Quantifying the Diffusion of Membrane Proteins and Peptides in Black Lipid Membranes with 2-Focus Fluorescence Correlation Spectroscopy

Protein diffusion in lipid membranes is a key aspect of many cellular signaling processes. To quantitatively describe protein diffusion in membranes, several competing theoretical models have been proposed. Among these, the Saffman-Delbrück model is the most famous. This model predicts a logarithmic dependence of a protein’s diffusion coefficient on its inverse hydrodynamic radius (D ∝ ln 1/R) for small radius values. For large radius values, it converges toward a D ∝ 1/R scaling. Recently, however, experimental data indicate a Stokes-Einstein-like behavior (D ∝ 1/R) of membrane protein diffusion at small protein radii. In this study, we investigate protein diffusion in black lipid membranes using dual-focus fluorescence correlation spectroscopy. This technique yields highly accurate diffusion coefficients for lipid and protein diffusion in membranes. We find that despite its simplicity, the Saffman-Delbrück model is able to describe protein diffusion extremely well and a Stokes-Einstein-like behavior can be ruled out.     

Quasi-elastic light scattering by diffusional fluctuations in RNase solutions

Using measurements of quasi-elastic light scattering spectra, we have investigated diffusional fluctuations of RNase. The diffusion coefficient for individual protein molecules, together with the corresponding calculated effective molecular radius R_eff, were determined. Between room temperature and the point of irreversible denaturation at 63.5°C, R_eff increased from 20-250 A. This is comparable to the plateau in R_eff of 300 A reached after about 200 min following chemical denaturation in 10 M urea. The measurements indicated the presence of a large size component even in the freshly prepared and chromatographically purified solutions. From the diffusion constants deduced for this large component we obtained effective sizes from 1000-5000 A. Concentration and temperature dependent measurements exclude the possibility that these large particles are impurities and indicate that they are the result of aggregations of RNase molecules.     

Predicting translational diffusion of evolutionary conserved RNA structures by the nucleotide number

Ribonucleic acids are highly conserved essential parts of cellular life. RNA function is determined to a large extent by its hydrodynamic behaviour. The presented study proposes a strategy to predict the hydrodynamic behaviour of RNA single strands on the basis of the polymer size. By atom-level shell-modelling of high-resolution structures, hydrodynamic radius and diffusion coefficient of evolutionary conserved RNA single strands (ssRNA) were calculated. The diffusion coefficients D of 17–174 nucleotides (nt) containing ssRNA depended on the number of nucleotides N with D = 4.56 × 10⁻¹⁰ N^−0.39 m² s⁻¹. The hydrodynamic radius R_H depended on N with R_H = 5.00 × 10⁻¹⁰ N^0.38 m. An average ratio of the radius of gyration and the hydrodynamic radius of 0.98 ± 0.08 was calculated in solution. The empirical law was tested by in solution measured hydrodynamic radii and radii of gyration and was found to be highly consistent with experimental data of evolutionary conserved ssRNA. Furthermore, the hydrodynamic behaviour of several evolutionary unevolved ribonucleic acids could be predicted. Based on atom-level shell-modelling of high-resolution structures and experimental hydrodynamic data, empirical models are proposed, which enable to predict the translational diffusion coefficient and molecular size of short RNA single strands solely on the basis of the polymer size.     

Translational diffusion in the plasma membrane of sea urchin eggs

Translational diffusion in the plasma membrane of individual egg cells from the sea urchin species Paracentrotus lividus has been studied by fluorescence microphotolysis (FM). In order to probe the lipid phase of the membrane, procedures have been worked out by which the fluorescent analog 3,3′-dioctadecyl-oxatricarbocyanine (C₁₈diO) can be incorporated into the membrane. In the unfertilized egg a fraction R = 0.9 of C₁₈diO was mobile having an apparent diffusion coefficient of D = 6.0 × 10^?9 cm² sec^?1. Fifteen to twenty-five minutes after fertilization R and D were reduced to 0.8 and 2.7 × 10^?9 cm² sec^?1, respectively. In order to study diffusion of membrane proteins, procedures have been worked out by which the cell surface can be labeled with fluorescein-isothiocyanate (FITC). FITC binds to both the plasma membrane and the vitelline layer. Together with the vitelline layer two-thirds of the FITC-fluorescence could be removed from the egg surface. Gel electropherograms of isolated egg cortices showed various protein bands; however, only two of the protein bands were labeled with FITC. In the unfertilized egg a fraction R = 0.9 of the FITC-labeled membrane proteins was mobile having an apparent diffusion coefficient of D = 35 × 10^?11 cm² sem^?1. Fiteen to twenty-five minutes after fertilization R and D were reduced to 0.8 and 7.0 × 10^?11 cm² sec^?1, respectively. FITC-labeled proteins of the fertilization envelope were immobile. Our studies have shown (i) that the egg surface can be fluorescently labeled without blocking fertilization and early development, (ii) that the plasma membrane of unfertilized eggs is a fluid environment permitting a rapid movement of lipids and proteins, and (iii) that after fertilization a substantial degree of lipid and protein mobility is maintained.     

