fluidity.

Gradient sensing error is dominated by cell-to-cell variation, not receptor noise
=================================================================================

![image](fig1again.png){width="180mm"}

We study a two-dimensional model of gradient sensing with CCV and ligand-receptor dynamics where cells sense a chemoattractant with concentration gradient ${\ensuremath{{ {\mathbf g}}}\xspace}$. Each cell at position ${\ensuremath{{ {\mathbf r}}}\xspace}$ measures local concentration, $c({\ensuremath{{ {\mathbf r}}}\xspace}) = c_0 (1 + {\ensuremath{{ {\mathbf g}}}\xspace}\cdot {\ensuremath{{ {\mathbf r}}}\xspace})$, via ligand-receptor binding, which is stochastic. This noise leads to unavoidable errors in the cluster’s estimate of ${\ensuremath{{ {\mathbf g}}}\xspace}$. In addition, even if concentration is perfectly sensed, each cell responds differently to a fixed $c$, which models known CCV in signal response [@wang2012diverse; @samadani2006cellular]. As a result, when the cluster combines measurements from its cells, it may develop a drift in the direction of stronger-responding cells ([Fig. ]{}\[fig:ccv\_illus\]). To combine these effects, we specify the “measured” signal in cell $i$, $M_i$, which is what the cluster believes the chemoattractant signal in cell $i$ to be, including ligand-receptor binding and CCV: $$M^i = \left[c({\ensuremath{{ {\mathbf r}}}\xspace}^i) + \delta c^i \eta^i\right]/\bar{c} + \Delta^i \label{eq:M}$$ where $\bar{c}$ is the mean concentration over the cluster, $\bar{c} = N^{-1} \sum_i c({\ensuremath{{ {\mathbf r}}}\xspace}^i)$, $\eta^i$ are uncorrelated Gaussian noises with zero mean and unit 