Emre Brookes

A two-dimensional spectrum analysis for sedimentation velocity experiments of mixtures with heterogeneity in molecular weight and shape

We report a model-independent analysis approach for fitting sedimentation velocity data which permits simultaneous determination of shape and molecular weight distributions for mono- and polydisperse solutions of macromolecules. Our approach allows for heterogeneity in the frictional domain, providing a more faithful description of the experimental data for cases where frictional ratios are not identical for all components. Because of increased accuracy in the frictional properties of each component, our method also provides more reliable molecular weight distributions in the general case. The method is based on a fine grained two-dimensional grid search over s and f/f0, where the grid is a linear combination of whole boundary models represented by finite element solutions of the Lamm equation with sedimentation and diffusion parameters corresponding to the grid points. A Monte Carlo approach is used to characterize confidence limits for the determined solutes. Computational algorithms addressing the very large memory needs for a fine grained search are discussed. The method is suitable for globally fitting multi-speed experiments, and constraints based on prior knowledge about the experimental system can be imposed. Time- and radially invariant noise can be eliminated. Serial and parallel implementations of the method are presented. We demonstrate with simulated and experimental data of known composition that our method provides superior accuracy and lower variance fits to experimental data compared to other methods in use today, and show that it can be used to identify modes of aggregation and slow polymerization.

Parsimonious regularization using genetic algorithms applied to the analysis of analytical ultracentrifugation experiments

Frequently in the physical sciences experimental data are analyzed to determine model parameters using techniques known as parameter estimation. Eliminating the effects of noise from experimental data often involves Tikhonov or Maximum-Entropy regularization. These methods introduce a bias which smoothes the solution. In the problems considered here, the exact answer is sharp, containing a sparse set of parameters. Therefore, it is desirable to find the simplest set of model parameters for the data with an equivalent goodness-of-fit. This paper explains how to bias the solution towards a parsimonious model with a careful application of Genetic Algorithms. A method of representation, initialization and mutation is introduced to efficiently find this model. The results are compared with results from two other methods on simulated data with known content. Our method is shown to be the only one to achieve the desired results. Analysis of Analytical Ultracentrifugation sedimentation velocity experimental data is the primary example application.

Characterization of size, anisotropy, and density heterogeneity of nanoparticles by sedimentation velocity.

A critical problem in materials science is the accurate characterization of the size dependent properties of colloidal inorganic nanocrystals. Due to the intrinsic polydispersity present during synthesis, dispersions of such materials exhibit simultaneous heterogeneity in density ρ, molar mass M, and particle diameter d. The density increments ∂ρ/∂d and ∂ρ/∂M of these nanoparticles, if known, can then provide important information about crystal growth and particle size distributions. For most classes of nanocrystals, a mixture of surfactants is added during synthesis to control their shape, size, and optical properties. However, it remains a challenge to accurately determine the amount of passivating ligand bound to the particle surface post synthesis. The presence of the ligand shell hampers an accurate determination of the nanocrystal diameter. Using CdSe and PbS semiconductor nanocrystals, and the ultrastable silver nanoparticle (M4Ag44(p-MBA)30), as model systems, we describe a Custom Grid method implemented in UltraScan-III for the characterization of nanoparticles and macromolecules using sedimentation velocity analytical ultracentrifugation. We show that multiple parametrizations are possible, and that the Custom Grid method can be generalized to provide high resolution composition information for mixtures of solutes that are heterogeneous in two out of three parameters. For such cases, our method can simultaneously resolve arbitrary two-dimensional distributions of hydrodynamic parameters when a third property can be held constant. For example, this method extracts partial specific volume and molar mass from sedimentation velocity data for cases where the anisotropy can be held constant, or provides anisotropy and partial specific volume if the molar mass is known.

Genetic algorithm optimization for obtaining accurate molecular weight distributions from sedimentation velocity experiments

Sedimentation experiments can provide a large amount of information about the composition of a sample, and the properties of each component contained in the sample. To extract the details of the composition and the component properties, experimental data can be described by a mathematical model, which can then be fitted to the data. If the model is nonlinear in the parameters, the parameter adjustments are typically performed by a nonlinear least squares optimization algorithm. For models with many parameters, the error surface of this optimization often becomes very complex, the parameter solution tends to become trapped in a local minimum and the method may fail to converge. We introduce here a stochastic optimization approach for sedimentation velocity experiments utilizing genetic algorithms which is immune to such convergence traps and allows high-resolution fitting of nonlinear multi-component sedimentation models to yield distributions for sedimentation and diffusion coefficients, molecular weights, and partial concentrations.

