Determination of the association constants and maximum binding capacities between estradiol and cytosol of the uterus by the least-squares analysis of the Scatchard plot.

The association constants and the binding capacities of association of small molecules with macromolecules have been determined by the tangent analysis, the graphical analysis, and the computer data analysis, by trial and convergence of the Scatchard plot. The analytical method for the calculation of the binding parameters based on the Scatchard plot was derived and the optimum values of the binding parameters were obtained by the least squares calculation based on the analytical method. The errors by the analytical method were smaller than those by the graphical method in the equilibrium system between 3H-estradiol and some cytosols of uterus.     

Application of the median method to the determination of kinetic constants for competitive enzyme inhibition

A procedure was developed to determine kinetic constants for competitive inhibition (Km, Ki, Vmax) by the median method. Simulated experiments were used to compare the accuracy and precision of kinetic constants determined by the median method with unweighted and weighted least-squares analysis. The median method was superior to unweighted least-squares analysis. The weighted least-squares method was superior to the median method when the error was normally distributed but the median method was superior when two or more outliers were present. The dependence of the accuracy and precision of kinetic constants obtained by the median method on several experimentally important parameters, including the number of experimental points, the number and range of substrate concentrations, and the number and range of inhibitor concentrations, was determined.     

An analysis of Kohonen's self-organizing maps using a system of energy functions

In this paper a new method for analyzing Kohonen's self-organizing feature maps is presented. The method makes use of a system of energy functions, one energy function for each processing unit. It is shown that the training process is equivalent to minimizing each energy function subject to constraints. The analysis is used to prove the formation of topologically correct maps when the inherent dimensionality of the input patterns matches that of the network. The energy equations can be used to compute the steady-state weight values of the network. In addition, the analysis allows bounds on the training parameters to be determined. Finally, examples of energy landscapes are presented to graphically show the behavior of the network.     

A combined method for determining inhibition type, kinetic parameters, and inhibition coefficients for aerobic cometabolism of 1,1,1-trichloroethane by a butane-grown mixed culture.

A combined method for determining inhibition type, kinetic parameters, and inhibition coefficients is developed and presented. The method was validated by applying it to data obtained from batch kinetics of the aerobic cometabolism of 1,1,1-trichloroethane (1,1,1-TCA) by a butane-grown mixed culture. The maximum degradation rates (k(max)) and half-saturation coefficients (K(s)) were independently determined in single compound tests, and compared with those obtained from inhibition tests. The inhibition type was determined using direct linear plots at various substrate and inhibitor concentrations. Kinetic parameters (k(max) and K(s)) and inhibition coefficients (K(ic) and K(iu)) were determined by nonlinear least squares regression (NLSR) fits of the inhibition model determined from the direct linear plots. Initial guesses of the kinetic parameters for NLSR were determined from linearized inhibition equations that were derived from the correlations between apparent maximum degradation rates (k(app)(max)) and/or the apparent half-saturation coefficient (K(app)(s)) and the k(max), K(s), and inhibitor concentration (I(L)) for each inhibition equation. Two different inhibition types were indicated from the direct linear plots: competitive inhibition of 1,1,1-TCA on butane degradation, and mixed inhibition of 1,1,1-TCA transformation by butane. Good agreement was achieved between independently measured k(max) and K(s) values and those obtained from both NLSR and the linearized inhibition equations. The initial guesses of all the kinetic parameters determined from linear plots were in the range of the values estimated from NLSR analysis. Overall the results show that use of the direct linear plot method to identify the inhibition type, coupled with initial guesses from linearized plots for NLSR analysis, results in an accurate method for determining inhibition types and coefficients. Detailed studies with pure cultures and purified enzymes are needed to further demonstrate the utility of this method.     

Dynamic quenchers in fluorescently labeled membranes. Theory for quenching in a three-phase system.

The theory for quenching of fluorescently labeled membranes by dynamic quenchers is described for a three-phase system: a fluorescently labeled membrane, a nonlabeled membrane, and an aqueous phase. Two different experimental protocols are possible to determine quenching parameters. Using the first protocol, partition coefficients and bimolecular quenching constants were determined for a hydrophobic quencher in carbazole-labeled membranes in the presence of an unlabeled reference membrane. These parameters determined for 1,1-dichloro-2,2-bis(p-chlorophenyl)ethylene (DDE) using this three-phase analysis were in good agreement with values determined by a two-phase analysis without the reference lipid. Hence, the theory was verified. In the second protocol, the quencher partition coefficient was determined for unlabeled membranes in the presence of a carbazole-labeled reference membrane. Partition coefficients for DDE determined by this method were the same as partition coefficients determined for carbazole-labeled membranes using the two-phase analysis. The greater ease in determining partition coefficients and bimolecular quenching constants by the three-phase analysis and, in particular, the ability to determine the partition coefficient in unlabeled membranes make the three-phase analysis especially useful. This method was used to study the effect varying the membrane lipid composition has on the partition coefficient. The data indicate that partition coefficients of DDE in fluid membranes are not dramatically dependent upon polar head group composition, fatty acid composition, or cholesterol content. However, partitioning into gel-phase lipids is at least 100-fold less than fluid-phase lipids.     

