Recent advances in macromolecular hydrodynamic modeling

First coarse grain then scale: How to estimate diffusion coefficients of confined molecules

An approach for approximating position and orientation dependent translational and rotational diffusion coefficients of rigid molecules of any shape suspended in a viscous fluid under geometric confinement is proposed. It is an extension of the previously developed scheme for evaluating near-wall diffusion of macromolecules, now applied to any geometry of boundaries. The method relies on shape based coarse-graining combined with scaling of mobility matrix components by factors derived based on energy dissipation arguments for Stokes flows. Tests performed for a capsule shaped molecule and its coarse-grained model, a dumbbell, for three different types of boundaries (a sphere, an open cylinder, and two parallel planes) are described. An almost perfect agreement between mobility functions of the detailed and coarse-grained models, even close to boundary surfaces, is obtained. The proposed method can be used to simplify hydrodynamic calculations and reduce errors introduced due to coarse-graining of molecular shapes.

Modeling of the Electrostatic Interaction and Catalytic Activity of [NiFe] Hydrogenases on a Planar Electrode

Hydrogenases are a group of enzymes that have caught the interest of researchers in renewable energies, due to their ability to catalyze the redox reaction of hydrogen. The exploitation of hydrogenases in electrochemical devices requires their immobilization on the surface of suitable electrodes, such as graphite. The orientation of the enzyme on the electrode is important to ensure a good flux of electrons to the catalytic center, through an array of iron-sulfur clusters. Here we present a computational approach to determine the possible orientations of a [NiFe] hydrogenase (PDB 1e3d) on a planar electrode, as a function of pH, salinity, and electrode potential. The calculations are based on the solution of the linearized Poisson-Boltzmann equation, using the PyGBe software. The results reveal that electrostatic interactions do not truly immobilize the enzyme on the surface of the electrode, but there is instead a dynamic equilibrium between different orientations. Nonetheless, after averaging over all thermally accessible orientations, we find significant differences related to the solution's salinity and pH, while the effect of the electrode potential is relatively weak. We also combine models for the protein adsoption-desorption equilibria and for the electron transfer between the proteins and the electrode to arrive at a prediction of the electrode's activity as a function of the enzyme concentration.

Predicting the Orientation of Adsorbed Proteins Steered with Electric Fields Using a Simple Electrostatic Model

Under the most common experimental conditions, the adsorption of proteins to solid surfaces is a spontaneous process that leads to a rather compact layer of randomly oriented molecules. However, controlling such orientation is critically important for the development of catalytic surfaces. In this regard, the use of electric fields is one of the most promising alternatives. Our work is motivated by experimental observations that show important differences in catalytic activity of a trypsin-covered surface, which depended on the applied potential during the adsorption. Even though adsorption results from the combination of several processes, we were able to determine that (under the selected conditions) mean-field electrostatics play a dominant role, determining the orientation and yielding a difference in catalytic activity. We simulated the electrostatic potential numerically, using an implicit-solvent model based on the linearized Poisson-Boltzmann equation. This was implemented in an extension of the code PyGBe that included an external electric field, and rendered the electrostatic component of the solvation free energy. Our model (extensions available at the Github repository) allowed estimating the overall affinity of the protein with the surface, and their most likely orientation as a function of the potential applied. Our results show that the active sites of trypsin are, on average, more exposed when the electric field is negative, which agrees with the experimental results of catalytic activity, and confirm the premise that electrostatic interactions can be used to control the orientation of adsorbed proteins.

Estimating near-wall diffusion coefficients of arbitrarily shaped rigid macromolecules

We developed a computationally efficient approach to approximate near-wall diffusion coefficients of arbitrarily shaped rigid macromolecules. The proposed method relies on extremum principles for Stokes flows produced by the motion of rigid bodies. In the presence of the wall, the rate of energy dissipation is decreased relative to the unbounded fluid. In our approach, the position- and orientation-dependent mobility matrix of a body suspended near a no-slip plane is calculated numerically using a coarse-grained molecular model and the Rotne-Prager-Yamakawa description of hydrodynamics. Effects of the boundary are accounted for via Blake's image construction. The matrix components are scaled using ratios of the corresponding bulk values evaluated for the detailed representation of the molecule and its coarse-grained model, leading to accurate values of the near-wall diffusion coefficients. We assess the performance of the approach for two biomolecules at different levels of coarse-graining.

