the gradient estimate and cell rearrangements, suggesting clusters should obey the bound [Eq. ]{}\[eq:snrt\].

We can, using the results of Section \[sec:timeaverage\], predict the cluster chemotactic index, $\textrm{CI} \equiv \langle V_x / |{ {\mathbf V}}| \rangle$, where ${ {\mathbf V}}$ is the cluster velocity. Assuming ${ {\mathbf V}} \sim {\ensuremath{\hat{{ {\mathbf g}}}}_T\xspace}$, we can compute $\textrm{CI}$ from ${\ensuremath{\sigma_{\mathbf{g},T}}}$ given by [Eq. ]{}\[eq:snrt\_simp\] ([*Methods*]{}). This requires parameters $\tau_r$ and $\chi$ (measured from simulations), and ${ {\mathbf g}}$, $T$, and ${\ensuremath{\sigma_{\Delta}}}$ (known). [We note that our approach, which extracts $\tau_r$ and $\chi$ from cell trajectories, could also be applied to experimental data; in that case, ${ {\mathbf g}}$ would still be known, but the extent of time-averaging ($T$) and the error due to CCV (${\ensuremath{\sigma_{\Delta}}}$) would have to be determined by fitting to the data.]{} This prediction should be an upper bound to the measured $\textrm{CI}$, because our model includes additional noise beyond the assumptions of [Eq. ]{}\[eq:snrt\_simp\], via $D_\psi$. As expected, cluster CI decreases significantly as clusters solidify and the relaxation time $\tau_r$ increases. The simulation data qualitatively follows the predicted upper bound ([Fig. ]{}\[fig:kappa\]b). When the averaging time $T$ is reduced below typical relaxation times, the CI significantly decreases. In 