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Mass isotopomer distribution analysis: a technique for measuring biosynthesis and turnover of polymers.

Mass isotopomer distribution analysis (MIDA) is a technique for measuring biosynthesis and turnover of polymers in vivo. A stable isotopically enriched precursor is administered, and the relative abundances of different mass isotopomers in the polymer of interest are measured by mass spectrometry (MS). By comparison of statistical distributions predicted from the binomial or multinomial expansion to the pattern of excess isotopomer frequencies observed in the polymer, the enrichment of the biosynthetic precursor subunits (p) for newly synthesized polymers is calculated. MIDA thereby provides a solution to the problem of determining the isotope content in the actual precursor molecules that entered a particular polymeric product (the "true" precursor). The fraction of polymer molecules in a mixture that were newly synthesized during an isotopic experiment (fractional synthesis) can then be calculated. We describe some mathematical characteristics of MIDA and point out certain advantageous features. For example, mathematical estimates of p remain valid even if there does not exist a single anatomic or functional precursor pool. The interpretation of decay curves of endogenously labeled polymers may be improved by the use of higher mass isotopomers, which better fulfill the assumption of flash labeling. By combining fractional synthesis values with rate constants of decay, absolute endogenous synthesis rates can be calculated. Thus, by using probability logic combined with MS analysis, MIDA allows dynamic measurements to be made through analyses on a polymer alone during both isotopic incorporation and decay phases. The method has been applied to fatty acids, cholesterol, and glucose and is potentially applicable to nucleic acids, porphyrins, perhaps proteins, and many other classes of polymers.

Indicator Dilution Techniques↗

Analysis of pig's coronary arterial blood flow with detailed anatomical data.

Blood flow to perfuse the muscle cells of the heart is distributed by the capillary blood vessels via the coronary arterial tree. Because the branching pattern and vascular geometry of the coronary vessels in the ventricles and atria are nonuniform, the flow in all of the coronary capillary blood vessels is not the same. This nonuniformity of perfusion has obvious physiological meaning, and must depend on the anatomy and branching pattern of the arterial tree. In this study, the statistical distribution of blood pressure, blood flow, and blood volume in all branches of the coronary arterial tree is determined based on the anatomical branching pattern of the coronary arterial tree and the statistical data on the lengths and diameters of the blood vessels. Spatial nonuniformity of the flow field is represented by dispersions of various quantities (SD/mean) that are determined as functions of the order numbers of the blood vessels. In the determination, we used a new, complete set of statistical data on the branching pattern and vascular geometry of the coronary arterial trees. We wrote hemodynamic equations for flow in every vessel and every node of a circuit, and solved them numerically. The results of two circuits are compared: one asymmetric model satisfies all anatomical data (including the mean connectivity matrix) and the other, a symmetric model, satisfies all mean anatomical data except the connectivity matrix. It was found that the mean longitudinal pressure drop profile as functions of the vessel order numbers are similar in both models, but the asymmetric model yields interesting dispersion profiles of blood pressure and blood flow. Mathematical modeling of the anatomy and hemodynamics is illustrated with discussions on its accuracy.

Animals↗

Modelling and simulation of variability and uncertainty in toxicokinetics and pharmacokinetics.

Two important methodological issues within the framework of the variability and uncertainty analysis of toxicokinetic and pharmacokinetic systems are discussed: (i) modelling and simulation of the existing physiologic variability in a population; and (ii) modelling and simulation of variability and uncertainty when there is insufficient or not well defined (e.g. small sample, semiquantitative, qualitative and vague) information available. Physiologically based pharmacokinetic models are especially suited for separating and characterising the physiologic variability from the overall variability and uncertainty in the system. Monte Carlo sampling should draw from multivariate distributions, which reflect all levels of existing dependencies in the intact organism. The population characteristics should be taken into account. A fuzzy simulation approach is proposed to model variability and uncertainty when there is semiquantitative, qualitative and vague information about the model parameters and their statistical distributions cannot be defined reliably.

Animals↗

Analytical theory of the stochastic dynamics of the power stroke in nonprocessive motor proteins.

