Isothermal titration calorimetry (ITC) is a traditional and powerful method for studying the linkage of ligand binding to proton uptake or release. The theoretical framework has been developed for more than two decades and numerous applications have appeared. In the current work, we explored strategic aspects of experimental design. To this end, we simulated families of ITC data sets that embed different strategies with regard to the number of experiments, range of experimental pH, buffer ionization enthalpy, and temperature. We then re-analyzed the families of data sets in the context of global analysis, employing a proton linkage binding model implemented in the global data analysis platform SEDPHAT, and examined the information content of all data sets by a detailed statistical error analysis of the parameter estimates. In particular, we studied the impact of different assumptions about the knowledge of the exact concentrations of the components, which in practice presents an experimental limitation for many systems. For example, the uncertainty in concentration may reflect imperfectly known extinction coefficients and stock concentrations or may account for different extents of partial inactivation when working with proteins at different pH values. Our results show that the global analysis can yield reliable estimates of the thermodynamic parameters for intrinsic binding and protonation, and that in the context of the global analysis the exact molecular component concentrations may not be required. Additionally, a comparison of data from different experimental strategies illustrates the benefit of conducting experiments at a range of temperatures.
protein interactions; thermodynamics; proton linkage; isothermal titration calorimetry; global analysis; SEDPHAT
Tripartite ATP-independent periplasmic transporters (TRAP-Ts) are bacterial transport systems that have been implicated in the import of small molecules into the cytoplasm. A newly discovered subfamily of TRAP-Ts (TPATs) has four components. Three are common to both TRAP-Ts and TPATs: the P component, a ligand-binding protein, and a transmembrane symporter apparatus comprising the M and Q components (M and Q are sometimes fused to form a single polypeptide). TPATs are distinguished from TRAP-Ts by the presence of a unique protein called the “T component”. In Treponema pallidum, this protein (TatT) is a water-soluble trimer whose protomers are each perforated by a pore. Its respective P component (TatPT) interacts with the TatT in vitro and in vivo. In this work, we further characterized this interaction. Co-crystal structures of two complexes between the two proteins confirm that up to three monomers of TatPT can bind to the TatT trimer. A putative ligand-binding cleft of TatPT aligns with the pore of TatT, strongly suggesting ligand transfer between T and PT. We used a combination of site-directed mutagenesis and analytical ultracentrifugation to derive thermodynamic parameters for the interactions. These observations confirm that the observed crystallographic interface is recapitulated in solution. These results prompt a hypothesis of the molecular mechanism(s) of hydrophobic ligand transport by the TPATs.
TRAP transporter; syphilis; Treponema pallidum; TPR motif; protein interactions; lipoproteins; SBPs; TPAT
Isothermal titration calorimetry (ITC) is a powerful classical method that enables researchers in many fields to study the thermodynamics of molecular interactions. Primary ITC data comprise the temporal evolution of differential power reporting the heat of reaction during a series of injections of aliquots of a reactant into a sample cell. By integration of each injection peak, an isotherm can be constructed of total changes in enthalpy as a function of changes in solution composition, which is rich in thermodynamic information on the reaction. However, the signals from the injection peaks are superimposed by the stochastically varying time-course of the instrumental baseline power, limiting the precision of ITC isotherms. Here, we describe a method for automated peak assignment based on peak-shape analysis via singular value decomposition in combination with detailed least-squares modeling of local pre- and post-injection baselines. This approach can effectively filter out contributions of short-term noise and adventitious events in the power trace. This method also provides, for the first time, statistical error estimates for the individual isotherm data points. In turn, this results in improved detection limits for high-affinity or low-enthalpy binding reactions and significantly higher precision of the derived thermodynamic parameters.
isothermal titration microcalorimetry; singular value decomposition; protein interactions; binding enthalpy
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.
