| Summary: | Dendrites of many neuron types exhibit complex morphologies and spatially modulated ionic channel compositions that generate non-trivial integrative properties (Major et al., 2013). These have been described as cascades of linear filters and static nonlinearities (Häusser and Mel, 2003; Larkum et al., 2009). Iso-response methods (see Gollisch and Herz, 2012) provide an alternative approach to understanding the intricate, nonlinear computations in dendrites, while making fewer prior assumptions.
Within an iso-response approach, inputs to a dynamical system are varied such that a chosen output measure stays constant. These stimuli define lower-dimensional “iso-response manifolds” whose shape directly reflects the stimulus interaction, regardless of any further nonlinearity that acts on the combined signal. The output measure can range from the neuron’s firing rate (Gollisch et al., 2002) or the probability of a single spike (Gollisch and Herz, 2005) to first-spike latency or even a spike’s phase with respect to some ongoing brain rhythm.
As an example (Fig. 1), take a 2D stimulus space parameterized by x1 and x2; the curved surfaces represent the response r(x1,x2) for two alternative models, which take the quadratic (a) and the linear sum (b) as the argument of a sigmoidal nonlinearity. The two scenarios are fundamentally different but generate identical one-dimensional responses. In addition, measurements along radial directions produce similar response curves, as shown by the black lines running along the surfaces. Iso-response curves (r=const), drawn as projections below the surface plots, however, reveal the different underlying processes.
Using detailed multi-compartment models, we here show three examples of how the iso-response framework aids in understanding dendritic computations: First, in a pyramidal cell model (Poirazi et al., 2003), we find (Fig. 2) that, in terms of the membrane potential at the soma, activation of synapses on two selected dendritic compartments can give rise to linear (b) as well as curved iso-response lines (a,c). Notably, even inputs to spatially separated compartments (a) can be integrated more non-linearly than nearby inputs (b). Long-range nonlinear interactions are facilitated by local dendritic spikes, which are easily elicited in distal compartments.
Second, we find that while the dendritic locations strongly influence the signature of nonlinear interactions, it is less sensitive to changes in the level of background synaptic activity.
Finally, we stimulate a Purkinje cell model (de Shutter and Bower, 1994) with a constant input, resulting in regular spiking. We define the output as change in spike timing caused by activating two synapses at different dendritic locations and phases of the regular oscillation. For a large number of parameters we find that the dendrite performs a temporal max-operation on the inputs).
These results demonstrate that iso-response methods are well suited to unravel complex dendritic computations in model neurons and that they can provide a powerful tool for experimental research with applications in multi-patch or optogenetic recordings.
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