Dendritic saturation introduces nonlinearities

The I-O function maps the neuronal response (output) onto the driving (input). However, prior studies have shown that dissecting further this relationship, to intermediate mappings that examine the relationship of input and output, with for example the excitatory conductance, can reveal where nonlinearities are introduced. For example, a nonlinear relationship between the presynaptic input firing rate and the time-averaged excitatory synaptic Figure 6.12 Changes in gain (ΔG%) for different neuronal subregions in the CN model. As per

Figure 6.11, the CN neuronal model is stimulated in different subregions with synaptic driving and modulatory inputs. ΔG% is calculated after fitting the simulations’ data (Figure 6.11) to sextic polynomial functions (Rothman et al., 2009). The distinct colours in the bars correspond to the ΔG% in the different neuronal subregions (Figure 6.11).

driving conductance underlies STD-dependent gain modulation (Rothman et al., 2009), while the nonlinear mapping between the excitatory dendritic conductance and the output firing rate caused by dendritic saturation enhances the divisive effect of shunting on the output firing rate (Prescott and De Koninck, 2003). Since the divisive modulation by inhibition in the CN model is more evident in the distal compartments, a hypothesis could be that the nonlinearity caused by dendritic saturation underlies the observed change in gain when the inhibitory modulatory input is applied.

As a first step to test this hypothesis, the relationships of the excitatory input rate to the excitatory conductance, and of the output firing rate to the excitatory input conductance are examined for two different locations, one proximal to the soma, and a very distal one (Figure Figure 6.13 Breaking down the I-O relationship in the CN model. The I-O function of the CN model

is analysed further for different dendritic locations (upper panels: 24 μm and lower panels: 151 μm) by investigating the relationships between neuronal output firing rate, synaptic excitatory conductance and synaptic excitatory input rate. The CN neuronal model is stimulated in different subregions with synaptic driving and modulatory inputs, as in Figure 6.9. Left panels: Mapping of excitatory input rate to excitatory input conductance. Right panels: Mapping of excitatory input conductance to output firing rate. Top: Schematic distance map from soma of the distinct synaptic excitatory input locations.

Figure 6.14 I-O relationships of CN model for non-synaptic inputs. The CN neuronal model is

injected with current steps confined in one dendritic compartment per time (green lines). Tonic inhibitory conductance (9 nS) is applied (pink lines), at the soma. Top: Schematic distance map from soma of the distinct synaptic excitatory input locations.

6.13). The first mapping (excitatory input rate to excitatory input conductance) exhibits a linear relationship, independent of the presence of the modulatory input, and of the location tested. Such a result is expected, because the excitatory input conductance is direct outcome of the activation of the excitatory synapses at the given excitatory input rate, and unaffected by the delivery site or the presence of inhibition. The second mapping (excitatory input conductance to output firing rate) has a different profile for the proximal and distal location. For the proximal location, the relationship between input conductance and output rate is linear, and the effect of the excitatory input conductance is attenuated by the modulatory input in an approximately subtractive manner. In the case of the distal location, however, a nonlinearity introduced in the excitatory synaptic conductance - output firing rate relationship, resembling is the one caused by dendritic saturation (Prescott and De Koninck, 2003).

The source of the dendritic saturation is a combination of the proportionally increased leakiness of the dendrites, when conductance is added, and the input current driving force, that is, the difference between membrane potential and excitatory synaptic reversal potential, which is reduced with strong depolarization. Increasing excitatory input firing rates for thinner dendrites are saturated faster than for thicker ones, due to the higher input resistance of thinner dendrites that causes larger membrane depolarizations and reduces the driving force (London and Häusser, 2005; Papoutsi et al., 2014). Therefore, increasing excitatory input to a distal dendrite has a gradually diminishing (and eventually negligible) effect on the output firing rate, resulting in the nonlinear relationship between the excitatory synaptic conductance and output firing rate (Prescott and De Koninck, 2003).

In order to investigate further the effect of dendritic saturation on the multiplication of dendritic inputs, a series of experiments is carried out where the CN neuron is driven by a depolarizing injected current to individual compartments and modulated by a tonic inhibitory conductance step in the soma. Voltage changes in response to injected current are independent of the driving force that affects conductance-based inputs and consequently, the output firing rate of the neuron is not affected by underlying dendritic nonlinearities.

The modulation of the I-O function, resulting from the mentioned current-based experimental protocol, for all locations along the somato-dendritic axis is mainly subtractive (Figure 6.14). The resulting change in gain is very small and independent of the distance from the soma, confirming further this result (Figure 6.10). The divisive modulation of inputs to the distal areas that has been observed for synaptic conductance-based inputs has almost vanished,

Figure 6.15 I-O relationships of CN model for synaptic and tonic inhibitory inputs. The CN

neuronal model is stimulated with 50 synchronous excitatory synapses confined in one dendritic compartment per time (green lines). Tonic inhibitory conductance (9 nS) is applied (pink lines), at the soma. Top: Schematic distance map from soma of the distinct synaptic excitatory input locations.

suggesting that the dendritic saturation is indeed the underlying gain modulation mechanism, as in previous studies (Prescott and De Koninck, 2003).