Cell Systems Bioelectricity: How Different Intercellular Gap Junctions Could Regionalize a Multicellular Aggregate

We wish to concentrate now on the biophysical insights gained and their connection with real systems. In particular, Figure 3, Figure 4, Figure 5 and Figure 6 suggest that (i) a dynamic voltage-gated intercellular connectivity constitutes a powerful regulatory mechanism to permit or suppress local bioelectrical heterogeneities in a multicellular system and (ii) cells with different connexins can participate in the establishment of instructive bioelectrical patterns that may activate subsequent voltage-dependent phenomena. For instance, changes in the Cx43/Cx45 ratio can influence the transition from quiescence to excitation in myometrium [26] where it has been suggested that as labor approaches, Cx45 is downregulated to permit the spread of electric signals. Note here that the high sharpness of the intercellular conductance corresponding to the homotypic Cx45/Cx45 (Figure 1B) gap junction compared with the Cx43/Cx43 (Figure 1A) case would make an efficient bioelectrical signal propagation in this cell system difficult [26].

The particular connexin composition of the gap junctions influences their function (Figure 3 and Equation (3)). If we consider that the polarized cell state is reminiscent of quiescent cells while the depolarized state is associated with proliferating cells [3,25], the bioelectrical concepts considered here may also be relevant to the tumorigenic role of specific connexin junctions. In this context, previous studies that analyzed the role of Cx46 promoter in lens and other hypoxic tissues concluded that loss of Cx46 upregulates Cx43 in the cell culture, suppressing tumor growth. Other reports have found that Cx43 acts as a positive regulator of stem cell differentiation [48] and thus this connexin is generally considered as anti-tumorigenic and beneficial for survival time [33,34]. Note the wide potential window where Cx43 is fully conductive and allows thus high intercellular coupling compared with other connexins (Figure 1, Figure 3, and Figure 8). Despite this qualitative insight, a limitation of our simulations is that the above connexins may show other non-junctional roles not considered here [49]. Thus, we should look for those cases where bioelectrical effects are clearly involved.

Cancer stem cells (CSCs) express Cx46 while non-CSCs predominantly express Cx43 and during differentiation, Cx46 is reduced while Cx43 is increased [14]. The difference between the Cx43 and Cx46 connexin proteins has been further reflected in distinct intercellular communication and reduced resting membrane potential in the case of CSCs [14]. Note here that Cx46 shows a voltage-gated response which is closer to Cx45 than to Cx43 in Figure 1 [50,51,52]. Thus, our bioelectrical approach suggests that both Cx45 and Cx46 should be more effective than Cx43 in the isolation of the inner patch against the normalization by the surrounding bulk because of their different voltage-gating dependences, as shown by Figure 3 for the case of the Cx45 and Cx43 junctions.

In summary, the pro-tumorigenic or inhibitor roles of particular gap junctions suggests context-dependent therapeutic actions based on the transcriptional control of specific connexin levels together with the postranslational modification of the junction function using inhibitors and blockers [14,32,33,34]. These results can also be relevant to the design of synthetic bioelectric systems, whether in vitro [12,53] or in vivo [54]. The problems to be faced in practical applications are the variety of bioelectrical responses that can be obtained as a function of the connexin type, intercellular coupling degree, and patch size, as shown in Figure 3, Figure 4, Figure 5 and Figure 6. This fact should make it difficult to predict the outcomes of using gap junction enhancers and inhibitors [14,32,33,34].

In particular, we cannot give more concrete, specific relations to cancer growth and treatment because of the following facts: (i)our approach is bioelectrical and focused only on the junctional effects. Other biochemical effects of connexin proteins are omitted here. For instance, these proteins may exchange specific small molecules between cells as well as between cells and the extracellular space. Thus, the outcomes associated with this exchange will depend not only on the conductive state of the junction but also on the particular signaling permeant being transferred between cells. Additionally, connexins can play non-junctional roles [49], mediating complex intracellular protein–protein interactions;(ii)although the loss of the intercellular junction communication could be an early event in tumorigenesis, there remains the possibility of gap junction restoration in more advanced tumor stages [35], with partial recovery of the community effect within the patch at later times. Thus, enhancing the intercellular gap junction communication may give different outcomes at distinct tumor time stages;(iii)gap junctions are also involved in biomechanical effects such as cell detachment and migration that are not accounted for in our bioelectrical model.

