Two-photon excitation and photolysis by pulsed laser illumination modelled by spatially non-uniform reactions with simultaneous diffusion

Two-photon absorption in the focus of a pulsed laser has the potential for localized photolysis of caged compounds, generating high concentrations of neurotransmitters, hormones and messengers. The concentrations of cage, intermediates and products in the femtolitre focal volume depend on reaction rates and diffusional exchange with the external volume. This problem of reaction with diffusion was analysed with analytical and numerical methods to determine simple relations between parameters useful in the design and interpretation of experiments. The diffraction-limited laser spot is approximated well by a sphere, radius A, in diffusional exchange with either an infinite uniform medium, representing extracellular photolysis, or within a non-permeable sphere, a "cell" of radius B, representing intracellular photolysis. Photolysis is modelled as sequential irreversible reactions, with either the excitation step alone, rate constant k(e), or with a subsequent "dark" reaction, rate constant k(p). For extracellular photolysis, steady-state depletion of a cage averaged in a spherical spot increases hyperbolically with k(e) with half-maximum depletion at k(e) = K0.5 = 2.5 D/A2, where D is the diffusion coefficient. With measured parameters for spot size A = 0.3 microm and diffusion D = 800 microm2/s, K0.5 = 22,200 s(-1). The optimal exposure for localized photolysis is the characteristic diffusion time tau = A2/D, 113 micros in this example, and is the time taken to reach 57% of steady state in the diffusion-limited case. In the two-step model, with excitation and "dark" reaction steps, rate constants both exceeding K0.5 are necessary to generate 50% of maximal product concentration in the illuminated volume. High concentrations of photolysis products depend particularly on a high excitation rate constant (k(e) > K0.5), and localization of the products requires fast dark reactions (k(p) > K0.5). If products diffuse faster than the cage, their steady-state concentrations are decreased, and concentration transients may occur. For localized intracellular photolysis, the duration of exposure that generates product concentration at the cell boundary, B, less than 10% of the spot concentration should be shorter than 0.043(B/A)3tau, and is determined by diffusion.     

Single-molecule anisotropy imaging

A novel method, single-molecule anisotropy imaging, has been employed to simultaneously study lateral and rotational diffusion of fluorescence-labeled lipids on supported phospholipid membranes. In a fluid membrane composed of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine, in which the rotational diffusion time is on the order of the excited-state lifetime of the fluorophore rhodamine, a rotational diffusion constant, D(rot) = 7 x 10(7) rad(2)/s, was determined. The lateral diffusion constant, measured by direct analysis of single-molecule trajectories, was D(lat) = 3.5 x 10(-8) cm(2)/s. As predicted from the free-volume model for diffusion, the results exhibit a significantly enhanced mobility on the nanosecond time scale. For membranes of DPPC lipids in the L(beta) gel phase, the slow rotational mobility permitted the direct observation of the rotation of individual molecules characterized by D(rot) = 1.2 rad(2)/s. The latter data were evaluated by a mean square angular displacement analysis. The technique developed here should prove itself profitable for imaging of conformational motions of individual proteins on the time scale of milliseconds to seconds.     

Lateral diffusion of membrane proteins in protein-rich membranes. A simple hard particle model for concentration dependence of the two-dimensional diffusion coefficient.

A model for the effect of protein concentration on the rate of lateral diffusion of integral membrane proteins is presented, in which the proteins are represented by equivalent hard circular particles on a surface. As the density of particles increases, the probability of finding a vacancy immediately adjacent to a tracer particle into which it may diffuse decreases, resulting in a concomitant reduction of the tracer diffusion coefficient. Using scaled particle theory to calculate the concentration-dependent probabilities, a simple approximate result is obtained in closed form, that is compared with the results of previously published Monte Carlo lattice simulations and experimental observations.     

Effect of hydrodynamic interactions on the diffusion of integral membrane proteins: diffusion in plasma membranes.

