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Observation of topological action potentials in engineered tissues

Nature Physics volume 19, pages 290–296 (2023)Cite this article

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Abstract

The interface between two tissues can have very different bioelectrical properties compared to either tissue on its own. Here we show that an interface between non-excitable tissues can be electrically excitable because of an interaction between the currents passing through the gap junctions—electrically resistive intercellular connections—and the non-linear current–voltage dependence in the ion channels on either side of the interface. Our theory shows that this topologically robust excitability occurs over a far larger range of ion channel expression levels than can support excitability in the bulk. The corresponding interfacial action potentials can cause local elevations in calcium concentration, possibly providing a bioelectrical mechanism for interface sensing. The observed topological action potentials point to the possibility of other types of topological effect in electrophysiology and at other diffusively coupled interfaces.

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Fig. 1: Topological APs arise at interfaces of non-excitable tissues.
Fig. 2: Quantification and numerical simulations of topological APs.
Fig. 3: Persistently propagating topological APs at a circular interface.
Fig. 4: Topological APs driven by Ca2+ currents.

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Data availability

Source data are available for this paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Code availability

Computer code for simulations of Supplementary Model 2 is provided in Supplementary Code. Computer codes for Supplementary Model 1 and for data analysis are available from the authors upon reasonable request.

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Acknowledgements

This work was supported by the Vannevar Bush Faculty Fellowship grant N00014-18-1-2859 (A.E.C.), National Science Foundation QuBBE QLCI grant OMA-2121044 (A.E.C.), an EMBO Fellowship ALTF 543-2020 (H.O.), a Bloomenthal Fellowship (C.S.), the National Science Foundation Graduate Research Fellowship grant 1746045 (C.S.), the Simons Foundation (V.V.), the Complex Dynamics and Systems Program of the Army Research Office grant W911NF-19-1-0268 (V.V.) and the National Science Foundation grant DMR-2118415 (V.V.). We thank N. Ziv and his laboratory for hosting H.O. during the COVID-19 pandemic. We thank T. Snutch for helpful discussions and for providing cells expressing CaV3.2 and Kir2.3. We thank E. Miller for the BeRST1 dye. We thank S. Xu for helpful discussions. We thank S. Begum, A. Preecha, T. Galateanu and L. Odessky for technical assistance.

Author information

Authors and Affiliations

  1. Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, USA

    Hillel Ori, Marc Duque, He Tian & Adam E. Cohen

  2. School of Engineering and Applied Science, Harvard University, Cambridge, MA, USA

    Rebecca Frank Hayward

  3. James Franck Institute and Department of Physics, University of Chicago, Chicago, IL, USA

    Colin Scheibner & Vincenzo Vitelli

  4. Department of Chemistry, University of California, Berkeley, CA, USA

    Gloria Ortiz

  5. Department of Physics, Harvard University, Cambridge, MA, USA

    Adam E. Cohen

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Contributions

H.O. and A.E.C. conceived and designed the study and developed the FHN-inspired model. H.O. conducted the experiments and simulations and analysed results with assistance from M.D. C.S. and V.V. defined the topological interpretation. R.F.H. and H.T. assisted with method development and cell line engineering. G.O. provided BeRST1 dye reagent. A.E.C., H.O., C.S. and V.V. wrote the manuscript.

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Correspondence to Adam E. Cohen.

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Nature Physics thanks Min Zhao, Chike Cao and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Control experiments showing absence of excitability in cells expressing only one voltage-dependent channel.

In both panels, the cells also expressed a channelrhodopsin, CheRiff. The stimulus was delivered as a bar of blue light at t = 0. Related to Fig. 1.

Extended Data Fig. 2 Control experiments establishing necessary conditions for topological action potentials.

a, b) Interfaces between populations of Kir2.1- or NaV1.5-expressing cells and cells not expressing either ion channel are not excitable. c) Topological AP propagation in a NaV-Kir interface was blocked in a region where cells did not migrate to fill the gap between the populations (red arrow). Scale bars 1 mm. Related to Fig. 1.

Extended Data Fig. 3 Effect of gap junction conductance on topological action potential dimensions and velocity.

The left y-axis corresponds to the simulated width and length of the topological AP, measured at half peak. The right y-axis corresponds to the AP velocity, extracted from AP kymographs. As expected from dimensional analysis, all three quantities scale with \(\left( {G_{gj}} \right)^{\frac{1}{2}}\). Related to Fig. 2.

Extended Data Fig. 4 I-V curves of a FHN- inspired model.

I-V curves of cells with equal amounts of Kir and NaV and different values of h (solid lines); a ‘Kir-only’ cell (red); and ‘NaV-only’ cells with corresponding values of h (dashed blue). In this example, A = 5, gNa = gK = 1, and gap junctional currents are omitted. The upper fixed point disappears via a saddle-node bifurcation at \(h \cong 0.164\). Related to Fig. 2.

Extended Data Fig. 5 Phase diagram of excitability of the FitzHugh-Nagumo-inspired model.

The phase diagram is calculated both for the interface (background) and homogenous (shaded areas) configurations. The parameter space is divided into non-excitable, excitable, and spontaneously active phases. Like the realistic model (see Fig. 2c), the interface configuration shows little sensitivity to the values of gK and gNa. Other parameters: \(\tau = 10^4;A = 5;B = 3;g_{stim} = 10^{ - 2}\). Related to Fig. 2.

Extended Data Fig. 6 Topological action potentials can propagate along a circular interface.

a) Montage showing application of the inactivation stimulus, the trigger stimulus, and AP propagating for > 150 s along the interface. b) Time-dependent fluorescence in the region indicated by the green polygon. Related to Fig. 3.

Extended Data Fig. 7 Calcium-driven action potentials.

Monolayers of HEK cells were grown expressing CaV3.2 (dox-induced), Kir2.3 and CheRiff. a) After dox application (1.5 μg/mL for 1 day) to turn on CaV3.2 channel expression, the monolayer supported optically evoked action potential wave propagation. The thinner ring of active cells compared to Fig. 1b is attributable to the slower activation kinetics of CaV3.2 compared to NaV1.5, leading to a slower wavefront velocity and hence a shorter wavelength. Scale bar: 1 mm. b) The CaV3.2 channel blocker nifedipine (50 μM) eliminated excitability of the cell monolayer. c) In the absence of doxycycline, the CaV3.2 channel was not expressed and the monolayer was not excitable. Related to Fig. 4.

Supplementary information

Supplementary Information

Supplementary Models 1 and 2 and Code.

Reporting Summary

Supplementary Video 1

Propagating AP in a mixed monolayer of cells expressing either NaV1.5 or Kir2.1.

Supplementary Video 2

Topological AP at a linear interface between cells expressing NaV1.5 and cells expressing Kir2.1.

Supplementary Video 3

Conductance-based simulation of a topological AP at a tissue interface.

Supplementary Video 4

Topological AP at a circular interface.

Supplementary Video 5

Propagating AP in cells co-expressing CaV3.2, Kir2.3 and CheRiff.

Supplementary Video 6

Topological AP at a Kir2.1–CaV3.2 interface (voltage signal).

Supplementary Video 7

Topological AP at a Kir2.1–CaV3.2 interface (Ca2+ signal).

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Ori, H., Duque, M., Frank Hayward, R. et al. Observation of topological action potentials in engineered tissues. Nat. Phys. 19, 290–296 (2023). https://doi.org/10.1038/s41567-022-01853-z

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