  When a single cell senses a chemical gradient and chemotaxes, stochastic
receptor-ligand binding can be a fundamental limit to the cell's accuracy. For
clusters of cells responding to gradients, however, there is a critical
difference: even genetically identical cells have differing responses to
chemical signals. With theory and simulation, we show collective chemotaxis is
limited by cell-to-cell variation in signaling. We find that when different
cells cooperate the resulting bias can be much larger than the effects of
ligand-receptor binding. Specifically, when a strongly-responding cell is at
one end of a cell cluster, cluster motion is biased toward that cell. These
errors are mitigated if clusters average measurements over times long enough
for cells to rearrange. In consequence, fluid clusters are better able to sense
gradients: we derive a link between cluster accuracy, cell-to-cell variation,
and the cluster rheology. Because of this connection, increasing the noisiness
of individual cell motion can actually increase the collective accuracy of a
cluster by improving fluidity.