Calibrating analytical ultracentrifuges

Analytical ultracentrifugation (AUC) is based on the concept of recording and analyzing macroscopic macromolecular redistribution that results from a centrifugal force acting on the mass of suspended macromolecules in solution. Since AUC rests on first principles, it can provide an absolute measurement of macromolecular mass, sedimentation and diffusion coefficients, and many other quantities, provided that the solvent density and viscosity are known, and provided that the instrument is properly calibrated. Unfortunately, a large benchmark study revealed that many instruments exhibit very significant systematic errors. This includes the magnification of the optical detection system used to determine migration distance, the measurement of sedimentation time, and the measurement of the solution temperature governing viscosity. We have previously developed reference materials, tools, and protocols to detect and correct for systematic measurement errors in the AUC by comparison with independently calibrated standards. This 'external calibration' resulted in greatly improved precision and consistency of parameters across laboratories. Here we detail the steps required for calibration of the different data dimensions in the AUC. We demonstrate the calibration of three different instruments with absorbance and interference optical detection, and use measurements of the sedimentation coefficient of NISTmAb monomer as a test of consistency. Whereas the measured uncorrected sedimentation coefficients span a wide range from 6.22 to 6.61 S, proper calibration resulted in a tenfold reduced standard deviation of sedimentation coefficients. The calibrated relative standard deviation and mean error of 0.2% and 0.07%, respectively, is comparable with statistical errors and side-by-side repeatability in a single instrument.

Protein intrinsic viscosity determination with the Viscosizer TD instrument: reaching beyond the initially expected applications

Intrinsic viscosity is a key hydrodynamic parameter to understand molecular structure and hydration, as well as intramolecular interactions. Commercially available instruments measure intrinsic viscosity by recording the macromolecular mobility in a capillary. These instruments monitor Taylor dispersion using an absorbance or fluorescence detector. By design, these instruments behave like U-tube viscometers. To our knowledge, there are no studies to date showing that the Viscosizer TD instrument (Malvern-Panalytical) is able to measure the intrinsic viscosity of macromolecules. In this study, we then performed our assays on the Poly(ethylene oxide) polymer (PEO), used classically as a standard for viscometry measurements and on three model proteins: the bovine serum albumin (BSA), the bevacizumab monoclonal antibody, and the RTX Repeat Domain (RD) of the adenylate cyclase toxin of Bordetella pertussis (CyaA). The presence of P20 in the samples is critical to get reliable results. The data obtained with our in-house protocol show a strong correlation with intrinsic viscosity values obtained using conventional techniques. However, with respect to them, our measurements could be performed at relatively low concentrations, between 2 and 5 mg/ml, using only 7 µL per injection. Altogether, our results show that the Viscosizer TD instrument is able to measure intrinsic viscosities in a straightforward manner. This simple and innovative approach should give a new boost to intrinsic viscosity measurements and should reignite the interest of biophysicists, immunologists, structural biologists and other researchers for this key physicochemical parameter.

Hydrodynamic and Electrophoretic Properties of Trastuzumab/HER2 Extracellular Domain Complexes as Revealed by Experimental Techniques and Computational Simulations

The combination of hydrodynamic and electrophoretic experiments and computer simulations is a powerful approach to study the interaction between proteins. In this work, we present hydrodynamic and electrophoretic experiments in an aqueous solution along with molecular dynamics and hydrodynamic modeling to monitor and compute biophysical properties of the interactions between the extracellular domain of the HER2 protein (eHER2) and the monoclonal antibody trastuzumab (TZM). The importance of this system relies on the fact that the overexpression of HER2 protein is related with the poor prognosis breast cancers (HER2++ positives), while the TZM is a monoclonal antibody for the treatment of this cancer. We have found and characterized two different complexes between the TZM and eHER2 proteins (1:1 and 1:2 TZM:eHER2 complexes). The conformational features of these complexes regulate their hydrodynamic and electrostatic properties. Thus, the results indicate a high degree of molecular flexibility in the systems that ultimately leads to higher values of the intrinsic viscosity, as well as lower values of diffusion coefficient than those expected for simple globular proteins. A highly asymmetric charge distribution is detected for the monovalent complex (1:1 complex), which has strong implications in correlations between the experimental electrophoretic mobility and the modeled net charge. In order to understand the dynamics of these systems and the role of the specific domains involved, it is essential to find biophysical correlations between dynamics, macroscopic transport and electrostatic properties. The results should be of general interest for researchers working in this area.

