Ultimate use of two-photon fluorescence microscopy to map orientational behavior of fluorophores

Abstract

The orientational distribution of fluorophores is an important reporter of the structure and function of their molecular environment. Although this distribution affects the fluorescence signal under polarized-light excitation, its retrieval is limited to a small number of parameters. Because of this limitation, the need for a geometrical model (cone, Gaussian, etc.) to effect such retrieval is often invoked. In this work, using a symmetry decomposition of the distribution function of the fluorescent molecules, we show that polarized two-photon fluorescence based on tunable linear dichroism allows for the retrieval of this distribution with reasonable fidelity and without invoking either an a priori knowledge of the system to be investigated or a geometrical model. We establish the optimal level of detail to which any distribution can be retrieved using this technique. As applied to artificial lipid vesicles and cell membranes, the ability of this method to identify and quantify specific structural properties that complement the more traditional molecular-order information is demonstrated. In particular, we analyze situations that give access to the sharpness of the angular constraint, and to the evidence of an isotropic population of fluorophores within the focal volume encompassing the membrane. Moreover, this technique has the potential to address complex situations such as the distribution of a tethered membrane protein label in an ordered environment.

Figure 1

(a) Orientational freedom of a single fluorescent probe in a membrane. (b) Space- and time-averaging in an ensemble of probes are described by a 3D distribution, f(θ,φ), of single dipoles oriented with angles (θ,φ), as probed by the electric field. (c) Corresponding 2D effective angular distribution, p(φ), given by Eq. 4. (d) A single fluorescent dipole linked to a membrane protein with a given angular constraint in the membrane. (e) Corresponding ensemble averaging orientation in a 3D distribution. (f) 2D effective distribution. To see this figure in color, go online.

Figure 2

Several examples of effective orientation distributions, p(φ) (first column), angular features carried by the second and fourth symmetry orders (second and third columns, respectively), and filtered-out angular distribution, $\tilde{p}\left(\phi \right)$, as seen by two-photon fluorescence (fourth column). To see this figure in color, go online.

Figure 3

Plot of the values of S₂, $S_4^{\left(\text{s}\right)}$, and $S_4^{\left(\text{a}\right)}$ for each distribution case in Fig. 2. (a) Plot projected in the $\left(S_2,S_4^{\left(\text{s}\right)}\right)$ plane. (b) Plot projected in the $\left(S_4^{\left(\text{a}\right)},S_4^{\left(\text{s}\right)}\right)$ plane. To see this figure in color, go online.

Figure 4

(a) Results on simulated data. The color at each pixel indicates the value of S₂ and $S_4^{\left(\text{s}\right)}$, based on the same colorscale as in b. The retrieved, $\tilde{p}\left(\phi \right)$, is shown for a few selected points. (b) Distribution of $\left(S_2,S_4^{\left(\text{s}\right)}\right)$ values. (c) Distribution of $\left(S_4^{\left(\text{a}\right)},S_4^{\left(\text{s}\right)}\right)$ values. To see this figure in color, go online.

Figure 5

(a) Results on the outer part of an MLV made of DPPC doped with the di-8-ANEPPQ lipid probe. The color at each pixel indicates the values of S₂ and $S_4^{\left(\text{s}\right)}$, based on the same colorscale as in b. The retrieved distribution, $\tilde{p}\left(\phi \right)$, is shown for a few selected points. (b) Distribution of $\left(S_2,S_4^{\left(\text{s}\right)}\right)$ values. (c) Distribution of $\left(S_4^{\left(\text{a}\right)},S_4^{\left(\text{s}\right)}\right)$ values. (d–f) Same analysis as described in c–e in the central area of the MLV. (g–i) Same analysis as in c–e on a COS 7 cell doped with di-8-ANEPPQ. Scale bars, 10 μm. To see this figure in color, go online.

Figure 6

Values of S₂ and $S_4^{\left(\text{s}\right)}$ for different geometrical models of angular distributions, for different values of the angular aperture ψ. The corresponding distribution, p(φ), is plotted for information near each data point. (Insets) Shapes of the geometrical models showing the angles. (a) Cone (black) and Gaussian (red) models. ψ varies from 0° to 180° in steps of 10°. (b) Double Gaussian, for σ = 20° (black) and σ = 50° (red). ψ varies from 0° to 90° in steps of 10°. To see this figure in color, go online.