Statistical distributions of the structural states of individual molecules of nonprocessive motor complexes such as actomyosins are examined theoretically by considering a two-state stochastic model coupled by chemical reactions along the reaction coordinate representing the internal conformational states of the motor. The use of a conformational reaction coordinate allows for the approximation of taking the rate constants as local in their dependence on the reaction coordinate, and yields a simple analytic solution of the stationary states. The approximation is also tested against numerical solutions with a nonlocal form of rate constants. The theory is well-suited for computational treatments based on atomic structures of protein constituents using free energy molecular dynamics simulations. With empirical sets of free energy functions, stationary distributions of forces exerted by a motor head compare well with known experimental data.

Actins↗

Endothelial injury in vivo: a technical and statistical approach to the study of aortic integrity.

The endothelium can be a link connecting risk factors with the development of cardiovascular disease, and methods for studying endothelial integrity are therefore important. We describe a method of studying endothelial injury in vivo by combining immunohistochemistry with an improved technique of producing "enface" preparations (Häutchens) aortic endothelium of rabbits and guinea pigs. These Häutchens enabled the study of large numbers of endothelial cells and adherent cells (probably leukocytes) at different locations along the aorta. The statistical distributions of the number of injured endothelial cells and adherent cells in a visual field were also investigated, and both closely followed a log-normal distribution. Based on this distribution, a method to estimate endothelial injury by grouping the cell count data, instead of exact counting, was developed. The grouped cell count data were then used to calculate the grouped mean and grouped standard deviation for each animal. The improvements of the technical and statistical methods offer good opportunities to study various aspects of endothelial integrity in a time efficient manner.

Animals↗

Two-dimensional probabilistic images discrimination. I. Simultaneously presented pairs of patterns.

Reaction time and judgment of similarity or dissimilarity were studied in an experiment on two-dimensional probabilistic images (TDPIs) composed of rectangular black and white cells with statistical distribution of these elements 0.5-0.5. The subjects were asked to report verbally whether pairs of TDPIs, presented for 700 ms, appeared to them similar or not. Three sets of TDPIs differed as to the size of their "grain". Within the pairs "physically identical patterns", "statistically same patterns" or "different patterns" have been used. The statistically same patterns pairs reached the lowest (39 percent) judgment correctness. Reaction times for these pairs were generally longer than for others. In the case of identical patterns and statistically same patterns pairs the results indicated a general increase of the processing time as the size of grain had increased. There was a general tendency of reaction time shortening in successive sessions. These results suggest that correct discrimination of TDPIs does not depend primarily upon their grain.

Adult↗

Development and distribution of proximal caries in 303 9-20-year-old individuals in a Copenhagen suburb.

The purpose of the present study was to establish a theoretical basis for the practice of screening for identification of caries risk groups. Longitudinal data concerning the development of proximal caries in 303 persons from the age of 9 to the age of 20 were examined with regard to statistical distribution. Data from each year and from the entire period showed a close fit to the negative binomial distribution. This distribution can be the result of independent random occurrences, but varying susceptibility. Thus the consistent existence of a caries risk group is illustrated by this analysis, but no prediction is made. It is suggested that future evaluations of preventive measure directed toward caries risk groups should express the degree to which the similarity between the distribution of proximal caries and the negative binomial distribution can be eliminated.

Adolescent↗

Crossover behavior in failure avalanches.

Composite materials, with statistically distributed thresholds for breakdown of individual elements, are considered. During the failure process of such materials under external stress (load or voltage), avalanches consisting of simultaneous rupture of several elements occur, with a distribution D(Delta) of the magnitude Delta of such avalanches. The distribution is typically a power law D(Delta) proportional to Delta (-xi). For the systems we study here, a crossover behavior is seen between two power laws, with a small exponent xi in the vicinity of complete breakdown and a larger exponent xi for failures away from the breakdown point. We demonstrate this analytically for bundles of many fibers where the load is uniformly distributed among the surviving fibers. In this case xi=3/2 near the breakdown point and xi=5/2 away from it. The latter is known to be the generic behavior. This crossover is a signal of imminent catastrophic failure of the material. Near the breakdown point, avalanche statistics show nontrivial finite size scaling. We observe similar crossover behavior in a network of electric fuses, and find xi=2 near the catastrophic failure and xi=3 away from it. For this fuse model power dissipation avalanches show a similar crossover near breakdown.