GRPY: An Accurate Bead Method for Calculation of Hydrodynamic Properties of Rigid Biomacromolecules

Two main problems that arise in the context of hydrodynamic bead modeling are an inaccurate treatment of bead overlaps and the necessity of using volume corrections when calculating intrinsic viscosity. We present a formalism based on the generalized Rotne-Prager-Yamakawa approximation that successfully addresses both of these issues. The generalized Rotne-Prager-Yamakawa method is shown to be highly effective for the calculation of transport properties of rigid biomolecules represented as assemblies of spherical beads of different sizes, both overlapping and nonoverlapping. We test the method on simple molecular shapes as well as real protein structures and compare its performance with other computational approaches.

A radial calibration window for analytical ultracentrifugation

Analytical ultracentrifugation (AUC) is a first-principles based method for studying macromolecules and particles in solution by monitoring the evolution of their radial concentration distribution as a function of time in the presence of a high centrifugal field. In sedimentation velocity experiments, hydrodynamic properties relating to size, shape, density, and solvation of particles can be measured, at a high hydrodynamic resolution, on polydisperse samples. In a recent multilaboratory benchmark study including data from commercial analytical ultracentrifuges in 67 laboratories, the calibration accuracy of the radial dimension was found to be one of the dominant factors limiting the accuracy of AUC. In the present work, we develop an artifact consisting of an accurately calibrated reflective pattern lithographically deposited onto an AUC window. It serves as a reticle when scanned in AUC control experiments for absolute calibration of radial magnification. After analysis of the pitch between landmarks in scans using different optical systems, we estimate that the residual uncertainty in radial magnification after external calibration with the radial scale artifact is ≈0.2 %, of similar magnitude to other important contributions after external calibration such as the uncertainty in temperature and time. The previous multilaboratory study had found many instruments with errors in radial measurements of 1 % to 2 %, and a few instruments with errors in excess of 15 %, meaning that the use of the artifact developed here could reduce errors by 5-to 10-fold or more. Adoption of external radial calibration is thus an important factor for assuring accuracy in studies related to molecular hydrodynamics and particle size measurements by AUC.

Molecular and hydrodynamic properties of human epidermal growth factor receptor HER2 extracellular domain and its homodimer: Experiments and multi-scale simulations

BACKGROUND

In a broad range of human carcinomas gene amplification leads to HER2 overexpression, which has been proposed to cause spontaneous dimerization and activation in the absence of ligand. This makes HER2 attractive as a therapeutic target. However, the HER2 homodimerization mechanism remains unexplored. It has been suggested that the "back-to-back" homodimer does not form in solution. Notwithstanding, very recently the crystal structure of the HER2 extracellular domain homodimer formed with a "back-to-head" interaction has been resolved. We intend to explore the existence of such interactions.

METHODS

A combination of experiments, molecular dynamics and hydrodynamic modeling were used to monitor the transport properties of HER2 in solution.

RESULTS & CONCLUSIONS

We have detected the HER2 extracellular domain homodimer in solution. The results show a high degree of molecular flexibility, which ultimately leads to quite higher values of the intrinsic viscosity and lower values of diffusion coefficient than those corresponding to globular proteins. This flexibility obeys to the open conformation of the receptor and to the large fluctuations of the different domains. We also report that for obtaining the correct hydrodynamic constants from the modeling one must consider the glycosylation of the systems.

GENERAL SIGNIFICANCE

Conformational features of epidermal growth factor receptors regulate their hydrodynamic properties and control their activity. It is essential to understand the dynamics of these systems and the role of the specific domains involved. To find biophysical correlations between dynamics and macroscopic transport properties is of general interest for researches working in this area. This article is part of a Special Issue entitled "Biochemistry of Synthetic Biology - Recent Developments" Guest Editor: Dr. Ilka Heinemann and Dr. Patrick O'Donoghue.

Sedimentation of Reversibly Interacting Macromolecules with Changes in Fluorescence Quantum Yield

