Global Multi-Method Analysis of Affinities and Cooperativity in Complex Systems of Macromolecular Interactions

Cooperativity, multisite, and multicomponent interactions are hallmarks of biological systems of interacting macromolecules. Their thermodynamic characterization is often very challenging due to the notoriously low information content of binding isotherms. We introduce a strategy for the global multimethod analysis of data from multiple techniques (GMMA) that exploits enhanced information content emerging from the mutual constraints of the simultaneous modeling of orthogonal observables from calorimetric, spectroscopic, hydrodynamic, biosensing, or other thermodynamic binding experiments. We describe new approaches to address statistical problems that arise in the analysis of dissimilar data sets. The GMMA approach can significantly increase the complexity of interacting systems that can be accurately thermodynamically characterized

Multi-Signal Sedimentation Velocity Analysis with Mass Conservation for Determining the Stoichiometry of Protein Complexes

<div><p>Multi-signal sedimentation velocity analytical ultracentrifugation (MSSV) is a powerful tool for the determination of the number, stoichiometry, and hydrodynamic shape of reversible protein complexes in two- and three-component systems. In this method, the evolution of sedimentation profiles of macromolecular mixtures is recorded simultaneously using multiple absorbance and refractive index signals and globally transformed into both spectrally and diffusion-deconvoluted component sedimentation coefficient distributions. For reactions with complex lifetimes comparable to the time-scale of sedimentation, MSSV reveals the number and stoichiometry of co-existing complexes. For systems with short complex lifetimes, MSSV reveals the composition of the reaction boundary of the coupled reaction/migration process, which we show here may be used to directly determine an association constant. A prerequisite for MSSV is that the interacting components are spectrally distinguishable, which may be a result, for example, of extrinsic chromophores or of different abundances of aromatic amino acids contributing to the UV absorbance. For interacting components that are spectrally poorly resolved, here we introduce a method for additional regularization of the spectral deconvolution by exploiting approximate knowledge of the total loading concentrations. While this novel mass conservation principle does not discriminate contributions to different species, it can be effectively combined with constraints in the sedimentation coefficient range of uncomplexed species. We show in theory, computer simulations, and experiment, how mass conservation MSSV as implemented in SEDPHAT can enhance or even substitute for the spectral discrimination of components. This should broaden the applicability of MSSV to the analysis of the composition of reversible macromolecular complexes.</p></div

Analysis of Protein Interactions with Picomolar Binding Affinity by Fluorescence-Detected Sedimentation Velocity

The study of high-affinity protein interactions with equilibrium dissociation constants (<i>K</i>_D) in the picomolar range is of significant interest in many fields, but the characterization of stoichiometry and free energy of such high-affinity binding can be far from trivial. Analytical ultracentrifugation has long been considered a gold standard in the study of protein interactions but is typically applied to systems with micromolar <i>K</i>_D. Here we present a new approach for the study of high-affinity interactions using fluorescence detected sedimentation velocity analytical ultracentrifugation (FDS-SV). Taking full advantage of the large data sets in FDS-SV by direct boundary modeling with sedimentation coefficient distributions <i>c</i>(s), we demonstrate detection and hydrodynamic resolution of protein complexes at low picomolar concentrations. We show how this permits the characterization of the antibody–antigen interactions with low picomolar binding constants, 2 orders of magnitude lower than previously achieved. The strongly size-dependent separation and quantitation by concentration, size, and shape of free and complex species in free solution by FDS-SV has significant potential for studying high-affinity multistep and multicomponent protein assemblies

Analysis of High Affinity Self-Association by Fluorescence Optical Sedimentation Velocity Analytical Ultracentrifugation of Labeled Proteins: Opportunities and Limitations

<div><p>Sedimentation velocity analytical ultracentrifugation (SV) is a powerful first-principle technique for the study of protein interactions, and allows a rigorous characterization of binding stoichiometry and affinities. A recently introduced commercial fluorescence optical detection system (FDS) permits analysis of high-affinity interactions by SV. However, for most proteins the attachment of an extrinsic fluorophore is an essential prerequisite for analysis by FDS-SV. Using the glutamate receptor GluA2 amino terminal domain as a model system for high-affinity homo-dimerization, we demonstrate how the experimental design and choice of fluorescent label can impact both the observed binding constants as well as the derived hydrodynamic parameter estimates for the monomer and dimer species. Specifically, FAM (5,6-carboxyfluorescein) was found to create different populations of artificially high-affinity and low-affinity dimers, as indicated by both FDS-SV and the kinetics of dimer dissociation studied using a bench-top fluorescence spectrometer and Förster Resonance Energy Transfer. By contrast, Dylight488 labeled GluA2, as well as GluA2 expressed as an EGFP fusion protein, yielded results consistent with estimates for unlabeled GluA2. Our study suggests considerations for the choice of labeling strategies, and highlights experimental designs that exploit specific opportunities of FDS-SV for improving the reliability of the binding isotherm analysis of interacting systems.</p></div

Dilution series for FAM-GluA2 ATD at different labeling ratios.

