Angular dependence of scattered light, rotary frictional coefficients, and distribution of sizes of associated oligomers in solutions of bovine liver glutamate dehydrogenase

The angular dependence of scattering in solutions of bovine liver glutamate dehydrogenase was studied in 0.2M Na-phosphate buffer, pH 7, 10^?4M EDTA, and in buffered solutions saturated with either toluene or benzene. Whereas the shape of the scattering curves is in qualitative accord with the previously reported polymerization to rodlike linear structures, quantitative agreement between the calculated and experimental curves is poor when the polydispersity consistent with the association mechanism (derived from molecular weight determinations by light scattering and equilibrium sedimentation) is properly taken into account. The measurement of rotary frictional coefficients of macroscopic models of linearly associated glutamate dehydrogenase oligomers allowed the calculation of intrinsic viscosities of enzyme solutions but did not permit discrimination, by hydrodynamic means, between systems with different distributions of length.     

Macromolecular size-and-shape distributions by sedimentation velocity analytical ultracentrifugation

Sedimentation velocity analytical ultracentrifugation is an important tool in the characterization of macromolecules and nanoparticles in solution. The sedimentation coefficient distribution c(s) of Lamm equation solutions is based on the approximation of a single, weight-average frictional coefficient of all particles, determined from the experimental data, which scales the diffusion coefficient to the sedimentation coefficient consistent with the traditional s approximately M(2/3) power law. It provides a high hydrodynamic resolution, where diffusional broadening of the sedimentation boundaries is deconvoluted from the sedimentation coefficient distribution. The approximation of a single weight-average frictional ratio is favored by several experimental factors, and usually gives good results for chemically not too dissimilar macromolecules, such as mixtures of folded proteins. In this communication, we examine an extension to a two-dimensional distribution of sedimentation coefficient and frictional ratio, c(s,f(r)), which is representative of a more general set of size-and-shape distributions, including mass-Stokes radius distributions, c(M,R(S)), and sedimentation coefficient-molar mass distributions c(s,M). We show that this can be used to determine average molar masses of macromolecules and characterize macromolecular distributions, without the approximation of any scaling relationship between hydrodynamic and thermodynamic parameters.     

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.     

Fossilized intestine casts located within closed bivalve shells: implications for palaeoecological and sedimentological studies

Marine organisms inhabiting soft‐bottom sediment are particularly susceptible to rapid sedimentation and erosion events. This article presents a novel example of fossilized intestine casts located within closed bivalve shells in relation to rapid sedimentation event from the Pleistocene sediment of the Oga Peninsula, Akita Prefecture, northern Japan. The mollusc shells were loosely packed in well‐sorted medium‐grained to coarse‐grained sandstone associated with low‐angle trough cross‐stratification. The closed shells of Glycymeris yessoensis were present in the shell concentration. The internal parts of the shells were almost hollow, being partially filled with yellow fine‐grained clay minerals (median grain size = 30.63 μm). The characteristic material within the shells clearly differed from the surrounding sediment, which consisted of coarse‐grained felsic minerals (median grain size = 449.73 μm). Furthermore, the yellow fine‐grained clay minerals within the shells were tube‐shaped, and located near the posterior adductor scar. On the basis of anatomical observation of living Glycymeris, we confirmed that part of the intestine and the anus are also placed near the posterior adductor muscle. Therefore, the yellow fine‐grained clay minerals within the shells represent the fossil remains of particles ingested by the G. yessoensis individual through suspension‐feeding, and the tube‐shaped material is interpreted as being fossilized intestine cast. These results suggest that G. yessoensis individuals were buried alive, as rapid sedimentation prevented ejection and destruction of the filling material of intestine. The presence of intestine cast within the mollusc fossils can be used for recognizing rapid sedimentation.     

Determination of molecular parameters by fitting sedimentation data to finite-element solutions of the Lamm equation.

