Nonlinear viscoelastic behavior of styrene‐[ethylene‐(ethylene‐propylene)]‐styrene block copolymer

Studies on the nonlinear viscoelastic behavior of styrene‐[ethylene‐(ethylene‐propylene)]‐styrene block copolymer (SEEPS) were carried out. The nonlinear viscoelastic region was determined through dynamic strain sweep test, and the critical shear strain (γ_c) of transition from linear viscoelastic region to nonlinear viscoealstic region was obtained. The relaxation time and modulus corresponding to the characteristic relaxation modes were also acquired through simulating the linear relaxation modulus curves using Maxwell model, and the damping functions were evaluated. Meanwhile, it is found that the nonlinear relaxation modulus obtained at relatively low shear strains follows the strain–time separation principle, and the damping function of SEEPS can be fit to Laun double exponential model well. Moreover, the successive start‐up of shear behavior, the steady shear behavior, and the relaxation behavior after steady shear were investigated, respectively. The results showed that Wagner model, derived from the K‐BKZ (Kearsley‐Bernstein, Kearsley, Zapas) constitutive equation, could simulate the experiment data well, and in addition, experiment data under the lower shear rates are almost identical with the fitting data, but there exists some deviation for data under considerable high shear rates. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1309–1319, 2006     

Design of Nonlinear Model‐Based Control Using Bifurcation Analysis for Solution Polymerizations Carried Out in Lumped‐Distributed Reactors

In order to implement nonlinear control, nonlinear system identification must be performed, however, there are open questions concerning this field of process control, for example, experimental planning, model structure selection, parameter estimation, and validation. Therefore, the study of nonlinear model identification is a relevant unsolved problem that needs to be handled for nonlinear control synthesis. This paper presents the use of bifurcation theory, dynamic and stability analysis for nonlinear identification, and control of polymerization reactors. Peroxide‐initiated styrene‐solution polymerization reactors (lumped‐distributed) are investigated: batch, continuous stirred‐tank reactor (CSTR), and tubular reactors. Open and closed loop analyses are carried out using jacket temperature and weight average molecular weight setpoints as the bifurcation parameters. Phenomenological mathematical models, neural network nonlinear models, and an experimental data from a polymerization unit are employed for validating the proposed methodology in order to implement confident nonlinear controllers.     

A self‐guided search for good local minima of the sum‐of‐squared‐error in nonlinear least squares regression

Hard modeling of nonlinear chemical or biological systems is highly relevant as a model function together with values for model parameters provides insights in the systems' functionalities. Deriving values for said model parameters via nonlinear regression, however, is challenging as usually one of the numerous local minima of the sum‐of‐squared errors (SSEs) is determined; furthermore, for different starting points, different minima may be found. Thus, nonlinear regression is prone to low accuracy and low reproducibility. Therefore, there is a need for a generally applicable, automated initialization of nonlinear least squares algorithms, which reaches a good, reproducible solution after spending a reasonable computation time probing the SSE‐hypersurface. For this purpose, a three‐step methodology is presented in this study. First, the SSE‐hypersurface is randomly probed in order to estimate probability density functions of initial model parameter that generally lead to an accurate fit solution. Second, these probability density functions then guide a high‐resolution sampling of the SSE‐hypersurface. This second probing focuses on those model parameter ranges that are likely to produce a low SSE. As the probing continues, the most appropriate initial guess is retained and eventually utilized in a subsequent nonlinear regression. It is shown that this “guided random search” derives considerably better regression solutions than linearization of model functions, which has so far been considered the best‐case scenario. Examples from infrared spectroscopy, cell culture monitoring, reaction kinetics, and image analyses demonstrate the broad and successful applicability of this novel method. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust and high‐resolution simulations of nonlinear electrokinetic processes in variable cross‐section channels

