Fluorescence correlation spectroscopy (FCS) provides an analysis of fluorescence fluctuations over time from one or a small number of molecules in a microscopic detection volume. Usually these fluctuations are provided by fluorescent molecules diffusing through the detection volume which is placed inside of an aqueous solution. If too many molecules are located in the detection volume at any given time (i.e., the concentration is too high or the detection volume is too large), fluctuations will average out to the mean. Thus the method is highly dependent on the number of molecules observed at any one moment. The general expression for the auto- and cross- correlation is as follows [

18,

19]

where δF

_{i} and δF

_{j} denote the variance of the fluorescence signal about the mean at time t and a later time, t + τ, for two fluorescent time traces, i and j. Also <F

_{i}> and <F

_{j}> are the time averaged fluorescent signals. In order to extract physical data from the correlation, a model of diffusion, G

_{D,} is fit in terms of the lag time, τ. The simplest of these models is the expression for pure diffusion of m fluorescent species [

20]

where ω is the is the width of the detection volume, z is the height of the detection volume, τ

_{m} is the average diffusion time of the m

^{th} diffusing species, and G(0) is the correlation at τ = 0, which is equal to the inverse of the average number of independent, diffusing molecules passing through the detection volume, N.

Of course, other phenomena, such as molecule orientation and antibunching, may contribute to the fluctuation of the fluorescence signal, but these phenomena occur at much shorter lag times and therefore do not affect the fitting of the diffusion model. However, the transition of an excited molecule to a triplet state will cause blinking, leading to erroneously short diffusion times and increased G(0). So the following term must be added to the diffusion model to account for a single triplet (dark) state with lifetime τ

_{T} [

20,

21]

Inserting

Equation (4) into

Equation (2) and simplifying the result to assume only one diffusing species with average diffusion time τ

_{1} yields

The diffusion constant, D, may then be calculated as

For more detailed derivations of these models, we refer the reader to [

18,

20,

21].

Measurements were conducted on a Microtime 200 system from PicoQuant, GmbH (Berlin, Germany). The system was arranged as the shown in . Excitation was provided by a 470 nm pulsed laser diode, which was directed into the sample by a 60x 1.2 NA water immersion objective, part of an Olympus IX71 microscope. Scattered light was removed by a 488 nm long pass filter, and the light passed through a 50 μm pinhole before being split by a 1:1 plate. The split light beams were then directed into two identical Single Photon Avalanche Detectors from Perkin Elmer (SPCM-AQR-14). The data from the two detectors were cross-correlated to eliminate afterpulsing [

22,

23]. All data processing was performed by the SymPhoTime software, version 5.3.2, also from PicoQuant. Some of the results were supported by a complementary analysis of the same data performed using the Fluctuation Analyzer TZ software package (ISS, Champagne, IL) developed by Zeno Foldes-Papp and Tiefeng You (see

supplementary data). Fluorescein is known to exhibit a blinking behavior due to population of a triplet state [

24–

25]. The laser power was therefore kept as low as possible, less than 2 μW, in order to minimize this behavior [

26,

27].

Equation (5) was fitted to the correlated data by the SymPhoTime software.

The HA-Fl substrate was first diluted down to concentrations appropriate for FCS measurements with the addition of PBS pH=6. The concentration of HA-Fl particles was later determined by FCS to be 0.9 nM. It must be noted that this measurement is independent of the number of fluorescein molecules bound to each HA molecule. The substrate was divided into 330 μL portions, each in an individual 1 mL centrifuge tube. To each of these tubes was added 20 μL of HA-ase in various concentrations. For the two hour measurements, 300 μL of this solution was dropped onto a No. 1 glass coverslip from Menzel-Gläser (Gerhard Menzel GmbH, Braunschweig, Germany) immediately after the addition of HA-ase. The large sample volume was used to reduce the effects of evaporation over two hours. Using the backscattered diffraction pattern, the focal volume was adjusted to 20 μm above the top surface of the coverslip. The 10 minute measurements differed in that each solution was incubated for 25 min after the addition of HA-ase. Then 50 μL were dropped onto the coverslip for the 10 minute measurement.

The detection volume of the system is dependent upon many factors: laser power, objective, the setting of the correction collar on the objective, the index of refraction of the measured solution, the thickness of the coverslip, etc. Precisely knowing the size of the detection volume is critical to determine the concentration and diffusion coefficient of the sample, so the detection volume was calibrated by measuring the diffusion properties of free fluorescein dye, whose diffusion coefficient has been well established [

28].