Somatic Proximity of the Axon Initial Segment Predicts Motoneuron Excitability

found to change together with neuronal excitability following experimentally-induced perturbations in neural activity. The present study was designed to test the possibility that variation in AIS structural parameters regulates the native range in intrinsic excitability for one class of mature neurons. Spinal motoneurons were selected for their naturally large range in excitability and for their experimental accessibility to in vivo study. We began by determining whether AIS length or distance differed for motoneurons in motor pools that exhibit different activity profiles. Motoneurons sampled from the medial gastrocnemius (MG) motor pool exhibited values for average AIS d that were significantly more than for motoneurons from the soleus (SOL) motor pool, which is more readily activated in low-level movements. Next, we tested whether AIS d covaried with intrinsic excitability of individual motoneurons. Using anesthetized rats, we measured rheobase current intracellularly from MG motoneurons before labeling them for later immunohistochemical study of AIS. This combinatory approach revealed a significant correlation between AIS d and rheobase, for 16 motoneurons sampled within the MG motor pool. Among multiple electrophysiological and morphological parameters measured here, AIS d stood out as the dominant predictor of motoneuron excitability. These findings suggest an important role for AIS d in setting the intrinsic excitability of spinal motoneurons. These findings provide direct evidence that at least for motoneurons that AIS d has a prominent role in establishing the intrinsic excitability. Our data demonstrate that AIS d co-varies with intrinsic excitability in healthy adult motoneurons, i.e., those with the lowest excitability (highest rheobase) tended to have larger AIS distance from the soma. We also demonstrate using multivariant modeling, that AIS d is the strongest predictor of rheobase among various morphological and electrophysiological parameters, including input conductance. These findings suggest an important role for AIS d in setting the intrinsic excitability of spinal motoneurons.


Introduction
Diversity in the intrinsic excitability of neurons is attributed in part to heterogeneity in biophysical and structural properties of the axon initial segment (AIS) 1 . By aggregating voltage-gated channels in high density, this specialized structure sets the threshold for action potential initiation in the proximal axon [2][3][4][5] . Action potential threshold can be regulated through the AIS not only by varying the mix, density or properties of ion channels, but also by varying AIS length (AISl) and/or distance from the soma (AISd) [6][7][8][9][10][11][12] . Roles for AIS morphology and location are supported by computational modeling and by biological experiments, which demonstrate that these AIS parameters change together with measures of neuronal excitability, e.g., threshold or firing behavior, in response to experimental manipulation of neural activity 4,9,13 . Indirect evidence for AIS regulation of neural excitability may also be reflected in the association between heterogeneity in AIS and diversity in the characteristic firing behavior of neurons belonging to either the same or different populations of cell types 14,15 . These observations promote inclusion of AISl and/or AISd among the candidate factors determining the intrinsic excitability of neurons.
Biophysical determinants of intrinsic excitability are well documented for alpha motoneurons in the mammalian spinal cord. Detailed examination of these neurons was motivated in part by interest in the mechanisms underlying reliable rank ordering in the recruitment of motoneurons within a motor pool, i.e., motoneurons supplying the same muscle. The 20-30-fold range in rheobase current observed among motoneurons in the same motor pool establishes a prominent role for mechanisms intrinsic to motoneurons in determining excitability and rank ordered recruitment [16][17][18][19][20] . Among those mechanisms, input conductance, subthreshold voltage-sensitive currents, and properties of the channels underlying spike generation all contribute in determining motoneuron excitability 21 . The possibility that AIS morphology and/or location might contribute in setting motoneuron excitability as it does for other classes of neurons is suggested by the substantial variation in these AIS parameters recently reported for rodent motoneurons 6,22,23 . Our findings advance this possibility by demonstrating an inverse relationship between AISd and intrinsic excitability measured in vivo from rat spinal motoneurons.