Journal Article↗

Genetically engineered polymers for drug delivery.

Genetic engineering methodology offers the ability to synthesize protein-based polymers with precisely controlled structures. Protein-based polymers synthesized by recombinant techniques have a well-defined monomer composition and sequence, stereochemistry, and a narrow molecular weight distribution. The structure of the polymeric carrier at the molecular level influences its biological disposition and drug release profile. Current methodologies of polymer synthesis (chemical polymerization) result in the production of polymers with heterogeneous molecular weights, and with monomer sequences and compositions defined in terms of statistical distributions. Genetic engineering methodologies can be used to design new polymeric drug carriers with improved properties, such as better-defined biorecognition, pharmacokinetic, biodegradation, and drug release profiles. In this review article the rationale and methodology of polymer synthesis using genetic engineering techniques, the status of such polymers in drug delivery to-date, and the potential of these polymers for the development of new systems in the future are discussed.

Drug Delivery Systems↗

The effect of neglecting correlations when propagating uncertainty and estimating the population distribution of risk.

Interest in examining both the uncertainty and variability in environmental health risk assessments has led to increased use of methods for propagating uncertainty. While a variety of approaches have been described, the advent of both powerful personal computers and commercially available simulation software have led to increased use of Monte Carlo simulation. Although most analysts and regulators are encouraged by these developments, some are concerned that Monte Carlo analysis is being applied uncritically. The validity of any analysis is contingent on the validity of the inputs to the analysis. In the propagation of uncertainty or variability, it is essential that the statistical distribution of input variables are properly specified. Furthermore, any dependencies among the input variables must be considered in the analysis. In light of the potential difficulty in specifying dependencies among input variables, it is useful to consider whether there exist rules of thumb as to when correlations can be safely ignored (i.e., when little overall precision is gained by an additional effort to improve upon an estimation of correlation). We make use of well-known error propagation formulas to develop expressions intended to aid the analyst in situations wherein normally and lognormally distributed variables are linearly correlated.

Analysis of Variance↗

Distribution of time to first postpartum estrus in beef cattle.

The function of a distribution that describes postpartum interval (PPI) under any experimental treatment is useful for simulation modeling, understanding the effects of stimuli on the endocrine system, and estimating the average PPI in experiments terminated before all animals have expressed estrus. This study was undertaken to compare the fit of three statistical distributions, the Weibull, the log-normal, and the linear hazard rate (LHR), to the empirical distribution of PPI for five treatment regimens: no bull exposure postpartum, bull exposure from 53 d postpartum, bull exposure from 3 d postpartum, and bull exposure from an average of 63 d postpartum for 2-yr-old cows and for mature cows. The Weibull and the log-normal distributions deviated considerably from the empirical distribution. The LHR distribution with parameters changing over three different regions gave an excellent fit. The resulting hazard rate (instantaneous probability of a cow expressing her first estrus at time t postpartum) revealed a low probability of expressing estrus within 27 d postpartum (43 d for 2-yr-olds). For cows not exposed to bulls, the hazard rate increased slowly with time. For cows exposed to bulls after 3 d postpartum, the hazard rate increased rapidly between d 27 and d 50. For cows exposed to bulls after 53 d postpartum, the hazard rate increased instantaneously approximately 12 d after initial exposure to bulls. This increase was also seen when cows were exposed to bulls beginning at a constant date (at an average of 63 d postpartum). Because of lack of fit, the Weibull and the log-normal distributions should not be used in survival analysis of PPI.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗

Bioequivalence: performance of several measures of extent of absorption.

