The application of robust calibration to radioimmunoassay.

The minute concentrations of many biochemically and clinically important substances are currently estimated by radioimmunoassay (RIA). Traditionally, the most popular approaches to the statistical analysis of RIA data have been to linearize the data through transformation and fit the calibration curve using least squares or to directly fit a nonlinear calibration curve using least squares. Estimates of the hormone concentration in patients are then obtained using this curve. Unfortunately, the transformation is frequently unsuccessful in linearizing the data. Furthermore, the least squares fit can lead to erroneous results in both approaches since the many sources of error which exist in the RIA process often result in outlier observations. In this paper, an approach to the analysis of RIA data which incorporates robust estimation methods is described. An algorithm is presented for obtaining the M-estimates of nonlinear calibration curves. The curves to be fitted are modified hyperbolae based on 12 to 16 observations. A procedure, based on the application of the Bonferroni Inequality, is presented for obtaining tolerance-like interval estimates of the concentration of the hormone of interest in the patients. Results of simulations are cited to support the method of construction of confidence bands for the fitted calibration curve. Data obtained from the Veteran's Hospital, Buffalo, New York are used to illustrate the application of the algorithm which is presented.     

Solution NMR structure of an immunodominant epitope of myelin basic protein. Conformational dependence on environment of an intrinsically unstructured protein

Using solution NMR spectroscopy, three-dimensional structures have been obtained for an 18-residue synthetic polypeptide fragment of 18.5 kDa myelin basic protein (MBP, human residues Q81-T98) under three conditions emulating the protein's natural environment in the myelin membrane to varying degrees: (a) an aqueous solution (100 mM KCl pH 6.5), (b) a mixture of trifluoroethanol (TFE-d2) and water (30 : 70% v/v), and (c) a dispersion of 100 mM dodecylphosphocholine (DPC-d38, 1 : 100 protein/lipid molar ratio) micelles. This polypeptide sequence is highly conserved in MBP from mammals, amphibians, and birds, and comprises a major immunodominant epitope (human residues N83-T92) in the autoimmune disease multiple sclerosis. In the polypeptide fragment, this epitope forms a stable, amphipathic, alpha helix under organic and membrane-mimetic conditions, but has only a partially helical conformation in aqueous solution. These results are consistent with recent molecular dynamics simulations that showed this segment to have a propensity to form a transient alpha helix in aqueous solution, and with electron paramagnetic resonance (EPR) experiments that suggested a alpha-helical structure when bound to a membrane [I. R. Bates, J. B. Feix, J. M. Boggs & G. Harauz (2004) J Biol Chem, 279, 5757-5764]. The high sensitivity of the epitope structure to its environment is characteristic of intrinsically unstructured proteins, like MBP, and reflects its association with diverse ligands such as lipids and other proteins.     

A 1H-NMR study of the solution conformation of secretin. Resonance assignment and secondary structure

The solution conformation of the 27 residue polypeptide hormone secretin has been investigated by 1H-NMR spectroscopy under conditions where it adopts a fully ordered structure as judged by circular dichroism spectroscopy, namely in an aqueous solution of 40% (v/v) trifluoroethanol. Using a combination of two-dimensional NMR techniques the 1H-NMR spectrum of secretin is completely assigned and its secondary structure is determined from a qualitative interpretation of the nuclear Overhauser enhancement data. It is shown that under these conditions secretin adopts a conformation consisting of an N-terminal irregular strand (residues 1-6) followed by two helices (residues 7-13 and 17-25) connected by a 'half-turn' (residues 14-16); the last two residues (26 and 27) are again irregular. This conformation is shown to be very similar to that of glucagon in perdeuterated dodecylphosphocholine micelles and to that of the active 1-29 fragment of growth hormone releasing factor in 30% (v/v) trifluoroethanol:     

Use and abuse of variance models in regression

In (nonlinear) regression with heteroscedastic errors, introduction of a variance model can be useful to obtain good estimators of the regression parameter. For example, the variance model can be used to obtain the optimal weights in weighted least squares. Methodology of this kind is often used in the analysis of assay data in clinical chemistry, pharmacokinetics, and toxicology. In a series of papers in the pharmacological literature, Sheiner and Beal and others advocate the extended least squares (ELS) methodology that combines regression and variance model into a single objective function based on normal-theory maximum likelihood. The inadequacy of this method is folklore in the (mathematical) statistical literature. In this article it is pointed out that this methodology may lead to inconsistent estimators in practically relevant situations. A review is given of other methods that may be preferable to ELS.     