Transient state isoelectric focusing. Experimental determination of apparent diffusion coefficients in polyacrylamide gels

A photoelectric scanning assembly utilizing uv absorption optics and an on-line digital data acquisition and processing system has been used to follow kinetically zone spreading during the defocusing stage (absence of electric field) of transient state isoelectric focusing (TRANSIF) in polyacrylamide gels. Measurement of the variance (σ²) of a diffusing zone as a function of time yields a linear relationship, the slope of which corresponds to the apparent diffusion coefficient (D) of the protein. A linear relationship is also obtained when the logarithm of the apparent diffusion coefficients (logD) are plotted vs acrylamide concentration (T). This relationship can be used to extrapolate D to zero gel concentration. The apparent diffusion coefficient measured in this way is significantly larger than the true diffusion coefficient. The slope of the plot logD vs T, designated C_R, is expected to be a measure of molecular size related to the retardation coefficient in polyacrylamide gel electrophoresis.     

Influence of the shape of phospholipid vesicles on the measurement of their size by photon correlation spectroscopy

The influence of shape transformation of large unilamellar vesicles (LUV) on their size measurement by photon correlation spectroscopy (PCS) has been investigated. The experimental size of vesicles after hyperosmotic contractions of increasing intensities have been compared to the theoretical volume decrease determined by applying Boyle Van't Hoff's law. The main observation is that PCS size measurement gives overestimated values when LUV have been subjected to a volume decrease of more than 20% of their initial volume. The PCS size overestimation is related to the influence of the shape transformation of the vesicles on their diffusion coefficient (D) as shown by modelling the evolution of D of a sphere which is transformed into an ellipsoid by internal volume reduction under constant area. Received: 4 December 1997 / Revised version: 2 March 1998 / Accepted: 15 April 1998     

Solvent effect on the relative quantum yield and fluorescence quenching of a newly synthesized coumarin derivative

We estimated the relative florescence quantum yield (Φ) of 8‐methoxy‐3‐[1‐(4,5‐dicarbomethoxy‐1,2,3‐triazoloacetyl)]coumarin [8MDTC] using a single‐point method with quinine sulfate in 0.1 M of sulfuric acid used as a standard reference. The fluorescence lifetimes, radiative and non‐radiative decay rate constants are calculated. Relative quantum yields were found to be less in the non‐polar solvents, indicating that the solute exhibits less fluorescence in a non‐polar environment. The fluorescence quenching of [8MDTC] by aniline was studied at room temperature by examining the steady state in five different solvents in order to explore various possible quenching mechanisms. The experimental results show a positive deviation in Stern–Volmer plots in all solvents. Ground state complex and sphere of action static quenching models were used to interpret the results. Many quenching rate parameters were calculated using these models. The values of these parameters suggest that the sphere of action static quenching model agrees well with the experimental results. Further, a finite sink approximation model was used to check whether these bimolecular reactions were diffusion limited or not. The values of the distance parameter R′ and the diffusion coefficient D were determined and are compared with the values of the encounter distance R and diffusion coefficient D calculated using the Stokes–Einstein equation. Copyright © 2014 John Wiley & Sons, Ltd.     

