Alterations of the axon initial segment in multiple sclerosis grey matter

Abstract Grey matter damage has been established as a key contributor to disability progression in multiple sclerosis. Aside from neuronal loss and axonal transections, which predominate in cortical demyelinated lesions, synaptic alterations have been detected in both demyelinated plaques and normal-appearing grey matter, resulting in functional neuronal damage. The axon initial segment is a key element of neuronal function, responsible for action potential initiation and maintenance of neuronal polarity. Despite several reports of profound axon initial segment alterations in different pathological models, among which experimental auto-immune encephalomyelitis, whether the axon initial segment is affected in multiple sclerosis is still unknown. Using immunohistochemistry, we analysed axon initial segments from control and multiple sclerosis tissue, focusing on layer 5/6 pyramidal neurons in the neocortex and Purkinje cells in the cerebellum and performed analysis on the parameters known to control neuronal excitability, i.e. axon initial segment length and position. We found that the axon initial segment length was increased only in pyramidal neurons of inactive demyelinated lesions, compared with normal appearing grey matter tissue. In contrast, in both cell types, the axon initial segment position was altered, with an increased soma-axon initial segment gap, in both active and inactive demyelinated lesions. In addition, using a computational model, we show that this increased gap between soma and axon initial segment might increase neuronal excitability. Taken together, these results show, for the first time, changes of axon initial segments in multiple sclerosis, in active as well as inactive grey matter lesions in both neocortex and cerebellum, which might alter neuronal function.

A hyperpolarization-activated current is implemented by Ih channels distributed in the soma and dendrites with an exponential increase in density with distance from the soma. The passive electrical properties of the reconstructed cell were set as follows: Cm = 0.9 µF/cm 2 , Ri = 100 Ωcm, and Rm = 15 kΩcm 2 . Purkinje cell. In the Purkinje cell model 2 the geometry of the AIS is not based on a morphological reconstruction but represented by a single segment of constant diameter. We did the following minor modifications to the AIS geometry: while keeping the original AIS length (21 µm), we changed the AIS diameter (to 1.94 µm) to accommodate for a larger fraction of Nav channels at the AIS.
The model contains Na + , K + , and Ca 2+ conductances with several subtypes for Kv, Cadependent potassium (Kca), and calcium (Ca) channels based on Markovian or Hodgkin-Huxley-like dynamics 2 . It furthermore contains a mixed cationic channel (HCN1) as well as explicit dynamics for the internal calcium buffer 2 . The model for the Nav channel is based on a Markovian state dynamics and accounts for transient, persistent and resurgent Na + -current components 3 . ENa = 75 mV. We kept the same total number of Nav channels as in the original model but distributed them slightly differently to reduce the ratio of somatic to AIS Nav channel density. Peak conductances were: gNav;D = 160 pS/µm 2 in dendrites, gNav;S = 1861 pS/µm 2

Simulation protocols
Modification of AIS morphology. We systematically varied the soma-AIS gap and AIS channel densities as follows. To mimic a finite soma-AIS gap, of length lgap, we set channel densities along this soma-AIS gap to their somatic values and accordingly extended the AIS distally at constant diameter on a length lgap to preserve the total AIS length.

Myelination and demyelination (pyramidal cell). Kole et al. originally mimicked myelination
by reducing Cm to 0.02 µF/cm 2 along the internodal sections 1 . Since effective channel conductances might have to reflect the high resistance imposed by a myelin sheath, we decided to additionally suppress ion channels in myelinated internodes (setting peak conductance values to zero). Conversely, demyelination was mimicked by restoring the internodal membrane capacitance to the default value Cm = 0.9 µF/cm 2 and by setting channel peak conductances to finite values that were determined as follows. Based on the observation that ion channels are redistributed in the membrane of axons upon disorganized nodes of Ranvier in demyelinated MS lesions 4, 5 , we considered peak conductances of demyelinated internodes and within the nodes to be given by the approximate mean value of the respective somatic and node peak conductances: gNav;dem = 106 pS/µm 2 , gKv;dem = 41 pS/µm 2 , gKv1; dem = 22 pS/µm 2 , and gKm; dem = 5.5 pS/µm 2 . Myelination and demyelination (Purkinje cell). In line with the original model, we mimicked myelination by a vanishing Cm and vanishing ionic conductances along the internode. In our study, we mimicked demyelination by restoring the internodal membrane capacitance to the default value Cm = 0.77 µF/cm 2 . We furthermore reduced channel concentrations within the nodes to the average densities between internodes and nodes in myelinated conditions. For Nav, we thus obtained gNav;dem = 13 pS/µm 2 .
Determination of the voltage threshold. Because we were mainly interested in the impact of AIS morphological parameters on the voltage threshold, the procedure used to determine a voltage threshold Vthr for APs recorded in the soma is the following: whenever the time derivative of the somatic voltage dV(t)/dt crosses a fixed threshold c, the voltage threshold is given by the somatic potential at the time tc of threshold crossing, Vthr = V(tc). In the case of multiple threshold crossings, Vthr did not vary between APs. While the absolute values of Vthr depend slightly on the choice of c, the relative variation does not, nor did the number of threshold crossings within a reasonable range. Throughout this study, we used c = 20 mV/ms. Current injection. To elicit stationary firing in the pyramidal cell, a constant current of 0.9 nA was injected in the soma during the simulation. The Purkinje cell was spontaneously active, thus no current was injected.