AISd differs in motor pools exhibiting different activity levels
Motoneurons from SOL and MG motor pools were examined for differences in AISl and AISd. These motor pools express distinct activity patterns in rats as they do in other species [24][25][26][27][28][29] . Motor pool activity assessed by EMG or force production of the associated muscle is prominent in SOL during quiet standing and slow locomotor speed in rats, while activity in MG develops progressively with movement intensity, approaching maximum only during rapid and more vigorous movements 30 . The differences in activity patterns parallel differences in intrinsic excitability of motoneurons, being greater for the type S motoneurons that dominate the SOL motor pool than for the preponderance of type F motoneurons that populate the MG pool 16,[31][32][33] . We examined these two motor pools in attempt to find preliminary support for the idea that AIS dimensions or location contribute to excitability of motoneurons as shown for some other neuron types 13 .
Retrograde CTB labeling revealed the motor pool identities for an unbiased sample of motoneurons (65 MG and 82 SOL) from 5 rats. Expression of AnkG reactivity 34,35 in 2dimensional images of motoneurons delineated AISl and AISd (Fig. 1a,b). Both parameters reported in Table 1 covered ranges similar to those provided in the only published reports on motoneurons, which were obtained from mice 6,22 and rats 23 .
Segregating motoneurons by motor pool exposed a significant difference in the AISd for the functionally distinct SOL and MG motor pools. A tendency for shorter AISd in the SOL vs MG motor pool is represented in comparison of images from two motoneurons shown in Fig. 1a,b. While the AISd distributions overlapped considerably over short distances (<10µm), very few SOL motoneurons exhibited AISd values extending beyond the mean value, 12.50µm, observed for the sample of MG motoneurons (Fig. 1c).
Computational modeling (HMC, Fig. 1d) established significant differences in PPD for both mean and standard deviation of AISd (Fig. 1e,f). No significant differences between pools were found for either AISl or motoneuron soma cross-sectional maximum diameter. These findings support AISd as a candidate contributor to differences in motor pool excitability and possibly also to differences in motor unit type.

AIS distance predicts motoneuron excitability
Next, we tested whether the relation with motor pool activity might emerge from an influence of AISd on the intrinsic excitability determined in vivo for individual motoneurons (n=18). MG motoneurons were selected for their wide range in rheobase, which would increase the chance of detecting a relationship with AISd. Restricting study to MG motoneurons had the additional benefit of eliminating confounding influences introduced in cross-pool comparisons.
Electrophysiological measures were recorded intracellularly before filling the motoneuron with Neurobiotin for immunohistochemical analysis of AIS morphology.
Example images of labeled motoneurons together with selected electrophysiological properties are illustrated in Fig. 2. Data from one motoneuron (Fig. 2a -e3) represent the majority of the sample (16/18 motoneurons) for which the AIS-bearing axons clearly emerged directly from the soma. Dendrite-derived axons were exhibited by the remaining minority (11%) of motoneurons sampled (see Fig. 2f1-3), comparable to the small percent found in mouse motoneurons 6 . Because the interposition of a dendrite confounded measurement of the distance between soma and AIS, these motoneurons were excluded from further analysis other than to note their low rheobase values (<3nA).
Detailed measurements of multiple morphological properties from confocal image stacks together with various electrophysiological properties are compiled from the 16 remaining MG motoneurons in Tables 2-3. All properties were comparable to those that have been measured in previous studies of rodent motoneurons 17,18,36 . The sample also represents a substantial portion of the reported distribution for rheobase among MG motoneurons 16 . Particularly pertinent was the range in AISd for our sample of MG motoneurons, which at 27m covers the span associated with meaningful differences in excitability of other neuron types 9 .
We focused on correlations between motoneuron excitability and AIS properties. Figure   3a shows that motoneurons with relatively short AISd tended to have lower rheobase, i.e., higher excitability than motoneurons with more distant AIS. Differences in AISd accounted for 63.1% of the variance in rheobase (R 2 ). This finding is qualitatively consistent with our indirect population comparisons (Fig. 1). Furthermore, through our multivariant model, we determined for every 0.846µm (1) increase in distance, there was a 1nA increase in rheobase. By contrast, AISl had no statistically significant correlation with either motoneuron excitability ( Fig. 3b) or with AISd ( Fig. 3c).

