Quantification of fluctuations from fluorescence correlation spectroscopy experiments in reaction-diffusion systems

Abstract

Fluorescence correlation spectroscopy (FCS) is commonly used to estimate diffusion and reaction rates. In FCS the fluorescence coming from a small volume is recorded and the autocorrelation function (ACF) of the fluorescence fluctuations is computed. Scaling out the fluctuations due to the emission process, this ACF can be related to the ACF of the fluctuations in the number of observed fluorescent molecules. In this paper the ACF of the molecule number fluctuations is studied theoretically, with no approximations, for a reaction-diffusion system in which the fluorescence changes with binding and unbinding. Theoretical ACFs are usually derived assuming that fluctuations in the number of molecules of one species are instantaneously uncorrelated to those of the others and obey Poisson statistics. Under these assumptions, the ACF derived in this paper is characterized only by the diffusive timescale of the fluorescent species and its total weight is the inverse of the mean number of observed fluorescent molecules. The theory is then scrutinized in view of previous experimental results which, for a similar system, gave a different total weight and correct estimates of other diffusive timescales. The total weight mismatch is corrected by assuming that the variance of the number of fluorescent molecules depends on the variance of the particle numbers of the other species, as in the variance decomposition formula. Including the finite acquisition time in its computation, it is shown that the ACF depends on various timescales of the system and that its total weight coincides with the one obtained with the variance decomposition formula. This calculation implies that diffusion coefficients of nonobservable species can be estimated with FCS experiments performed in reaction-diffusion systems. Ways to proceed in future experiments are also discussed.

High rates of calcium-free diffusion in the cytosol of living cells

“…This is consistent with the observation that the means over each subpopulation, D 2a and D 2b , decrease with increasing Ca 2þ (see Table 3), a behavior that has been observed in the largest coefficient derived in the experiments performed in aqueous solutions presented in Fig. 7 of Villarruel and Dawson (50). The means, D 2b , over the subpopulations with the largest values obtained in the Gch/BC and Gch/HC experiments in S. cerevisiae (698 and 605 mm 2 /s, respectively), differ by less than 10% with respect to the value obtained in oocytes, D 2b ¼ 644 mm 2 /s.…”

“…This occurs even if the actual underlying dynamical system is characterized by the diffusive timescales of the various species that Ca 2þ interacts with. Which of these timescales can be captured in an experiment in which only one fluorescenct species is observed (Ca 2þbound dye) depends on the (spatially local) equilibrium situation that is being probed in each case (50). All the results reported in Table 3 showed a large variability of the coefficients estimated under the same conditions.…”

“…The design of the experiments described in this section was inspired by our previous work (48)(49)(50) on the use of FCS in aqueous solutions in which the fluorescence was emitted by SW Ca 2þ sensor. These sensors increase their fluorescence intensity by a large factor when bound to Ca 2þ (45).…”

“…Knowing the range of values over which the Ca 2þ diffusion rate can vary, particularly its highest (free diffusion) end, is key for a comprehensive understanding of the signals. In this work, we have built upon our previous theoretical and experimental works in aqueous solutions (48)(49)(50) to quantify the Ca 2þ diffusion coefficient directly in intact living cells using FCS. As reflected in Figs.…”

Analytical Form of the Fluorescence Correlation Spectroscopy Autocorrelation Function in Chemically Reactive Systems

“…However, the dependence of eigenvalues and eigenvectors on q is relatively complex. Therefore, integrating over the wave vector in eq cannot be done analytically unless the eigenvalues and eigenvectors are approximated. − To avoid this problem, we express δ C̃ A , δ C̃ B , and δ C̃ C using new functions δ C̃ 1 , δ C̃ 2 , and δ C̃ 3 as follows δ C̃ A = δ C̃ 1 − δ C̃ 3 , goodbreak0em2em⁣ δ C̃ B = δ C̃ 2 , goodbreak0em2em⁣ δ C̃ C = k A k C δ C̃ 1 + δ C̃ 3 …”