From: John Philo <jphilo@earthlink.net> To : rasmb (E-mail) <rasmb@bbri.harvard.edu> Date: Tue, 24 Mar 1998 15:33:09 -0800

In response to Yujia's comments, and with all due respect, in my view (and in my experience) things are generally not quite that easy. One problem arises from the fact that NONLIN does not really deal with concentration units---internally it simply works in instrument units (fringes or absorbance). As long as one is just doing self-association, there is only a single type of monomer so this doesn't really matter and you can convert the association constants to mg/ml or molar units at the end of the analysis. However, for heteroassociations such as A + B --> AB, the equations only hold true in molar units (one mole of A + one mole of B gives one mole of AB). It will generally NOT be true that one fringe or one AU of species A combines with one (fringe or AU) of B. For heteroassociations the association equations and fitting functions really need to be written on a molar scale. Thus I believe Yujia's suggestion of using non-integer 'n' values in NONLIN will work correctly ONLY with an additional assumption that all types of monomer contribute to the experimentally observed signal in a manner exactly proportional to their mass. That is, for interference data all species must have the same dn/dc, and for absorbance data all species must have the same extinction coefficient (per milligram) in order to use this approach. It has, of course, traditionally been assumed for interference data that all non-conjugated proteins have the same dn/dc (and this is indeed probably a good assumption within a per cent or two), but it is certainly false that all glycoproteins have the same dn/dc, and obviously false that all proteins the same extinction coefficient. In addition, a more subtle, but quite serious, problem arises when you try to fit hetero-associations using the NONLIN approach whenever the system makes complexes containing two or more of one type of monomer (e.g. an AB2 or A2B2 complex). In such systems the overall weight average molecular weight of the sample is generally a MULTI-VALUED function of the monomer concentrations, i.e. two (or more) sets of monomer concentrations give the same overall Mw and therefore virtually indistinguishable concentration profiles in the centrifuge, particularly when the system is strongly associated and the free monomers contribute very little to the total signal. Consequently what happens when you try to fit such data is that for given value(s) of association constant(s), for each data set in the fit there are two or more solutions (monomer concentrations at some reference radius) that fit the experimental data nearly equivalently. Thus if you are globally fitting, say, 10 data sets, there are generally at least 1024 (2^10) local minima with nearly equivalent variances and residuals! This multiple minima problem is not intractable, however, provided we can input more information into the analysis. One approach that has been used successfully, particularly by Alan Minton and Marc Lewis at the NIH, is to somehow measure the concentration distribution of each type of monomer independently, using approaches such as post-run collection of fractions to be analyzed via gels, or using a multi-wavelength approach to take advantage of a difference in spectral properties among the monomers. An alternative approach to this multiple minima problem which does NOT require the ability to separate the contributions of different species, and the one that I use in work, is to use numerical constraints to impose mass balance onto the solutions. It turns out that for each data set only one of the possible solutions is physically realistic, based on the amounts of each protein that were actually put into the cell. Thus if you can input into the fitter the initial concentration of each species (or at least their molar ratios), and then use this information to penalize solutions which deviate strongly from mass balance, the fitter can avoid the physi cally unrealistic minima and converge on a true and unique solution. In my view, without these or some alternative approach to solving this multiple minima problem, the use of the NONLIN approach on complex heteroassociations is, at best, fraught with peril and, at worst, impossible. John Philo, Alliance Protein Laboratories On Tuesday, March 24, 1998 8:34 AM, yujia xu [SMTP:yujia@hxiris.med.upenn.edu] wrote: > > For the analysis of heteromeric system using equilibrium sedimentation, > commercial mathematicl modeling software packages could be usefull, but > acctually NONLIN can do all the work with little or no modification. The > parameter 'n' in NONLIN, which stands for 'the degree of association' does not > have to be an interger. For self-associating systems n is set to 2 for > dimerization, 3 for trimerization etc.. For heteromeric association, the n can > be set to the ratio of the molecular weight of the two types of monomer > involved in the interaction, and the analysis can be carried out as one would > for a self-association system. > > Yujia > > > -- > Yujia Xu > Department of Biochemistry and Biophysics > University of Pennsylvania, School of Medicine > Philadelphia, PA 19104 > (215) 898-6580 >

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