Evaluation of Taylor dispersion injections: determining kinetic/affinity interaction constants and diffusion coefficients in label-free biosensing

In label-free biomolecular interaction analysis, a standard injection provides an injection of uniform analyte concentration. An alternative approach exploiting Taylor dispersion produces a continuous analyte titration allowing a full analyte dose response to be recorded in a single injection. The enhanced biophysical characterization that is possible with this new technique is demonstrated using a commercially available surface plasmon resonance-based biosensor. A kinetic interaction model was fitted locally to Taylor dispersion curves for estimation of the analyte diffusion coefficient in addition to affinity/kinetic constants. Statistical confidence in the measured parameters from a single Taylor dispersion injection was comparable to that obtained for global analysis of multiple standard injections. The affinity constants for multisite interactions were resolved with acceptable confidence limits. Importantly, a single analyte injection could be treated as a high-resolution real-time affinity isotherm and was demonstrated using the complex two-site interaction of warfarin with human serum albumin. In all three model interactions tested, the kinetic/affinity constants compared favorably with those obtained from standard kinetic analysis and the estimates of analyte diffusion coefficients were in good agreement with the expected values.     

Microfluidics and the quantification of biomolecular interactions

Microfluidic systems under laminar flow conditions provide in-solution information about species size and binding affinities at very modest sample costs. Flow-induced dispersion analysis directly measures the spread of the analyte profile using Taylor dispersion analysis, whereas microfluidic diffusional sizing quantifies the transfer of analyte from one phase to another. Species of sizes between 0.5 and 1000 nm can be analyzed, and different populations resolved. Both techniques also allow analysis in complex media and medium throughput analysis. These properties make them valuable complements to existing approaches to measure biomolecular interactions.     

Biosensor-based fragment screening using FastStep injections

We have developed a novel analyte injection method for the SensíQ Pioneer surface plasmon resonance-based biosensor referred to as “FastStep.” By merging buffer and sample streams immediately prior to the reaction flow cells, the instrument is capable of automatically generating a two- or threefold dilution series (of seven or five concentrations, respectively) from a single analyte sample. Using sucrose injections, we demonstrate that the production of each concentration within the step gradient is highly reproducible. For kinetic studies, we developed analysis software that utilizes the sucrose responses to automatically define the concentration of analyte at any point during the association phase. To validate this new approach, we compared the results of standard and FastStep injections for ADP binding to a target kinase and a panel of compounds binding to carbonic anhydrase II. Finally, we illustrate how FastStep can be used in a primary screening mode to obtain a full concentration series of each compound in a fragment library.     

Increasing throughput of surface plasmon resonance-based biosensors by multiple analyte injections

Surface plasmon resonance-based biosensors are now acknowledged as robust and reliable instruments to determine the kinetic parameters related to the interactions between biomolecules. These kinetic parameters are used in screening campaigns: there is a considerable interest in reducing the experimental time, thus improving the throughput of the surface plasmon resonance assays. Kinetic parameters are typically obtained by analyzing data from several injections of a given analyte at different concentrations over a surface where its binding partner has been immobilized. It has been already proven that an iterative optimization approach aiming at determining optimal analyte injections to be performed online can significantly reduce the experimentation time devoted to kinetic parameter determination, without any detrimental effect on their standard errors. In this study, we explore the potential of this iterative optimization approach to further reduce experiment duration by combining it with the simultaneous injection of two analytes.     

Continuous measurements of a binding reaction using a capacitive biosensor

A capacitive biosensor with polyclonal antibodies raised against human serum albumin (HSA) immobilized on a gold transducer has been developed for continuous measurement of HSA in the muM-range. A mathematical model has been refined to describe integral HSA-binding curves assuming that (i) binding is essentially irreversible under the conditions used, (ii) the signal is scaled as the number of non-occupied binding sites and (iii) the rate of disappearance of available binding sites is scaled as the number of available binding sites and analyte concentration in solution. Deconvolution of the curves using the mathematical model indicates clearly that it is possible to retrieve concentration profiles (isocratic, linearly or exponentially increasing gradients) of the analyte in the continuous sample flow from the normalized integral binding (NIB) curves. The data presented constitutes the theoretical background and the first step towards the development of an analytical system allowing on-line detection of the concentration profile of the analyte from NIB-curves. Since the system can be used for extended time periods between regeneration steps, a low frequency of regeneration steps can be expected.     

Antibody-antigen interactions measured by surface plasmon resonance: global fitting of numerical integration algorithms

The interactions between adenylate kinase (AK) and a monoclonal antibody against AK (McAb3D3) were examined by means of optical biosensor technology, and the sensograms were fitted to four models using numerical integration algorithms. The interaction of a solution of McAb3D3 with immobilized AK follows a double exponential function and the data fitted well to an inhomogeneous ligand model. The interaction of a solution AK with immobilized McAb3D3 follows a single exponential function and the data fitted well to a pseudo-first order reaction model. The true association constants of AK binding to McAb3D3 in solution were obtained from competition BIAcore measurements. The difference in results obtained with solid-phase BIAcore and competition BIAcore may be due to rebinding of the dissociated analyte to the immobilized surface. The results obtained with BIAcore are compared to those obtained by ELISA methods. We suggest that the best method for analysis of BIAcore data is direct, global fitting of sensorgrams to numerical integration algorithms corresponding to the different possible models for binding.     

