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

Flotation Coefficient Distributions of Lipid Nanoparticles by Sedimentation Velocity Analytical Ultracentrifugation

The robust characterization of lipid nanoparticles (LNPs) encapsulating therapeutics or vaccines is an important and multifaceted translational problem. Sedimentation velocity analytical ultracentrifugation (SV-AUC) has proven to be a powerful approach in the characterization of size-distribution, interactions, and composition of various types of nanoparticles across a large size range, including metal nanoparticles (NPs), polymeric NPs, and also nucleic acid loaded viral capsids. Similar potential of SV-AUC can be expected for the characterization of LNPs, but is hindered by the flotation of LNPs being incompatible with common sedimentation analysis models. To address this gap, we developed a high-resolution, diffusion-deconvoluted sedimentation/flotation distribution analysis approach analogous to the most widely used sedimentation analysis model c(s). The approach takes advantage of independent measurements of the average particle size or diffusion coefficient, which can be conveniently determined, for example, by dynamic light scattering (DLS). We demonstrate the application to an experimental model of extruded liposomes as well as a commercial LNP product and discuss experimental potential and limitations of SV-AUC. The method is implemented analogously to the sedimentation models in the free, widely used SEDFIT software.

Cooperative nucleic acid binding by Poly ADP-ribose polymerase 1

Poly (ADP)-ribose polymerase 1 (PARP1) is an abundant nuclear protein well-known for its role in DNA repair yet also participates in DNA replication, transcription, and co-transcriptional splicing, where DNA is undamaged. Thus, binding to undamaged regions in DNA and RNA is likely a part of PARP1's normal repertoire. Here we describe analyses of PARP1 binding to two short single-stranded DNAs, a single-stranded RNA, and a double stranded DNA. The investigations involved comparing the wild-type (WT) full-length enzyme with mutants lacking the catalytic domain (∆CAT) or zinc fingers 1 and 2 (∆Zn1∆Zn2). All three protein types exhibited monomeric characteristics in solution and formed saturated 2:1 complexes with single-stranded T20 and U20 oligonucleotides. These complexes formed without accumulation of 1:1 intermediates, a pattern suggestive of positive binding cooperativity. The retention of binding activities by ∆CAT and ∆Zn1∆Zn2 enzymes suggests that neither the catalytic domain nor zinc fingers 1 and 2 are indispensable for cooperative binding. In contrast, when a double stranded 19mer DNA was tested, WT PARP1 formed a 4:1 complex while the ∆Zn1Zn2 mutant binding saturated at 1:1 stoichiometry. These deviations from the 2:1 pattern observed with T20 and U20 oligonucleotides show that PARP's binding mechanism can be influenced by the secondary structure of the nucleic acid. Our studies show that PARP1:nucleic acid interactions are strongly dependent on the nucleic acid type and properties, perhaps reflecting PARP1's ability to respond differently to different nucleic acid ligands in cells. These findings lay a platform for understanding how the functionally versatile PARP1 recognizes diverse oligonucleotides within the realms of chromatin and RNA biology.

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.

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.

Metallo-Supramolecular Complexation Behavior of Terpyridine- and Ferrocene-Based Polymers in Solution-A Molecular Hydrodynamics Perspective

The contribution deals with the synthesis of the poly(methacrylate)-based copolymers, which contain ferrocene and/or terpyridine moieties in the side chains, and the subsequent analysis of their self-assembly behavior upon supramolecular/coordination interactions with Eu3+ and Pd2+ ions in dilute solutions. Both metal ions provoke intra and inter molecular complexation that results in the formation of large supra-macromolecular assembles of different conformation/shapes. By applying complementary analytical approaches (i.e., sedimentation-diffusion analysis in the analytical ultracentrifuge, dynamic light scattering, viscosity and density measurements, morphology studies by electron microscopy), a map of possible conformational states/shapes was drawn and the corresponding fundamental hydrodynamic and macromolecular characteristics of metallo-supramolecular assemblies at various ligand-to-ion molar concentration ratios (M/L) in extremely dilute polymer solutions (c[η]≈0.006) were determined. It was shown that intramolecular complexation is already detected at (L≈0.1), while at M/L>0.5 solution/suspension precipitates. Extreme aggregation/agglomeration behavior of such dilute polymer solutions at relatively “high” metal ion content is explained from the perspective of polymer-solvent and charge interactions that will accompany the intramolecular complexation due to the coordination interactions.

