Using prior knowledge in the determination of macromolecular size-distributions by analytical ultracentrifugation

Hybrid modeling of an ultracentrifugation process for separation of full and empty adeno-associated virus particles

Ultracentrifugation is an attractive method for separating full and empty capsids, exploiting their density difference. Changes of the serotype/capsid, density of loading material, or the genetic information contained in the adeno-associated viruses (AAVs) require the adaptation of the harvesting parameters and the density gradient loaded onto the centrifuge. To streamline these adaptations, a mathematical model could support the design and testing of operating conditions.Here, hybrid models, which combine empirical functions with artificial neural networks, are proposed to describe the separation of full and empty capsids as a function of material and operational parameters, i.e., the harvest model. In addition, critical quality attributes are estimated by a quality model which is operating on top of the harvest model. The performance of these models was evaluated using test data and two additional blind runs. Also, a "what-if" analysis was conducted to investigate whether the models' predictions align with expectations.It is concluded that the models are sufficiently accurate to support the design of operating conditions, though the accuracy and applicability of the models can further be increased by training them on more specific data with higher variability.

Phase separation promotes a highly active oligomeric scaffold of the MLL1 core complex for regulation of histone H3K4 methylation

Enzymes that regulate the degree of histone H3 lysine 4 (H3K4) methylation are crucial for proper cellular differentiation and are frequently mutated in cancer. The Mixed lineage leukemia (MLL) family of enzymes deposit H3K4 mono-, di-, or trimethylation at distinct genomic locations, requiring precise spatial and temporal control. Despite evidence that the degree of H3K4 methylation is controlled in part by a hierarchical assembly pathway with key subcomplex components, we previously found that the assembled state of the MLL1 core complex is not favored at physiological temperature. To better understand this paradox, we tested the hypothesis that increasing the concentration of subunits in a biomolecular condensate overcomes this thermodynamic barrier via mass action. Here, we demonstrate that MLL1 core complex phase separation stimulates enzymatic activity up to 60-fold but not primarily by concentrating subunits into droplets. Instead, we found that stimulated activity is largely due to the formation of an altered oligomeric scaffold that greatly reduces substrate Km. We posit that phase separation-induced scaffolding of the MLL1 core complex is a potential "switch-like" mechanism for spatiotemporal control of H3K4 methylation through the rapid formation or dissolution of biomolecular condensates within RNA Pol II transcription factories.

An automated interface for sedimentation velocity analysis in SEDFIT

Sedimentation velocity analytical ultracentrifugation (SV-AUC) is an indispensable tool for the study of particle size distributions in biopharmaceutical industry, for example, to characterize protein therapeutics and vaccine products. In particular, the diffusion-deconvoluted sedimentation coefficient distribution analysis, in the software SEDFIT, has found widespread applications due to its relatively high resolution and sensitivity. However, a lack of suitable software compatible with Good Manufacturing Practices (GMP) has hampered the use of SV-AUC in this regulatory environment. To address this, we have created an interface for SEDFIT so that it can serve as an automatically spawned module with controlled data input through command line parameters and output of key results in files. The interface can be integrated in custom GMP compatible software, and in scripts that provide documentation and meta-analyses for replicate or related samples, for example, to streamline analysis of large families of experimental data, such as binding isotherm analyses in the study of protein interactions. To test and demonstrate this approach we provide a MATLAB script mlSEDFIT.

AAV analysis by sedimentation velocity analytical ultracentrifugation: beyond empty and full capsids

The recent surge of therapeutic interest in recombinant adeno-associated viral (AAV) vectors for targeted DNA delivery has brought analytical ultracentrifugation (AUC) into the spotlight. A major concern during formulation of AAV therapeutics is purity of the active species (DNA-containing capsid, or "filled capsids"). Insertion of DNA into AAV is not a highly efficient process; thus, a significant amount of empty and partial/intermediate AAV molecules may exist. Recent guidance from the FDA includes limiting the presence of empty AAV capsids and other impurities to reduce immunotoxicity. While chromatographic techniques (SEC, SEC-MALS, AEX) are often used for empty and full capsid quantitation due to the ease of accessibility and familiarity among most biochemists, the resolution and sensitivity attained by sedimentation velocity (SV-AUC) in the formulation buffer and purification buffers is unmatched. Approaches for using SV-AUC to determine the empty-to-full capsid ratio have already been discussed by others; however, in this report, we focus on the importance of characterizing other impurities, such as free DNA, partially filled capsids, and aggregates that are recognized as species of concern for immunotoxicity. We also demonstrate the usefulness of applying multiple analyses (e.g., c(s), g(s*), WDA) in confirming the presence of and determining the hydrodynamic parameters of these various species.

Comparative sedimentation equilibrium analysis of two IgG1 glycoforms: IgGCri and IgGWid

The solution properties of two different glycoforms of IgG1 (IgG1Cri and IgG1Wid) are compared using primarily sedimentation equilibrium analysis with two complementary analysis routines: SEDFIT-MSTAR and MULTISIG. IgGCri bears diantennary complex-type glycans on its Fc domain that are fully core fucosylated and partially sialylated, whilst on IgGWid, they are non-fucosylated, partially galactosylated and non-sialylated. IgGWid is also Fab glycosylated. Despite these differences, SEDFIT-MSTAR analysis shows similar weight average molar masses Mw of ~ (150 ± 5) kDa for IgGCri and ~ (154 ± 5) kDa for IgGWid and both glycoforms show evidence of the presence of a small fraction of dimer confirmed by MULTISIG analysis and also by sedimentation coefficient distributions from supportive sedimentation velocity measurements. The closeness of the sedimentation equilibrium behaviour and sedimentation coefficient distributions with a main peak sedimentation coefficient of ~ 6.4S for both glycoforms at different concentrations suggest that the different glycosylation profiles do not significantly impact on molar mass (molecular weight) nor conformation in solution.

