Quantitative Interpretation Of Experimental Data Research Articles

A method to assess the robustness of complex mathematical models used for quantitative interpretation of experimental data by nonlinear regression analysis: application to high-affinity binding models.

Nonlinear regression is widely used to fit experimental data to a specific mathematical model to extract numerical values for parameters representing the studied process. However, assessing the degree of precision that can be expected from such an analysis for a given parameter can be quite challenging for complex mathematical models. To address this issue, we propose here a method based on the analysis of a large number of data sets generated in such a way to mimic specific experimental conditions. Applying this methodology to high-affinity binding models, we report here a quantitative analysis of the robustness of such models, and how the precision on the fitting parameters can be expected to vary based on, e.g., the initial experimental conditions, the number or distribution of experimental points, or the experimental variability. We also show that these models, although widely used, are intrinsically limited by the fact that the two main fitting parameters, one representing the concentration of the studied species and the other its affinity, are inversely correlated, but demonstrate that this limitation can be overcome by global analysis of multiple data series generated at different concentrations of the titrated species.

Nanoparticle and Bioparticle Deposition Kinetics: Quartz Microbalance Measurements.

Controlled deposition of nanoparticles and bioparticles is necessary for their separation and purification by chromatography, filtration, food emulsion and foam stabilization, etc. Compared to numerous experimental techniques used to quantify bioparticle deposition kinetics, the quartz crystal microbalance (QCM) method is advantageous because it enables real time measurements under different transport conditions with high precision. Because of its versatility and the deceptive simplicity of measurements, this technique is used in a plethora of investigations involving nanoparticles, macroions, proteins, viruses, bacteria and cells. However, in contrast to the robustness of the measurements, theoretical interpretations of QCM measurements for a particle-like load is complicated because the primary signals (the oscillation frequency and the band width shifts) depend on the force exerted on the sensor rather than on the particle mass. Therefore, it is postulated that a proper interpretation of the QCM data requires a reliable theoretical framework furnishing reference results for well-defined systems. Providing such results is a primary motivation of this work where the kinetics of particle deposition under diffusion and flow conditions is discussed. Expressions for calculating the deposition rates and the maximum coverage are presented. Theoretical results describing the QCM response to a heterogeneous load are discussed, which enables a quantitative interpretation of experimental data obtained for nanoparticles and bioparticles comprising viruses and protein molecules.

Temperature dependence of dislocation-related photoluminescence (D1) of self-implanted silicon subjected to additional boron implantation

The goal of this work is the qualitative and quantitative interpretation of experimental data obtained for the effect of additional boron ion implantation on the temperature dependence of dislocation-related luminescence (D1 line) of self-implanted silicon. This goal is motivated by the need in development of effective light emitter for silicon-based optoelectronics. The model explaining the previously established improvement of the D1 line temperature dependence is suggested and supported by computer calculations based on a set of kinetic equations taking into account the radiative and nonradiative electron transitions between energy levels.

A Study of Fracture Scenarios on the Basis of Acoustic Emission Data

A system of equations for studying the fracture of solids has been formulated using a physico-mathematical model that describes the heat and mass transfer in heterogeneous media. The derived relations are used to analyze the energy balance equation and to study the fracture of a concrete sample under uniaxial compression. The analysis is performed by a quantitative interpretation of experimental data on two acoustic emission amplitude and frequency spectra recorded during sample loading. The spectra provided data on the time evolution of the structural characteristics of the material and were used to evaluate the relationship between the rates of change of surface energy and acoustic emission intensity per unit volume of the compressed concrete sample at the time of recording the spectra. Conditions for the occurrence of possible fracture scenarios by the time of recording the second spectrum were investigated. With experimental data on acoustic emission amplitude-frequency spectra for more than two time points, it is possible to study in more detail the changes in the structural characteristics, surface energy, and acoustic emission intensity per unit volume of a solid. The beginning of particular fracture stages can be predicted with higher accuracy.

