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Protein concentration in a living cell fluctuates over time due to noise ingrowth and division processes. From extensive single-cell experiments by usingE. coli strains with different promoter strength (over two orders of magnitude)and under different nutrient conditions, we found that the variance of proteinconcentration fluctuations follows a robust square power-law dependence on itsmean, which belongs to a general phenomenon called Taylor's law. To understandthe mechanistic origin of this observation, we use a minimal mechanistic modelto describe the stochastic growth and division processes in a single cell witha feedback mechanism for regulating cell division. The model reproduces theobserved Taylor's law. The predicted protein concentration distributions agreequantitatively with those measured in experiments for different nutrientconditions and a wide range of promoter strength. By using a mean-fieldapproximation, we derived a single Langevin equation for protein concentrationwith multiplicative noise, which can be solved exactly to prove the squareTaylor's law and to obtain an analytical solution for the protein concentrationdistribution function that agrees with experiments. Analysis of experiments byusing our model showed that noise in production rates dominates over noise fromcell division in contributing to protein concentration fluctuations. Ingeneral, a multiplicative noise in the underlying stochastic dynamics may beresponsible for Taylor's law in other systems.

Multiplicative noise underlies Taylor's law in protein concentration fluctuations in single cells