Excitatory synaptic input to one location

In order to explore the impact of channel noise on neuronal computations, a model of the CN neuron enriched with noisy ion channels (stochastic CN, see Chapter 5) is used and its behaviour is compared to a fully deterministic CN model, under a number of different experimental conditions.

In the first set of experiments, excitatory synaptic input is delivered to the stochastic and deterministic CN models, in different neuronal branches (somatic, proximal and distal) and the Input - Output relationships are identified. Both of the models show similar integration of their excitatory inputs, with distal inputs giving rise to lower firing rates, compared to the somatic and proximal ones, as it is also expected, due to the dendritic signal attenuation and low-pass filtering (London and Häusser, 2005; Papoutsi et al., 2014) (Figure 6.1). The neuronal response of the two models is also similar, indicating not a significant impact of ion channel noise on the mean firing output rate. However, such a model matching should be expected since

the number of the ion channels used per compartment is probably large enough (>100) for the stochastic model to approach the deterministic behaviour (Figure 6.2). Nevertheless, a discrepancy could be observed in the most distal areas of the neuron, where the effect of the stochastic channel-induced noise could be enhanced by the higher input resistance of thinner dendritic branches, but potentially this would take place for smaller number of channels.

Figure 6.1 I-O relationships of CN models for synaptic inputs. The CN neuronal model is stimulated

with 50 synchronous excitatory synapses confined in one dendritic compartment per time, in the presence of ion channel noise (dashed green lines) or not (solid green lines). When synaptic inhibition (450 synapses at 10 Hz) is applied (pink lines), it is distributed along the dendritic tree and soma. Top: Schematic distance map from soma of the distinct synaptic excitatory input locations.

6.2.1.2 Effect of single channel conductance

One of the core differences between the two CN formalisms, is the definition of the total channel specific conductance and consequently, the macroscopic channel current. In the deterministic model, the channel population is considered homogenous in terms of open channel probability, and its total specific conductance is expressed as the product of this total open channel probability and the maximum possible specific channel conductance. On the other hand, in the stochastic model it is assumed that each single channel is governed by its own independent gating probability, and channel conductance is the product of the single channel conductance and the number of open channels per neuronal segment. For a given area, the total number of channels is therefore given by the fraction of the total channel conductance divided by the single channel specific conductance (see Chapter 3). This allows for the experimental manipulation of the total number of a specific channel in a neuronal compartment, by simple changing the value of its single channel conductance (and keeping the total conductance constant).

To investigate if there are any conditions where the ion channel noise could distinguish the behaviour of the stochastic CN neuron, the number of ion channels is decreased by the same factor in all the neuronal subregions, but the total conductance of each channel type is kept the same. In that way, the mean macroscopic current generated by each cannel would be the same, but fewer channels are expected to give rise to more fluctuations in the membrane voltage (Diba et al., 2006; Kole et al., 2006; White et al., 2000). Hence, the integration of the synaptic Figure 6.2 Number per channels type in the stochastic CN model. Left panel: Soma. Right panel:

Dendritic compartments. The type of channels in the dendritic compartments (right panel) corresponds to the colour mapping in the soma bar chart (left panel).

inputs and the neuronal output might be affected, since the channel gating induced voltage fluctuations underlie the variability to the spiking threshold, propagation and timing (Cannon et al., 2010; Diba et al., 2006; Faisal et al., 2008; Kole et al., 2006; White et al., 2000). Moreover, thinner dendrites are expected to have greater voltage fluctuations, because they have a smaller diameter, and thus a greater input resistance. In contrast, larger compartments, like the soma, have a large capacitance, which could act as a filter for membrane fluctuations, and are expected to contain a larger number of channels, resulting in averaging out of the Figure 6.3 I-O relationships of CN models for synaptic inputs, and 100 fewer ion channels per compartment. Same as Figure 6.1, but for 100 times fewer channels per compartment, in the stochastic

random voltage fluctuations (Cannon et al., 2010; Faisal et al., 2005; London and Häusser, 2005).

Still the stochastic CN neuron, even with 100 times fewer channels all over the neuronal compartments, exhibits similar firing rates as the deterministic one, in response to increasing firing rates of the excitatory synaptic input and for all the different synaptic locations (Figure 6.3). To explore in more detail the impact of the ion channel noise, the mean non-spiking membrane voltage and standard deviation are estimated in both models, during the stimulation with excitatory and inhibitory synaptic input. The total mean membrane voltage is similar to the deterministic CN model (Figure 6.4). A smaller number of channels per compartment is predicted to trigger more and steeper membrane fluctuations (Faisal et al., 2008; White et al., 2000). However, when the number of channels is 100 times fewer the standard deviation is still Figure 6.4 Impact of ion channel noise in the non-spiking membrane voltage. The CN neuronal

model is stimulated with 50 synchronous excitatory synapses at 30 Hz, confined in one dendritic compartment per time, in the presence of ion channel noise (dashed green lines) or not (solid green lines). When synaptic inhibition (450 synapses at 10 Hz) is applied (pink lines), it is distributed along the dendritic tree and soma. The spikes were removed by applying median filter with a window of 200 points. Top: Schematic distance map from soma of the distinct synaptic excitatory input locations. Upper panels: Stochastic vs deterministic CN model, without (left panel) or with (right panel) synaptic inhibition. Lower panels: Same, but for 100 times fewer channels per compartment.

Figure 6.5 Impact of ion channel noise in the fidelity of spiking. Samples of voltage traces of the

response of the deterministic and stochastic CN models at (a) soma and (b) 151 μm further form soma. As in Figure 6.4, the CN neuronal model is stimulated with 50 synchronous excitatory synapses at 30 Hz, confined in one dendritic compartment per time. The coloured lines show the spikes removed by applying median filter with a window of 200 points, in the presence of ion channel noise (dashed lines) or not (solid lines). When synaptic inhibition (450 synapses at 10 Hz) is applied (pink lines) it is distributed along the dendritic tree and soma. Top: Schematic distance map from soma of the distinct synaptic excitatory input

at similar levels with the corresponding deterministic (Figure 6.3 and 6.4) Moreover, a stochastic formulation of the ion channels in the CN model introduces some variability in the timing of individual output spikes (Figure 6.5 and 6.6) as indicated also by previous studies (Cannon et al., 2010; Diba et al., 2006; Faisal et al., 2008; Kole et al., 2006; White et al., 2000). Figure 6.6 Impact of ion channel noise in the fidelity of spiking for 100 fewer channels per compartment. Same as Figure 6.5, but for 100 times fewer channels per compartment, in the stochastic

Thus, the level of noise generated by the random ion channel gating in the stochastic CN neuron is not sufficient to cause a change in the firing rate and the behaviour of the model might be dominated by the noisy synaptic input (Destexhe et al., 2014). Yet, the stochastic ion channel gating affects the spike timing. Furthermore, the level of the neuronal response across the different dendritic branches is also in accordance with the expected outcome, namely, the further the location of the excitatory input, the weaker the neuronal activation (London and Häusser, 2005; Papoutsi et al., 2014).