How long should a system be observed to obtain reliable concentration estimates from the measurement of fluctuations?

Abstract

The interior of cells is a highly fluctuating environment. Fluctuations set limits to the accuracy with which endogenous processes can occur. The physical principles that rule these limits also affect the experimental quantification of biophysical parameters in situ. The characterization of fluctuations, on the other hand, provides a way to quantify biophysical parameters. But as with any random process, enough data has to be collected to achieve a reliable quantitative description. In this article we study the accuracy with which intracellular concentrations can be estimated using fluorescence correlation spectroscopy. We show that, when the observed molecules interact with immobile species or experience other restrictions to their movement, the hypotheses commonly used to estimate concentrations are no longer valid. The interactions with immobile sites reduce the fluorescence variance by a finite amount. The time that is necessary to obtain an accurate concentration estimate, on the other hand, is hundreds of times larger than the slowest correlation time and is much larger when the sites move slowly than when they are immobile. Our analysis is applicable to other related techniques and it also sheds light on the way in which effector concentrations are read by target molecules in cells.