Engineering prokaryotic channels for control of mammalian tissue excitability

The ability to directly enhance electrical excitability of human cells is hampered by the lack of methods to efficiently overexpress large mammalian voltage-gated sodium channels (VGSC). Here we describe the use of small prokaryotic sodium channels (BacNav) to create de novo excitable human tissues and augment impaired action potential conduction in vitro. Lentiviral co-expression of specific BacNav orthologues, an inward-rectifying potassium channel, and connexin-43 in primary human fibroblasts from the heart, skin or brain yields actively conducting cells with customizable electrophysiological phenotypes. Engineered fibroblasts (‘E-Fibs') retain stable functional properties following extensive subculture or differentiation into myofibroblasts and rescue conduction slowing in an in vitro model of cardiac interstitial fibrosis. Co-expression of engineered BacNav with endogenous mammalian VGSCs enhances action potential conduction and prevents conduction failure during depolarization by elevated extracellular K+, decoupling or ischaemia. These studies establish the utility of engineered BacNav channels for induction, control and recovery of mammalian tissue excitability.

V oltage-gated sodium channels (VGSCs) exist in all animal organisms and govern processes fundamental to life including neuronal communication, muscle contractions or hormonal release 1 . In electrically excitable tissues, VGSCs enable firing and spread of action potentials (APs) and their lossof-function mutations 2 cause a variety of neuronal 3-6 , cardiac 7,8 and skeletal muscle 9,10 disorders. Similarly, acute tissue injuries resulting in permanent excitability loss (for example, stroke, spinal cord injury and heart attack) are associated with long-term disability and death. In addition to excitable tissues, the VGSCs are expressed in many unexcitable cells including macrophages, microglia and islet b-cells, where they play important roles in phagocytosis, migration, insulin secretion and other cellular processes 11 . The ion-conducting a-subunits of mammalian VGSCs have four structurally homologous domains, each consisting of B300 amino acids 12 . These four domains are simultaneously transcribed and translated from a single, relatively large (46 kb) gene. This large gene size precludes stable and efficient expression of mammalian VGSCs in primary cells, a strategy that could potentially lead to new remedies for impaired tissue excitability.
The recent discovery of a large bacterial VGSC family (BacNa v ) has provided novel insights into the structure and biophysical properties of eukaryotic VGSCs [13][14][15][16][17] . In contrast to their eukaryotic counterparts, BacNa v 13 consist of four identical domains, individually transcribed and translated from single genes of only B900 bp in size. Although the small size of BacNa v facilitates their overexpression and purification for crystallography studies 18 , it is plausible that BacNa v genes could be efficiently packaged into viral vectors, either alone or with other ion channel genes, and used to stably introduce or modify electrical excitability of mammalian tissues. Furthermore, utilization of BacNa v orthologues with diverse biophysical properties [13][14][15][16]19,20 , combined with targeted channel mutations, may allow custom engineering of cellular electrophysiological phenotypes tailored to specific tissue types, diseases and individuals.
Here we combined electrophysiological, computational and genetic engineering techniques to establish a versatile BacNa vbased platform that enables stable conversion of unexcitable primary human fibroblasts into AP conducting cells that can successfully recover conduction slowing in an in vitro model of cardiac interstitial fibrosis. Moreover, we demonstrate that direct expression of engineered BacNa v channels in mammalian excitable cells can enhance their excitability and prevent loss of AP conduction in pathological conditions when endogenous Na þ channels fail to activate.

Results
Genetic engineering of actively conducting human fibroblasts. To stably convert unexcitable primary fibroblasts into actively conducting cells (named engineered fibroblasts or 'E-Fibs'), we first explored a BacNa v variant from Roseobacter denitrificans, Na v RosD G217A, shown in our preliminary tests to be capable of generating AP propagation when transfected in a monolayer of HEK293 cells stably expressing Kir2.1 and connexin-43 (Cx43). We generated a high-titre bi-cistronic lentivirus pRRL-CMV-RosDG217A-P2A-eGFP-Kir2.1 encoding both Na v RosD G217A and inward-rectifier potassium channel Kir2.1 (gene KCNJ2) fused with enhanced green fluorescent protein (eGFP) (eGFP-Kir2.1), separated by the self-cleaving peptide P2A. Adult human dermal fibroblasts (HDFs) transduced with this virus stably expressed inward-rectifier K þ current, I K1 (Fig. 1a,b), and bacterial Na þ current, I NaRosD G217A (Fig. 1c,d), at much higher levels compared with endogenous currents, and exhibited a significantly hyperpolarized resting membrane potential of À 78.4 ± 0.2 mV (n ¼ 6) compared with that of wild-type (wt)-HDFs ( À 23.3±2.9 mV; n ¼ 5). The resulting voltage dependencies of activation and inactivation of Na v RosD G217A (Fig. 1e) in transduced HDFs were similar to those previously reported in transfected HEK293s (ref. 15). Importantly, transduced HDFs became electrically excitable, whereby injection of 1 ms current pulses of increasing amplitude elicited reproducible firing of an 'all-or-none' AP (Fig. 1f). These results demonstrated the ability of BacNa v to yield creation of de novo electrically excitable cells.