Treponema pallidum, the bacterial agent of syphilis, is predicted to encode one tripartite ATP- independent periplasmic transporter (TRAP-T). TRAP-Ts typically employ a periplasmic substrate-binding protein (SBP) to deliver the cognate ligand to the transmembrane symporter. Herein, we demonstrate that the genes encoding the putative TRAP-T components from T. pallidum, tp0957 (the SBP) and tp0958 (the symporter) are in an operon with an uncharacterized third gene, tp0956. We determined the crystal structure of recombinant Tp0956; the protein is trimeric and perforated by a pore. Part of Tp0956 forms an assembly similar to those of “tetratricopeptide repeat” (TPR) motifs. The crystal structure of recombinant Tp0957 was also determined; like the SBPs of other TRAP-Ts, there are two lobes separated by a cleft. In these other SBPs, the cleft binds a negatively charged ligand. However, the cleft of Tp0957 has a strikingly hydrophobic chemical composition, indicating that its ligand may be substantially different and likely hydrophobic. Analytical ultracentrifugation of the recombinant versions of Tp0956 and Tp0957 established that these proteins associate avidly. This unprecedented interaction was confirmed for the native molecules using in vivo cross-linking experiments. Finally, bioinformatic analyses suggested that this transporter exemplifies a new subfamily of TPR-protein associated TRAP transporters (TPATs) that require the action of a TPR-containing accessory protein for the periplasmic transport of a potentially hydrophobic ligand(s).
TRAP transporter; syphilis; Treponema pallidum; TPR motif; protein interactions
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.
In 1962 H. Fujita (Mathematical Theory of Sedimentation Analysis, Academic Press, New York, pp. 182–192) 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 = κM0.5, where κ 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 was 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 = κMb, 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) vs M obtained for polysaccharides from SEDFIT derived least squares g(s) vs 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 0.2 mg/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.
Epithelial- and Neural-cadherins are specifically localized at synapses in neurons which can change 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 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.
Kinetically-trapped dimer; Slow disassembly; Size Exclusion Chromatography; Sedimentation Velocity
γ-crystallins constitute the major protein component in the nucleus of the vertebrate eye lens. Present at very high concentrations, they exhibit extreme solubility and thermodynamic stability to prevent scattering of light and the formation of cataracts. However, functions beyond this structural role have remained mostly unclear. Here, we calculate molecular refractive index increments of crystallins. We show that all lens γ-crystallins have evolved a significantly elevated molecular refractive index increment, which is far above those of most proteins, including non-lens members of the βγ-crystallin family from different species. The same trait has evolved in parallel in crystallins of different phyla, including in the S-crystallins of cephalopods. A high refractive index increment can lower the crystallin concentration required to achieve a suitable refractive power of the lens, and thereby reduce their propensity to aggregate and form cataract. To produce a significant increase of the refractive index increment, a substantial global shift in the amino acid composition is required, which can naturally explain the highly unusual amino acid composition of γ-crystallins and their functional homologues. This function provides a new perspective for interpreting their molecular structure.
crystallin; protein structure function; protein refractive index; excluded volume
Crystallins are present in the lens at extremely high concentrations in order to provide transparency and generate a high refractive power of the lens. The crystallin families prevalent in the highest density lens tissues are γ crystallins in vertebrates and S crystallins in cephalopods. In parallel evolution, both have evolved molecular refractive index increments 5 – 10 % above those of most proteins. Although this is a small increase, it is statistically very significant and can be achieved only by very unusual amino acid compositions. In contrast, such a molecular adaptation to aid in the refractive function of the lens did not occur in crystallins that are preferentially located in lower density lens tissues, such as vertebrate α crystallin and taxon specific crystallins. In the current work, we apply a model of non-interacting hard spheres to examine the thermodynamic contributions of volume exclusion at lenticular protein concentrations. We show that the small concentration decrease afforded by the higher molecular refractive index increment of crystallins can amplify nonlinearly to produce order of magnitude differences in chemical activities, and lead to reduced osmotic pressure and the reduced propensity for protein aggregation. Quantitatively, this amplification sets in only at protein concentrations as high as those found in hard lenses or the nucleus of soft lenses, in good correspondence to the observed crystalline properties in different tissues and different species. This suggests that volume exclusion effects provide the evolutionary driving force for the unusual refractive properties and the unusual amino acid compositions of γ crystallins and S crystallins.
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 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 can be further improved in c(s) 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) and their assembly into isotherms as a function of total loading concentrations, which are fitted with EPT in a second stage. 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.
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 H2O, or isotopically enriched H218O 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.
