Determination of the sedimentation coefficient distribution by least-squares boundary modeling

A new method is presented for the calculation of apparent sedimentation coefficient distributions g*(s) for the size-distribution analysis of polymers in sedimentation velocity experiments. Direct linear least-squares boundary modeling by a superposition of sedimentation profiles of ideal nondiffusing particles is employed. It can be combined with algebraic noise decomposition techniques for the application to interference optical ultracentrifuge data at low loading concentrations with significant systematic noise components. Because of the use of direct boundary modeling, residuals are available for assessment of the quality of the fits and the consistency of the g*(s) distribution with the experimental data. The method can be combined with regularization techniques based on F statistics, such as used in the program CONTIN, or alternatively, the increment of s values can be adjusted empirically. The method is simple, has advantageous statistical properties, and reveals precise sedimentation coefficients. The new least-squares ls-g*(s) exhibits a very high robustness and resolution if data acquired over a large time interval are analyzed. This can result in a high resolution for large particles, and for samples with a high degree of heterogeneity. Because the method does not require a high frequency of scans, it can also be easily used in experiments with the absorbance optical scanning system. Published 2000 John Wiley & Sons, Inc.     

A method for directly fitting the time derivative of sedimentation velocity data and an alternative algorithm for calculating sedimentation coefficient distribution functions

The time-derivative method for deriving the sedimentation coefficient distribution, g(s*), from sedimentation velocity data that was developed by Walter Stafford has many advantages and is now widely used. By fitting Gaussian functions to the g(s*) distribution both sedimentation and diffusion coefficients (and therefore molecular masses) for individual species can be obtained. However, some of the approximations used in these procedures limit the accuracy of the results. An alternative approach is proposed in which the dc/dt data are fitted rather than g(s*). This new approach gives improved accuracy, extends the range to sedimentation coefficients below 1 S, and enhances resolution of multiple species. For both approaches the peaks from individual species are broadened when the data cover too wide a time span, and this effect is explored and quantified. An alternative algorithm for calculating ?(s*) from the dc/dt curves is presented and discussed. Rather than first averaging the dc/dt data for individual scan pairs and then calculating ?(s*) from that average, the ?(s*) distributions are calculated for every scan pair and then subsequently averaged. This alternative procedure yields smaller error bars for g(s*) and somewhat greater accuracy for fitted hydrodynamic properties when the time span becomes large.     

Filtration-fluorescence determination of DNA sedimentation profiles

A method for determination of DNA sedimentation profiles in density gradients of sucrose or salts is proposed. The method consists in isolation and purification of DNA from the fractions by molecular filtration and a subsequent determination of DNA content by the fluorescence of the DNA-ethidium bromide complex.     

Enhanced error-prone RCA mutagenesis by concatemer resolution

Error-prone rolling circle amplification (RCA) is a promising alternative to error-prone PCR for random mutagenesis. The main disadvantage of error-prone RCA is the low transformation efficiency of the DNA concatemer produced in the amplification reaction. We improved the method by introducing loxP recombination site of bacteriophage P1 Cre recombinase into the target plasmid and reducing the concatemer by Cre recombinase to plasmid-sized units, increasing the number of transformants 50-fold in non-error-prone and 13-fold in error-prone conditions. The efficiency improvement was verified by obtaining 115 ± 57 ceftazidime resistant colonies per recombined RCA reaction from randomly mutated TEM-1 β-lactamase gene library whereas only 9 ± 11 colonies were gained without recombination. Supplementation of the error-prone RCA with Cre/loxP recombination is a simple and useful tool to increase the transformable library size.     

Reduced sedimentation equilibrium time by two-step initial loading

Computer simulation shows that the time required to attain near sedimentation equilbrium is dramatically reduced by a two-step initial loading in which a macromolecular solution at low or zero concentration is layered above one at a higher concentration. To achieve the minimum time requires a good estimate of the molecular weight, but at least a 50% reduction in time can be achieved if the molecular weight of the macromolecule is known only within a factor of 2. Numerical solutions to the differential equation of the ultracentrifuge are calculated using the finite element method. An efficient Gaussian elimination algorithm can be used to minimize calculation time and computer storage requirements.     

Improved methods for fitting sedimentation coefficient distributions derived by time-derivative techniques

Time-derivative approaches to analyzing sedimentation velocity data have proven to be highly successful and have now been used routinely for more than a decade. For samples containing a small number of noninteracting species, the sedimentation coefficient distribution function, g(s *), traditionally has been fitted by Gaussian functions to derive the concentration, sedimentation coefficient, and diffusion coefficient of each species. However, the accuracy obtained by that approach is limited, even for noise-free data, and becomes even more compromised as more scans are included in the analysis to improve the signal/noise ratio (because the time span of the data becomes too large). Two new methods are described to correct for the effects of long time spans: one approach that uses a Taylor series expansion to correct the theoretical function and a second approach that creates theoretical g(s *) curves from Lamm equation models of the boundaries. With this second approach, the accuracy of the fitted parameters is approximately 0.1% and becomes essentially independent of the time span; therefore, it is possible to obtain much higher signal/noise when needed. This second approach is also compared with other current methods of analyzing sedimentation velocity data.     

