Analytical bounding functions for diffusion problems with michaelis-menten kinetics

Pointwise upper and lower bounds for the solution of a class of nonlinear diffusion problems with Michaelis-Menten kinetics are presented. Simple analytical bounding curves are obtained and for an illustrative case the calculated values bound the recent numerical solution of P. Hiltmann and P. Lory, 1983.Bull. math. Biol. 45, 661–664.     

Validation of Bayesian analysis of compartmental kinetic models in medical imaging

IntroductionKinetic compartmental analysis is frequently used to compute physiologically relevant quantitative values from time series of images. In this paper, a new approach based on Bayesian analysis to obtain information about these parameters is presented and validated.Materials and methodsThe closed-form of the posterior distribution of kinetic parameters is derived with a hierarchical prior to model the standard deviation of normally distributed noise. Markov chain Monte Carlo methods are used for numerical estimation of the posterior distribution. Computer simulations of the kinetics of F18-fluorodeoxyglucose (FDG) are used to demonstrate drawing statistical inferences about kinetic parameters and to validate the theory and implementation. Additionally, point estimates of kinetic parameters and covariance of those estimates are determined using the classical non-linear least squares approach.Results and discussionPosteriors obtained using methods proposed in this work are accurate as no significant deviation from the expected shape of the posterior was found (one-sided P > 0.08). It is demonstrated that the results obtained by the standard non-linear least-square methods fail to provide accurate estimation of uncertainty for the same data set (P < 0.0001).ConclusionsThe results of this work validate new methods for a computer simulations of FDG kinetics. Results show that in situations where the classical approach fails in accurate estimation of uncertainty, Bayesian estimation provides an accurate information about the uncertainties in the parameters. Although a particular example of FDG kinetics was used in the paper, the methods can be extended for different pharmaceuticals and imaging modalities.     

The folding and aggregation properties of a single KH-domain protein: Ribosome binding factor A (RbfA) from Pseudomonas aeruginosa

BackgroundRibosome-binding factor A from the pathogenic bacterium Pseudomonas aeruginosa (PaRbfA) is a small ribosome assembly factor, composed by a single KH domain, involved in the maturation of the 30S subunit. These domains are characterized by the ability to bind RNA or ssDNA and are often located in proteins involved in a variety of cellular functions. However, although the ability of proteins to fold properly, to misfold or to aggregate is of paramount importance for their cellular functions, limited information is available on these dynamic properties in the case of KH domains.MethodsPaRbfA thermodynamic stability and folding mechanism: Far-UV CD and fluorescence spectroscopy, stopped-flow kinetics and chevron plot analysis, site-directed mutagenesis. Fibrils characterization: FT-IR spectroscopy, Thioflavin T fluorescence, Transmission Electron Microscopy (TEM) and X-ray fibrils diffraction.ResultsQuantitative analysis of the (un)folding kinetics of PaRbfA show that, in vitro, the protein folds via a 3-states mechanism involving a transiently populated folding intermediate. We also provide experimental evidences that PaRbfA can form ordered fibrils endowed with cross-β structure even in mild conditions.ConclusionThese results lead to the hypothesis that the folding intermediate of PaRbfA may expose (some of) the predicted amyloidogenic regions, which could act as aggregation nuclei in the fibrillogenesis.General significanceThe methodological approach presented herein could be readily adapted to verify the ability of other KH domain proteins to form cross-β structured fibrils and to transiently populate a folding intermediate.     

Continuous cultivation of fission yeast: Analysis of single-cell protein synthesis kinetics

A fundamental problem in microbial reactor analysis is identification of the relationship between environment and individual cell metabolic activity. Population balance equations provide a link between experimental measurements of composition frequency functions in microbial populations on the one hand and macromolecular synthesis kinetics and cell division control parameters for single cells on the other. Flow microfluorometry measurements of frequency functions for single-cell protein content in Schizosaccharomyces pombe in balanced exponential growth have been analyzed by two different methods. One approach utilizes the integrated form of the population balance equation known as the Collins-Richmond equation, and the other method involves optimization of parameters in assumed kinetic and cell division functional forms in order to best fit measured frequency functions with corresponding model solutions. Both data interpretation techniques indicate that rates of protein synthesis increase most in small protein content cells as the population specific growth rate increases, leading to parabolic single-cell protein synthesis kinetics at large specific growth rates. Utilization of frequency function data for an asynchronous population is shown in this case to be a far more sensitive method for determination of single-cell kinetics than is monitoring the metabolic dynamics of a single cell or, equivalently, synchronous culture analyses.     