A method for fitting experimental sedimentation velocity data to finite-element solutions of various models based on the Lamm equation is presented. The method provides initial parameter estimates and guides the user in choosing an appropriate model for the analysis by preprocessing the data with the G(s) method by van Holde and Weischet. For a mixture of multiple solutes in a sample, the method returns the concentrations, the sedimentation (s) and diffusion coefficients (D), and thus the molecular weights (MW) for all solutes, provided the partial specific volumes (v) are known. For nonideal samples displaying concentration-dependent solution behavior, concentration dependency parameters for s(sigma) and D(delta) can be determined. The finite-element solution of the Lamm equation used for this study provides a numerical solution to the differential equation, and does not require empirically adjusted correction terms or any assumptions such as infinitely long cells. Consequently, experimental data from samples that neither clear the meniscus nor exhibit clearly defined plateau absorbances, as well as data from approach-to-equilibrium experiments, can be analyzed with this method with enhanced accuracy when compared to other available methods. The nonlinear least-squares fitting process was accomplished by the use of an adapted version of the "Doesn't Use Derivatives" nonlinear least-squares fitting routine. The effectiveness of the approach is illustrated with experimental data obtained from protein and DNA samples. Where applicable, results are compared to methods utilizing analytical solutions of approximated Lamm equations.     

A comparison of weight average and direct boundary fitting of sedimentation velocity data for indefinite polymerizing systems

Analysis of sedimentation velocity data for indefinite self-associating systems is often achieved by fitting of weight average sedimentation coefficients (s(20,w)) However, this method discriminates poorly between alternative models of association and is biased by the presence of inactive monomers and irreversible aggregates. Therefore, a more robust method for extracting the binding constants for indefinite self-associating systems has been developed. This approach utilizes a set of fitting routines (SedAnal) that perform global non-linear least squares fits of up to 10 sedimentation velocity experiments, corresponding to different loading concentrations, by a combination of finite element simulations and a fitting algorithm that uses a simplex convergence routine to search parameter space. Indefinite self-association is analyzed with the software program isodesfitter, which incorporates user provided functions for sedimentation coefficients as a function of the degree of polymerization for spherical, linear and helical polymer models. The computer program hydro was used to generate the sedimentation coefficient values for the linear and helical polymer assembly mechanisms. Since this curve fitting method directly fits the shape of the sedimenting boundary, it is in principle very sensitive to alternative models and the presence of species not participating in the reaction. This approach is compared with traditional fitting of weight average data and applied to the initial stages of Mg(2+)-induced tubulin self-associating into small curved polymers, and vinblastine-induced tubulin spiral formation. The appropriate use and limitations of the methods are discussed.     

Size-distribution analysis of proteins by analytical ultracentrifugation: strategies and application to model systems.

Strategies for the deconvolution of diffusion in the determination of size-distributions from sedimentation velocity experiments were examined and developed. On the basis of four different model systems, we studied the differential apparent sedimentation coefficient distributions by the time-derivative method, g(s*), and by least-squares direct boundary modeling, ls-g*(s), the integral sedimentation coefficient distribution by the van Holde-Weischet method, G(s), and the previously introduced differential distribution of Lamm equation solutions, c(s). It is shown that the least-squares approach ls-g*(s) can be extrapolated to infinite time by considering area divisions analogous to boundary divisions in the van Holde-Weischet method, thus allowing the transformation of interference optical data into an integral sedimentation coefficient distribution G(s). However, despite the model-free approach of G(s), for the systems considered, the direct boundary modeling with a distribution of Lamm equation solutions c(s) exhibited the highest resolution and sensitivity. The c(s) approach requires an estimate for the size-dependent diffusion coefficients D(s), which is usually incorporated in the form of a weight-average frictional ratio of all species, or in the form of prior knowledge of the molar mass of the main species. We studied the influence of the weight-average frictional ratio on the quality of the fit, and found that it is well-determined by the data. As a direct boundary model, the calculated c(s) distribution can be combined with a nonlinear regression to optimize distribution parameters, such as the exact meniscus position, and the weight-average frictional ratio. Although c(s) is computationally the most complex, it has the potential for the highest resolution and sensitivity of the methods described.     

