Bioelectricity Console. A Tissue That Remembers a Voltage Pattern

Cells that are not neurons also hold a voltage across their membrane, and in a developing body the pattern of these voltages helps decide what grows where. A cell with the right pair of ion channels has two resting voltages it can stay in, so a sheet of such cells can hold a pattern, and keep it after the signal that set it is gone. This console lets you paint that pattern, cut the connections that hold it, and block it with a drug.

Every number here was computed by bioelectrics, the open-source bioelectricity library of this project, installed from PyPI on our build server. The browser runs the same equations live, with the parameters the library wrote.

What the console computes

Each cell has two voltage-gated channels, from the model of Cervera, Alcaraz and Mafe (2016). One pulls the voltage down toward -60 mV and closes as the cell depolarizes. The other pulls it up toward 0 mV and opens as the cell depolarizes. The current through the two crosses zero three times, so the cell has two stable resting voltages and an unstable threshold between them.

• Chapter 1, One cell. The membrane current against the voltage. Tap a voltage and the cell falls to the polarized mV or the depolarized mV, depending on which side of the threshold mV it starts. Time runs four times slower than in the model.
• Chapter 2, A tissue. 32 by 32 of these cells, each joined to its four neighbours by gap junctions. Paint a domain of depolarized cells and watch the sheet decide whether to keep it.
• Chapter 3, A drug, and memory. A drug blocks part of the depolarizing channel. Play lowers the open fraction and raises it again.

The gap junctions come in two kinds. Constant junctions, as in the paper, pass current whatever the voltage across them. Gated junctions close when the voltage across them passes 20 mV. Many connexin junctions close at a large voltage across them, but the 20 mV threshold is the library’s default, not a measured value for one connexin. The gating is not in the paper; the console says which kind is on.

What it finds

• Constant junctions erase a pattern. A domain of 144 depolarized cells is gone after a short time s. The polarized majority pulls the border cells below the threshold, from the edge inward. This is the paper’s own result: coupling normalizes a depolarized region.
• Gated junctions keep it. With the same open conductance, the junctions on the border of the domain see about 50 mV across them and close. The domain is cut off from its neighbours and all its cells stay depolarized. The border draws itself in gold.
• A small block erases it, and the pattern does not come back. Blocking a few percent of the depolarizing channel removes the depolarized state of a single cell. The domain collapses. When the channel opens fully again, the cells have two states again, but they sit in the polarized one and stay there: no cells come back. The tissue remembers its history, not only its present conditions.

What the console shows and does not show

• A model, not a measurement. One square is one model cell. Nothing on the screen is an image of tissue or a recording.
• Two phenomenological channels. The model has no named ion species, no pumps and a fixed bath. The library’s ion-level model, ported from BETSE, has these, and is not what runs here.
• A drug as a fraction. The slider is the fraction of the channel left open. It does not name a compound or a dose; the library’s drug table does that, with sources, for real channels.

Why this belongs on this site

This project asks which physical systems can hold the kind of state a mind needs. A memory held by cells that are not neurons, in their voltages and in the junctions between them, is one of the clearest cases outside the brain. The bioelectricity section follows that work, and this console shows its smallest working part.

Sources

• Cervera, J., Alcaraz, A. and Mafe, S. (2016). Bioelectrical signals and ion channels in the modeling of multicellular patterns and cancer biophysics. Scientific Reports 6, 20403. doi:10.1038/srep20403
• bioelectrics, a differentiable engine for somatic bioelectricity, version 0.3.0, MIT licence. github.com/tlcdv/bioelectrics, doi:10.5281/zenodo.23531183. The data was built by scripts/bioelectric/build_bioelectric.py, which stops unless the library reproduces the paper’s three voltages.