To enable electrical coupling in excitable HDFs, we co-transduced them with a pRRL-CMV-Cx43-P2A-mCherry lentivirus. Transduced cells robustly expressed membrane-bound Cx43 gap junctions (Fig. 1g), which resulted in improved intercellular coupling compared with wt-HDFs as revealed by fluorescence recovery after photobleaching 21 , albeit not to the same level as measured in neonatal rat cardiomyocytes (Fig. 1h). These engineered HDFs (E-HDFs) were then cultured at confluence in 2 cm diameter monolayers in a random or aligned configuration ( Supplementary Fig. 1). When electrically stimulated by a bipolar platinum electrode, randomly oriented E-HDFs supported circular AP spread at an average conduction velocity (CV) of 3.63±0.23 cm s À 1 ( Fig. 1i and Supplementary Video 1). As expected, aligned E-HDFs exhibited elliptical (anisotropic) AP spread with higher CVs along (3.86 ± 0.14 cm s À 1 , n ¼ 5) versus across (2.07 ± 0.19 cm s À 1 , n ¼ 5) cell orientation ( Fig. 1j and Supplementary Video 1). Although the above approach enabled AP propagation in initially unexcitable human fibroblasts, CVs were low, which could be at least in part attributed to the relatively slow activation kinetics of Na v RosD G217A.
Improved E-Fib electrical properties with NavSheP mutants. To augment the excitability and conduction of E-HDFs, we developed a combined computational and experimental strategy to screen and identify BacNa v variants with more favourable properties (Fig. 2a). We set to explore the BacNa v orthologue from Shewanella putrefaciens, Na v SheP, for its fast current kinetics 15 . As the wt Na v SheP channel has a highly hyperpolarized voltage dependency of steady-state inactivation, it does not yield AP firing when co-expressed with Kir2.1. We thus proceeded to shift the activation and inactivation curves of Na v SheP to more depolarized voltages based on the previous studies of specific residues in NaChBac channels 22 and significant homology between different BacNa v orthologues ( Supplementary  Fig. 2); we created a library of Na v SheP mutants where either the D60 or E43 residue was substituted with other standard amino acids. These 38 Na v SheP mutants were transiently expressed in a monoclonal HEK293 line stably expressing Kir2.1 and the resulting sodium current was recorded by voltage clamp. The E43 mutants exhibited highly depolarized voltage dependence of activation (Supplementary Table 1); therefore, we focused on detailed characterization of D60 mutants. The D60 mutant channels exhibited a wide range of steady-state and kinetic parameters (Supplementary Fig. 3 Supplementary Fig. 4) and constructed Na v SheP D60X-Kir2.1 lentiviruses for three D60X mutants (D60A, D60N and D60S) that exhibited the steepest AP upstrokes and highest CVs among different BacNa v models. All three mutants exhibited significantly faster kinetics compared with Na v RosD G217A in transduced cells (Fig. 2f,g), which allowed generation of APs with shorter duration and sharper upstroke velocity (Fig. 2h-j). Co-transduction of these viruses with Cx43 in HDFs yielded a 2.5-fold improvement in CV compared with the use of Na v RosD (Fig. 2k,l and Supplementary Video 2). This demonstrated the potential for combining BacNa v mutagenesis and computational modelling, to engineer primary human fibroblasts with desired electrophysiological phenotypes.
