Collective gradient sensing with limited positional information

Eukaryotic cells cooperate to sense chemical gradients more effectively. For individual cells, the accuracy of gradient sensing is limited by the cell size and the error in measuring chemoattractant concentration, set by the fluctuations of ligand-receptor binding. Clusters of cells improve this limit by sharing individual measurements and spanning over larger regions. However, in the simplest way of interpreting these measurements, cells must determine their location within the cluster - which is also a noisy measurement. Here, we apply the maximum likelihood estimation method (MLE) to study the accuracy of gradient sensing of a cluster of cells when there is limited positional information. We consider different models for how cells obtain their positional information and we compare our results with (1) the case of cells with perfect positional information and (2) a tug-of-war model where cells respond to the gradient by polarizing away from neighbors without relying on positional information. Our findings show that under certain conditions, as positional uncertainty increases, there is a trade-off where the tug-of-war model responds more accurately to the chemical gradient.