The determination of the area under the concentration-time curve (AUC) is the method most commonly used by regulatory agencies to assess extent of drug absorption after single-dose administration of oral products. Using simulations, several approaches toward measuring the actual area, in whole or part, were tested. In addition, the performance of the peak concentration (Cmax), usually taken as a measure of the rate of absorption was assessed evaluating extent. Model scenarios for drugs with typical mean characteristics and statistical distributions were investigated. Using different kinetic models of disposition, the time course of the drug concentration in plasma was simulated. Intraindividual and interindividual variability and assay error were modeled using Monte Carlo techniques. The accuracy, precision, and ease of use of the various measures of extent were evaluated, and statistical power analyses were performed. Among the measures tested, the most reliable were the AUC computed up to the time of the last quantifiable concentration, without extrapolation, and Cmax. However, being also sensitive to rate, Cmax as a measure of extent is of limited potential.

Absorption↗

A structurally based stress-stretch relationship for tendon and ligament.

We propose a mechanical model for tendon or ligament stress-stretch behavior that includes both microstructural and tissue level aspects of the structural hierarchy in its formulation. At the microstructural scale, a constitutive law for collagen fibers is derived based on a strain-energy formulation. The three-dimensional orientation and deformation of the collagen fibrils that aggregate to form fibers are taken into consideration. Fibril orientation is represented by a probability distribution function that is axisymmetric with respect to the fiber. Fiber deformation is assumed to be incompressible and axisymmetric. The matrix is assumed to contribute to stress only through a constant hydrostatic pressure term. At the tissue level, an average stress versus stretch relation is computed by assuming a statistical distribution for fiber straightening during tissue loading. Fiber straightening stretch is assumed to be distributed according to a Weibull probability distribution function. The resulting comprehensive stress-stretch law includes seven parameters, which represent structural and microstructural organization, fibril elasticity, as well as a failure criterion. The failure criterion is stretch based. It is applied at the fibril level for disorganized tissues but can be applied more simply at a fiber level for well-organized tissues with effectively parallel fibrils. The influence of these seven parameters on tissue stress-stretch response is discussed and a simplified form of the model is shown to characterize the nonlinear experimentally determined response of healing medial collateral ligaments. In addition, microstructural fibril organizational data (Frank et al., 1991, 1992) are used to demonstrate how fibril organization affects material stiffness according to the formulation. A simplified form, assuming a linearly elastic fiber stress versus stretch relationship, is shown to be useful for quantifying experimentally determined nonlinear toe-in and failure behavior of tendons and ligaments. We believe this ligament and tendon stress-stretch law can be useful in the elucidation of the complex relationships between collagen structure, fibril elasticity, and mechanical response.

Animals↗

Estimating the number of plasmids taken up by a eukaryotic cell during transfection and evidence that antisense RNA abolishes gene expression in Physarum polycephalum.

We have estimated the statistical distribution of the number of plasmids taken up by individual Jurkat lymphoma cells during electroporation in the presence of two plasmids, one encoding for yellow (EYFP) the other for cyan (ECFP) fluorescent protein. The plasmid concentration at which most of the cells take up only one plasmid or several molecules was determined by statistical analysis. We found that cells behaved slightly heterogeneous in plasmid uptake and describe how the homogeneity of a cell population can be quantified by Poisson statistics in order to identify experimental conditions that yield homogeneously transfection-competent cell populations. The experimental procedure worked out with Jurkat cells was applied to assay the effectiveness of antisense RNA in knocking down gene expression in Physarum polycephalum. Double transfection of flagellates with vectors encoding EYFP and antisense-EYFP revealed for the first time that gene expression can be suppressed by co-expression of antisense RNA in Physarum. Quantitative analysis revealed that one copy of antisense expressing gene per EYFP gene was sufficient to completely suppress formation of the EYFP protein in Physarum.

Animals↗

Relative effects of left ventricular mass and conduction disturbance on activation in patients with pathological left ventricular hypertrophy.