Sedimentation velocity analytical ultracentrifugation with fluorescence detection has emerged as a powerful method for the study of interacting systems of macromolecules. It combines picomolar sensitivity with high hydrodynamic resolution, and can be carried out with photoswitchable fluorophores for multicomponent discrimination, to determine the stoichiometry, affinity, and shape of macromolecular complexes with dissociation equilibrium constants from picomolar to micromolar. A popular approach for data interpretation is the determination of the binding affinity by isotherms of weight-average sedimentation coefficients s_w. A prevailing dogma in sedimentation analysis is that the weight-average sedimentation coefficient from the transport method corresponds to the signal- and population-weighted average of all species. We show that this does not always hold true for systems that exhibit significant signal changes with complex formation-properties that may be readily encountered in practice, e.g., from a change in fluorescence quantum yield. Coupled transport in the reaction boundary of rapidly reversible systems can make significant contributions to the observed migration in a way that cannot be accounted for in the standard population-based average. Effective particle theory provides a simple physical picture for the reaction-coupled migration process. On this basis, we develop a more general binding model that converges to the well-known form of s_w with constant signals, but can account simultaneously for hydrodynamic cotransport in the presence of changes in fluorescence quantum yield. We believe this will be useful when studying interacting systems exhibiting fluorescence quenching, enhancement, or Förster resonance energy transfer with transport methods.

3D-Printing for Analytical Ultracentrifugation

Analytical ultracentrifugation (AUC) is a classical technique of physical biochemistry providing information on size, shape, and interactions of macromolecules from the analysis of their migration in centrifugal fields while free in solution. A key mechanical element in AUC is the centerpiece, a component of the sample cell assembly that is mounted between the optical windows to allow imaging and to seal the sample solution column against high vacuum while exposed to gravitational forces in excess of 300,000 g. For sedimentation velocity it needs to be precisely sector-shaped to allow unimpeded radial macromolecular migration. During the history of AUC a great variety of centerpiece designs have been developed for different types of experiments. Here, we report that centerpieces can now be readily fabricated by 3D printing at low cost, from a variety of materials, and with customized designs. The new centerpieces can exhibit sufficient mechanical stability to withstand the gravitational forces at the highest rotor speeds and be sufficiently precise for sedimentation equilibrium and sedimentation velocity experiments. Sedimentation velocity experiments with bovine serum albumin as a reference molecule in 3D printed centerpieces with standard double-sector design result in sedimentation boundaries virtually indistinguishable from those in commercial double-sector epoxy centerpieces, with sedimentation coefficients well within the range of published values. The statistical error of the measurement is slightly above that obtained with commercial epoxy, but still below 1%. Facilitated by modern open-source design and fabrication paradigms, we believe 3D printed centerpieces and AUC accessories can spawn a variety of improvements in AUC experimental design, efficiency and resource allocation.

Hydrodynamic Modeling and Its Application in AUC

The hydrodynamic parameters measured in an AUC experiment, s(20,w) and D(t)(20,w)(0), can be used to gain information on the solution structure of (bio)macromolecules and their assemblies. This entails comparing the measured parameters with those that can be computed from usually "dry" structures by "hydrodynamic modeling." In this chapter, we will first briefly put hydrodynamic modeling in perspective and present the basic physics behind it as implemented in the most commonly used methods. The important "hydration" issue is also touched upon, and the distinction between rigid bodies versus those for which flexibility must be considered in the modeling process is then made. The available hydrodynamic modeling/computation programs, HYDROPRO, BEST, SoMo, AtoB, and Zeno, the latter four all implemented within the US-SOMO suite, are described and their performance evaluated. Finally, some literature examples are presented to illustrate the potential applications of hydrodynamics in the expanding field of multiresolution modeling.

A multilaboratory comparison of calibration accuracy and the performance of external references in analytical ultracentrifugation

Analytical ultracentrifugation (AUC) is a first principles based method to determine absolute sedimentation coefficients and buoyant molar masses of macromolecules and their complexes, reporting on their size and shape in free solution. The purpose of this multi-laboratory study was to establish the precision and accuracy of basic data dimensions in AUC and validate previously proposed calibration techniques. Three kits of AUC cell assemblies containing radial and temperature calibration tools and a bovine serum albumin (BSA) reference sample were shared among 67 laboratories, generating 129 comprehensive data sets. These allowed for an assessment of many parameters of instrument performance, including accuracy of the reported scan time after the start of centrifugation, the accuracy of the temperature calibration, and the accuracy of the radial magnification. The range of sedimentation coefficients obtained for BSA monomer in different instruments and using different optical systems was from 3.655 S to 4.949 S, with a mean and standard deviation of (4.304 ± 0.188) S (4.4%). After the combined application of correction factors derived from the external calibration references for elapsed time, scan velocity, temperature, and radial magnification, the range of s-values was reduced 7-fold with a mean of 4.325 S and a 6-fold reduced standard deviation of ± 0.030 S (0.7%). In addition, the large data set provided an opportunity to determine the instrument-to-instrument variation of the absolute radial positions reported in the scan files, the precision of photometric or refractometric signal magnitudes, and the precision of the calculated apparent molar mass of BSA monomer and the fraction of BSA dimers. These results highlight the necessity and effectiveness of independent calibration of basic AUC data dimensions for reliable quantitative studies.

