Table S1 Primers used in this study.  On computational approaches for size-and-shape distributions from sedimentation velocity analytical ultracentrifugation Sedimentation velocity analytical ultracentrifugation has become a very popular technique to study size distributions and interactions of macromolecules. Recently, a method termed two-dimensional spectrum analysis (2DSA) for the determination of size-and-shape distributions was described by Demeler and colleagues (Eur Biophys J 2009). It is based on novel ideas conceived for fitting the integral equations of the size-and-shape distribution to experimental data, illustrated with an example but provided without proof of the principle of the algorithm. In the present work, we examine the 2DSA algorithm by comparison with the mathematical reference frame and simple well-known numerical concepts for solving Fredholm integral equations, and test the key assumptions underlying the 2DSA method in an example application. While the 2DSA appears computationally excessively wasteful, key elements also appear to be in conflict with mathematical results. This raises doubts about the correctness of the results from 2DSA analysis. The use of sedimentation velocity analytical ultracentrifugation (SV) has significantly expanded in the last decade (Howlett et al. 2006; Scott and Schuck 2006; Cole et al. 2008) , and new computational methods for SV analysis are being actively developed by several groups (Balbo et al. 2005; Philo 2006; Brown et al. 2007 Brown et al. , 2009 Behlke and Ristau 2009; Brookes et al. 2009; Correia and Stafford 2009) . In particular, diffusion-deconvoluted sedimentation coefficient distributions calculated from direct boundary modeling of experimental data (Schuck 2000; Schuck et al. 2002) have proven to be very useful tools in many biophysical applications (for a list of references see Schuck 2007) . They can achieve relatively high hydrodynamic resolution of pauci-and polydisperse macromolecular mixtures, exhibit exquisite sensitivity for trace components (Berkowitz 2006; Liu et al. 2006; Brown et al. 2008a, b; Gabrielson et al. 2009 ), and can be related to sedimentation coefficient isotherms and Gilbert-Jenkins theory for the analysis of slowly or rapidly interacting systems (Dam and Schuck 2005; . The extension of sedimentation coefficient distributions to two-dimensional sizeand-shape distributions was introduced (Schuck 2002 ; Brown and Schuck 2006) and applied in numerous studies (Markossian et al. 2006; Chang et al. 2007; Deng et al. 2007; Race et al. 2007; Broomell et al. 2008; Brown et al. 2008; Chebotareva et al. 2008; Iseli et al. 2008; Moncrieffe et al. 2008; Paz et al. 2008; Sivakolundu et al. 2008; Wang et al. 2008; Eronina et al. 2009; Mortuza et al. 2009 ). More recently, the Demeler laboratory has described the concept of a novel algorithm (''2DSA'') for determining size-and-shape distributions, as implemented in the software ULTRASCAN (Brookes et al. 2006 , 2009 Demeler et al. 2009 ). In the present work, we critically compare the background of the different algorithms and assess their performance.