Efficient transmission of unique cell identities via correlated fluctuations, emergent discreteness, and error-correcting codes

In a developing embryo, information about the position of cells is carried by the concentrations of specific molecules. In the fruit fly, these molecules are known, and form a network with several layers—maternal inputs, gap genes, and pair-rule genes whose expression forms a blueprint for the segments of the developed organism. Recent work shows that the concentrations of the gap gene products point to positions with an accuracy comparable to the spacing between neighboring cells. This is nearly enough to specify unique cellular identities. We make three observations which suggest theoretical mechanisms for precisely and efficiently encoding cellular identities. (1) Correlations in the fluctuations of signaling molecule concentrations enhance the transmission of information about positions along the embryo.(2) Although the positional information is carried by continuous concentration gradients, maximum information transmission is achieved by a discrete set of cell identities. (3) Inference of these discrete identities corresponds to a statistical physics problem. Noise acts as a random field and its correlations couple neighboring variables. We consider the possibility of an ordered phase which is stable against the random field, and hence defines an error-correcting code.