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August - December 201

Data from: High-frequency resonance in the gerbil medial superior olive

A high-frequency, subthreshold resonance in the guinea pig medial superior olive (MSO) was recently linked to the efficient extraction of spatial cues from the fine structure of acoustic stimuli. We report here that MSO neurons in gerbil also have resonant properties and, based on our whole-cell recordings and computational modeling, that a low-voltage-gated potassium current, IKLT, underlies the resonance. We show that resonance was lost following dynamic clamp replacement of IKLT with a leak conductance and in the model when voltage-gating of IKLT was suppressed. Resonance was characterized using small amplitude sinusoidal stimuli to generate impedance curves as typically done for linear systems analysis. Extending our study into the nonlinear, voltage-dependent regime, we increased stimulus amplitude and found, experimentally and in simulations, that the subthreshold resonant frequency (242Hz for weak stimuli) increased continuously to the resonant frequency for spiking (285Hz). The spike resonance of these phasic-firing (type III excitable) MSO neurons and of the model is of particular interest also because previous studies of resonance typically involved neurons/models (type II excitable, such as the standard Hodgkin-Huxley model) that can fire tonically for steady inputs. To probe more directly how these resonances relate to MSO neurons as slope-detectors, we presented periodic trains of brief, fast-rising excitatory post-synaptic potentials (EPSCs) to the model. While weak subthreshold EPSC trains were essentially low-pass filtered, resonance emerged as EPSC amplitude increased. Interestingly, for spike-evoking EPSC trains, the threshold amplitude at spike resonant frequency (317Hz) was lower than the single ESPC threshold. Our finding of a frequency-dependent threshold for repetitive brief EPSC stimuli and preferred frequency for spiking calls for further consideration of both subthreshold and suprathreshold resonance to fast and precise temporal processing in the MSO

High-frequency resonance in the gerbil medial superior olive

A high-frequency, subthreshold resonance in the guinea pig medial superior olive (MSO) was recently linked to the efficient extraction of spatial cues from the fine structure of acoustic stimuli. We report here that MSO neurons in gerbil also have resonant properties and, based on our whole-cell recordings and computational modeling, that a low-voltage-gated potassium current, IKLT, underlies the resonance. We show that resonance was lost following dynamic clamp replacement of IKLT with a leak conductance and in the model when voltage-gating of IKLT was suppressed. Resonance was characterized using small amplitude sinusoidal stimuli to generate impedance curves as typically done for linear systems analysis. Extending our study into the nonlinear, voltage-dependent regime, we increased stimulus amplitude and found, experimentally and in simulations, that the subthreshold resonant frequency (242Hz for weak stimuli) increased continuously to the resonant frequency for spiking (285Hz). The spike resonance of these phasic-firing (type III excitable) MSO neurons and of the model is of particular interest also because previous studies of resonance typically involved neurons/models (type II excitable, such as the standard Hodgkin-Huxley model) that can fire tonically for steady inputs. To probe more directly how these resonances relate to MSO neurons as slope-detectors, we presented periodic trains of brief, fast-rising excitatory post-synaptic potentials (EPSCs) to the model. While weak subthreshold EPSC trains were essentially low-pass filtered, resonance emerged as EPSC amplitude increased. Interestingly, for spike-evoking EPSC trains, the threshold amplitude at spike resonant frequency (317Hz) was lower than the single ESPC threshold. Our finding of a frequency-dependent threshold for repetitive brief EPSC stimuli and preferred frequency for spiking calls for further consideration of both subthreshold and suprathreshold resonance to fast and precise temporal processing in the MSO.23 page(s

Effects of increasing stimulus amplitude on resonant properties.

<p>(A) Increasing stimulus amplitude from 0.1nA to 0.8nA caused sine- to increase both experimentally (individual neurons in grey, average in black) and in model (red). (B) At the same time, the Q factor dropped both experimentally (individual neurons in grey, average in black) and in model neuron (red).</p

Effect of synaptic input on subthreshold and spike resonance in the neuron model.

<p>(A) An example 100Hz sinusoidal stimulus. (B) An example 100Hz train of simulated EPSCs. (C) Comparing subthreshold resonance for sinusoidal and synaptic trains of inputs required normalization of stimulus amplitude as the input threshold for spiking increased from 1.19nA for the sinusoidal input to 1.84nA for the synaptic input. Using excitatory synaptic current inputs (black) led to a larger range of than using sinusoidal stimuli (red) (202Hz to 316Hz for EPSCs compared to 242Hz to 281Hz for sinusoidal stimuli). (Inset i and ii) Impedance profiles for sinusoidal (red) and synaptic (black) stimulus at 0.1 (inset i) and 0.95 (inset ii) normalized stimulus strength demonstrate that the Q factor was consistently larger for sinusoidal stimuli (red curve) compared to EPSCs (black curve) especially at low stimulus amplitudes. (D) Response map combining subthreshold (below 1.84nA) and suprathreshold responses (above 1.84nA) to trains of EPSCs in neuron model. Spike threshold is displayed by the horizontal dashed green line. EPSC- is shown by the red curve; the EPSC- is shown by the green asterisk. Where Q factor was smaller than 1.1 for the subthreshold resonance (<1.4nA), the red line is dashed and the impedance profile is effectively low-pass. The largest EPSC- (316Hz) closely matched the EPSC- for the EPSC trains (317Hz, green asterisk).</p

I_KLT underlies the subthreshold resonance in the gerbil MSO.

