Evaluation of diffusion coefficients by means of an approximate steady-state condition in sedimentation velocity distributions

This investigation examined the feasibility of manipulating the rotor speed in sedimentation velocity experiments to spontaneously generate an approximate steady-state condition where the extent of diffusional spreading is matched exactly by the boundary sharpening arising from negative s–c dependence. Simulated sedimentation velocity distributions based on the sedimentation characteristics for a purified mucin preparation were used to illustrate a simple procedure for determining the diffusion coefficient from such steady-state distributions in situations where the concentration dependence of the sedimentation coefficient, s = s⁰/(1 + Kc), was quantified in terms of the limiting sedimentation coefficient as c → 0 (s⁰) and the concentration coefficient (K). Those simulations established that spontaneous generation of the approximate steady state could well be a feature of sedimentation velocity distributions for many unstructured polymer systems because the requirement that Kc_oω²s⁰/D be between 46 and 183 cm⁻² is not unduly restrictive. Although spontaneous generation of the approximate steady state is also a theoretical prediction for structured macromolecular solutes exhibiting linear concentration dependence of the sedimentation coefficient, s = s⁰(1 − kc), the required value of k is far too large for any practical advantage to be taken of this approach with globular proteins.     

Comparison of molecular weight determination of sodium alginate by sedimentation-diffusion and light scattering

The weight average molecular weight, M̄_w, of sodium alginates were determined by the sedimentation-diffusion technique using photon correlation spectroscopy rather than boundary spreading in the analytical ultracentrifuge to determine the translational diffusion coefficients. This enables the diffusion coefficients to be determined easily and accurately. Excellent correlation is found between the observed zero concentration translational diffusion coefficient, D_O and the M̄_W values in a emphirical power law. The M̄_W obtained by sedimentation-diffusion and laser light scattering compare very favourably. The concentration dependence of the photon correlation spectroscopy data allowed determination of the coil overlap concentration, c*. The inverse proportionality of c* to both M̄_W and [η] is demonstrated.     

Numerical solutions of the Lamm equation. III. Velocity centrifugation

We have generated solutions to the Lamm equation to examine the effects of concentration dependence on velocity experiments. Two forms of c dependence are considered: s/s₀ = 1 – kc and s/s₀ = (1 + kc)^?1. Features of these solutions are discussed. The magnitude of the errors resulting from the usual procedure of measuring the rate of movement of schlieren maxima or of the position at which the concentration is one half the plateau value have been examined. These errors are usually negligible after sufficient centrifugation time. The errors in using the half-plateau concentration are less than those using the movement of the peak. We have also examined a technique due to Fujita for determining D from boundary spreading when s/s₀ = (1+kc)^?1. This method is satisfactory when s/s₀ is actually of this form, or under certain limitations when s/s₀ = (1 + kc)^?1. Creeth has shown that under certain conditions the concentration gradient, curve remains virtually unchanged in shape after separating from the meniscus. When this occurs it is possible to estimate s/D from the data. The condition for such a steady state is that kc₀ be sufficiently large. Numerical confirmation of this method is presented in the final section.     

Scanning gel chromatography: determination of transport parameters from dynamic profiles measured at low solute concentration

Direct optical scanning of solute boundaries in large zone gel Chromatography experiments provides an accurate means of determining boundary profile shapes and rates of motion. A method has been developed for correcting such boundaries to a constant time frame, eliminating the distortion which arises from finite column scanning rate Centroids or the corrected profiles can be used to determine the partition cross section for the solute of interest The partition cross section and flow rate determine translational motion within the column. The axial dispersion coefficient, L, which characterizes rate of boundary spreading may also be calculated from the profiles. In order to explore these procedures a study of four noninteracting solutes was conducted. Partition cross sections determined from rates of motion of boundary centroids were found to be in good agreement with those determined by the equilibrium saturation method on the same column.In order to explore the lowest concentration limits of the technique and to illustrate the boundary characteristics for a selfassociating solute, a study of carboxyhemoglobin was conducted over a wide concentration range. From measurements at 220 nm the lowest concentration where useful data could be obtained was 2 micrograms per ml (0.12 πM heme) These results establish validity of the procedures used in analyzing the rates of boundary transport and in studying solute transport over a wide range of conditions.     