OBJECTIVE: To investigate the relative effects of left ventricular mass and conduction disturbance on the duration and axis of the QRS complex in patients with left ventricular hypertrophy and a normal cavity size. STUDY DESIGN: Retrospective and prospective study of 42 patients with pathological left ventricular hypertrophy and 17 normal controls by electrocardiography, echocardiography, and pulsed Doppler recordings. SETTING: Tertiary cardiac referral centre. PATIENTS: 42 patients (mean (SD) age 58(16)) with left ventricular hypertrophy and normal cavity size. 17 had stenotic or replaced aortic valves, 14 had hypertension, 9 had hypertrophic cardiomyopathy and 2 had left ventricular hypertrophy without obvious cause. 17 normal people (mean (SD) age 47(20)) were used as controls. RESULTS: The values of QRS duration segregated into two normally distributed populations, with a cut off point at 135 ms. When patients with QRS duration of < 135 ms (n = 30) were compared with those with QRS duration of > or = 135 ms (n = 12), there were no significant differences in age, heart rate, left ventricular size, shortening fraction, left ventricular mass and total QRS amplitude. Both the PR and QT intervals were, however, longer in patients with a QRS duration of > or = 135 ms, and the extent of incoordinate left ventricular wall motion during the preejection period was greater. When it was < 135 ms the QRS duration was strikingly correlated with left ventricular mass (r = 0.81, p < 0.01). The onsets of transverse septal motion and of posterior wall thickening were normal, as were the onsets of the longitudinal motion of left, septal, and right atrioventricular junctions. When the QRS duration was > or = 135 ms the onset of transverse septal motion and of the longitudinal right atrioventricular junction were both normal, but that of the posterior wall thickening (p < 0.01) and the longitudinal motion of the septum (p < 0.05) and lateral left ventricular wall (p < 0.01) were significantly delayed. Peak rates of left ventricular dimension decrease (p < 0.01) and increase (p < 0.01) were both reduced, as were the peak rates of the long axis shortening of the septum (p < 0.01) and left atrioventricular junction (p < 0.05), whereas the peak rates of posterior wall thickening and thinning did not differ between the two groups. Mean isovolumic relaxation time was longer (p < 0.05) in patients with QRS duration of > or = 135 ms and the peak velocity of the A wave and thus the A to E ratio was greater than in patients with a QRS duration of < 135 ms and that of the E wave was similar in the two groups. CONCLUSION: In patients with left ventricular hypertrophy the values of QRS duration are bimodally distributed, with a cut off point at 135 ms. When QRS duration is < 135 ms, left ventricular mass seems to be closely related to QRS duration, making it the dominant factor determining the activation time. Once QRS duration reaches > or = 135 ms the correlation with mass no longer exists. The statistical distribution, electrocardiographic characteristics, and incoordination pattern of left ventricular wall motion all suggest the development of a proximal left bundle branch block.

Adolescent↗

Basal, pulsatile, entropic, and 24-hour rhythmic features of secondary hyperprolactinemia due to functional pituitary stalk disconnection mimic tumoral (primary) hyperprolactinemia.