New Methods for Characterization of Complex Receptor Systems Involving 3 or More Binding Sites: Application to Brain Opiate Receptors

Abstract

The problems of evaluating results based on the analysis of complex binding models are considered and new methods are proposed to provide independent confirmation of the existence of multiple sites. A new plotting format for the results from experiments involving two ligands is introduced, and its utility is demonstrated for a) finding initial estimates for nonlinear least squares curve fitting; b) presenting the results of multiple experiments; and c) giving a new means for evaluating the significance of a third site. The general problem of finding initial estimates for models involving three classes of sites, and strategies for using nonlinear least squares curve fitting algorithms to optimize the fit are considered.     

Avian pancreatic polypeptide fragments refold to native aPP conformation when combined in solution: a CD and VCD study

An equimolar mixture of avian pancreatic polypeptide (aPP) fragments aPP(1-11)-NH2 and Ac-aPP(12-36) had an electronic circular dichroism (ECD) spectrum that was similar to that of whole aPP in H2O and even more so in 30% (v/v) trifluoroethanol (TFE) in 15 mM Na2HPO4, but was different from the sum of the spectra of the individual fragments. The vibrational circular dichroism (VCD) spectrum of the combined fragments in 30% (v/v) TFE in 15 mM Na2HPO4 in D2O was also similar to that of the intact aPP and unlike the sum of the VCD spectra of the fragments. The interaction of these fragments is thus sufficient to support the conformation of whole aPP. This study demonstrates that VCD, in combination with ECD, is useful for the study of protein-protein interactions.     

Dissecting the effect of trifluoroethanol on ribonuclease A. Subtle structural changes detected by nonspecific proteases.

With the aim to distinguish between local and global conformational changes induced by trifluoroethanol in RNase A, spectroscopic and activity measurements in combination with proteolysis by unspecific proteases have been exploited for probing structural transitions of RNase A as a function of trifluoroethanol concentration. At > 30% (v/v) trifluoroethanol (pH 8.0; 25 degrees C), circular dichroism and fluorescence spectroscopy indicate a cooperative collapse of the tertiary structure of RNase A coinciding with the loss of its enzymatic activity. In contrast to the denaturation by guanidine hydrochloride, urea or temperature, the breakdown of the tertiary structure in trifluoroethanol is accompanied by an induction of secondary structure as detected by far-UV circular dichroism spectroscopy. Proteolysis with the nonspecific proteases subtilisin Carlsberg or proteinase K, both of which attack native RNase A at the Ala20-Ser21 peptide bond, yields refined information on conformational changes, particularly in the pretransition region. While trifluoroethanol at concentrations > 40% results in a strong increase of the rate of proteolysis and new primary cleavage sites (Tyr76-Ser77, Met79-Ser80) were identified, the rate of proteolysis at trifluoroethanol concentrations < 40% (v/v) is much smaller (up to two orders of magnitude) than that of the native RNase A. The proteolysis data point to a decreased flexibility in the surrounding of the Ala20-Ser21 peptide bond, which we attribute to subtle conformational changes of the ribonuclease A molecule. These changes, however, are too marginal to alter the overall catalytic and spectroscopic properties of ribonuclease A.     

Why, when, and how biochemists should use least squares.

One of the most commonly used methods for the analysis of experimental data in the biochemical literature is nonlinear least squares (regression). This group of methods are also commonly misused. The purpose of this article is to review the assumptions inherent in the use of least-squares techniques and how these assumptions govern the ways that least-squares techniques can and should be used. Since these assumptions pertain to the nature of the experimental data to be analyzed they also dictate many aspects of the data collection protocol. The examination of these assumptions includes a discussion of questions like: Why would a biochemist want to use nonlinear least-squares techniques? When is it appropriate for a biochemist to use nonlinear least-squares techniques? What confidence can be assigned to the results of a nonlinear least-squares analysis?     

