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First published online November 30, 2007
Journal of Experimental Biology 210, 4437-4447 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.010322
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Control of neuronal firing by dynamic parallel fiber feedback: implications for electrosensory reafference suppression

John E. Lewis1,*, Benjamin Lindner2, Benoit Laliberté1 and Sally Groothuis1

1 Department of Biology and Center for Neural Dynamics, University of Ottawa, 30 Marie Curie, Ottawa, Ontario, K1N 6N5, Canada
2 Max-Planck-Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany


Figure 1
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  		Fig. 1. The early electrosensory pathways. The schematic diagram of the ELL sub-network shows two types of principle neurons, deep (DP) and superficial (P) pyramidal neurons, as well as the primary feedback nuclei, nucleus praeminentialis (nP) and eminentia granularis posterior (EGp). The nP and EGp give rise to the direct feedback pathway (not shown) and the indirect feedback pathway (via parallel fibers), respectively. Feedforward input to these nuclei arises primarily from DP neurons; EGp also receives input from other sensory modalities, such as proprioception. The indirect feedback is indicated by a population of parallel fiber synaptic inputs (numbered 1 to Nf) to the P neuron, and combines direct excitation (solid triangles) with disynaptic inhibition via interneurons I (denoted by open circles). Sensory input is faithfully transmitted to parallel fibers via DP neurons and nP. The dynamics of the parallel fiber synapses then determine the sign of the reafferent image onto P neurons (see Results).

 

Figure 2
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  		Fig. 2. Conductance-based model for the parallel fiber synapse. (A) Membrane potential trace for both model (black) and experiment (gray). (B) The predicted PSP amplitudes for the model (normalized to the first PSP in the sequence) are plotted versus those from an intracellular recording of an ELL pyramidal neuron using identical parallel fiber stimulation patterns (poisson-distributed inter-stimulus intervals, 16 Hz mean). Over 200 stimuli, the mean error was 17% (regression line slope=0.98, R2=0.69). Parameter values for the model are as in Table 1, except that Vo= –77 mV.

 

Figure 3
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  		Fig. 3. Dynamic clamp studies showing non-monotonic firing response. (A,B) Example traces from one ELL pyramidal neuron showing membrane potential (black, Vm) and injected current (gray, Im) for two different values of re (5 Hz and 20 Hz). Scale bars are the same for both A and B (40 mV, 0.4 nA, 1 s). (C) Non-monotonic firing response of ELL pyramidal neurons; normalized mean firing rate (mean ± s.d.; 16 neurons) is shown as a function of mean excitation rate, re (binned in 2 Hz increments).

 

Figure 4
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  		Fig. 4. Basis of non-monotonic firing in an LIF model neuron. (A) Changes in FDI model variables with excitation rate, re. FD (black) denotes the product of the facilitation and depression variables and ID (gray) denotes the inhibition variable (see Materials and methods for details). Values plotted are means for 120 independent inputs over 30 s of simulation time. (B) The effective rate of inhibition, ri, as a function of excitation rate, re, for the FDI conductance-based model (solid line); for comparison, the inhibition rate at which excitation and inhibition is balanced is also indicated (dotted line). (C) Mean and (D) standard deviation of the membrane potential in the LIF neuron as a function of excitation rate, re. Also shown are the values resulting from the balanced condition (dotted lines, as in B). (E) Spike rate of the LIF neuron as a function of excitation rate, re, showing non-monotonic response profile; spike rate resulting from the balanced condition is also shown (dotted line, as in B; see Materials and methods for details). Values plotted in C–E are means over 20 simulated trials of 20 s of simulation time for 120 excitatory and 120 inhibitory inputs (standard errors are less than the line width). For all panels, Fo=0.05, with other parameter values provided in Table 1.

 

Figure 5
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  		Fig. 5. Negative image generation in ELL pyramidal neurons (right panels) and LIF model neurons (left panels). Spiking response to 1 Hz sinusoidal modulation of parallel fiber rate, re±5 Hz; denoted schematically in (D). (A–C) Phase histograms as the baseline input rate of the modulation re increases from 10 Hz to 25 Hz. Over this range, the phase histograms in both model and experiment indicate a change from in-phase responses to out-of-phase responses. Histograms were computed for 10 000 spikes in the model, and the combined responses of five pyramidal neurons (individual neuron responses are quantified in Fig. 6). Parameter values are as in Fig. 4.

 

Figure 6
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  		Fig. 6. Quantification of the negative image response as a function of baseline input rate re. (A,B) Phase histograms were quantified in terms of the preferred phase (A) and the vector strength (B). Each panel shows the results for both model (Fo=0.05 in black, Fo=0.2 in gray) and experiment (Fo=0.05, open symbols; mean ± s.d., N=5 neurons). As indicated, a positive preferred phase represents an in-phase response and a negative preferred phase represents an out-of-phase response (i.e. negative image). (C) Similar to Fig. 4E, the firing rate response of the LIF model is shown for Fo=0.05 (black) and Fo=0.2 (gray). Also indicated are the regions of re in which the preferred phases are positive and negative (plus-image and minus-image respectively). Note that this corresponds to the sign of the slope of the non-monotonic response curve. Also note that for intermediate values of re the responses depend on Fo and are characterized by preferred phases of either sign and relatively low vector strength.

 

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© The Company of Biologists Ltd 2007