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From equations describing dose/response curves of drug combinations the nonlinear dependence of the ECx value (concentration for X% effect) of a racemate on the ECx values of the pure enantiomers was derived. This equation was used in QSAR analyses of series of substances containing pure compounds (i.e. pure enantiomers or achiral molecules) and stereoisomeric mixtures.
The question addressed is whether or not childhood epidemics such as measles and chickenpox are characterized by low-dimensional chaos. We propose a new method for the detection and extraction of hidden periodic components embedded in an irregular cyclical series, and study the characterization of the epidemiological series in terms of the characteristic features or periodicity attributes of the extracted components. It is shown that the measles series possesses two periodic components each having a period of one year. Both the periodic components have time-varying pattern, and the process is nonlinear and deterministic; there is no evidence of strong chaoticity in the measles dynamics. The chickenpox series has one seasonal component with stable pattern, and the process is deterministic but linear, and hence non-chaotic. We also propose surrogate generators based on null hypotheses relating to the variability of the periodicity attributes to analyse the dynamics in the epidemic series. The process dynamics is also studied using seasonally forced SEIR epidemic model, and the characterization performance of the proposed schemes is assessed.
BACKGROUND: Heart rate variability might predict arrhythmias after coronary artery bypass grafting. METHODS: Off-line processing of 10-min electrocardiogram recordings of consecutive patients provided R-R intervals for time domain, frequency domain, Poincaré, and point correlation analyses and subsequent association with postoperative atrial fibrillation by stepwise multivariate logistic regression. RESULTS: Of 88 patients who met entry criteria, 13 developed atrial fibrillation. Peak point correlation dimension (odds ratio 3.985/unit, P = 0.0096) and age (odds ratio 1.144/yr, P = 0.0019) were independently associated with atrial fibrillation (c-statistic = 0.839). CONCLUSIONS: Further study should confirm the ability of peak point correlation dimension to predict atrial fibrillation after coronary artery surgery with cardiopulmonary bypass.
A theoretical model is presented for stress-modulated growth in the aorta. The model consists of a pseudoelastic tube composed of two layers representing the intima/media and the adventitia. Finite volumetric growth is included by letting the time-rate of change of the zero-stress dimensions of each volume element depend linearly on the local stresses. After analysing the model, we examine its fundamental growth response under changes in loads, material properties, and growth parameters. The behavior of the model is quite sensitive to changes in material nonlinearity and in the coefficients of the growth law. Next, growth of the aorta is simulated during development and maturity. For an appropriate choice of the parameters, the model exhibits patterns of growth that agree qualitatively with known characteristics of aortic growth. Comparison of model results with published experimental data during hypertension in the rat shows good agreement in the time course of the vessel radii and residual strain. Finally, the implications of the results are discussed in the context of deducing a general mechanical growth law for soft tissues. The proposed model should be useful in studies to determine the biomechanical factor that regulates growth.
A method is proposed for estimating the (asymmetrical and non-uniform) band broadening function (BBF) in size-exclusion chromatography (SEC). The following data are required: the molar mass calibration and the concentration- and molar mass chromatograms of a set of narrow standards. In the narrow range of each standard, the BBF is uniform but skewed. Each uniform BBF is estimated through a nonlinear optimization procedure that compares one (of the two) measured chromatograms with its theoretical prediction based on the other chromatogram. The method is validated with numerical examples that simulate the analyses of narrow standards exhibiting log-normal and Poisson weight chain length distributions. The BBF can be assumed of arbitrary shape, or represented by an exponentially-modified Gaussian (EMG). From the uniform BBF estimate, the true polydispersity of the standard can be determined. The global non-uniform BBF is obtained by interpolation between a set of uniform BBFs covering a wide range of elution volumes.