Monitoring bacterial growth using tunable resistive pulse sensing with a pore-based technique

A novel bacterial growth monitoring method using a tunable resistive pulse sensor (TRPS) system is introduced in this study for accurate and sensitive measurement of cell size and cell concentration simultaneously. Two model bacterial strains, Bacillus subtilis str.168 (BSU168) and Escherichia coli str.DH5α (DH5α), were chosen for benchmarking the growth-monitoring performance of the system. Results showed that the technique of TRPS is sensitive and accurate relative to widely used methods, with a lower detection limit of cell concentration measurement of 5?×?10⁵ cells/ml; at the same time, the mean coefficient of variation from TRPS was within 2 %. The growth of BSU168 and DH5α in liquid cultures was studied by TRPS, optical density (OD), and colony plating. Compared to OD measurement, TRPS-measured concentration correlates better with colony plating (R?=?0.85 vs. R?=?0.72), which is often regarded as the gold standard of cell concentration determination. General agreement was also observed by comparing TRPS-derived cell volume measurements and those determined from microscopy. We have demonstrated that TRPS is a reliable method for bacterial growth monitoring, where the study of both cell volume and cell concentration are needed to provide further details about the physical aspects of cell dynamics in real time.     

Fluorescence correlation spectroscopy. II. An experimental realization

This paper describes the first experimental application of fluorescence correlation spectroscopy, a new method for determining chemical kinetic constants and diffusion coefficients. These quantities are measured by observing the time behaviour of the tiny concentration fluctuations which occur spontaneously in the reaction system even when it is in equilibrium. The equilibrium of the system is not disturbed during the experiment. The diffusion coefficients and chemical rate constants which determine the average time behaviour of these spontaneous fluctuations are the same as those sought by more conventional methods including temperature-jump or other perturbation techniques. The experiment consists essentially in measuring the variation with time of the number of molecules of specified reactants in a defined open volume of solution. The concentration of a reactant is measured by its fluorescence; the sample volume is defined by a focused laser beam which excites the fluorescence. The fluorescent emission fluctuates in proportion with the changes in the number of fluorescent molecules as they diffuse into and out of the sample volume and as they are created or eliminated by the chemical reactions. The number of these reactant molecules must be small to permit detection of the concentration fluctuations. Hence the sample volume is small (10^?8 ml) and the concentration of the solutes is low (～ 10^?9 M). We have applied this technique to the study of two prototype systems: the simple example of pure diffusion of a single fluorescent species, rhodamine 6G, and the more interesting but more challenging example of the reaction of macromolecular DNA with the drug ethidium bromide to form a fluorescent complex. The increase of the fluorescence of the ethidium bromide upon formation of the complex permits the observation of the decay of concentration fluctuations via the chemical reaction and consequently the determination of chemical rate constants.     

Stages of bacteriophage lambda head morphogenesis: physical analysis of particles in solution

Intermediates in the morphogenesis of bacteriophage lambda are characterized in solution by classical light-scattering, using a modified version of the Zimm plot procedure, by quasi-elastic light-scattering and analytical ultracentrifugation. Partial specific volumes are determined simultaneously with molecular weights by a variant of the conventional combination of sedimentation and diffusion constants. Our measurements were performed within a short time and allowed the characterisation of metastable intermediates.Comparison of hydration of DNA-containing and empty heads shows that dehydration plays a minor role in the stabilisation of the DNA within the heads. The molecular weight of the scaffolding protein is 4 × 10⁶, about twice the value estimated so far. Enlargement of preheads (21% and 13% increase in dry and hydrodynamic radius, respectively) leaves the molecular weight unchanged, whereas the volume of hydration water increases from 70% to 90% of the total hydrodynamic volume. Addition of protein pD to the enlarged preheads leads to a further increase in the radius, indicating that pD is attached to the outside of the protein shell.In order to determine simultaneously the molecular weight and the partial specific volume of large and sometimes labile structures, such as a virus, the conventional sedimentation-diffusion method is modified by measuring sedimentation and diffusion coefficients in buffers containing different amounts of ²H₂O. If diffusion coefficients are determined by quasi-elastic light-scattering, experiments can be performed in a few hours. In addition, the method allows a check on the sample for changes in the frictional coefficient due, for instance, to DNA abortively ejected from a virus preparation. This method is described in the Appendix.     

