Numerical inversion of the Perrin equations for rotational and translational diffusion constants by iterative techniques.

An iterative numerical technique is presented which allows the semiaxes for prolate and oblate ellipsoids to be determined from the Perrin equations for rotational and translational diffusion constants. The use of this inversion technique is illustrated by application to the proteins: lysozyme, bovine serum albumin, human transferrin, and bovine rhodopsin solubilized in digitonin.     

Tracking single proteins within cells

We present experiments in which single proteins were imaged and tracked within mammalian cells. Single proteins of R-phycoerythrin (RPE) were imaged by epifluorescence microscopy in the nucleoplasm and cytoplasm at 71 frames/s. We acquired two-dimensional trajectories of proteins (corresponding to the projection of three-dimensional trajectories onto the plane of focus) for an average of 17 frames in the cytoplasm and 16 frames in the nucleus. Diffusion constants were determined from linear fits to the mean square displacement and from the mean displacement squared per frame. We find that the distribution of diffusion constants for RPE within cells is broader than the distributions obtained from RPE in a glycerol solution, from a Monte Carlo simulation, and from the theoretical distribution for simple diffusion. This suggests that on the time scales of our measurements, the motion of single RPE proteins in the cytoplasm and nucleoplasm cannot be modeled by simple diffusion with a unique diffusion constant. Our results demonstrate that it is possible to follow the motion of single proteins within cells and that the technique of single molecule tracking can be used to probe the dynamics of intracellular macromolecules.     

Measuring surface dynamics of biomolecules by total internal reflection fluorescence with photobleaching recovery or correlation spectroscopy.

The theoretical basis of a new technique for measuring equilibrium adsorption/desorption kinetics and surface diffusion of fluorescent-labeled solute molecules at solid surfaces has been developed. The technique combines total internal reflection fluorescence (TIR) with either fluorescence photobleaching recovery (FPR) or fluorescence correlation spectroscopy (FCS). A laser beam totally internally reflects at a solid/liquid interface; the shallow evanescent field in the liquid excites the fluorescence of surface adsorbed molecules. In TIR/FPR, adsorbed molecules are bleaching by a flash of the focused laser beam; subsequent fluorescence recovery is monitored as bleached molecules exchange with unbleached ones from the solution or surrounding nonilluminated regions of the surface. In TIR/FCS, spontaneous fluorescence fluctuations due to individual molecules entering and leaving a well-defined portion of the evanescent field are autocorrelated. Under appropriate experimental conditions, the rate constants and surface diffusion coefficient can be readily obtained from the TIR/FPR and TIR/FCS curves. In general, the shape of the theoretical TIR/FPR and TIR/FCS curves depends in a complex manner upon the bulk and surface diffusion coefficients, the size of the iluminated or observed region, and the adsorption/desorption/kinetic rate constants. The theory can be applied both to specific binding between immobilized receptors and soluble ligands, and to nonspecific adsorption processes. A discussion of experimental considerations and the application of this technique to the adsorption of serum proteins on quartz may be found in the accompanying paper (Burghardt and Axelrod. 1981. Biophys. J. 33:455).     

Using FRAP and mathematical modeling to determine the in vivo kinetics of nuclear proteins

Fluorescence recovery after photobleaching (FRAP) has become a popular technique to investigate the behavior of proteins in living cells. Although the technique is relatively old, its application to studying endogenous intracellular proteins in living cells is relatively recent and is a consequence of the newly developed fluorescent protein-based living cell protein tags. This is particularly true for nuclear proteins, in which endogenous protein mobility has only recently been studied. Here we examine the experimental design and analysis of FRAP experiments. Mathematical modeling of FRAP data enables the experimentalist to extract information such as the association and dissociation constants, distribution of a protein between mobile and immobilized pools, and the effective diffusion coefficient of the molecule under study. As experimentalists begin to dissect the relative influence of protein domains within individual proteins, this approach will allow a quantitative assessment of the relative influences of different molecular interactions on the steady-state distribution and protein function in vivo.     