We have developed a fitting procedure, based on nonlinear mixed effect modelling and original work by Richards (1959, J Exp Botany 10, 290-300), to describe the degree of asymmetry of concentration-effect E/[A] curves and analysed the shape of E/[A] curves obtained with alpha1-adrenoceptor agonists in rat aorta. The four-parameter Richards model provided a significantly better fit of the data than the standard logistic/Hill model for all ligands investigated, which implies that E/[A] curves were asymmetrical. With the exception of ST 587, the asymmetry parameter (delta) tended toward zero and the Richards model could be replaced without significant loss of goodness-of-fit by the three-parameter, asymmetrical Gompertz model. The alpha1-adrenoceptor antagonist, prazosin (10 nM), had no effect on the asymmetry of the noradrenaline E/[A] curve but significantly increased the slope at the point of inflection. In contrast, pretreatment with the irreversible antagonist, phenoxybenzamine (60 nM), produced a shift of the delta estimate for noradrenaline from zero to unity, indicating a change from an asymmetrical to a symmetrical curve. Therefore, detailed statistical analysis of E/[A] curve asymmetry demonstrates that alpha1-adrenoceptors in rat aorta do not operate as a homogenous one-receptor-one-transducer system. This conclusion could not have been reached by either an analysis with the standard logistic/Hill model or visual inspection of experimental data. Overall, the curve-fitting analysis developed in this study provides a quantitative and sensitive measure of asymmetry and a novel method for the objective discrimination of agonist action on the basis of curve shape. The method is generally applicable to other pharmacological assays and provides a new tool in receptor classification studies.
The relevance of terms other than linear when deriving quantitative structure-activity relationship/quantitative structure-property relationship (QSAR/QSPR) models has been rarely considered so far. In this study, the impact of quadratic and interacting terms has been taken into account. The first effect of including such highly structured terms is a significant extension of the parametric domain that moves from the initial N to N(N + 3)/2 parameters. This substantial enlargement over the conventional linear boundaries involves a higher computational cost due to the increased combinatorial number of resulting theoretical QSAR/QSPR models. To face this issue, novel genetic-algorithm-based software, MGZ (multigenetic zooming), was developed and used for both variable selection and model building. To speed up the entire process of domain searching, MGZ was supported with multiple independent evolving populations and genetic storms to further QSAR/QSPR analyses. In addition, a novel fitness function was developed to score models on the basis of their inner predictive capability, assessed on the training set, structure complexity, and presence of nonlinear terms. The models were further validated by monitoring model redundancy and performing intensive randomization runs. The Selwood data set was used as a reference set to derive QSAR models. Furthermore, a QSPR study was conducted on the solubility data set of a large array of organic compounds. The results reported in the present paper demonstrate that our approach is successful in finding linear models, which are at least as good as the models previously derived using standard statistical approaches, and in deriving new nonlinear models with good statistical figures.
Two previously studied cohorts of women with nonmetastatic breast cancer (Ns = 230 and 136) were reexamined. Participants were assessed during the year after surgery and 5-8 years later. Associations were examined between benefit finding (BF) and several indicators of psychosocial adjustment (e.g., perceived quality of life, positive affect, negative affect, social disruption, and intrusive thoughts). Significant curvilinear relations between BF and other outcomes were observed cross-sectionally during initial assessment and at long-term follow-up in both samples. Compared with the intermediate BF group, low and high BF groups had better psychosocial adjustment. Further analyses indicated that the high BF group reported higher optimism and more use of positive reframing and religious coping than the other BF groups. Discussion highlights the need to examine nonlinear as well as linear relationships.
Ten isofemale lines of Zaprionus indianus were analysed to study the reaction norms of five morphometrical traits (wing and thorax length, body weight, sternopleural bristle and ovariole number) in relation to growth temperature. All these traits exhibited nonlinear concave reaction norms and were characterized by the coordinates of their maximum: MV (maximum value), and TMV (temperature of maximum value). Wing/thorax ratio, which is related to flight capacity, was also calculated and exhibited a monotonically decreasing reaction norm. Intraclass correlations were on average quite low, with no significant differences between traits, temperature or sex; a highly significant trait-temperature interaction was, however, observed. Sex dimorphism was very low in Zaprionus, contrasting with data previously obtained in other species. MVs among lines were positively correlated for the three size-related traits, whereas sternopleural bristle and ovariole number were genetically independent. TMVs were different between the traits, but higher than in D. melanogaster and other cold-adapted species, in agreement with the hypothesis that the norm shape evolves according to species thermal adaptation. MVs and TMVs were never correlated, indicating that mean values and plasticity are genetically independent. Some positive correlations were observed among TMVs of different traits, suggesting that the same genetic system might regulate plasticity of different traits.
