concept

geometric ratio

Also known as: GR, geometrical ratio

Facts (12)

Sources

Branching morphology determines signal propagation dynamics in ... nature.com Nature Aug 21, 2017 12 facts

claimNon-symmetric responses in branched axons can occur even when the geometric ratio (GR) is 1.

claimIn axons with high geometric ratios that still allow propagation, reflection can occur where one action potential spike continues into the daughter branches while another spike reverses into the mother branch.

formulaWilfrid Rall defined the geometric ratio (GR) for branching points as GR = (da^(3/2)) / (sum(dj^(3/2))), where da is the diameter of the mother branch and dj are the diameters of the daughter branches.

claimConstructing a branched axon by concatenating an axonal segment to one daughter branch of a symmetric branching point—while maintaining an identical geometrical ratio (GR)—results in asymmetric responses when stimulated with high-frequency current spikes.

claimFor a geometric ratio (GR) of 1, there is a perfect impedance match, allowing action potentials to smoothly cross branching points.

claimFor stimulus frequencies lower than 50 Hz in branched axons, signal propagation is determined solely by the geometric ratio (GR) of the axon: the signal propagates uninterruptedly if the GR is less than 34.2, and fails otherwise.

claimResponses in daughter branches of axons are identical if the geometrical ratio (GR) is the same, regardless of differences in the radii of the branches.

claimWhen the geometric ratio (GR) of an axon is less than 1, action potentials cross branching points with slight changes in shape and velocity; when the geometric ratio is greater than 1, action potentials cross with a delay that scales exponentially with the ratio.

claimSignal propagation at intermediate frequencies in branched axons is modulated symmetrically based on the geometrical ratio (GR) value along the two daughter branches.

claimExisting literature on branched axons typically uses the geometrical ratio (GR) as the single geometrical parameter to determine activity coding at branching points, which results in symmetric responses.

claimAction potential propagation fails at axonal branching points, leading to a blockage, when the geometric ratio exceeds a critical value that is dependent on temperature.

claimIntermediate frequency response patterns in neurons depend on the geometric ratio (GR) and frequency, but are independent of the scale of daughter branch radii.