Bromate electroreduction from sulfuric acid solution at rotating disk electrode: Experimental study

Our recent theoretical analysis of the bromate reduction from acidic media at rotating disk electrode (RDE) under steady-state conditions gave astonishing predictions for the current at the plateau of the voltammogram (called “the maximal current”, jmax) which deviated cardinally from those for the previously known mechanisms of electrochemical processes. Because of the non-electroactivity of the bromate anion itself, its transformation (without an added catalyst) can only take place owing to the redox cycle composed of the rapid reduction of bromine species (which are always present in low amounts inside strongly acidic solutions of bromates) into bromide ions at the electrode and of the comproportionation reaction between bromate and bromide ions inside the solution phase which regenerates bromine molecules. According to this theory, owing to the autocatalytic features of this mechanism the dependence of the maximal current density, jmax, on the RDE revolution frequency, f, is complicated. In particular, it includes a range of relatively low frequencies where the maximal current can exceed the bromate diffusion-limited one, even for tracer amounts of bromine in the bulk solution. Another surprising conclusion of the theory is the existence of an intermediate range of frequencies (“anomalous region”) where the maximal current increases if the rotation frequency diminishes, i.e. for the weaker agitation intensity. This study presents the first experimental verification of these predictions for a series of bromate solutions of various concentrations in 2 M sulfuric acid. Qualitative analysis of these experimental data has confirmed the principal theoretical expectations, first of all the existence of the anomalous region of frequencies. At the same time it has been found that the previously published theoretical model based on the literature data for the parameters of the system (diffusion coefficients of solution components, rate constant of the comproportionation reaction, etc.) corresponding to dilute solutions is not able to provide a quantitative interpretation of experimental data. An advanced variant of the theory has been proposed that takes into account the dependence of these parameters on the solution composition, first of all on the effect of the acid concentration. Comparison of predictions of this model with experimental data has shown their quantitative agreement, i.e. the simulated plots for the dependence, jmax(f), turned out to be close to experimental data within the whole range of frequencies available experimentally. This result represents an unambiguous proof of validity both of the principles of the underlying theory of this process and of the predictions derived within its framework.

Theoretical models of Rashba spin splitting in asymmetric SrTiO3 -based heterostructures

Rashba spin splitting in two-dimensional (2D) semiconductor systems is generally calculated in a ${\bf k} \cdot {\bf p}$ Luttinger-Kohn approach where the spin splitting due to asymmetry emerges naturally from the bulk band structure. In recent years, several new classes of 2D systems have been discovered where electronic correlations are believed to have an important role. In these correlated systems, the effects of asymmetry leading to Rashba splitting have typically been treated phenomenologically. We compare these two approaches for the case of 2D electron systems in SrTiO$_3$-based heterostructures, and find that the two models produce fundamentally different behavior in regions of the Brillouin zone that are particularly relevant for magnetotransport. Our results demonstrate the importance of identifying the correct approach in the quantitative interpretation of experimental data, and are likely to be relevant to a range of 2D systems in correlated materials.

Vibrational Probes: From Small Molecule Solvatochromism Theory and Experiments to Applications in Complex Systems.