Tracer diffusion coefficients of integral membrane proteins (IMPs) in intact plasma membranes are often much lower than those found in blebbed, organelle, and reconstituted membranes. We calculate the contribution of hydrodynamic interactions to the tracer, gradient, and rotational diffusion of IMPs in plasma membranes. Because of the presence of immobile IMPs, Brinkman's equation governs the hydrodynamics in plasma membranes. Solutions of Brinkman's equation enable the calculation of short-time diffusion coefficients of IMPs. There is a large reduction in particle mobilities when a fraction of them is immobile, and as the fraction increases, the mobilities of the mobile particles continue to decrease. Combination of the hydrodynamic mobilities with Monte Carlo simulation results, which incorporate excluded area effects, enable the calculation of long-time diffusion coefficients. We use our calculations to analyze results for tracer diffusivities in several different systems. In erythrocytes, we find that the hydrodynamic theory, when combined with excluded area effects, closes the gap between existing theory and experiment for the mobility of band 3, with the remaining discrepancy likely due to direct obstruction of band 3 lateral mobility by the spectrin network. In lymphocytes, the combined hydrodynamic-excluded area theory provides a plausible explanation for the reduced mobility of sIg molecules induced by binding concanavalin A-coated platelets. However, the theory does not explain all reported cases of "anchorage modulation" in all cell types in which receptor mobilities are reduced after binding by concanavalin A-coated platelets. The hydrodynamic theory provides an explanation of why protein lateral mobilities are restricted in plasma membranes and why, in many systems, deletion of the cytoplasmic tail of a receptor has little effect on diffusion rates. However, much more data are needed to test the theory definitively. We also predict that gradient and tracer diffusivities are the same to leading order. Finally, we have calculated rotational diffusion coefficients in plasma membranes. They decrease less rapidly than translational diffusion coefficients with increasing protein immobilization, and the results agree qualitatively with the limited experimental data available.     

Organization and dynamics of the proteolipid complexes formed by annexin V and lipids in planar supported lipid bilayers

The consequences of the binding of annexin V on its lateral mobility and that of lipids were investigated by means of experimental and simulated FRAP experiments. Experiments were carried out on planar supported bilayers (PC/PS 9:1 mol/mol mixtures) in the presence of 1 mM CaCl2 in the subphase. The probes C12-NBD-PS and fluorescein-labeled annexin V were used and the data compared with that previously obtained for C12-NBD-PC [Saurel, O., Cézanne, L., Milon, A., Tocanne, J. F., & Demange, P. (1998) Biochemistry 37, 1403-1410]. At complete coverage of the lipid bilayer by the protein (Cannexin = 80 nM), the lateral mobility of C12-NBD-PC was reduced by 40% while C12-NBD-PS and bound annexin V molecules were nearly immobilized (D < 10(-)11 cm2/s). At moderate protein concentration (20 nM < Cannexin < 80 nM), best fitting of the lipid and protein probe recoveries was achieved with one single diffusion coefficient and a mobile fraction close to 100%, indicating homogeneous lipid and protein populations. In contrast, at low protein concentration (Cannexin < 20 nM), C12-NBD-PS showed a two-component diffusion. The slow PS population at Cannexin < 20 nM and the single PS population at Cannexin > 20 nM moved at the same rate that bound annexin V (mobile fraction close to 100%), indicating strong PS/protein interactions. With the aid of computer simulations of the lateral motion of PC molecules, based on the 2-D crystalline networks formed by annexin V in contact with the lipid bilayer, these FRAP results may be accounted for by considering a rather simple model of a proteolipidic complex consisting of an extended 2-D crystalline protein network facing the lipid bilayer and stabilized by strong interactions between annexin V and PS molecules. In this model, immobilization of annexin V and PS molecules originates from their mutual interactions. The slowing down of PC molecules is due to various obstacles to their lateral diffusion which can be described as: the four PS molecules bound to the protein, the tryptophan 187 which presumably interacts with the lipids at the level of their polar headgroups and probably the three other hydrophobic amino acid residues located on the AB calcium-binding loops of the protein.     

几种物质对苯噻草胺在水中光降解的影响

高压汞灯下不同物质对水中的苯噻草胺光化学降解的影响研究表明,NO₂^-和NO₃^-对苯噻草胺的光解有猝灭作用,其中NO₃^-在10∶1的添加浓度(质量浓度)下猝灭作用最明显,照光15 min猝灭率达53.3%;卤素离子对苯噻草胺光解有重原子猝灭效应,作用最强的是添加10∶1的I^-(质量浓度),照光15 min 猝灭率达76.9%;4种表面活性剂随添加浓度的增大对苯噻草胺光解的阻滞作用增强,除农乳404在较低添加浓度下(质量浓度比1∶5和1∶1)对苯噻草胺的光解表现出微弱的敏化效应外,其余均表现为猝灭作用;4种除草剂(杀草丹、苄嘧磺隆、甲草胺和绿磺隆)中,只有苄嘧磺隆在低添加浓度(质量浓度比1∶10)时对苯噻草胺有光敏化作用,照光25 min光敏率为18.2%,其余除草剂各添加浓度下均对苯噻草胺表现出光猝灭作用;充氮气10 min,苯噻草胺的光解半衰期由不充氮气的7.14 min缩短为6.70 min.     