Simulation of protein diffusion: a sensitive probe of protein–solvent interactions

Aqueous solutions of Candida antarctica lipase B (CALB) were simulated considering three different water models (SPC/E, TIP3P, TIP4P) by a series of molecular dynamics (MD) simulations of three different box sizes (L = 9, 14, and 19 nm) to determine the diffusion coefficient, the water viscosity and the protein density. The protein–water systems were equilibrated for 500 ns, followed by 100 ns production runs which were analysed. The diffusional properties of CALB were characterized by the Stokes radius (R_S), which was derived from the diffusion coefficient and the viscosity. R_S was compared to the geometric radius (R_G) of CALB, which was derived from the protein density. R_S and R_G differed by 0.27 nm for SPC/E and by 0.40 and 0.39 nm for TIP3P and TIP4P, respectively, which characterizes the thickness of the diffusive hydration layer on the protein surface. The simulated hydration layer of CALB resulted in agreement with those experimentally determined for other seven different proteins of comparable size. By avoiding the most common pitfalls, protein diffusion can be reliably simulated: simulating different box sizes to account for the finite size effect, equilibrating the protein–water system sufficiently, and using the complete production run for the determination of the diffusion coefficient.     

Influence of obstacles on lipid lateral diffusion: computer simulation of FRAP experiments and application to proteoliposomes and biomembranes

Fluorescence Recovery After Photobleaching experiments were simulated using a computer approach in which a membrane lipid leaflet was mimicked using a triangular lattice obstructed with randomly distributed immobile and non-overlapping circular obstacles. Influence of the radius r and area fraction c of these obstacles and of the radius R of the observation area on the relative diffusion coefficient D ^* (Eq. (1)) and mobile fraction M was analyzed. A phenomenological equation relating D ^* to r and c was established. Fitting this equation to the FRAP data we obtained with the probe NBD-PC embedded in bacteriorhodopsin/egg-PC multilayers suggests that this transmembrane protein rigidifies the surrounding lipid phase over a distance of about 18 Å (two lipid layers) from the protein surface. In contrast, analysis of published diffusion constants obtained for lipids in the presence of gramicidin suggests that in terms of lateral diffusion, this relatively small polypeptide does not significantly affect the surrounding lipid phase. With respect to the mobile fraction M, and for point obstacles above the percolation threshold, an increase in R led to a decrease in M which can be associated with the existence of closed domains whose average size and diffusion properties can be determined. Adaptation of this model to the re-interpretation of the FRAP data obtained by Yechiel and Edidin (J Cell Biol (1987) 115:755–760) for the plasma membrane of human fibroblasts consistently leads to the suggestion that the lateral organization of this membrane would be of the confined type, with closed lipid domains of 0.5 µm² in area.Abbreviations and notations used BR bacteriorhodopsin - DMPC dimyristoylphosphatidylcholine - diOC18 dioctadecyloxatricarbocyanine - egf-PC egg-yolk phosphatidylcholine - NBD-PC 1-acyl2-[t2-[(7-nitro-2-1,3-benzoxadiazol-4-yl)amino]dodecanoyl]-sn-glycero-3-phosphocholine - MOPS 3-[N-morpholino]propane sulfonic acid - FRAP Fluoresence Recovery After photobleaching - D observed diffusion coefficient - D0 diffusion coefficient in the absence of obstacles - D ^* relative diffusion constant (Eq. 1) - M mobile fraction - c obstacle area fraction - r obstacle radius - R observation area radius - r _d diffusion area radius Correspondence to: A. Lopez     

Random-walk model of diffusion in three dimensions in brain extracellular space: comparison with microfiberoptic photobleaching measurements

Diffusion through the extracellular space (ECS) in brain is important in drug delivery, intercellular communication, and extracellular ionic buffering. The ECS comprises ∼20% of brain parenchymal volume and contains cell-cell gaps ∼50 nm. We developed a random-walk model to simulate macromolecule diffusion in brain ECS in three dimensions using realistic ECS dimensions. Model inputs included ECS volume fraction (α), cell size, cell-cell gap geometry, intercellular lake (expanded regions of brain ECS) dimensions, and molecular size of the diffusing solute. Model output was relative solute diffusion in water versus brain ECS (D_o/D). Experimental D_o/D for comparison with model predictions was measured using a microfiberoptic fluorescence photobleaching method involving stereotaxic insertion of a micron-size optical fiber into mouse brain. D_o/D for the small solute calcein in different regions of brain was in the range 3.0-4.1, and increased with brain cell swelling after water intoxication. D_o/D also increased with increasing size of the diffusing solute, particularly in deep brain nuclei. Simulations of measured D_o/D using realistic α, cell size and cell-cell gap required the presence of intercellular lakes at multicell contact points, and the contact length of cell-cell gaps to be least 50-fold smaller than cell size. The model accurately predicted D_o/D for different solute sizes. Also, the modeling showed unanticipated effects on D_o/D of changing ECS and cell dimensions that implicated solute trapping by lakes. Our model establishes the geometric constraints to account quantitatively for the relatively modest slowing of solute and macromolecule diffusion in brain ECS.     