Beaded nanofibers assembled from double‐hydrophobic elastin‐like block polypeptides: Effects of trifluoroethanol

A “double‐hydrophobic” elastin‐like triblock polypeptide GPG has been constructed by mimicking the localization of proline‐ and glycine‐rich hydrophobic domains of native elastin, a protein that provides elasticity and resilience to connective tissues. In this study, the effects of trifluoroethanol (TFE), an organic solvent that strongly affects secondary structures of polypeptides on self‐assembly of GPG in aqueous solutions were systematically studied. Beaded nanofiber formation of GPG , where nanoparticles are initially formed by coacervation of the polypeptides followed by their connection into one‐dimensional nanostructures, is accelerated by the addition of TFE at the concentrations up to 30% (v/v), whereas aggregates of nanoparticles are formed at 60% TFE. The concentration‐dependent assembly pattern discussed is based on the influence of TFE on the secondary structures of GPG . Well‐defined nanofibers whose diameter and secondary structures are controlled by TFE concentration may be ideal building blocks for constructing bioelastic materials in tissue engineering. © 2014 Wiley Periodicals, Inc. Biopolymers 103: 175–185, 2015.     

Treatment of missing values for multivariate statistical analysis of gel-based proteomics data

The presence of missing values in gel-based proteomics data represents a real challenge if an objective statistical analysis is pursued. Different methods to handle missing values were evaluated and their influence is discussed on the selection of important proteins through multivariate techniques. The evaluated methods consisted of directly dealing with them during the multivariate analysis with the nonlinear estimation by iterative partial least squares (NIPALS) algorithm or imputing them by using either k-nearest neighbor or Bayesian principal component analysis (BPCA) before carrying out the multivariate analysis. These techniques were applied to data obtained from gels stained with classical postrunning dyes and from DIGE gels. Before applying the multivariate techniques, the normality and homoscedasticity assumptions on which parametric tests are based on were tested in order to perform a sound statistical analysis. From the three tested methods to handle missing values in our datasets, BPCA imputation of missing values showed to be the most consistent method.     

Conformational properties of the isolated 1-23 fragment of human hemoglobin alpha-chain

With the purpose of establishing whether, as a general rule, regions of a protein chain that are helical in the native structure maintain, at least partially, the same helical structure when isolated in solution, we have prepared the 1-23 fragment of human hemoglobin alpha-chain, and studied its conformational properties in aqueous solution by CD and 1H-NMR. From the analysis of CD and NMR spectral changes with temperature, salt and addition of trifluoroethanol (TFE) it can be concluded that the 1-23 peptide forms a measurable population (18% at 22 degrees C (pH 5.6) TFE/H2O, 30:70 (v/v)) of an alpha-helix structure that spans the same residues that are helical in the native protein (namely, 6 to 17). These results, taken together with similar ones obtained previously in the 1-19, 21-42 and 50-61 RNAase fragments, support the idea that no helices other than the native ones are actually formed in solution by protein fragments. This implies that the final helical structure of a protein is present from the very beginning of the folding process, and also that such elements of secondary structure can act as primary nucleation centers.     

Main-chain Dynamics of a Partially Folded Protein:15N NMR Relaxation Measurements of Hen Egg White Lysozyme Denatured in Trifluoroethanol

¹⁵N NMR relaxation measurements have been used to study the dynamic behaviour of the main-chain of hen lysozyme in a partially folded state, formed in a 70% (v/v) trifluoroethanol (TFE)/30% water mixture at 37°C and pH 2. This state is characterised by helical secondary structure in the absence of extensive tertiary interactions. The NMR relaxation data were interpreted by mapping of spectral density functions and by derivation of segmental as well as global order parameters. The results imply that the dynamics of lysozyme in TFE can, at least for the great majority of residues, be adequately described by internal motions which are superimposed on an overall isotropic tumbling of the molecule. Although the dynamic behaviour shows substantial variations along the polypeptide chain, it correlates well with the conformational preferences identified in the TFE state by other NMR parameters. Segments of the polypeptide chain which are part of persistent helical structures are highly restricted in their motion (S²> 0.8, with effective internal correlation times τ_e< 200 ps) but are also found to experience conformational exchange on a millisecond timescale. Regions which are stabilised in less persistent helical structure possess greater flexibility (0.6 <S²< 0.8, 200 ps < τ_e< 1 ns) and those which lack defined conformational preferences are highly flexible (S²< 0.6, τ_e∼1 ns). The dynamic behaviour of the main-chain was found to be correlated with other local features of the polypeptide chain, including hydrophobicity and the position of the disulphide bridges. Despite the absence of extensive tertiary interactions, preferential stabilisation of native-like secondary structure by TFE results in a pattern of main-chain dynamics which is similar to that of the native state.     

