Neuron Morphology Influences Axon Initial Segment Plasticity

Diagrams of somatodendritic (left) and axonal (right) compartments in a model neuron. Somata (20 × 20 µm) were attached to a variable number of dendrites (300 µm long, tapering from 2.5 to 0.5 µm in diameter), and to one of five AISs. The AIS in Model A was variable in length (5-100 µm), while AIS Model B had a 30-µm-long AIS that was translocatable (from 0 to 70 µm from the soma) within a 100-µm-long proximal axon segment (1.5 µm diameter) having somatic membrane properties. AIS Model C had a similar 30 µm AIS fixed to the axon proper on one end, and to a variable amount of proximal axon (0-70 µm long, 1.5 µm diameter, with somatic membrane properties) bridging itself and the soma. AIS Model D was a hybrid model combining a variable-length proximal axon with a variable-length AIS (maximum combined length was 100 µm). Finally, AIS Model E lacked an AIS altogether and consisted of an unmyelinated axon attached directly to the soma. AIS Models A through D were attached to myelinated or unmyelinated axons (see Materials and Methods). Inset at left illustrates the simulation setup in which rheobase current injections at the soma (40 ms duration) initiate action potentials.

Interaction of neuron size and AIS length in regulating action potential threshold. A, Diagrams (top) of ball-and-stick neurons having a variable-length AIS (AIS Model A) with uniform maximum sodium and potassium conductance densities (left), or with conserved (i.e., length-independent) total conductances (right). Voltage traces (below) show somatic (blue) and AIS (red) responses to somatic current injections in neurons with the indicated number of dendrites and AIS lengths of 20 (left), 40 (middle), or 60 µm (right). B, Plots of normalized rheobase currents in neurons having the indicated numbers of dendrites and AIS lengths, with uniform conductance densities (left) or conserved total conductances (right). Inset, Plots of optimal (i.e., lowest rheobase current) AIS length vs the number of dendrites in model neurons having myelinated or unmyelinated axons, as indicated. Larger neurons had longer optimal AIS lengths. To facilitate comparisons across neurons, rheobase currents from the soma-only neuron having uniform AIS conductance densities were normalized to the rheobase occurring when the AIS was adjacent to the soma, as at very long AIS lengths, rheobase increased above this level in the soma-only model.

Dendritic architecture influences the impact of AIS location on excitability. A, Diagrams (top) of the AIS of ball-and-stick models having a translocating AIS within the proximal axon (AIS Model B, left) or an AIS connected to the axon proper and positioned at variable distance from the soma (AIS Model C, right). Voltage traces show somatic (blue) and AIS (red) responses to somatic current injections in neurons in which the AIS was positioned 0 µm from the soma (left), 35 µm from the soma (middle), or 70 µm from the soma (right). Data are from models with one or four dendrites (AIS Model B), or five or eight dendrites (AIS Model C), as indicated. Note that in both model configurations the addition of dendrites increased the rheobase current, but shifted the most excitable AIS locations distally. B, Plots of normalized rheobase currents in myelinated neurons having the indicated number of dendrites and AIS locations for neurons with AIS Model B (left) or AIS Model C (right). Inset, Plots of optimal (i.e., lowest rheobase current) AIS locations vs the number of dendrites in models having myelinated or unmyelinated axons. In all cases, increasing the number of dendrites led to more distal optimal AIS locations.

AIS performance across a range of sodium conductance properties. A, Diagrams of the AIS of a one-dendrite myelinated neuron having a 50- or 65-µm-long AIS beginning at the soma (A₁ ), and of a five-dendrite model with a 30-µm-long AIS beginning either at the soma or 10 µm away (A₂ ). B, Voltage responses at the soma (blue), AIS (red), or 10th node of Ranvier (∼1 mm from the soma; yellow) in response to the indicated current steps in models having the indicated sodium conductance properties and AIS architectures. In most one-dendrite models, increasing AIS length from 50 to 65 µm reduced neuron excitability (B₁ ), while in the five-dendrite model, moving the 30-µm-long AIS 10 µm away from the soma increased neuron excitability (B₂ ). C, Comparisons of “optimal” (i.e., lowest rheobase) AIS lengths (left) and locations (right) for myelinated (top) and unmyelinated (bottom) model neurons having the indicated number of dendrites and sodium conductance properties.

AIS performance across a range of AIS sodium conductance densities. A, Top, Diagram of a model neuron having a 30-µm-long AIS positioned 10 µm from the soma. Bottom, Voltage responses measured at the soma (blue), in the AIS (red), or in the 10th node of Ranvier (∼1 mm from the soma; yellow) in response to the indicated rheobase current steps in models having the indicated number of dendrites and AIS-to-soma sodium conductance density ratios. B, Comparisons of optimal (i.e., lowest rheobase) AIS lengths (left) and locations (right) for myelinated (top) and unmyelinated (bottom) model neurons having the indicated number of dendrites and AIS-to-soma sodium conductance densities.