The protein and contrast agent-specific influence of pathological plasma-protein concentration levels on contrast-enhanced magnetic resonance imaging

OBJECTIVE

The objective of this study was to measure the protein-specific response of r1 and r2 relaxivities of commercially available gadolinium-based magnetic resonance imaging contrast agents to variation of plasma-protein concentrations.

MATERIALS AND METHODS

In this in vitro study, contrast agent (gadofosveset trisodium, gadoxetate disodium, gadobutrol, and gadoterate meglumine) dilution series (0-2.5 mmol Gd/L) were prepared with plasma-protein (human serum albumin [HSA] and immunoglobulin G [IgG]) concentrations at physiological (42 and 10 g/L HSA and IgG, respectively, Normal) and at 3 pathological levels with HSA/IgG concentrations of 10/10 (solution Alb low), 42/50 (IgG mild), and 42/70 (IgG severe) g/L. Contrast-agent molar relaxivities and relaxivity-enhancing protein-contrast-agent interaction coefficients were determined on the basis of inversion-recovery and spin-echo data acquired at 1.5 and 3.0 T at 37°C. Protein-induced magnetic resonance imaging signal changes were calculated.

RESULTS

The effective r1 and r2 molar relaxivities consistently increased with albumin and IgG concentrations. At 1.5 T, the r1 values increased by 10.2 (gadofosveset), 4.3 (gadoxetate), 1.3 (gadobutrol), and 1.1 L s mmol (gadoterate), respectively, from the Alb low to the IgG severe solution. At 3.0 T, the r1 values increased by 2.9 (gadofosveset), 2.3 (gadoxetate), 0.7 (gadobutrol), and 0.9 (gadoterate) L s mmol, respectively. An excess of IgG most strongly increased the r1 of gadoxetate (+40 and +19% at 1.5 and 3.0 T, respectively, from Normal to IgG severe). An albumin deficiency most strongly decreased the r1 of gadofosveset (-44% and -20% at 1.5 and 3.0 T, respectively, from Normal to Alb low). The modeling confirmed a strong gadofosveset r1 enhancement by albumin and suggested stronger IgG than albumin effects on the apparent molar relaxivity of the other agents per protein mass concentration at 1.5 T.

CONCLUSIONS

Pathological deviations from normal plasma-protein concentrations in aqueous solutions result in changes of effective r1 and r2 contrast-agent relaxivities and projected signal enhancements that depend on the contrast agent, the blood-serum protein profile, and the field strength.

A histogram approach to the quality of fit in sedimentation velocity analyses

The quality of fit of sedimentation velocity data is critical to judge the veracity of the sedimentation model and accuracy of the derived macromolecular parameters. Absolute statistical measures are usually complicated by the presence of characteristic systematic errors and run-to-run variation in the stochastic noise of data acquisition. We present a new graphical approach to visualize systematic deviations between data and model in the form of a histogram of residuals. In comparison with the ideally expected Gaussian distribution, it can provide a robust measure of fit quality and be used to flag poor models.

Hard sphere-like glass transition in eye lens α-crystallin solutions

We study the equilibrium liquid structure and dynamics of dilute and concentrated bovine eye lens α-crystallin solutions, using small-angle X-ray scattering, static and dynamic light scattering, viscometry, molecular dynamics simulations, and mode-coupling theory. We find that a polydisperse Percus-Yevick hard-sphere liquid-structure model accurately reproduces both static light scattering data and small-angle X-ray scattering liquid structure data from α-crystallin solutions over an extended range of protein concentrations up to 290 mg/mL or 49% vol fraction and up to ca. 330 mg/mL for static light scattering. The measured dynamic light scattering and viscosity properties are also consistent with those of hard-sphere colloids and show power laws characteristic of an approach toward a glass transition at α-crystallin volume fractions near 58%. Dynamic light scattering at a volume fraction beyond the glass transition indicates formation of an arrested state. We further perform event-driven molecular dynamics simulations of polydisperse hard-sphere systems and use mode-coupling theory to compare the measured dynamic power laws with those of hard-sphere models. The static and dynamic data, simulations, and analysis show that aqueous eye lens α-crystallin solutions exhibit a glass transition at high concentrations that is similar to those found in hard-sphere colloidal systems. The α-crystallin glass transition could have implications for the molecular basis of presbyopia and the kinetics of molecular change during cataractogenesis.

