1. Description of the Problem: ● How do we distinguish between transport due to diffusion and transport due to sedimentation? ● How do we distinguish boundary spreading due to heterogeneity from boundary spreading due to diffusion? ● For unknown samples, can we analyze the sample in a model-independent way? Enhanced van Holde – Weischet Method:

2. ...is a graphical transformation of the velocity data: transport due to Diffusion ~ transport due to sedimentation ~ At infinity transport due to diffusion will be negligible compared to transport due to sedimentation - i.e., all components will separate out if the rotorspeed is fast enough....yields diffusion corrected sedimentation coefficient distributions van Holde, K. E. and W. O. Weischet. (1978). Boundary Analysis of Sedimentation Velocity Experiments with Monodisperse and Paucidisperse Solutes. Biopolymers, 17:1387-1403 Demeler, B. and K. E. van Holde. Sedimentation velocity analysis of highly heterogeneous systems. (2004). Anal. Biochem. Vol 335(2):279-288 Enhanced van Holde – Weischet Method:

3. Calculation of apparent Sedimentation Coefficients:

5. van Holde – Weischet Extrapolation Plot:

6. Scan 1 – start of Experiment

7. van Holde – Weischet Extrapolation Plot: Scan 10 – middle of Experiment

8. van Holde – Weischet Extrapolation Plot: Scan 20 – end of Experiment

9. van Holde – Weischet Extrapolation Plot: Division 1 (Baseline) Boundary Fraction = 5%

10. van Holde – Weischet Extrapolation Plot: Division 10 (Midpoint) Boundary Fraction = 50%

11. van Holde – Weischet Extrapolation Plot: Division 20 (Plateau) Boundary Fraction = 95%

12. van Holde – Weischet Integral Distribution Plot (G(s)):

13. van Holde – Weischet method: s 1 :5.35 x 10 -13 (52 %) s 2 :1.87 x 10 -13 (39 %) Enhanced van Holde – Weischet Method:

14. Green: Back diffusion distorts boundary – data points are excluded Cyan: boundary has not cleared meniscus – data points are excluded DEMO

15. van Holde – Weischet Analysis Application Examples: ● Concentration dependent nonideality of s. ● Aggregation and irreversible self-association ● Composition Analysis ● Reversibly Self-Associating Systems vs. non- interacting systems ● Stoichiometry of Association ● Relative quantification of individual components ● Conformational information Application Examples:

16. Concentration Dependency of the Sedimentation Coefficient

21. Aggregation:

22. Aggregation, Integral Distribution

23. Composition Analysis:

24. Three different Loading Concentrations for two Different Association Equilibrium Constants Self-Associating Equilibrium:

25. All concentrations sediment at the same rate Each concentration sediments differently Self-Associating Equilibrium vs. Non-interacting Sample:

26. ● Use 3 different loading concentrations at the same wavelength ● Increase concentration range by measuring at different wavelenths such as 280 nm, 230 nm and ~210 nm, check absorbance spectrum! ● If interference optics are available, use them to extend concentration range. Always run several concentrations of your sample! Self -Associating Equilibrium Experimental Design:

27. Binding Stoichiometry

30. van Holde – Weischet Analysis: Limitations The van Holde – Weischet method cannot be used for fitting diffusion coefficients, molecular weights, association constants or frictional coefficients, only sedimentation coefficients and partial concentrations are reported. A few early scans with a stable plateau are desirable to obtain a reliable first guess for the initial concentration.

31. van Holde – Weischet Applications: Summary ● Model independent analysis ● Initial characterization of an unknown sample ● Composition analysis: ● Homogeneous or heterogeneous? ● Aggregation? ● Binding Stoichiometry ● Molecular weight distribution transformations ● Relative quantification of individual components ● Conformational analysis ● Qualitative information about diffusion ● Identify concentration dependency: ● Self-association or non-interacting? ● Reversible or irreversible? ● Concentration dependent solution nonideality?

32. Second Moment Analysis The Second Moment Analysis provides a single, weight-average sedimentation coefficient. By observing the second moment value over the course of the run, important diagnostics can be obtained: ● Aggregation ● Degradation ● Concentration Dependency ● second Moment analysis requires a cleared meniscus and a stable plateau ● Second Moment S-value should not change over course of the run Velocity traces must have cleared the meniscus and have a stable plateau (not influenced by back diffusion) in order to be included in the analysis