The vibrational frequency of a chosen normal mode is one of the most accurately measurable spectroscopic properties of molecules in condensed phases. Accordingly, infrared absorption and Raman scattering spectroscopy have provided valuable information on both distributions and ensemble-average values of molecular vibrational frequencies, and these frequencies are now routinely used to investigate structure, conformation, and even absolute configuration of chemical and biological molecules of interest. Recent advancements in coherent time-domain nonlinear vibrational spectroscopy have allowed the study of heterogeneous distributions of local structures and thermally driven ultrafast fluctuations of vibrational frequencies. To fully utilize IR probe functional groups for quantitative bioassays, a variety of biological and chemical techniques have been developed to site-specifically introduce vibrational probe groups into proteins and nucleic acids. These IR-probe-labeled biomolecules and chemically reactive systems are subject to linear and nonlinear vibrational spectroscopic investigations and provide information on the local electric field, conformational changes, site-site protein contacts, and/or function-defining features of biomolecules. A rapidly expanding library of data from such experiments requires an interpretive method with atom-level chemical accuracy. However, despite prolonged efforts to develop an all-encompassing theory for describing vibrational solvatochromism and electrochromism as well as dynamic fluctuations of instantaneous vibrational frequencies, purely empirical and highly approximate theoretical models have often been used to interpret experimental results. They are, in many cases, based on the simple assumption that the vibrational frequency of an IR reporter is solely dictated by electric potential or field distribution around the vibrational chromophore. Such simplified description of vibrational solvatochromism generally referred to as vibrational Stark effect theory has been considered to be quite appealing and, even in some cases, e.g., carbonyl stretch modes in amide, ester, ketone, and carbonate compounds or proteins, it works quantitatively well, which makes it highly useful in determining the strength of local electric field around the IR chromophore. However, noting that the vibrational frequency shift results from changes of solute-solvent intermolecular interaction potential along its normal coordinate, Pauli exclusion repulsion, polarization, charge transfer, and dispersion interactions, in addition to the electrostatic interaction between distributed charges of both vibrational chromophore and solvent molecules, are to be properly included in the theoretical description of vibrational solvatochromism. Since the electrostatic and nonelectrostatic intermolecular interaction components have distinctively different distance and orientation dependences, they affect the solvatochromic vibrational properties in a completely different manner. Over the past few years, we have developed a systematic approach to simulating vibrational solvatochromic data based on the effective fragment potential approach, one of the most accurate and rigorous theories on intermolecular interactions. We have further elucidated the interplay of local electric field with the general vibrational solvatochromism of small IR probes in either solvents or complicated biological systems, with emphasis on contributions from non-Coulombic intermolecular interactions to vibrational frequency shifts and fluctuations. With its rigorous foundation and close relation to quantitative interpretation of experimental data, this and related theoretical approaches and experiments will be of use in studying and quantifying the structure and dynamics of biomolecules with unprecedented time and spatial resolution when combined with time-resolved vibrational spectroscopy and chemically sensitive vibrational imaging techniques.

Established Static Models of Spin Crossover

AbstractVarious models describing the stationary temperature‐induced phenomenon of spin crossover in metal complexes are briefly discussed. The emphasis is put on the usability of the presented models as tools for the quantitative interpretation of experimental data. The empirical approaches are first reviewed, which are usually called thermodynamic models or Ising‐like models depending on their macroscopic or microscopic representation. These form a suitable reference base for the other, more principal approaches that covers ligand field models, elasticity models and vibronic models for which interpretation of the ad hoc parameters is offered and eventually new consequences are appearing. Finally, insight into Monte Carlo modelling is presented, which appears as a perspective for theoretical analysis of spin transition.

Reconstructing the temporal changes in the structural-petrophysical characteristics of a disintegrating massif of rocks

Using the proposed algorithm as a basis, we performed the quantitative interpretation of experimental data on several temporally successive high-amplitude radon anomalies. As a result, the relative changes in the open porosity, the specific internal surface, and the pressure of a deteriorating massif of rocks were restored.

Mechanisms of Fibrinogen Adsorption at Solid Substrates

Adsorption of fibrinogen, modeled as a linear chain of touching beads of various sizes, was theoretically studied using the random sequential adsorption (RSA) model. The adsorption process was assumed to consist of two steps: (i) formation of an irreversibly bound fibrinogen monolayer under the side-on orientation, which is independent of the bulk protein concentration and (ii) formation of the reversibly bound, end-on monolayer, whose coverage was dependent on the bulk concentration. Calculation based on the RSA model showed that the maximum surface concentration of the end-on (reversible) monolayer equals N(⊥∞) = 6.13 × 10(3) μm(-2) which is much larger than the previously found value for the side-on (irreversible) monolayer, equal to N(∞) = 2.27 × 10(3) μm(-2). Hence, the maximum surface concentration of fibrinogen in both orientations is determined to be 8.40 × 10(3) μm(-2) corresponding to the protein coverage of 5.70 mg m(-2) assuming 20% hydration. Additionally, the surface blocking function (ASF) was determined for the end-on fibrinogen adsorption, approximated for the entire range of coverage by the interpolating polynomial. For the coverage approaching the jamming limit, the surface blocking function (ASF) was shown to vanish proportionally to (θ(⊥∞) - θ(⊥))(2). These calculation allowed one to theoretically predict adsorption isotherms for the end-on regime of fibrinogen and adsorption kinetics under various transport conditions (diffusion and convection). Using these theoretical results, a quantitative interpretation of experimental data obtained by TIRF and ellipsometry was successfully performed. The equilibrium adsorption constant for the end-on adsorption regime was found to be 8.04 × 10(-3) m. On the basis of this value, the depth of the adsorption energy minimum, equal to -17.4 kT, was predicted, which corresponds to ΔG = -41.8 kJ mol(-1). This is in accordance with adsorption energy derived as the sum of the van der Waals and electrostatic interactions. Besides having significance for predicting fibrinogen adsorption, theoretical results derived in this work also have implications for basic science providing information on mechanisms of anisotropic protein molecule adsorption on heterogeneous surfaces.