"Bridge" structures between nucleic acid molecules fixed in the structure of a liquid crystal

The binding of daunomycin and copper ions to poly(I).poly(C) molecules fixed in a particle of a liquid-crystalline dispersion was studied. A thermodynamic model of adsorption was developed, which makes it possible to describe the formation of complexes of a particular kind, "bridges" that connect adjacent nucleic acid molecules fixed in a liquid crystal. The bridges represent chelate complexes, which incorporate the molecules of the antibiotic daunomycin and copper ions. Equations describing the dependence of the concentration of these bridges in solution on the concentration of their constituents were derived. The family of dependences of experimental amplitudes of bands in CD spectra typical of "bridge" structures on the concentration of copper ions represents a set of S-shaped curves, and, as the concentration of daunomycin in solution increases, the level of saturation of these curves increases. The analysis of experimental data with the use of this model suggests that the structures of this type compete with daunomycin molecules for the binding sites on poly(I).poly(C). By using this model, the energies of formation of bridge structures were calculated.     

Model Testing in Radioligand/Receptor Interaction by Monte Carlo Simulation

Abstract

Monte Carlo simulations have been applied for evaluating the reliability of parameter estimates as well as for testing models in radioligand saturation binding experiments. Scatchard analysis was compared to the nonlinear least-square curve fitting method for one-site saturation binding curves. It was found that linear regression analysis from the transformed data in the Scatchard plot yielded generally less accurate parameter estimates than nonlinear regression analysis of untransformed data. The advantage of the nonlinear least-squares curve fitting method was especially pronounced in cases where the scatter and number of data points, as well as the radioligand concentration range, were chosen similar to less optimal experimental conditions. Under such circumstances, several K_D and B_max values derived by Scatchard analysis led to physically impossible negative values whereas the same data analyzed by nonlinear regression yielded reasonable parameter estimates. Furthermore, it was found that for both means of analysis, K_D and B_max correlated positively. In another set of Monte Carlo experiments, saturation binding curves involving two receptor sites were generated and subsequently analyzed according to both a one-site and a two-site model. The confidence with which one is able to distinguish the two-site model from nonlinear least-squares curve fitting was then estimated for optimal, as well as for, less ideal experimental condigions.     

不同性别河北柴鸡早期生长规律及其生长曲线拟合

本研究运用Logistic、Gompertz和Bertalanffy三种非线性模型对不同性别河北柴鸡早期生长规律和生长曲线进行分析及拟合比较.结果表明,3种曲线模型拟合度均达到0.99以上,但Gompertz曲线模型在拟合度和预测极限生长量、拐点周龄和最大周增重等方面相对较好.进一步分析表明,河北柴鸡公鸡的极限体重和拐点体重均高于母鸡,拐点周龄性别间差异不大,公鸡最大周增重与实际观测值接近.本文有助于了解不同性别河北柴鸡各自的生长模式及其对营养、环境的需求,为开展规模化饲养提供参考.     

New multi-step kinetics using common affinity biosensors saves time and sample at full access to kinetics and concentration

Today, affinity-based biosensorics is a standard technology in quantitative biomolecular interaction analysis, but suffers from low sample throughput and sometimes from inaccessible kinetics. A new methodology for such biosensors is introduced here that cuts down measurement time dramatically and increases confidentiality of results. In contrast to traditional applications, the ligand immobilized on the sensor chip is exposed to the binding analyte at a rapid stepwise change of the analyte concentration without the need for regenerations between analyte additions. In the application presented here, each addition of the analyte is succeeded by a buffer flow, yielding alternating association and dissociation phases in a "zigzag" style. This binding curve pattern is analyzed by means of novel fitting algorithms, which render detailed kinetics rate constants at a high level of self-consistency, and hence, validity due to multiple cross-checks. In comparison with traditional sequential kinetics analysis, this new multi-step kinetics approach returns practically identical (or improved) kinetics constants--at valuable savings in time/material since regeneration steps, ligand re-captures, or titration equilibrations are unnecessary.     

The identification of transport parameters from truncated physiological tracer curves

The primary data curves from the injection of tracers into the circulation are often obscured by the appearance of a recirculation hump. Previous techniques for parameter identification in the presence of such a complication have been extended from compartmental models to include circulatory models consisting of partial differential equations of the Taylor dispersion and Turner capacitance types. A comparative analysis of the efficiency of parameter identification by several computational strategies is presented.     