We present a model and an associated numerical scheme to simulate complex electrokinetic processes in channels with nonuniform cross‐sectional area. We develop a quasi‐1D model based on local cross‐sectional area averaging of the equations describing unsteady, multispecies, electromigration‐diffusion transport. Our approach uses techniques of lubrication theory to approximate electrokinetic flows in channels with arbitrary variations in cross‐section; and we include chemical equilibrium calculations for weak electrolytes, Taylor–Aris type dispersion due of nonuniform bulk flow, and the effects of ionic strength on species mobility and on acid–base equilibrium constants. To solve the quasi‐1D governing equations, we provide a dissipative finite volume scheme that adds numerical dissipation at selective locations to ensure both unconditional stability and high accuracy. We couple the numerical scheme with a novel adaptive grid refinement algorithm that further improves the accuracy of simulations by minimizing numerical dissipation. We benchmark our numerical scheme with existing numerical schemes by simulating nonlinear electrokinetic problems, including ITP and electromigration dispersion in CZE. Simulation results show that our approach yields fast, stable, and high‐resolution solutions using an order of magnitude less grid points compared to the existing dissipative schemes. To highlight our model's capabilities, we demonstrate simulations that predict increase in detection sensitivity of ITP in converging cross‐sectional area channels. We also show that our simulations of ITP in variable cross‐sectional area channels have very good quantitative agreement with published experimental data.     

A multidimensional approach to the analysis of chemical shift titration experiments in the frame of a multiple reaction scheme

We present a method for fitting curves acquired by chemical shift titration experiments, in the frame of a three‐step complexation mechanism. To that end, we have implemented a fitting procedure, based on a nonlinear least squares fitting method, that determines the best fitting curve using a “coarse grid search” approach and provides distributions for the different parameters of the complexation model that are compatible with the experimental precision. The resulting analysis protocol is first described and validated on a theoretical data set. We show its ability to converge to the true parameter values of the simulated reaction scheme and to evaluate complexation constants together with multidimensional uncertainties. Then, we apply this protocol to the study of the supramolecular interactions, in aqueous solution, between a lanthanide complex and three different model molecules, using NMR titration experiments. We show that within the uncertainty that can be evaluated from the parameter distributions generated during our analysis, the affinities between the lanthanide derivative and each model molecule can be discriminated, and we propose values for the corresponding thermodynamic constants. Copyright © 2013 John Wiley & Sons, Ltd.     

Skew‐normal linear calibration: a Bayesian perspective

In this paper, we present a Bayesian approach for estimation in the skew‐normal calibration model, as well as the conditional posterior distributions which are useful for implementing the Gibbs sampler. Data transformation is thus avoided by using the methodology proposed. Model fitting is implemented by proposing the asymmetric deviance information criterion, ADIC, a modification of the ordinary DIC. We also report an application of the model studied by using a real data set, related to the relationship between the resistance and the elasticity of a sample of concrete beams. Copyright © 2008 John Wiley & Sons, Ltd.     

Simultaneous determination of two‐component isotherm parameters and lumped mass transfer coefficients in RPLC with the 0‐1 model‐inverse method

The 0‐1 model‐inverse method of nonequilibrium nonlinear chromatography was developed to simultaneously determine the isotherm parameters and the lumped mass transfer coefficients of the two‐component systems in RPLC. By comparing the simulated elution curves with experimental curves with regard to profiles and areas, the suitable isotherm parameters and the lumped mass transfer coefficients were obtained with the 0‐1 model‐inverse method. With a solute cell unit width of cm, the average errors of the peak areas were 0.178% for one component and ?0.40% for two components, and the numerical diffusions of the 0‐1 model for the contribution to band broadening may be negligible. In addition, the results showed that the lumped mass transfer coefficients decrease as the solute concentration increases. The 0‐1 model‐inverse method has not only the advantages of high calculation speed (less than 10 min for one‐component systems or approximately 3 h for two‐component systems using an ordinary computer) and high accuracy in simultaneously obtaining thermodynamic parameters and kinetic parameters of two‐component systems, but this method also possesses the potential to optimally design and control the time‐variant preparative chromatographic system due to the thermodynamic state recursion and the Lagrangian‐Eulerian presentation of the 0‐1 model.     

Co‐evolution of non‐linear PLS model components

The issue of outer model weight updating is important in extending partial least squares (PLS) regression to modelling data that shows significant non‐linearity. This paper presents a novel co‐evolutionary component approach to the weight updating problem. Specification of the non‐linear PLS model is achieved using an evolutionary computational (EC) method that can co‐evolve all non‐linear inner models and all input projection weights simultaneously. In this method, modular symbolic non‐linear equations are used to represent the inner models and binary sequences are used to represent the projection weights. The approach is flexible, and other representations could be employed within the same co‐evolutionary framework. The potential of these methods is illustrated using a simulated pH neutralisation process data set exhibiting significant non‐linearity. It is demonstrated that the co‐evolutionary component architecture can produce results which are competitive with non‐linear neural network‐based PLS algorithms that use iterative projection weight updating. In addition, a data sampling method for mitigating overfitting to the training data is described. Copyright © 2007 John Wiley & Sons, Ltd.     

