Power calculations for matched case-control studies

Power calculations are derived for matched case-control studies in terms of the probability po of exposure among the control patients, the correlation coefficient phi for exposure between matched case and control patients, and the odds ratio psi for exposure in case and control patients. For given Type I and Type II error probabilities alpha and beta, the odds ratio that can be detected with a given sample size is derived as well as the sample size needed to detect a specified value of the odds ratio. Graphs are presented for paired designs that show the relationship between sample size and power for alpha = .05, beta = .2, and different values of po, phi, and psi. The sample size needed for designs involving M matched control patients can be derived from these graphs by means of a simple equation. These results quantify the loss of power associated with increasing correlation between the exposure status of matched case and control patients. Sample size requirements are also greatly increased for values of po near 0 or 1. The relationship between sample size, psi, phi, and po is discussed and illustrated by examples.     

Empirical torsional potential functions from protein structure data. Phi- and psi-potentials for non-glycyl amino acid residues.

The torsional potential functions Vt(phi) and Vt(psi) around single bonds N--C alpha and C alpha--C, which can be used in conformational studies of oligopeptides, polypeptides and proteins, have been derived, using crystal structure data of 22 globular proteins, fitting the observed distribution in the (phi, psi)-plane with the value of Vtot(phi, psi), using the Boltzmann distribution. The averaged torsional potential functions, obtained from various amino acid residues in L-configuration, are Vt(phi) = 1.0 cos (phi + 60 degrees); Vt(psi) = 0.5 cos (psi + 60 degrees) - 1.0 cos (2 psi + 30 degrees) - 0.5 cos (3 psi + 30 degrees). The dipeptide energy maps Vtot(phi, psi) obtained using these functions, instead of the normally accepted torsional functions, were found to explain various observations, such as the absence of the left-handed alpha helix and the C7 conformation, and the relatively high density of points near the line psi = 0 degrees. These functions derived from observational data on protein structures, will, it is hoped, explain various previously unexplained facts in polypeptide conformation.     

Estimation of surface charges in some biological membranes.

The resting membrane potential data existing in the literature for the giant axon of the squid, frog muscle and barnacle muscle have been analyzed from the standpoint of the theory of membrane potential due to Kobatake and co-workers. The average values derived for the effective charge density phi chi (where phi is a constant, 0 less than phi less than 1, and represents the fraction of counterions that are free, and chi is the stoichiometric charge density in the membrane) present on the different biomembranes existing in their normal ionic environment are 0.3, 0.325 and 0.17 M for the squid axon, frog and barnacle muscles, respectively. On the assumption that the values of phi are 0.4 and 0.2 for nerve and muscle membranes, respectively, values of 0.75, 1.62 and 0.85 M have been derived for the stoichiometric charge density (chi) present in the respective biological membranes. These correspond to 1 negative charge per 222, 103 and 195 A2 of the membrane area of the squid axon, frog and barnacle muscles, respectively.     

Electrodiffusion of ions approaching the mouth of a conducting membrane channel.

The movement of ions in the aqueous medium as they approach the mouth (radius a) of a conducting membrane channel is analyzed. Starting with the Nernst-Planck and Poisson equations, we derive a nonlinear integrodifferential equation for the electric potential, phi(r), a less than or equal to r less than infinity. The formulation allows deviations from charge neutrality and dependence of phi(r) on ion flux. A numerical solution is obtained by converting the equation to an integral equation that is solved by an iterative method for an assumed mouth potential, combined with a shooting method to adjust the mouth potential until the numerical solution agrees with an asymptotic expansion of the potential at r-a much greater than lambda (lambda = Debye length). Approximate analytic solutions are obtained by assuming charge neutrality (Läuger, 1976) and by linearizing. The linear approximation agrees with the exact solution under most physiological conditions, but the charge-neutrality solution is only valid for r much greater than lambda and thus cannot be used unless a much greater than lambda. Families of curves of ion flux vs. potential drop across the electrolyte, phi(infinity)-phi (a), and of permeant ion density at the channel mouth, n1(a), vs. flux are obtained for different values of a/lambda and S = a d phi/dr(a). If a much greater than lambda and S = O, the maximum flux (which is approached when n1(a)----0) is reduced by 50% compared to the value predicted by the charge-neutrality solution. Access resistance is shown to be a factor a/[2 (a + lambda)] times the published formula (Hille, 1968), which was derived without including deviations from charge neutrality and ion density gradients and hence does not apply when there is no counter-ion current. The results are applied to an idealized diffusion-limited channel with symmetric electrolytes. For S = O, the current/voltage curves saturate at a value dependent on a/lambda; for S greater than O, they increase linearly for large voltage.     