Batch Tests To Determine Activity Distribution and Kinetic Parameters for Acetate Utilization in Expanded-Bed Anaerobic Reactors

Batch tests to measure maximum acetate utilization rates were used to determine the distribution of acetate utilizers in expanded-bed sand and expanded-bed granular activated carbon (GAC) reactors. The reactors were fed a mixture of acetate and 3-ethylphenol, and they contained the same predominant aceticlastic methanogen, Methanothrix sp. Batch tests were performed both on the entire reactor contents and with media removed from the reactors. Results indicated that activity was evenly distributed within the GAC reactors, whereas in the sand reactor a sludge blanket on top of the sand bed contained approximately 50% of the activity. The Monod half-velocity constant (K_s) for the acetate-utilizing methanogens in two expanded-bed GAC reactors was searched for by combining steady-state results with batch test data. All parameters necessary to develop a model with Monod kinetics were experimentally determined except for K_s. However, K_s was a function of the effluent 3-ethylphenol concentration, and batch test results demonstrated that maximum acetate utilization rates were not a function of the effluent 3-ethylphenol concentration. Addition of a competitive inhibition term into the Monod expression predicted the dependence of K_s on the effluent 3-ethylphenol concentration. A two-parameter search determined a K_s of 8.99 mg of acetate per liter and a K_i of 2.41 mg of 3-ethylphenol per liter. Model predictions were in agreement with experimental observations for all effluent 3-ethylphenol concentrations. Batch tests measured the activity for a specific substrate and determined the distribution of activity in the reactor. The use of steady-state data in conjunction with batch test results reduced the number of unknown kinetic parameters and thereby reduced the uncertainty in the results and the assumptions made.     

Determination of protein complex stoichiometry through multisignal sedimentation velocity experiments

Determination of the stoichiometry of macromolecular assemblies is fundamental to an understanding of how they function. Many different biophysical methodologies may be used to determine stoichiometry. In the past, both sedimentation equilibrium and sedimentation velocity analytical ultracentrifugation have been employed to determine component stoichiometries. Recently, a method of globally analyzing multisignal sedimentation velocity data was introduced by Schuck and coworkers. This global analysis removes some of the experimental inconveniences and inaccuracies that could occur in the previously used strategies. This method uses spectral differences between the macromolecular components to decompose the well-known c(s) distribution into component distributions c_k(s); that is, each component k has its own c_k(s) distribution. Integration of these distributions allows the calculation of the populations of each component in cosedimenting complexes, yielding their stoichiometry. In our laboratories, we have used this method extensively to determine the component stoichiometries of several protein-protein complexes involved in cytoskeletal remodeling, sugar metabolism, and host-pathogen interactions. The overall method is described in detail in this work, as are experimental examples and caveats.     

Efficient biokinetic experimental designs

Of the experimental methods available for obtaining data to estimate the biological kinetic parameters μ_m, K_s, and Yeach requires considerable experimental effort, yet often yields somewhat imprecise estimates of the parameters, particularly K_s. Therefore it would be worthwhile to seek ways to get parameter estimates of greater precision using less experimental effort. The precision of parameter estimates is strongly dependent, upon the settings of the independent, variables used in the experiments. This dependence is explained and an attempt made to show how experimental settings can be determined that lead efficiently to precise parameter estimates with minimal effort.     

Biomass estimation on the basis of yeast cultivation model with morphophysiological parameters

An approach of biomass estimation of yeast fed-batch cultivation is proposed. It is based on the model that takes into account the information about the morphophysiological parameters: size, coefficients of shape and skewness of optical density of yeast cells. Procedure for parameter identification of the model, r ₁-rate of transformation of active cells into weakened cells, r ₂-rate of transformation of weakened cells into dead cells, r ₃-rate of transformation of weakened cells into active cells, r ₄-rate by which the buds of the budding cells grow and transform after their separation into active cells and r ₅-rate of transformation of active cells into budding cells, is described. The procedure is performed in MATLAB environment.     