Amyloid fibrils and their oligomeric intermediates accumulate in several age-related diseases where their presence is considered to play an active role in disease progression. A common characteristic of amyloid fibril formation is an initial lag phase indicative of a nucleation-elongation mechanism for fibril assembly. We have investigated fibril formation by human apolipoprotein (apo) C-II. ApoC-II readily forms amyloid fibrils in a lipid-dependent manner via an initial nucleation step followed by fibril elongation, breaking and joining. We used fluorescence techniques and stopped-flow analysis to identify the individual kinetic steps involved in the activation of apoC-II fibril formation by the short-chain phospholipid dihexanoyl phosphatidylcholine (DHPC). Sub-micellar DHPC activates fibril formation by promoting the rapid formation of a tetrameric species followed by a slow isomerisation that precedes monomer addition and fibril growth. Global fitting of the concentration dependence of apoC-II fibril formation showed that DHPC increased the overall tetramerization constant from 7.5 × 10−13 to 1.2 × 10−6 μM−3 without significantly affecting the rate of fibril elongation, breaking or joining. Studies on the effect of DHPC on the free pool of apoC-II monomer and on fibril formation by cross-linked apoC-II dimers further demonstrate DHPC affects nucleation but not elongation. These studies demonstrate the capacity of small lipid compounds to selectively target individual steps in the amyloid fibril forming pathway.
Sedimentation velocity; protein self-assembly; kinetic mechanism; amyloid kinetics; Amyloid fibrils; phospholipid; nucleation
For the detailed analysis of sedimentation velocity data, the consideration of radial-dependent baseline offsets is indispensable. Two main approaches are data differencing (‘delta-c’ approach), and explicit inclusion of baseline parameters (‘direct boundary model’ of the raw data). The present work aims to clarify the relationships between the two approaches. To this end, a simple model problem is examined. We show that the explicit consideration of the baseline in the model is equivalent to a differencing scheme where from all data points their average value is subtracted. Pair-wise differencing in the ‘delta-c’ approach always results in higher parameter uncertainty. For equidistant time points, the increase is smallest when the reference points are taken at intervals of 1/3 or 2/3 of the total number of time points. If the difference data are misinterpreted to be statistically independent samples, errors in the calculation of the parameter uncertainties can occur. Contrary to claims in the literature, we observe there is no distinction in the approaches regarding their ‘model-dependence’: both approaches arise from the integral or differential form of same model, and both can and should provide explicit estimates of the baseline values in the original data space for optimal discrimination between macromolecular sedimentation models.
analytical ultracentrifugation; model-free analysis; direct boundary modeling; statistical data analysis
Cytomegaloviruses (CMVs) are ubiquitous species-specific viruses that establish acute, persistent, and latent infections. Both human and mouse CMVs encode proteins that inhibit the activation of natural killer (NK) cells by downregulating cellular ligands for the NK cell activating receptor, NKG2D. The MCMV glycoprotein m152/gp40 downregulates the surface expression of RAE-1 in order to avoid NK cell control in vivo. So far it is unclear if there is a direct interaction between m152 and RAE-1, and if so, if m152 interacts differentially with the five identified RAE-1 isoforms, which are expressed as two groups in MCMV-susceptible or resistant mouse strains. To address these questions, we expressed and purified the extracellular domains of RAE-1 and m152, and performed size exclusion chromatography binding assays as well as analytical ultracentrifugation and isothermal titration calorimetry to characterize these interactions quantitatively. We further evaluated the role of full-length and naturally glycosylated m152 and RAE-1 in cotransfected HEK293T cells. Our results confirmed that m152 binds RAE-1 directly, relatively tightly (Kd < 5 μM), and with 1:1 stoichiometry. The binding is quantitatively different depending on particular RAE-1 isoforms, corresponding to the susceptibility to downregulation by m152. A PLWY motif found in RAE-1β, although contributing to its affinity for m152, does not influence the affinity of RAE-1 γ or δ, suggesting that other differences contribute to the RAE-1/m152 interaction. Molecular modeling of the different RAE-1 isoforms suggests a potential site for the m152 interaction.
We introduce NanoPen, a novel technique for low optical power intensity, flexible, real-time reconfigurable, and large-scale light-actuated patterning of single or multiple nanoparticles such as metallic spherical nanocrystals, and one-dimensional nanostructures such as carbon nanotubes. NanoPen is capable of dynamically patterning nanoparticles over thousands of μm2 areas with light intensities <10 W/cm2 (using a commercial projector) within seconds. Various arbitrary nanoparticle patterns and arrays (including a 10×10 array covering a 0.025 mm2 area) are demonstrated using this capability. One application of NanoPen is presented through the creation of surface-enhanced Raman spectroscopy (SERS) hot-spots by patterning gold nanoparticles of 90 nm diameters with enhancement factors exceeding 107 and pico-molar concentration sensitivities.