Fine-tuning of E-Fib electrical properties via FACS. The use of fluorescence reporters in multi-cistronic lentiviruses (for example, pRRL-CMV-SheP D60N-P2A-eGFP-Kir2.1) allowed us to further vary I NaSheP and I K1 levels, and characterize their functional effects on E-HDFs. Using fluorescence-activated cell sorting (FACS), we sorted E-HDFs into three populations with low, medium and high GFP expression levels ( Supplementary Fig. 5a), which yielded corresponding low, medium and high levels of I K1 (Fig. 3a) and I NaSheP (Fig. 3b), and distinct changes in AP shape (Fig. 3c). Specifically, a trend towards more hyperpolarized resting membrane potential (Fig. 3d, one-way analysis of variance, P ¼ 0.15) and the significantly higher maximum upstroke velocity (Fig. 3e) could be attributed to higher I K1 and I NaSheP , respectively, whereas the increased APD (Fig. 3f) resulted from net depolarizing effect of increased I K1 and I NaSheP on membrane repolarization. Although higher AP upstroke velocities expectedly yielded higher CVs (Fig. 3g,h), this effect was moderate, which we hypothesized was due to simultaneous increase in I K1 along with I NaSheP . We thus modelled concurrent increase in I K1 and I NaSheP to simulate the experiment (model 1; Supplementary Fig. 6) and compared resulting CVs with those caused by an increase in I NaSheP alone (model 2; Supplementary  Fig. 6). Despite the same AP upstroke velocities in both models ( Supplementary Fig. 6a), CV in model 1 increased less ( Supplementary Fig. 6b), because more depolarizing current was needed to overcome high I K1 , reach threshold and elicit AP ( Supplementary Fig. 6c). Examining a wide range of channel conductances ( G Na and G K1 ) further revealed that although threshold current required to elicit AP is primarily sensitive to level of I K1 ( Supplementary Fig. 6d), AP upstroke velocity is mainly dependent on I NaSheP ( Supplementary Fig. 6e Fig. 5c) allowed us to vary Cx43 expression and gap junctional coupling of engineered cells. Optical mapping revealed that E-HDFs with higher mCherry/Cx43 expression supported faster AP propagation (Fig. 3i), whereas contrary to eGFP sorting ( Supplementary  Fig. 5b), mCherry sorting had no effect on APD 80 (Supplementary Fig. 5d). Simulation results further revealed that intercellular coupling strength does not influence the relative effects of varying I K1 and I NaSheP on CV ( Supplementary Fig. 6g).
Robustness of E-Fib electrical phenotype. To test whether E-HDFs can maintain stable electrophysiological phenotype under various perturbations, we expanded them 500-fold over a 4-week period, either directly or after 2 freeze-thaw cycles. In both cases, expanded E-HDFs retained proliferative potential (Fig. 4a) and were able to undergo additional rounds of expansion (for example, 100-fold, 4 passages; Fig. 4b). In addition, as fibroblasts can differentiate into smooth muscle actin expressing myofibroblasts during wound healing and tissue repair 23 , we treated the expanded E-HDFs with 10 ng ml À 1 transforming growth factor-b1 for 7 days, to induce their conversion to myofibroblasts (Fig. 4c,d). Subsequent electrophysiological analysis revealed that despite significant cell expansion or myofibroblast differentiation, the I K1 , I NaSheP (Fig. 4e,f) and AP characteristics ( Fig. 4g-i) of E-HDFs remained unchanged, demonstrating the stability of the acquired functional phenotype. The ability of these cells to undergo repeated freeze-thaw cycles without phenotypic alterations suggested the potential for off-the-shelf delivery applications. Electrophysiological phenotype of E-HDFs remained stable until the cells reached senescence (after additional eight passages and B10 6 -fold expansion; Supplementary Fig. 7a-d). Furthermore, using a classical heterologous expression system-monoclonal HEK293 line expressing Cx43, K ir 2.1 and Na v SheP D60A-stable electrical properties were maintained beyond 20 passages   Na v SheP mutants give rise to APs (h) with faster upstroke (i; n ¼ 10-18) and shorter duration (j; n ¼ 10-18) than Na v RosD G217A (n ¼ 11 for i,j).
(k) Na v SheP D60X expressions in anisotropic E-HDF monolayers yield faster CV than RosDm expression (n ¼ 5-10). (l) Representative isochrone map of AP conduction in an electrically stimulated anisotropic monolayer of E-HDFs stably co-expressing Kir2.1, Na v SheP D60N and Cx43 (compare also with Fig. 1j). *Po0.001 versus RosDm (i-k). All electrophysiological data obtained at 37°C, unless otherwise specified. Error bars indicate s.e.m; statistical significance was determined by one-way analysis of variance, followed by Tukey's post-hoc test to calculate P-values.
