1HST.723 Joseph Feingold May 5, 2001 Lab 4: Compartmental Model of Binaural Coincidence Detector Neurons Sim1: Threshold of intracellular current injections Hypothesis: We should not see any spikes until reaching a threshold current, whereupon spiking should begin immediately, as an all-or-none event. The figure shows three voltage traces, produced with Iinjected = 1, 1.5, and 2 nA, from top to bottom, respectively. While the dashed line represents the threshold chosen in this model, it is apparent from the traces that the size of the modeled spike can vary, contrary to the biological evidence, according to which a spike is an all-or-none event. The model is thus only an approximation, albeit a fairly good one, to the true non-linear mechanism underlying spike generation. For less than 1 nA we did not see any significant spikes crossing the threshold, and for more than 1.5 nA, the generated spike ceased growing with increasing current (except for physiologically ludicrous currents), suggesting a minimum value for the injected current (rheobase) of 1.5 nA. However, since the threshold was chosen on the basis of physiological evidence, 1 nA appears sufficient for generating a “spike” (defined by the chosen threshold). Notice that regardless of how large the applied current gets, repetitive spiking is not observed. This results from the particular ionic channels chosen in the model. It is interesting, in this regard, to see that the membrane voltage never quite returns to its baseline. Instead, it eventually settles to a slightly depolarized state, as a consequence of the continuously applied current. This might make it more difficult to push the cell toward action potential once again, perhaps by changing some ionic conductance, and could help explain the lack of repetitive firing. Insofar as no synaptic input was required to obtain these results, we did not need to use the compartmental model to run this simulation. Sim2: Effect of synchronization index of the CN inputs Hypothesis: “With pure tone stimuli, the synaptic inputs must be phase-locked for the coincidence detector to operate.” As instructed, we covaried the conductance with the vector strength (VS), to reduce the order of magnitude differences in rate among the different IPD tuning curves, in order to allow us to make more meaningful comparisons among them. The peak normalized firing rate at zero IPD, for each VS value, clearly illustrates the action of a coincidence detection mechanism, requiring the input signals to reach the soma within a certain window, if they are to cause any appreciable firing. Furthermore, the figure shows pretty nicely the increased IPD tuning with increasing VS. For high VS (e.g., 0.9), firing essentially vanishes for IPD values larger than about 80 degrees, as opposed to lower VS (e.g., 0.5), for which the firing rate drops off farther out toward 130 degrees. The idea here is that for larger VS values, the PSTH of a given input is narrower, so that the input tends to fire at a fairly consistent time during a stimulus period. As VS decreases, however, the PSTH of each input spreads out, resulting in overlapping firing of different inputs, even in the absence of true coincidence among the inputs. This causes the MSO neuron to “misfire” (that is, fire at a higher rate for a less-coincident set of2inputs than it would were the inputs more synchronized) —giving broader IPD tuning with decreasing VS, as shown. The lower plot reveals the high synchrony of the output of the modeled NL cell, for a large range of IPD values, which is in stark contrast to the sharp peak seen in the upper plot, representing the input synchrony as discussed above. This broad region of high synchrony stems from the cell’s function as a coincidence detector, so that, at least for a range of IPD values, the cell will fire in sync with the stimulus. The particular range depends on the IPD tuning of the cell, as this determines the degree to which the cell’s firing corresponds to coincident inputs derived from the actual stimulus, as opposed to random coincidences. As the IPD values increase, the output synchrony falls to zero, roughly where the rate itself falls (in the upper plot), so that for IPD = 180 degrees, there is no synchrony in the output and no firing. Unfortunately, this doesn’t appear to hold for the lowest VS (0.3), in which case, though the firing rate does decrease to near zero for the out-of-phase condition, the output synchrony remains at around 1 over the whole range of IPD. I can only suggest that we see this at very low VS because the IPD tuning is so broad that the firing rate does not decrease enough. But it could just be that at low VS, this model isn’t working so well (recall that we had to covary the conductance to get the maximal rates somewhat closer in order of magnitude even before normalizing!). Sim3: Effect of number of synapses per dendrite Hypothesis: IPD tuning should scale with the number of synapses. The underlying idea here is that the sharpness of IPD tuning reflects the degree of coincidence required to make the NL cell fire. This being the case, the cell’s IPD tuning ought to improve if its inputs fire in sync with the stimulus. To reduce the probability that less synchronous input activity will successfully drive the firing of the cell, we can average the inputs. This can be achieved by increasing the number of inputs, while concomitantly reducing the conductance of each synapse, to maintain constant overall synaptic strength. Whereas with only a few inputs, random input firing or synaptic jitter can cause the cell to fire erroneously, with larger numbers of weaker inputs, such random noise is averaged out, increasing the likelihood that the cell fires in response to coincidence related to the actual stimulus. Though they are not shown, the individual voltage traces revealed a marked decrease in firing rate as the number of synapses increased, suggesting that such an averaging was, indeed, taking place. The results shown in the figure are not, however, too convincing. While there does appear to be some sharpening of IPD tuning when the number of synapses increases from 5 to 10, the added benefit is not so evident from 10 to 20, and only occurs for large IPD values when the number is increased from 20 to 40. The reality of the situation may then be that there is some optimal number of synapses that gives