Fig 1.
Blue filled circles represent model neurons. Blue empty circles indicate inputs to model neurons. Red bullet-headed connections are inhibitory and blue arrow-headed connections are excitatory connections from inputs to neurons and from neurons to other neurons, respectively. Top right corner is a enlarged view on the synaptic connections of an LSO neuron. The output of such a neuron modulates its afferent connections.
Table 1.
Model parameters.
Fig 2.
Input generation and parameter influences.
(A) Input generation for the model system for ILD calculation. Red line shows excitatory input from cells of the ipsilateral cochlear nucleus to LSO neurons. Blue line shows excitatory input from cells of the contralateral cochlear nucleus to MNTB neurons which are converted to inhibitory input to LSO neurons. Vertical grey dashed lines indicate measurement points of neuron’s response. (B) Model response of an LSO neuron for a default set of parameter values. Blue line shows the response rate of a single LSO neuron to stimuli as presented in (A) over interaural level difference. The ILD is determined by subtracting the level of the ipsilateral stimulus from the level of the contralateral stimulus. Inset shows membrane potentials for LSO (activity r, red) and MNTB (activity q, blue) neurons. Probing times (grey dashed lines) are chosen to ensure that both membrane potentials have reached a steady state before measuring. These states can be identified by horizontal plateaus in the display where the membrane potential is constant. (C,D) Model response for parameter values γr and κr, respectively. (C) Parameter values of γr are varied in range [0.0, 3.5] which control the strength of subtractive inhibition. (D) Model responses for different κr values in range [0.0, 14] that regulates the effect of shunting inhibition on the membrane potential. Filled areas are approximated from simulation results.
Fig 3.
Effectiveness of GABA receptor on LSO response.
(A) Adaptation range of model LSO neuron for inverse GABAb receptor effectiveness. Parameters λE and λI describe the inhibition effectiveness on excitatory and inhibitory inputs respectively. Normal (dark blue line) and shifted (light blue line) responses are shown. For λE = λI = 0 the ILD response curve is the same as the default response (Fig 2B) and no dynamic adaptation process takes place. For λE = 0.70 and λI = 1.0 (inverse ratio) the response curve’s slope and consequently its sensitivity is decreased while the dynamic coding range is increased. (B) Adaptation range of model LSO neuron for increasing parameter values. Normal (dark blue line) and shifted (light blue line) responses are shown. Again, for λE = λI = 0 the ILD response function is similar to the default response. Light blue area indicates the adaptation range. (C) Exhaustive parameter evaluation of the GABA parameters λE, λI. Each point in the heat map indicates the coding precision value for a certain combination of λE (abscissa) and λI (ordinate). We assume that the neuron’s task is to achieve a preferably high coding precision value. Black dots depict these values (the maxima of the map). A linear function (dashed line) was fitted to those points and the slope (m = 0.80) and bias (b = − 0.06) calculated. (D) Influence of model parameters κr and γr on the gain (left panel) and bias (right panel) of the linear regression.
Fig 4.
Left column: stimuli and results of the adapter tone experiment 3. Right column: results of the timing experiment 4. (A) input stimulus example for Experiment 4. The first ridge depicts the ILD of the adapter tone with a duration of 1.2s followed by a break of 500ms. The second ridge shows the ILD of the actual test stimulus. Differently shaded areas illustrate different test stimulus ILDs for the same adapter tone. Grey dashed line marks 0dB ILD. (B) Responses of model neuron to different adapter tone intensities. Blue 40dB, orange 20dB, green 0dB and constant test stimulus intensity (40dB). The response of the neuron to an adapter tone sound level of 40dB (blue line) is maximal. However, the responses to the consecutive test stimuli is reduced through adaptation i.e. the higher the ILD of the adapter tone the lower the response to the test stimulus. (C) Response of a single LSO neuron to stimuli of constant ILD after the presentation of various adapter tone ILDs. Light blue dashed line depicts the response to a test stimulus of ILD 40dB after presenting an adapter ILD of 0dB. Dark blue line draws the response to the same test stimulus after presenting an adapter ILD of −40dB. No adaptation takes place and the response is similar to the default response of the neuron (compare Fig 2B). Light blue line draws the attenuated response to the same test stimulus after presenting an adapter ILD of 40dB. (D) Responsiveness of LSO neuron for different ILDs over ITDs. The blue line indicates the neuron response for 0dB level difference, the darker blue area shows possible responses for higher ILD values, whereas the light blue area indicates possible responses for negative ILD values. The depicted ILD range is limited to −20dB and + 20dB for a clearer plot. Note the u-shape (dark blue) and v-shape (light blue) response curves. (E) Neuron responses over various ITD and ILD values. (F) Adaptation range of model LSO neuron for various ITDs of the input signals. Light blue line and corresponding filled area indicates model response for stimuli with positive ITDs. Dark blue area shows responses for stimuli with negative ITDs. Area filled with blue is inferred from simulation results.
Fig 5.
Comparison of coding precision between GABA and ITD induced adaptation.
Green lines indicate the coding precision of the adapter tone experiment (no. 3). The peak of the coding precision curve is shifted by a maximum of 6dB for increased adapter tone intensity and gains an sensitivity increment of 53%. Blue lines depict the coding precision of the timing experiment (no. 4). The peak of the coding precision curve is shifted by a maximum of 38dB between stimuli of different ITDs. The increment of sensitivity for this shift is 106% but is dramatically decreased.