Size-distribution analysis of macromolecules by sedimentation velocity ultracentrifugation and lamm equation modeling

A new method for the size-distribution analysis of polymers by sedimentation velocity analytical ultracentrifugation is described. It exploits the ability of Lamm equation modeling to discriminate between the spreading of the sedimentation boundary arising from sample heterogeneity and from diffusion. Finite element solutions of the Lamm equation for a large number of discrete noninteracting species are combined with maximum entropy regularization to represent a continuous size-distribution. As in the program CONTIN, the parameter governing the regularization constraint is adjusted by variance analysis to a predefined confidence level. Estimates of the partial specific volume and the frictional ratio of the macromolecules are used to calculate the diffusion coefficients, resulting in relatively high-resolution sedimentation coefficient distributions c(s) or molar mass distributions c(M). It can be applied to interference optical data that exhibit systematic noise components, and it does not require solution or solvent plateaus to be established. More details on the size-distribution can be obtained than from van Holde-Weischet analysis. The sensitivity to the values of the regularization parameter and to the shape parameters is explored with the help of simulated sedimentation data of discrete and continuous model size distributions, and by applications to experimental data of continuous and discrete protein mixtures.     

Downscaling European species atlas distributions to a finer resolution: implications for conservation planning

Aim One of the limitations to using species’ distribution atlases in conservation planning is their coarse resolution relative to the needs of local planners. In this study, a simple approach to downscale original species atlas distributions to a finer resolution is outlined. If such a procedure yielded accurate downscaled predictions, then it could be an aid to using available distribution atlases in real‐world local conservation decisions. Location Europe. Methods An iterative procedure based on generalized additive modelling is used to downscale original European 50 × 50 km distributions of 2189 plant and terrestrial vertebrate species to c. 10 × 10 km grid resolution. Models are trained on 70% of the original data and evaluated on the remaining 30%, using the receiver operating characteristic (ROC) procedure. Fitted models are then interpolated to a finer resolution. A British dataset comprising distributions of 81 passerine‐bird species in a 10 × 10 km grid is used as a test bed to assess the accuracy of the downscaled predictions. European‐wide, downscaled predictions are further evaluated in terms of their ability to reproduce: (1) spatial patterns of coincidence in species richness scores among different groups; and (2) spatial patterns of coincidence in richness, rarity and complementarity hotspots. Results There was a generally good agreement between downscaled and observed fine‐resolution distributions for passerine species in Britain (median Jaccard similarity = 70%; lower quartile = 36%; upper quartile = 88%). In contrast, the correlation between downscaled and observed passerine species richness was relatively low (rho = 0.31) indicating a pattern of error propagation through the process of overlaying downscaled distributions for many species. It was also found that measures of model accuracy in fitting original data (ROC) were a poor predictor of models’ ability to interpolate distributions at fine resolutions (rho = ?0.10). Although European hotspots were not fully coincident between observed and modelled coarse‐resolution data, or between modelled coarse resolution and modelled downscaled data, there was evidence that downscaled distributions were able to maintain original cross‐taxon coincidence of species‐richness scores, at least for terrestrial vertebrate groups. Downscaled distributions were also able to uncover important environmental gradients otherwise blurred by coarse‐resolution data. Main conclusions Despite uncertainties, downscaling procedures may prove useful to identify reserves that are more meaningfully related to local patterns of environmental variation. Potential errors arising from the presence of false positives may be reduced if downscaled‐distribution records projected to occur outside the range of original coarse‐resolution data are excluded. However, the usefulness of this procedure may be limited to data‐rich regions. If downscaling procedures are applied to data‐poor regions, then there is a need to undertake further research to understand the structure of error in models. In particular, it would be important to investigate which species are poorly modelled, where and why. Without such an assessment it is difficult to support unsupervised use of downscaled data in most real‐world situations.     

Limiting the sedimentation coefficient for sedimentation velocity data analysis: partial boundary modeling and g(s) approaches revisited

Brown and coworkers (Eur. Biophys. J. 38 (2009) 1079–1099) introduced partial boundary modeling (PBM) to simplify sedimentation velocity data analysis by excluding species outside the range of interest (e.g., aggregates, impurities) via restricting the sedimentation coefficient range being fitted. They strongly criticized the alternate approach of fitting g(s^∗) distributions using similar range limits, arguing that (i) it produces “nonoptimal fits in the original data space” and (ii) the g(s^∗) data transformations lead to gross underestimates of the parameter confidence intervals. It is shown here that neither of those criticisms is valid. These two approaches are not truly fitting the same data or in equivalent ways; thus, they should not actually give the same best-fit parameters. The confidence limits for g(s^∗) fits derived using F statistics, bootstrap, or a new Monte Carlo algorithm are in good agreement and show no evidence for significant statistical distortion. Here 15 g(s^∗) measurements on monoclonal antibody samples gave monomer mass estimates with experimental standard deviations of less than 1%, close to the confidence limit estimates. Tests on both real and simulated data help to clarify the strengths and drawbacks of both approaches. New algorithms for computing g(s^∗) and a scan-differencing approach for PBM are introduced.     