Iterative Optimization of Molecular Mechanics Force Fields from NMR Data of Full-Length Proteins.

High quality molecular mechanics force fields of proteins are key for the quantitative interpretation of experimental data and the predictive understanding of protein function based on computer simulations. A strategy is presented for the optimization of protein force fields based on full-length proteins in their native environment that is guided by experimental NMR chemical shifts and residual dipolar couplings (RDCs). An energy-based reweighting approach is applied to a long molecular dynamics trajectory, performed with a parent force field, to efficiently screen a large number of trial force fields. The force field that yields the best agreement with the experimental data is then used as the new parent force field, and the procedure is repeated until no further improvement is obtained. This method is demonstrated for the optimization of the backbone φ,ψ dihedral angle potential of the Amber ff99SB force field using six trial proteins and another 17 proteins for cross-validation using (13)C chemical shifts with and without backbone RDCs. The φ,ψ dihedral angle potential is systematically improved by the inclusion of correlation effects through the addition of up to 24 bivariate Gaussian functions of variable height, width, and tilt angle. The resulting force fields, termed ff99SB_φψ(g24;CS) and ff99SB_φψ(g8;CS,RDC), perform significantly better than their parent force field in terms of both NMR data reproduction and Cartesian coordinate root-mean-square deviations between the MD trajectories and the X-ray crystal structures. The strategy introduced here represents a powerful addition to force field optimization approaches by overcoming shortcomings of methods that are solely based on quantum-chemical calculations of small molecules and protein fragments in the gas phase.

Kinks and waterfalls in the dispersion of ARPES features

In this paper we use a generic form for the Green function G( k, ω) in a correlated metal, already proven successful in describing ARPES line shapes [1]. The associated many body self-energy function has only a single pole. We now investigate, whether this generic model can be used all the way to the limit of strong correlations and, when applied to ARPES intensities, whether it is able to explain some of the ubiquitous dispersive crossover phenomena that have been attributed to dynamical, i.e.: ω-dependent effects. We argue that a quantitative interpretation of experimental data requires to calculate extrema not only in the momentum distribution curve but also in the energy distribution curve. In passing, we give a formula for the extrema in the latter distribution that is valid for the general G( k, ω) in a many body system. To our knowledge, this is a new formula, not found in the literature. The investigation of the generic model proceeds on two levels: on the one hand, we explore the rich variety of crossovers that can be predicted and linked to well defined features in the complex ω-plain. On the other hand, we show that the generic one-pole self-energy can be viewed as a projection on the low energy sector of a microscopic solution, belonging to a lattice model of interacting fermions. To obtain approximate microscopic solutions, we use our continued fraction method [2,3]. As an explicit example, we study the projection for the case of a hole doped Hubbard model in infinite dimension. A discussion section gives examples, how the generic model is able to cope with the ubiquity of the crossover phenomena, also in finite dimension and beyond the Hubbard model.