Boundary analysis in sedimentation transport experiments: a procedure for obtaining sedimentation coefficient distributions using the time derivative of the concentration profile.

A procedure is described for computing sedimentation coefficient distributions from the time derivative of the sedimentation velocity concentration profile. Use of the time derivative, (delta c/delta t)r, instead of the radial derivative, (delta c/delta r)t, is desirable because it is independent of time-invariant contributions to the optical baseline. Slowly varying baseline changes also are significantly reduced. An apparent sedimentation coefficient distribution (i.e., uncorrected for the effects of diffusion), g*(s), can be calculated from (delta c/delta t)r as [formula: see text] where s is the sedimentation coefficient, omega is the angular velocity of the rotor, c0 is the initial concentration, r is the radius, rm is the radius of the meniscus, and t is time. An iterative procedure is presented for computing g*(s)t by taking into account the contribution to (delta c/delta t)r from the plateau region to give (delta c/delta t)corr. Values of g*(s)t obtained this way are identical to those of g*(s) calculated from the radial derivative to within the roundoff error of the computations. Use of (delta c/delta t)r, instead of (delta c/delta r)t, results in a significant increase (greater than 10-fold) in the signal-to-noise ratio of data obtained from both the uv photoelectric scanner and Rayleigh optical systems of the analytical ultracentrifuge. The use of (delta c/delta t)r to compute apparent sedimentation coefficient distributions for purposes of boundary analysis is exemplified with an antigen-antibody system.     

Mean time to resolution of gene duplication

The mean time to resolution of gene duplication (T_r) is studied in this paper under the double null recessive (DNR) and haplo-insufficient (HI) models within the same analytical and simulation framework. We show that when population size is not too small (more precisely Nμ > 0.1), T_r for unlinked duplication is usually larger than that for linked and T_r for unlinked duplication under the HI model might be greatly prolonged, which were consistent with previous observations. Furthermore, by analytical approach we here indicate the primary underlying mechanism is that the frequency of the original (or wild-type) chromosomal haplotype of the linked duplication decreases nearly exponential to zero with time while that of the unlinked decreases quickly to an quasi-equilibrium; and this phenomenon is particularly profound under the HI model, because the quasi-equilibrium frequency of the original chromosomal haplotype (x₀) under the HI model is higher than that under the DNR model. These results suggest that recombination and HI model might jointly contribute to the marked prolongation of T_r even in a modest population. The prolonged T_r and higher quasi-equilibrium frequency of the original allele at both duplicated loci might have offered more opportunities for the emergence of novel genes.     

Simultaneous rapid estimation of sedimentation coefficient and molecular weight

Data obtained from the early portion of sedimentation velocity experiments may be analyzed to simultaneously estimate both s and s/D. The C versus r data obtained are analyzed using a nonlinear least squares algorithm and an approximate solution to the Lamm equation. This procedure was tested both with simulated noisy data and with experimental data obtained using ribonuclease, ovalbumin, and somatostatin.dodecylsulfate. The procedure assumes that both s and D are independent of concentration. The results suggest that optimal estimation of both s and s/D is obtained at values of (= 2D/(s.omega(2).r(a)(2))) in the range of 0.002 to 0.01 and values of tau(= 2 somega(2)t) less than 0.04. Appropriate selection of rotor speed allows the estimation of both s and s/D for nearly globular macromolecules in the range of 10(4) to 10(6) daltons with data obtained during the first 3000-5000 seconds of a sedimentation velocity experiment.     

Analysis of the length distribution of amyloid fibrils by centrifugal sedimentation

The aggregation of normally soluble peptides and proteins into amyloid fibrils is a process associated with a wide range of pathological conditions, including Alzheimer's and Parkinson's diseases. It has become apparent that aggregates of different sizes possess markedly different biological effects, with aggregates of lower relative molecular weight being associated with stronger neurotoxicity. Yet, although many approaches exist to measure the total mass concentration of aggregates, the ability to probe the length distribution of growing aggregates in solution has remained more elusive. In this work, we applied a differential centrifugation technique to measure the sedimentation coefficients of amyloid fibrils produced during the aggregation process of the amyloid β (M1–42) peptide (Aβ42). The centrifugal method has the advantage of providing structural information on the fibril distribution directly in solution and affording a short analysis time with respect to alternative imaging and analytical centrifugation approaches. We show that under quiescent conditions interactions between Aβ42 fibrils lead to lateral association and to the formation of entangled clusters. By contrast, aggregation under shaking generates a population of filaments characterized by shorter lengths. The results, which have been validated by cryogenic transmission electron microscopy (cryo-TEM) analysis, highlight the important role that fibril–fibril assembly can play in the deposition of aggregation-prone peptides.     