Solvent effects on the conformation of the transmembrane peptide gramicidin A: insights from electrospray ionization mass spectrometry

The binding of sodium ions to the transmembrane channel peptide gramicidin A has permitted the use of electrospray ionization mass spectrometry to study its conformation in different solvent environments. The mass spectra of the peptide in the various solvents suggest that different conformations of gramicidin A differ in their ability to bind metal ions. The data are consistent with monomeric behavior of gramicidin A in trifluoroethanol and dimethyl sulfoxide solutions, but reveal the presence of noncovalent intermolecular interactions in ethanol solution through the observation of heterodimers formed between the naturally occurring variants of the peptide. The addition of 50% v/v of water to the ethanolic solution causes changes in the circular dichroism spectrum of the peptide, suggestive of a shift in the equilibrium mixture of conformers present toward monomeric species, a result supported by its mass spectrum. The structure of gramicidin A in trifluoroethanol has also been investigated by hydrogen exchange measurements monitored by mass spectrometry. The observation of significant protection against exchange suggests that the monomeric peptide is highly structured in trifluoroethanol. The results indicate that mass spectrometry has the potential to probe the conformational behavior of neutral hydrophobic peptides in environments that mimic their functional states.     

Alcohol induced structural and dynamic changes in β-lactoglobulin in aqueous solution: A neutron scattering study

Structural and dynamic properties of β-lactoglobulin (β-LG) were revealed as a function of alcohol concentration in ethanol- and trifluoroethanol(TFE)-water mixtures with circular dichroism (CD), small-angle neutron scattering (SANS) and quasi-elastic neutron scattering (QENS). The CD spectra showed that an increase in TFE concentration promotes the formation of the β-sheet structure of β-LG. The SANS-intensities were fitted using form factors for two attached spheres for the native and native-like states of the protein. At higher alcohol concentrations, where aggregation takes place, a form factor modelling diffusion limited colloidal aggregation (DLCA) was employed. The QENS-data were analyzed in terms of internal motions for all alcohol concentrations. While low concentrations of TFE (10% (v/v)) lead to an increase of the mean square amplitudes of vibrations and a retention of a native-like structure - but not to an increase of the characteristic radius of proton diffusion processes a. Addition of 20% (v/v) of TFE induces aggregation, going along with a further increase of . Further increase of TFE concentration to 30% (v/v) changes the nanoscale structure of the oligomeric nucleate, but induces no further significant changes in . The present study underlines the necessity of methods sensitive to the dynamics of a system to obtain a complete picture of a molecular process.     

Structural requirements for thymosin beta4 in its contact with actin. An NMR-analysis of thymosin beta4 mutants in solution and correlation with their biological activity.

We examined the conformational preferences of mutants of thymosin beta4, an actin monomer sequestering protein by NMR spectroscopy in 60% (v/v) trifluoroethanol. Under these conditions, the wild-type thymosin beta4 conformation consists of an alpha-helix (helix I) extending from residues 5-16 with a more stable fragment from lysine 11 to lysine 16 and a second alpha-helix (helix II) encompassing residues 31-39. The point mutations studied here are located in helix I or in the LKKTET segment (residues 17-22) that form the two main entities of interaction with the actin molecule. The alpha-1H conformational shifts allow us to investigate the helicity of the polypeptides at the residue level and to correlate these structures with their biological activity. We determine that an extension of helix I at its C-terminal end over the LKK-segment results in loss of activity. The correct termination of this helix is connected to a specific orientation of the polypeptide essential for a cooperative action of the thymosin beta4 binding entities required for full activity.     

