Detection of long-range electrostatic interactions between charged molecules by means of fluorescence correlation spectroscopy

In the present paper, an experimental feasibility study on the detection of long-range intermolecular interactions through three-dimensional molecular diffusion in solution is performed. This follows recent theoretical and numerical analyses reporting that long-range electrodynamic forces between biomolecules could be identified through deviations from Brownian diffusion. The suggested experimental technique was fluorescence correlation spectroscopy (FCS). By considering two oppositely charged molecular species in aqueous solution, namely, lysozymes and fluorescent dye molecules (Alexa488), the diffusion coefficient of the dyes has been measured for different values of the concentration of lysozyme, that is, for different average distances between the oppositely charged molecules. For our model, long-range interactions are of electrostatic origin, suggesting that their action radius can be varied by changing the ionic strength of the solution. The experimental outcomes clearly prove the detectability of long-range intermolecular interactions by means of the FCS technique. Molecular dynamics simulations provide a clear and unambiguous interpretation of the experimental results.

Figure 1

FCS measurements. Semilog plot of the normalized autocorrelation function of fluorescence fluctuations, defined in Eq. (6), obtained at $\langle d\rangle =240\text{Å}$ (red line), at $\langle d\rangle =920\text{Å}$ (blue line), and at $\langle d\rangle =4200\text{Å}$ (black line). Working temperature $30{}^{\circ }\text{C}$.

Figure 2

Semilog plot of the normalized diffusion coefficients $D/D_0$ of AF488 as a function of the distance in $\text{Å}$ between proteins and dyes (a); semilog plot of the diffusion coefficient $D$ for a single experiment with 0 mM of NaCl in solution (b); semilog plot of hydrodynamic radius (c) of AF488 (1 nM) versus the average distance between all the molecules in pure water.

Figure 3

The diffusion coefficient (blue diamonds) and the fraction of free AF488 molecules (white squares) are compared. In the two-species fitting to compute the fraction of free dye molecules the following parameters have been kept fixed: ${\tau }_{\text{AF}488}=78.8\mu \mathrm{s}$, ${\tau }_{\text{Lys}}=210\mu \mathrm{s}$, triplet time of AF488 $3.4\mu \mathrm{s}$, and triplet time of Lysozyme $3.34\mu \mathrm{s}$.

Figure 4

Semilog plot of the normalized diffusion coefficients $D/D_0$ at different concentrations of NaCl in solution: 0 mM (blue diamonds), 20 mM (orange circles), 50 mM (red squares), 100 mM (green triangles), and 150 mM (purple rhombs).

Figure 5

Normalized diffusion coefficients at isoelectric points of Myoglobin at pH = 7 (full circles), and of Lysozyme at pH = 11 (open triangles). Electrostatic interactions are switched off.

Figure 6

Schematic diagram of the FCCS apparatus. The excitation beam starts from the diode laser (on the top right of the image), goes through an optic fiber, through a set of lenses and a dichroic mirror (on the middle of the image), and reaches the sample placed in a confocal microscope through the objective (on the right). The emitted fluorescence beam goes back through the objective, is reflected on the dichroic mirror, then is split into two beams that are finally collected by two detectors (on the left). For more details see Sec. 3c. (Adapted from ISS Inc. ALBA.)

Figure 7

Comparison among experimental results and numerical simulations for non-screened Coulomb potential. Semilog plot of the normalized diffusion coefficients $D/D_0$: experimental values (red diamonds), $N_A=200$ and $N_B=20$ (light-green circles), $N_A=500$ and $N_B=50$ (light-blue squares). Red squares and full black circles correspond to experimental and numerical results, respectively, in the case of a Debye-Hückel potential with a Debye length ${\lambda }_D=27\mathring{\mathrm{A}}$.

Figure 8

Check of Brownian versus anomalous diffusion. The $\alpha$ values reported here refer to 0 mM of NaCl in solution (blue diamonds), and 100 mM (green triangles). $\alpha =1$ corresponds to Brownian diffusion, $\alpha <0.6–0.7$ can be attributed to anomalous diffusion.

Figure 9

FCCS measurements. Semilog plot of the normalized autocorrelation function of fluorescence fluctuations, defined in Eq. (6), obtained at $\langle d\rangle =240\text{Å}$ (red line), at $\langle d\rangle =920\text{Å}$ (blue line), and at $\langle d\rangle =4200\text{Å}$ (black line). Working temperature $20{}^{\circ }\text{C}$.

Figure 10

Comparison between the FCS and the FCCS measurements. Semilog plot of the diffusion coefficients $D$ of AF488 as a function of the distance in $\text{Å}$—and of the concentration of the solution in Moles—between proteins and dyes. The FCS results have been obtained at $30{}^{\circ }\text{C}$, 0 mM (blue diamonds), and 100 mM (green triangles), of NaCl in solution. The FCCS results have been obtained at $20{}^{\circ }\text{C}$, 0 mM (black diamonds), and 100 mM (white triangles), of NaCl in solution.