Binding of proteins to specific target sites in membranes measured by total internal reflection fluorescence microscopy

A new quantitative technique for measuring the binding of proteins to membranes is described. The method is based on a combination of total internal reflection fluorescence microscopy and the preparation of supported planar bilayers. Specific and reversible binding of a fluorescence-labeled monoclonal antibody to lipid haptens that were embedded in supported bilayers has been measured by this technique and compared to binding experiments that were conducted on membrane vesicles in solution. Equilibrium binding constants and kinetic parameters have been determined and used to expand the picture of the antibody-lipid hapten reaction. Estimates demonstrate that this technique is capable of measuring a broad range of binding constants (down to about 10(4) M-1) using only small amounts of ligand and receptor.     

Monte Carlo simulation of diffusion and reaction in two-dimensional cell structures.

Diffusion and reaction processes control the dynamics of many different biological systems. For example, tissue respiration can be limited by the delivery of oxygen to the cells and to the mitochondria. In this case, oxygen is small and travels quickly compared with the mitochondria, which can be considered as immobile reactive traps in the cell cytoplasm. A Monte Carlo theoretical investigation quantifying the interplay of diffusion, reaction, and structure on the reaction rate constant is reported here for diffusible particles in two-dimensional, reactive traps. The placement of traps in overlapping, nonoverlapping, and clustered spatial arrangements can have a large effect on the rate constant when the process is diffusion limited. However, under reaction-limited conditions the structure has little effect on the rate constant. For the same trap fractions and reactivities, nonoverlapping traps have the highest rate constants, overlapping traps yield intermediate rate constants, and clustered traps have the lowest rate constants. An increase in the particle diffusivity in the traps can increase the rate constant by reducing the time required by the particles to reach reactive sites. Various diffusive, reactive, and structural conditions are evaluated here, exemplifying the versatility of the Monte Carlo technique.     

Diffusion rates of cell surface antigens of mouse-human heterokaryons. I. Analysis of the population

The rate of appearance, in a newly formed heterokaryon population, of cells bearing completely intermixed mouse and human surface antigens may be used to estimate diffusion constants for antigens on individual cells. From this estimate, it appears that the surface antigens in most cells do not diffuse at the rate expected, but rather move more slowly, by a factor of ten or more, than expected from either measured or calculated diffusion constants for proteins freely mobile in the plane of a lipid membrane. Differences in diffusion rates between cells are not due to effects of Sendai virus, or of trypsin. Restrictions on diffusion are apparently not due to cytochalasin B- or Colcemid- sensitive elements.     

Determination of Protein-ligand Interactions Using Differential Scanning Fluorimetry

A wide range of methods are currently available for determining the dissociation constant between a protein and interacting small molecules. However, most of these require access to specialist equipment, and often require a degree of expertise to effectively establish reliable experiments and analyze data. Differential scanning fluorimetry (DSF) is being increasingly used as a robust method for initial screening of proteins for interacting small molecules, either for identifying physiological partners or for hit discovery. This technique has the advantage that it requires only a PCR machine suitable for quantitative PCR, and so suitable instrumentation is available in most institutions; an excellent range of protocols are already available; and there are strong precedents in the literature for multiple uses of the method. Past work has proposed several means of calculating dissociation constants from DSF data, but these are mathematically demanding. Here, we demonstrate a method for estimating dissociation constants from a moderate amount of DSF experimental data. These data can typically be collected and analyzed within a single day. We demonstrate how different models can be used to fit data collected from simple binding events, and where cooperative binding or independent binding sites are present. Finally, we present an example of data analysis in a case where standard models do not apply. These methods are illustrated with data collected on commercially available control proteins, and two proteins from our research program. Overall, our method provides a straightforward way for researchers to rapidly gain further insight into protein-ligand interactions using DSF.     