Photon correlation spectroscopy of human IgG

The translational diffusion coefficient D _20,w ⁰ , of monomeric human immunoglobulin G (IgG) has been studied by photon-correlation spectroscopy as a function of pH and protein concentration. At pH 7.6, we find D _20,w ⁰ =3.89×10^–7±0.02 cm²/sec, in good agreement with the value determined by classic mehods. This value corresponds to an effective hydrodynamic radius R, of 55.1±0.3 Å. As pH is increased to 8.9; with the same ionic strength, the molecule appears to expand slightly (3.5% increase in hydrodynamic radius). The concentration dependence of the IgG diffusion constant is interpreted in terms of solution electrostatic effects and shows that long-range repulsive interactions are negligible in the buffer used. The diffusion coefficient for dimeric IgG has also been determined to be D_20,w=2.81×10^–7±0.04 cm²/sec at 1.6 mg/ml, which corresponds to a hydrodynamic radius of 75 Å. For light-scattering studies of protein molecules in the dimension range of 5–10 nm (M_r=10⁵–10⁷) we find monomeric horse spleen ferritin well suited as a reference standard. Ferritin is a spherical molecule with a hydrodynamic radius R of 6.9±0.1 nm and is stable for years in our standard Tris-HCl-NaCl buffer even at room temperature.     

From microscopy data to in silico environments for in vivo-oriented simulations

In our previous study, we introduced a combination methodology of Fluorescence Correlation Spectroscopy (FCS) and Transmission Electron Microscopy (TEM), which is powerful to investigate the effect of intracellular environment to biochemical reaction processes. Now, we developed a reconstruction method of realistic simulation spaces based on our TEM images. Interactive raytracing visualization of this space allows the perception of the overall 3D structure, which is not directly accessible from 2D TEM images. Simulation results show that the diffusion in such generated structures strongly depends on image post-processing. Frayed structures corresponding to noisy images hinder the diffusion much stronger than smooth surfaces from denoised images. This means that the correct identification of noise or structure is significant to reconstruct appropriate reaction environment in silico in order to estimate realistic behaviors of reactants in vivo. Static structures lead to anomalous diffusion due to the partial confinement. In contrast, mobile crowding agents do not lead to anomalous diffusion at moderate crowding levels. By varying the mobility of these non-reactive obstacles (NRO), we estimated the relationship between NRO diffusion coefficient (D_nro) and the anomaly in the tracer diffusion (α). For D_nro=21.96 to 44.49 μm²/s, the simulation results match the anomaly obtained from FCS measurements. This range of the diffusion coefficient from simulations is compatible with the range of the diffusion coefficient of structural proteins in the cytoplasm. In addition, we investigated the relationship between the radius of NRO and anomalous diffusion coefficient of tracers by the comparison between different simulations. The radius of NRO has to be 58 nm when the polymer moves with the same diffusion speed as a reactant, which is close to the radius of functional protein complexes in a cell.     

Diffusion of insulin-like growth factor-I and ribonuclease through fibrin gels

A fluorescence-based method for simultaneously determining the diffusion coefficients of two proteins is described, and the diffusion coefficient of insulin-like growth factor (IGF-I) and ribonuclease (RNase) in a 0.27% fibrin hydrogel is reported. The method is based on two-color imaging of the relaxation of the protein concentration field with time and comparing the results with a transport model. The gel is confined in a thin (200 μm) capillary and the protein is labeled with a fluorescent dye. The experimentally determined diffusion coefficient of RNase (D = 1.21 × 10⁻⁶ cm²/s) agrees with literature values for dilute gels and bulk aqueous solutions, thus indicating the gel and the dye had a negligible effect on diffusion. The experimental diffusion coefficient of IGF-I (D = 1.59 × 10⁻⁶ cm²/s), in the absence of binding to the fibrin matrix, is consistent with the dimensions of the molecule known from x-ray crystallography and a correlation between D and molecular weight based on 14 other proteins. The experimental method developed here holds promise for determining molecular transport properties of biomolecules under a variety of conditions, for example, when the molecule adsorbs to the gel or is convected through the gel by fluid transport.     