The activation process of pepsinogen was analyzed by a combination of computer simulation and experiment. In order to investigate in detail the behavior of the basic schemes proposed in the previous study, further computer simulations were conducted. Some experiments were performed based on the information obtained. The changes in the UV difference spectrum in the early stage was measured by the stopped-flow technique and the conversion of pepsinogen to pepsin [EC 3.4.23.1] was followed by sodium dodecyl sulfate-polyacrylamide gel electrophoresis. Furthermore, on the basis of the experimental results, the most reasonable scheme was selected and modified. As a result, a scheme for the activation process of pepsinogen was obtained (Scheme 8). On the basis of the above analyses, it was assumed that the first step and the third step are pH-dependent based on the change in the UV spectrum, that the second step is a nonlinear reaction containing a looped reaction with a dimeric intermediate (in this step, peptide fragments are released and pepsinogen is converted to a pepsin-like molecule), and that the third step is an equilibrium reaction involving proton binding.
1. Previous computational studies of models of neuron R15 in Aplysia have indicated that several distinct modes of electrical activity may coexist at a given set of parameters, that this multistability can be modulated by transmitters such as serotonin (5-HT) and that brief perturbations of the membrane potential can induce persistent changes in the mode of electrical activity. To test these predictions, the responses of R15 neurons to injections of brief (1.5 s) current pulses were recorded intracellularly in the absence and presence of 5-HT. 2. In the absence of 5-HT, brief perturbations induced abrupt transitions in the electrical activity from bursting to beating. Such transitions were observed in approximately 20% of the cases. The duration of beating activity varied from several seconds to tens of minutes. In the presence of low concentrations (1 microM) of 5-HT, both the probability of mode transitions and the duration of induced beating activity increased significantly. 3. These results indicate that at least two stable modes of electrical activity can coexist in R15 neurons and that this bistability can be regulated by 5-HT. In general, these conclusions agree with the results from analyses of mathematical models of R15. Although the function of these dynamic properties in R15 is speculative, our results, interpreted on the background of the model, support the notion that nonlinear dynamical properties of individual neurons can endow them with richer forms of information processing than has generally been appreciated.
Numerous linear and nonlinear correlations between the contents of alkaloids and mineral elements in the aerial parts and roots of greater celandine (Chelidonium majus L.) were revealed by means of correlation and regression analyses. These relationships became more significant with the transition from the sum of alkaloids to individual groups or fractions, which included compounds of similar compositions. The mathematical models describing the regulation of alkaloid metabolism by some mineral elements (Ba, Mg, Sr, Co, Cr, Zn, etc.) were developed in the analytical form. These models were tested in experiments with geochemical modeling using Zn.
"Building on the tabular analyses exemplified in our first paper and widely used in the medical literature, we use generalised linear models to provide a formal, statistical approach to the analysis of mortality and deprivation relationships, and their change over time. Three types of fixed effects model are specified and estimated with the same ward-level data sets for Wales examined in our first paper. They are: Poisson models for analysing mortality and deprivation at a single cross section in time; repeated-measures Poisson models for analysing mortality-deprivation relations, not only at cross sections in time, but also their changes over time; and logit models focusing on temporal changes in mortality-deprivation relationships. Nonlinear effects of deprivation on mortality have been explored by using dummy variables representing deprivation categories to establish the connection between formal statistical models and the tabular approach"
In nonlinear mixed-effects models, estimation methods based on a linearization of the likelihood are widely used although they have several methodological drawbacks. Kuhn and Lavielle (Comput. Statist. Data Anal. 49:1020-1038 (2005)) developed an estimation method which combines the SAEM (Stochastic Approximation EM) algorithm, with a MCMC (Markov Chain Monte Carlo) procedure for maximum likelihood estimation in nonlinear mixed-effects models without linearization. This method is implemented in the Matlab software MONOLIX which is available at http://www.math.u-psud.fr/~lavielle/monolix/logiciels. In this paper we apply MONOLIX to the analysis of the pharmacokinetics of saquinavir, a protease inhibitor, from concentrations measured after single dose administration in 100 HIV patients, some with advance disease. We also illustrate how to use MONOLIX to build the covariate model using the Bayesian Information Criterion. Saquinavir oral clearance (CL/F) was estimated to be 1.26 L/h and to increase with body mass index, the inter-patient variability for CL/F being 120%. Several methodological developments are ongoing to extend SAEM which is a very promising estimation method for population pharmacockinetic/pharmacodynamic analyses.
