Ranking of Reactions Based on Sensitivity of Protein Noise Depends on the Choice of Noise Measure

Gene expression is a stochastic process. Identification of the step maximally affecting noise in the protein level is an important aspect of investigation of gene product distribution. There are numerous experimental and theoretical studies that seek to identify this important step. However, these studies have used two different measures of noise, viz. coefficient of variation and Fano factor, and have compared different processes leading to contradictory observations regarding the important step. In this study, we performed systematic global and local sensitivity analysis on two models of gene expression to investigate relative contribution of reaction rate parameters to steady state noise in the protein level using both the measures of noise. We analytically and computationally showed that the ranking of parameters based on the sensitivity of the noise to variation in a given parameter is a strong function of the choice of the noise measure. If the Fano factor is used as the noise measure, translation is the important step whereas for coefficient of variation, transcription is the important step. We derived an analytical expression for local sensitivity and used it to explain the distinct contributions of each reaction parameter to the two measures of noise. We extended the analysis to a generic linear catalysis reaction system and observed that the reaction network topology was an important factor influencing the local sensitivity of the two measures of noise. Our study suggested that, for the analysis of contributions of reactions to the noise, consideration of both the measures of noise is important.