Computer stimulation of sedimentation in the ultracentrifuge. VII. Solutes undergoing indefinite self-association

The velocity sedimentation of solutes involved in self-association equilibria of the indefinite type was simulated using a computer model. The changes in boundary shape that resulted from varying the association constant and the molecular weight of the self-associating monomer were examined. Both ideally and nonideally sedimenting solutes were considered, and several alternative treatments of the variation of the frictional ratio with molecular size were used. All of the calculated boundaries were skewed, with the leading limb of the gradient profile steeper than the trailing limb. For relatively tightly self-associating solutes, the boundaries were very broad and strongly skewed. No shoulders or subsidiary peaks were observed for any of the model solutes used.     

Effect of microheterogeneity on the sedimentation behavior of self-associating proteins

The effect of microheterogeneity on the sedimentation behavior of self-associating proteins has been examined theoretically with particular reference to rapidly equilibrating tetramerization reactions. Scieral models of microheterogeneity have been considered. Each one exhibits a sedimentation behavior departing substantially from that expected of homogeneous systems. It is anticipated that the results may be helpful for interpreting the sedimentation patterns of self-associating proteins when the patterns cannot be analyzed in terms of the Gilbert theory.     

Sedimentation analysis of noninteracting and self-associating solutes using numerical solutions to the Lamm equation.

The potential of using the Lamm equation in the analysis of hydrodynamic shape and gross conformation of proteins and reversibly formed protein complexes from analytical ultracentrifugation data was investigated. An efficient numerical solution of the Lamm equation for noninteracting and rapidly self-associating proteins by using combined finite-element and moving grid techniques is described. It has been implemented for noninteracting solutes and monomer-dimer and monomer-trimer equilibria. To predict its utility, the error surface of a nonlinear regression of simulated sedimentation profiles was explored. Error contour maps were calculated for conventional independent and global analyses of experiments with noninteracting solutes and with monomer-dimer systems at different solution column heights, loading concentrations, and centrifugal fields. It was found that the rotor speed is the major determinant for the shape of the error surface, and that global analysis of different experiments can allow substantially improved characterization of the solutes. We suggest that the global analysis of the approach to equilibrium in a short-column sedimentation equilibrium experiment followed by a high-speed short-column sedimentation velocity experiment can result in sedimentation and diffusion coefficients of very high statistical accuracy. In addition, in the case of a protein in rapid monomer-dimer equilibrium, this configuration was found to reveal the most precise estimate of the association constant.     

Anomalies in sedimentation. IV. Decrease in sedimentation coefficients of chains at high fields

A theory is presented for the decrease of sedimentation coefficient at high centrifugal fields recently reported for samples of DNA by Rubenstein and Leighton and others. The theory uses the model of a chain of beads and springs to represent the molecule. Kirkwood's approximation is used for the sedimentation coefficient. The decrease in sedimentation coefficient with field comes about as a result of the uneven frictional forces in the chain, which on the average are less on segments near the center of the chain than on those near the ends. As a result the ends of the chain tend to drag behind the center, and the average intersegment distances are increased; consequently the hydrodynamic shielding of one segment by another is reduced, and the average friction is increased. The effect is thus characteristic of single molecules; intermolecular interaction is not involved. The sedimentation coefficient, S, varies as a power series in a parameter y that measures the distortion produced by the uneven friction: S = S⁰(1?D₂y² + D₄y⁴ ? ·). where S⁰ is the limiting value of S at zero centrifugal field and D₂ and D₄ are constants; y is proportional to the cen speed squared tunes the molecular weight squared divided by S⁰. It has been observed that the effects of centrifuge speed on S are negligible below certain critical values of the speed and molecular weight, but increase dramatically immediately above these values; this follows naturally from the high powers of the speed and molecular weight that appear in the above equation.     