Accounting for photophysical processes and specific signal intensity changes in fluorescence-detected sedimentation velocity

Fluorescence detected sedimentation velocity (FDS-SV) has emerged as a powerful technique for the study of high-affinity protein interactions, with hydrodynamic resolution exceeding that of diffusion-based techniques, and with sufficient sensitivity for binding studies at low picomolar concentrations. For the detailed quantitative analysis of the observed sedimentation boundaries, it is necessary to adjust the conventional sedimentation models to the FDS data structure. A key consideration is the change in the macromolecular fluorescence intensity during the course of the experiment, caused by slow drifts of the excitation laser power, and/or by photophysical processes. In the present work, we demonstrate that FDS-SV data have inherently a reference for the time-dependent macromolecular signal intensity, resting on a geometric link between radial boundary migration and plateau signal. We show how this new time-domain can be exploited to study molecules exhibiting photobleaching and photoactivation. This expands the application of FDS-SV to proteins tagged with photoswitchable fluorescent proteins, organic dyes, or nanoparticles, such as those recently introduced for subdiffraction microscopy and enables FDS-SV studies of their interactions and size distributions. At the same time, we find that conventional fluorophores undergo minimal photobleaching under standard illumination in the FDS. These findings support the application of a high laser power density for the detection, which we demonstrate can further increase the signal quality.

Measurement of the temperature of the resting rotor in analytical ultracentrifugation

Accurate measurements of rotor temperature are critical for the interpretation of hydrodynamic parameters in analytical ultracentrifugation. We have recently developed methods for a more accurate determination of the temperature of a spinning rotor using iButton temperature loggers. Here we report that the temperature measured with the iButton on the counterbalance of a resting rotor, following thermal equilibration under high vacuum, closely corresponded to the temperature of the spinning rotor with a precision better than 0.2°C. This strategy offers an inexpensive and straightforward approach to monitor the accuracy of the temperature calibration and determine corrective temperature offsets.

Improved measurement of the rotor temperature in analytical ultracentrifugation

Sedimentation velocity is a classical method for measuring the hydrodynamic, translational friction coefficient of biological macromolecules. In a recent study comparing various analytical ultracentrifuges, we showed that external calibration of the scan time, radial magnification, and temperature is critically important for accurate measurements (Anal. Biochem. 440 (2013) 81-95). To achieve accurate temperature calibration, we introduced the use of an autonomous miniature temperature logging integrated circuit (Maxim Thermochron iButton) that can be inserted into an ultracentrifugation cell assembly and spun at low rotor speeds. In the current work, we developed an improved holder for the temperature sensor located in the rotor handle. This has the advantage of not reducing the rotor capacity and allowing for a direct temperature measurement of the spinning rotor during high-speed sedimentation velocity experiments up to 60,000rpm. We demonstrated the sensitivity of this approach by monitoring the adiabatic cooling due to rotor stretching during rotor acceleration and the reverse process on rotor deceleration. Based on this, we developed a procedure to approximate isothermal rotor acceleration for better temperature control.

Solution properties of γ-crystallins: hydration of fish and mammal γ-crystallins

Lens γ crystallins are found at the highest protein concentration of any tissue, ranging from 300 mg/mL in some mammals to over 1000 mg/mL in fish. Such high concentrations are necessary for the refraction of light, but impose extreme requirements for protein stability and solubility. γ-crystallins, small stable monomeric proteins, are particularly associated with the lowest hydration regions of the lens. Here, we examine the solvation of selected γ-crystallins from mammals (human γD and mouse γS) and fish (zebrafish γM2b and γM7). The thermodynamic water binding coefficient B₁ could be probed by sucrose expulsion, and the hydrodynamic hydration shell of tightly bound water was probed by translational diffusion and structure-based hydrodynamic boundary element modeling. While the amount of tightly bound water of human γD was consistent with that of average proteins, the water binding of mouse γS was found to be relatively low. γM2b and γM7 crystallins were found to exhibit extremely low degrees hydration, consistent with their role in the fish lens. γM crystallins have a very high methionine content, in some species up to 15%. Structure-based modeling of hydration in γM7 crystallin suggests low hydration is associated with the large number of surface methionine residues, likely in adaptation to the extremely high concentration and low hydration environment in fish lenses. Overall, the degree of hydration appears to balance stability and tissue density requirements required to produce and maintain the optical properties of the lens in different vertebrate species.