Developments in the US-SOMO bead modeling suite: New features in the direct residue-to-bead method, improved grid routines, and influence of accessible surface area screening

The US-SOMO suite provides a flexible interface for accurately computing solution parameters from 3D structures of biomacromolecules through bead-modeling approaches. We present an extended analysis of the influence of accessible surface area screening, overlap reduction routines, and approximations for non-coded residues and missing atoms on the computed parameters for models built by the residue-to-bead direct correspondence and the cubic grid methods. Importantly, by taking the theoretical hydration into account at the atomic level, the performance of the grid-type models becomes comparable or exceeds that of the corresponding hydrated residue-to-bead models.

Fibrinogen species as resolved by HPLC-SAXS data processing within the UltraScan Solution Modeler (US-SOMO) enhanced SAS module

The usefulness of a new high-performance liquid chromatography/small-angle X-ray scattering (HPLC-SAXS) data analysis module within the multi-resolution modeling suite US-SOMO is illustrated with size-exclusion small-angle X-ray scattering (SE-SAXS) data of a crude bovine serum albumin sample. The module is then applied to the SE-SAXS study of a human plasma fibrinogen high-molecular-weight fraction presenting severe aggregation problems and a split non-symmetrical main elution peak probably resulting from in-column degradation.

Characterization of Reversible Associations by Sedimentation Velocity with UltraScan

We compare here the utility of sedimentation velocity (SV) to sedimentation equilibrium (SE) analysis for the characterization of reversible systems. Genetic algorithm optimization in UltraScan is used to optimize the model and to obtain solution properties of all components present in the system. We apply our method to synthetic and experimental data, and suggest limits for the accessible kinetic range. We conclude that equilibrium constants obtained from SV and SE analysis are equivalent, but that SV experiments provide better confidence for the K(d), can better account for the presence of contaminants and provide additional information including rate constants and shape parameters.

Computing large sparse multivariate optimization problems with an application in biophysics

We present a novel divide and conquer method for parallelizing a large scale multivariate linear optimization problem, which is commonly solved using a sequential algorithm with the entire parameter space as the input. The optimization solves a large parameter estimation problem where the result is sparse in the parameters. By partitioning the parameters and the associated computations, our technique overcomes memory constraints when used in the context of a single workstation and achieves high processor utilization when large workstation clusters are used. We implemented this technique in a widely used software package for the analysis of a biophysics problem, which is representative for a large class of problems in the physical sciences. We evaluate the performance of the proposed method on a 512-processor cluster and offer an analytical model for predicting the performance of the algorithm

A parametrically constrained optimization method for fitting sedimentation velocity experiments.

A method for fitting sedimentation velocity experiments using whole boundary Lamm equation solutions is presented. The method, termed parametrically constrained spectrum analysis (PCSA), provides an optimized approach for simultaneously modeling heterogeneity in size and anisotropy of macromolecular mixtures. The solutions produced by PCSA are particularly useful for modeling polymerizing systems, where a single-valued relationship exists between the molar mass of the growing polymer chain and its corresponding anisotropy. The PCSA uses functional constraints to identify this relationship, and unlike other multidimensional grid methods, assures that only a single molar mass can be associated with a given anisotropy measurement. A description of the PCSA algorithm is presented, as well as several experimental and simulated examples that illustrate its utility and capabilities. The performance advantages of the PCSA method in comparison to other methods are documented. The method has been added to the UltraScan-III software suite, which is available for free download from http://www.ultrascan.uthscsa.edu.

Chapter 4 Analysis of Heterogeneity in Molecular Weight and Shape by Analytical Ultracentrifugation Using Parallel Distributed Computing

A computational approach for fitting sedimentation velocity experiments from an analytical ultracentrifuge in a model-independent fashion is presented. This chapter offers a recipe for obtaining high-resolution information for both the shape and the molecular weight distributions of complex mixtures that are heterogeneous in shape and molecular weight and provides suggestions for experimental design to optimize information content. A combination of three methods is used to find the solution most parsimonious in parameters and to verify the statistical confidence intervals of the determined parameters. A supercomputer implementation with a MySQL database back end is integrated into the UltraScan analysis software. The UltraScan LIMS Web portal is used to perform the calculations through a Web interface. The performance and limitations of the method when employed for the analysis of complex mixtures are demonstrated using both simulated data and experimental data characterizing amyloid aggregation.