<p>(A) Impedance profile of resonant MSO neuron (black circles) displayed high impedance and low-pass properties after 4-AP was applied (red inverted triangles). Adding a simulated g_KLT (dynamic clamp) with voltage-gated parameters (red circles) returned resonance to the neuron; however if the simulated conductance’s gating properties were frozen at resting potential (red righted triangles), the impedance profile shifted down to normal values but low-pass properties remained. (B and inset) Impedance profiles generated with a nonlinear model neuron also demonstrated that I_KLT was necessary for resonance (solid black line). Removing g_KLT altogether (dashed black line) or freezing g_KLT (solid red line) led to low-pass properties. Note that freezing g_KLT also shifted the impedance profile to lower values. (C) Impedance profile for the nonlinear model (solid red line) matched those of a linearized model where the only free parameter was activation of g_KLT (dotted black line). Freezing g_KLT activation gating parameter produced non-resonance (dotted blue line).</p

Subthreshold resonance in gerbil MSO and its origins.

<p>(A) Plot of impedance profiles of resonant medial superior olive (MSO) neuron (black dots) and non-resonant lateral superior olive (LSO) principal neuron (red dots). Arrows on impedance axis represent input resistance of MSO (black arrow, 14.25MOhm) and LSO (red arrow, 59.3MOhm). (A inset) The sine- (212Hz) is shown for the MSO neuron from (A). (B) Graph of sine- versus R_in for all gerbil MSO neurons. Linear regression gave a line of best fit with the following equation: <i>y</i> = −9.31<i>x</i> + 390.2. (C) Q-factor versus sine- for all gerbil MSO neurons. Linear regression gave a line of best fit with the following equation: <i>y</i> = −0.02<i>x</i> + 1.638. (D) Q factor versus R_in for all gerbil MSO neurons. Linear regression gave a line of best fit with the following equation: <i>y</i> = 0.001<i>x</i> + 1.04.</p

Increase in sine- with stimulus amplitude can be explained by differences in I_KLT activation.

<p>(A) Graph of sine- versus stimulus amplitude for a reduced nonlinear model where only <i>w-</i>gating is free (Control voltage-gated <i>τ</i>_w (red); Frozen <i>τ</i>_w (black)). Sine- increased to a maximum of 321Hz at 3nA when <i>τ</i>_w was voltage-gated but plateaued at 254Hz when <i>τ</i>_w was frozen at a <i>V</i>_<i>rest</i>. (B, C) Phase plane representation of dynamical responses (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005166#sec002" target="_blank">Methods</a>). <i>V-w</i>^<i>4</i> phase plane trajectories for 0.1nA (B) and (C) 3nA sinusoidal inputs presented to the reduced nonlinear model above. Stimulus frequencies shown are: 10Hz (green); 245Hz (turquoise); 321Hz (golden) and 1000Hz (black). <i>V</i>-nullcline at rest (solid red) i.e. when <i>I(t)</i> = 0nA; <i>V</i>-nullcline at minimum sinusoidal currents (large dashed red) i.e. when ; <i>V</i> nullcline at maximum sinusoidal current (mixed dash red) i.e. when <i>I</i>(<i>t</i>) = <i>A</i> and <i>w</i>-nullcline (blue).</p

Comparing subthreshold and spike resonant peaks, and regions of spike entrainment.

<p>(A) Example of discrete frequency protocol used to measure suprathreshold responses experimentally. Ten 1.2nA sinusoidal current inputs of increasing frequency (250Hz to 500Hz) were injected somatically into an MSO neuron (amplitude halved in hyperpolarizing direction). (B) Corresponding voltage response of MSO neuron to sinusoidal stimuli in (A). (C) Expanded view of voltage response in (B) to 333Hz sinusoidal stimulus demonstrates the difference between spikes and subthreshold responses (green asterisks). (D) A suprathreshold response map for an example MSO neuron displayed a sine- at 275Hz (green asterisk). The color represents the spike probability per cycle. (E) An equivalently sampled heat map for full, nonlinear model shows a similar asymmetric V-shape and sine- of 280Hz (green asterisk). (F) Response map combining subthreshold (below 1.19nA) and suprathreshold responses (above 1.19nA) to sinusoidal stimuli in full, nonlinear neuron model. Spike threshold is displayed by the horizontal dashed green line. Subthreshold resonance is shown by the red curve; the sine- is shown by the green asterisk. Note that the largest sine- (281Hz) closely matched the sine- (285Hz, green asterisk). (G) The perithreshold sine- and sine- closely matched in both the grouped MSO data (mean in black; individual neurons in grey) and the simulation data (red).</p