Motoneuron rheobase correlates stronger with AISd than with input conductance
Biophysical principles and observed correlation with rheobase support consensus that input conductance (Gin) is a primary determinant of motoneuron intrinsic excitability 16,17,19 . Reliable measurement of input conductance in a subset of 10 motoneurons from our sample made it possible to test the correlation with rheobase. Input conductance explained a significant amount of variance in rheobase, 64.8% (95% HDI:10.9 -42.2, β1 = 26.0), within this sample. In order to validate our findings, we then calculated the PPD between rheobase and input conductance for a large MG motoneuron database obtained in our lab (n=44). For this larger sample, input conductance explained 64.4% of the variance (95% HDI:15.5 -25.0, β1 = 20.2) in rheobase. Figure 4 illustrates the observed data and predicted slopes for both groups of neurons derived from the probabilistic model. Near complete overlap of slopes indicates strong evidential support that the small subset of neurons does not differ in their expected relationships (i.e., slope) from neurons previously collected in our laboratory or those described in the literature 17,19 or from experimental parameters such as recording with Neurobiotin filled electrodes.
Next, we developed a set of candidate Bayesian models to test the independent and combinatorial influence of AISd and/or Gin in determining motoneuron rheobase. This allowed us to identify which, if any, set(s) of parameters were most predictive. Pareto smoothed importance sampling, leave-one-out cross-validation (PSIS-LOO) was used to evaluate the four fitted models 37 . We focused on the ELPD (expected log pointwise predictive density) as an unbiased estimate of each model's predictive performance. We find clear evidence that the model containing AISd alone contained more predictive information than the model containing Gin alone (ELPD diff = -7.2, SE = 4.8). There was, however, no evidence that additive (ELPD diff = -0.8, SE = 1.5) or multiplicative (ELPD diff = -2.2, SE = 1.5) models, including both parameters, improved performance (see Methods) over the AISd model alone. We conclude that when considering single parameters, AISd provides superior predictive information to motoneuron excitability when compared to Gin alone.

Morphological and biophysical parameter comparison
A comprehensive pairwise comparison of all biophysical and morphological parameters is presented in figure 5. Several significant relationships emerged by conducting a classic frequentist correlation approach. Most notable for this report, not previously discussed here, is the relationship between rheobase and muscle twitch contraction time (R 2 = -0.50) and twitch force (R 2 = 0.23), which has been used as a predictor of recruitment order 18,38 . We provide these comparisons to help put our findings in the context of previous studies of the mechanisms of orderly recruitment of motoneurons according to various motoneuron and muscle unit properties.

Discussion
The present study provides, to our knowledge, the first direct examination of the relationship between AISd and intrinsic excitability for individual neurons of any type.
We selected motoneurons for their wide range in excitability and asked whether this range might relate to AIS location and/or length, both of which have been shown to covary with homeostatic changes in excitability for other types of neurons. Our findings suggest that AISd plays a role in establishing the native excitability of motoneurons in healthy adult mammals. Results show that AISd co-varied with rheobase measured in vivo, such that motoneurons with the greatest rheobase (lowest excitability) tended to have AIS located further away from the soma. Moreover, AISd emerged as the best predictor of motoneuron excitability among all physiological and anatomical parameters measured in this study. These findings suggest an important role for AISd in establishing diversity in intrinsic excitability among spinal motoneurons.