Productivity and heat generation of fermentation under oxygen limitation

The elemental balance equation of microbial growth on carbon substrate of generalized composition is given. Yield of dried bio-mass per oxygenY _o is calculated. Yield per oxygenY _o is found to be determined by two factors—carbon yieldy and the reducing power of substrate γ _s . The mode of dependence ofY _o on these two quantities is studied. The energetic interpretation ofy and γ _s is given. The dependence ofY _o ony and γ _s is shown to be equivalent to the dependence on a single factor, the energetie yield of growth η. Fermentor productivity increases with growth of η, the increase being directly proportional if η is not large (up to 25%) and becoming steeper if η is larger. The restrictions on a range of workable carbon yields during growth on various substrates are found. Metabolic heat generation of fermentor is shown to be proportional to oxygen consumption and to average 3.38 kcal per gram of O₂ irrespective of substrate and microorganism used.     

Comparing real-time quantitative polymerase chain reaction analysis methods for precision,linearity, and accuracy of estimating amplification efficiency

New methods are used to compare seven qPCR analysis methods for their performance in estimating the quantification cycle (C_q) and amplification efficiency (E) for a large test data set (94 samples for each of 4 dilutions) from a recent study. Precision and linearity are assessed using chi-square (χ²), which is the minimized quantity in least-squares (LS) fitting, equivalent to the variance in unweighted LS, and commonly used to define statistical efficiency. All methods yield C_qs that vary strongly in precision with the starting concentration N₀, requiring weighted LS for proper calibration fitting of C_q vs log(N₀). Then χ² for cubic calibration fits compares the inherent precision of the C_qs, while increases in χ² for quadratic and linear fits show the significance of nonlinearity. Nonlinearity is further manifested in unphysical estimates of E from the same C_q data, results which also challenge a tenet of all qPCR analysis methods — that E is constant throughout the baseline region. Constant-threshold (C_t) methods underperform the other methods when the data vary considerably in scale, as these data do.     

Nature of the individual Ca2+ binding sites in Ca2+-regenerated bacteriorhodopsin

The binding constants, K₁ and K₂, and the number of Ca²⁺ ions in each of the two high affinity sites of Ca²⁺-regenerated bacteriorhodopsin (bR) are determined potentiometrically at different pH values in the range of pH 3.5-4.5 by using the Scatchard plot method. From the pH dependence of K₁ and K₂, it was found that two hydrogen ions are released for each Ca²⁺ bound to each of the two high affinity sites. Furthermore, we have measured by a direct spectroscopic method the association constant, K_s, for the binding of Ca²⁺ to deionized bR, which is responsible for producing the blue to purple color change. Comparing the value of K_s and its pH dependence with those of K₁ and K₂ showed that the site corresponding to K_s is to be identified with that of K₂. This is in agreement with the conclusion reached previously, using a different approach, which showed that it is the second Ca²⁺ that causes the blue to purple color change.

Our studies also show that in addition to the two distinct high affinity sites, there are about four to six sites with lower binding constants. These are attributed to the nonspecific binding in bR.

     

Auxin quantification based on histochemical staining of GUS under the control of auxin-responsive promoter

To visualize phytohormone localization in plant tissues, transgenic plants comprising the GUS reporter gene are often used. However, until now only qualitative assessment of the hormone presence was available. In this work, we suggested the method for IAA quantification in transgenic DR5::GUS Arabidopsis thaliana L. plants by the analysis of digital images. An empirical quadratic dependence was established between the IAA concentration in medium and the level of GUS-dependent staining. Using this method, we demonstrated that, after A. thaliana root gravistimulation for 90 min, auxin lateral redistribution occurred. It resulted in the increase in the IAA concentration in the lower root part (in the elongation zone and apical meristem) by 200% on the average.     