Monte Carlo uncertainty analysis of dose estimates in radiochromic film dosimetry with single-channel and multichannel algorithms

PurposeTo provide a multi-stage model to calculate uncertainty in radiochromic film dosimetry with Monte-Carlo techniques. This new approach is applied to single-channel and multichannel algorithms.Material and methodsTwo lots of Gafchromic EBT3 are exposed in two different Varian linacs. They are read with an EPSON V800 flatbed scanner. The Monte-Carlo techniques in uncertainty analysis provide a numerical representation of the probability density functions of the output magnitudes. From this numerical representation, traditional parameters of uncertainty analysis as the standard deviations and bias are calculated. Moreover, these numerical representations are used to investigate the shape of the probability density functions of the output magnitudes. Also, another calibration film is read in four EPSON scanners (two V800 and two 10000XL) and the uncertainty analysis is carried out with the four images.ResultsThe dose estimates of single-channel and multichannel algorithms show a Gaussian behavior and low bias. The multichannel algorithms lead to less uncertainty in the final dose estimates when the EPSON V800 is employed as reading device. In the case of the EPSON 10000XL, the single-channel algorithms provide less uncertainty in the dose estimates for doses higher than four Gy.ConclusionA multi-stage model has been presented. With the aid of this model and the use of the Monte-Carlo techniques, the uncertainty of dose estimates for single-channel and multichannel algorithms are estimated. The application of the model together with Monte-Carlo techniques leads to a complete characterization of the uncertainties in radiochromic film dosimetry.     

Molecular Dynamics as a Mathematical Mapping. III. Efficient Evaluation of the Differentiable Force Functions and Their Derivatives

Abstract

The fully continuous and differentiable framework for performing molecular dynamics calculations introduced in parts I and II of this paper [1,2] requires the evaluation of rather complex force functions and their spatial partial derivatives. This paper presents an efficient interpolation scheme for the evaluation of these quantities over a finite spatial domain.

The modified force function is approximated by a linear combination of Hermite cubic basis functions such that both the interpolant of the force and its spatial derivatives are continuous across the grid boundaries. In order to achieve better accuracy for a given grid size, a nonuniform rectilinear grid is constructed via iterative refinement procedure. The latter guarantees the accuracy of the force computed by interpolation within any specified tolerance > ε O.

For many potential functions of practical interest, it is possible for polynomial interpolants to be constructed for parts of the force functions which are independent of the potential parameters and system density (the so-called “separable force functions”). In such cases, a single interpolation grid which is applicable for a wide range of potential parameters and system densities can be constructed a priori.     

The determination of sensitivity parameters for auxin-induced H+-efflux from Avena coleoptile segments

Abstract A method is described for the measurement of auxin-induced H⁺-efflux from small populations of Avena coleoptile segments. The method allows the simultaneous investigation of the kinetics of rapid auxin responses over a wide concentration range. IAA promoted linear rates of H⁺-efflux and the change in amplitude of response occurred mainly over a low, narrow concentration range (10–50 μmol m^-3). The sigmoidal curve of best-fit to each set of dose-response data was determined using non-linear regression techniques, allowing the objective determination of characteristic tissue sensitivity parameters (R_MIN, R_MAX, K_D and p). The sensitivity parameters for the auxin-type herbicide fluroxypyr are also presented as well as IAA parameters determined in the presence of abscisic acid and the ‘antiauxin’ PCIB. The interpretation of the parameter values and the potential use of sensitivity parameter analysis for the evaluation of theories concerning plant hormone action and interaction is discussed.     

Further evidence for the parallel pathway model of the metabolic control of the electrogenic pump inNitella as obtained from the high frequency slope of the action of light

Summary Previous investigations of the frequency response of the action of light on the membrane potential inNitella have revealed 5 time constants and 3 zeros in the range of 2 sec to 20 min. Now, the frequency range is extended by means of filter and correlation techniques to its upper theoretical limit of about 20 Hz. Thus the number of experimentally accessible time constants is increased from 5 to 8, the number of the zeros from 3 to 5. The time constant at 0.01 sec is shown to originate from the electrical impedance of the membrane. The other 7 time constants are labels for the reactions mediating the light effect, and the zeros provide information about the arrangement of these reactions. The new results support and extend the basic concept proposed by Hansen (Hansen, U.-P. 1978;J. Membrane Biol. 41: 197) that light acts via three parallel pathways on membrane potential. This model predicts two essential parameters obtained from the high-frequency measurements correctly from the data gained at low frequencies and is capable of reducing the great variety of measured curve shapes of the frequency responses to much smaller changes in two basic parameters.     