AIS location and dimensions in relation to neuronal excitability
Our data fit well with other studies establishing AISd as a predictor of excitability. Early experimental evidence obtained from cultured hippocampal neurons by Grubb and Burrone demonstrated that chronic depolarization resulted in a distal relocation of the AIS while having little impact on the AIS length 9 . This shift was associated with a compensatory decrease in excitability as indicated by an increase in current threshold compared to controls. Another example comes from the more recent work of Lee et al., who demonstrated that KO of proteasome adapter protein Ecm29 produced a hypersusceptibility phenotype to drug induced seizers in mutant mice. Pyramidal neurons in these animals exhibited proximal relocation of the AIS together with increased spiking probability, number, and frequency measured in brain slice 12 . Together, these studies suggest a homeostatic tuning, whereby excitability increases or decreases inversely with AISd consistent with the relationship we find for motoneurons.
AISl has also been shown to be associated with neuronal excitability. Meza et al. report that spontaneous firing rate had a significant positive correlation with AISl and a significant negative correlation with distance in nigral dopaminergic interneurons 15 .
However, through computational modeling the authors demonstrated that changes in distance may be secondary to length in determining excitability. In fact, AISl has been shown to be the dominate factor over distance in establishing excitability in other neuron types as well 8,39,40 . So, it appears that both distance and length are related to excitability but biased towards one or the other in different systems.

Modeling the impact of AIS on excitability.
Biophysical models also demonstrate that AISl and/or AISd influence excitability. AISl has a strong and consistent effect with greater length producing an increase in excitability by increasing sodium conductance. While we did not find a strong correlation between excitability and AIS length in our study, we did find a small, but significant, negative correlation between rheobase and AIS surface area (R = -0.51). Lower rheobase motoneurons tended to have the largest AIS surface area which could allow for an increase in sodium conductance through a higher density of Nav 1.1 and 1.6 channels, both of which are known to expressed at the AIS in motoneurons 6 . This would allow motoneurons to initiate and backpropagate action potentials at lower input currents.
By contrast, simulations yield effects of AISd that are small and, in most studies, opposite to our experimental findings. Specifically, excitability increases as the AIS moves away from the large capactitive load, or "current sink," introduced by the soma.
The discrepancy between observation and simulation remains unresolved but possible explanations have been considered. Simulated data move more in line with biological observations by increasing outward current activated by low-threshold voltage-gated potassium channels, such as those from the Kv1 and Kv7 family at the AIS [41][42][43][44][45] . These channels could provide a resting hyperpolarizing current at the axon that results in higher rheobase as a function of distance from the soma 13 . This is a plausible mechanism given the high expression of these channels in the motoneuron AIS 6,46 .
Further support derives from simulations showing that higher Kv conductance at the AIS results in more current needed to reach threshold for distal AIS 44 .

Primary determinants of intrinsic motoneuron excitability
Rheobase is commonly used to measure neuronal excitability. By establishing action potential threshold in response to injected current, rheobase emphasizes the intrinsic as opposed to synaptic determinants of neuronal excitability. However, rheobase is also thought to emerge from the interaction of multiple properties, including somatic leak and inward current conductances 19 . For more accurate determination of the AIS contribution to neuronal excitability, Goethals and Brette recommend measuring somatic voltage threshold, defined as the maximum change in membrane potential that does not elicit an action potential 13 . In their computer simulation, this parameter is not impacted by input conductance or dendritic morphology. However, measurement of voltage threshold is subjective and sometimes affected by membrane potential fluctuations arising during in vivo recording. All considered, we selected rheobase for its common use and practical utility in representing neuronal excitability.
Our main objective was to identify which parameters from our data set were best at predicting rheobase. For that purpose, we applied a multivariate model based on a Bayesian framework. AISd proved to be the strongest predictor of excitability.
Surprisingly, input conductance was not a strong predictor of rheobase, and neither an additive nor multiplicative model integrating both AISd and Gin provided any significant improvement over AISd alone. However, the influence of Gin as a predictor of rheobase may have been confounded by various factors. One such factor arises from the possible expression of subthreshold conductances having the potential to influence somatic leak conductance. Nonetheless, data extracted from our sample of 16 motoneurons factor firmly establish AISd as a prominent predictor of intrinsic excitability.