Estimation of surface charges in some biological membranes

Summary The resting membrane potential data existing in the literature for the giant axon of the squid, frog muscle and barnacle muscle have been analyzed from the standpoint of the theory of membrane potential due to Kobatake and co-workers. The average values derived for the effective charge density (where is a constant, , and represents the fraction of counterions that are free, and is the stoichiometric charge density in the membrane) present on the different biomembranes existing in their normal ionic environment are 0.3, 0.325 and 0.17 M for the squid axon, frog and barnacle muscles, respectively. On the assumption that the values of are 0.4 and 0.2 for nerve and muscle membranes, respectively, values of 0.75, 1.62 and 0.85 M have been derived for the stoichiometric charge density present in the respective biological membranes. These correspond to 1 negative charge per 222, 103 and 195 Å of the membrane area of the squid axon, frog and barnacle muscles, respectively.     

Meiotic Gene Conversion Tract Length Distribution within the Rosy Locus of Drosophila Melanogaster

Employing extensive co-conversion data for selected and unselected sites of known molecular location in the rosy locus of Drosophila melanogaster, we determine the parameters of meiotic gene conversion tract length distribution. The tract length distribution for gene conversion events can be approximated by the equation P(L >/= n) = (n) where P is the probability that tract length (L) is greater than or equal to a specified number of nucleotides (n). From the co-conversion data, a maximum likelihood estimate with standard error for is 0.99717 +/- 0.00026, corresponding to a mean conversion tract length of 352 base pairs. (Thus, gene conversion tract lengths are sufficiently small to allow for extensive shuffling of DNA sequence polymorphisms within a gene.) For selected site conversions there is a bias towards recovery of longer tracts. The distribution of conversion tract lengths associated with selected sites can be approximated by the equation P(L >/= n| selected = (n)(1 - n + n/), where P is now the probability that a selected site tract length (L) is greater than or equal to a specified number of nucleotides (n). For the optimal value of determined from the co-conversion analysis, the mean conversion tract length for selected sites is 706 base pairs. We discuss, in the light of this and other studies, the relationship between meiotic gene conversion and P element excision induced gap repair and determine that they are distinct processes defined by different parameters and, possibly, mechanisms.     

Evolutionary comparison of murine and human delta T-cell receptor deleting elements

The gene for the T-cell antigen receptor (TCR) delta chain is a gene within a gene, being located in the TCR alpha chain gene in both mice and humans. The human delta locus is flanked by delta deleting elements that undergo preferential rearrangement in the thymus, resulting in deletion of internal delta coding segments. The mouse has conserved analogous elements, m delta Rec and m phi J alpha, which separate delta from alpha and undergo a m delta Rec/m phi J alpha rearrangement in polyclonal thymus. The 5' element, m delta Rec, which is an isolated heptamer-spacer-nonamer (h-s-n), lies within 200 kb of D delta 1, and displays two areas of nearly 80% homology to human delta Rec. The downstream element, m phi J alpha, lies 12.5 kb 3' to C delta, lacks the consensus amino acids for J alpha, and retains 80% homology to human phi J alpha. Cells from murine neonatal thymus show three prominent m delta Rec rearrangements consisting of the m delta Rec/m phi J alpha recombination, a delta Rec/D delta 1/D delta 2/J delta 1 recombination, and two hybrid recombinations. A consequence of the m delta Rec/M phi J alpha rearrangement is a deletion of internal D delta and J delta coding segments that would prevent their incorporation into alpha TCR products. The conservation of noncoding deleting elements flanking the delta TCR in mice and humans is similar to the evolutionarily preserved kappa deleting element of the B-cell lineage and argues for an important role in receptor utilization.     