Short‐time stretch relaxation of entangled polymer solutions investigated using full Rouse model predictions

We conduct a systematical investigation into the short‐time stretch relaxation behavior (i.e., shorter than the Rouse time but sufficiently longer than the glassy time) of entangled polymer liquid in single‐step strain flows, on the basis of theory/data comparisons for a broad series of type‐A entangled polymer solutions. First, within existing normal‐mode formulations, the Rouse model predictions on a full‐chain stretch relaxation in single‐step strain flows are derived for a popular 1‐D model proposed within the Doi–Edwards tube model, as well as for the original 3‐D model for nonentangled systems. In addition, an existing formula for the aforementioned 1‐D model that, however, rested upon a consistent‐averaging or the so‐called uniform‐chain‐stretch approximation is simultaneously examined. Subsequently, the previously derived formulas on chain stretch relaxation are directly incorporated into a reliable mean‐field tube model that utilizes the linear relaxation spectrum and the Rouse time constant consistently determined from linear viscoelastic data. It is found that the predictions of the 1‐D model differ substantially from that of the original 3‐D model at short times. Theory/data comparisons further indicate that the 1‐D model without approximations seems able to describe fairly well the nonlinear relaxation data under investigation. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1199–1211, 2006     

Sample size determination for within‐device precision

The within‐device precision for quantitative assays is the square root of the total variance, which is defined as the sum of the between‐day, between‐run, and within‐run variances under a two‐stage nested random‐effects model. Currently, methods for point and interval estimations have been proposed. However, the literature on sample size determination for within‐device precision is scarce. We propose an approach for the determination of sample size for within‐device precision. Our approach is based on the probability for which the 100(1 − α)% upper confidence bound for the within‐device precision smaller than the pre‐specified claim is greater than 1 − β. We derive the asymptotic distribution of the confidence upper bound based on the modified large‐sample method for sample size determination and allocation. Our study reveals that the dominant term for sample size determination is the between‐day variance. Results of simulation studies are reported. An example with real data is used to illustrate the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.     

Modeling of salt and pH gradient elution in ion‐exchange chromatography

The separation of proteins by internally and externally generated pH gradients in chromatofocusing on ion‐exchange columns is a well‐established analytical method with a large number of applications. In this work, a stoichiometric displacement model was used to describe the retention behavior of lysozyme on SP Sepharose FF and a monoclonal antibody on Fractogel SO₃ (S) in linear salt and pH gradient elution. The pH dependence of the binding charge B in the linear gradient elution model is introduced using a protein net charge model, while the pH dependence of the equilibrium constant is based on a thermodynamic approach. The model parameter and pH dependences are calculated from linear salt gradient elutions at different pH values as well as from linear pH gradient elutions at different fixed salt concentrations. The application of the model for the well‐characterized protein lysozyme resulted in almost identical model parameters based on either linear salt or pH gradient elution data. For the antibody, only the approach based on linear pH gradients is feasible because of the limited pH range useful for salt gradient elution. The application of the model for the separation of an acid variant of the antibody from the major monomeric form is discussed.     

Mechanism of Iron Oxide Formation from Iron Pentacarbonyl‐Doped Low‐Pressure Hydrogen/Oxygen Flames

A chemical reaction mechanism was developed for the formation of iron oxide (Fe₂O₃) from iron pentacarbonyl (Fe(CO)₅) in a low‐pressure hydrogen–oxygen flame reactor. In this paper, we describe an extensive approach for the flame‐precursor chemistry and the development of a novel model for the formation of Fe₂O₃ from the gas phase. The detailed reaction mechanism is reduced for the implementation in two‐dimensional, reacting flow simulations. The comprehensive simulation approach is completed by a model for the formation and growth of the iron oxide nanoparticles. The exhaustive and compact reaction mechanism is validated using experimental data from iron‐atom laser‐induced fluorescence imaging. The particle formation and growth model are verified with new measurements from particle mass spectrometry.     