Crystallographic evaluation of internal motion of human alpha-lactalbumin refined by full-matrix least-squares method

The low temperature form of human alpha-lactalbumin (HAL) was crystallized from a 2H2O solution and its structure was refined to the R value of 0.119 at 1.15 A resolution by the full-matrix least-squares method. Average estimated standard deviations of atomic parameters for non-hydrogen atoms were 0.038 A for coordinates and 0.044 A2 for anisotropic temperature factors (Uij). The magnitude of equivalent isotropic temperature factors (Ueqv) was highly correlated with the distance from the molecular centroid and fitted to a quadratic equation as a function of atomic coordinates. The atomic thermal motion was rather isotropic in the core region and the anisotropy increased towards the molecular surface. The statistical analysis revealed the out-of-plane motion of main-chain oxygen atoms, indicating that peptide groups are in rotational vibration around a Calpha.Calpha axis. The TLS model, which describes the rigid-body motion in terms of translation, libration, and screw motions, was adopted for the evaluation of the molecular motion and the TLS parameters were determined by the least-squares fit to Uij. The reproduced Ueqvcal from the TLS parameters was in fair agreement with observed Ueqv, but differences were found in regions of residues, 5-22, 44-48, 70-75, and 121-123, where Ueqv was larger than Ueqvcal because of large local motions. To evaluate the internal motion of HAL, the contribution of the rigid-body motion was determined to be 42.4 % of Ueqv in magnitude, which was the highest estimation to satisfy the condition that the Uijint tensors of the internal motion have positive eigen values. The internal motion represented with atomic thermal ellipsoids clearly showed local motions different from those observed in chicken-type lysozymes which have a backbone structure very similar to HAL. The result indicates that the internal motion is closely related to biological function of proteins.     

Global analysis of three-state protein unfolding data

A new method for analyzing three-state protein unfolding equilibria is described that overcomes the difficulties created by direct effects of denaturants on circular dichroism (CD) and fluorescence spectra of the intermediate state. The procedure begins with a singular value analysis of the data matrix to determine the number of contributing species and perturbations. This result is used to choose a fitting model and remove all spectra from the fitting equation. Because the fitting model is a product of a matrix function which is nonlinear in the thermodynamic parameters and a matrix that is linear in the parameters that specify component spectra, the problem is solved with a variable projection algorithm. Advantages of this procedure are perturbation spectra do not have to be estimated before fitting, arbitrary assumptions about magnitudes of parameters that describe the intermediate state are not required, and multiple experiments involving different spectroscopic techniques can be simultaneously analyzed. Two tests of this method were performed: First, simulated three-state data were analyzed, and the original and recovered thermodynamic parameters agreed within one standard error, whereas recovered and original component spectra agreed within 0.5%. Second, guanidine-induced unfolding titrations of the human retinoid-X-receptor ligand-binding domain were analyzed according to a three-state model. The standard unfolding free energy changes in the absence of guanidine and the guanidine concentrations at zero free-energy change for both transitions were determined from a joint analysis of fluorescence and CD spectra. Realistic spectra of the three protein states were also obtained.     

Numerical method to analyze pH-profile from initial velocity data and semi-empirical procedure to identify catalytic residues of enzymes using pK and heat of ionization

A numerical computing method to estimate pK and heat of ionization directly from initial velocity data was developed for systematic analysis of rate parameters. Values of rate and thermodynamic parameters were determined together with standard deviations, without using Arrhenius and van't Hoff plots. Distributions of pK and heat of ionization of small-molecular derivatives of aliphatic carboxylates, imidazoles, thiols, and aliphatic amines as possible models for catalytic residues of enzymes were analyzed from a thermodynamic point of view. Each group was classified in a parallelogram without overlapping, except for a part of the imidazole and thiol groups. It was shown that values of pK and heat of ionization of carboxylates and histidine residues involved in the catalytic activity of enzymes determined from pH-profile experiments can be classified into similar, though somewhat extended, areas to those of the corresponding small-molecular derivatives. Identification of catalytic residues using values of pK and heat of ionization is proved to be a reliable method when the procedure is properly used.     