Applicability to other sources of human unexcitable cells. To further demonstrate the versatility of this approach, we used the Kir2.1-Na v SheP D60N lentivirus to stably convert human ventricular fibroblasts (HVFs), human astrocytes (HAs) and HEK293s into engineered electrically excitable cells (E-HVFs, E-HAs and E-HEK293, respectively). All engineered cell types displayed strong I NaSheP and I K1 , and fired APs on stimulation ( Supplementary Fig. 8). Expression of the Kir2.1 channels hyperpolarized the resting membrane potentials in all transduced cells to a similar value (Fig. 4j), whereas similar I NaSheP levels resulted in comparable upstroke velocities (Fig. 4k). Significant differences in AP duration among different cell types (Fig. 4l) could be attributed to differences in their endogenous currents (Fig. 4m) and potentially other differences in epigenetic, posttranscriptional and posttranslational regulation of ion channel expression and function. Collectively, these results confirmed the robustness of the BacNa v engineering approach against the starting unexcitable cell phenotype.
E-Fibs improve conduction in model of interstitial fibrosis. To test whether E-Fibs could improve impaired AP conduction in native excitable tissues, we designed a zig-zag micropattern of neonatal rat cardiomyocytes ( Fig. 5a and Supplementary Fig. 9a), which mimics the tortuous electrical conduction of cardiac tissue with interstitial fibrosis 24,25 . The cardiomyocyte zig-zag micropattern displayed normal AP propagation in the longitudinal direction ( Supplementary Fig. 9b), but significantly slowed down transverse CV (3.2±0.4 cm s À 1 ; Supplementary  Fig. 9c), which was fully rescued (12.0 ± 0.5 cm s À 1 ) by the electrical coupling of actively conducting E-HDFs and cardiomyocytes (Fig. 5b, Fig. 5c and Supplementary Fig. 9d,e), whereas unexcitable HDFs with overexpressed Cx43 yielded only a small conduction improvement (to 6.5±0.3 cm s À 1 ; Fig. 5c and Supplementary Fig. 9f). All groups had similar AP durations (Fig. 5d); thus, wavelength differences (Fig. 5e) reflected the differences in CV. Importantly, these studies suggested that slow electrical propagation in cardiac tissues with interstitial fibrosis could be significantly improved if fibroblasts were engineered to actively conduct APs by becoming both excitable and robustly coupled.
BacNa v augment and rescue mammalian tissue excitability.
Our computational results showed that select BacNa v mutant (Na v SheP D60A) displayed comparable AP upstroke and slightly lower CV than mammalian Na v 1.5 channel in an excitable cell model (Fig. 2d,e), suggesting that in addition to custom design of de novo excitable cells and tissues, BacNa v channels could be exploited to directly manipulate or augment 26 Fig. 10). Furthermore, expression of BacNa v channels could ameliorate reduced cardiac tissue excitability and arrhythmogenic conduction slowing in various pathological conditions (for example, ischaemia, infarction and congenital disease) associated with membrane depolarization and inactivation of Na v 1.5 channels 2,28,29 or diminished intercellular coupling 30,31 . For proof-of-concept studies, we used a Na v SheP D60A mutant, which exhibits B10 mV more depolarized inactivation V 1/2 ( À 76.8 mV) compared with Na v 1.5 channel ( À 87.4 mV) (Fig. 6a,b). Elevating extracellular K þ concentration to depolarize resting potential and inactivate Nav1.5 channels in Ex293 cells (a monoclonal HEK293 line engineered to stably express Kir2.1, Cx43 and Na v 1.5 (ref. 32) resulted in conduction failure after addition of as little as 3 mM KCl. In contrast, Ex293 monolayers transduced with the Na v SheP D60A lentivirus sustained AP conduction at significantly higher extracellular K þ concentrations (up to 12.4 mM; Fig. 6c). Furthermore, Na v SheP D60A expression in Ex293 monolayers subjected to increased doses of gap junctional blocker palmitoleic acid (PA) attenuated conduction slowing and prevented conduction block at 60 mM PA when cells expressing only Na v 1.5 channel failed to conduct (Fig. 6d). Finally, we tested whether viral expression of Na v SheP D60A could increase the resistance to conduction failure in cardiomyocyte cultures that underwent regional ischaemia after being covered with a glass coverslip 33 (Fig. 6e). During ischaemia, cardiomyocytes exhibited gradual conduction slowing (Fig. 6f,g) and APD shortening ( Supplementary Fig. 11a,b), followed by the partial (Supplementary Fig. 11c) and eventually complete conduction block (Fig. 6h and Supplementary  Video 4). Importantly, Na v SheP D60A expression preserved cell excitability to significantly prolong the time to conduction block (from 10.5±1.0 min in control to 14.2±0.7 min in BacNa vexpressing cardiomyocytes; Fig. 6i). All electrophysiological data obtained at 37°C, unless otherwise specified. Error bars indicate s.e.m; statistical significance was determined by one-way analysis of variance, followed by Tukey's post-hoc test to calculate P-values.