Energetics of cooperative protein-DNA interactions: comparison between quantitative deoxyribonuclease footprint titration and filter binding

Using the binding of cI repressor protein to the lambda right and left operators as a model system, we have analyzed the two common experimental techniques for studying the interactions of genome regulatory proteins with multiple, specific sites on DNA. These are the quantitative DNase footprint titration technique [Brenowitz, M., Senear, D. F., Shea, M. A., & Ackers, G. K. (1986) Methods Enzymol. 130, 132-181] and the nitrocellulose filter binding assay [Riggs, A., Suzuki, H., & Bourgeois, S. (1970) J. Mol. Biol. 48, 67-83]. The footprint titration technique provides binding curves that separately represent the fractional saturation for each site. In principle, such data contain the information necessary to determine the thermodynamic constants for local site binding and cooperativity. We show that in practice, this is not possible for all values of the constants in multisite systems, such as the lambda operators. We show how these constants can nevertheless be uniquely determined by using additional binding data from a small number of mutant operators in which the number of binding sites has been reduced. The filter binding technique does not distinguish binding to the individual sites and yields only macroscopic binding parameters which are composite averages of the various local site and cooperativity constants. Moreover, the resolution of even macroscopic constants from filter binding data for multisite systems requires ad hoc assumptions as to a relationship between the number of ligands bound and the filter retention of the complex. Our results indicate that no such relationship exists. Hence, the technique does not permit determination of thermodynamically valid interaction constants (even macroscopic) in multisite systems.     

Lateral diffusion of rhodopsin in photoreceptor cells measured by fluorescence photobleaching and recovery.

Frog rod outer segments were labeled with the sulfhydryl-reactive label iodoacetamido tetramethylrhodamine. The bulk of the label reacted with the major disk membrane protein, rhodopsin. Fluorescence photobleaching and recovery (FPR) experiments on labeled rods showed that the labeled proteins diffused rapidly in the disk membranes. In these FPR experiments we observed both the recovery of fluorescence in the bleached spot and the loss of fluorescence from nearby, unbleached regions of the photoreceptor. These and previous experiments show that the redistribution of the fluorescent labeled proteins after bleaching was due to diffusion. The diffusion constant, D, was (3.0 +/- 10(-9) cm2 s-1 if estimated from the rate of recovery of fluorescence in the bleached spot, and (5.3 +/- 2.4) x 10(-9) cm2 s-1 if estimated from the rate of depletion of fluorescence from nearby regions. The temperature coefficient, Q10, for diffusion was 1.7 +/- 0.5 over the range 10 degrees--29 degrees C. These values obtained by FPR are in good agreement with those previously obtained by photobleaching rhodopsin in fresh, unlabeled rods. This agreement indicates that the labeling and bleaching procedures required by the FPR method did not significantly alter the diffusion rate of rhodopsin. Moreover, the magnitude of the diffusion constant for rhodopsin is that to be expected for an object of its diameter diffusing in a bilayer with the viscosity of the disk membrane. In contrast to the case of rhodopsin, FPR methods applied to other membrane proteins have yielded much smaller diffusion constants. The present results help indicate that these smaller diffusion constants are not artifacts of the method but may instead be due to interactions the diffusing proteins have with other components of the membrane in addition to the viscous drag imposed by the lipid bilayer.     

The role of the maltodextrin-binding site in determining the transport properties of the LamB protein

