prevalence of the polarised rather than the depolarised state (see Fig. 2c; compare Fig. 6a with Fig. 4a). This decreased conductance ratio is assumed to occur post-translationally and gives values of |V| higher than those of Fig. 4a, as it should be expected from Fig. 2c. Initially, the cell potentials are depolarised within the two small regions while the rest of the system is polarised. The electrical relaxation results now in a polarised ensemble that supports high values of the protein concentration at long times (Fig. 6b,c) because of the positive regulation.

Note the different protein regionalisations which are obtained in Figs 4b and 6b despite the fact that the genetic map of rate constants is the same in these figures. This result shows that the integration of bioelectric circuits with transcriptional regulation may have implications for multicellular patterning and regeneration. In particular, Figs 4b and 6b suggest that distinct bioelectric states resulting from different post-translational gating of the conductance ratio can override identical genetic pre-patterns. This conclusion is relevant for the developmental and regeneration problems described in ref. 7 concerning endogenous bioelectrical networks.

Figures 5 and 6 show that regions of cells initially in different genetic and bioelectric states can eventually reach the same isopotential state. Figure 7 considers the opposite case: a system of cells initially at the same potential can eventually undergo an electrical regionalisation (Fig. 7a) because of the genetic differences between adjacent spatial regions (Fig. 7b). In this case, it is the genetic regulation change that precedes the electrical regionalisation (Fig. 7c). Note also that the depolarised cells are not able now to impose their electrical state over the whole ensemble because the genetic differences lead to distinct potentials at the interfacial regions, which decreases the voltage-dependent connectivity, as shown in Fig. 3b. In all the cases studied, the dynamics of the single-cell potential (Fig. 2c) together with the intercellular voltage-gated gap junctions (Fig. 3a) determine the cell bioelectric states which are coupled with the corresponding genetic states (Fig. 1).

Interestingly, shifts in the normal cell electrical state could trigger significant changes in the genetic regulation. The complex interplay between bioelectrical and genetic signals has been noted in different experimental contexts1257910. In particular, Fig. 4 shows the ensemble nature of the electrical potential1930, Fig. 5 suggests that bioelectric signals could override slightly different genetic pre-patterns1730, Fig. 6 emphasises the importance of post-translational gating730, and Fig. 7 describes a mechanism by which an ensemble of cells initially at the same potential can undergo an electrical regionalisation because of persistent genetic differences between adjacent regions.

The single cell-centred approach emphasises channels as specific proteins that determine individual cell properties, thus disregarding their contribution to the multicellular outcomes of Figs 4, 5, 6 and 7. We have shown here that heterogeneous multicellular patterns can be obtained by altering the electrical balance between the ion channels in the cell membranes over local regions of the system19. Obviously, the particular ion channels and pumps involved for each biological cell should be different1252956 but the present model provides useful qualitative insights with only two generic voltage-gated channels. While intercellular diffusional processes leading to response times longer than those found here should be incorporated in the model1922, the results suggest that the interplay between the bioelectric and genetic regulations can certainly play a role in the establishment of spatial patterns in multicellular systems. In particular, the conceptual scheme of Figs 4, 5, 6 and 7 should be useful for the modelling of left-right patterning2232 where bioelectrical asymmetry can eventually result in asymmetric gene expression. Also, extensions of the model equations to include additional feedback scenarios may have qualitative implications for other experimental problems where cell potentials are involved1141617182530.

Most biological ensembles show a significant individual diversity and we consider finally the problem of heterogeneity within the cell population. To this end, we have introduced statistical distributions in Fig. 8 for the rate constants and rp which take values between 0.1 and 0.2 min−1 in the darker regions of low protein concentration whereas these constants are between 0.4 and 0.5 min−1 in the lighter regions of high protein population. To better show the interplay between the genetic and bioelectrical regulations, this heterogeneity coexists with a spatial distribution of gap junction conductance values which are in the top half of the ensemble but in the bottom half.

Figure 8 shows that the heterogeneous prepatterns of rate constants and coupling conductance values increase the dynamic range of the system response, allowing complex regionalisations in the multicellular ensemble1723. In particular, the results suggest that a spatially heterogeneous coupling between bioelectric and genetic signals should drive distinct biological outcomes: a quasi-homogenous potential in the top of the ensemble coexists with a heterogeneous distribution of potentials in the bottom. Because it is experimentally possible to establish a partial disruption of the intercellular connectivity and identify spatially different bioelectrical and genetic patterns23, Fig. 8 provides qualitative insights into experimental studies on electrical and genetic regionalisations17. Note also that the different isopotential domains of Fig. 8 should produce a heterogeneous map of local concentrations (see Fig. 8 of ref. 19) for charged signalling molecules which are relevant to embryogenesis and regeneration processes12427.

There are solid experimental evidences relating genetic regulation and cell electrical polarisation125910114647. Because ion channel and gap junction proteins are regulated by the cell potential and in turn regulate this potential, it is of interest to study the interplay between bioelectrical signaling and gene regulatory networks in multicellular processes such as patterning. Because of the inherent non-linearity of genetic and bioelectrical processes, complex feedback scenarios arise from the spatio-temporal integration of the corresponding networks. In this biological context, simple models aimed at understanding the emerging dynamics should be useful. Note also the potential biomedical opportunities that may offer a qualitative understanding of the basic concepts involved for reprogramming cells and tissue patterning via bioelectrical pathways110.

The single-cell genetic regulation considered here is based on mean-field kinetic equations for the mRNA and protein relative concentrations. These equations could now be extended to more complex genetic networks4145 and coupled to the bioelectrical description of Fig. 1. In our case, the transcription is assumed to depend on the cell potential, which is modulated by the voltage-gated cell ion channels and the intercellular gap junctions. This theoretical approach constitutes a preliminary attempt to integrate different regulation pathways, from the local cell level to the long range multicellular system. In particular, we describe simple physical mechanisms to translate single-cell bioelectric states into multicellular regionalisations that can be observed using voltage-sensitive dyes232425. While the importance of chemical signals and concentrations gradients in the genetic regulation and establishment of biological patterns is well documented26, the regionalisation of single-cell polarisations is not well understood and contributes also to the spatial distribution of signalling molecules in the ensemble172328.

In conclusion, Figs 4, 5, 6, 7 and 8 show that the bioelectric state of the multicellular ensemble may not be uniquely determined by the underlying transcriptional state because of the feedback mechanisms and the fact that ion channels and gap junctions can be gated post-translationally, as noted in previous experimental work118. The local sensing ability of a single-cell should not be sufficient to develop and maintain efficiently complex biological patterns1. Multicellular phenomena could achieve a spatially distributed control by the conversion of local genetic and electric processes into long range effects using intercellular coupling. This conversion may involve not only reaction-diffusion processes but also bioelectrical signals and genetic regulation because the resulting coupling may provide different multistability and feedback scenarios ideally suited to establish long-term memory patterns1719.

How to cite this article: Cervera, J. et al. The interplay between genetic and bioelectrical signaling permits a spatial regionalisation of membrane potentials in model multicellular ensembles. Sci. Rep. 6, 35201; doi: 10.1038/srep35201 (2016).