Specialised gastrointestinal absorption of amoxicillin has been suggested in man and has been demonstrated in animals. In order to study the rate and extent of amoxicillin absorption, six healthy subjects were given 500 mg IV and two oral doses (500 mg and 3 g as a suspension). Absorption kinetics was analysed by compartmental modelling, noncompartmental methods and by calculation of absorption rates using deconvolution. Dose-dependency of the extent of amoxicillin absorption was observed, with a lower than expected mean maximum plasma concentration (49%), and fraction of the dose absorbed (39%) after the 3 g dose calculated from the 500 mg dose, assuming kinetic linearity. Zero-order kinetics of absorption was apparent in some subjects after the 500 mg dose, both from model fitting and absorption rate profile. However, no pattern consistent with pure first-order or zero-order absorption was observed after both oral doses in any individual. The dose-dependency of amoxicillin absorption was confirmed by a trend to an increased time of absorption for the high dose. The results show the variable nature and nonlinearity of the gastrointestinal absorption of amoxicillin and indicate the involvement of a number of factors, in addition to simple diffusion.
Many behavioural and physiological processes are periodic with a period of approximately 24 hours. For descriptive purposes, linear regression using a simple sinusoid with a fixed 24 hour period is sometimes an adequate tool for analysing data from such processes. Inference based on regression models under the assumption of independent and identically distributed errors, however, can often mislead seriously. In this paper we present a general class of models for fitting biological rhythms, with use of higher-order harmonic terms of one or more unknown fundamentals and ARMA processes for the errors. We describe the procedures for model specification and estimation and give the theoretical justification for these procedures. Analysis of a series of human core body temperature illustrates the methodology.
Acid-base properties of the natural polyamine wasp toxin PhTX-433 (1) and seven synthetic analogues [PhTX-343 (2), PhTX-334 (3), PhTX-443 (4), PhTX-434 (5), PhTX-344 (6), PhTX-444 (7), and PhTX-333 (8)], each having four protolytic sites, were characterized by 13C NMR spectroscopy. Nonlinear, multiparameter, simultaneous fit of all chemical shift data obtained from the NMR titration curves yielded macroscopic pKa values as well as intrinsic chemical shift data of all differently protonated macrospecies. Analyses of the chemical shift data demonstrated strong interactions between all four sites and provided information about complex relationships between chemical shift values and protonation state. Deprotonation of fully protonated forms starts at the central amino group of the polyamine moiety, and the extent of this trend depends on the distance to the flanking, protonated amino groups. The pKa1 values of 1-8 are in the range 8.2-9.4. Hence, some of the toxins are incompletely protonated at the pH and ionic strength conditions used for assessment of their interactions with ionotropic glutamate and nicotinic acetylcholine receptors, and the degree of protonation is expected to have pharmacological importance in the ion-channel binding event.
On the basis of anatomical and physiological results of the vertebrate retina, a method is proposed for analysing the respective fields of ganglion cells in the cat retina. In the model, we assume the following: (a) Ganglion cells receive their input from bipolar and/or amacrine cells. (b) The nonlinearity of ganglion cell responses is due to the activities of transient type amacrine cells. The method has been proved to be effective. According to the results of this investigation, the receptive field properties of X type and Y type ganglion cells are heterogeneous. Thus, it may be considered that their receptive fields consist of center and surround mechanisms. The receptive field properties of X-cells are almost linear and the X-cells seem to receive most of their input from bipolar cells. On the other hand, the ones of Y-cells are highly nonlinear. Consequently, it is conceivable that the Y-cells receive their input mainly from transient type amacrine cells.