Sedimentation coefficients of self-associating species: I. Basic theory

Under the same solution conditions, the apparent weight average sedimentation coefficient, s_wa, and some quantities obtained from it can be combined with the equilibrium constant or constants, K_i, and the monomer concentration, c_I, obtained from sedimentation equilibrium, light scattering or osmotic pressure experiments on the same self-associating solute, so that the individual sedimentation coefficients, s_i, of the self-associating species, and also the hydrodynamic concentration dependence parameter,g or $\text{g}$, can be evaluated. Using two different models for the hydrodynamic concentration parameter, four different methods are presented for the evaluation of the s_i's. Methods for evaluating g or $\text{g}$, once the s_i's are known, are presented. A method for obtaining the number average sedimentation coefficient, s_N, and its application to self-associations is presented. Methods are shown for the evaluation of Z average properties, x_zc, as well as number average properties,x_Nc, of a self-associating solute from its weight average properties, x_wc.     

Laser interferometric investigation of solute transport through membrane-concentration boundary layer system

We investigate diffusive transport in a membrane system with a horizontally mounted membrane under concentration polarization conditions performed by a laser interferometry method. The data obtained from two different theoretical models are compared to the experimental results of the substance flux. In the first model, the membrane is considered as infinitely thin, while in the second one as a wall of finite thickness. The theoretical calculations show sufficient correspondence with the experimental results. On the basis of interferometric measurements, the relative permeability coefficient (ζ_s) for the system, consisting of the membrane and concentration boundary layers, was also obtained. This coefficient reflects the concentration polarization of the membrane system. The obtained results indicate that the coefficient ζ_s of the membrane-concentration boundary layer system decreases in time and seems to be independent of the initial concentration of the solute.     

Extraction and Quantification of Solutes in Solidified Agar Culture Media

A method is described for determining the concentration of certain solutes in solidified culture media. The method is based upon the finding that under specified conditions the concentration of solute in an agar gel (C_g) is related to the concentration of solute in a centrifugally extracted gel supernatant (C_s) by the ratio, C_g/C_s, which is characteristic for each solute. The method avoids direct assays of the gels and instead involves assaying the supernatants from inoculated and uninoculated (control) gels with conventional liquid assay techniques and then calculating solute concentrations in the inoculated gels by use of the C_g/C_s ratios determined from the controls. Uninoculated agar gels containing known concentrations of various solutes and similar gels inoculated with Neurospora crassa or Escherichia coli were centrifuged at various times, and the supernatants were assayed for solute concentrations. The solute concentrations in the supernatants from the inoculated gels multiplied by the C_g/C_s ratios for those solutes determined at the same times for the uninoculated controls gave calculated solute concentrations in the inoculated gels. The differences between these calculated solute concentrations and those initially present in the inoculated gels indicated the amounts of solutes utilized from the gels by the microorganisms at various incubation times.     

The carbon dioxide hydration activity of brush-border carbonic anhydrase from the dog kidney

The steady-state kinetic parameters for the hydration of CO₂ catalyzed by membrane-bound carbonic anhydrase from the renal brush-border of the dog are compared with the same parameters for water-soluble bovine erythrocyte carbonic anhydrase. For the membrane-bound enzyme, the turnover number k_cat is 6.5 × 10⁵ s^?1 and the Michaelis constant is 7.5 mm for CO₂ hydration at pH 7.4 and 25 °C. The corresponding constants for bovine carbonic anhydrase under these conditions are 6.3 × 10⁵ s^?1 and 15 mm (Y. Pocker and D.W. Bjorkquist (1977)Biochemistry16, 5698–5707). The rate constant for the transfer of a proton between carbonic anhydrase and buffer was determined from the dependence of the catalytic rate on the concentration of the buffers imidazole and N-2-hydroxyethylpiperazine-N′-2-ethanesulfonic acid (Hepes); the value of 2 × 10⁸m^?1s^?1 describes this constant for both forms of carbonic anhydrase at pH 7.4. Furthermore, the pH dependence of the initial velocity of hydration of CO₂ in the range of pH 6.5 to 8.0 is identical for the membrane-bound and soluble enzyme at low buffer concentration (1–2 mm imidazole). We conclude that the membrane plays no detectable role in affecting the CO₂ hydration activity and that the active site of the renal, membrane-bound carbonic anhydrase is exposed to the aqueous phase.     

