Sometimes extracellular recordings fail for good reasons.

Figures

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  Fig. 1. Cable equation computations of a simplified neuron. The neuron is shaped as a cylinder with a diameter 10 μm and a length of 1000 μm. In the left column, there is a uniform distribution of ion channels along the cell membrane. Spontaneously firing action potentials (APs) are reported for two points along the cell. Below, the extracellular potential (EP) is shown and is zero. The EP is computed using the point source method (see the Methods section or, e.g., refs. 11,12). In the lower panel, a snapshot of the transmembrane potential and EP is shown for a point in time when the cell fires. Here, we focus on the center 500 μm of the neuron. In the second column, a mild concentration of sodium channels (Na Ch) in the center 40 μm of the neuron results in a small but non-zero EP. In the third column, further concentration of sodium channels increases the amplitude of the EP. In the fourth column, applied stimulation in the center of a neuron with a uniform distribution of ion channels yields a non-zero EP. The stimulation is applied with a 120 Hz frequency.

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  Fig. 2. Bidomain model simulations of a sinoatrial node (SAN) tissue sample. A small cube of SAN tissue is modeled using the bidomain model equations. In the left column, the tissue is completely homogeneous, with identical membrane properties in all regions. The transmembrane potential exhibits spontaneous pacemaker activity, but the extracellular potential (EP) remains undetectable. In the middle column, moderate heterogeneity is introduced by varying membrane properties across four spatial regions, leading to a small but measurable extracellular signal. In the right column, larger inhomogeneities result in stronger EPs. The action potentials (APs) and EPs are plotted for the two points indicated by circles in the upper panel. Note that all major ion channel conductances are varied between regions, as illustrated for gNa in the upper panel (see the Methods section).

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  Fig. 3. KNM simulation of a heart-on-a-chip. The chip consists of hiPSC-CMs connected by gap junctions. The chip geometry, parameters, and membrane dynamics model are adapted from ref. 41 and described in the Methods section. In the left panel, there is no variation between the cells, and spontaneous action potentials (APs) are fired uniformly across the chip. The AP and extracellular potential (EP) traces are taken from a point in the center of the cell collection (marked by a blue circle in the upper panel). In addition, we show snapshots of the transmembrane potential and the EP at three points in time close to AP firing. For a chip with uniform cell properties, the EP is zero. In the second panel, 10% cell-to-cell variation is introduced by altering the conductance of all transmembrane currents. This gives rise to an excitation wave and weak EPs. In the third panel, the variation is increased to 50%, producing a stronger propagating wave accompanied by more pronounced EPs. In the rightmost panel, a 1 Hz stimulation current is applied to the left side of the chip, initiating a robust excitation wave and strong EPs throughout the tissue.

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  Fig. 4. KNM simulation of a pancreatic islet consisting of β-cells. The membrane dynamics of the β-cells are modeled using the Riz et al. model46 and the cells are connected to neighbors by gap junctions. In the left panel, there is no variation between the cells. Spontaneous action potentials (APs) are fired in bursting periods, but no extracellular potentials (EPs) are generated. The red lines show the solutions for the cell with the largest EP amplitude, and the blue lines show the solutions for the cell with the smallest EP amplitude. When no EP is produced, this corresponds to two arbitrary cells. In the lower panels, the membrane potential and the EP on the surface of the islet are depicted at three points in time during a single AP firing. In the left panel, all cells are equal, the transmembrane potential is uniform, and the EP is zero. In the middle panel, cell variation is introduced by varying the value of gNa, gCaL, and gKATP between each cell. Again, APs are fired, and now weak EPs are visible. In the lower panel, small transmembrane potential gradients are visible during bursting. In the right panel, more extensive variations are introduced between cells, resulting in more…

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  Fig. 5. EMI model simulations of a cerebellar Purkinje neuron. a Illustration of the different geometrical parts of the neuron. The model parameterizations for each neuron section are based on ref. 7 and specified in the Methods section. b Illustration of the three-dimensional finite element mesh close to the soma and dendrites used in the EMI model simulations. c Simulation results for a uniform channel distribution. The channel densities of the soma are applied to the entire neuron. The average membrane potential (APs) and extracellular potential (EPs) over different parts of the neuron are illustrated. More specifically, we consider the axon initial segment (AIS), the soma, and the outermost part of the dendrites (diameter < 3.5 μm). Even though APs are clearly present, no EPs are visible. In the lower panel, snapshots of the transmembrane potential and EP is illustrated at the point in time when the AIS membrane potential reaches a value above 0 mV, t*, and 0.05 ms and 0.5 ms after t*. Again, no EP is visible. d Same setup as in panel c, but for a physiological, non-uniform distribution of ion channels, based on7. In this case, the neuron displays both APs and EPs.

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  Fig. 6. Synchronization in EMI model simulations of two cerebellar Purkinje neurons. The neuron geometry and parameterizations are the same as in Fig. 5, but the neurons are set up such that the lower neuron, C1, fires action potentials (APs) 5 ms before the upper neuron, C2. a Both neurons have a uniform ion channel distribution. A solution snapshot is shown at a point in time when C1 fires, and no extracellular potential (EP) is visible. In addition, the average transmembrane potential of the AIS of C1, the average EP of the AIS of C2, and the average transmembrane potential of the AIS of C2 are plotted as functions of time during the time of a C1 AP. b Both neurons have a non-uniform distribution of ion channels, based on7 like in Fig. 5d. When C1 fires an AP, a negative EP reaches from the AIS of C1 to the AIS of C2. Below, we observe that this results in a negative EP for C2 and a small positive notch in the transmembrane potential of C2. c. As the simulation of the two uniform cells is continued for 10 seconds, the distance between the AP peaks remains constant at 5 ms. d For the non-uniform Purkinje neurons, the EP affects the transmembrane potential of the neighboring cell, and a…

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  Fig. 7. Schematic of intracellular and extracellular compartments used to illustrate Kirchhoff’s current law. In the absence of intracellular voltage gradients, axial currents Ii,l and Ii,r vanish, implying Im = 0 and therefore no extracellular current Ie. The total membrane current Im is the sum of the capacitive and ionic components, Im = Ic + Iion.