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. 2023 May;51(2):283-298.
doi: 10.1007/s10827-023-00849-9. Epub 2023 Apr 14.

Responses in fast-spiking interneuron firing rates to parameter variations associated with degradation of perineuronal nets

Kine Ødegård Hanssen  1   2 , Sverre Grødem  3   4 , Marianne Fyhn  3   4 , Torkel Hafting  3   5 , Gaute T Einevoll  6   3   7 , Torbjørn Vefferstad Ness  3   7 , Geir Halnes  3   7
Affiliations

Responses in fast-spiking interneuron firing rates to parameter variations associated with degradation of perineuronal nets

Kine Ødegård Hanssen et al. J Comput Neurosci. 2023 May.

Abstract

The perineuronal nets (PNNs) are sugar coated protein structures that encapsulate certain neurons in the brain, such as parvalbumin positive (PV) inhibitory neurons. As PNNs are theorized to act as a barrier to ion transport, they may effectively increase the membrane charge-separation distance, thereby affecting the membrane capacitance. Tewari et al. (2018) found that degradation of PNNs induced a 25%-50% increase in membrane capacitance [Formula: see text] and a reduction in the firing rates of PV-cells. In the current work, we explore how changes in [Formula: see text] affects the firing rate in a selection of computational neuron models, ranging in complexity from a single compartment Hodgkin-Huxley model to morphologically detailed PV-neuron models. In all models, an increased [Formula: see text] lead to reduced firing, but the experimentally reported increase in [Formula: see text] was not alone sufficient to explain the experimentally reported reduction in firing rate. We therefore hypothesized that PNN degradation in the experiments affected not only [Formula: see text], but also ionic reversal potentials and ion channel conductances. In simulations, we explored how various model parameters affected the firing rate of the model neurons, and identified which parameter variations in addition to [Formula: see text] that are most likely candidates for explaining the experimentally reported reduction in firing rate.

Keywords: Capacitance; Fast-spiking interneurons; Firing rate; Multicompartment models of neurons; PV cells; Perineuronal nets.

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Conflict of interest statement

The authors have no competing interests to declare.

Figures

Fig. 1
Fig. 1
Fast-spiking interneurons without perineuronal nets show reduced firing rate in experimental data from Tewari et al. (2018). Recordings were made from brain slices from mice injected with the following: Sham - phosphate-buffered saline, GBM14 - Non-glutamate releasing tumor, GBM22 - Glutamate-releasing tumor. Measurements were made on a minimum of seven neurons for each injection type. The tumors were shown to break down PNNs in their proximity. Firing rate f is plotted against input current I. The decrease in f was 38% from Sham to GBM22 and 41% from Sham to GBM14, as measured for the highest input current in the figure. The data were provided by Tewari et al. (2018)
Fig. 2
Fig. 2
Properties of the neuron model as a function of specific membrane capacitance cm. cm0 is the default value of cm in the model. A Voltage trace for Allen model 1 for default cm and 1.5cm. Inset: normalized voltage trace over the duration of one peak. The two traces have been shifted to align the peak maxima, B Threshold current vs cm, C Frequency f vs cm for all models for input current I = 0.2 nA, D f vs cm for the Allen models for I = 0.4 nA, E Spike duration (defined as the width of the spike at -40 mV) for I = 0.2 nA, F Spike duration at -40 mV for I = 0.4 nA. Note that the one-compartment model and the ball-and-stick model do not fire for I=0.4 nA. OC - one-compartment model, BAS - ball-and-stick model, A1 - Allen model 1, A2 - Allen model 2, A3 - Allen model 3, all - cm changed at every segment of the neuron, sprx - cm only changed at the soma and proximal dendrites
Fig. 3
Fig. 3
Frequency-input curves for selected values of cm for the various models. cm is altered in the soma and proximal dendrites. A The one-compartment Hodgkin-Huxley model, B The ball-and-stick Hodgkin-Huxley model, C Allen model 1, D Allen model 2, E Allen model 3, F The relative difference in f between the 1.0cm- and 1.5cm curves computed at the largest current that gave sustained firing in both cases
Fig. 4
Fig. 4
Frequency-input curves when varying the different reversal potentials in the Allen models. Note that the reversal potential of calcium in the Allen models was found using calcium dynamics together with Eq. (4), so ECa is given at t=0 ms and will vary throughout the simulations
Fig. 5
Fig. 5
Frequency-input curves when varying different conductances in Allen model 1. g¯X is the default value of the conductance. A g¯CaHVA, B g¯CaLVA, C g¯NaV, D g¯Kv3, E g¯Kv2like, F g¯SK, G g¯Kd, H g¯Imv2, I g¯KT, J g¯h, K g¯L
Fig. 6
Fig. 6
Frequency-input curves of Allen model 1 when varying cm and A ENa, g¯Kv2like and g¯SK, B ECa(t=0) and g¯SK, C ECa(t=0), g¯Kv2like and g¯SK, D g¯Kv2like and g¯SK, E ECa(t=0), ENa, g¯Kv2like and g¯SK, F Relative difference between each parameter combination and default at the largest current that gave sustained firing in both cases. The horizontal dashed line indicate the relative difference between f of Sham and GBM22 in Tewari et al.’s experiments. The difference between Sham and GBM14 is a bit larger. Default - default values, ENa=53 mV and ECa(0)=131.06 mV. For the altered models, ENa=63 mV and ECa(0)=161.53 mV, cm is increased by a factor 1.5 and the conductances are indicated in the legend
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