Continuous fluorescence microphotolysis to observe lateral diffusion in membranes. Theoretical methods and applications

Lipid membranes supported by polydimethylsiloxane substrates with designed geometry

The membrane curvature of cells and intracellular compartments continuously adapts to enable cells to perform vital functions, from cell division to signal trafficking. Understanding how membrane geometry affects these processes in vivo is challenging because of the biochemical and geometrical complexity as well as the short time and small length scales involved in cellular processes. By contrast, in vitro model membranes with engineered curvature would provide a versatile platform for this investigation and applications to biosensing and biocomputing. Here, we present a strategy that allows fabrication of lipid membranes with designed shape by combining 3D micro-printing and replica-molding lithography with polydimethylsiloxane to create curved micrometer-sized scaffolds with virtually any geometry. The resulting supported lipid membranes are homogeneous and fluid. We demonstrate the versatility of the system by fabricating structures of interesting combinations of mean and Gaussian curvature. We study the lateral phase separation and how local curvature influences the effective diffusion coefficient. Overall, we offer a bio-compatible platform for understanding curvature-dependent cellular processes and developing programmable bio-interfaces for living cells and nanostructures.

Quantifying green fluorescent protein diffusion in Escherichia coli by using continuous photobleaching with evanescent illumination

Fluorescence recovery after photobleaching and fluorescence correlation spectroscopy are the primary means for studying translational diffusion in biological systems. Both techniques, however, present numerous obstacles for measuring translational mobility in structures only slightly larger than optical resolution. We report a new method using through-prism total internal reflection fluorescence microscopy with continuous photobleaching to overcome these obstacles. Small structures, such as prokaryotic cells or isolated eukaryotic organelles, containing fluorescent molecules are adhered to a surface. This surface is continuously illuminated by an evanescent wave created by total internal reflection. The characteristic length describing the decay of the evanescent intensity with distance from the surface is smaller than the structures. The fluorescence decay rate resulting from continuous evanescent illumination is monitored as a function of the excitation intensity. The data at higher excitation intensities provide apparent translational diffusion coefficients for the fluorescent molecules within the structures because the decay results from two competing processes (the intrinsic photobleaching propensity and diffusion in the small structures). We present the theoretical basis for the technique and demonstrate its applicability by measuring the diffusion coefficient, 6.3 +/- 1.1 microm(2)/s, of green fluorescent protein in Escherichia coli cells.

Continuous fluorescence microphotolysis and correlation spectroscopy using 4Pi microscopy

Continuous fluorescence microphotolysis (CFM) and fluorescence correlation spectroscopy (FCS) permit measurement of molecular mobility and association reactions in single living cells. CFM and FCS complement each other ideally and can be realized using identical equipment. So far, the spatial resolution of CFM and FCS was restricted by the resolution of the light microscope to the micrometer scale. However, cellular functions generally occur on the nanometer scale. Here, we develop the theoretical and computational framework for CFM and FCS experiments using 4Pi microscopy, which features an axial resolution of approximately 100 nm. The framework, taking the actual 4Pi point spread function of the instrument into account, was validated by measurements on model systems, employing 4Pi conditions or normal confocal conditions together with either single- or two-photon excitation. In all cases experimental data could be well fitted by computed curves for expected diffusion coefficients, even when the signal/noise ratio was small due to the small number of fluorophores involved.

FCS cell surface measurements—Photophysical limitations and consequences on molecular ensembles with heterogenic mobilities

BACKGROUND

Fluorescence Correlation Spectroscopy is a powerful method to analyze densities and diffusive behavior of molecules in membranes, but effects of photodegradation can easily be overlooked.

METHOD

Based on experimental photophysical parameters, calculations were performed to analyze the consequences of photobleaching in fluorescence correlation spectroscopy (FCS) cell surface experiments, covering a range of standard measurement conditions.

RESULTS

Cumulative effects of photobleaching can be prominent, although an absolute majority of the fluorescent molecules would pass the laser excitation beam without being photo-bleached. Given a distribution of molecules on a cell surface with different diffusive properties, the fraction of molecules that is actually analyzed depends strongly on the excitation intensities and measurement times, as well as on the size of the reservoir of freely diffusing molecules. Both the slower and the faster diffusing molecules can be disfavored.

CONCLUSIONS

Apart from quantifying photobleaching effects, the calculations suggest that the effects can be used to extract additional information, for instance about the size of the reservoirs of free diffusion. By certain choices of measurement conditions, it may be possible to more specifically analyze certain species within a population, based on their different diffusive properties, different areas of free diffusion, or different kinetics of possible transient binding.

Simulations of (an)isotropic diffusion on curved biological surfaces

We present a computational particle method for the simulation of isotropic and anisotropic diffusion on curved biological surfaces that have been reconstructed from image data. The method is capable of handling surfaces of high curvature and complex shape, which are often encountered in biology. The method is validated on simple benchmark problems and is shown to be second-order accurate in space and time and of high parallel efficiency. It is applied to simulations of diffusion on the membrane of endoplasmic reticula (ER) in live cells. Diffusion simulations are conducted on geometries reconstructed from real ER samples and are compared to fluorescence recovery after photobleaching experiments in the same ER samples using the transmembrane protein tsO45-VSV-G, C-terminally tagged with green fluorescent protein. Such comparisons allow derivation of geometry-corrected molecular diffusion constants for membrane components from fluorescence recovery after photobleaching data. The results of the simulations indicate that the diffusion behavior of molecules in the ER membrane differs significantly from the volumetric diffusion of soluble molecules in the lumen of the same ER. The apparent speed of recovery differs by a factor of approximately 4, even when the molecular diffusion constants of the two molecules are identical. In addition, the specific shape of the membrane affects the recovery half-time, which is found to vary by a factor of approximately 2 in different ER samples.

Theory of heterogeneous relaxation in compartmentalized tissues

A new model of compartmentalized relaxation--that which occurs for spins (protons) exchanging between compartments of different relaxation rates--is presented. This model generalizes previous ones by allowing spatially dependent relaxation within compartments. Solutions for the diffusion-Bloch equations are found via an efficient numerical technique known as the generalized moment expansion, and they agree well with the solutions to the standard two-site exchange equations (TSEE) for many typical situations. Specific models are developed for liposomes, red blood cells, capillaries, and arteries with respect to applied contrast agents. A parameter derived from tissue characteristics is introduced to predict the nature of the solutions. A new method is proposed for using contrast agents to detect capillaries, which exploits their high surface-to-volume ratio relative to the other elements of the vasculature.

Theory of paramagnetic contrast agents in liposome systems

We develop a theoretical description of nuclear spin relaxation mediated by MRI contrast agents and transport processes in liposome systems. Such systems compartmentalize the physical space such that paramagnetic contrast agents, which enhance relaxation, are trapped in some subvolume. Due to diffusive transport across compartmental barriers, i.e., across liposome membranes, nuclear spins in the whole volume exhibit fast relaxation. The description developed is based on the diffusion-Bloch equations for the nuclear magnetization with appropriate boundary and continuity conditions. From this set of equations a new inhomogeneous differential equation for the local relaxation times is derived. For simple geometries of compartmentalized spaces the equation can be solved analytically. A simple formula for average relaxation times in liposome systems is presented. The resulting relaxation times agree well with observations.