Dependence upon temperature of corrected sedimentation coefficients measured in a Beckman analytical ultracentrifuge

The corrected sedimentation coefficient (s_{20, w}) has been examined as a function of temperature for bovine liver catalase and for a small linear duplex DNA in a Beckman Model E analytical ultracentrifuge. These measurements were carried out using both the standard Beckman rotor temperature indicator and control system and a modified version of this system which was designed to reduced thermal gradients in the rotor [Hearst, J. E., and Gray, H. B., Jr. (1968) Anal. Biochem.24, 70–79)]. The temperature dependence of s_{20, w} for both the protein and the DNA were identical between the two systems. The slight increase of s_{20, w} with increasing temperature observed for the DNA is in agreement with that predicted on the basis of the temperature dependence of the Kuhn statistical length for DNA. Intrinsic viscosity measurements as a function of temperature were also carried out for the DNA in a low-shear viscometer. These data indicate a slight decrease of intrinsic viscosity with increasing temperature. Previous investigations, which have suggested that the actual temperature of the ultracentrifuge cell is substantially higher [Incardona, N. L., Notarius, H., and Flanegan, J. B. (1971) Anal. Biochem.40, 267–280] or lower [Rowe, A. J., and Khan, G. M. (1972) Anal. Biochem.45, 488–497] than that indicated by the temperature monitoring system of the Model E centrifuge at temperatures below ambient, are not supported by the present studies. Discrepancies between the actual temperature of the sedimenting sample and the indicated temperature are thus shown in this work not to be an inherent problem of the design of the Beckman instrument.     

An improved function for fitting sedimentation velocity data for low-molecular-weight solutes.

Many traditional approaches to the analysis of sedimentation velocity data work poorly with data for low-molecular-weight solutes, which have sedimentation boundaries that are severely broadened by diffusion. An approach that has previously had some success is to directly fit these broad boundaries to approximate solutions of the Lamm equation that directly account for the high diffusion. However, none of the available approximate solutions work well at times both early and late in the run, or give boundary shapes that are highly accurate, especially for species of molecular weight < 10,000. An improved fitting function has been developed to overcome some of these limitations. The new function adds two correction terms to the Fujita-MacCosham solution. The optimum coefficients for these new correction terms were determined by a least-squares approach. The accuracy and limitations of fitting with this new function were tested against synthetic data sets obtained by finite-element methods, for analysis of samples containing either single species or several noninteracting species. We also compare the strengths and weaknesses of this method of analysis, and its ability to work with noisy data, relative to recently developed time-derivative methodologies.     

Computer simulation of flagellar movement. IV. Properties of an oscillatory two-state cross-bridge model.

A stochastic computational method is used to examine the properties of a simple two-state cross-bridge model, of a type which has been shown previously to self-oscillate without requiring any feedback control of the active process. The force transients obtained with this model show the major features observed with oscillatory insect fibrillar flight muscle. The effects of viscosity and cross-bridge detachment rate on the frequency of oscillation of the model resemble the effects of viscosity and ATP concentration on flagellar oscillation, and the relationship between turnover rate and frequency of oscillation is also consistent with observations on flagella. However, the amplitude of oscillation of the model does not show the degree of frequency-independence which is typical of flagella.     

Molecular weight of human high-molecular-weight kininogen light chain by equilibrium sedimentation in an air-driven ultracentrifuge

High-molecular-weight kininogen, a nonenzymatic glycoprotein of the intrinsic blood coagulation system, is proteolytically cleaved by kallikrein as an early event in the activation of this system. The light chain of cleaved kininogen retains the ability to form specific noncovalent complexes with prekallikrein and factor XI, other members of this system. We have determined the molecular weight of human kininogen light chain by equilibrium sedimentation in buffers of differing density, using an air-driven benchtop ultracentrifuge. The resulting molecular weight (30,500 +/- 800 g/mol) and partial specific volume (0.660 +/- 0.008 ml/g) are consistent with the idea that a sizeable fraction of the carbohydrate of high-molecular-weight kininogen is associated with the light chain. This level of precision is relatively easy to attain. The procedures are detailed, along with expressions for error propagation, to permit ready application of the technique.