A greater rate of change in spike rate for motion in the preferred relative to null direction arises because the response (driven rate of firing) to 0% coherent motion (
R0%) is typically closer to the response to 100% coherent null direction motion (
\({R_{{N_{100\% }}}}\)) than to the response to 100% coherent preferred direction motion (
\({R_{{P_{100\% }}}},\;\)Figure 1B). Normalization dictates that a neuron's
R0% will be the average of its responses across the full range of directions. This average will depend on the width of the neuron's direction tuning. When direction tuning is extremely narrow, the average response across all directions approaches
\({R_{{N_{100\% }}}}\). Conversely, when direction tuning is extremely broad, the average response across all directions approaches
\({R_{{P_{100\% }}}}\). If we assume MT direction tuning follows a Gaussian function then:
\begin{eqnarray*}
{R_{0\% }} &\;=& \frac{{\sigma \left( {{R_{{P_{100\% }}}} - {R_{{N_{100\% }}}}} \right)}}{{\sqrt {8\pi } }}\\
&& \left[ {erf\left( {\frac{\pi }{{\sqrt 2 \sigma }}} \right) - erf\left( {\frac{{ - \pi }}{{\sqrt 2 \sigma }}} \right)} \right] + {R_{{N_{100\% }}}},\end{eqnarray*}
which is the average response over the range ±180°. Because
R0% is the average of the response function it is independent of the spontaneous rate of firing (
m,
Figure 1B), but it will depend on the width of the tuning curve (σ).
Albright (1984) measured the direction tuning of monkey MT neurons using dynamic random dots and found an average tuning width corresponding to σ = 36°.
Britten and Newsome (1998) similarly found an average tuning width of σ = 39°. These values yield
R0% equal to 0.25 and 0.27 times
\({R_{{P_{100\% }}}}\), implying a roughly 3:1 difference in the change in rate of firing for neurons preferring the drift direction and the opposite direction when coherence changes. This ratio is slightly less than the values reported by
Britten and colleagues (1993), who found the
R0% to be 0.20 times
\({R_{{P_{100\% }}}}\) on average in MT, and a 3.5:1 difference in the change in rate of firing for neurons preferring the drift direction and the opposite direction.