Best Practices for Aggregate Quantitation of Antibody Therapeutics by Sedimentation Velocity Analytical Ultracentrifugation

Analytical ultracentrifugation (AUC) is a critical analytical tool supporting the development and manufacture of protein therapeutics. AUC is routinely used as an assay orthogonal to size exclusion chromatography for aggregate quantitation. This article distills the experimental and analysis procedures used by the authors for sedimentation velocity AUC into a series of best-practices considerations. The goal of this distillation is to help harmonize aggregate quantitation approaches across the biopharmaceutical industry. We review key considerations for sample and instrument suitability, experimental design, and data analysis best practices and conversely, highlight potential pitfalls to accurate aggregate analysis. Our goal is to provide experienced users benchmarks against which they can standardize their analyses and to provide guidance for new AUC analysts that will aid them to become proficient in this fundamental technique.

Enhanced Sample Handling for Analytical Ultracentrifugation with 3D-Printed Centerpieces

The centerpiece of the sample cell assembly in analytical ultracentrifugation holds the sample solution between windows, sealed against high vacuum, and is shaped such that macromolecular migration in centrifugal fields exceeding 200 000g can proceed undisturbed by walls or convection while concentration profiles are imaged with optical detection systems aligned perpendicular to the plane of rotation. We have recently shown that 3D printing using various materials allows inexpensive and rapid manufacturing of centerpieces. In the present work, we expand this endeavor to examine the accuracy of the measured sedimentation process, as well as short-term durability of the centerpieces. We find that 3D-printed centerpieces can be used many times and can provide data equivalent in quality to commonly used commercial epoxy resin centerpieces. Furthermore, 3D printing enables novel designs adapted to particular experimental objectives because they offer unique opportunities, for example, to create well-defined curved surfaces, narrow channels, and embossed features. We present examples of centerpiece designs exploiting these capabilities for improved AUC experiments. This includes narrow sector centerpieces that substantially reduce the required sample volume while maintaining the standard optical path length; thin centerpieces with integrated window holders to provide very short optical pathlengths that reduce optical aberrations at high macromolecular concentrations; long-column centerpieces that increase the observable distance of macromolecular migration for higher-precision sedimentation coefficients; and three-sector centerpieces that allow doubling the number of samples in a single run while reducing the sample volumes. We find each of these designs allows unimpeded macromolecular sedimentation and can provide high-quality sedimentation data.

Cooperative assembly of a four-molecule signaling complex formed upon T cell antigen receptor activation

The T cell antigen receptor encounters foreign antigen during the immune response. Receptor engagement leads to activation of specific protein tyrosine kinases, which then phosphorylate multiple enzymes and adapter proteins. One such enzyme, phospholipase-Cγ1, is responsible for cleavage of a plasma membrane lipid substrate, a phosphoinositide, into two second messengers, diacylglycerol, which activates several enzymes including protein kinase C, and an inositol phosphate, which induces intracellular calcium elevation. In T cells, phospholipase-Cγ1 is recruited to the plasma membrane as part of a four-protein complex containing three adapter molecules. We have used recombinant proteins and synthetic phosphopeptides to reconstitute this quaternary complex in vitro. Extending biophysical tools to study concurrent interactions of the four protein components, we demonstrated the formation and determined the composition of the quaternary complex using multisignal analytical ultracentrifugation, and we characterized the thermodynamic driving forces of assembly by isothermal calorimetry. We demonstrate that the four proteins reversibly associate in a circular arrangement of binding interfaces, each protein interacting with two others. Three interactions are of high affinity, and the fourth is of low affinity, with the assembly of the quaternary complex exhibiting significant enthalpy-entropy compensation as in an entropic switch. Formation of this protein complex enables subsequent recruitment of additional molecules needed to activate phospholipase-Cγ1. Understanding the formation of this complex is fundamental to full characterization of a central pathway in T cell activation. Such knowledge is critical to developing ways in which this pathway can be selectively inhibited.

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.

