Sedimentation Velocity Analytical Ultracentrifugation

Discrete Species and Size-Distributions of Macromolecules and Particles

Peter Schuck

• Publisher: CRC Press
• Year: 2016
• Topic: Biological Sciences
• eBook ISBN:
  9781315350127
• Subtopic: Biochemistry in Medicine
• Index: Biological Sciences

A follow-up to the experimental and instrumental aspects described in Basic Principles of Analytical Ultracentrifugation, the volume Sedimentation Velocity Analytical Ultracentrifugation: Discrete Species and Size-Distributions of Macromolecules and Particles describes the theory and practice of data analysis. Mathematical models for the sedimentation process and the evolution of detected signals are developed in a comprehensive framework, jointly with the description of current and historical strategies for how to extract from noisy experimental data the physical parameters of interest, such as size, mass, and shape, composition, and polydispersity of sedimenting particles.

The methods are extensively illustrated, and supported with practical applications, as well as cross-references where to find the methods in the public domain software SEDFIT and SEDPHAT. The systems covered are discrete or polydisperse mixtures of sedimenting molecules or particles in dilute solution, such as proteins and other biomolecules and their stable complexes, man-made polymers, and nanoparticles, observed in different optical systems. A useful reference for researchers and graduate students of macromolecular disciplines, these methods form the essential foundation for the analysis of dynamic interacting systems, which are covered in the volume Sedimentation Velocity Analytical Ultracentrifugation: Interacting Systems.

Software referenced in the book is available for download at: https://sedfitsedphat.nibib.nih.gov/default.aspx

CHAPTER 1

Basic Analysis Principles

SEDIMENTATION velocity (SV) analysis is concerned with the interpretation of the temporal evolution of the radial concentration gradients of particles in solution under the influence of a centrifugal field. This is distinct in theory and practice from the thermodynamic analysis of the final equilibrium state, which is subject to sedimentation equilibrium (SE) analysis. Both are different flavors of analytical ultracentrifugation (AUC), a technique to monitor macromolecular sedimentation in solution in real time [1].

The time course of sedimentation in an SV experiment is typically recorded as two-dimensional or three-dimensional data sets consisting of radial distributions of one or multiple spectral signals at different points in time, expressed as a(r,t) or a_λ(r,t). Sometimes higher dimensional families of such data sets are available from parallel experiments in different solution conditions, or for a range of macromolecular concentrations. Optimally taking advantage of such rich data sets — using principles resting on molecular hydrodynamics, thermodynamics, and chemical kinetics, as well as optics and photophysics to extract the molecular parameters of interest — poses a formidable data analysis problem.

Before discussing specific sedimentation models and their applications, in the present chapter we will first outline the general strategy underlying modern SV analysis. We will then recapitulate briefly the basic phenomenology of sedimentation, with the goal to establish molecular sedimentation parameters that constitute essential features of any sedimentation model, as well as their fundamental relationships. This will establish the terminology and link to the basic principles outlined in Part I of this series [1].¹

1.1 CONCEPTS OF MODERN SEDIMENTATION VELOCITY DATA ANALYSIS

The fundamental principle of biophysical data analysis, as applied to most of the SV analysis in the present volume, proceeds in the following steps:²

1. Hypothesize a molecular model of sedimentation for the molecules (potentially) observed in the sedimentation experiment, resting on fundamental forces and molecular mechanism of transport and interactions.

2. Derive from this the spatio-temporal evolution of concentration ${\text{χ}}_k\left(r,t\right)$ of all macromolecular solution components k.

3. Combine this sedimentation model with a model for optical detection, $\text{S}\left[{\text{χ}}_k\left(r,t\right)\right]$, given the macromolecular concentration distributions.

4. Identify known and unknown parameters in this model, establish bounds for parameter values and, if possible, relationships between unknown parameters.

5. Fit the signal model to the experimental data, refining the unknown parameters to optimize the match between data and model.

6. Accept or reject the quality of fit: If it is acceptable, assess the information content of the data for the parameters of interest, for example, by determining confidence intervals, and if the fit is unacceptable proceed to a better hypothesis regarding sample or sedimentation process.

Each of these points will be described below in more detail.

Not surprisingly, this approach is quite different from the analysis approach in the first half of the 20^th century, which was necessarily based on linearizing transformations and graphical analysis [2–4]. These were largely limited to the determination of one s-value, and often required the adaptation of experimental design to produce suitable data and/or to match the approximations embedded in the data analysis approaches. A direct fit of raw sedimentation boundary data by non-linear regression with explicit models for macromolecular sedimentation was conceptually anticipated already many decades ago [4–8], but became practical only with the availability of computational hardware in the 1990s [9–12]. It became the method of choice in routine applications of SV after combination with modern mathematical tools for distribution analysis of poly- and paucidisperse samples, diffusional deconvolution, and the possibility of incorporating explicit noise models [13–15].

The modern strategy allows a statistically optimal data analysis, naturally including all meaningful acquired data. It can be further enhanced by the art of formulating a model that incorporates all available prior knowledge into the data analysis. In this way, significantly more detail can be extracted from the sedimentation experiment than in the traditional graphical or transformation-based methods. In turn, this leads to increased reliability and accuracy of the sedimentation coefficients, and naturally makes other parameters, such a...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Foreword
• Preface
• CHAPTER 1 ■ Basic Analysis Principles
• CHAPTER 2 ■ Sedimentation of Discrete Non-Interacting Particles
• CHAPTER 3 ■ Properties of Sedimentation Coefficient Distributions
• CHAPTER 4 ■ Distributions of Non-Diffusing Particles
• CHAPTER 5 ■ Distributions of Diffusing Particles
• CHAPTER 6 ■ Sedimentation Coefficient Distributions from Boundary Derivatives and Extrapolations
• CHAPTER 7 ■ Multi-Component Distributions
• CHAPTER 8 ■ Practical Analysis of Non-Interacting Systems
• APPENDIX A ■ Numerical Solutions of the Lamm Equation
• APPENDIX B ■ Calculating Distributions
• Bibliography
• Index