Interaction of AIS length and location in setting neuron excitability. A, Diagrams (top) of the proximal axons of ball-and-stick neurons having variable-length AISs located at different distances from the soma (AIS Model D). The AISs had either uniform sodium and potassium conductance densities (i.e., sodium and potassium conductances increased with length; left) or conserved total sodium and potassium conductances (i.e., length-independent conductances; right). Voltage traces show somatic (blue) and AIS (red) responses to somatic current injections in model neurons having the indicated AIS lengths and locations. Note that in the 40-µm-long AIS model with conserved total conductances, rheobase (to the nearest 100 fA) was identical in models having the AIS beginning at 0 or 25 µm from the soma (minimal rheobase in this model occurred when the AIS was 10 µm from the soma). B, Plots of optimal (i.e., lowest rheobase current) AIS position for each AIS length in models having “uniform conductance densities” (left) or “conserved total conductances” (right) in the AIS.

Impact of AIS plasticity on neuron excitability. A, Plots of mean changes in rheobase currents (percentage ±SD) observed after elongating or shortening a 30-µm-long AIS by 5, 10, or 15 µm across all possible AIS locations (within 100 µm of the soma) in model neurons having the indicated number of dendrites (AIS Model D; myelinated axon). Uniform sodium and potassium conductance densities were maintained across all AIS lengths (i.e., increasing AIS length proportionally increased total maximum sodium and potassium conductances). B, Plots of the mean absolute values of changes in rheobase (percentage ±SD) observed after translocating a 30-µm-long AIS by 5, 10, or 15 µm across all possible AIS positions within 100 µm of the soma (e.g., 14 possible 5 µm shifts of the 30 µm AIS) in neurons having the indicated number of dendrites (AIS Model C). To facilitate comparisons, data are shown at the same scale as in A, with a close-up of the data inset.

AIS performance in morphologically realistic neurons. A, Morphologies of reconstructed neurons. For illustrative purposes, each morphology includes a 40-µm-long proximal axon (green), a 30-µm-long AIS (red), and a myelinated (in the Purkinje and L5 neurons) or unmyelinated (in the medium spiny, dentate granule, and CA3 pyramidal neurons) axon (yellow arrow). For each morphology, somatic and AIS voltage traces in response to the indicated somatic current injections are shown for models having a 30 µm AIS located adjacent to the soma or 10 µm away. Note that excitability in the smaller neurons is promoted by proximal AIS placement, but that the larger neurons favor a more distal AIS. B, Left panels, Plots of normalized rheobase current vs AIS length (AIS Model A; uniform sodium and potassium conductance densities) for reconstructed neurons having smooth dendrites (top) or simulated synaptic spines (bottom; see Materials and Methods). Smaller neurons exhibited minimal rheobase currents at intermediate AIS lengths, while the simulation of dendritic spines favored an elongated AIS. Right panels, Plots of normalized rheobase current vs location of a 30-µm-long AIS (AIS Model C) in reconstructed neurons having smooth (top) or simulated spiny (bottom) dendrites. Smaller neurons favored a proximal AIS, while simulating spiny dendrites shifted optimal AIS locations away from the soma.

Impact of AIS plasticity on the excitability of morphologically realistic neurons. A, Plots of the mean changes in rheobase currents (percentage ±SD) observed after elongating or shortening the AIS by 5, 10, or 15 µm (relative to a 30-µm-long baseline AIS), across all possible AIS locations within 100 µm of the soma, in reconstructed neuron morphologies having simulated dendritic spines (see Materials and Methods) and uniform sodium and potassium conductance densities in the AIS (AIS Model D). B, Plots of the mean absolute values of changes in rheobase (percentage ±SD) observed after translocating the AIS by 5, 10, or 15 µm across all possible AIS positions within 100 µm of the soma. Note the different y-axis scales in A and B.

Impact of dendritic topology on AIS performance. A, Diagrams of ball-and-stick model neurons (AIS Model C) having zero, one, or eight nontapering (2.5 µm diameter) passive dendrites that conserve a total somatodendritic surface area of 12,566 µm² in each model. In the soma-only model, the densities of active somatic conductances were reduced in the enlarged soma to conserve the same total conductances present in the baseline soma. B, Plots of normalized rheobase currents for different AIS lengths (AIS Model A; conserved sodium and potassium conductance densities) in model neurons having variable somatodendritic topology, but conserved total surface areas. Top inset, Plots of optimal AIS length vs the number of dendrites in models having preserved total somatodendritic surface area. Bottom inset, An expanded view of the indicated data points. C, Plots of normalized rheobase currents for the same model neurons having a 30-µm-long AIS placed at the indicated distances from the soma (AIS Model C). Inset, Plots of optimal AIS distance from the soma vs the number of dendrites in models having preserved total somatodendritic surface area.