Role of Munc13-4 as a Ca2+-dependent tether during platelet secretion

The Munc13 family of exocytosis regulators has multiple Ca(2+)-binding, C2 domains. Here, we probed the mechanism by which Munc13-4 regulates in vitro membrane fusion and platelet exocytosis. We show that Munc13-4 enhances in vitro soluble NSF attachment protein receptor (SNARE)-dependent, proteoliposome fusion in a Ca(2+)- and phosphatidylserine (PS)-dependent manner that was independent of SNARE concentrations. Munc13-4-SNARE interactions, under the conditions used, were minimal in the absence or presence of Ca(2+). However, Munc13-4 was able to bind and cluster liposomes harbouring PS in response to Ca(2+). Interestingly, Ca(2+)-dependent liposome binding/clustering and enhancement of proteoliposome fusion required both Munc13-4 C2 domains, but only the Ca(2+)-liganding aspartate residues of the C2B domain. Analytical ultracentrifugation (AUC) measurements indicated that, in solution, Munc13-4 was a monomeric prolate ellipsoid with dimensions consistent with a molecule that could bridge two fusing membranes. To address the potential role of Munc13-4 as a tethering protein in platelets, we examined mepacrine-stained, dense granule mobility and secretion in platelets from wild-type and Munc13-4 null (Unc13d(Jinx)) mice. In the absence of Munc13-4, dense granules were highly mobile in both resting and stimulated platelets, and stimulation-dependent granule release was absent. These observations suggest that dense granules are stably docked in resting platelets awaiting stimulation and that Munc13-4 plays a vesicle-stabilizing or tethering role in resting platelets and also in activated platelets in response to Ca(2+). In summary, we show that Munc13-4 conveys Ca(2+) sensitivity to platelet SNARE-mediated membrane fusion and reveal a potential mechanism by which Munc13-4 bridges and stabilizes apposing membranes destined for fusion.

Structural analysis of an oxygen-regulated diguanylate cyclase

Cyclic di-GMP is a bacterial second messenger that is involved in switching between motile and sessile lifestyles. Given the medical importance of biofilm formation, there has been increasing interest in understanding the synthesis and degradation of cyclic di-GMPs and their regulation in various bacterial pathogens. Environmental cues are detected by sensing domains coupled to GGDEF and EAL or HD-GYP domains that have diguanylate cyclase and phosphodiesterase activities, respectively, producing and degrading cyclic di-GMP. The Escherichia coli protein DosC (also known as YddV) consists of an oxygen-sensing domain belonging to the class of globin sensors that is coupled to a C-terminal GGDEF domain via a previously uncharacterized middle domain. DosC is one of the most strongly expressed GGDEF proteins in E. coli, but to date structural information on this and related proteins is scarce. Here, the high-resolution structural characterization of the oxygen-sensing globin domain, the middle domain and the catalytic GGDEF domain in apo and substrate-bound forms is described. The structural changes between the iron(III) and iron(II) forms of the sensor globin domain suggest a mechanism for oxygen-dependent regulation. The structural information on the individual domains is combined into a model of the dimeric DosC holoprotein. These findings have direct implications for the oxygen-dependent regulation of the activity of the cyclase domain.

Comparison of binding characteristics and in vitro activities of three inhibitors of vascular endothelial growth factor A

The objectives of this study were to evaluate the relative binding and potencies of three inhibitors of vascular endothelial growth factor A (VEGF), used to treat neovascular age-related macular degeneration, and assess their relevance in the context of clinical outcome. Ranibizumab is a 48 kDa antigen binding fragment, which lacks a fragment crystallizable (Fc) region and is rapidly cleared from systemic circulation. Aflibercept, a 110 kDa fusion protein, and bevacizumab, a 150 kDa monoclonal antibody, each contain an Fc region. Binding affinities were determined using Biacore analysis. Competitive binding by sedimentation velocity analytical ultracentrifugation (SV-AUC) was used to support the binding affinities determined by Biacore of ranibizumab and aflibercept to VEGF. A bovine retinal microvascular endothelial cell (BREC) proliferation assay was used to measure potency. Biacore measurements were format dependent, especially for aflibercept, suggesting that biologically relevant, true affinities of recombinant VEGF (rhVEGF) and its inhibitors are yet to be determined. Despite this assay format dependency, ranibizumab appeared to be a very tight VEGF binder in all three formats. The results are also very comparable to those reported previously.1-3 At equivalent molar ratios, ranibizumab was able to displace aflibercept from preformed aflibercept/VEGF complexes in solution as assessed by SV-AUC, whereas aflibercept was not able to significantly displace ranibizumab from preformed ranibizumab/VEGF complexes. Ranibizumab, aflibercept, and bevacizumab showed dose-dependent inhibition of BREC proliferation induced by 6 ng/mL VEGF, with average IC50 values of 0.088 ± 0.032, 0.090 ± 0.009, and 0.500 ± 0.091 nM, respectively. Similar results were obtained with 3 ng/mL VEGF. In summary Biacore studies and SV-AUC solution studies show that aflibercept does not bind with higher affinity than ranibizumab to VEGF as recently reported,4 and both inhibitors appeared to be equipotent with respect to their ability to inhibit VEGF function.