An automated interface for sedimentation velocity analysis in SEDFIT

Sedimentation velocity analytical ultracentrifugation (SV-AUC) is an indispensable tool for the study of particle size distributions in biopharmaceutical industry, for example, to characterize protein therapeutics and vaccine products. In particular, the diffusion-deconvoluted sedimentation coefficient distribution analysis, in the software SEDFIT, has found widespread applications due to its relatively high resolution and sensitivity. However, a lack of available software compatible with Good Manufacturing Practices (GMP) has hampered the use of SV-AUC in this regulatory environment. To address this, we have created an interface for SEDFIT so that it can serve as an automatically spawned module with controlled data input through command line parameters and output of key results in files. The interface can be integrated in custom GMP compatible software, and in scripts that provide documentation and meta-analyses for replicate or related samples, for example, to streamline analysis of large families of experimental data, such as binding isotherm analyses in the study of protein interactions. To test and demonstrate this approach we provide a MATLAB script mlSEDFIT.

Hierarchical assembly of the MLL1 core complex regulates H3K4 methylation and is dependent on temperature and component concentration

Enzymes of the mixed lineage leukemia (MLL) family of histone H3 lysine 4 (H3K4) methyltransferases are critical for cellular differentiation and development and are regulated by interaction with a conserved subcomplex consisting of WDR5, RbBP5, Ash2L, and DPY30. While pairwise interactions between complex subunits have been determined, the mechanisms regulating holocomplex assembly are unknown. In this investigation, we systematically characterized the biophysical properties of a reconstituted human MLL1 core complex and found that the MLL1-WDR5 heterodimer interacts with the RbBP5-Ash2L-DPY30 subcomplex in a hierarchical assembly pathway that is highly dependent on concentration and temperature. Surprisingly, we found that the disassembled state is favored at physiological temperature, where the enzyme rapidly becomes irreversibly inactivated, likely because of complex components becoming trapped in nonproductive conformations. Increased protein concentration partially overcomes this thermodynamic barrier for complex assembly, suggesting a potential regulatory mechanism for spatiotemporal control of H3K4 methylation. Together, these results are consistent with the hypothesis that regulated assembly of the MLL1 core complex underlies an important mechanism for establishing different H3K4 methylation states in mammalian genomes.

EGCG binds intrinsically disordered N-terminal domain of p53 and disrupts p53-MDM2 interaction

Epigallocatechin gallate (EGCG) from green tea can induce apoptosis in cancerous cells, but the underlying molecular mechanisms remain poorly understood. Using SPR and NMR, here we report a direct, μM interaction between EGCG and the tumor suppressor p53 (KD = 1.6 ± 1.4 μM), with the disordered N-terminal domain (NTD) identified as the major binding site (KD = 4 ± 2 μM). Large scale atomistic simulations (>100 μs), SAXS and AUC demonstrate that EGCG-NTD interaction is dynamic and EGCG causes the emergence of a subpopulation of compact bound conformations. The EGCG-p53 interaction disrupts p53 interaction with its regulatory E3 ligase MDM2 and inhibits ubiquitination of p53 by MDM2 in an in vitro ubiquitination assay, likely stabilizing p53 for anti-tumor activity. Our work provides insights into the mechanisms for EGCG's anticancer activity and identifies p53 NTD as a target for cancer drug discovery through dynamic interactions with small molecules.

Modulation of Amyloidogenic Protein Self-Assembly Using Tethered Small Molecules

Protein–protein interactions (PPIs) are involved in many of life’s essential biological functions yet are also an underlying cause of several human diseases, including amyloidosis. The modulation of PPIs presents opportunities to gain mechanistic insights into amyloid assembly, particularly through the use of methods which can trap specific intermediates for detailed study. Such information can also provide a starting point for drug discovery. Here, we demonstrate that covalently tethered small molecule fragments can be used to stabilize specific oligomers during amyloid fibril formation, facilitating the structural characterization of these assembly intermediates. We exemplify the power of covalent tethering using the naturally occurring truncated variant (ΔN6) of the human protein β₂-microglobulin (β₂m), which assembles into amyloid fibrils associated with dialysis-related amyloidosis. Using this approach, we have trapped tetramers formed by ΔN6 under conditions which would normally lead to fibril formation and found that the degree of tetramer stabilization depends on the site of the covalent tether and the nature of the protein–fragment interaction. The covalent protein–ligand linkage enabled structural characterization of these trapped, off-pathway oligomers using X-ray crystallography and NMR, providing insight into why tetramer stabilization inhibits amyloid assembly. Our findings highlight the power of “post-translational chemical modification” as a tool to study biological molecular mechanisms.

Using modern approaches to sedimentation velocity to detect conformational changes in proteins

It has been known for decades that proteins undergo conformational changes in response to binding ligands. Such changes are usually accompanied by a loss of entropy by the protein, and thus conformational changes are integral to the thermodynamics of ligand association. Methods to detect these alterations are numerous; here, we focus on the sedimentation velocity (SV) mode of AUC, which has several advantages, including ease of use and rigorous data-selection criteria. In SV, it is assumed that conformational changes manifest primarily as differences in the sedimentation coefficient (the s-value). Two methods of determining s-value differences were assessed. The first method used the widely adopted c(s) distribution to gather statistics on the s-value differences to determine whether the observed changes were reliable. In the second method, a decades-old technique called "difference SV" was revived and updated to address its viability in this era of modern instrumentation. Both methods worked well to determine the extent of conformational changes to three model systems. Both simulations and experiments were used to explore the strengths and limitations of the methods. Finally, software incorporating these methodologies was produced.