Kinetic assessment on the autohydrolysis of pectin-rich by-products

Fractionation in aqueous media is an environmentally friendly technology suitable for obtaining oligomeric products from pectins and hemicelluloses. Sugar beet pulp (SBP) samples were subjected to aqueous processing under non-isothermal conditions to reach maximal temperatures in the range 140–200 °C, in order to cause the conversion of pectins into soluble compounds of lower molecular weight with potential applications as prebiotic ingredients. Mixtures of arabinooligosaccharides, oligogalacturonides and oligomers made up of other structural units were obtained by non-isothermal processing of SBP in aqueous media. Kinetic models suitable for reproducing and predicting compositional data of reaction liquors as a function of the operational conditions were developed. According to the model predictions, the maximum arabinooligosaccharides yield (15.7 g/100 g SBP) corresponded to a treatment carried out to achieve 171.5 °C. Alternatively, the maximum oliogogalacturonide yield (14.1 g/100 g SBP) was predicted for a treatment performed to achieve 158.2 °C. In both cases, the overall yield of oligomeric saccharides was near to 30 g/100 g dry SBP, whereas the oligosaccharide mixture of higher purity was obtained operating at 158.2 °C. Depending on the operational conditions, SBP processing in aqueous media yielded oligomers with different compositional profiles. The developed models were suitable for a quantitative interpretation of experimental data, and provided key information for both design calculations and economic evaluation.

Diafiltration of Eucalyptus wood autohydrolysis liquors: Mathematical modeling

Liquors from the aqueous processing of Eucalyptus wood were diafiltered through a nanofiltration ceramic membrane, and experimental data concerning the time-course of flux and concentrations of the different compounds present in the medium (monosaccharides, oligosaccharides, oligosaccharide substituents and other non-volatile compounds) were determined. A mathematical model based on a combination of osmotic pressure and an additional in-series resistance provided a quantitative interpretation of experimental data.

Comparison of Microtubule Dynamics for A- and B-Lattice Geometries

Accurate quantitative interpretation of experimental data and prediction of the effects of microtubule-targeted anti-mitotic drugs require a detailed model of the events that occur at microtubule ends. Before searching the large parameter space of a model with few constraints on lattice symmetry, binding site configuration, GTP-hydrolysis rate, and oligomerisation state of the associating and dissociating species, we performed an extensive, systematic investigation into the dynamics of a series of simplified models with significantly smaller parameter spaces. The models had regular A or B-lattice geometries, tightly coupled GTP-hydrolysis, and association-dissociation events involving the formation or breakage of just two lateral bonds. GTP-hydrolysis weakened the two lateral bonds to the β-tubulin subunit by 4.6 kBT, in either a balanced (+2.3 kBT each) or an unbalanced way (+4.6 kBT for one and 0 for the other bond). Association rate constants were 1 μM-1s-1, and dissociation rates were thus dependent on the lateral bond energies. We observed the following:1. Values for CC (the concentration of free tubulin-GTP at which the net growth is zero) varied from 1.2 to 80 μM2. All configurations showed discernable phases of growth (G) and shrinkage (S) around their CC3. Effective growth rates at CC (average growth rate during the G-phase divided by the maximum attainable growth rate at that CC) varied from less than 0.1 in most of the B-lattice geometries to 0.9 in the A-lattices with a balanced effect of hydrolysis4. G-phase lifetimes were relatively short (10-15 s), and growth was significantly more uniform in the balanced A-lattice geometries, compared with those in the unbalanced geometries (lifetimes > 100 s)Thus, balanced A-lattice configurations support efficient growth on relatively unstable microtubule ends, whereas most other configurations grow less efficiently on more stable ends.

Charge density distribution at interfaces between polyelectrolyte layers and aqueous solutions—Experimental access and limitations of traditional electrokinetics