Proteins located on the surface of the pathogenic malaria parasite Plasmodium falciparum are objects of intensive studies due to their important role in the invasion of human cells and the accessibility to host antibodies thus making these proteins attractive vaccine candidates. One of these proteins, merozoite surface protein 3 (MSP3) represents a leading component among vaccine candidates; however, little is known about its structure and function. Our biophysical studies suggest that the 40 residue C-terminal domain of MSP3 protein self-assembles into a four-stranded α–helical coiled coil structure where α–helices are packed “side-by-side”. A bioinformatics analysis provides an extended list of known and putative proteins from different species of Plasmodium which have such MSP3-like C-terminal domains. This finding allowed us to extend some conclusions of our studies to a larger group of the malaria surface proteins. Possible structural and functional roles of these highly conserved oligomerization domains in the intact merozoite surface proteins are discussed.
α-helical coiled coil; oligomerization; protein structure; Plasmodium falciparum.
Three chimpanzee Fabs reactive with lethal factor (LF) of anthrax toxin were isolated and converted into complete monoclonal antibodies (MAbs) with human γ1 heavy-chain constant regions. In a macrophage toxicity assay, two of the MAbs, LF10E and LF11H, neutralized lethal toxin (LT), a complex of LF and anthrax protective antigen (PA). LF10E has the highest reported affinity for a neutralizing MAb against LF (dissociation constant of 0.69 nM). This antibody also efficiently neutralized LT in vitro, with a 50% effective concentration (EC50) of 0.1 nM, and provided 100% protection of rats against toxin challenge with a 0.5 submolar ratio relative to LT. LF11H, on the other hand, had a slightly lower binding affinity to LF (dissociation constant of 7.4 nM) and poor neutralization of LT in vitro (EC50 of 400 nM) and offered complete protection in vivo only at an equimolar or higher ratio to toxin. Despite this, LF11H, but not LF10E, provided robust synergistic protection when combined with MAb W1, which neutralizes PA. Epitope mapping and binding assays indicated that both LF10E and LF11H recognize domain I of LF (amino acids 1 to 254). Although domain I is responsible for binding to PA, neither MAb prevented LF from binding to activated PA. Although two unique MAbs could protect against anthrax when used alone, even more efficient and broader protection should be gained by combining them with anti-PA MAbs.
The amino terminal domain of glutamate receptor ion channels, which controls their selective assembly into AMPA, kainate and NMDA receptor subtypes, is also the site of action of NMDA receptor allosteric modulators. Here we report the crystal structure of the ATD from the kainate receptor GluR6. The ATD forms dimers in solution at micromolar protein concentrations and crystallizes as a dimer. Unexpectedly, each subunit adopts an intermediate extent of domain closure compared to the apo and ligand bound complexes of LIVBP and G-Protein coupled glutamate receptors, and the dimer assembly has a strikingly different conformation from that found in mGluRs. This conformation is stabilized by contacts between large hydrophobic patches in the R2 domain which are absent in NMDA receptors, suggesting that the ATDs of individual glutamate receptor ion channels have evolved into functionally distinct families.
The analytical ultracentrifuge (AUC) is a powerful biophysical tool that allows us to record macromolecular sedimentation profiles during high speed centrifugation. When properly planned and executed, an AUC sedimentation velocity or sedimentation equilibrium experiment can reveal a great deal about a protein in regards to size and shape, sample purity, sedimentation coefficient, oligomerization states and protein-protein interactions.