We have examined by the liposome swelling technique the permeability properties of the modified LamB proteins isolated from mutants of Escherichia coli K12 with altered affinities toward starch and/or maltose (Ferenci, T., and Lee, K-S. (1982) J. Mol. Biol. 160, 431-444). The results revealed the following. A mutant strain exhibiting a markedly lowered affinity toward starch produced a LamB protein that has lost the ability to permeate longer maltodextrins. This protein retained a nonspecific pore for a wide variety of small sugars. A mutant strain with partially reduced affinity for starch produced a LamB protein which still permeated maltodextrins, maltose, and non-maltose sugars but had also gained an ability to permit the diffusion of sucrose and raffinose; in this strain sucrose and raffinose could now compete for the starch-binding site. A mutant with enhanced affinity for both maltose and starch produced a protein which exhibited elevated rates of diffusion for longer maltodextrins but still permeated other small sugars. Two other mutants with altered affinities showed relatively minor changes in the diffusion of maltose and non-maltose sugars. It could be concluded from these studies that the LamB proteins form pores allowing the diffusion of a wide variety of monosaccharides irrespective of the presence or the absence of affinity of a binding site for maltodextrins. However, the presence of a sugar-binding site is crucial in determining the rate of the diffusion of maltodextrins or other oligosaccharides.     

Protein-ligand interactions measured by 15N-filtered diffusion experiments

NMR diffusion coefficient measurements have been shown to be sensitive to the conformational and oligomeric states of proteins. Recently, heteronuclear-filtered diffusion experiments have been proposed [Dingley et al. (1997) J. Biomol. NMR, 10, 1–8]. Several new heteronuclear-filtered diffusion pulse sequences are proposed which are shown to have superior sensitivity to those previously proposed. One of these new heteronuclear-filtered diffusion experiments has been used to study the binding of an SH3 domain to a peptide. Using this system, we show that it is possible to measure binding constants from diffusion coefficient measurements.     

Penetration of dioxygen into proteins studied by quenching of phosphorescence and fluorescence

Experiments were done to measure the ability of dioxygen to collisionally quench the phosphorescent and fluorescent tryptophans in alcohol dehydrogenase and alkaline phosphatase. In all cases, luminescence is quenched with rate constants close to 1 x 10(9) M-1 s-1. The rate of reaching the buried tryptophans is little affected by solvent viscosity due to added glycerol. Quenching by dioxygen is not due to a protein-opening reaction. It appears to be rate limited by internal protein diffusion rather than at the entry step. Dioxygen appears to enter the proteins directly, as in liquidlike diffusion, rather than through transiently forming channels that are only present a small fraction of the time. A high-pressure oxygen system is described that considerably facilitates fluorescence quenching experiments.     

A closed-form analytic expression for FRAP formula for the binding diffusion model

One of the most dominant methods cells use for a large class of cellular processes is reaction (or binding) diffusion kinetics, which are controlled by kinetic constants such as diffusion coefficients and on/off binding rate constants. Fluorescence recovery after photobleaching (FRAP) can be used to determine these kinetic constants in living cells. While an analytic expression for FRAP formulae for pure diffusion has been available for some time, an analytic FRAP formula for the binding diffusion model has not been reported yet. Here, we present an analytic FRAP formula for the binding diffusion model in an explicit form allowing for diffusion of the bound complex for either a uniform circle laser profile or a Gaussian laser profile.     

Lateral diffusion in an archipelago. The effect of mobile obstacles.

Lateral diffusion of mobile proteins and lipids (tracers) in a membrane is hindered by the presence of proteins (obstacles) in the membrane. If the obstacles are immobile, their effect may be described by percolation theory, which states that the long-range diffusion constant of the tracers goes to zero when the area fraction of obstacles is greater than the percolation threshold. If the obstacles are themselves mobile, the diffusion constant of the tracers depends on the area fraction of obstacles and the relative jump rate of tracers and obstacles. This paper presents Monte Carlo calculations of diffusion constants on square and triangular lattices as a function of the concentration of obstacles and the relative jump rate. The diffusion constant for particles of various sizes is also obtained. Calculated values of the concentration-dependent diffusion constant are compared with observed values for gramicidin and bacteriorhodopsin. The effect of the proteins as inert obstacles is significant, but other factors, such as protein-protein interactions and perturbation of lipid viscosity by proteins, are of comparable importance. Potential applications include the diffusion of proteins at high concentrations (such as rhodopsin in rod outer segments), the modulation of diffusion by release of membrane proteins from cytoskeletal attachment, and the diffusion of mobile redox carriers in mitochondria, chloroplasts, and endoplasmic reticulum.     