Self‐ and cross‐associations in two‐component mixed polymer gels

The gel properties of two‐component mixed polymer gels are investigated using a cascade model, which assumes that the gel network is formed via the self‐association of one of the two components and the cross‐association of the two components. The effects of the model parameters, such as the equilibrium constants and the functionalities for cross‐associations and self‐associations, on the composition dependence of the modulus and gel point curves are examined to elucidate the contribution of self‐associations to the gel network. The results show that the characteristics of self‐associations become pronounced when the equilibrium constant or the functionality for self‐associations is comparable to that for cross‐associations. The model is applied to analyze the critical gelling concentration data for xanthan/locust bean gum mixed gels, which shows significant self‐associations at high xanthan compositions. The resulting model curves agree well with the experimental data at all temperatures. The analysis of the temperature dependence of the best‐fit equilibrium constant yields values of enthalpy change that are consistent with previous findings. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 80–91, 2008     

ST‐PLS: a multi‐directional nearest shrunken centroid type classifier via PLS

The nearest shrunken centroid (NSC) Classifier is successfully applied for class prediction in a wide range of studies based on microarray data. The contribution from seemingly irrelevant variables to the classifier is minimized by the so‐called soft‐thresholding property of the approach. In this paper, we first show that for the two‐class prediction problem, the NSC Classifier is similar to a one‐component discriminant partial least squares (PLS) model with soft‐shrinkage of the loading weights. Then we introduce the soft‐threshold‐PLS (ST‐PLS) as a general discriminant‐PLS model with soft‐thresholding of the loading weights of multiple latent components. This method is especially suited for classification and variable selection when the number of variables is large compared to the number of samples, which is typical for gene expression data. A characteristic feature of ST‐PLS is the ability to identify important variables in multiple directions in the variable space. Both the ST‐PLS and the NSC classifiers are applied to four real data sets. The results indicate that ST‐PLS performs better than the shrunken centroid approach if there are several directions in the variable space which are important for classification, and there are strong dependencies between subsets of variables. Copyright © 2007 John Wiley & Sons, Ltd.     

High‐throughput ultra‐high‐performance liquid chromatography/tandem mass spectrometry quantitation of insulin‐like growth factor‐I and leucine‐rich α‐2‐glycoprotein in serum as biomarkers of recombinant human growth hormone administration

Insulin‐like growth factor‐I (IGF‐I) is a known biomarker of recombinant human growth hormone (rhGH) abuse, and is also used clinically to confirm acromegaly. The protein leucine‐rich α‐2‐glycoprotein (LRG) was recently identified as a putative biomarker of rhGH administration. The combination of an ACN depletion method and a 5‐min ultra‐high‐performance liquid chromatography/tandem mass spectrometry (uHPLC/MS/MS)‐based selected reaction monitoring (SRM) assay detected both IGF‐I and LRG at endogenous concentrations. Four eight‐point standard addition curves of IGF‐I (16–2000 ng/mL) demonstrated good linearity (r² = 0.9991 and coefficients of variance (CVs) <13%). Serum samples from two rhGH administrations were extracted and their uHPLC/MS/MS‐derived IGF‐I concentrations correlated well against immunochemistry‐derived values. Combining IGF‐I and LRG data improved the separation of treated and placebo states compared with IGF‐I alone, further strengthening the hypothesis that LRG is a biomarker of rhGH administration. Artificial neural networks (ANNs) analysis of the LRG and IGF‐I data demonstrated an improved model over that developed using IGF‐I alone, with a predictive accuracy of 97%, specificity of 96% and sensitivity of 100%. Receiver operator characteristic (ROC) analysis gave an AUC value of 0.98. This study demonstrates the first large scale and high throughput uHPLC/MS/MS‐based quantitation of a medium abundance protein (IGF‐I) in human serum. Furthermore, the data we have presented for the quantitative analysis of IGF‐I suggest that, in this case, monitoring a single SRM transition to a trypsin peptide surrogate is a valid approach to protein quantitation by LC/MS/MS. Copyright © 2009 John Wiley & Sons, Ltd.     

Force‐field parameters of the Ψ and Φ around glycosidic bonds to oxygen and sulfur atoms

