1. Convergence of auditory nerve (AN) fibers onto bushy cells of the ventral cochlear nucleus (VCN) was investigated with a model that describes the electrical membrane properties of these cells. The model consists of a single compartment, representing the soma, and includes three voltage- sensitive ion channels (fast sodium, delayed-rectifier-like potassium, and low-threshold potassium). These three channels have characteristics derived from voltage clamp data of VCN bushy cells. The model also contains a leakage channel, membrane capacitance, and synaptic inputs. The model accurately reproduces the membrane rectification seen in current clamp studies of bushy cells, as well as their unique current clamp responses. 2. In this study, the number and synaptic strength of excitatory AN inputs to the model were varied to investigate the relationship between input convergence parameters and response characteristics. From 1 to 20 excitatory synaptic inputs were applied through channels in parallel with the voltage-gated channels. Each synapse was driven by an independent AN spike train; spike arrivals produced brief (≃0.5 ms) conductance increases. The number (N(S)) and conductance (A(E)) of these inputs were systematically varied. The input spike trains were generated as a renewal point process that accurately models characteristics of AN fibers (refractoriness, adaptation, onset latency, irregularity of discharge, and phase locking). Adaptation characteristics of both high and low spontaneous rate (SR) AN fibers were simulated. 3. As N(S) and A(E) vary over the ranges 1-20 and 3-80 nS, respectively, the full range of response types seen in VCN bushy cells are produced by the model, with AN inputs typical of high-SR AN fibers. These include primarylike (PL), primarylike-with-notch (Pri-N), and onset-L (On-L). In addition, Onset responses, whose association with bushy cells is uncertain, and 'dip' responses, which are not seen in the VCN, are produced. Dip responses occur with large N(S) and/or A(E), and are due to depolarization block. When the AN inputs have the adaptation characteristics of low-SR AN fibers, PL-but not Pri-N or On-L responses-are produced. This suggests that neurons showing Pri- N and On-L responses must receive high-SR AN inputs. 4. The regularity of discharge of the model is compared with that of VCN bushy cells, using a measure derived from the mean and standard deviation of interspike intervals. Regularity is an important constraint on the model because the regularity of VCN bushy cells is the same as that of their AN inputs. Model regularity falls within the range of VCN bushy cell data when A(E) is suprathreshold, but generally does not when A(E) is near or below threshold. This result suggests that bushy cells receive secure synapses, each of which is capable of producing an output without postsynaptic summation of excitatory postsynaptic potentials (EPSPs). 5. Phase locking also constrains the input convergence parameters in the model. At frequencies >1 kHz, the strength of phase locking in the model is similar to that of bushy cells when the model receives suprathreshold inputs; subthreshold inputs give weaker phase locking. Thus the phase locking results agree with the regularity results for high-best-frequency (BF) units. By contrast, at low frequencies (<1 kHz) the model shows bushy-cell-like phase locking (stronger than AN fibers at these frequencies) with all inputs subthreshold, or one suprathreshold input and several (>10) subthreshold inputs: this result suggests that low-BF units receive convergence of many subthreshold inputs. 6. The model accounts well for the characteristics of spherical bushy cells, which receive a small number of large AN inputs. However, it fails to account for the properties of globular bushy cells, which receive a larger number of inputs (as many as 50) and produce Pri-N or On-L responses. To produce these responses, the model needs high-SR inputs, and in order that the spike trains be irregular and phase lock appropriately for high-BF units, the inputs must be suprathreshold. However, under these conditions the model has a very high SR and, with as many as 50 inputs, shows depolarization block and Dip responses. By contrast, many Pri-N and On-L responses have low-rate or no spontaneous activity. 7. An inhibitory input, applied as a constant hyperpolarizing conductance, lowers the model's steady-state discharge rate and SR, prevents depolarization block, and makes the output spike trains more irregular. Dip responses become Pri-N and Pri-N responses become On-L with inhibition. This result suggests that the inhibitory inputs known to exist on VCN bushy cells serve a role in regulating the cell's responses to the large synaptic inputs that they receive.
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