An allosteric network in spastin couples multiple activities required for microtubule severing

The AAA+ ATPase spastin remodels microtubule arrays through severing and its mutation is the most common cause of hereditary spastic paraplegias (HSP). Polyglutamylation of the tubulin C-terminal tail recruits spastin to microtubules and modulates severing activity. Here, we present a ~3.2 Å resolution cryo-EM structure of the Drosophila melanogaster spastin hexamer with a polyglutamate peptide bound in its central pore. Two electropositive loops arranged in a double-helical staircase coordinate the substrate sidechains. The structure reveals how concurrent nucleotide and substrate binding organizes the conserved spastin pore loops into an ordered network that is allosterically coupled to oligomerization, and suggests how tubulin tail engagement activates spastin for microtubule disassembly. This allosteric coupling may apply generally in organizing AAA+ protein translocases into their active conformations. We show that this allosteric network is essential for severing and is a hotspot for HSP mutations.

Generation, Characterization, and Quantitative Bioanalysis of Drug/Anti-drug Antibody Immune Complexes to Facilitate Dedicated In Vivo Studies

PURPOSE

Immunogenicity against biotherapeutics can lead to the formation of drug/anti-drug-antibody (ADA) immune complexes (ICs) with potential impact on safety and drug pharmacokinetics (PK). This work aimed to generate defined drug/ADA ICs, characterized by quantitative (bio) analytical methods for dedicated determination of IC sizes and IC profile changes in serum to facilitate future in vivo studies.

METHODS

Defined ICs were generated and extensively characterized with chromatographic, biophysical and imaging methods. Quantification of drug fully complexed with ADAs (drug in ICs) was performed with an acid dissociation ELISA. Sequential coupling of SEC and ELISA enabled the reconstruction of IC patterns and thus analysis of IC species in serum.

RESULTS

Characterization of generated ICs identified cyclic dimers, tetramers, hexamers, and larger ICs of drug and ADA as main IC species. The developed acid dissociation ELISA enabled a total quantification of drug fully complexed with ADAs. Multiplexing of SEC and ELISA allowed unbiased reconstruction of IC oligomeric states in serum.

CONCLUSIONS

The developed in vitro IC model system has been properly characterized by biophysical and bioanalytical methods. The specificity of the developed methods enable discrimination between different oligomeric states of ICs and can be bench marking for future in vivo studies with ICs.

A Cholesterol Analog Induces an Oligomeric Reorganization of VDAC

The oligomeric organization of the voltage-dependent anion-selective channel (VDAC) and its interactions with hexokinase play integral roles in mitochondrially mediated apoptotic signaling. Various small to large assemblies of VDAC are observed in mitochondrial outer membranes, but they do not predominate in detergent-solubilized VDAC samples. In this study, a cholesterol analog, cholesteryl-hemisuccinate (CHS), was shown to induce the formation of detergent-soluble VDAC multimers. The various oligomeric states of VDAC induced by the addition of CHS were deciphered through an integrated biophysics approach using microscale thermophoresis, analytical ultracentrifugation, and size-exclusion chromatography small angle x-ray scattering. Furthermore, CHS stabilizes the interaction between VDAC and hexokinase (K_d of 27 ± 6 μM), confirming the biological relevance of oligomers generated. Thus, sterols such as cholesterol in higher eukaryotes or ergosterol in fungi may regulate the VDAC oligomeric state and may provide a potential target for the modulation of apoptotic signaling by effecting VDAC-VDAC and VDAC-hexokinase interactions. In addition, the integrated biophysical approach described provides a powerful platform for the study of membrane protein complexes in solution.

Mechanism of 53BP1 activity regulation by RNA-binding TIRR and a designer protein

Dynamic protein interaction networks such as DNA double-strand break (DSB) signaling are modulated by post-translational modifications. The DNA repair factor 53BP1 is a rare example of a protein whose post-translational modification-binding function can be switched on and off. 53BP1 is recruited to DSBs by recognizing histone lysine methylation within chromatin, an activity directly inhibited by the 53BP1-binding protein TIRR. X-ray crystal structures of TIRR and a designer protein bound to 53BP1 now reveal a unique regulatory mechanism in which an intricate binding area centered on an essential TIRR arginine residue blocks the methylated-chromatin-binding surface of 53BP1. A 53BP1 separation-of-function mutation that abolishes TIRR-mediated regulation in cells renders 53BP1 hyperactive in response to DSBs, highlighting the key inhibitory function of TIRR. This 53BP1 inhibition is relieved by TIRR-interacting RNA molecules, providing proof-of-principle of RNA-triggered 53BP1 recruitment to DSBs.

Analytical ultracentrifugation in structural biology

Researchers in the field of structural biology, especially X-ray crystallography and protein nuclear magnetic resonance, are interested in knowing as much as possible about the state of their target protein in solution. Not only is this knowledge relevant to studies of biological function, it also facilitates determination of a protein structure using homogeneous monodisperse protein samples. A researcher faced with a new protein to study will have many questions even after that protein has been purified. Analytical ultracentrifugation (AUC) can provide all of this information readily from a small sample in a non-destructive way, without the need for labeling, enabling structure determination experiments without any wasting time and material on uncharacterized samples. In this article, I use examples to illustrate how AUC can contribute to protein structural analysis. Integrating information from a variety of biophysical experimental methods, such as X-ray crystallography, small angle X-ray scattering, electrospray ionization-mass spectrometry, AUC allows a more complete understanding of the structure and function of biomacromolecules.

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.