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.     

Molecular mass determination by sedimentation velocity experiments and direct fitting of the concentration profiles.

A new method for the direct molecular mass determination from sedimentation velocity experiments is presented. It is based on a nonlinear least squares fitting procedure of the concentration profiles and simultaneous estimation of the sedimentation and diffusion coefficients using approximate solutions of the Lamm equation. A computer program, LAMM, was written by using five different model functions derived by Fujita (1962, 1975) to describe the sedimentation of macromolecules during centrifugation. To compare the usefulness of these equations for the analysis of hydrodynamic results, the approach was tested on data sets of Claverie simulations as well as experimental curves of some proteins. A modification for one of the model functions is suggested, leading to more reliable sedimentation and diffusion coefficients estimated by the fitting procedure. The method seems useful for the rapid molecular mass determination of proteins larger than 10 kDa. One of the equations of the Archibald type is also suitable for compounds of low molecular mass, probably less than 10 kDa, because this model function requires neither the plateau region nor a meniscus free of solute.     

Determination of sedimentation coefficients for small peptides.

Direct fitting of sedimentation velocity data with numerical solutions of the Lamm equations has been exploited to obtain sedimentation coefficients for single solutes under conditions where solvent and solution plateaus are either not available or are transient. The calculated evolution was initialized with the first experimental scan and nonlinear regression was employed to obtain best-fit values for the sedimentation and diffusion coefficients. General properties of the Lamm equations as data analysis tools were examined. This method was applied to study a set of small peptides containing amphipathic heptad repeats with the general structure Ac-YS-(AKEAAKE)nGAR-NH2, n = 2, 3, or 4. Sedimentation velocity analysis indicated single sedimenting species with sedimentation coefficients (s(20,w) values) of 0.37, 0.45, and 0.52 S, respectively, in good agreement with sedimentation coefficients predicted by hydrodynamic theory. The described approach can be applied to synthetic boundary and conventional loading experiments, and can be extended to analyze sedimentation data for both large and small macromolecules in order to define shape, heterogeneity, and state of association.     

Spatial scale,topography and thermoregulatory behaviour interact when modelling species’ thermal niches

The spatial scale at which climate and species’ occupancy data are gathered, and the resolution at which ecological models are run, can strongly influence predictions of species performance and distributions. Running model simulations at coarse rather than fine spatial resolutions, for example, can determine if a model accurately predicts the distribution of a species. The impacts of spatial scale on a model's accuracy are particularly pronounced across mountainous terrain. Understanding how these discrepancies arise requires a modelling approach in which the underlying processes that determine a species’ distribution are explicitly described. Here we use a process‐based model to explore how spatial resolution, topography and behaviour alter predictions of a species thermal niche, which in turn constrains its survival and geographic distribution. The model incorporates biophysical equations to predict the operative temperature (T_e), thermal‐dependent performance and survival of a typical insect, with a complex life‐cycle, in its microclimate. We run this model with geographic data from a mountainous terrain in South Africa using climate data at three spatial resolutions. We also explore how behavioural thermoregulation affects predictions of a species performance and survival by allowing the animal to select the optimum thermal location within each coarse‐grid cell. At the regional level, coarse‐resolution models predicted lower T_e at low elevations and higher T_e at high elevations than models run at fine‐resolutions. These differences were more prominent on steep, north‐facing slopes. The discrepancies in T_e in turn affected estimates of the species thermal niche. The modelling framework revealed how spatial resolution and topography influence predictions of species distribution models, including the potential impacts of climate change. These systematic biases must be accounted for when interpreting the outputs of future modelling studies, particularly when species distributions are predicted to shift from uniform to topographically heterogeneous landscapes.     

