Fig 1.
Processing of ITDs by MSO cells and fitting the membrane properties of a simplified MSO model to experimental data.
(A) MSO cells use the time difference for sound to reach both ears (interaural time difference, ITD) to encode the location of a sound source in the horizontal plane. Top: Sound waves arrive at both cochlea and, via several intermediate stages, reach the principal neurons of the MSO nuclei in the brainstem. Bottom left: Fibers arriving from the ipsilateral (blue) and contralateral (green) ear are segregated on the two main dendrites of the principal MSO cells. Bottom right: MSO cell firing activity strongly depends on ITD because of precise coincidence detection of the ipsilateral and contralateral signals. (B) Schematic of minimal model of principal MSO cell. In experiments by Mathews et al. [25] an EPSC current waveform was injected in one dendrite at a distance of 0–100 μm from the soma (“dist soma”) and the voltage attenuation (i.e., the ratio of dendritic amplitude to somatic amplitude) was determined (circles). The experiment was simulated numerically with the default minimal model (solid curve; see Methods). (C) The width of the propagated EPSP at soma at halfmaximal amplitude as determined by experiments [25] (circles) and from numerical simulations of the default minimal model (solid curve). (D) Somatic input resistance determined in experiments [25] and from numerical simulations of the default model under control conditions (left) and with KLT blocked (right). (E) Densities for the leak conductance and KLT peak conductance were varied from 0.2 to 10 mS/cm2 and from 1 to 40 mS/cm2, respectively, and the sum squared error for EPSP attenuation, somatic EPSP halfwidth and input resistance was computed. The parameter combination with the lowest fitting error (open circle) was used for the default model. Panels B and C were adapted with permission from Fig 2 in ref. [25].
Fig 2.
Quantifying MSO cell model performance and energy consumption.
(A) Voltage and membrane currents of minimal MSO model in response to 500 Hz pure tone sound wave. Synaptic conductances to the left, ipsilateral (blue) and right, contralateral (green) dendrite are phase-locked to the sound wave, which creates an ITD of 0.5 ms. Somatic (black curve) and axonal (orange) voltages and the total cell membrane currents fluctuate at 500 Hz in response to the synaptic input. Total sodium membrane currents (i.e., summed across entire cell) resulting from leak (dark blue) and synaptic input (light blue) as well as the total potassium currents resulting from IKLT (purple), leak (red) and synaptic input (orange) are shown. Model uses default parameters as defined in the Methods. (B) Firing rate of default cell model in response to a 5 s soundwave for a range of ITDs. Maximal firing rate at ITD = 0 ms (r0) and firing rate at ITD = 0.5 ms (r0.5) are marked. (C) Firing rate at ITD = 0 ms (r0, solid black curve) and ITD = 0.5 ms (r0.5, dashed curve) are shown when the synaptic peak conductance varies from 3 to 300 nS. Difference between the two curves (gray area in top panel, gray curve r0 − r0.5 in bottom panel) gives the rate modulation (“Rate mod.”) for the default model as a function of synapse strength. Maximal rate modulation is marked by open circles. (D) Time-averaged total cell membrane currents (summed over entire cell, see bottom panel in A), averaged for a 5 s pure tone sound wave stimulus with ITD = 0 ms.
Fig 3.
Length of MSO cell dendrites impose a trade-off between performance and energy consumption.
(A) Performance (i.e., maximal rate modulation, see Fig 2C; black curve) and energy costs (blue curve) as a function of dendrite length. Stimulus is a 5 s pure tone stimulus of 500 Hz. Default dendrite length is indicated by vertical gray bar. (B) Somatic EPSP halfwidth (black curve) and dendritic saturation (red curve), defined as the peak dendritic voltage normalized by its absolute maximum amplitude (i.e., Erev−Vrest = 60 mV). (C) Simulation setup to obtain EPSP halfwidth and dendritic saturation. Voltage is measured in dendrite (red) and soma (black). All synaptic inputs are activated simultaneously with a strength that gives a 10 mV EPSP at the soma (dotted line). Amplitude of the local dendritic response (dash-dotted line) and halfwidth of the somatic EPSP (dashed line) are measured. (D) Somatic EPSP traces are shown for three levels of dendritic saturation (top) and the somatic EPSP halfwidth is shown for the full range of dendritic saturation (bottom). Simulations use the default model; different levels of saturation are achieved by varying synaptic strength, leaving all model parameters constant. (E) Probability distributions of somatic voltage during 5 s simulations with ITD = 0 ms and ITD = 0.5 ms for the default model with a dendritic length of 185 μm (top) or 360 μm (bottom).
Fig 4.
Trade-offs between performance and energy costs when cell morphology and membrane parameters are varied.
(A)-(E). Performance (black curves) and energy costs (blue curves) as a function of dendrite diameter (A), soma surface area (B), leak density (C), KLT density (D) and KLT activation time constant (E). Default model parameters are indicated by vertical gray bars. Stimulus is a 5 s pure tone stimulus of 500 Hz. (F) Data from panels A-E and Fig 3A plotted in the energy costs versus performance space. Performance is plotted as its reciprocal value, such that the lower, left corner gives the optimal model with high performance and low energy consumption. Default model is depicted by open star, and the pareto boundary that combines all optimal models as a thick gray curve.
Fig 5.
Membrane channel densities allow an improved performance and cell size allows for energy reduction.
(A) Energy cost is plotted against reciprocal performance for the default model for parameter combinations where leak density is varied from 0.2 to 10 mS/cm2 and KLT density from 0.2 to 40 mS/cm2. Dashed curve indicates best models (i.e., best performance for a given energy consumption level) that maintain a resting potential at −60 mV (see Methods). Five curves depict models with a fixed leak density (0.35, 0.8, 1.4, 2.5, 4.3 mS/cm2) and range of KLT densities. Default model is depicted by open star. Arrow on abscissa indicates performance of a point neuron model with leak-KLT combination that gives it the best performance. Simulations consist of responses to 5 s long pure tones of 500 Hz. (B) Energy cost is plotted against reciprocal performance for combinations of dendrite diameter and dendrite length that give a constant dendrite surface area. Surface area is equal to the control (black curve; see Methods), twice the control (blue curve) or half the control (red curve). Models with short, thick dendrites are at the bottom right, and models with long, thin dendrites are at the top of the energy costs-performance space. Default model is depicted by open star. Simulations consist of responses to 5 s long pure tones of 500 Hz.