Identification of novel dual-specificity phosphatase 26 inhibitors by a hybrid virtual screening approach based on pharmacophore and molecular docking

Dual-specificity phosphatase 26 (DUSP26) has recently emerged as a target for treatment of human cancers. However, only two small-molecule inhibitors of DUSP26 are known so far, namely NSC-87877 and ethyl-3, 4-dephostatin. DUSP26 contains an N-terminal region (residues 1-60) and a conserved C-terminal catalytic domain (residues 61-211, DUSP26-C). The crystal structure of DUSP26-C, showing a catalytically inactive conformation of the active site, was reported in a previous study. However, the detailed catalytic mechanism of DUSP26 cannot be described based on that structure. In this study, the 3D structure of DUSP26 (residues 42-211) adopting catalytically active conformation, was built by homology modeling, and the established 3D structure was validated using enzyme kinetic assays. Pharmacophore modeling based on the validated 3D structure of human DUSP26 was carried out. The established pharmacophore model was considered as a 3D query for retrieving novel DUSP26 inhibitors from the chemical databases "Diversity Libraries" (129,087 compounds). Next, a docking study was performed to refine the obtained hit compounds. Then a total of 100 compounds were selected based on the ranking order and visual examination, which were then evaluated by an enzyme-based assay. Eight compounds were found to have inhibitory activities against DUSP26, and the most potent compound was assigned No. F1063-0967 with an IC₅₀ value of 11.62μM. The inhibitory activity of F1063-0967 against DUSP26 is higher than that of NCS87877 (IC₅₀ value: 16.67±2.89μM), but lower than that of ethyl-3, 4-dephostatin (IC₅₀ value: 6.8±0.41μM). MTT assay results revealed that F1063-0967 can induce apoptosis in IMR-32 cell line with an IC₅₀ value of 4.13μM. These results suggest that F1063-0967 should be investigated further for other pharmacological properties.

A combination of mutational and computational scanning guides the design of an artificial ligand-binding controlled lipase

Allostery, i.e. the control of enzyme activity by a small molecule at a location distant from the enzyme’s active site, represents a mechanism essential for sustaining life. The rational design of allostery is a non-trivial task but can be achieved by fusion of a sensory domain, which responds to environmental stimuli with a change in its structure. Hereby, the site of domain fusion is difficult to predict. We here explore the possibility to rationally engineer allostery into the naturally not allosterically regulated Bacillus subtilis lipase A, by fusion of the citrate-binding sensor-domain of the CitA sensory-kinase of Klebsiella pneumoniae. The site of domain fusion was rationally determined based on whole-protein site-saturation mutagenesis data, complemented by computational evolutionary-coupling analyses. Functional assays, combined with biochemical and biophysical studies suggest a mechanism for control, similar but distinct to the one of the parent CitA protein, with citrate acting as an indirect modulator of Triton-X100 inhibition of the fusion protein. Our study demonstrates that the introduction of ligand-dependent regulatory control by domain fusion is surprisingly facile, suggesting that the catalytic mechanism of some enzymes may be evolutionary optimized in a way that it can easily be perturbed by small conformational changes.

Conformational dynamics and self-association of intrinsically disordered Huntingtin exon 1 in cells

In-cell temperature jump experiments induce monomer collapse, misfolding and self-association of the Huntingtin exon 1 protein.

Variable Field Analytical Ultracentrifugation: II. Gravitational Sweep Sedimentation Velocity

Sedimentation velocity (SV) analytical ultracentrifugation is a classical biophysical technique for the determination of the size-distribution of macromolecules, macromolecular complexes, and nanoparticles. SV has traditionally been carried out at a constant rotor speed, which limits the range of sedimentation coefficients that can be detected in a single experiment. Recently we have introduced methods to implement experiments with variable rotor speeds, in combination with variable field solutions to the Lamm equation, with the application to expedite the approach to sedimentation equilibrium. Here, we describe the use of variable-field sedimentation analysis to increase the size-range covered in SV experiments by ∼100-fold with a quasi-continuous increase of rotor speed during the experiment. Such a gravitational-sweep sedimentation approach has previously been shown to be very effective in the study of nanoparticles with large size ranges. In the past, diffusion processes were not accounted for, thereby posing a lower limit of particle sizes and limiting the accuracy of the size distribution. In this work, we combine variable field solutions to the Lamm equation with diffusion-deconvoluted sedimentation coefficient distributions c(s), which further extend the macromolecular size range that can be observed in a single SV experiment while maintaining accuracy and resolution. In this way, approximately five orders of magnitude of sedimentation coefficients, or eight orders of magnitude of particle mass, can be probed in a single experiment. This can be useful, for example, in the study of proteins forming large assemblies, as in fibrillation process or capsid self-assembly, in studies of the interaction between very dissimilar-sized macromolecular species, or in the study of broadly distributed nanoparticles.

Sedimentation coefficient distributions of large particles

The spatial and temporal evolution of concentration boundaries in sedimentation velocity analytical ultracentrifugation reports on the size distribution of particles with high hydrodynamic resolution. For large particles such as large protein complexes, fibrils, viral particles, or nanoparticles, sedimentation conditions usually allow migration from diffusion to be neglected relative to sedimentation. In this case, the shape of the sedimentation boundaries of polydisperse mixtures relates directly to the underlying size-distributions. Integral and derivative methods for calculating sedimentation coefficient distributions g*(s) of large particles from experimental boundary profiles have been developed previously, and are recapitulated here in a common theoretical framework. This leads to a previously unrecognized relationship between g*(s) and the time-derivative of concentration profiles. Of closed analytical form, it is analogous to the well-known Bridgman relationship for the radial derivative. It provides a quantitative description of the effect of substituting the time-derivative by scan differences with finite time intervals, which appears as a skewed box average of the true distribution. This helps to theoretically clarify the differences between results from time-derivative method and the approach of directly fitting the integral definition of g*(s) to the entirety of experimental boundary data.