Discussion
Since their discovery 15 years ago 13 , prokaryotic Na þ channels have contributed greatly to understanding structure 16,20 , function 34,35 and pharmacology 36 of the more complex eukaryotic VGSCs. Yet, it has remained unexplored if large diversity and small gene size of BacNa v could be employed to stably modify and augment the excitability of mammalian tissues, a feat difficult to achieve using large mammalian VGSCs. In this study, we presented a combined experimental and computation strategy for use of BacNa v channels in the de novo induction and control of mammalian tissue excitability. Our goal was to develop a versatile platform that would be cost-effective, applicable to a variety of cell types and amenable to rapid production of large quantities of excitable cells for off-the-shelf use. Previously, we applied a non-viral stepwise expression of cardiac Na þ channel Na v 1.5, inward rectifier K þ channel Kir2.1 and gap junctional protein Cx43, combined with antibiotic selection, to generate a stable monoclonal HEK293 line capable of active AP conduction 32 . Other proof-of-concept studies applied adenoviral expressions of mammalian VGSCs to induce or modify excitability in primary tissues [37][38][39] ; however, these effects were transient and unsuitable for long-term studies or the development of antiarrhythmic gene therapies 38,39 . Although the use of split-intein-mediated protein trans-splicing strategy 40 might be adapted in the future to induce stable expression of mammalian VGSCs in primary cells, efficacy of this approach may be limited due to the need for co-transduction of two or more viruses to reconstitute functional channels. To circumvent the need for expressing large mammalian VGSCs, we exploited much smaller BacNa v genes and designed high-titre multi-cistronic lentiviruses coding minimum sets of ion channels required for stable and efficient induction of excitability in primary cells. In fact, using BacNa v þ Kir2.1 lentiviruses, human and rodent fibroblasts were routinely transduced with 90% efficiency without any loss of cell viability (not shown). Including a fluorescent reporter in the same virus allowed us to further purify transduced cells and fine-tune their electrical properties ( Fig. 3 and Supplementary Fig. 5).
Importantly, lentivirally expressed ion currents in all engineered fibroblasts were much larger than their endogenous currents (Fig. 1). As such, resulting electrophysiological phenotype of engineered cells was relatively insensitive to the cell's epigenetic state and both predictable in silico and for the most part reproducible among different cell types in vitro (Fig. 4j-l and Supplementary Fig. 8). The ability to generate actively conducting HVFs, in particular, suggested a potential therapeutic strategy whereby in situ fibroblast engineering could improve impaired conduction in fibrotic heart tissues. As a proof of concept, we showed that well-coupled and excitable (but not weakly coupled and/or unexcitable) fibroblasts successfully restored normal neonatal rat cardiomyocyte conduction in an in vitro model of interstitial fibrosis (Fig. 5). On the other hand, distinct forms of cardiac fibroses, differing in size, and cellular and non-cellular components can result from various types of heart disease or injury 41 . In situ engineering of actively conducting fibroblasts, while potentially beneficial in improving cardiac conduction in small regions of interstitial or diffuse fibrosis where these cells come in close contacts with cardiomyocytes, may not prove as effective in large cardiac scars with low cellularity. Of note is also that without the prominent Ca 2 þ currents, engineered fibroblasts are unlikely to spontaneously fire APs or be a source of triggered activity, which could potentially make them less arrhythmogenic compared with the use of pluripotent stem cell-derived cardiomyocytes 42,43 .