Improving the thermal, radial, and temporal accuracy of the analytical ultracentrifuge through external references

Sedimentation velocity (SV) is a method based on first principles that provides a precise hydrodynamic characterization of macromolecules in solution. Due to recent improvements in data analysis, the accuracy of experimental SV data emerges as a limiting factor in its interpretation. Our goal was to unravel the sources of experimental error and develop improved calibration procedures. We implemented the use of a Thermochron iButton temperature logger to directly measure the temperature of a spinning rotor and detected deviations that can translate into an error of as much as 10% in the sedimentation coefficient. We further designed a precision mask with equidistant markers to correct for instrumental errors in the radial calibration that were observed to span a range of 8.6%. The need for an independent time calibration emerged with use of the current data acquisition software (Zhao et al., Anal. Biochem., 437 (2013) 104-108), and we now show that smaller but significant time errors of up to 2% also occur with earlier versions. After application of these calibration corrections, the sedimentation coefficients obtained from 11 instruments displayed a significantly reduced standard deviation of approximately 0.7%. This study demonstrates the need for external calibration procedures and regular control experiments with a sedimentation coefficient standard.

Hydrodynamic effects on the relative rotational velocity of associating proteins

Hydrodynamic steering effects on the barnase-barstar association were studied through the analysis of the relative rotational velocity of the proteins. We considered the two proteins approaching each other in response to their electrostatic attraction and employed a method that accounts for the long-range and many-body character of the hydrodynamic interactions, as well as the complicated shapes of the proteins. Hydrodynamic steering effects were clearly seen when attractive forces were applied to the geometric centers of the proteins (resulting in zero torques) and the attraction acted along the line that connects centers of geometry of proteins in their crystallographic complex. When we rotated barstar relative to barnase around this line by an angle in the range from -90° to 60°, the rotational velocity arising solely from hydrodynamic interactions restored the orientation of the proteins in the crystal structure. However, because, in reality, both electrostatic forces and torques act on the proteins and these forces and torques depend on the protein-protein distance and the relative orientation of the binding partners, we also investigated more realistic situations employing continuum electrostatics calculations based on atomistic protein models. Overall, we conclude that hydrodynamic interactions aid barnase and barstar in assuming a proper relative orientation upon complex formation.

Analytical Ultracentrifugation as a Tool for Studying Protein Interactions

The last two decades have led to significant progress in the field of analytical ultracentrifugation driven by instrumental, theoretical, and computational methods. This review will highlight key developments in sedimentation equilibrium (SE) and sedimentation velocity (SV) analysis. For SE, this includes the analysis of tracer sedimentation equilibrium at high concentrations with strong thermodynamic non-ideality, and for ideally interacting systems the development of strategies for the analysis of heterogeneous interactions towards global multi-signal and multi-speed SE analysis with implicit mass conservation. For SV, this includes the development and applications of numerical solutions of the Lamm equation, noise decomposition techniques enabling direct boundary fitting, diffusion deconvoluted sedimentation coefficient distributions, and multi-signal sedimentation coefficient distributions. Recently, effective particle theory has uncovered simple physical rules for the co-migration of rapidly exchanging systems of interacting components in SV. This has opened new possibilities for the robust interpretation of the boundary patterns of heterogeneous interacting systems. Together, these SE and SV techniques have led to new approaches to study macromolecular interactions across the entire the spectrum of affinities, including both attractive and repulsive interactions, in both dilute and highly concentrated solutions, which can be applied to single-component solutions of self-associating proteins as well as the study of multi-protein complex formation in multi-component solutions.

Overview of current methods in sedimentation velocity and sedimentation equilibrium analytical ultracentrifugation

Modern computational strategies have allowed for the direct modeling of the sedimentation process of heterogeneous mixtures, resulting in sedimentation velocity (SV) size-distribution analyses with significantly improved detection limits and strongly enhanced resolution. These advances have transformed the practice of SV, rendering it the primary method of choice for most existing applications of analytical ultracentrifugation (AUC), such as the study of protein self- and hetero-association, the study of membrane proteins, and applications in biotechnology. New global multisignal modeling and mass conservation approaches in SV and sedimentation equilibrium (SE), in conjunction with the effective-particle framework for interpreting the sedimentation boundary structure of interacting systems, as well as tools for explicit modeling of the reaction/diffusion/sedimentation equations to experimental data, have led to more robust and more powerful strategies for the study of reversible protein interactions and multiprotein complexes. Furthermore, modern mathematical modeling capabilities have allowed for a detailed description of many experimental aspects of the acquired data, thus enabling novel experimental opportunities, with important implications for both sample preparation and data acquisition. The goal of the current unit is to describe the current tools for the study of soluble proteins, detergent-solubilized membrane proteins and their interactions by SV and SE.