Conclusion:
These findings provide direct evidence that at least for motoneurons that AISd has a prominent role in establishing the intrinsic excitability. Our data demonstrate that AISd co-varies with intrinsic excitability in healthy adult motoneurons, i.e., those with the lowest excitability (highest rheobase) tended to have larger AIS distance from the soma.
We also demonstrate using multivariant modeling, that AISd is the strongest predictor of rheobase among various morphological and electrophysiological parameters, including input conductance. These findings suggest an important role for AISd in setting the intrinsic excitability of spinal motoneurons.

Collecting and processing both in vivo electrophysiology and tissue samples from individual motoneurons
Rats (n=8) were prepared for in vivo study in terminal experiments as described previously 48,49 . Briefly, each rat was deeply anesthetized for the duration of the experiment, which typically lasted 8 hours and ended with euthanasia and spinal cord extraction as described above. Experimental preparation began with monitoring and regulating vital signs including heart rate (300-500 beats/min), oxygen saturation (>90%), end-tidal CO2 (2-5%), respiration rate (40-60 breaths/min), and core body temperature (37-38 o C). Next, surgical procedures were used to expose the spinal cord (L4-S1) and the MG muscle and nerve in the left hindlimb. All other peripheral nerves in the left hindlimb were crushed. Finally, each rat was secured in a stereotaxic frame configured to support recording and stimulation devices applied to exposed tissues  16,20 . Rheobase current, referred to as rheobase from this point forward, was our designated measure of the motoneuron intrinsic excitability and was recorded as the first among progressively incrementing current pulse amplitudes (50ms duration) to produce an action potential. Input conductance (Gin) was calculated as the steadystate voltage response elicited and normalized by 1 or 3 nA hyperpolarizing current pulses (50ms duration) averaged over several repeated trials. Inadequate bridge balance eliminated Gin measurement for some motoneurons. Afterhyperpolarization (ahp) was measured from action potentials elicited by suprathreshold current pulses (0.5ms duration). Action potentials elicited in the motoneuron during the ahp test evoked isometric motor unit twitch contractions, which were measured by a force transducer attached to the MG muscle tendon. For 2 animals, it was necessary to administer the paralytic drug, pancuronium bromide (0.2mg/kg i.p.), in order to minimize respiratory movement as needed to obtain stable intracellular records of membrane potential. Motor unit contractile properties were not measurable in these cases. Finally, current injection through the micropipette (5nA square pulses, 1ms duration delivered continuously at 2 Hz for 5mins) was used to fill the motoneuron with Neurobiotin (Fig.   2).
Terminal experiments concluded with rat perfusion and extraction of lumbosacral spinal segments for processing and sectioning as described above. Spinal cord sections we incubated with streptavidin conjugated to an Alexa Fluor 488 (1:50; Invitrogen, RRID:AB_2315383) mixed with the secondary antibody solution for purposes of identifying Neurobiotin-filled motoneurons. Sections were also processed for AnkG immunoreactivity as described above.
All recorded data (electrode current and membrane voltage together with muscle force) were digitized (20kHz; Cambridge Electronic Design Power 1401), stored and later analyzed with Spike2 software.

Image Analysis
Sections containing motoneurons labeled retrogradely with CTB or injected intracellularly with Neurobiotin were imaged at high magnification using confocal microscopy (Zeiss LSM 700). Image stacks (0.5μm steps) were captured with a 63X oil immersion objective (N.A 1.4) at 0.5 digital zoom.