Untersuchungen zur Dynamik der Gärprozesse

A total of 37 dose‐response experiments with essential amino acids performed with rainbow trout and broiler chicken were re‐evaluated with different mathematical approaches: an exponential model, a four‐parameter logistic function, the saturation kinetics model and the broken line approach. The different approaches were compared both with regard to the goodness of fit (r² and s_y.x) and with regard to the allowances which were derived regarding the optimal amino acid level in the diet. The experimental design, particularly the chosen range in dietary amino acid concentration was found to be important for the comparison of models. Amongst the non‐linear models, the four‐parameter logistic function and the saturation kinetics model appeared superior to the exponential approach, when the range in dietary amino acid concentration was very wide and included both a severely deficient basal level and a level that exceeded the needs of the animal by approximately the factor 2. In these cases, allowances derived from individual experiments were considerably different depending on the model. The allowances based on the exponential and the saturation kinetics approach were 27.7 and 20.7 g lysine/kg DM and 8.0 and 6.3 g methionine/kg DM, respectively, for rainbow trout. For other amino acids studied in rainbow trout the difference due to model was less. Consequently, the predicted ‘ideal protein’ for rainbow trout was considerably different depending on the model used. The maximum deviation found in different experiments with broiler chicken for the exponential vs. the saturation kinetics approach was 13.0 and 9.7 g lysine/kg and 11.4 and 8.2 g sulfur‐containing amino acids/kg, respectively. However, the more restricted the range in dietary concentration was, the lesser became the differences between the different non‐linear models. No definite recommendation can therefore be extracted regarding the most suitable, generally applicable mathematical model.     

A versatile modelling approach to determine the hydrophobicity of peptides at the atomic level

This study describes a versatile computational method to determine the hydrophobicity of small peptides at the atomic level. Free energies of transfer for individual atoms in peptide structures were derived, utilising two specifically defined parameters: (i) the water-excluding distance to define the dynamic interface between a peptide solute and its surrounding solvent and (ii) the corresponding hydrophobicity index as a relative measure for water occlusion/repulsion. The method was tested on a range of small peptide models (Ac-X-NH₂, G-X-G, Ac-WL-X-LL and Ac-GG-X-GG-NH₂) and several derivatives of these structures, whereby X was any of the 20 most common amino acids that naturally occur in polypeptides or proteins. The advantage of this new method lies in its versatility, ease to implement and capability to provide information on the hydrophobicity characteristics at the atomic level. The approach also encapsulates the impact of factors that influence these properties, but which have hitherto been difficult to accurately quantify, e.g. steric hindrance or proximity effects due to nearby polarised atoms. The method is not conditional on the knowledge of hydrophobicity parameters from the literature and does not require a sophisticated computer software/hardware to enable the atomic solvent-accessible surface areas or other hydrophobicity parameters to be de novo obtained.     

Analysis of Trends in Proportions with an Ordinally Scaled Determinant

In this paper the analysis of several proportions in a comparative study setting is discussed. The case of ordinal grouping variates is considered. F statistics are formulated to test for trend in the proportions over the scored values of the determinant variate. The null chi-square or F (t square) functions are presented separately for the unstratified and stratified analysis, and in either situation the corresponding functions with angular transformed proportions are also expressed. Generalizations to deal with the parameters in the nonnull range are outlined. Throughout, the intimate relation between the presented statistics and standard methods is pointed out.     

Enzyme-catalyzed and binding reaction kinetics determined by titration calorimetry