Taken together, the above facts have implications for specific therapies targeting the role of gap junctions and make it difficult to predict the outcomes of using specific gap junction enhancers and inhibitors [14,32,33,34]. With the above caveats in mind, however, we believe that the bioelectrical mean field results discussed here deserve more attention as a complement to traditional biochemical approaches based on molecular single-cell characteristics.

We computationally showed that cells may express different connexin proteins as a way to regionalize membrane potentials in multicellular aggregates (Figure 3, Figure 4, Figure 5 and Figure 6) and relate the connexin composition of the intercellular gap junction with different stages of cancer bioelectricity. Additionally, we suggested that enhancing the multicellular connectivity, e.g., via increased connexin expression and gained gap junction function, does not necessarily contribute to bioelectrical normalization (Figure 4). In principle, two normally and abnormally polarized regions which are highly intra-connected but poorly inter-connected could coexist because of their high internal connectivity and low interfacial connectivity. Remarkably, this result suggests that from a purely bioelectric viewpoint, the reduction rather than the increase of specific connexin levels may be a suitable therapeutic approach in some cases and time stages.

While cell potentials are not transcription factors themselves, they can influence transcription through biochemical and biomechanical downstream processes [3,5,8,9,55]. Thus, if the cell fate is not terminal and some epigenetic barriers can be manipulated via bioelectrical inputs, cellular reprogramming and large-scale morphogenesis might benefit from the spatio-temporal correlation of cell potentials at the multicellular level, as suggested by Levin and coworkers [3,5,9,15,56]. At this point, it is tempting to speculate that the forced normalization of an abnormally depolarized patch by the polarized surrounding bulk might constitute a control mechanism avoiding local depolarization and subsequent proliferation in a quiescent multicellular aggregate [36,39]. This normalization may fail, however, if the interfacial connectivity is low, as it may occur in the initiation of tumorigenic processes [29,39,57]. In addition, it might also fail if the intercellular connectivity within the abnormal patch is high and opposes to normalization, as it might occur in more advanced tumor stages. Note, however, that the biological complexity of real systems is not fully captured by our bioelectrically-based approach: modifying the connexin expression or introducing gap junction inhibitors may also cause unintended effects because of the ubiquitous connexin presence and the different functions of these proteins. Additionally, we considered only the junctional role of connexin proteins as transducers of electrical signals, ignoring the transference of biochemical signals. In addition, connexins can show channel-independent functions that are not only stage but also tissue specific, thus displaying both pro- and anti-tumorigenic effects [49,58].

Experimentally, the relevance of bioelectrical activity in cell cycle and proliferation has been documented [58,59,60,61]. In particular, the normally polarized cell state may be reminiscent of quiescent cells while the abnormally depolarized state is associated with proliferating cells [25,59,60]. As to the multicellular states, they emerge as complex outcomes that depend not only on the above single-cell states but also on the intercellular coupling in the patch, the surrounding bulk, and the interfacial region between them [36,39]. Thus, although the single-cell characteristics are crucial, we believe also that the bioelectrical coupling in multicellular aggregates warrants further study. In this scenario, Equations (1)–(4) constitute a minimum model based on conductances ultimately related to specific proteins. In principle, the transcription, translation, and post-translational gating of these ion channel and junction proteins are amenable to external modulation and future therapeutic strategies [3,12,13,15,45,56,62,63,64,65,66,67,68,69,70,71]. Consequently, the bioelectrical patterns and their encoded information could be externally regulated by acting on multicellular mean field phenomena such as electrical potential, potassium, and calcium waves [3,4,5,9,72,73] as a complementary procedure to addressing individual cell characteristics. In this context, the intercellular gap junctions can offer future opportunities [10,28,29,30,31,32,33,34,35,74,75]. Indeed, it has been suggested that ion channel drugs can be used as electroceuticals for treatment of cancer, given appropriate computational modeling tools [76,77], as they have been used for other instances of the control of collective cell behavior in regenerative medicine approaches [78], and repair of birth defects [15,20].

Continued interplay between computational modeling and testing in vivo is sure to reveal fascinating dynamics with practical relevance for biomedical repair and synthetic bioengineering.