Under physiological conditions, PRL secretion is regulated precisely by various stimulating and inhibiting factors. Hyperprolactinemia may arise as a primary consequence of a PRL-secreting pituitary adenoma. Secondary hyperprolactinemia (SH) may emerge in patients with hypothalamic disease, hypophyseal stalk compression, or suprasellar extension of a (nonlactotrope) pituitary adenoma. The latter may reflect diminished delivery of dopamine or other inhibitory factors to normal lactotropes. We hypothesized that diurnal and ultradian rhythms of PRL secretion would differ in secondary (e.g. hypothalamic) and primary (e.g. tumoral states) hyperprolactinemia (PH), assuming that the underlying pathophysiologies differ. To test this clinical postulate, we investigated the patterns of 24-h PRL release in eight patients with SH associated with functional hypothalamo-pituitary disconnection and in eight patients with PH attributable to microprolactinoma. Data in each group were compared with values in healthy gender-matched controls. PRL time series were obtained by repetitive 10-min blood sampling, followed by high- precision immunofluorometric assay. PRL concentration profiles were analyzed by the complementary tools of model-free discrete peak detection, waveform-independent deconvolution analysis, cosinor regression, and the approximate entropy metric to quantitate pulsatile, basal, 24-h rhythmic, and pattern-dependent (entropic) PRL secretion. Patients with tumoral hyperprolactinemia (PH) showed a 2-fold higher 24-h mean serum PRL concentration than patients with SH (62 +/- 13 microg /L vs. 30 +/- 6.9 microg/L, respectively, P = 0.029). Estimated PRL pulse frequency (events/24 h) was similar in the two patient groups (18.5 +/- 0.7 vs. 17.6 +/- 0.8; P = 0.395) but elevated over that in euprolactinemic controls (P < 0.0001 for both). Deconvolution analysis disclosed a mean daily PRL secretion rate of 790 +/- 170 microg in PH patients vs. 380 +/- 85 microg in SH patients (P = 0.030). Nonpulsatile PRL secretion comprised nearly 70% of total secretion in both patient groups and 50% in controls (P < 0.0001). Cosinor analysis revealed similar acrophases in all three study cohorts. The mean skewness of the statistical distribution of the individual PRL sample secretory rates was reduced, compared with controls (P < 10 (-5) for each), but equivalent in SH and PH patients (0.83 +/- 0.12 vs. 0.78 +/- 0.08, respectively), denoting a loss of the normal spectrum of low- and higher-amplitude secretion rates. Approximate entropy, a regularity statistic, was markedly elevated in both patient groups over controls (P < 10 (-6) for each) and was slightly higher in PH patients than in SH patients (1.639 +/- 0.029 vs. 1.482 +/- 0.067, P = 0.048). In summary, patterns of PRL secretion in PH and SH states exhibit an equivalently increased frequency of PRL pulses, a comparably marked rise in nonpulsatile (basal) PRL secretion. Despite overlap, the regularity of PRL release patterns is disrupted even more profoundly in PH (tumoral), compared with SH. Assuming that the orderliness of serial PRL output monitors normal integration within a feedback-controlled neurohormone axis, then the more disorderly patterns of tumoral PRL secretion point to greater regulatory disruption in PH. The latter may reflect abnormal secretory behavior associated with lactotrope neoplastic transformation and/or isolation of the tumor cell mass from normal hypothalamic controls.

Adult↗

Structure of a synthetic halogen sulfosalt, Cu3Bi2S3I3.

Cu(3)Bi(2)S(3)I(3) was crystallized during an attempt to synthesize Cu-Pb-Bi sulfosalts with iodine as the transport medium. The crystal structure was solved from a black needle-like crystal on a four-circle diffractometer with a CCD detector. The solution was obtained by direct methods and subsequent difference-Fourier syntheses. S and I atoms are arranged in a systematically distorted cubic eutaxy (close packing). Bi atoms have monocapped trigonal prismatic coordinations, while Cu atoms occupy coordination sites which vary from trigonal planar to distorted tetrahedral. A prominent feature is the distribution of Cu atoms over many closely spaced sites in the structure, the majority of them being only partly occupied, which strengthens the case for mobile Cu atoms during crystal growth at elevated temperatures. In this respect, Cu(3)Bi(2)S(3)I(3) represents an extreme example of a statistical distribution of Cu in the structure; a frequently observed property of this element in sulfosalts.

Bismuth↗

Some quantitative results on Golgi impregnated axons in rat visual cortex using a computer assisted video digitizer.

Axonal fiber distributions of pyramidal cells in the visual cortex of the albino rat have been investigated using the rapid Golgi method and modern data collecting techniques. Three dimensional coordinate information was extracted from Golgi-impregnated axonal networks using a computer-assisted video digitizer. Computer programs used this data to generate various statistical distributions. In particular, angular distributions of the initial collateral segments and their endpoints were examined and found to reveal anisotropies. Inspection of the spatial distributions of the endpoints indicated a clustering at two distinct levels with respect to the pyramidal cell from which they originate. Dynamic graphic displays of the three dimensional data have been obtained and presented in the form of computer tracings of various orthogonal projections.

Animals↗