Incorporation kinetics in a membrane, studied with the pore-forming peptide alamethicin.

The reaction of fluorescence-labeled alamethicin with unilamellar phospholipid vesicles (DOPC and DMPC) has been investigated in a stopped-flow apparatus. Clearly single exponential time functions have been observed at temperatures above the phase transition of the bilayer. This can be interpreted in terms of an essentially one-step incorporation process. The pseudo first-order forward rate is found to be quite fast, falling in a range somewhat below the diffusion controlled upper bound. The data are quantitatively very well described on the basis of a simple mechanism. This comprises diffusion of peptide into the bilayer accompanied by a more or less slower change of the secondary structure. Aggregation of the incorporated molecules at higher concentrations is indicated to be comparatively rapid.     

Effective diffusion rate through a polymer network: influence of nonspecific binding and intersegment transfer

The effective diffusion rate of a tracer molecule through a polymer network can be influenced by nonspecific binding. If such binding occurs, the local density fluctuations (segmental diffusion) of the network molecules will contribute to the net displacements of tracer molecules. If the network is strongly interconnected by entanglement or cross-linking, these local motions will only carry the tracer molecules over a small region, and effective transport would require dissociation and reassociation of the tracer molecule to another part of the network. Alternatively, tracer molecules could be transferred directly (intersegment transfer) between different parts of the network whenever they are brought sufficiently close by the density fluctuations. A wormlike-chain model for the segmental diffusion of a polymer is used to describe the network motions and to derive the effective diffusion rate for a tracer molecule as a function of network density and binding constant with or without intersegment transfer contributing. It is found that the density dependence for the effective diffusion of ethidium bromide through dense DNA solutions studied by photobleaching recovery [R. D. Icenogle and E. L. Elson (1983) Biopolymers 22 , 1949–1966] agrees with an intersegment-transfer mechanism limited by the segmental DNA motions. The calculations are also applied to a model for the intracellular diffusion of molecules loosely bound to the cytomatrix. If intersegment transfer dominates it can account for the observed size independence for the intracellular diffusion rates of various injected macromolecules.     

Lateral diffusion of saturated phosphatidylcholines in cholesterol-containing bilayers

A pulsed field gradient NMR was used to study lateral diffusion in the cholesterol-containing oriented bilayers of saturated (dipalmitoyl- and dimyristoyl-) phosphatidylcholines, upon their limiting hydration. Similar dependences of lateral diffusion coefficients on temperature and cholesterol concentration were observed, which agree with phase diagram showing the presence of the regions of disordered and ordered liquid-crystalline phases and a two-phase region. Under the same conditions, the lateral diffusion coefficient of dipalmitoylphosphatidylcholine is lower, which agrees qualitatively with its larger molecular weight. The comparison of data for dipalmitoylphosphatidylcholine with previous results for dipalmitoylsphingomyelin-cholesterol bilayers under the same conditions, in spite of similarity of phase diagrams, shows large (two–three times) differences in the lateral diffusion coefficient and a different profile of its dependence on cholesterol concentration. The comparison of data for dimyristoylphosphatidylcholine with previous results shows that the values of lateral diffusion coefficient and the shape of its dependence on cholesterol concentration coincide at high concentrations (>15 mol%) but differ at lower concentrations The revealed disagreement may be caused by the fact that the measurements were carried out at different water content in the system. At limiting hydration (more than 35% of water), the lateral diffusion coefficient for lipids decreases when cholesterol concentration rises, while at water content about 25% (as a result of equilibrium hydration from vapors) the lateral diffusion coefficient of phosphatidylcholine may be independent of cholesterol concentration. This is the consequence of the denser packing of molecules in the bilayer at reduced water content, an effect that competes with the ordering effect of cholesterol.     