A mass-length scaling law for modeling muscle strength in the lower limb

Musculoskeletal computer models are often used to study muscle function in children with and without impaired mobility. Calculations of muscle forces depend in part on the assumed strength of each muscle, represented by the peak isometric force parameter, which is usually based on measurements obtained from cadavers of adult donors. The aim of the present study was twofold: first, to develop a method for scaling lower-limb peak isometric muscle forces in typically-developing children; and second, to determine the effect of this scaling method on model calculations of muscle forces obtained for normal gait. Muscle volumes were determined from magnetic resonance (MR) images obtained from ten children aged from 7 to 13yr. A new mass-length scaling law was developed based on the assumption that muscle volume and body mass are linearly related, which was confirmed by the obtained volume and body mass data. Two musculoskeletal models were developed for each subject: one in which peak isometric muscle forces were estimated using the mass-length scaling law; and another in which these parameters were determined directly from the MR-derived muscle volumes. Musculoskeletal modeling and quantitative gait analysis were then used to calculate lower-limb muscle forces in normal walking. The patterns of muscle forces predicted by the model with scaled peak isometric force values were similar to those predicted by the MR-based model, implying that assessments of muscle function obtained from these two methods are practically equivalent. These results support the use of mass-length scaling in the development of subject-specific musculoskeletal models of children.     

Simulation of Electrical Interaction of Cardiac Cells

A model of the electrical activity of excitable membrane was used to simulate action potential propagation in cardiac cells. Using an implicit method for solving finite difference equations, propagation through the intercalated disc region between two abutting cells was studied. A model of interaction was constructed and parameters of the cellular junction determined. Estimates of the intercalated disc resistance were then made from these junction parameters using a field analysis of the junction. Values of approximately 4 Ω-cm² were found and correlate well with experimentally measured values.     

Optimizing cardiac material parameters with a genetic algorithm

Determining the unknown material parameters of intact ventricular myocardium can be challenging due to highly nonlinear material behavior. Previous studies combining a gradient-search optimization procedure with finite element analysis (FEA) were limited to two-dimensional (2D) models or simplified three-dimensional (3D) geometries. Here we present a novel scheme to estimate unknown material parameters for ventricular myocardium by combining a genetic algorithm (GA) with nonlinear finite element analysis. This approach systematically explores the domain of the material parameters. The objective function to minimize was the error between simulated strain data and finite element model strains. The proposed scheme was validated for a 2D problem using a realistic material law for ventricular myocardium. Optimized material parameters were generally within 0.5% of the true values. To demonstrate the robustness of the new scheme, unknown material parameters were also determined for a realistic 3D heart model with an exponential hyperelastic material law. When using strains from two material points, the algorithm converged to parameters within 5% of the true values. We conclude that the proposed scheme is robust when estimating myocardial material parameters in 2D and 3D models.     

Synergic analysis of upper limb target-reaching movements

The topological invariance and synergies of human movements are discussed through the analysis and comparison of upper-limb target-reaching tasks. Five subjects were asked to perform different target-reaching tasks with different indices of difficulty, and the movements were captured using a Vicon 3D motion analysis system.Topological invariance was observed in the trajectories of different task performances. After normalization, the trajectories of the arm tips had very close patterns for different target-reaching tasks. Synergy in the target-reaching movements of the upper limbs was also found among the different joint angles. The joint angles can be fitted using the same format of functions proposed in this study. The parameters in the function can be taken as a characteristic feature of target-reaching movement patterns. A target-reaching movement can be determined by these parameters and the start and end positions.     

A new method for the determination of stability parameters of proteins from their heat-induced denaturation curves

A new method has been developed for determining the stability parameters of proteins from their heat-induced transition curves followed by observation of changes in the far-UV circular dichroism (CD). This method of analysis of the thermal denaturation curve of a protein gave values of stability parameters that not only are identical to those measured by the differential scanning calorimetry (DSC), but also are measured with the same error as that observed with a calorimeter. This conclusion has been reached from our studies of the reversible heat-induced denaturation of lysozyme and ribonuclease A at various pH values. For each protein, the conventional method of analysis of the conformational transition curve, which assumes a linear temperature dependence of the pre- and posttransition baselines, gave the estimate of DeltaH(van)(m) (enthalpy change on denaturation at T(m), the midpoint of denaturation) which is significantly lower than DeltaH(cal)(m), the value obtained from DSC measurements. However, if the analysis of the same denaturation curve assumes that a parabolic function describes the temperature dependence of the pre- and posttransition baselines, there exists an excellent agreement between DeltaH(van)(m) and DeltaH(cal)(m) of the protein. The latter analysis is supported by the far-UV CD measurements of the oxidized ribonuclease A as a function of temperature, for the temperature dependence of this optical property of the protein is indeed nonlinear. Furthermore, it has been observed that, for each protein, the constant-pressure heat capacity change (DeltaC(p)) determined from the plots of DeltaH(van)(m) versus T(m) is independent of the method of analysis of the transition curve.     