<p>Shown are the sedimentation coefficient distribution distributions <i>c</i>(<i>s</i>) (Panels A, C, and E) and the resulting <i>s_w</i> isotherms (Panels B, D, and F) from integration of <i>c</i>(<i>s</i>) for FAM-GluA2 ATD at labeling ratios of 0.68 (first row), 1.05 (second row) and 2.26 (third row). Analogous to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0083439#pone-0083439-g003" target="_blank">Figure 3</a>, in the <i>c</i>(<i>s</i>) plots the distributions were normalized with respect to the loading concentrations indicated, and in the isotherm plots, solid circles are the <i>s_w</i> data from the dilution series, and the solid line is the best-fit isotherm with a monomer-dimer model. This resulted in best-fit values at the labeling ratio of 0.68 (Panel B) of <i>K_D</i> = 3.1 nM (95% CI 0.16 – 30.5), <i>s</i>₁ = 3.43 S (95% CI 2.53 – 3.82), and <i>s</i>₂ = 5.01 S (95% CI 4.60 – 5.51); for the labeling ratio of 1.05 (Panel D) the best-fit values were <i>K_D</i> = 2.6 nM (95% CI 1.1 – 5.9), <i>s</i>₁ = 3.42 S (95% CI 3.27 – 3.56), and <i>s</i>₂ = 5.00 S (95% CI 4.88 – 5.14); and for the labeling ratio of 2.26 (Panel F) the best-fit values were <i>K_D</i> = 4.7 nM (95% CI 3.0 – 7.3), <i>s</i>₁ = 3.57 S (95% CI 3.49 – 3.63), and <i>s</i>₂ = 5.03 S (95% CI 4.96 – 5.11).</p

Global density variation SV analysis of the interference optical data from the BSA sample.

<p>The sets of panels present the data in (A) H₂O, (B) 50% H₂¹⁸O, and (C) 90% H₂¹⁸O based buffer. The presentation is analogous to that in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0026221#pone-0026221-g001" target="_blank">Figure 1</a>. Rmsd of the fit was 0.00346 fringes (A), 0.00337 fringes (B), and 0.00416 fringes (C). The best-fit <i>c</i>(<i>s</i>) distribution from this analysis is shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0026221#pone-0026221-g008" target="_blank">Figure 8</a>, and the projections of the error surface in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0026221#pone-0026221-g009" target="_blank">Figure 9</a>.</p

Total sedimentation boundary signals as determined from integration of the <i>c</i>(<i>s</i>) distribution, divided by the loaded protein concentration for GluA2 ATD labeled with Dylight488 at labeling ratio 1.43 (black), FAM at labeling ratio 1.32 (grey), and expressed as an EGFP fusion protein (red).

<p>Data were acquired at a constant PMT voltage of 36% (Dylight488 and FAM), or 38% (EGFP fusion protein) and signals were divided by the gain factor.</p

Projections of the error surface as a function of

<p><b>-values.</b> Shown are the relative increase in the χ² of the fit as a function of different fixed -values, for each value freely adjusting all other unknown parameters <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0026221#pone.0026221-Bevington1" target="_blank">[79]</a>. Data are shown for the absorbance IgG data set (black) and the interference data set from the BSA sample (blue). For each, the dashed line shows the increase predicted by F-statistics for the 68% confidence level <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0026221#pone.0026221-Bevington1" target="_blank">[79]</a>. This critical increase of χ² is lower for the BSA data set due to the significantly larger number of data points.</p

Tools for the Quantitative Analysis of Sedimentation Boundaries Detected by Fluorescence Optical Analytical Ultracentrifugation

<div><p>Fluorescence optical detection in sedimentation velocity analytical ultracentrifugation allows the study of macromolecules at nanomolar concentrations and below. This has significant promise, for example, for the study of systems of high-affinity protein interactions. Here we describe adaptations of the direct boundary modeling analysis approach implemented in the software SEDFIT that were developed to accommodate unique characteristics of the confocal fluorescence detection system. These include spatial gradients of signal intensity due to scanner movements out of the plane of rotation, temporal intensity drifts due to instability of the laser and fluorophores, and masking of the finite excitation and detection cone by the sample holder. In an extensive series of experiments with enhanced green fluorescent protein ranging from low nanomolar to low micromolar concentrations, we show that the experimental data provide sufficient information to determine the parameters required for first-order approximation of the impact of these effects on the recorded data. Systematic deviations of fluorescence optical sedimentation velocity data analyzed using conventional sedimentation models developed for absorbance and interference optics are largely removed after these adaptations, resulting in excellent fits that highlight the high precision of fluorescence sedimentation velocity data, thus allowing a more detailed quantitative interpretation of the signal boundaries that is otherwise not possible for this system.</p></div

The dependence of the best-fit beam radius <i>δ</i> (Eq. 4) on focal depth (circles).

<p>The solid line is a linear fit, leading to an apparent beam angle of 5.8°.</p