Analysis of primate IBN spike trains using system identification techniques. III. Relationship to motor error during head-fixed saccades and head-free gaze shifts

The classic model of saccade generation assumes that the burst generator is driven by a motor-error signal, the difference between the actual eye position and the final "desired" eye position in the orbit. Here we evaluate objectively, using system identification techniques, the dynamic relationship between motor-error signals and primate inhibitory burst neuron (IBN) discharges (upstream analysis). The IBNs presented here are the same neurons whose downstream relationships were characterized during head-fixed saccades and head-free gaze shifts in our companion papers. In our analysis of head-fixed saccades we determined how well IBN discharges encode eye motor error (epsilon(e)) compared with downstream saccadic eye movement dynamics and whether long-lead IBN (LLIBN) discharges encode epsilon(e) better than short-lead IBNs (SLIBNs), given that it is commonly assumed that short-lead burst neurons (BNs) are closer than long-lead BNs to the motor output and thus further from the epsilon(e) signal. In the epsilon(e)-based models tested, IBN tiring frequency B(t) was represented by one of the following: I) model lu, a nonlinear function of epsilon(e); 2) model 2u, a linear function of epsilon(e) [B(t) = r(k) + a(1) epsilon(e)(t)] where the bias term r(k) was estimated separately for each saccade; 3) model 3u, a version of model 2u wherein the bias term was a function of saccade amplitude; or 4) model 4u, a linear function of epsilon(e) with an added pole term (the derivative of firing rate). Models based on epsilon(e) consistently produced worse predictions of IBN activity than models of comparable complexity based on eye movement dynamics (e.g., eye velocity). Hence, the simple two parameter downstream model 2d [B(t) = r + b(1)(E) over dot(t)] was much better than any upstream (epsilon(e)-based) model with a comparable number of parameters. The link between B(t) and epsilon(e) is due primarily to the correlation between the declining phases of B(t) and epsilon(e); motor-error models did not predict well the rising phase of the discharge. We could improve substantially the performance of upstream models by adding an (epsilon)over dot(e) term. Because (epsilon)over dot(e) = -(E)over dot, this process was equivalent to incorporating B terms into upstream models thereby erasing the distinction between upstream and downstream analyses. Adding an (epsilon)over dot(e) term to the upstream models made them as good as downstream ones in predicting B(t). However, the (E)over dot term now became redundant because its removal did not affect model accuracy. Thus, when (E)over dot is available as a parameter, epsilon(e) becomes irrelevant. In the head-free monkey the ability of upstream : models to predict IBN firing during head-free gaze shifts when gaze, eye, or head motor-error signals were model inputs was poor and similar to the upstream analysis of the head-fixed condition. We conclude that during saccades (head-fixed) or gaze shifts (head-free) the activity of both SLIBNs and LLIBNs is more closely linked to downstream events (i.e., the dynamics of ongoing movements) than to the coincident upstream motor-error signal. Furthermore, SLIBNs and LLIBNs do not differ in their characteristics; the latter are not, as is usually hypothesized, closer to a motor-error signal than the former.