Quantitative dual-probe microdialysis: mathematical model and analysis

Steady-state microdialysis is a widely used technique to monitor the concentration changes and distributions of substances in tissues. To obtain more information about brain tissue properties from microdialysis, a dual-probe approach was applied to infuse and sample the radiotracer, [3H]mannitol, simultaneously both in agar gel and in the rat striatum. Because the molecules released by one probe and collected by the other must diffuse through the interstitial space, the concentration profile exhibits dynamic behavior that permits the assessment of the diffusion characteristics in the brain extracellular space and the clearance characteristics. In this paper a mathematical model for dual-probe microdialysis was developed to study brain interstitial diffusion and clearance processes. Theoretical expressions for the spatial distribution of the infused tracer in the brain extracellular space and the temporal concentration at the probe outlet were derived. A fitting program was developed using the simplex algorithm, which finds local minima of the standard deviations between experiments and theory by adjusting the relevant parameters. The theoretical curves accurately fitted the experimental data and generated realistic diffusion parameters, implying that the mathematical model is capable of predicting the interstitial diffusion behavior of [3H]mannitol and that it will be a valuable quantitative tool in dual-probe microdialysis.     

Making the most of survey data: Incorporating age uncertainty when fitting growth parameters

Individual growth is an important parameter and is linked to a number of other biological processes. It is commonly modeled using the von Bertalanffy growth function (VBGF), which is regularly fitted to age data where the ages of the animals are not known exactly but are binned into yearly age groups, such as fish survey data. Current methods of fitting the VBGF to these data treat all the binned ages as the actual ages. We present a new VBGF model that combines data from multiple surveys and allows the actual age of an animal to be inferred. By fitting to survey data for Atlantic herring (Clupea harengus) and Atlantic cod (Gadus morhua), we compare our model with two other ways of combining data from multiple surveys but where the ages are as reported in the survey data. We use the fitted parameters as inputs into a yield‐per‐recruit model to see what would happen to advice given to management. We found that each of the ways of combining the data leads to different parameter estimates for the VBGF and advice for policymakers. Our model fitted to the data better than either of the other models and also reduced the uncertainty in the parameter estimates and models used to inform management. Our model is a robust way of fitting the VBGF and can be used to combine data from multiple sources. The model is general enough to fit other growth curves for any taxon when the age of individuals is binned into groups.     

The reliability of Michaelis constants and maximum velocities estimated by using the integrated Michaelis–Menten equation

1. Experimental progress curves were simulated for a reaction obeying Michaelis-Menten kinetics. 2. K(m) and V were estimated (a) by fitting the integrated Michaelis-Menten equation to the progress curves, and (b) from the initial slopes of the curves (i.e. from initial velocities). 3. The integrated equation could not be fitted successfully by a non-linear method, so it was transformed and fitted by a linear method. 4. Provided that the initial substrate concentration was greater than K(m) and the data were precise enough, the integrated equation gave parameter estimates which were unbiased and as reliable as those derived from initial velocities although based on fewer experiments. 5. The integrated equation could be used for progress curves of unknown origin.     

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.     

Graphical Methods for Analysing Combination Effects in Dose-Response Experiments

An organbath experiment with bovine tracheal muscle strips with cumulative increases in concentrations of a substance A in the absence and presence of a fixed concentration of a second substance B is considered as an example for demonstrating graphical methods to analyse drug combination effects. The response of each strip is individually described and estimated by a nonlinear dose response curve. From the curves of the combined action theoretical curves of substance A are derived, which were expected if the combination effect was simple similar or independent, respectively. The first graphical method consists in comparing the derived curves for substance A with the curves for substance A directly fitted. It is cheeked by eye if the group of derived curves can clearly be distinguished from the group of directly fitted curves. The second graphical method differs from the first method in so far, as not the curves are visualized but the parameter vectors corresponding to them. In contrast to widely used analytical methods the proposed graphical methods allow to treat individual instead of averaged dose response relationships. The methods can help to decide if the combination effect may be considered as independent, simple similar or none of both.     

Time-resolved fluorescence resonance energy transfer studies of DNA bending in double-stranded oligonucleotides and in DNA-protein complexes

Time-resolved F?rster resonance energy transfer (trFRET) has been used to obtain interdye distance distributions. These distributions give the most probable distance as well as a parameter, sigma, that characterize the width of the distribution. This latter parameter contains information not only on the flexibility of the dyes tethered to macromolecules, but on the flexibility of the macromolecules. Both the most probable interdye distance as well as sigma provide insight into DNA static bending and DNA flexibility. Time-resolved fluorescence anisotropy and static anisotropy measurements can be combined to provide a measure of the cone angle within which the tethered dyes appear to wobble. When this motion is an order of magnitude faster than the average lifetime that characterizes transfer, an average value of the dipolar orientational parameter kappa2 can be calculated for various mutual dye orientations. The resulting kappa2 distribution is very much narrower than the limiting values of 0 and 4, allowing more precise distances and distance changes to be determined. Static and time-resolved fluorescence data can be combined to constrain the analyses of DNA-protein kinetics to provide thermodynamic parameters for binding and for conformational changes along a reaction coordinate. The parameter sigma can be used to model multiple DNA-protein complexes with varying DNA bend angles in a global fitting of trFRET data. Such a global fitting approach has shown how the range of bends in single base DNA variants, when bound by the TATA binding protein (TBP), can be understood in terms of two limiting forms. Time-resolved FRET, combined with steady-state FRET, can be used to show not only how osmolytes affect the binding of DNA to proteins, but also how DNA bending depends on osmolyte concentration in the DNA-protein complexes.