Kinetics of Thermal Denaturation and Aggregation of Bovine Serum Albumin

Thermal aggregation of bovine serum albumin (BSA) has been studied using dynamic light scattering, asymmetric flow field-flow fractionation and analytical ultracentrifugation. The studies were carried out at fixed temperatures (60°C, 65°C, 70°C and 80°C) in 0.1 M phosphate buffer, pH 7.0, at BSA concentration of 1 mg/ml. Thermal denaturation of the protein was studied by differential scanning calorimetry. Analysis of the experimental data shows that at 65°C the stage of protein unfolding and individual stages of protein aggregation are markedly separated in time. This circumstance allowed us to propose the following mechanism of thermal aggregation of BSA. Protein unfolding results in the formation of two forms of the non-native protein with different propensity to aggregation. One of the forms (highly reactive unfolded form, U_hr) is characterized by a high rate of aggregation. Aggregation of U_hr leads to the formation of primary aggregates with the hydrodynamic radius (R_h,1) of 10.3 nm. The second form (low reactive unfolded form, U_lr) participates in the aggregation process by its attachment to the primary aggregates produced by the U_hr form and possesses ability for self-aggregation with formation of stable small-sized aggregates (A_st). At complete exhaustion of U_lr, secondary aggregates with the hydrodynamic radius (R_h,2) of 12.8 nm are formed. At 60°C the rates of unfolding and aggregation are commensurate, at 70°C the rates of formation of the primary and secondary aggregates are commensurate, at 80°C the registration of the initial stages of aggregation is complicated by formation of large-sized aggregates.

Biointeractions of ultrasmall glutathione-coated gold nanoparticles: effect of small size variations

Recent in vivo studies have established ultrasmall (<3 nm) gold nanoparticles coated with glutathione (AuGSH) as a promising platform for applications in nanomedicine. However, systematic in vitro investigations to gain a more fundamental understanding of the particles' biointeractions are still lacking. Herein we examined the behavior of ultrasmall AuGSH in vitro, focusing on their ability to resist aggregation and adsorption from serum proteins. Despite having net negative charge, AuGSH particles were colloidally stable in biological media and able to resist binding from serum proteins, in agreement with the favorable bioresponses reported for AuGSH in vivo. However, our results revealed disparate behaviors depending on nanoparticle size: particles between 2 and 3 nm in core diameter were found to readily aggregate in biological media, whereas those strictly under 2 nm were exceptionally stable. Molecular dynamics simulations provided microscopic insight into interparticle interactions leading to aggregation and their sensitivity to the solution composition and particle size. These results have important implications, in that seemingly small variations in size can impact the biointeractions of ultrasmall AuGSH, and potentially of other ultrasmall nanoparticles as well.

Calculations and Publication-Quality Illustrations for Analytical Ultracentrifugation Data

The analysis of analytical ultracentrifugation (AUC) data has been greatly facilitated by the advances accumulated in recent years. These improvements include refinements in AUC-based binding isotherms, advances in the fitting of both sedimentation velocity (SV) and sedimentation equilibrium (SE) data, and innovations in calculations related to posttranslationally modified proteins and to proteins with a large amount of associated cosolute, e.g., detergents. To capitalize on these advances, the experimenter often must prepare and collate multiple data sets and parameters for subsequent analyses; these tasks can be cumbersome and unclear, especially for new users. Examples are the sorting of concentration-profile scans for SE data, the integration of sedimentation velocity distributions (c(s)) to arrive at weighted-average binding isotherms, and the calculations to determine the oligomeric state of glycoproteins and membrane proteins. The significant organizational and logistical hurdles presented by these approaches are streamlined by the software described herein, called GUSSI. GUSSI also creates publication-quality graphics for documenting and illustrating AUC and other biophysical experiments with minimal effort on the user's part. The program contains three main modules, allowing for plotting and calculations on c(s) distributions, SV signal versus radius data, and general data/fit/residual plots.

The structure of the atypical killer cell immunoglobulin-like receptor, KIR2DL4

The engagement of natural killer cell immunoglobulin-like receptors (KIRs) with their target ligands, human leukocyte antigen (HLA) molecules, is a critical component of innate immunity. Structurally, KIRs typically have either two (D1-D2) or three (D0-D1-D2) extracellular immunoglobulin domains, with the D1 and D2 domain recognizing the α1 and α2 helices of HLA, respectively, whereas the D0 domain of the KIR3DLs binds a loop region flanking the α1 helix of the HLA molecule. KIR2DL4 is distinct from other KIRs (except KIR2DL5) in that it does not contain a D1 domain and instead has a D0-D2 arrangement. Functionally, KIR2DL4 is also atypical in that, unlike all other KIRs, KIR2DL4 has both activating and inhibitory signaling domains. Here, we determined the 2.8 Å crystal structure of the extracellular domains of KIR2DL4. Structurally, KIR2DL4 is reminiscent of other KIR2DL receptors, with the D0 and D2 adopting the C2-type immunoglobulin fold arranged with an acute elbow angle. However, KIR2DL4 self-associated via the D0 domain in a concentration-dependent manner and was observed as a tetramer in the crystal lattice by size exclusion chromatography, dynamic light scattering, analytical ultracentrifugation, and small angle x-ray scattering experiments. The assignment of residues in the D0 domain to forming the KIR2DL4 tetramer precludes an interaction with HLA akin to that observed for KIR3DL1. Accordingly, no interaction was observed to HLA by direct binding studies. Our data suggest that the unique functional properties of KIR2DL4 may be mediated by self-association of the receptor.

Combining biophysical methods for the analysis of protein complex stoichiometry and affinity in SEDPHAT

Reversible macromolecular interactions are ubiquitous in signal transduction pathways, often forming dynamic multi-protein complexes with three or more components. Multivalent binding and cooperativity in these complexes are often key motifs of their biological mechanisms. Traditional solution biophysical techniques for characterizing the binding and cooperativity are very limited in the number of states that can be resolved. A global multi-method analysis (GMMA) approach has recently been introduced that can leverage the strengths and the different observables of different techniques to improve the accuracy of the resulting binding parameters and to facilitate the study of multi-component systems and multi-site interactions. Here, GMMA is described in the software SEDPHAT for the analysis of data from isothermal titration calorimetry, surface plasmon resonance or other biosensing, analytical ultracentrifugation, fluorescence anisotropy and various other spectroscopic and thermodynamic techniques. The basic principles of these techniques are reviewed and recent advances in view of their particular strengths in the context of GMMA are described. Furthermore, a new feature in SEDPHAT is introduced for the simulation of multi-method data. In combination with specific statistical tools for GMMA in SEDPHAT, simulations can be a valuable step in the experimental design.