A review of some statistical methods for covariance analysis of categorical data

Three general methods for covariance analysis of categorical data are reviewed and applied to an example from a clinical trial in rheumatoid arthritis. The three methods considered are randomization-model nonparametric procedures, maximum likelihood logistic regression, and weighted least squares analysis of correlated marginal functions. A fourth heuristic approach, the unweighted linear model analysis, is an approximate procedure but it is easy to implement. The assumptions and statistical issues for each method are discussed so as to emphasize philosophical differences between their rationales. Attention is given to computational differences, but it is shown that the methods lead to similar results for analogous problems. It is argued that the essential differences between the methods lie in their underlying assumptions and the generality of the conclusions which may be drawn.     

Vesicle sizing: Number distributions by dynamic light scattering

A procedure is described which optimizes nonnegative least squares and exponential sampling fitting methods for analysis of dynamic light scattering (DLS) data from aqueous suspensions of vesicle/liposome systems. This approach utilizes a Rayleigh-Gans-Debye form factor for a coated sphere and yields number distributions which can be compared directly to distributions obtained by freeze-fracture electron microscopy (EM). Excellent agreement between the DLS and EM results are obtained for vesicle size distributions in the 100-200-nm range.     

Hodgkin-Huxley type ion channel characterization: an improved method of voltage clamp experiment parameter estimation

The Hodgkin-Huxley formalism for quantitative characterization of ionic channels is widely used in cellular electrophysiological models. Model parameters for these individual channels are determined from voltage clamp experiments and usually involve the assumption that inactivation process occurs on a time scale which is infinitely slow compared to the activation process. This work shows that such an assumption may lead to appreciable errors under certain physiological conditions and proposes a new numerical approach to interpret voltage clamp experiment results. In simulated experimental protocols the new method was shown to exhibit superior accuracy compared to the traditional least squares fitting methods. With noiseless input data the error in gating variables and time constants was less than 1%, whereas the traditional methods generated upwards of 10% error and predicted incorrect gating kinetics. A sensitivity analysis showed that the new method could tolerate up to approximately 15% perturbation in the input data without unstably amplifying error in the solution. This method could also assist in designing more efficient experimental protocols, since all channel parameters (gating variables, time constants and maximum conductance) could be determined from a single voltage step.     

Snake inhibitors of phospholipase A(2) enzymes

Fragment 53--103 of bovine alpha-lactalbumin, prepared by limited peptic digestion of the protein at low pH, is a 51-residue polypeptide chain crosslinked by two disulfide bonds encompassing helix C (residues 86--98) of the native protein. Refolding of the fully reduced fragment (four--SH groups) is expected to lead to three fully oxidized isomers, the native (61--77, 73--91) and the two misfolded species named ribbon (61--91, 73--77) and beads (61--73, 77--91) isomers. The fragment with correct disulfide bonds was formed in approx. 30% yield when refolding was conducted in aqueous solution at neutral pH in the presence of the redox system constituted by reduced and oxidized glutathione. On the other hand, when the reaction was conducted in 30% (v/v) trifluoroethanol (TFE), the oxidative refolding to the native isomer was almost quantitative. To provide an explanation of the beneficial effect of TFE in promoting the correct oxidative folding, the conformational features of the various fragment species were analyzed by far-UV circular dichroism measurements. The fully reduced fragment is largely unfolded in water, but it becomes helical in aqueous TFE. Correctly refolded fragment is produced most when the helical contents of the reduced and oxidized fragment in aqueous TFE are roughly equal. It is proposed that 30% TFE promotes a native-like format of the fragment and thus an efficient and correct pairing of disulfides. Higher concentrations of TFE, instead, promote some non-native helical secondary structure in the fragment species, thus hampering correct folding.     

Integrated framework of nonlinear prediction and process monitoring for complex biological processes

Bioprocesses and biosystems have nonlinear and multiple operation patterns depending on the influent loads, temperatures, the activity of microorganisms, and other factors. In this paper, an integrated framework of nonlinear modeling and process monitoring methods is developed for a complex biological process. The proposed method is based on modeling by fuzzy partial least squares (FPLS) and on process monitoring by a statistical decomposition, which is suitable for predicting and supervising a nonlinear biological process. Case studies in the bio-simulated process and industrial biological plant show that the proposed method can give superior prediction and monitoring performance in complex biological plants compared to other linear and nonlinear methods, since it can effectively capture the nonlinear causal relationship within the biosystem. This gives us the integrated framework that is able to both model and monitor the nonlinear bioprocess simultaneously.