Determination of oxygen saturation and hematocrit of flowing human blood using two different spectrally resolving sensors.

The blood parameters oxygen saturation and hematocrit were determined by two different spectral sensors using reflectance spectra from 550 to 900 nm and partial transmission spectra centered at 660 nm. The spectra were analyzed by the method of partial least squares. One sensor consists of a miniature integrating sphere, while the other was fiber-guided. The results show that the geometry of the sensors and different blood flows do not influence the spectral analysis significantly. Independent of the sensor geometry, both hematocrit and oxygen saturation could be determined with an absolute predicted root mean square error of less than 3%. Furthermore, the analysis showed that hematocrit prediction requires eight wavelength regions and oxygen saturation prediction requires four wavelength regions using reflectance spectroscopy. This implies that if the measurement is restricted to reflectance, a spectrometer is indispensable for determining both blood parameters. Hematocrit determination could be improved using reflectance measurements in combination with transmission.     

Comparison of partial least-square method and canonical correlation analysis in a quantitative structure–retention relationship study

The retention of 7 monotetrazolium and 9 ditetrazolium salts was determined on alumina and reversed-phase (RP) alumina layers using n-hexane-1-propanol and water-1-propanol mixtures as eluents. The retention capacity and the specific surface area of solutes in contact with the stationary phases were calculated. The relationship between retention characteristics and physicochemical parameters of solutes was elucidated by canonical correlation analysis and partial least-square regression analysis. Both methods found significant relationships between the chromatographic and physicochemical parameters, however, the results were different according to the method applied. Calculations suggested that the retention on both alumina and RP alumina layers is of mixed character, hydrophobic, electronic and steric parameters are equally involved in the retention.     

Temperature optimization for reactor operation with chitin-immobilized lactase under modulated inactivation

Temperature effects on all kinetic and inactivation parameters have been determined for chitin immobilized lactase from Kluyveromyces marxianus var. marxianus, and proper temperature functions have been validated. Maximum reaction rate, Michaelis constant referred to lactose, inhibition constant for galactose and inactivation rates increased with temperature. Enzyme inactivation was adequately modelled by a two-stage series mechanism. The effect of galactose and lactose on enzyme inactivation was determined in terms of modulation factors that were positive for galactose and negative for lactose over the whole range of temperature studied. Modulation factors were mild functions of temperature in the first stage and strong functions in the second stage of CIL inactivation where galactose positive modulation factors increase with temperature and lactose negative modulation factors decrease with temperature. Temperature explicit functions for all kinetic and inactivation parameters were incorporated into a scheme to optimize the temperature of operation for a sequential batch reactor with chitin-immobilized lactase, based on an annual cost objective function for reactor operation. Software for temperature optimization was developed creating a friendly interface with user that allows the introduction of variations in all parameters and operational criteria to perform sensitivity analysis.     

Measuring enzymatic activity of a recombinant amidase using Fourier transform infrared spectroscopy

A method based on Fourier transform infrared spectroscopy (FT-IR) has been developed for assaying the Pseudomonas aeruginosa native amidase (E.C. 3.5.1.4), overproduced in an Escherichia coli strain. The kinetic of acetamide hydrolysis by the enzyme, in aqueous media, was monitored by measuring the intensity of the acetamide amide I band maximum at 1635 cm(-1) as a function of time. A value of 0.5mM(-1) cm(-1) was obtained for the extinction coefficient (epsilon) of acetamide at this frequency. The rate of the hydrolysis was found to be linear with the concentration of the enzyme up to 90 microM. The Michaelis-Menten kinetics parameters V and K(m) were determined as 30.7 U/mg and 4mM, respectively. These results were similar to those obtained using high-performance liquid chromatography analysis of the same hydrolytic reaction catalyzed by amidase either in water or in buffer. This suggests that the precision of the FT-IR method is suitable for the kinetic studies of amidase with the additional advantage of being able to perform a real-time measurement of the enzymatic activity.     

Calculation of DNA molecule packing in crystals by the method of atom-atom potentials I. B-form of DNA]

The van-der-Waals interaction of DNA molecules in the B-form has been studied by the method of atom-atom potentials. This study was carried out to clarify to what degree does this interaction determinate packing of DNA molecules in a crystal lattice. Interaction energy of two parallel molecules has been calculated as a function of 4 parameters (interaxial distance, axial shift, screw rotation of molecules). Energy as a function of these parameters is shown to have two minima, one of them exactly corresponding to mutual arrangement of DNA molecules in the lattice determined from X-ray data.