Effect of organic loading rate on the stability, operational parameters and performance of a secondary upflow anaerobic sludge bed reactor treating piggery waste

A study of anaerobic digestion of piggery wastewater was carried out in a laboratory-scale sludge bed reactor as a secondary treatment. The effect of organic volumetric loading rates (BV) in the range of 1.0-8.1 g TCOD/ld on the process performance was evaluated. The best results were obtained at BV equal to or lower than 4 g TCOD/ld. At higher BV values, the removal efficiency of the process decreased suddenly. A linear relationship was found between the effluent SCOD and the TVFA/alkalinity ratio (P). A relationship was found among the different operational variables (BV , removal efficiency, effluent soluble COD, soluble COD removal rate (R), retention factor (phi), specific microbial growth rate (mu), methane production rate per volume of reactor and per volume of waste treated--QM and qM, respectively) and the corresponding regression equations were obtained. An increase of BV determined a decrease of removal efficiency, phi and qM and an increase of effluent soluble COD, mu, R and QM. The value of the maximum specific microbial growth rate (muM) determined through the equation that correlated BV and mu was found to be 0.19 d(-1). This value was of the same magnitude as those reported in other works of anaerobic digestion of piggery waste.     

Yield per recruit of the pacu Piaractus mesopotamicus (Holmberg, 1887) in the pantanal of Mato Grosso do Sul, Brazil.

Among the several fish species comercially exploited at the Pantanal of Mato Grosso do Sul, the "pacu" (Piaractus mesopotamicus) stands as one of the most important. Information regarding its exploitation level is necessary for the proper management of its stocks. Between 1996 and 1997 data on total length of the pacu were collected on a monthly basis from specimens caught by professional and sport fishers in the municipality of Corumbá. These data were used to estimate growth parameters and to assess the exploitation level for this species, applying the Beverton and Holt yield per recruit model. Length frequency analysis, carried out with the software FISAT (ELEFAN), was used to estimate growth parameters: 1996: L(infinity) = 87.20 cm; K = 0.34 year(-1); phi(')=3.41; C = 0.74; WP = 0.81; Longevity = 8.40 years; and 1997: L(infinity) = 86.50 cm; K = 0.34 year(-1); phi(')=3.40; C = 0.60; WP = 0.80; Longevity = 8.40 years. The value for t(0) is -0.363 years for mean values of L(infinity) and k. The weight-length relationship, calculated from data derived from experimental fisheries carried out in 1999 and 2000, is described by the equation: W = 0.048LF(2.835). Estimated mortalities and survival rates were: 1996: Z = 1.51 year(-1); M = 0.62 year(-1); F = 0.89 year(-1); S = 21.9%; and 1997: Z = 1.65 year(-1); M = 0.63 year(-1); F = 1.02 year(-1); S = 19.1%. The yield per recruit analysis showed the following values: F(Present) = 0.96 year(-1); F(max) = 0.67 year(-1) ; F(0.1) = 0.51 year(-1) (for L(c) = 26.7 cm). These results suggest that the pacu is overexploited in the area, so that restrictive measures are in need to manage the pacu fisheries.     

A master equation theory of fluorescence induction, photochemical yield, and singlet-triplet exciton quenching in photosynthetic systems.

A master equation theory is formulated to describe the dependence of the fluorescence yield (phi) in photosynthetic systems on the number of photons (Y) absorbed per photosynthetic unit (or domain). This theory is applied to the calculation of the dependence of the fluorescence yield on Y in (a) fluorescence induction, and (b) singlet exciton-triplet excited-state quenching experiments. In both cases, the fluorescence yield depends on the number of previously absorbed photons per domain, and thus evolves in a nonlinear manner with increasing Y. In case a, excitons transform the photosynthetic reaction centers from a quenching state to a nonquenching state, or a lower efficiency of quenching state; subsequently, absorbed photons have a higher probability of decaying by radiative pathways and phi increases as Y increases. In case b, ground-state carotenoid molecules are converted to long-lived triplet excited-state quenchers, and phi decreases as Y increases. It is shown that both types of processes are formally described by the same theoretical equations that relate phi to Y. The calculated phi (Y) curves depend on two parameters m and R, where m is the number of reaction centers (or ground-state carotenoid molecules that can be converted to triplets), and R is the ratio phi (Y leads to infinity)/(Y leads to 0). The finiteness of the photosynthetic units is thus taken into account. The m = 1 case corresponds to the "puddle" model, and m leads to infinity to the "lake," or matrix, model. It is shown that the experimental phi (Y) curves for both fluorescence induction and singlet-triplet exciton quenching experiments are better described by the m leads to infinity cases than the m = 1 case.     

