# Ultracentrifugation Data

The data obtained in an ultracentrifuge can be described as a 3-dimensional surface. The primary axes are usually radius and time. Both axes are monotonically increasing, but are not necessarily linear. The third dimension is the reading from the optical system of the centrifuge. It can be optical density (OD), interference fringes, or another unit depending on the optical system used for data acquisition.

## Data Acquisition

Data in an ultracentrifuge is acquired by placing a chemical sample into a buffer. This solution is, in turn, placed into a sector of a centerpiece (a channel), and the centerpiece is placed in a hole (a cell) of the rotor.

For the purposes of this page, the data is considered only for a single channel and for a single set of scans for that channel. Additionally, the data is only considered for a single wavelength. This combination of cell-channel-wavelength is referred to as a 'triple'.

Data for a single triple are read into an internal data structure in !UltraScan3. This triple can be thought of as a 3-dimensional surface, f(radius, time).

double meniscus; // radius start double bottom; // radius end vector< scan > scans; vector< double > radius; // The radius values for all scans are made // the same

Where scan is basically:

double time; double rpm; double omega2t; vector< double > concentration;

## Data Simulation

### Input

Simulation of data for a triple is done by defining a Model and the Simulation Parameters to be used.

The Model consists of the components to be used in the buffer and the solute and their association properties.

These components are defined as:

double molar_concentration; double signal_concentration; double vbar20; // Specific volume at 20 deg C double mw; // Molecular weight double s; // Sedimentation coefficient double D; // Diffusion coefficient double sigma; // ? not currently used double delta // ? not currently used double f_f0; // Frictional ratio // Basically a scan vector< double > initial_radius; vector< double > initial_concentration;

And the associations are defined as:

double keq; // equilibrium binding constant, in Molar units double k_off; // dissociation rate constant in inverse minutes vector< uint > comp; // vector of all components involved in this // reaction vector< uint > stoich; // vector of stoichiometry of each component vector< int > reactant; // =1 for reactant, = -1 for product

The simulation parameters are:

vector< SpeedProfile > speed_step; uint simpoints; // number of radial grid points used in sim vector< double > mesh_radius; // For mesh == USER double meniscus; // radius of meniscus double bottom; // Bottom of cell position w/o rotor stretch double rnoise; // Random noise double tinoise; // Time invariant noise double rinoise; // Radially invariant noise int rotor; // Rotor serial number in database bool band_forming; // True for band-forming centerpieces double band_volume; // Loading volume (of lamella) in a // band-forming centerpiece bool initConc // When true, use 1st scan as inital // concentration distribution

And a speed profile is:

uint duration_hours; // hours at this speed uint duration_minutes; // minutes at this speed (0-59) uint delay_hours; // not used in sim double delay_minutes; // not used in sim uint scans; // number of scans in this step uint acceleration; // rpms / second uint rotorspeed; // target rpm bool acceleration_flag; // simulate acceleration or change immediately

### Output

The simulation uses a technique called Adaptive Space Time Finite Element Model - Reacting Systems Algorithm (ASTFEM-RSA)

The output of this simulation is the same as the data acquisition format.

## Using the data

The overall method used to accurately estimate the parameters of an experiment is to minimize the differences in the surfaces representing the simulation and the experimental data by varying the characteristics of a Model for the given simulation parameters that match the actual experimental parameters.

This can be represented mathematically as:

min sum( f_{1}(r,t) - f_{2}(r,t) )

for all radii and time values.

The algorithms for determining the minimum of the error function above include using Monte Carlo techniques, Genetic Algorithms, and 2-Dimensional Spectrum Analysis. Description of these techniques is documented in:

http://www.demeler.uthscsa.edu/ultrascan-publications/

Brookes, E. and B. Demeler. Genetic Algorithm Optimization for obtaining accurate Molecular Weight Distributions from Sedimentation Velocity Experiments. Analytical Ultracentrifugation VIII, Progr. Colloid Polym. Sci.131:78-82. C. Wandrey and H. Cölfen, Eds. Springer (2006)

Brookes, E and B. Demeler. Parsimonious Regularization using Genetic Algorithms Applied to the Analysis of Analytical Ultracentrifugation Experiments. GECCO Proceedings ACM 978-1-59593-697-4/07/0007 (2007)

Demeler, B. and E. Brookes. Monte Carlo Analysis of Sedimentation Experiments. Prog. Colloid. Polym. Sci. 2008 286(2) 129-137

Cao, W and B. Demeler. Modeling Analytical Ultracentrifugation Experiments with an Adaptive Space-Time Finite Element Solution for Multi-Component Reacting Systems. Biophys. J. 2008 95(1):54-65

Brookes, E., W. Cao, B. Demeler. A two-dimensional spectrum analysis for sedimentation velocity experiments of mixtures with heterogeneity in molecular weight and shape. Eur. Biophys. J. 2009 (in press)