This technique, however, requires a rigorous level of technical attention. Sample cells hold a sectored center piece sandwiched between two window assemblies. They are sealed with a torque pressure of around 120-140 in/lbs. Reference buffer and sample are loaded into the centerpiece sectors and then after sealing, the cells are precisely aligned into a titanium rotor so that the optical detection systems scan both sample and reference buffer in the same radial path midline through each centerpiece sector while rotating at speeds of up to 60, 000 rpm and under very high vacuum
Not only is proper sample cell assembly critical, sample cell components are very expensive and must be properly cared for to ensure they are in optimum working condition in order to avoid leaks and breakage during experiments. Handle windows carefully, for even the slightest crack or scratch can lead to breakage in the centrifuge. The contact between centerpiece and windows must be as tight as possible; i.e. no Newton s rings should be visible after torque pressure is applied. Dust, lint, scratches and oils on either the windows or the centerpiece all compromise this contact and can very easily lead to leaking of solutions from one sector to another or leaking out of the centerpiece all together. Not only are precious samples lost, leaking of solutions during an experiment will cause an imbalance of pressure in the cell that often leads to broken windows and centerpieces. In addition, plug gaskets and housing plugs must be securely in place to avoid solutions being pulled out of the centerpiece sector through the loading holes by the high vacuum in the centrifuge chamber. Window liners and gaskets must be free of breaks and cracks that could cause movement resulting in broken windows.
This video will demonstrate our procedures of sample cell assembly, torque, loading and rotor alignment to help minimize component damage, solution leaking and breakage during the perfect AUC experiment.
Once a homogeneous ensemble of a protein ligand is taken from solution and immobilized to a surface, for many reasons the resulting ensemble of surface binding sites may be heterogeneous. For example, this can be due to the intrinsic surface roughness causing variations in the local microenvironment, non-uniform density distribution of polymeric linkers, or non-uniform chemical attachment producing different protein orientations and conformations. We have previously described a computational method for determining the distribution of affinity and rate constants of surface sites from the analysis of experimental surface binding data. It fully exploits the high signal/noise ratio and reproducibility provided by optical biosensor technology, such as surface plasmon resonance. Since the computational analysis is ill-conditioned, the previous approach used a regularization strategy assuming a priori all binding parameters to be equally likely, resulting in the broadest possible parameter distribution consistent with the experimental data. We have now extended this method in a Bayesian approach to incorporate the opposite assumption, i.e. that the surface sites a priori are expected to be uniform (as one would expect in free solution). This results in a distribution of binding parameters as close to monodispersity as possible, given the experimental data. Using several model protein systems immobilized on a carboxymethyl dextran surface and probed with surface plasmon resonance, we show micro-heterogeneity of the surface sites, in addition to broad populations of significantly altered affinity. The distributions obtained are highly reproducible. Immobilization conditions and the total surface density of immobilized sites can have a substantial impact on the functional distribution of the binding sites.
protein surface immobilization; protein interactions; binding kinetics; binding affinity; Fredholm integral equations; size-distribution; regularization; Bayesian analysis
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.
Analytical ultracentrifugation; Fredholm integral equations; 2DSA; Sedimentation velocity; Lamm equation; Size distribution
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.
Analytical ultracentrifugation; Hydrodynamics; Direct boundary modeling; Lamm equation
Sedimentation velocity analytical ultracentrifugation (SV-AUC) has become an important tool for the characterization of the purity of protein therapeutics. The work presented here addresses a need for methods orthogonal to size-exclusion chromatography for ensuring the reliable quantitation of immunogenic oligomers, for example, in antibody preparations. Currently the most commonly used approach for SV-AUC analysis is the diffusion-deconvoluted sedimentation coefficient distribution c(s) method, previously developed by us as a general purpose technique and implemented in the software SEDFIT. In both practical and theoretical studies, different groups have reported a sensitivity of c(s) for trace oligomeric fractions well below the 1% level. In the present work we present a variant of c(s) designed for the purpose of trace detection, with customized Bayesian regularization. The original c(s) method relies on maximum entropy regularization providing the most parsimonious distribution consistent with the data. In the present paper, we use computer simulations of an antibody system as example to demonstrate that the standard maximum entropy regularization, due to its design, leads to a theoretical lower limit for the detection of oligomeric traces and a consistent underestimate of the trace populations by ∼0.1% (dependent on the level of regularization). This can be overcome with a recently developed Bayesian extension of c(s) (Brown et al., Biomacromolecules, 8:2011–2024, 2007), utilizing the known regions of sedimentation coefficients for the monomer and oligomers of interest as prior expectation for the peak positions in the distribution. We show that this leads to more clearly identifiable and consistent peaks and lower theoretical limits of quantization by approximately an order of magnitude for some experimental conditions. Implications for the experimental design of SV-AUC and practical detection limits are discussed.
analytical ultracentrifugation; Bayesian analysis; hydrodynamic separation; sedimentation velocity; size-distribution; trace aggregates