Analysis of high-affinity assembly for AMPA receptor amino-terminal domains

Analytical ultracentrifugation (AUC) and steady-state fluorescence anisotropy were used to measure the equilibrium dissociation constant (Kd) for formation of dimers by the amino-terminal domains (ATDs) of the GluA2 and GluA3 subtypes of AMPA receptor. Previous reports on GluA2 dimerization differed in their estimate of the monomer-dimer Kd by a 2,400-fold range, with no consensus on whether the ATD forms tetramers in solution. We find by sedimentation velocity (SV) analysis performed using absorbance detection a narrow range of monomer-dimer Kd values for GluA2, from 5 to 11 nM for six independent experiments, with no detectable formation of tetramers and no effect of glycosylation or the polypeptide linker connecting the ATD and ligand-binding domains; for GluA3, the monomer-dimer Kd was 5.6 µM, again with no detectable tetramer formation. For sedimentation equilibrium (SE) experiments, a wide range of Kd values was obtained for GluA2, from 13 to 284 nM, whereas for GluA3, the Kd of 3.1 µM was less than twofold different from the SV value. Analysis of cell contents after the ∼1-week centrifuge run by silver-stained gels revealed low molecular weight GluA2 breakdown products. Simulated data for SE runs demonstrate that the apparent Kd for GluA2 varies with the extent of proteolysis, leading to artificially high Kd values. SV experiments with fluorescence detection for GluA2 labeled with 5,6-carboxyfluorescein, and fluorescence anisotropy measurements for GluA2 labeled with DyLight405, yielded Kd values of 5 and 11 nM, consistent with those from SV with absorbance detection. However, the sedimentation coefficients measured by AUC using absorbance and fluorescence systems were strikingly different, and for the latter are not consistent with hydrodynamic protein models. Thus, for unknown reasons, the concentration dependence of sedimentation coefficients obtained with fluorescence detection SV may be unreliable, limiting the usefulness of this technique for quantitative analysis.

Contributions of far-field hydrodynamic interactions to the kinetics of electrostatically driven molecular association

We simulated the diffusional encounters in periodic systems of model isotropic and anisotropic molecules using Brownian dynamics. We considered the electrostatic, excluded volume, and far-field hydrodynamic forces between diffusing molecules. Our goal was to estimate to what extent the hydrodynamic interactions influence the association kinetics when the associating partners are oppositely charged and their direct electrostatic interactions are screened by small mobile ions of dissolved salt. Overall, including hydrodynamic interactions decreases the association rate constants. The relative magnitude of this decrease does not depend on the ionic strength for the association of isotropic charged objects. This also holds true for nonspecific association (i.e., without restrictions regarding the relative orientation of binding partners in an encounter complex) of anisotropic objects. However, such dependence is visible for orientation-specific association of anisotropic objects. Moreover, we observe that some orientations of anisotropic molecules are hydrodynamically favorable during their mutual approach, and that such molecules can be hydrodynamically steered toward a particular relative orientation. This hydrodynamic orientational steering is impeded in case of strong electrostatic interactions or steric hindrance.

Density contrast sedimentation velocity for the determination of protein partial-specific volumes

The partial-specific volume of proteins is an important thermodynamic parameter required for the interpretation of data in several biophysical disciplines. Building on recent advances in the use of density variation sedimentation velocity analytical ultracentrifugation for the determination of macromolecular partial-specific volumes, we have explored a direct global modeling approach describing the sedimentation boundaries in different solvents with a joint differential sedimentation coefficient distribution. This takes full advantage of the influence of different macromolecular buoyancy on both the spread and the velocity of the sedimentation boundary. It should lend itself well to the study of interacting macromolecules and/or heterogeneous samples in microgram quantities. Model applications to three protein samples studied in either H(2)O, or isotopically enriched H(2) (18)O mixtures, indicate that partial-specific volumes can be determined with a statistical precision of better than 0.5%, provided signal/noise ratios of 50-100 can be achieved in the measurement of the macromolecular sedimentation velocity profiles. The approach is implemented in the global modeling software SEDPHAT.