Determination of response latency

In order to determine response latency in MT neurons, we developed an automated method to find the latency within a given range. We used this method exclusively in our data from MT neurons in Chapter 7, but it would easily extend to other sources of data gathered using a continuous sequence of random stimuli.

For each neuron, we took the spike train and computed the mean firing rate for each of the 28 stimuli (12 gratings, 12 plaids, 4 blank screens) from time $\Delta$t ms to $\Delta$t$+ 320$ ms. This creates a 320 ms sliding window (equal to the stimulus duration) with a position that can be modified by varying the value of $\Delta$t. Our goal was to position this analysis window such that it best captures the response of each neuron. This can be done by setting $\Delta$t equal to the response latency for that neuron. This would allow the entire neuronal response to be aligned within the 320 ms window.

When $\Delta$t is set at any value other than the response latency, the cell's response is not well aligned with the window used to compute the mean firing rate. If we kept $\Delta$t set to zero, and the true response latency was 100 ms, the neuron would presumably continue to respond for approximately 100 ms after the stimulus changed (420 ms). In this case, much of the neuron's response would fall outside the 320 ms analysis window. Because the stimuli occur in random order, a poor choice for $\Delta$t will tend to bring the mean firing rate for a given interval closer to the average firing rate to all stimuli. As we alter $\Delta$t to move the analysis window closer to the true response latency, the mean firing rate for the preferred stimuli over the window would increase and for the non-preferred stimuli would decrease. So, when the value of $\Delta$t is set to the true response latency, the tuning curve should have the highest possible modulation.

Using this principle, we devised an algorithm to search for the response latency for each cell. We chose values of $\Delta$t over some range, and for each value we computed the tuning curve for the 28 stimuli. We then simply determined the variance of this tuning curve. Specifically, we took the 28 numbers which represented the mean firing rates to each stimulus at that value of $\Delta$t and computed the variance in these 28 values, the average squared difference from the mean. Storing this result, we proceeded to the next value of $\Delta$t. Having computed these variance measures over some range, we plotted them as a function of $\Delta$t. We found that the relationship between $\Delta$t and tuning curve variance was invariably parabolic. This led us to a more efficient searching algorithm.

We used a binary search method, with 20 ms as the lower bound and 200 ms as the upper bound. These numbers were chosen to be below and above the expected latency range for MT neurons. We first coarsely sampled a much larger range to confirm that the latencies for all cells in our population fell within this smaller range. The binary search was set to finish when the next step in the search was less than 2 ms. For approximately one-half of the cells our population, we compared the latency resulting from the binary search with that from a linear search over the same range. These two methods showed an extremely high correlation, never varying by more than a few milliseconds. We therefore used the binary search method, which could achieve the same accuracy within a fraction of the search time.