Fast and accurate fitting of relaxation dispersion data using the flexible software package GLOVE

Relaxation dispersion spectroscopy is one of the most widely used techniques for the analysis of protein dynamics. To obtain a detailed understanding of the protein function from the view point of dynamics, it is essential to fit relaxation dispersion data accurately. The grid search method is commonly used for relaxation dispersion curve fits, but it does not always find the global minimum that provides the best-fit parameter set. Also, the fitting quality does not always improve with increase of the grid size although the computational time becomes longer. This is because relaxation dispersion curve fitting suffers from a local minimum problem, which is a general problem in non-linear least squares curve fitting. Therefore, in order to fit relaxation dispersion data rapidly and accurately, we developed a new fitting program called GLOVE that minimizes global and local parameters alternately, and incorporates a Monte-Carlo minimization method that enables fitting parameters to pass through local minima with low computational cost. GLOVE also implements a random search method, which sets up initial parameter values randomly within user-defined ranges. We demonstrate here that the combined use of the three methods can find the global minimum more rapidly and more accurately than grid search alone.     

Dinoflagellate cyst distribution along a shelf to slope transect of an oligotrophic tropical sea (Sunda Shelf, South China Sea)

From 51 surface samples collected along a shelf to slope transect of the Sunda Shelf, South China Sea, 36 taxa of organic‐walled dinoflagellate cysts are identified. Oligotrophic tropical shelf assemblages on the Sunda Shelf are dominated by gonyaulacoids such as Spiniferites species, Operculodinium centmcarpum and Operculodinium israelianum. Concentrations of dinoflagellate cysts in the shelf sediments are generally low and correlate well with the content of fine‐grained (clay and silt fraction) sediments. Detailed comparisons of sediment grain‐size distributions to concentrations of dominant dinoflagellate taxa (Spiniferites species, 0. centmcarpum and 0. israelianum) in the shelf sediments indicate that these taxa behave in water like sediment particles with size range φ 5.75–6.25 (13–18 μm). In contrast, slope assemblages in fine‐grained sediments are dominated by protoperidinioids. This may reflect higher nutrient availability as a result of weak winter upwelling. The concentrations of dinoflagellate cysts in the shelf sediments are mainly controlled by transport and winnowing processes and are probably not representative of surface water conditions.     

Recent developments for making gastric evacuation and daily ration determinations

Synopsis Gastric evacuation rate estimates often suffer from an important bias caused by fitting experimentally-derived data distributions that are inherently constricted by the X-axis (Y = 0). Monte Carlo simulations were used to evaluate the bias. Truncating constricted distributions prior to curve fitting was suggested as a means to circumvent the problem. A food consumption model developed by D.S. Robson was presented. It employs the integral of the function fit to percentage gastric evacuation data, and does not require an a priori assumption of exponential gastric evacuation. The methods were illustrated using experimental gastric evacuation data and stomach contents data for fishery-caught yellowfin tuna, Thunnus albacares.     

The concept of population in clonal organisms: mosaics of temporally colonized patches are forming highly diverse meadows of Zostera marina in Brittany

Seagrasses structure some of the world’s key coastal ecosystems presently in decline due to human activities and global change. The ability to cope with environmental changes and the possibilities for shifts in distribution range depend largely on their evolvability and dispersal potential. As large‐scale data usually show strong genetic structure for seagrasses, finer‐grained work is needed to understand the local processes of dispersal, recruitment and colonization that could explain the apparent lack of exchange across large distances. We aimed to assess the fine‐grained genetic structure of one of the most important and widely distributed seagrasses, Zostera marina, from seven meadows in Brittany, France. Both classic population genetics and network analysis confirmed a pattern of spatial segregation of polymorphism at both regional and local scales. One location exhibiting exclusively the variety ‘angustifolia’ did not appear more differentiated than the others, but instead showed a central position in the network analysis, confirming the status of this variety as an ecotype. This phenotypic diversity and the high allelic richness at nine microsatellites (2.33–9.67 alleles/locus) compared to levels previously reported across the distribution range, points to Brittany as a centre of diversity for Z. marina at both genetic and phenotypic levels. Despite dispersal potential of several 100 m, a significant pattern of genetic differentiation, even at fine‐grained scale, revealed ‘genetic patchiness’. Meadows seem to be composed of a mosaic of clones with distinct origins in space and time, a result that calls into question the accuracy of the concept of populations for such partially clonal species.