Dynamics of adhesion molecule domains on neutrophil membranes: surfing the dynamic cell topography

Lateral organization and mobility of adhesion molecules play a significant role in determining the avidity with which cells can bind to target cells or surfaces. Recently, we have shown that the lateral mobility of the principal adhesion molecules on neutrophils is lower for rolling associated adhesion molecules (RAAMs: L-selectin and PSGL-1) than for β₂ integrins (LFA-1 and Mac-1). Here we report that all four adhesion molecules exhibit distinct punctate distributions that are mobile on the cell surface. Using uniform illumination image correlation microscopy, we measure the lateral mobility of these topologically distinct domains. For all four molecules, we find that diffusion coefficients calculated from domain mobility agree with measurements we made previously using fluorescence recovery after photobleaching. This agreement indicates that the transport of receptors on the surface of the resting neutrophil is dominated by the lateral movement of domains rather than individual molecules. The diffusion of pre-assembled integrin domains to zones of neutrophil/endothelial contact may provide a mechanism to facilitate high avidity adhesion during the earliest stages of firm arrest.     

Fluorescence Correlation Spectroscopy Measures Molecular Transport in Cells

Fluorescence correlation spectroscopy (FCS) can measure dynamics of fluorescent molecules in cells. FCS measures the fluctuations in the number of fluorescent molecules in a small volume illuminated by a thin beam of excitation light. These fluctuations are processed statistically to yield an autocorrelation function from which rates of diffusion, convection, chemical reaction, and other processes can be extracted. The advantages of this approach include the ability to measure the mobility of a very small number of molecules, even down to the single molecule level, over a wide range of rates in very small regions of a cell. In addition to rates of diffusion and convection, FCS also provides unique information about the local concentration, states of aggregation and molecular interaction using fluctuation amplitude and cross-correlation methods. Recent advances in technology have rendered these once difficult measurements accessible to routine use in cell biology and biochemistry. This review provides a summary of the FCS method and describes current areas in which the FCS approach is being extended beyond its original scope.     

Analysis of cell surface interactions by measurements of lateral mobility

Interactions of cell surface components with one another and with structures inside and outside the cell may have important physiological functions in the transmission of signals and the assembly of specialized structures. These interactions may be detected and analyzed through their effects on the lateral mobility of cell surface molecules. Measurements by a fluorescence photobleaching method have shown that in general lipid-like molecules diffuse rapidly and freely through the plasma membrane, whereas proteins move much more slowly or appear to be immobile. This dichotomy has been supposed to result from forces beyond the viscosity of the lipid bilayer, which specifically retard the diffusion of membrane proteins. This general picture should be qualified, however, by noting that the lateral mobility of lipid-like molecules can be influenced in detail by changes in the state of the plasma membrane such as result from mitosis or fertilization. The interactions of cell surface proteins that limit their lateral mobility are unknown. The effects of binding concanavalin A to localized regions of cell surface show that these interactions can vary in subtle and complex ways. It may soon be useful to interpret mobility experiments in terms of simple reaction models that attempt to describe surface interactions in physicochemical terms. More experimental data are needed to carry out this program and to relate interactions that affect mobility to the structural connections between cell surface components and the cytoskeleton, which have been detected by biochemical methods and electron and immunofluorescence microscopy.     

Weak effect of membrane diffusion on the rate of receptor accumulation at adhesive contacts

To assess if membrane diffusion could affect the kinetics of receptor recruitment at adhesive contacts, we transfected neurons with green fluorescent protein-tagged immunoglobin cell adhesion molecules of varying length (25-180 kD), and measured the lateral mobility of single quantum dots bound to those receptors at the cell surface. The diffusion coefficient varied within a physiological range (0.1-0.5 microm(2)/s), and was inversely proportional to the size of the receptor. We then triggered adhesive contact formation by placing anti-green fluorescent protein-coated microspheres on growth cones using optical tweezers, and measured surface receptor recruitment around microspheres by time-lapse fluorescence imaging. The accumulation rate was rather insensitive to the type of receptor, suggesting that the long-range membrane diffusion of immunoglobin cell adhesion molecules is not a limiting step in the initiation of neuronal contacts.     

Mobility measurement by analysis of fluorescence photobleaching recovery kinetics.