The Ψ and Φ torsion angles around glycosidic bonds in a glycoside chain are the most important determinants of the conformation of a glycoside chain. We determined force‐field parameters for Ψ and Φ torsion angles around a glycosidic bond bridged by a sulfur atom, as well as a bond bridged by an oxygen atom as a preparation for the next study, i.e., molecular dynamics free energy calculations for protein‐sugar and protein‐inhibitor complexes. First, we extracted the Ψ or Φ torsion energy component from a quantum mechanics (QM) total energy by subtracting all the molecular mechanics (MM) force‐field components except for the Ψ or Φ torsion angle. The Ψ and Φ energy components extracted (hereafter called “the remaining energy components”) were calculated for simple sugar models and plotted as functions of the Ψ and Φ angles. The remaining energy component curves of Ψ and Φ were well represented by the torsion force‐field functions consisting of four and three cosine functions, respectively. To confirm the reliability of the force‐field parameters and to confirm its compatibility with other force‐fields, we calculated adiabatic potential curves as functions of Ψ and Φ for the model glycosides by adopting the Ψ and Φ force‐field parameters obtained and by energetically optimizing other degrees of freedom. The MM potential energy curves obtained for Ψ and Φ well represented the QM adiabatic curves and also these curves' differences with regard to the glycosidic oxygen and sulfur atoms. Our Ψ and Φ force‐fields of glycosidic oxygen gave MM potential energy curves that more closely represented the respective QM curves than did those of the recently developed GLYCAM force‐field. © 2009 Wiley Periodicals, Inc., J Comput Chem, 2009     

Estimation of monomer reactivity ratios in free‐radical solution copolymerization of lauryl methacrylate–isobutyl methacrylate

Copolymers of isobutyl methacrylate (i‐BMA) and lauryl methacrylate (LMA) were prepared by free‐radical solution copolymerizations at 70 °C with azobisisobutyronitrile (AIBN) as an initiator. The synthesis of these copolymers was investigated over a wide composition range both at low and high conversion levels. Copolymer compositions were determined from the %C, %H, and %O contents of copolymer by elemental analysis. Monomer reactivity ratios were estimated by analyzing composition data with nonlinear least‐squares (NLLS) models based on Marquardt optimization and van Herk methods. The point estimates, 95% individual confidence intervals and 95% joint confidence intervals are obtained from differential and integral approaches. Even though no explicit integral form for penultimate unit model (PUM) is available, a numerical approach is developed for integral estimation of reactivity ratios from PUM. A simulator program was developed which upon coupling of experimental data, NLLS analysis, and D‐optimal criteria calculates the best optimized values of monomer reactivity ratios and monomer feed compositions in a sequential and iterative order for terminal and penultimate unit models. Moreover, the simulator has the capibilities to calculate all features of van Herk method, maximum compositional drift in each monomer feed composition, and data reconciliation. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 112–129, 2004     

Mitigating dead‐time effects during multivariate analysis of ToF‐SIMS spectral images

ToF‐SIMS spectra are formed by bombarding a surface with a pulse of primary ions and detecting the resultant ionized surface species using a time‐of‐flight mass spectrometer. Typically, the detector is a time‐to‐digital converter. Once an ion is detected using such detectors, the detector becomes insensitive to the arrival of additional ions for a period termed as the (detector) dead‐time. Under commonly used ToF‐SIMS data acquisition conditions, the time interval over which ions arising from a single chemical species reach the detector is on the order of the detector dead‐time. Thus, only the first ion reaching the detector at any given mass is counted. The event registered by the data acquisition system, then, is the arrival of one or more ions at the detector. This behavior causes ToF‐SIMS data to violate, in the general case, the assumption of linear additivity that underlies many multivariate statistical analysis techniques. In this article, we show that high‐mass‐resolution ToF‐SIMS spectral‐image data follow a generalized linear model, and we propose a data transformation and scaling procedure that enables such data sets to be successfully analyzed using standard methods of multivariate image analysis. Copyright © 2008 John Wiley & Sons, Ltd.     

A Direct Fluorescent Activity Assay for Glycosyltransferases Enables Convenient High‐Throughput Screening: Application to O‐GlcNAc Transferase

Glycosyltransferases carry out important cellular functions in species ranging from bacteria to humans. Despite their essential roles in biology, simple and robust activity assays that can be easily applied to high‐throughput screening for inhibitors of these enzymes have been challenging to develop. Herein, we report a bead‐based strategy to measure the group‐transfer activity of glycosyltransferases sensitively using simple fluorescence measurements, without the need for coupled enzymes or secondary reactions. We validate the performance and accuracy of the assay using O‐GlcNAc transferase (OGT) as a model system through detailed Michaelis–Menten kinetic analysis of various substrates and inhibitors. Optimization of this assay and application to high‐throughput screening enabled screening for inhibitors of OGT, leading to a novel inhibitory scaffold. We believe this assay will prove valuable not only for the study of OGT, but also more widely as a general approach for the screening of glycosyltransferases and other group‐transfer enzymes.