Charge formation within surface-confined polyelectrolyte layers (PL)—including biopolymer films—is of highest importance in the application of biomedical materials in demanding products. However, due to the lack of adequate analytical tools the impact of electrical charging on the intra- and intermolecular structure of surface-confined PL so far remained poorly understood. The traditional characterization of hard surfaces by electrokinetic (zeta potential) measurements cannot be applied for the characterization of the internal structure of thick PL, although the traditional electrokinetics remains important for characterizing PL/electrolyte interfaces. Systematic investigations revealed that surface conductivity (SC) measurements provide a unique opportunity for the characterization of PL, including the determination of Donnan and surface potentials, maximal PL charge at complete dissociation, fractional PL charge, counterion condensation, and even PL thickness. This was achieved through advanced electrokinetic measurements in microchannels and an extension of the related theoretical modeling. A serious restriction in modeling as well as in the quantitative interpretation of experimental data is the assumption of a uniform segment distribution within the PL while the gradual decay of the segment concentration with the distance to the solid surface is rather abundant. Recently, we showed that the concept of local Donnan potentials holds true for cases of a nonuniform segment concentration if the characteristic length h of the segment concentration decay exceeds the Debye length κ m −1 of the PL. We demonstrate that the incorporation of the concept of local Donnan potentials into the SC theory permits us to derive an analytical equation for the fractional charge of PL and for the SC at nonuniform segment distribution. In addition, the measurement of the fractional PL charge can provide information about layer thickness, the length of the segment concentration decay, and concentration values near the solid surface and near the PL/electrolyte interface.

Using Long-Term Anomalies in Radon Concentration to Study the Characteristics of Destructive Processes in a Geologic Environment

A technique for studying long-term radon anomalies is proposed. It is intended for anomalies originating from a impulse of the radon concentration generated in a center of destruction during the period of its activation. This technique has been used for quantitative interpretation of experimental data during determination of the spatiotemporal characteristics of a center of destruction and parameters of radon migration.

Calculation of anharmonic vibrational spectroscopy of small biological molecules

R. B. Gerber, B. Brauer, S. K. Gregurick and G. M. Chaban, PhysChemComm, 2002, 5, 142 DOI: 10.1039/B208000A

Rejection of single salts versus transmembrane volume flow in RO/NF: thermodynamic properties, model of constant coefficients, and its modification

The general features of dependences of single salt rejection on the transmembrane volume flow in RO/NF are analysed thermodynamically for a macroscopically homogeneous membrane. At no concentration polarisation (CP), the rejection is shown to monotonely approach a limiting value irrespective of the rejection mechanism. The popular approximation of constant transport coefficients introduced by Spiegler and Kedem yields correct asymptotics of rejection at both small and large transmembrane volume flows. Therefore, it often works relatively well also at intermediate volume flow. However, when the transport coefficients essentially depend on the salt concentration, that approximation is not suitable for a really quantitative interpretation of experimental data. That is demonstrated for the model of charged membrane in the limiting case of excluded coions. The analytical solution obtained in this case is semi-empirically extended to the cases when the dependence of transport coefficients on salt concentration is not that pronounced. The applicability of new semi-empirical equation is checked by the comparison with model numerical calculations as well as some experimental data. It is shown that, in principle, the new approach may work essentially better than the classical Spiegler–Kedem method, especially in the mode of considerable CP, which often occurs in membrane modules used for practical separations. However, to make a real use of potentialities of new approach, much more careful and purposeful bench-scale measurements of salt rejection have to be performed than currently common.

INTERPRETATION OF REFLECTION HIGH ENERGY ELECTRON DIFFRACTION FROM DISORDERED SURFACES: DYNAMICAL THEORY AND ITS APPLICATION TO THE EXPERIMENT

Reflection high energy electron diffraction (RHEED) is one of the few surface science techniques that are applied in a fabrication process, namely to monitor the epitaxial growth of ultrathin films and advanced materials. In spite of this technological relevance the multiple scattering nature of the involved scattering processes has hindered the quantitative interpretation of RHEED in the case of real, i.e. imperfect, surfaces for a long time. This article reviews recent progress in the understanding of RHEED from surfaces exhibiting various types of disorder. It concentrates on a multiple scattering formalism — based on perturbation theory with the nonperiodic part of the structure as perturbation — that allows the computation and interpretation of RHEED from real systems. The validity regime of the approach is discussed. We demonstrate the potential of the method by its application to the quantitative interpretation of experimental data. The range of treated problems comprises occupational disorder, intensity oscillations, structure of disordered metal/adsorbate systems, diffuse scattering from adatoms, Kikuchi scattering and phonon scattering.