Morphological analysis of motoneurons neurons identified by retrograde labeling
Image stacks of retrogradely labeled motoneurons with clear AnkG labeling were analyzed using Imaris (Bitplane, Zurich, Switzerland). Confocal image stacks were uploaded and the soma max cross-sectional diameter, AIS metrics were obtained using the polygon measurement tool. AISd was measured from the axon hillock to the proximal end of AnkG immunoreactivity ( Figure 1B, between white and red arrows), while AISl was measured between the proximal to the distal ends of AnkG immunoreactivity (region between two red arrows).

Morphological analysis of motoneurons examined electrophysiologically
Motoneurons filled with Neurobiotin and immunolabeled with AnkG were analyzed using Neurolucida (Microbrightfield, Williston, VT). Motoneuron cell bodies were reconstructed in 3D through a series of contours traced in each optical plane. AISd and AISl were traced in 3D following their tortuosity through each optical plane to accurately measure both AIS distance and length. These reconstructions were also used to measure motoneuron soma surface and volume. All morphological measures were performed blind in regard to biophysical properties including rheobase. Mixed-effects statistical models are preferred for answering these questions, because they have the power to reduce type I error rates. However, implementation of these models in a traditional frequentist framework relies on maximum likelihood estimation, which generally requires large sample sizes for model convergence and to mitigate type II errors. For small sample sizes, such as those typical in vivo electrophysiological studies of single neurons, mixed-effects models implemented in a Bayesian framework can overcome convergence issues, will more accurately reflect the uncertainty in effects that are based on small sample data, and are more robust to guard against the overinterpretation of unlikely results 50 . Thus, models were fit in a fully Bayesian inferential framework to empirically derive the full joint posterior probability distributions (PPD) of model parameters simultaneously (e.g., means, standard deviations, and effect sizes) 54 .

Statistical analysis and Bayesian modeling.
Our models describe uncertainty in the response variable, e.g., rheobase, AIS distance, y, conditional on unknown parameters θ (e.g., regression coefficients) and predictors (e.g., biophysical and morphological parameters or motor pool membership), x, as well as the a priori uncertainty about these parameters and predictors 56  Marginally informative priors were applied to model parameters and variance components such that inferences were driven predominantly by the experimental data to explicitly answer our central questions. Prior specifications were based on results from previous preliminary data and published studies by our group 52 and others 17,19 .
All models were fit using Hamiltonian Markov Chain Monte Carlo sampling to compute credible parameter values (θ), e.g., means, standard deviations, regression coefficients, effect sizes. Each model was run with four independent chains for 400 warm-up and 4,000 sampling steps. Steps to perform model evaluation and validation have been extensively described in our previous work [53][54][55] . Briefly, for all parameters, the number of effective samples was >2000, convergence was assessed and assumed to have Data Availability All data, models, and code are immediately available upon request. the NIH National Research Service Award F32NS112556 (TMR). We wish to acknowledge the core facilities at the Parker H. Petit Institute for Bioengineering and Bioscience at the Georgia Institute of Technology for the use of their shared equipment, services and expertise. The authors would also like to thank Ms. Emily Pfahl for assisting with AIS measurements.     Plots are based on a generative model conditioned on previous reports and the current data set. Each grey line represents a single trial from 4,000 generative samples and each black dot is an observed data point (n=16). From the 4,000 samples we provide a 95% high density interval (HDI). The median slope from the generative sample is represented as a blue line (1). From the slopes and generative model, we compute an R 2 equivalent, and this is presented with an HDI and a median. a) Rheobase: AIS distance. As rheobase increases the AIS distance increased from the motoneuron soma.   Each value listed in the matrix is an r-squared value. The number of red asterisks refer to significance level for Pearson correlation coefficients (*p<0.05, **p<0.01, ***p<0.001).

Author Contributions
Red squared indicates a relationship between two variables but did not reach statistical significance.   Table 3: Biophysical measurements from intracellularly recorded MG motoneurons. *Two motoneuronap heights were excluded. In both instances spikes were blocked and not able to produce a full spike even with positive current injection.