Quaternary structure of human small heat shock protein HSPB6 (Hsp20) in crowded media modeled by trimethylamine N-oxide (TMAO): Effect of protein phosphorylation

Effect of trimethylamine N-oxide (TMAO), well-known osmolyte, widely used to imitate crowded intracellular conditions, on the quaternary structure of recombinant human small heat shock protein HspB6 (Hsp20) was analyzed by means of size-exclusion chromatography, chemical crosslinking and analytical ultracentrifugation. Consistent with previous reports, in the absence of TMAO unphosphorylated, pseudophosphorylated (S16D mutant) and phosphorylated HspB6 form only small oligomers (presumably dimers). Addition of TMAO to unphosphorylated HspB6 leads to formation of different large oligomers being in equilibrium with dimers. Pseudophosphorylation (S16D mutation) or phosphorylation partially or completely prevent TMAO-induced oligomerization of HspB6. Pseudophosphorylation affects bis-ANS binding suggesting decreased hydrophobicity of HspB6. According to size-exclusion chromatography, TMAO-induced changes of HspB6 oligomerization result in its altered interaction with HspB1 and this effect can be reversed by HspB6 phosphorylation. It is concluded that under conditions of molecular crowding, characteristic for intracellular environment, HspB6 undergoes reversible changes of its oligomeric state which can affect its physiologically important properties and can be delicately regulated by phosphorylation.

Analysis of protein interactions with picomolar binding affinity by fluorescence-detected sedimentation velocity

The study of high-affinity protein interactions with equilibrium dissociation constants (K_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 K_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 c(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.

Quantification of anti-aggregation activity of chaperones: a test-system based on dithiothreitol-induced aggregation of bovine serum albumin

The methodology for quantification of the anti-aggregation activity of protein and chemical chaperones has been elaborated. The applicability of this methodology was demonstrated using a test-system based on dithiothreitol-induced aggregation of bovine serum albumin at 45°C as an example. Methods for calculating the initial rate of bovine serum albumin aggregation (v agg) have been discussed. The comparison of the dependences of v agg on concentrations of intact and cross-linked α-crystallin allowed us to make a conclusion that a non-linear character of the dependence of v agg on concentration of intact α-crystallin was due to the dynamic mobility of the quaternary structure of α-crystallin and polydispersity of the α-crystallin-target protein complexes. To characterize the anti-aggregation activity of the chemical chaperones (arginine, arginine ethyl ester, arginine amide and proline), the semi-saturation concentration [L]0.5 was used. Among the chemical chaperones studied, arginine ethyl ester and arginine amide reveal the highest anti-aggregation activity ([L]0.5 = 53 and 58 mM, respectively).

Multi-signal sedimentation velocity analysis with mass conservation for determining the stoichiometry of protein complexes

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.

An unusual effect of NADP+ on the thermostability of the nonphosphorylating glyceraldehyde-3-phosphate dehydrogenase from Streptococcus mutans

Adiabatic differential scanning calorimetry was used to investigate the effect of NADP+ on the irreversible thermal denaturation of the nonphosphorylating glyceraldehyde-3-phosphate dehydrogenase (GAPN) from Streptococcus mutans. The GAPN-NADP+ binary complex showed a strongly decreased thermal stability, with a difference of about 20 °C between the temperatures of the thermal transition peak maxima of the complex and the free protein. This finding was similar to the previously described thermal destabilization of GAPN upon binding of inorganic phosphate to the substrate binding site and can be interpreted as the shift of the equilibrium between 2 conformers of tetrameric GAPN upon addition of the coenzyme. Single amino acid substitution, known to abolish the NADP+ binding, cancelled the calorimetric effect of the coenzyme. GAPN thermal inactivation was considerably decelerated in the presence of NADP+ showing that the apparent change in stability of the active centre can be the opposite to that of the whole protein molecule. NADP+ could also reactivate the inactive GAPN* species, obtained by the heating of the apoenzyme below the thermal denaturation transition temperature. These effects may reflect a mechanism that provides GAPN the sufficient flexibility for the earlier observed profound active site reorganizations required during the catalytic cycle. The elevated thermal stability of the apoenzyme may, in turn, be important for maintaining a constant level of active GAPN--an enzyme that is known to be crucial for the effective supply of the reducing equivalents in S. mutans and its ability to grow under aerobic conditions.

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.

Bovine β-lactoglobulin is dimeric under imitative physiological conditions: dissociation equilibrium and rate constants over the pH range of 2.5-7.5

The oligomerization of β-lactoglobulin (βLg) has been studied extensively, but with somewhat contradictory results. Using analytical ultracentrifugation in both sedimentation equilibrium and sedimentation velocity modes, we studied the oligomerization of βLg variants A and B over a pH range of 2.5-7.5 in 100 mM NaCl at 25°C. For the first time, to our knowledge, we were able to estimate rate constants (k(off)) for βLg dimer dissociation. At pH 2.5 k(off) is low (0.008 and 0.009 s(-1)), but at higher pH (6.5 and 7.5) k(off) is considerably greater (>0.1 s(-1)). We analyzed the sedimentation velocity data using the van Holde-Weischet method, and the results were consistent with a monomer-dimer reversible self-association at pH 2.5, 3.5, 6.5, and 7.5. Dimer dissociation constants K(D)(2-1) fell close to or within the protein concentration range of ∼5 to ∼45 μM, and at ∼45 μM the dimer predominated. No species larger than the dimer could be detected. The K(D)(2-1) increased as |pH-pI| increased, indicating that the hydrophobic effect is the major factor stabilizing the dimer, and suggesting that, especially at low pH, electrostatic repulsion destabilizes the dimer. Therefore, through Poisson-Boltzmann calculations, we determined the electrostatic dimerization energy and the ionic charge distribution as a function of ionic strength at pH above (pH 7.5) and below (pH 2.5) the isoelectric point (pI∼5.3). We propose a mechanism for dimer stabilization whereby the added ionic species screen and neutralize charges in the vicinity of the dimer interface. The electrostatic forces of the ion cloud surrounding βLg play a key role in the thermodynamics and kinetics of dimer association/dissociation.

