The role of noise in gain modulation has been thoroughly researched. Both background synaptic noise and the inherently noisy synaptic driving input can contribute to gain changes in I-O relationships (see Chapter 4). In the present study, the modulatory input is synaptic and delivered ubiquitously distributed across the somatic and dendritic area of the neuron. Thus, it could account as a source of background noise too, which could enhance its divisive effect on excitatory input to the distal dendrites.
Thus far, the CN behaviour has been studied with inputs of pure synaptic or pure non- synaptic nature Figure 6.9, 6.10, 6.11 and 6.13). To evaluate the contribution of the synaptic inhibitory modulatory input as a source of background noise to the numerical operations of the CN neuron, different combinations of synaptic and tonic current or conductance inputs are applied to distinct neuronal locations: (a) synaptic excitation as driving input, and somatic tonic inhibition as modulatory input (Figure 6.15 and 6.16), (b) injected current as driving input, and synaptic inhibition as modulatory input (Figure 6.17 and 6.18).
In the first scenario, the modulation of the CN neuron does not follow a similar pattern as if the modulatory input was synaptic, but more as if the neuron was driven by current injections. This behaviour is consistent with the hypothesis that the enhanced change in gain Figure 6.16 Changes in gain (ΔG%) for different neuronal locations in the CN model. As per
Figure 6.10, the CN neuronal model is stimulated in different locations along the somato-dendritic area, either with synaptic driving and modulatory inputs (circles), or, as per Figure 6.15, with synaptic driving and somatic tonic inhibitory conductance (squares). ΔG% is calculated after fitting the simulations’ data (Figure 6.10 and 6.15) to sextic polynomial functions (Rothman et al., 2009). The dotted and dashed lines are linear trend fits, to the data shown in circles and squares, respectively. Mint shapes: soma. Other shapes: dendritic compartments
Figure 6.17 I-O relationships of CN model for current and synaptic inputs. The CN neuronal model
is injected with current steps confined in one dendritic compartment per time (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.
of the I-O function in the distal areas is caused by the nonlinearities introduced by the dendritic saturation, in the presence of a modulatory inhibitory synaptic input (Figure 6.15 and 6.16). However, there is a slight increase in the change in gain, when inspecting it individually at some distal compartments, for instance at 71 μm and 120 μm away from the soma, implying that the variability present at driving synaptic input might contribute to the distant-dependent multiplicative operations (Figure 6.16). Moreover, the synaptic inhibition appears to cause a stronger reduction of the output firing rate, compared to the tonic somatic inhibition (Figure 6.9 and 6.15). The degree of inhibition is not normalized for the two conditions, namely, the degree of the applied tonic inhibition to the soma is not adjusted to produce the same effect as the synaptic inhibition to every location. However, even for a normalized somatic tonic inhibition the activation of synaptic inhibition along the cell is expected to result in greater reduction of, the firing output, because it renders the neuronal membrane leakier.
In the second scenario, the modulation of the CN neuron is different compared to the one when the driving input is synaptic (Figure 6.9 and 6.17). It has been assumed up to now that the change in gain is introduced by dendritic nonlinearities and, hence, driving the neuron with injected current is expected to result in predominantly subtractive operations, independently of the synaptic location and the nature of the modulatory input. Still, the change in gain with modulation by the synaptic input is increased slightly in all the locations, compared to the somatic tonic inhibition, and in accordance when both driving and modulatory inputs are Figure 6.18 Changes in gain (ΔG%) for different neuronal locations in the CN model. As per
Figure 6.10, the CN neuronal model is stimulated in different locations along the somato-dendritic area, either with synaptic driving and modulatory inputs (circles), or, as per Figure 6.17, with driving current steps and synaptic inhibition distributed along the somato-dendritic area (squares). ΔG% is calculated after fitting the simulations’ data (Figure 6.10 and 6.17) to sextic polynomial functions (Rothman et al., 2009). The dotted and dashed lines are linear trend fits, to the data shown in circles and squares, respectively. Mint shapes: soma. Other shapes: dendritic compartments
Figure 6.19 I-O relationships of CN model for synaptic inputs. The CN neuronal model is stimulated
with 50 asynchronous excitatory synapses confined in one dendritic compartment per time (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.
synaptic (Figure 6.10 and 6.18). Therefore, modulatory inhibitory synaptic input can introduce small gain changes in the absence of nonlinearities in the driving input, and it can add to the divisive modulation of the output firing rate originating from the dendritic saturation.
Since, in this experimental configuration, no other known factor could contribute to the gain changes, it is postulated that the intrinsic high variability of the inhibitory synaptic input, in combination with its distribution all over the neuron, serves as background noise, with divisive modulatory effects on the output firing rate (Chance et al., 2002; Hamann et al., 2002; Ly and Doiron, 2009; Mitchell and Silver, 2003). Nonetheless, the combination of synaptic driving and modulatory input results in the largest change in gain, for location further from the soma (Figure 6.9 and 6.10).