Fluorescence photobleaching recovery (FPR) denotes a method for measuring two-dimensional lateral mobility of fluorescent particles, for example, the motion of fluorescently labeled molecules in approximately 10 mum2 regions of a single cell surface. A small spot on the fluorescent surface is photobleached by a brief exposure to an intense focused laser beam, and the subsequent recovery of the fluorescence is monitored by the same, but attenuated, laser beam. Recovery occurs by replenishment of intact fluorophore in the bleached spot by lateral transport from the surrounding surface. We present the theoretical basis and some practical guidelines for simple, rigorous analysis of FPR experiments. Information obtainable from FPR experiments includes: (a) identification of transport process type, i.e. the admixture of random diffusion and uniform directed flow; (b) determination of the absolute mobility coefficient, i.e. the diffusion constant and/or flow velocity; and (c) the fraction of total fluorophore which is mobile. To illustrate the experimental method and to verify the theory for diffusion, we describe some model experiments on aqueous solutions of rhodamine 6G.     

Multiple diffusion mechanisms due to nanostructuring in crowded environments

One of the key questions regarding intracellular diffusion is how the environment affects molecular mobility. Mostly, intracellular diffusion has been described as hindered, and the physical reasons for this behavior are: immobile barriers, molecular crowding, and binding interactions with immobile or mobile molecules. Using results from multi-photon fluorescence correlation spectroscopy, we describe how immobile barriers and crowding agents affect translational mobility. To study the hindrance produced by immobile barriers, we used sol-gels (silica nanostructures) that consist of a continuous solid phase and aqueous phase in which fluorescently tagged molecules diffuse. In the case of molecular crowding, translational mobility was assessed in increasing concentrations of 500 kDa dextran solutions. Diffusion of fluorescent tracers in both sol-gels and dextran solutions shows clear evidence of anomalous subdiffusion. In addition, data from the autocorrelation function were analyzed using the maximum entropy method as adapted to fluorescence correlation spectroscopy data and compared with the standard model that incorporates anomalous diffusion. The maximum entropy method revealed evidence of different diffusion mechanisms that had not been revealed using the anomalous diffusion model. These mechanisms likely correspond to nanostructuring in crowded environments and to the relative dimensions of the crowding agent with respect to the tracer molecule. Analysis with the maximum entropy method also revealed information about the degree of heterogeneity in the environment as reported by the behavior of diffusive molecules.     

Fluorescence pattern photobleaching recovery for samples with multi-component diffusion

The translational mobility of proteins and lipids in phospholipid bilayers is often not well described as ideal self diffusion. One of the best methods for characterizing such non-ideal diffusion is to use fluorescence pattern photobleaching recovery. In this method, the spatial gradient of the monitoring and bleaching intensity is created by using epi-fluorescence and an expanded Gaussian-shaped laser beam which passes though a Ronchi ruling placed at the back image plane of a microscope. A difficulty arises when the fluorescence recovery from the exchange of slowly diffusing molecules between illuminated and non-illuminated stripes temporally overlaps with the recovery from the exchange of more rapidly diffusing molecules through the gradient produced by the broad Gaussian shape of the illumination. In the work presented here, a general theory is developed that describes the shape of the resulting fluorescence recovery curve for these typical experimental conditions. Approximate expressions amenable to non-linear curve fitting are also given. The new theoretical formalism has been demonstrated on data for the translational mobility of a fluorescent lipid probe in phospholipid bilayers deposited on planar-fused silica substrates.     

Statistical Analysis of Lateral Diffusion and Multistate Kinetics in Single-Molecule Imaging

Single-molecule trajectories of molecules on the membrane of living cells have indicated the possibility that the lateral mobility of individual molecules is variable with time. Such temporal variation in mobility may indicate intrinsic kinetics of multiple molecular states. To clarify the mechanisms of signal processing on the membrane, quantitative characterizations of such temporal variations are necessary. Here we propose a method to analyze and characterize the multiple states in lateral mobility and their transition kinetics from single-molecule trajectories based on a displacement probability density function and an autocorrelation function of squared displacements. We performed our method for three cases: a molecule with a single diffusion coefficient (D), a mixture of molecules in two states with different D-values, and a molecule switching between two states with different D-values. Our analysis of numerically generated trajectories successfully distinguished the three cases and estimated the characteristic parameters for mobility and the kinetics of state transitions. This method is applicable to single-molecule tracking analysis of molecules in multiple functional states with different lateral mobility on the membrane of living cells.