Huaying Zhao

High-Precision Isothermal Titration Calorimetry with Automated Peak Shape Analysis

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 postinjection 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.

On the Distribution of Protein Refractive Index Increments

The protein refractive index increment, dn/dc, is an important parameter underlying the concentration determination and the biophysical characterization of proteins and protein complexes in many techniques. In this study, we examine the widely used assumption that most proteins have dn/dc values in a very narrow range, and reappraise the prediction of dn/dc of unmodified proteins based on their amino acid composition. Applying this approach in large scale to the entire set of known and predicted human proteins, we obtain, for the first time, to our knowledge, an estimate of the full distribution of protein dn/dc values. The distribution is close to Gaussian with a mean of 0.190 ml/g (for unmodified proteins at 589 nm) and a standard deviation of 0.003 ml/g. However, small proteins <10 kDa exhibit a larger spread, and almost 3000 proteins have values deviating by more than two standard deviations from the mean. Due to the widespread availability of protein sequences and the potential for outliers, the compositional prediction should be convenient and provide greater accuracy than an average consensus value for all proteins. We discuss how this approach should be particularly valuable for certain protein classes where a high dn/dc is coincidental to structural features, or may be functionally relevant such as in proteins of the eye.

The role of mass transport limitation and surface heterogeneity in the biophysical characterization of macromolecular binding processes by SPR biosensing.

This chapter presents an introduction to the kinetic analysis of SPR biosensor data for the determination of affinity and kinetic rate constants of biomolecular interactions between an immobilized and a soluble binding partner. The need to be aware of and critically test the assumptions underlying the analysis models is emphasized and the consequences for the experimental design are discussed. The two most common sources of deviation in SPR surface binding kinetics from the ideal pseudo-first-order binding kinetics of bimolecular reactions are mass transport limitations and the heterogeneity of the surface sites. These problems are intrinsic to the use of a biosensor surface for characterizing interactions. The effect of these factors on the observed binding kinetics, and strategies to account for them are reviewed, both in the context of mathematical data analysis, as well as the design of the experiments and controls.

Recorded scan times can limit the accuracy of sedimentation coefficients in analytical ultracentrifugation.

We report systematic and large inaccuracies in the recorded elapsed time in data files from the analytical ultracentrifuge, leading to overestimates of the sedimentation coefficients of up to 10%. This far exceeds previously considered factors contributing to the uncertainty in this parameter and has significant ramifications for derived parameters such as hydrodynamic shape and molar mass estimates. The source of this error is currently unknown, but we found it to be quantitatively consistent across different instruments, increasing with rotor speed. Furthermore, its occurrence appears to correlate with the use of the latest data acquisition software from the manufacturer, in use in some of our laboratories for nearly 2 years. Many of the recently published sedimentation coefficients may need to be reexamined. The problem can be easily recognized by comparing the file timestamps provided by the operating system with the elapsed scan times recorded within the data files. Therefore, we implemented a routine in SEDFIT that can automatically examine the data files, alert the user to significant discrepancies, and correct the scan times accordingly. This eliminates errors in the recorded scan times.

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. Curr. Protoc. Protein Sci. 71:20.12.1‐20.12.49.

Integration and global analysis of isothermal titration calorimetry data for studying macromolecular interactions

Isothermal titration calorimetry (ITC) is a powerful and widely used method to measure the energetics of macromolecular interactions by recording a thermogram of differential heating power during a titration. However, traditional ITC analysis is limited by stochastic thermogram noise and by the limited information content of a single titration experiment. Here we present a protocol for bias-free thermogram integration based on automated shape analysis of the injection peaks, followed by combination of isotherms from different calorimetric titration experiments into a global analysis, statistical analysis of binding parameters and graphical presentation of the results. This is performed using the integrated public-domain software packages NITPIC, SEDPHAT and GUSSI. The recently developed low-noise thermogram integration approach and global analysis allow for more precise parameter estimates and more reliable quantification of multisite and multicomponent cooperative and competitive interactions. Titration experiments typically take 1–2.5 h each, and global analysis usually takes 10–20 min.

Improving the Thermal, Radial and Temporal Accuracy of the Analytical Ultracentrifuge through External References

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

The molecular refractive function of lens γ-crystallins

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 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 nonlens members of the βγ-crystallin family from different species. The same trait has evolved in parallel in crystallins of different phyla, including 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 cataracts. To produce a significant increase in the refractive index increment, a substantial global shift in 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.

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.

Global multi-method analysis of affinities and cooperativity in complex systems of macromolecular interactions.

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