BackgroundIsothermal calorimetry allows monitoring of reaction rates via direct measurement of the rate of heat produced by the reaction. Calorimetry is one of very few techniques that can be used to measure rates without taking a derivative of the primary data. Because heat is a universal indicator of chemical reactions, calorimetry can be used to measure kinetics in opaque solutions, suspensions, and multiple phase systems and does not require chemical labeling. The only significant limitation of calorimetry for kinetic measurements is that the time constant of the reaction must be greater than the time constant of the calorimeter which can range from a few seconds to a few minutes. Calorimetry has the unique ability to provide both kinetic and thermodynamic data.Scope of reviewThis article describes the calorimetric methodology for determining reaction kinetics and reviews examples from recent literature that demonstrate applications of titration calorimetry to determine kinetics of enzyme-catalyzed and ligand binding reactions.Major conclusionsA complete model for the temperature dependence of enzyme activity is presented. A previous method commonly used for blank corrections in determinations of equilibrium constants and enthalpy changes for binding reactions is shown to be subject to significant systematic error.General significanceMethods for determination of the kinetics of enzyme-catalyzed reactions and for simultaneous determination of thermodynamics and kinetics of ligand binding reactions are reviewed. This article is part of a Special Issue entitled Microcalorimetry in the BioSciences — Principles and Applications, edited by Fadi Bou-Abdallah.     

Design of delay-dependent state estimator for discrete-time recurrent neural networks with interval discrete and infinite-distributed time-varying delays

The state estimation problem for discrete-time recurrent neural networks with both interval discrete and infinite-distributed time-varying delays is studied in this paper, where interval discrete time-varying delay is in a given range. The activation functions are assumed to be globally Lipschitz continuous. A delay-dependent condition for the existence of state estimators is proposed based on new bounding techniques. Via solutions to certain linear matrix inequalities, general full-order state estimators are designed that ensure globally asymptotic stability. The significant feature is that no inequality is needed for seeking upper bounds for the inner product between two vectors, which can reduce the conservatism of the criterion by employing the new bounding techniques. Two illustrative examples are given to demonstrate the effectiveness and applicability of the proposed approach.     

Prediction of Protein Structure by Simulating Coarse-grained Folding Pathways: A Preliminary Report

Abstract

A set of software tools designed to study protein structure and kinetics has been developed. The core of these tools is a program called Folding Machine (FM) which is able to generate low resolution folding pathways using modest computational resources. The FM is based on a coarse-grained kinetic ab initio Monte-Carlo sampler that can optionally use information extracted from secondary structure prediction servers or from fragment libraries of local structure. The model underpinning this algorithm contains two novel elements: (a) the conformational space is discretized using the Ramachandran basins defined in the local φ-ψ energy maps; and (b) the solvent is treated implicitly by rescaling the pairwise terms of the non-bonded energy function according to the local solvent environments. The purpose of this hybrid ab initio/knowledge-based approach is threefold: to cover the long time scales of folding, to generate useful 3-dimensional models of protein structures, and to gain insight on the protein folding kinetics. Even though the algorithm is not yet fully developed, it has been used in a recent blind test of protein structure prediction (CASP5). The FM generated models within 6 Å backbone rmsd for fragments of about 60–70 residues of a-helical proteins. For a CASP5 target that turned out to be natively unfolded, the trajectory obtained for this sequence uniquely failed to converge. Also, a new measure to evaluate structure predictions is presented and used along the standard CASP assessment methods. Finally, recent improvements in the prediction of β-sheet structures are briefly described.     

A model of cell firing patterns during epileptic seizures

A simplified model is presented of the dynamics of excitatory and inhibitory neurons in the cerebral cortex. A key feature of the model is that neurons may cease to fire when strongly depolarized (spike inactivation). Computer simulations for different parameters reveal five classes of solutons: a) steady states in which neither excitatory nor inhibitory cells are active, b) steady states in which one or both types of cells fire repetitively, c) states in which one type of cell fluctuates rapidly between bursts of action potentials and inactivity due to strong depolarization, d) rhythmic activity in which both types of cells fire in unison followed by a period of spike inactivation and e) states similar to d but in which the inhibitory cells never produce action potentials. Solutions b, c, d, and e qualitatively resemble the different firing patterns observed during experimental seizures. It is shown that changes in those parameters that are functions of potassium concentration can induce changes in the type of solution. It is therefore proposed that the increase in extracellular potassium concentration during seizures may be responsible for the progressive changes observed in firing patterns and particularly for the transition from tonic to clonic patterns. A method is also outlined for testing the predictions of the model.     