A method for measuring sedimentation and diffusion of macromolecules in capillary tubes by total intensity and quasi-elastic light-scattering techniques.

Light scattered from a macromolecular solution in a capillary tube is used to determine both the sedimentation and translational diffusion coefficients. The capillary tube is spun in a preparative centrifuge, removed, and placed in a light-scattering photometer equipped with a scanning mechanism. The intensity distribution of scattered light along the tube represents the concentration profile in the tube and provides the measure of boundary migration. The sedimentation coefficient is determined from this measure and the applied centrifugal field. The diffusion coefficient is obtained from a time-autocorrelation analysis of fluctuations in intensity of light scattered from any fixed point of the profile. These coefficients were obtained for two monodisperse systems, R17 bacteriophage and 28s ribosomal rat liver RNA. The molecular weights obtained from ratios of these coefficients are in good agreement with literature values. In the sedimentation analysis, deviations from linearity between boundary displacement and applied field were found to be less than 1%. This precision confirms that the boundary is stable for the capillary geometry even in the absence of a preformed density gradient. The sedimentation coefficients of identical samples were also measured with the Spinco Model E analytical ultracentrifuge; results of the two methods agree to within 4%. As a consequence of the capillary tube geometry and light-scattering detection, sedimentation coefficients can be obtained from sample volumes of less than 100 μl. This detection techniques is thus far demonstrated to be at least an order of magnitude more sensitive than Schlieren optics, thereby useful when uv absorption is not applicable. For diffusion measurements there are also several inherent advantages. The diffusion coefficient is obtained from the identical sample, and scanning provides the capability to measure D from various parts of the sedimentation profiles and thereby directly explore concentration dependence, homogeneity, and integrity of the sample. The capillary tube with a layer of silicone oil over the sample and centrifugation provides an effective method to cleanse the solution and trap all dust.     

Calculating extinction coefficients for enzymatically produced o-quinones

Molar extinction coefficients of o-quinones produced from o-diphenols by the action of o-diphenol: O₂ oxidoreductase were calculated by least-squares linear regression at several wavelengths in the pH range 5.8–7.8. The accuracy of each extinction coefficient is verified by the standard errors of the regression coefficient and the estimate, and by 95% confidence limits. The seven o-diphenols used in the present study were pyrocatechol, 4-methylcatechol, 4-tertiarybutylcatechol, 3,4-l-dihydroxyphenylalanine, 3,4-dihydroxyphenylethylamine, 3,4-dihydroxyphenylacetic acid, and 3,4-dihydroxyhydrocinnamic acid.     

Intensity Correlation-Based Calibration of FRET

Dual-laser flow cytometric resonance energy transfer (FCET) is a statistically efficient and accurate way of determining proximity relationships for molecules of cells even under living conditions. In the framework of this algorithm, absolute fluorescence resonance energy transfer (FRET) efficiency is determined by the simultaneous measurement of donor-quenching and sensitized emission. A crucial point is the determination of the scaling factor α responsible for balancing the different sensitivities of the donor and acceptor signal channels. The determination of α is not simple, requiring preparation of special samples that are generally different from a double-labeled FRET sample, or by the use of sophisticated statistical estimation (least-squares) procedures. We present an alternative, free-from-spectral-constants approach for the determination of α and the absolute FRET efficiency, by an extension of the presented framework of the FCET algorithm with an analysis of the second moments (variances and covariances) of the detected intensity distributions. A quadratic equation for α is formulated with the intensity fluctuations, which is proved sufficiently robust to give accurate α-values on a cell-by-cell basis in a wide system of conditions using the same double-labeled sample from which the FRET efficiency itself is determined. This seemingly new approach is illustrated by FRET measurements between epitopes of the MHCI receptor on the cell surface of two cell lines, FT and LS174T. The figures show that whereas the common way of α determination fails at large dye-per-protein labeling ratios of mAbs, this presented-as-new approach has sufficient ability to give accurate results. Although introduced in a flow cytometer, the new approach can also be straightforwardly used with fluorescence microscopes.