Furthermore, transduction of mammalian excitable tissue cultures with specific BacNa v mutants augmented or rescued conduction in healthy ( Supplementary Fig. 10) and pathological (depolarization, decoupling and ischaemia; Fig. 6 and Supplementary Fig. 11) conditions, suggesting that BacNa v -based gene therapies could be targeted directly to excitable cells. In addition, previous studies have shown that BacNa v could be converted into Ca 2 þ -selective channel (BacCa v ) by substituting three amino acid residues of the selectivity filter with Aspartate 19,44,45 . Hence, stable expression of engineered BacNa v channels or their Ca 2 þ -selective derivatives may enable direct therapeutic effects on excitable and unexcitable cells whose function relies on voltage-gated Na þ or Ca 2 þ channels.
Although in this study we focused on altering specific amino acid residues (E43 or D60) in a particular BacNa v orthologue (Na v SheP), various combinations of other BacNa v orthologues and residues 18,46,47 could be explored to customize phenotype of engineered or native excitable cells. For example, mutations in the 'glycine hinge' region in some BacNa v orthologues could change channel inactivation rate 15 , and along with tuning of Kir2.1 expression via an independent promoter, could be used to control AP duration to avoid arrhythmogenic dispersion of refractoriness if E-Fibs were used for cardiac cell or in situ gene therapy. Furthermore, replacing the highly conserved negative residues (E70 and D91) of BacNa v voltage-sensitive domain with positively charged residues could shift activation to more hyperpolarized voltages 48 and be used to reduce AP threshold. Similarly, substituting the negatively charged residues in the neck region of the carboxy-terminal domain (CTD) of the BacNa v channel into glycine could destabilize the helix conformation of this region, decrease the depolarization energy required for channel opening 49 and further augment cell excitability and conduction. Furthermore, a recent study by Arrigoni et al. 50 showed that BacNa v CTD plays a critical role in voltage dependence of activation, suggesting CTD swapping among different orthologues could provide yet another method to control excitability of engineered cells.
Basic studies in 'lower' organisms, including prokaryotes, have led to versatile approaches to manipulate and study mammalian biology. Recent examples include optogenetics 51 and genomeediting techniques 52 that, in addition to becoming powerful research tools, have been extensively investigated for potential medical applications. In line with these undertakings, our work supports expansion of prokaryotic ion channel research to basic studies of mammalian tissue excitability and development of new human therapies.

Methods
Screening of bacterial sodium channels. To engineer excitable cells, we first explored use of NaChBac channel, the longest studied BacNa v orthologue 13,17,45,53 . However, its slow recovery from inactivation yielded excitable cells with very low maximum capture rate (o1 Hz). This prompted us to instead use Na v RosD G217A and Na v SheP channels that were kindly provided by Dr Katsumasa Irie from Kyoto University 15 . Libraries of SheP(D60X) and SheP(E43X) mutants were generated using Quikchange II XL Site-Directed Mutagenesis Kit (Agilent Technologies), as per the manufacturer's instructions. All the primers used are listed in Supplementary Table 2. Each gene was subcloned into the mammalian expression vector pCMV5(CuO)-IRES-GFP (Qbiogene) and transfected into HEK293 cells stably expressing Kir2.1 using Lipofectamine 2000 transfection reagent (Life Technologies). GFP fluorescence was usually detected after 12 h and cells were patch clamped 24 h after transfection, to derive AP parameters.
Lentivirus production. Lentiviral plasmids were constructed from the pRRL-CMV vector (a gift from Dr Inder Verma, Salk Institute). BacNa v (Na v RosD G217A or Na v SheP mutant, without a stop codon) was ligated with eGFP-Kir2.1 (Kir2.1 fused with eGFP at the amino terminus) via the viral P2A peptide 54  Isotropic and anisotropic monolayers of HDFs. E-HDFs were seeded onto 22 mm-diameter Aclar (Electron Microscopy Sciences) coverslips coated with fibronectin (Sigma, 15 mg ml À 1 , 30 min) at a density of 5 Â 10 4 cells per cm 2 to form isotropic monolayers. Anisotropic E-HDF monolayers were formed on Aclar coverslips microcontact printed with a pattern of parallel fibronectin lines (10 mm width, 10 mm spacing) as previously described 55 . Cells were cultured for 24 h to become confluent and form intercellular junctions followed by optical mapping of AP propagation and immunostaining.