Binding of Net-Fla,a Netropsin-Flavin Hybrid Molecule,to DNA: Molecular Mechanics and Dynamics Studies in vacuo and in Water Solution

Abstract

We have studied the binding of the hybrid netropsin-flavin (Net-Fla) molecule onto four sequences containing four A.T base pairs. Molecular mechanics minimizations in vacuo show numerous minimal conformations separated by one base pair. 400 ps molecular dynamics simulations in vacuo have been performed using the lowest minima as the starting conformations. During these simulations, the flavin moiety of the drug makes two hydrogen bonds with an amino group of a neighboring guanine. A 200 ps molecular dynamics simulation in explicit water solution suggests that the binding of Net-Fla upon the DNA substrate is enhanced by water bridges. A water molecule bridging the amidinium of Net-Fla to the N3 atom of an adenine seems to be stuck in the dmg-DNA complex during the whole simulation. The fluctuations of the DNA helical parameters and of the torsion angles of the sugar-phosphate backbone are very similar in the simulations in vacuo and in water. The time auto-correlation functions for the DNA helical parameters decrease rapidly in the picosecond range in vacuo. The same functions computed from the water solution molecular dynamics simulations seem to have two modes: the rapid mode is similar to the behavior in vacuo, and is followed by a slower mode in the 10 ps range.     

Nucleosome DNA Bendability Matrix (C. elegans)

Abstract

An original signal extraction procedure is applied to database of 146 base nucleosome core DNA sequences from C. elegans (S. M. Johnson et al. Genome Research 16, 1505–1516, 2006). The positional preferences of various dinucleotides within the 10.4 base nucleosome DNA repeat are calculated, resulting in derivation of the nucleosome DNA bendability matrix of 16x10 elements. A simplified one-line presentation of the matrix (“consensus” repeat) is…A(TTTCCGGAAA)T…. All 6 chromosomes of C. elegans conform to the bendability pattern. The strongest affinity to their respective positions is displayed by dinucleotides AT and CG, separated within the repeat by 5 bases. The derived pattern makes a basis for sequence-directed mapping of nucleosome positions in the genome of C. elegans. As the first complete matrix of bendability available the pattern may serve for iterative calculations of the species-specific matrices of bendability applicable to other genomic sequences.     

THE CROSSFLOW INJECTION TECHNIQUE: AN IMPROVEMENT OF THE ETHANOL INJECTION METHOD

ABSTRACT

A novel scalable liposome preparation technique for pharmaceutical application is presented. Previous experiments have shown that the concept of continuous crossflow injection is a promising approach. For the characterization of the process, we focus on the influencing parameters like the lipid concentration, the injection hole diameter, the injection pressure, the buffer flow rate, and system performance. These experiments demonstrate that the injection hole diameter and the system performance do not influence the vesicle forming process and that a minimum of buffer flow rate is required to affect batch homogeneity. In contrast, strongly influencing parameters are lipid concentration in combination with increasing injection pressures. After exceeding the upper pressure limit of the linear range, where injection velocities remain constant, the vesicle batches are narrowly distributed, also when injecting higher lipid concentrations. Reproducibility and scalability data show similar results with respect to vesicle size and size distribution and demonstrate the stability and robustness of the novel continuous liposome preparation technique.     

长江三峡上游水域细菌群落结构与功能预测

[目的]揭示三峡附近支流和长江干流细菌群落组成,共现网络特征和对网络有重要作用的中心节点微生物,进一步研究三峡上游水域细菌群落的代谢功能.[方法]本研究于长江北岸四条一级支流和附近干流(香溪河、大宁河、朱衣河、梅溪河、长江干流)采集水样,基于16SrRNA基因Pacbio测序技术和生物信息学方法分析细菌群落结构,Tax...     

The Influence of Protein Concentration on Oligomer Structure and Catalytic Function of Two Pyruvate Decarboxylases

As a general rule protein concentration typical for structural studies differs considerably from that chosen for kinetic investigations. Consequently, structure-function relationships are often postulated without appropriate knowledge, whether the functional behaviour of the enzyme is the same in both protein concentration ranges. To deal with this question, substrate activation kinetics of two well-characterised yeast pyruvate decarboxylases, from Saccharomyces cerevisiae and from Kluyveromyces lactis, were analysed over the broad protein concentration range 2-2,000 μg/mL. Analytical ultracentrifugation and small-angle X-ray scattering were used to analyse the enzymes’ oligomer structure in aqueous solution. For the upper part of the concentration range the determined parameters, like catalytic activity, observed substrate activation rates, sedimentation coefficients and scattering parameters are independent on enzyme concentration changes. No indication of protein aggregation is detectable. However, significant changes occur at low enzyme concentration. The catalytically active tetramer dissociates progressively into dimers with comparable catalytic activity, but with significantly accelerated substrate activation.