A predictive model of moment-angle characteristics in human skeletal muscle: application and validation in muscles across the ankle joint

In the present work, a generic model for the prediction of moment-angle characteristics in individual human skeletal muscles is presented. The model's prediction is based on the equation M = V x Lo(-1)sigma c cos phi x d, where M, V, and Lo are the moment-generating potential of the muscle, the muscle volume and the optimal muscle fibre length, respectively, and sigma, phi and d are the stress-generating potential of the muscle fibres, their pennation angle and the tendon moment arm length, respectively, at any given joint angle. The input parameters V, Lo, sigma, phi and d can be measured or derived mechanistically. This eliminates the common problem of the necessity to estimate one or more of the input parameters in the model by fitting its outcome to experimental results often inappropriate for the function modelled. The model's output was validated by comparisons with the moment-angle characteristics of the gastrocnemius (GS) and tibialis anterior (TA) muscles in six men, determined experimentally using voluntary contractions at several combinations of ankle and knee joint angles for the GS muscle and electrical stimulation for the TA muscle. Although the model predicted realistically the pattern of moment-angle relationship in both muscles, it consistently overestimated the GS muscle M and consistently underestimated the TA muscle M, with the difference gradually increasing from dorsiflexion to plantarflexion in both cases. The average difference between predicted and measured M was 14% for the GS muscle and 10% for the TA muscle. Approximating the muscle fibres as a single sarcomere in both muscles and failing to achieve complete TA muscle activation by electrical stimulation may largely explain the differences between theory and experiment.     

The crystal structure of the alpha-cellobiose.2 NaI.2 H(2)O complex in the context of related structures and conformational analysis

The crystal structure of beta-D-glucopyranosyl-(1-->4)-alpha-D-glucopyranose (alpha-cellobiose) in a complex with water and NaI was determined with Mo K(alpha) radiation at 150 K to R=0.027. The space group is P2(1) and unit cell dimensions are a=9.0188, b=12.2536, c=10.9016 A, beta=97.162 degrees. There are no direct hydrogen bonds among cellobiose molecules, and the usual intramolecular hydrogen bond between O-3 and O-5' is replaced by a bridge involving Na+, O-3, O-5', and O-6'. Both Na+ have sixfold coordination. One I(-) accepts six donor hydroxyl groups and three C-H***I(-) hydrogen bonds. The other accepts three hydroxyls, one Na+, and five C-H***I(-) hydrogen bonds. Linkage torsion angles phi(O-5) and psi(C-5) are -73.6 and -105.3 degrees, respectively (phi(H)=47.1 degrees and psi(H)=14.6 degrees ), probably induced by the Na+ bridge. This conformation is in a separate cluster in phi,psi space from most similar linkages. Both C-6-O-H and C-6'-O-H are gg, while the C-6'-O-H groups from molecules not in the cluster have gt conformations. Hybrid molecular mechanics/quantum mechanics calculations show <1.2 kcal/mol strain for any of the small-molecule structures. Extrapolation of the NaI cellobiose geometry to a cellulose molecule gives a left-handed helix with 2.9 residues per turn. The energy map and small-molecule crystal structures imply that cellulose helices having 2.5 and 3.0 residues per turn are left-handed.     