Repair of O6-methylguanine adducts in human telomeric G-quadruplex DNA by O6-alkylguanine-DNA alkyltransferase

O⁶-alkylguanine-DNA alkyltransferase (AGT) is a single-cycle DNA repair enzyme that removes pro-mutagenic O⁶-alkylguanine adducts from DNA. Its functions with short single-stranded and duplex substrates have been characterized, but its ability to act on other DNA structures remains poorly understood. Here, we examine the functions of this enzyme on O⁶-methylguanine (6mG) adducts in the four-stranded structure of the human telomeric G-quadruplex. On a folded 22-nt G-quadruplex substrate, binding saturated at 2 AGT:DNA, significantly less than the ∼5 AGT:DNA found with linear single-stranded DNAs of similar length, and less than the value found with the telomere sequence under conditions that inhibit quadruplex formation (4 AGT:DNA). Despite these differences, AGT repaired 6mG adducts located within folded G-quadruplexes, at rates that were comparable to those found for a duplex DNA substrate under analogous conditions. Repair was kinetically biphasic with the amplitudes of rapid and slow phases dependent on the position of the adduct within the G-quadruplex: in general, adducts located in the top or bottom tetrads of a quadruplex stack exhibited more rapid-phase repair than did adducts located in the inner tetrad. This distinction may reflect differences in the conformational dynamics of 6mG residues in G-quadruplex DNAs.

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.

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.

Sedimentation velocity of intrinsically disordered proteins: what information can we actually obtain?

Intrinsically disordered proteins are a challenge to characterise structurally because of their innate flexibility. Hydrodynamic methods such as sedimentation velocity analytical ultracentrifugation have been proposed as methods for their characterisation. By examining in detail this assumption we show that although velocity measurements do yield information on gross conformation, the information is restricted to only the weight averaged sedimentation and diffusion coefficients of the conformational ensemble.

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.

Extended Fujita approach to the molecular weight distribution of polysaccharides and other polymeric systems

In 1962 H. Fujita (H. Fujita, Mathematical Theory of Sedimentation Analysis, Academic Press, New York, 1962) examined the possibility of transforming a quasi-continuous distribution g(s) of sedimentation coefficient s into a distribution f(M) of molecular weight M for linear polymers using the relation f(M)=g(s)·(ds/dM) and showed that this could be done if information about the relation between s and M is available from other sources. Fujita provided the transformation based on the scaling relation s=κ(s)M(0.5), where κ(s) is taken as a constant for that particular polymer and the exponent 0.5 essentially corresponds to a randomly coiled polymer under ideal conditions. This method has been successfully applied to mucus glycoproteins (S.E. Harding, Adv. Carbohyd. Chem. Biochem. 47 (1989) 345-381). We now describe an extension of the method to general conformation types via the scaling relation s=κM(b), where b=0.4-0.5 for a coil, ∼0.15-0.2 for a rod and ∼0.67 for a sphere. We give examples of distributions f(M) versus M obtained for polysaccharides from SEDFIT derived least squares g(s) versus s profiles (P. Schuck, Biophys. J. 78 (2000) 1606-1619) and the analytical derivative for ds/dM performed with Microcal ORIGIN. We also describe a more direct route from a direct numerical solution of the integral equation describing the molecular weight distribution problem. Both routes give identical distributions although the latter offers the advantage of being incorporated completely within SEDFIT. The method currently assumes that solutions behave ideally: sedimentation velocity has the major advantage over sedimentation equilibrium in that concentrations less than 0.2mg/ml can be employed, and for many systems non-ideality effects can be reasonably ignored. For large, non-globular polymer systems, diffusive contributions are also likely to be small.

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.

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.