Impact of dendritic membrane properties on optimal AIS length. A, Diagram of a neuron with four dendrites having variable dendritic membrane properties and a variable-length AIS attached to a myelinated axon (AIS Model A). B, Voltage responses in the AIS following somatic current injections under baseline conditions (far left) and after manipulations of dendritic R_M and/or C_M, as indicated. Responses from three model neurons having AIS lengths of 75 (blue), 85 (green), and 95 (red) µm are superimposed. C, Plots of normalized rheobase current vs AIS length for the four dendrite model having modified dendritic R_M (top left; inset shows close-up of indicated area), dendritic C_M (top right), parallel changes in both dendritic R_M and C_M (bottom left), or reciprocal changes in dendritic R_M and C_M (bottom right). Dendritic C_M and/or R_M were multiplied by the indicated modification factors. In experiments testing reciprocal changes in dendritic properties (bottom right), the C_M/R_M ratios represent reciprocal changes to C_M and R_M around the baseline (C_M/R_M ratio = 1) values (e.g., a ratio of 0.25 indicates that dendritic C_M was multiplied by 0.5 and dendritic R_M was multiplied by 2.0). Increasing dendritic C_M favored a longer AIS, regardless of whether there were also co-occurring changes in dendritic conductance (i.e., changes in dendritic R_M). Shaded bars indicate the AIS lengths for which traces are shown in B.

Dendritic membrane properties influence optimal AIS location relative to the soma. A, Diagram of a neuron with four dendrites having variable dendritic membrane properties and a 30 µm AIS positioned at variable distances from the soma (AIS Model C; myelinated axon). B, Voltage responses in the AIS during somatic current injections under baseline conditions (far left) and after manipulations of dendritic R_M and/or C_M, as indicated. Responses from three models are superimposed: those having the AIS beginning 0 (blue), 20 (green), or 50 µm (red) from the soma. C, Plots of normalized rheobase current vs AIS location for the four-dendrite models having modified dendritic R_M (top left), dendritic C_M (top right), parallel changes in both dendritic R_M and C_M (bottom left), or reciprocal changes in dendritic properties (bottom right). Dendritic C_M and/or R_M were multiplied by the indicated modification factors. C_M/R_M ratios in reciprocal manipulations of R_M and C_M are centered around baseline (C_M/R_M ratio = 1) values. Increasing dendritic C_M and/or dendritic conductance (lower dendritic R_M) enhanced excitability at more distal AIS locations. Shaded bars indicate the AIS locations for which traces are shown in B.

Dendritic architecture influences action potential initiation. A, Left, Diagram of a model neuron having zero to eight dendrites, a 30 µm AIS located 20 µm from the soma, and a myelinated axon. Pipettes indicate the location of recording electrodes at the soma (where rheobase current is injected), toward the end of the AIS (where action potential initiation occurred) and at the first node of Ranvier. Right, Traces of the action potential generated by rheobase somatic current injection, as recorded at the indicated locations in the model cell. These simulations were run with 100 ns time steps to pinpoint action potential initiation to the nearest 1 µm. B, Plot of spike latency vs location of spike initiation for myelinated and unmyelinated neurons with different numbers of dendrites (as indicated by color) and variable AIS locations (AIS Model C), and for neurons having uniform unmyelinated axons lacking an AIS (AIS Model E). The AIS constrained the location of action potential initiation, but increased the influence of dendrite number on spike latency. C, Plot of the location of action potential initiation within the AIS for myelinated and unmyelinated neurons vs the distance of the AIS from the soma. When the AIS was placed at distal locations, action potential initiation occurred in slightly more proximal AIS compartments, an effect that was more pronounced in neurons with unmyelinated axons.

Impact of rheobase precision on action potential initiation and AIS plasticity. A, Plots of action potential waveforms recorded in the AIS (red; 30 µm long and 30 µm from the soma) or in the soma (blue) of neurons with four dendrites and either an AIS associated with a myelinated axon (left), an unmyelinated (middle) axon (AIS Model C), or an unmyelinated axon lacking an AIS (AIS Model E; right). Shown are traces in which rheobase current was calculated to the nearest pA or to the nearest zA, as indicated (simulations used 100 ns time-steps). B, Plots of spike latency vs the location of spike initiation in myelinated and unmyelinated neurons having an AIS (Model C), or in a neuron lacking an AIS (Model E), for rheobase current injections at the indicated precision levels (i.e, rounded up to the nearest suprathreshold stated unit). Note that approaching ever more precise rheobase currents increased the latency to spike initiation and, in the absence of an AIS, moved the location of initiation to very distal regions of the axon. C, Plots of AIS lengths (left) or locations (right) having the lowest rheobase currents, as determined to the nearest 100 fA (open symbols) or 1 zA (closed symbols) in myelinated and unmyelinated neurons.