Analysis of the force-sharing problem using an optimization model

In biomechanics, one frequently used approach for finding a unique set of muscle forces in the 'force-sharing problem' is to formulate and solve a non-linear optimization problem of the form: min phi(f)= summation operator (f(i)/omega(i))(alpha) subject to Af = b and f > or = 0. Solutions to this problem have typically been obtained numerically for complex models, or analytically for specific musculoskeletal geometries. Here, we present simple geometrical methods for analyzing the solution to this family of optimization problems for a general n-degrees-of-freedom musculoskeletal system. For example, it is shown that the moment-arm vectors of active (f(i) > 0) and passive (f(i) = 0) muscles are separated by a hyperplane through the origin of the moment-arm vector space. For the special case of a system with two degrees-of-freedom, solutions can be readily represented in graphical form. This allows for powerful interpretations of force-sharing calculated using optimization.     

Comparison of a QM/MM force field and molecular mechanics force fields in simulations of alanine and glycine "dipeptides" (Ace-Ala-Nme and Ace-Gly-Nme) in water in relation to the problem of modeling the unfolded peptide backbone in solution

We compare the conformational distributions of Ace-Ala-Nme and Ace-Gly-Nme sampled in long simulations with several molecular mechanics (MM) force fields and with a fast combined quantum mechanics/molecular mechanics (QM/MM) force field, in which the solute's intramolecular energy and forces are calculated with the self-consistent charge density functional tight binding method (SCCDFTB), and the solvent is represented by either one of the well-known SPC and TIP3P models. All MM force fields give two main states for Ace-Ala-Nme, beta and alpha separated by free energy barriers, but the ratio in which these are sampled varies by a factor of 30, from a high in favor of beta of 6 to a low of 1/5. The frequency of transitions between states is particularly low with the amber and charmm force fields, for which the distributions are noticeably narrower, and the energy barriers between states higher. The lower of the two barriers lies between alpha and beta at values of psi near 0 for all MM simulations except for charmm22. The results of the QM/MM simulations vary less with the choice of MM force field; the ratio beta/alpha varies between 1.5 and 2.2, the easy pass lies at psi near 0, and transitions between states are more frequent than for amber and charmm, but less frequent than for cedar. For Ace-Gly-Nme, all force fields locate a diffuse stable region around phi = pi and psi = pi, whereas the amber force field gives two additional densely sampled states near phi = +/-100 degrees and psi = 0, which are also found with the QM/MM force field. For both solutes, the distribution from the QM/MM simulation shows greater similarity with the distribution in high-resolution protein structures than is the case for any of the MM simulations.     

Can reliable torsion elastic constants be determined from FPA data on 24 and 27 base-pair DNAs?

Torsion elastic constants obtained from fluorescence polarization anisotropy (FPA) measurements on fifty-three 24 and 27 base-pair (bp) DNAs were recently reported [F. Pedone, F. Mazzei, D. Santoni, Sequence-dependent DNA torsional rigidity: a tetranucleotide code, Biophys. Chem. 112 (2004) 77-88; F. Pedone, F. Mazzei, M. Matzeu, F. Barone, Torsional constant of 27-mer DNA oligomers of different sequences, Biophys. Chem. 94 (2001) 175-184]. The problem of extracting reliable torsion elastic constants (alpha) from FPA measurements on such short DNAs is examined in detail. The difficulty is illustrated by two (fictitious) 24 bp DNAs with approximately 5-fold different torsion elastic constants and 10% different initial anisotropies (r(0)), which exhibit practically indistinguishable anisotropy decays for all t>1 ns. FPA data were simulated for 24 bp DNAs with different input values of alpha and r(0) in the presence and absence of Poisson noise, and were fitted using different choices of the adjustable and fixed parameters. Experimental data for a 24 bp DNA were fitted in a similar manner. For either the simulated or experimental FPA data, it was not possible to determine both the initial anisotropy, r(0), and the torsion elastic constant, alpha, in a reliable (i.e. statistically significant) manner in the presence of Poisson noise. When r(0) is assumed to be fixed at any particular value in the fitting protocol, a unique best-fit value of alpha is obtained, but that best-fit alpha is extremely sensitive to small deviations of the assumed fixed value of r(0) away from the input r(0)-value of the simulated data. Pedone et al. fitted their FPA data by assuming that r(0)=0.360, and adjusting alpha, the hydrodynamic radius (R(H)), and effective length (L). In fact, the reported best-fit values of R(H) and L lay significantly outside their expected ranges. When this same fitting protocol is applied to simulated data for 27 bp DNAs, better overall agreement with the reported experimental values (alpha, R(H), and L) is obtained for a model, wherein all DNAs have the same typical input alpha=5.9 x 10(-12) dyn cm, R(H)=10.0 A, and L=27 (3.4)+2.7=94.5 A, but a 1.00- to 1.13-fold range of r(0)-values, than for the model of Pedone et al., wherein all DNAs have the same input r(0)=0.360, R(H)=10.0 A, and L=94.5 A, but a approximately 3-fold range of alpha-values. It is concluded that, in the absence of reliable independent estimates of r(0) for every DNA, the alpha-values reported for 24 and 27 bp DNAs cannot be regarded as experimentally justified. The reliability of the torsion elastic constants reported for the 136 distinct tetranucleotide steps, which are inferred from the values reported for the fifty-three 24 and 27 bp DNAs, is also briefly discussed.     

