 # Manual

## Estimating Equilibrium Times: The Equilibrium Time Estimation module can be loaded from the Equilibrium Menu or the Simulation Menu in the Main Menu section of UltraScan.

Whenever you are planning or designing an equilibrium experiment, the question comes up of how long it takes to reach equilibrium at a certain speed. The time it takes depends on several factors:

• The diffusion coefficient. The smaller the diffusion coefficient, the longer it will take to reach equilibrium, since the sample will diffuse slower. Asymmetric and random coil molecules will take longer to equilibrate than globular molecules with the same molecular weight.

• The sedimentation coefficient. The larger the sedimentation coefficient, the faster the molecule will equilibrate, provided the diffusion coefficient stays constant, which is rarely the case. As molecular weight and sedimentation coefficient increase, the diffusion coefficient will generally decrease, which has the opposite effect.

• The position inside the rotor. The further to the outside of the rotor the sample is positioned, the faster the sample will equilibrate, since the centrifugal force is larger at the outside.

• The column length. The longer the column (the more volume is loaded), the longer it will take to equilibrate.

• Finally the rotor speed. The larger the rotorspeed, the faster the sample will approach equilibrium.

• How many components are in the system. When more than one component is in the system, always simulate the component with the smallest diffusion coefficient, since this molecure with generally take the longest to equilibrate. Once this molecule is equilibrated, all other molecules will have equilibrated already.

• It also matters if the system is at chemical equilibrium, and if that equilibrium can be established rapidly enough (on the time order of the experiment). If a monomer-dimer equilibrium experiment takes a long time to equilibrate (i.e., the equilibrium kinetics are not diffusion controlled), then it may take substantially longer than predicted by this program. THis program will only predict the experiment of a diffusion controlled kinetics environment.

How to use this module:

When designing an equilibrium experiment, you should plan to acquire equilibria at multiple speeds (4-5 speeds, ranging from sigma=1 - sigma=5, use this program to predict the correct speeds), and therefore it would be nice to estimate before you start the experiment how long it will take to reach equilibrium. Using the finite element simulator programmed in this module, you can predict the time it takes to reach equilibrium for all practical purposes, i.e., the change over time is less than a certain tolerance value. You can then pre-program the speeds into the XLA and are not required to check for equilibrium evertime before you change to the next speed.

When simulating these times, you should simulate a molecule that is sedimenting slightly slower than the actual molecule, perhaps by simulating a system with a larger frictional ratio or larger axial ratio, and perhaps a nonglobular model rather than a spherical model. While the equilibrium times may be longer than needed, at least they won't be too short. In this module you can change the parameters that influence the time it takes to reach equilibrium.

## Explanation for fields and buttons: Simulation Settings: Simulate Component Before you can simulate the equilibrium times, you will have to define the molecular parameters for the system to be simulated. Clicking on this button will invoke an UltraScan module used for the prediction of s, D and f from the estimated molecular weight for 4 basic shapes. Once the system is defined in this module, the values will be automatically transferred to the equilibrium times prediction module. Molecular Weight: The molecular weight of the simulated component. Sedimentation Coeff.: The sedimentation coefficient for the simulated component. Diffusion Coeff.: The diffusion coefficient for the simulated component. Prolate Ellipsoid/Oblate Ellipsoid/Long Rod/Sphere These are the possible models for the selected molecular weight. Selecting the prolate ellipsoid (default) will handle most cases, even spherical molecules with a small time penalty. It is therefore a good default setting. Radius Settings Here you can select the column length and position. You can select from pre-set radii for the 6-channel centerpieces or select custom top and bottom radii for the column. The column height depends on the loading volume and the centerpiece geometry. You can either perform a quick radial scan or determine the radius positions empirically. The longer the column height, the longer the experiment will take to equilibrate. Rotorspeed Settings: Use Sigma/Use RPM Select if you want to enter the speeds in terms of sigma (reduced molecular weight term: [(M * omega^2 * (1 - vbar * rho))/ 2 * R * T]) or by RPM. Either unit will be interconverted. Check this program for appropriate speeds. Low Speed:Select the first speed to be equilibrated High SpeedSelect the last speed to be equilibrated Speed StepsThe total number of speeds to be simulated, including the high and low speed. These will be chose linearly spaced between the high and low speed. Current Speed ListAll selected speeds will be listed here. Please Note: All speeds will be adjusted to the nearest 100 rpm, so they can be programmed in the XLA, which only allows 100 rpm steps. Simulation Settings These settings allow you to control the simulation. ToleranceThis value is the tolerance setting that determines if a scan has reached equilibrium. Successive scans are subtracted from each other and the differences between them are summed up. If the sum is less or equal to this tolerance value, the program will consider the speed equilibrated and automatically proceed to the next speed. For a 3 mm column with 0.001 cm resolution the accuracy of the computer allows about 1.0x10-5 for the smallest practical tolerance (noise-free data). Time Increment (min) This is the time between successive scans. The larger the time difference, the coarser is the time determineation, but the more reliable is the time estimation. A good default setting is 15 minutes, to be used with a 5 x 10-4 tolerance setting. Delta-r (cm) This is the radial resolution used in the finite element analysis and defines the radial discretization step size. A good default value is 0.001 cm, the lowest possible setting in the XLA. Delta-t (sec) This is the time resolution used in the finite element analysis and defines the time discretization step size. A good default value is 15 seconds, since changes over time are rather slow, especially in the end. Monitor Simulation Progress Show all intermediate scans, otherwise only plot the equilibrium scans. Help Show this helpfile. Estimate Times Perform the time estimation. This function can only be used after the molecule has been defined. Save to File Save the contents of the text dialogue to a file. Same function as selecting "Save" from the file menu. Close Close the program.

Shown below is the text editor window that will display the incremental and total times for reaching equilibrium: www contact: Borries Demeler

This document is part of the UltraScan Software Documentation distribution.