Measurement of the local translational diffusion rates of proteins by saturation transfer EPR spectroscopy.

The concentration dependence of the normalized integral of the saturation-transfer EPR spectrum of human serum albumin spin-labelled on amino groups is found to be sensitive to viscosity and to temperature in aqueous solution and in 60% glycerol. The dependence on protein concentration is consistent with theoretical predictions for a diffusion-controlled Heisenberg spin-exchange interaction and the experimentally derived bimolecular collision rate constants are in reasonable agreement with those calculated theoretically for a diffusion-controlled process. The method is therefore applicable to the determination of translational diffusion coefficients of proteins in solution and, because of the nature of the saturation transfer EPR method, should be ideally suited to the study of local translational diffusion of proteins in membranes.     

Survey of the year 2009: applications of isothermal titration calorimetry

Isothermal titration calorimetry (ITC) is now an established and invaluable method for determining the thermodynamic constants, association constant and stoichiometry of molecular interactions in aqueous solutions. The technique has become widely used by biochemists to study protein interaction with other proteins, small molecules, metal ions, lipids, nucleic acids and carbohydrates; and nucleic acid interaction with small molecules. The drug discovery industry has utilized this approach to measure protein (or nucleic acid) interaction with drug candidates. ITC has been used to screen candidates, guide the design of potential drugs and validate the modelling used in structure-based drug design. Emerging disciplines including nanotechnology and drug delivery could benefit greatly from ITC in enhancing their understanding and control of nano-particle assembly, and drug binding and controlled release.     

Macromolecular diffusion in crowded solutions.

The effects of crowding on the self or tracer diffusion of macromolecules in concentrated solutions is an important but difficult problem, for which, so far, there has been no rigorous treatment. Muramatsu and Minton suggested a simple model to calculate the diffusion coefficient of a hard sphere among other hard spheres. In this treatment, scaled particle theory is used to evaluate the probability that the target volume for a step in a random walk is free of any macromolecules. We have improved this approach by using a more appropriate target volume which also allows the calculation to be extended to the diffusion of a hard sphere among hard spherocylinders. We conclude that, to the extent that proteins can be approximated as hard particles, the hindrance of globular proteins by other proteins is reduced when the background proteins aggregate (the more so the greater the decrease in particle surface area), the hindrance due to rod-shaped background particles is reduced slightly if the rod-like particles are aligned, and the anisotropy of the diffusion of soluble proteins among cytoskeletal proteins will normally be small.     

Molecular basis for the effect of urea and guanidinium chloride on the dynamics of unfolded polypeptide chains

Chemical denaturants are frequently used to unfold proteins and to characterize mechanisms and transition states of protein folding reactions. The molecular basis of the effect of urea and guanidinium chloride (GdmCl) on polypeptide chains is still not well understood. Models for denaturant--protein interaction include both direct binding and indirect changes in solvent properties. Here we report studies on the effect of urea and GdmCl on the rate constants (k(c)) of end-to-end diffusion in unstructured poly(glycine-serine) chains of different length. Urea and GdmCl both lead to a linear decrease of lnk(c) with denaturant concentration, as observed for the rate constants for protein folding. This suggests that the effect of denaturants on chain dynamics significantly contributes to the denaturant-dependence of folding rate constants for small proteins. We show that this linear dependency is the result of two additive non-linear effects, namely increased solvent viscosity and denaturant binding. The contribution from denaturant binding can be quantitatively described by Schellman's weak binding model with binding constants (K) of 0.62(+/-0.01)M(-1) for GdmCl and 0.26(+/-0.01)M(-1) for urea. In our model peptides the number of binding sites and the effect of a bound denaturant molecule on chain dynamics is identical for urea and GdmCl. The results further identify the polypeptide backbone as the major denaturant binding site and give an upper limit of a few nanoseconds for residence times of denaturant molecules on the polypeptide chain.     

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.