Swelling and de-swelling kinetics of gelatin hydrogels in ethanol-water marginal solvent

Controlled osmotic swelling and de-swelling measurements have been performed on gelatin, a polyampholyte, hydrogels suspended in water-ethanol marginal solvent at room temperature (20 degrees C) where the alcohol concentration was changed from 0 to 100% (v/v). The change in gel mass was monitored as function of time until osmotic equilibrium was established with the surrounding solvent. It was observed that osmotic pressure of polymer-solvent mixing, pi(m)相似文献   

Evaluation of the predictive power of calculation procedure for molecular hydrophobicity of some estradiol derivates

Several calculation procedures for log P values based on the fragmental and atomic contributions are compared with experimental reversed-phase liquid chromatography (RPLC) retention of estradiol derivates. The RPLC experiments were performed on HPTLC and HPLC commercially available stationary phases. Binary solvent mixtures of methanol-water and acetonitrile-water were used as mobile phases. The correlation between log P and various chromatographically obtained hydrophobicity parameters (R(M)0, log k(w) and phi0) are quantified. The R(M)0, i.e., log k(w) were obtained by linear extrapolation of retention to 0% organic modifier. Phi0 values were obtained from the slopes and intercepts of such linear relationship. The mutual relationship between phi(0,MeOH) and phi(0,ACN) values of the compounds were discussed. The obtained statistical results can be summarized in the following order of reliabilities for different log P calculation methods: Broto>ACD/logP>Crippen>Rekker>Viswanadhan.     

Measurement of membrane potential and estimation of effective fixed-charge density in membranes.

Electrical potentials Em arising across cross-linked phenolsulfonate membrane separating NaCl solutions of molality M1 and M2 have been measured at 25 degrees C. These values of Em have been used in the Nernst equation to calculate values for the apparent transport number ti(app) for the counterion or the co-ion in the membrane. Values of ti(app) together with the limiting value for the cation transport number in the aqueous phase have been used in the equation developed by Kobatake and co-workers to evaluate the membrane permselectivity Ps as a function of external electrolyte concentration. With the help of the equation relating Ps to phiX, the effective fixed-charge density in the membrane (where phi is a constant, 0 less than phi less than 1, and X is the membrane stochiometric charge density and can be evaluated by chemical analysis of the membrane phase), values for phiX and phi have been determined. Values of phi were low in dilute solutions and increased with increase in the concentration of the external solution. Similar behavior was noted in the case of another membrane system, cross-linked polymethacrylic acid in contact with KOH solutions. On the other hand, the membrane system, "untreated" collodion in contact with KCl solutions, exhibited a behavior in which the values of phi, low in dilute solutions, increased and then decreased following a gradual increase in the external concentration. This slight divergence in its behavior was attributed to the heterogeneity of the collodion membrane structure. The reliability of this potentiometric method to estimate effective fixed-charge density in membranes has been discussed in relation to a similar but old method due to Teorell, Meyer and Sievers. Also the significance of the values derived for phi has been pointed out.