Sedimentation velocity analysis of heterogeneous protein-protein interactions: sedimentation coefficient distributions c(s) and asymptotic boundary profiles from Gilbert-Jenkins theory

Interacting proteins in rapid association equilibrium exhibit coupled migration under the influence of an external force. In sedimentation, two-component systems can exhibit bimodal boundaries, consisting of the undisturbed sedimentation of a fraction of the population of one component, and the coupled sedimentation of a mixture of both free and complex species in the reaction boundary. For the theoretical limit of diffusion-free sedimentation after infinite time, the shapes of the reaction boundaries and the sedimentation velocity gradients have been predicted by Gilbert and Jenkins. We compare these asymptotic gradients with sedimentation coefficient distributions, c(s), extracted from experimental sedimentation profiles by direct modeling with superpositions of Lamm equation solutions. The overall shapes are qualitatively consistent and the amplitudes and weight-average s-values of the different boundary components are quantitatively in good agreement. We propose that the concentration dependence of the area and weight-average s-value of the c(s) peaks can be modeled by isotherms based on Gilbert-Jenkins theory, providing a robust approach to exploit the bimodal structure of the reaction boundary for the analysis of experimental data. This can significantly improve the estimates for the determination of binding constants and hydrodynamic parameters of the complexes.     

Enhanced resolution of histochemical distribution of glucose-6-phosphate dehydrogenase activity in rat neural tissue by use of a semipermeable membrane

We examined the histochemical distribution of glucose-6-phosphate dehydrogenase (G6PD) activity in neural tissue using different diffusion barriers. Although polyvinyl alcohol and agar overlays permitted regional localization of G6PD, a semipermeable membrane revealed cellular differences in G6PD activity within populations of neurons. Distribution of G6PD activity in selected regions of the nervous system was examined using the membrane technique. White matter usually exhibited strong G6PD activity. The neuronal somata of the dorsal root ganglia (L4-L6) and anterior horns of the spinal lumbar enlargement demonstrated a variation in activity which was independent of somal size. Satellite cells showed intense activity when the membrane technique was used. Hippocampal pyramidal and granular cells of the dentate gyrus exhibited moderate, uniform G6PD activity, but only weak activity was seen in hippocampal and dentate molecular layers. High levels of activity were observed in the vascular endothelial cells of the brain, spinal cord, and choroid plexus, and in the ependymal cells of the spinal central canal and ventricles of the brain. The superior vestibular nucleus appeared to have little G6PD activity in either the neuron cell bodies or the surrounding parenchyma. The use of a semipermeable membrane for localization of G6PD activity in neural tissues permits enhanced resolution of neuron elements and may provide a more accurate assessment of G6PD activity in histological preparations.     

Enhanced migratory waterfowl distribution modeling by inclusion of depth to water table data

In addition to being used as a tool for ecological understanding, management and conservation of migratory waterfowl rely heavily on distribution models; yet these models have poor accuracy when compared to models of other bird groups. The goal of this study is to offer methods to enhance our ability to accurately model the spatial distributions of six migratory waterfowl species. This goal is accomplished by creating models based on species-specific annual cycles and introducing a depth to water table (DWT) data set. The DWT data set, a wetland proxy, is a simulated long-term measure of the point either at or below the surface where climate and geological/topographic water fluxes balance. For species occurrences, the USGS' banding bird data for six relatively common species was used. Distribution models are constructed using Random Forest and MaxEnt. Random Forest classification of habitat and non-habitat provided a measure of DWT variable importance, which indicated that DWT is as important, and often more important, to model accuracy as temperature, precipitation, elevation, and an alternative wetland measure. MaxEnt models that included DWT in addition to traditional predictor variables had a considerable increase in classification accuracy. Also, MaxEnt models created with DWT often had higher accuracy when compared with models created with an alternative measure of wetland habitat. By comparing maps of predicted probability of occurrence and response curves, it is possible to explore how different species respond to water table depth and how a species responds in different seasons. The results of this analysis also illustrate that, as expected, all waterfowl species are tightly affiliated with shallow water table habitat. However, this study illustrates that the intensity of affiliation is not constant between seasons for a species, nor is it consistent between species.     

Measurement of the size distribution of human erythrocytes by a sedimentation method

The distribution of sedimentation velocities was determined, by a photoelectric method, for human erythrocytes at low concentrations in Ringer solution. The light absorption at 414 nm was measured, as a function of time, 10 mm below the top of the column. From the frequency distribution of cell velocities that of R_s √ρ-σ was found; R_s being the Stokes' radius, ρ the cell density and σ the density of the solution. Cell density was measured by the phthalate method and the mean Stokes' radius was found to be 2.58 μm. The size distributions showed some skewness but were in good general agreement with those measured by Celloscope counter, and with reported measurements from photomicrographs of cells in hanging drop suspensions. The skewness was much less than that encountered with electric sensing zone instruments (e.g. Celloscope) and the sedimentation method, being based on entirely different premises, provides an important check on such data. The skewness is due to a bias in the orientation of human erythrocytes during sedimentation. This bias may be a characteristic of biconcave cells; it could be absent in many species and reliable measurements of size distribution would then be obtained.