Effects of rotational speed on the hydrodynamic properties of pharmaceutical antibodies measured by analytical ultracentrifugation sedimentation velocity

Analytical ultracentrifugation sedimentation velocity (AUC-SV) has recently become one of the most important tools for the measurement of hydrodynamic properties of proteins. Although a number of studies using AUC-SV as applied to pharmaceutical antibodies have been conducted, the effect of rotational speed on molecular properties has not been systematically examined. The present study aimed to elucidate the influence of rotational speed on the hydrodynamic parameters of pharmaceutical antibodies. A monoclonal and a polyclonal antibody were studied by using AUC-SV at 5 different rotor speeds, and the acquired data were analyzed either by using the computer programs SEDFIT or UltraScan. The frictional ratio of the studied antibodies decreased at high rotor speeds, resulting in underestimation of molecular weight. The frictional ratio value of the monoclonal antibody measured at the low rotor speed was consistent with that of human immunoglobulin G1 computed from its three-dimensional structure. The best agreement between the measured molecular weight and the value calculated from the antibody sequence was achieved at the lower rotor speed. Similar to the results obtained using antibodies, AUC-SV analysis of human serum albumin revealed that the frictional ratio and apparent molecular weight behave in a speed-dependent manner. We deduced that the findings were mainly attributable to the hydrostatic pressure in the analytical ultracentrifuge. The current study implies that rotor speed should be carefully considered in antibody studies using AUC-SV.

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.

A novel, noncatalytic carbohydrate-binding module displays specificity for galactose-containing polysaccharides through calcium-mediated oligomerization

The enzymic degradation of plant cell walls plays a central role in the carbon cycle and is of increasing environmental and industrial significance. The catalytic modules of enzymes that catalyze this process are generally appended to noncatalytic carbohydrate-binding modules (CBMs). CBMs potentiate the rate of catalysis by bringing their cognate enzymes into intimate contact with the target substrate. A powerful plant cell wall-degrading system is the Clostridium thermocellum multienzyme complex, termed the "cellulosome." Here, we identify a novel CBM (CtCBM62) within the large C. thermocellum cellulosomal protein Cthe_2193 (defined as CtXyl5A), which establishes a new CBM family. Phylogenetic analysis of CBM62 members indicates that a circular permutation occurred within the family. CtCBM62 binds to d-galactose and l-arabinopyranose in either anomeric configuration. The crystal structures of CtCBM62, in complex with oligosaccharides containing α- and β-galactose residues, show that the ligand-binding site in the β-sandwich protein is located in the loops that connect the two β-sheets. Specificity is conferred through numerous interactions with the axial O4 of the target sugars, a feature that distinguishes galactose and arabinose from the other major sugars located in plant cell walls. CtCBM62 displays tighter affinity for multivalent ligands compared with molecules containing single galactose residues, which is associated with precipitation of these complex carbohydrates. These avidity effects, which confer the targeting of polysaccharides, are mediated by calcium-dependent oligomerization of the CBM.

Dimeric states of neural- and epithelial-cadherins are distinguished by the rate of disassembly

Epithelial- and neural-cadherins are specifically localized at synapses in neurons which can change the shape and contact surface on a time scale of seconds to months. We have focused our studies on the role of the extracellular domains of cadherins in the dynamics of synapses. The kinetics of dimer disassembly of the first two extracellular domains of E- and N-cadherin, ECAD12 and NCAD12, were studied with analytical size exclusion chromatography and sedimentation velocity. NCAD12 forms three different dimers that are distinguished by assembly conditions and kinetics of dissociation. ECAD12 dimer disassembles rapidly regardless of the calcium concentration, whereas the disassembly of NCAD12 dimers was strongly dependent on calcium concentration. In addition to the apo- and saturated-dimeric forms of NCAD12, there is a third dimeric form that is a slow exchange dimer. This third dimeric form for NCAD12, formed by decalcification of the calcium-saturated dimer, was kinetically trapped in apo-conditions and did not disassemble over a period of months. Sedimentation velocity experiments showed that this dimer, upon addition of calcium, had similar weighted averages as a calcium-saturated dimer. These studies provide evidence that the kinetics of dimer disassembly of the extracellular domains may be a major contributor to the morphological dynamics of synapses in vivo.

The boundary structure in the analysis of reversibly interacting systems by sedimentation velocity

Sedimentation velocity (SV) experiments of heterogeneous interacting systems exhibit characteristic boundary structures that can usually be very easily recognized and quantified. For slowly interacting systems, the boundaries represent concentrations of macromolecular species sedimenting at different rates, and they can be interpreted directly with population models based solely on the mass action law. For fast reactions, migration and chemical reactions are coupled, and different, but equally easily discernable boundary structures appear. However, these features have not been commonly utilized for data analysis, for the lack of an intuitive and computationally simple model. The recently introduced effective particle theory (EPT) provides a suitable framework. Here, we review the motivation and theoretical basis of EPT, and explore practical aspects for its application. We introduce an EPT-based design tool for SV experiments of heterogeneous interactions in the software SEDPHAT. As a practical tool for the first step of data analysis, we describe how the boundary resolution of the sedimentation coefficient distribution c(s) can be further improved with a Bayesian adjustment of maximum entropy regularization to the case of heterogeneous interactions between molecules that have been previously studied separately. This can facilitate extracting the characteristic boundary features by integration of c(s). In a second step, these are assembled into isotherms as a function of total loading concentrations and fitted with EPT. Methods for addressing concentration errors in isotherms are discussed. Finally, in an experimental model system of alpha-chymotrypsin interacting with soybean trypsin inhibitor, we show that EPT provides an excellent description of the experimental sedimentation boundary structure of fast interacting systems.