Cheek cell membrane fluidity measured by fluorescence recovery after photobleaching and steady-state fluorescence anisotropy

Membrane fluidity of human cheek cells was determined using fluorescence recovery after photobleaching (FRAP) and steady-state fluorescence anisotropy. The FRAP data showed that the lateral diffusion coefficient (D) and mobile fraction (%R) of lipid in the plasma membrane of control cells were 2.01×10^–9 cm²/ sec and 54.25%, respectively. Trypsin treatment increased D and %R to 6.4×10^–9 cm²/sec and 72.15%. In contrast, the anisotropy (r) for control cells was 0.270 which remained unchanged by trypsin treatment. The results show that diffusion of lipids in the plane of the membrane is restricted by trypsin-sensitive barriers.     

Rapid characterization of protein molecular weights and hydrodynamic structures by quasielastic laser-light scattering

Two methods for the characterization of protein molecular weights from their diffusion coefficients are discussed. These measurements can be made quickly and reliably at low concentrations using quasielastic light-scattering techniques. First, an empirical calibration of the diffusion coefficient at infinite dilution of denatured random coils against molecular weight is reported. The second method combines the measurement of D₀ with the intrinsic viscosity [η]. This D₀–[η] relationship proves to be very insensitive to polymers structure or solvent type. The data indicate that the ratio of the hydrodynamic radius measured by viscosity to the hydrodynamic radius measured by diffusion is about 15% smaller than that predicted by theoretical models. The nature of the molecular-weight average obtained for polydisperse systems is defined for a Schulz distribution. These hydrodynamic methods have also been used to demonstrate the presence of chain branching in the glycoprotein ovomucoid. In addition, a method is proposed by which the effective segment length and an excluded volume parameter for random coils may be evaluated for diffusion measurements.     

A Generalization of Theory for Two-Dimensional Fluorescence Recovery after Photobleaching Applicable to Confocal Laser Scanning Microscopes

Fluorescence recovery after photobleaching (FRAP) using confocal laser scanning microscopes (confocal FRAP) has become a valuable technique for studying the diffusion of biomolecules in cells. However, two-dimensional confocal FRAP sometimes yields results that vary with experimental setups, such as different bleaching protocols and bleaching spot sizes. In addition, when confocal FRAP is used to measure diffusion coefficients (D) for fast diffusing molecules, it often yields D-values that are one or two orders-of-magnitude smaller than that predicted theoretically or measured by alternative methods such as fluorescence correlation spectroscopy. Recently, it was demonstrated that this underestimation of D can be corrected by taking diffusion during photobleaching into consideration. However, there is currently no consensus on confocal FRAP theory, and no efforts have been made to unify theories on conventional and confocal FRAP. To this end, we generalized conventional FRAP theory to incorporate diffusion during photobleaching so that analysis by conventional FRAP theory for a circular region of interest is easily applicable to confocal FRAP. Finally, we demonstrate the accuracy of these new (to our knowledge) formulae by measuring D for soluble enhanced green fluorescent protein in aqueous glycerol solution and in the cytoplasm and nucleus of COS7 cells.     

Protein Mobility in the Cytoplasm of Escherichia coli

The rate of protein diffusion in bacterial cytoplasm may constrain a variety of cellular functions and limit the rates of many biochemical reactions in vivo. In this paper, we report noninvasive measurements of the apparent diffusion coefficient of green fluorescent protein (GFP) in the cytoplasm of Escherichia coli. These measurements were made in two ways: by photobleaching of GFP fluorescence and by photoactivation of a red-emitting fluorescent state of GFP (M. B. Elowitz, M. G. Surette, P. E. Wolf, J. Stock, and S. Leibler, Curr. Biol. 7:809–812, 1997). The apparent diffusion coefficient, D_a, of GFP in E. coli DH5α was found to be 7.7 ± 2.5 μm²/s. A 72-kDa fusion protein composed of GFP and a cytoplasmically localized maltose binding protein domain moves more slowly, with D_a of 2.5 ± 0.6 μm²/s. In addition, GFP mobility can depend strongly on at least two factors: first, D_a is reduced to 3.6 ± 0.7 μm²/s at high levels of GFP expression; second, the addition to GFP of a small tag consisting of six histidine residues reduces D_a to 4.0 ± 2.0 μm²/s. Thus, a single effective cytoplasmic viscosity cannot explain all values of D_a reported here. These measurements have implications for the understanding of intracellular biochemical networks.