Micropatterned zig-zag cultures. All animals were treated in accordance with protocols approved by the Duke University Institutional Animal Care and Use Committee. Neonatal rat cardiomyocytes were enzymatically dissociated from ventricles of 2-day-old Sprague-Dawley rats and enriched using differential pre-plating 56 . Specifically, ventricles were excised, minced and incubated with 0.1% trypsin overnight and dissociated in four sequential steps using 0.1% collagenase. Isolated cells were centrifuged (5 min, 200 g) and further enriched by two 45 min pre-plating steps to select for cardiomyocyte-enriched cells that remained unattached after the second pre-plating. Zig-zag cultures were generated as previously described 25 . Briefly, Aclar coverslips (22 mm diameter) were coated with 5 mg ml À 1 collagen I (rat tail, BD Biosciences) for 30 min, rinsed with PBS, then micro-contact printed with a zig-zag network of fibronectin (100 mm-wide lines spaced 100 mm apart and connected by 100 mm-wide transverse bridges staggered every 6 mm). Cardiomyocytes were seeded at a density of 2 Â 10 5 cells per cm 2 in DMEM/F-12 medium (Gibco, 11320-033) supplemented with 10% calf serum and 10% horse serum, followed by a switch to 5% fetal bovine serum media at culture day 2. The following day, E-HDFs were added to the cardiomyocyte zig-zag cultures at a density of 2.5 Â 10 4 cells per cm 2 . On day 5, co-cultured monolayers were assessed for AP propagation by optical mapping and subsequently fixed for immunostaining.
Immunostaining. Cell monolayers or tissue patches were fixed in 2% paraformaldehyde (15 min  Fluorescence images were acquired using inverted fluorescence (Nikon TE2000) or confocal (Leica SP5) microscope and processed with ImageJ software.
Fluorescence recovery after photobleaching. Functional coupling in wt and Cx43-expressing HDFs was assessed using fluorescence recovery after photobleaching 21,57 as previously described 58   properties, membrane voltage was stepped from a holding potential of À 100 mV to varying 500 ms test potentials ( À 50 to 60 mV, increments of 10 mV). Inactivation of BacNa v was derived from peak currents measured at 0 mV after varying 3 s prepulse potentials ( À 160 to À 30 mV, increments of 10 mV). For the channels with more hyperpolarized activation and inactivation (Na v SheP WT and D60E), holding voltage for steady-state activation protocol was set at À 160 mV, whereas steady-state inactivation protocol included prepulse potentials from À 180 mV to À 30 mV. Steady-state I K1 -V curve was constructed from the current responses to varying 1 s test potentials ( À 130 to 50 mV, increments of 10 mV) from a holding potential of À 40 mV. APs were elicited by injecting a 1 ms current pulse at 1.1 Â threshold amplitude.
Optical mapping of AP propagation. Cell monolayers or zig-zag cultures were optically mapped with a 20 mm diameter hexagonal array of 504 optical fibres (Redshirt Imaging), as previously described 32,55,56 . Specifically, cultures were stained with a voltage-sensitive dye (Di-4-ANEPPS, 10 mM) for 5 min at room temperature, transferred to a recording chamber filled with Tyrode's solution at 37°C and illuminated by a solid-state excitation light source (Lumencor, SOLA SM) filtered through a 520 ± 30 nm bandpass filter. Emitted red fluorescence signals (l4590 nm) were collected by the optical fiber array, converted to voltage signals by photodiodes and recorded at a 2.4 kHz sampling rate with a 750 mm spatial resolution. AP propagation was triggered by a 10 ms, 1.2 Â threshold, 1 Hz stimulus from either a bipolar point electrode (in isotropic or anisotropic monolayers of E-HDFs) or a line electrode (in the zig-zag cultures). Generation of isochrone maps and calculation of CV, AP duration at 80% repolarization (APD 80 ) and impulse wavelength were performed using custom MATLAB software, as previously described 59,60 .
Depolarization and decoupling studies. Similar to previous studies 61 , membrane depolarization in Ex293 monolayers was induced by applying increasing doses of KCl (in 1 mM increments starting from 5.4 mM). After 5 min equilibration at each KCl dose, cells were paced at 1 Hz and AP conduction optically mapped. For gap junction decoupling studies, PA (Sigma, 76168) was dissolved in dimethyl sulfoxide and sonicated (10 min, 37°C) to yield a stock concentration of 50 mM. Ex293 monolayers were exposed to increasing doses of PA (0, 20, 40 and 60 mM) and after 15 min equilibration at each dose, cells were paced at 1 Hz and AP conduction optically mapped.