Interaction of Hsp27 with native phosphorylase kinase under crowding conditions

Interaction of the wild type (wt) heat shock protein Hsp27 and its three-dimensional (3D) mutant (mimicking phosphorylation at Ser15, 78, and 82) with rabbit skeletal muscle phosphorylase kinase (PhK) has been studied under crowding conditions modeled by addition of 1 M trimethylamine N-oxide (TMAO). According to the data of sedimentation velocity and dynamic light scattering, crowding provokes the formation of large-sized associates of both PhK and Hsp27. Under crowding conditions, small associates of PhK and Hsp27 interact with each other thus leading to dissociation of large homooligomers of each protein. Taking into account high concentrations of PhK in the cell, we speculate that native PhK might modulate the oligomeric state and chaperone-like activity of Hsp27.

Diffusion of the reaction boundary of rapidly interacting macromolecules in sedimentation velocity

Sedimentation velocity analytical ultracentrifugation combines relatively high hydrodynamic resolution of macromolecular species with the ability to study macromolecular interactions, which has great potential for studying dynamically assembled multiprotein complexes. Complicated sedimentation boundary shapes appear in multicomponent mixtures when the timescale of the chemical reaction is short relative to the timescale of sedimentation. Although the Lamm partial differential equation rigorously predicts the evolution of concentration profiles for given reaction schemes and parameter sets, this approach is often not directly applicable to data analysis due to experimental and sample imperfections, and/or due to unknown reaction pathways. Recently, we have introduced the effective particle theory, which explains quantitatively and in a simple physical picture the sedimentation boundary patterns arising in the sedimentation of rapidly interacting systems. However, it does not address the diffusional spread of the reaction boundary from the cosedimentation of interacting macromolecules, which also has been of long-standing interest in the theory of sedimentation velocity analytical ultracentrifugation. Here, effective particle theory is exploited to approximate the concentration gradients during the sedimentation process, and to predict the overall, gradient-average diffusion coefficient of the reaction boundary. The analysis of the heterogeneity of the sedimentation and diffusion coefficients across the reaction boundary shows that both are relatively uniform. These results support the application of diffusion-deconvoluting sedimentation coefficient distributions c(s) to the analysis of rapidly interacting systems, and provide a framework for the quantitative interpretation of the diffusional broadening and the apparent molar mass values of the effective sedimenting particle in dynamically associating systems.

Comparative analysis of the effects of alpha-crystallin and GroEL on the kinetics of thermal aggregation of rabbit muscle glyceraldehyde-3-phosphate dehydrogenase

Effects of alpha-crystallin and GroEL on the kinetics of thermal aggregation of rabbit muscle glyceraldehyde-3-phosphate dehydrogenase (GAPDH) have been studied using dynamic light scattering and analytical ultracentrifugation. The analysis of the initial parts of the dependences of the hydrodynamic radius of protein aggregates on time shows that in the presence of alpha-crystallin or GroEL the kinetic regime of GAPDH aggregation is changed from the regime of diffusion-limited cluster-cluster aggregation to the regime of reaction-limited cluster-cluster aggregation, wherein the sticking probability for the colliding particles becomes lower the unity. In contrast to alpha-crystallin, GroEL does not interfere with formation of the start aggregates which include denatured GAPDH molecules. On the basis of the analytical ultracentrifugation data the conclusion has been made that the products of dissociation of GAPDH and alpha-crystallin or GroEL play an important role in the interactions of GAPDH and chaperones at elevated temperatures.

On computational approaches for size-and-shape distributions from sedimentation velocity analytical ultracentrifugation

Sedimentation velocity analytical ultracentrifugation has become a very popular technique to study size distributions and interactions of macromolecules. Recently, a method termed two-dimensional spectrum analysis (2DSA) for the determination of size-and-shape distributions was described by Demeler and colleagues (Eur Biophys J 2009). It is based on novel ideas conceived for fitting the integral equations of the size-and-shape distribution to experimental data, illustrated with an example but provided without proof of the principle of the algorithm. In the present work, we examine the 2DSA algorithm by comparison with the mathematical reference frame and simple well-known numerical concepts for solving Fredholm integral equations, and test the key assumptions underlying the 2DSA method in an example application. While the 2DSA appears computationally excessively wasteful, key elements also appear to be in conflict with mathematical results. This raises doubts about the correctness of the results from 2DSA analysis.

On the analysis of sedimentation velocity in the study of protein complexes

Sedimentation velocity analytical ultracentrifugation has experienced a significant transformation, precipitated by the possibility of efficiently fitting Lamm equation solutions to the experimental data. The precision of this approach depends on the ability to account for the imperfections of the experiment, both regarding the sample and the instrument. In the present work, we explore in more detail the relationship between the sedimentation process, its detection, and the model used in the mathematical data analysis. We focus on configurations that produce steep and fast-moving sedimentation boundaries, such as frequently encountered when studying large multi-protein complexes. First, as a computational tool facilitating the analysis of heterogeneous samples, we introduce the strategy of partial boundary modeling. It can simplify the modeling by restricting the direct boundary analysis to species with sedimentation coefficients in a predefined range. Next, we examine factors related to the experimental detection, including the magnitude of optical aberrations generated by out-of-focus solution columns at high protein concentrations, the relationship between the experimentally recorded signature of the meniscus and the meniscus parameter in the data analysis, and the consequences of the limited radial and temporal resolution of the absorbance optical scanning system. Surprisingly, we find that large errors can be caused by the finite scanning speed of the commercial absorbance optics, exceeding the statistical errors in the measured sedimentation coefficients by more than an order of magnitude. We describe how these effects can be computationally accounted for in SEDFIT and SEDPHAT.