Regional ischaemia studies. Regional ischaemia in neonatal rat cardiomyocyte monolayers was induced as described previously 33,62 . Briefly, 12 mm round glass coverslip was placed onto the central area of a 22 mm cardiac monolayer to induce regional ischaemia. Cells were continuously paced at 1 Hz and AP conduction optically mapped every 1 min during ischaemia, until complete conduction failure in the ischaemic region. CV, APD 80 and optical AP amplitude measured at the recording sites of the central ischemic region were normalized to corresponding baseline values before ischemia. Recording site was defined as inactive (not conducting) if its AP amplitude failed below 10% of baseline value.
Computational modelling. Experimentally derived modelling parameters are listed in Supplementary Table 3. The AP generation in HEK293 cells co-expressing K ir 2.1 and BacNa v channels was simulated using the Hodgkin-Huxley formalism 63 and the following differential equation: where V is the cell transmembrane potential, C m is the total membrane capacitance, I Na is the BacNa v channel current, I K1 is the inward-rectifier potassium current, I endo is the endogenous background current and I stim is the stimulus current. Based on the similarities between BacNa v and mammalian Ca v channels 13,45 , the BacNa v conductance was modelled as a simple product of activation and inactivation gating variables and I Na was expressed using the following equation: I Na ðV; tÞ¼ G Na ÃmðV; tÞÃhðV; tÞÃðV À E Na Þ ð 2Þ where G Na is the maximum conductance of the BacNa v channel, m and h are the first-order activation and inactivation gating variables, respectively, and E Na is the sodium Nernst potential given in Supplementary Table 3. Mathematical model of human Na v 1.5 was adopted from a previous model of human ventricular tissue 64 with a slightly modified inactivation time constant to better fit voltage clamp recordings in Na v 1.5-expressing HEK293 cells.
From the voltage-clamp activation and inactivation protocols, the steady-state values of the gating variables as a function of V were plotted and fit to the Boltzmann equation 63 , to derive the midpoint voltage and slope factor listed in Supplementary Table 1: The initial and late phases of I Na traces for each clamp potential were fit as single exponentials to derive time constants of activation (t m ) and inactivation (t h ) as functions of V. The t m and t h at V ¼ þ 20 mV are listed in Supplementary Table 1.
Voltage-clamp recordings of inward-rectifying potassium current were used to fit steady-state I K1 values to a time-independent Nygren et al. 65 model as follows: where G K1 is the maximum conductance of the K ir 2.1 channel and E K is the potassium Nernst potential given in Supplementary Table 3.
Finally, the endogenous background current of wt HEK293 or HDF cells, I endo (in pA), was fit by a time-independent linear equation: where V is given in millivolts. Simulations of single-cell APs for different BacNa v mutants were performed using constant G K1 and G Na values (measured by patch clamp in a monoclonal HEK293 line expressing K ir 2.1, Cx43 and Na v SheP D60A; Supplementary Table 3), to allow direct comparisons of how kinetic properties of BacNa v on their own affect AP characteristics (upstroke velocity, APD 80 and threshold potential). As the whole-cell voltage clamp recordings were performed at 25°C, to model AP generation at 37°C, we scaled up E K and E Na from Supplementary Table 3  where Dt and Dx are the time (index i) and space (index j) discretization steps, respectively, c m is the specific membrane capacitance, a is the cable radius, R i is the intracellular resistivity, and J ion ¼ J Na þ J K1 þ J endo is the total ionic current density (in pA cm À 2 ), calculated by dividing the total ionic current ðI Na þ I K1 þ I endo Þ from equation (1) with total membrane surface area. The R i value was adopted to simulate the mean CV measured in optically mapped monolayers of a monoclonal HEK293 line expressing K ir 2.1, Cx43 and Na v SheP D60A. All simulations were performed with the identical model parameters given in Supplementary Table 3 and distinct kinetic properties measured in different BacNa v mutants (adjusted to 37°C as described above). The total length of the simulated cable was 0.72 cm (that is, 300 nodes). The first three nodes in the cable were stimulated by current injection (1.2 Â threshold) at 1 Hz rate and activation time at each node was determined as the time of maximum upstroke velocity of propagated AP. Inverse slope of activation time versus distance line fit in the central 0.24 cm of the cable was used to calculate CV.
Statistical analysis. All data are presented as mean ± s.e.m. and statistical significance was determined by one-way analysis of variance, followed by Tukey's post-hoc test to calculate P-values. Statistical significance was defined as^Po0.05, # Po0.01 and *Po0.0001.
Data availability. All data supporting the findings of this study are available within the article and its Supplementary Information files or can be requested from the authors.