A matrix‐based method of moments for fitting the multivariate random effects model for meta‐analysis and meta‐regression

Multivariate meta‐analysis is becoming more commonly used. Methods for fitting the multivariate random effects model include maximum likelihood, restricted maximum likelihood, Bayesian estimation and multivariate generalisations of the standard univariate method of moments. Here, we provide a new multivariate method of moments for estimating the between‐study covariance matrix with the properties that (1) it allows for either complete or incomplete outcomes and (2) it allows for covariates through meta‐regression. Further, for complete data, it is invariant to linear transformations. Our method reduces to the usual univariate method of moments, proposed by DerSimonian and Laird, in a single dimension. We illustrate our method and compare it with some of the alternatives using a simulation study and a real example.     

Murine plasma cells secreting more than one class of immunoglobulin heavy chain. III. Immunoglobulin production by established cultures and cloned lines of SAMM 368.

SAMM 368, a plasmacytoma which produces IgA-kappa and IgG2b-kappa was established in vitro from primary explants or after animal passage. The 9 lines that were established produced both paraproteins. The production of both immunoglobulins by single cells was demonstrated by immunofluorescent staining and cloning. Continuous culture of 3 parent lines for 18 months and 11 cloned lines for periods from 5 to 7 months demonstrated that double production is a stable characteristic of this plasmacytoma. Two single paraprotein-producing varients (IgG2b or IgA) were derived when cells were cultured in the presence of Fungizone. Chromosomal analysis of SAMM 368 indicates that this double producing tumor has a modal number similar to those observed in myelomas producing a single immunoglobulin class.     

Flagellar hydrodynamics. A comparison between resistive-force theory and slender-body theory.

This paper investigates the accuracy of the resistive-force theory (Gray and Hancock method) which is commonly used for hydrodynamic analysis of swimming flagella. We made a comparison between the forces, bending moments, and shear moments calculated by resistive-force theory and by the more accurate slender-body theory for large-amplitude, planar wave forms computed for a flagellar model. By making an upward empirical adjustment, by about 35%, of the classical drag coefficient values used in the resistive-force theory calculations, we obtained good agreement between the distributions of the forces and moments along the length of the flagellum predicted by the two methods when the flagellum has no cell body attached. After this adjustment, we found the rate of energy expenditure calculated by the two methods for the few typical test cases to be almost identical. The resistive-force theory is thus completely satisfactory for use in analysis of mechanisms for the control of flagellar bending, at the current level of sophistication of this analysis. We also examined the effects of the presence of a cell body attached to one end of the flagellum, which modifies the flow field experienced by the flagellum. This interaction, which is not considered in resistive-force theory, is probably insignificant for small cell bodies, such as the heads of simple spermatozoa, but for larger cell bodies, or cell bodies that have large-amplitude motions transverse to the swimming direction, use of slender-body theory is required for accurate analysis.     

Quantitative approaches to utilizing mutational analysis and disulfide crosslinking for modeling a transmembrane domain.

The transmembrane domain of chemoreceptor Trg from Escherichia coli contains four transmembrane segments in its native homodimer, two from each subunit. We had previously used mutational analysis and sulfhydryl cross-linking between introduced cysteines to obtain data relevant to the three-dimensional organization of this domain. In the current study we used Fourier analysis to assess these data quantitatively for periodicity along the sequences of the segments. The analyses provided a strong indication of alpha-helical periodicity in the first transmembrane segment and a substantial indication of that periodicity for the second segment. On this basis, we considered both segments as idealized alpha-helices and proceeded to model the transmembrane domain as a unit of four helices. For this modeling, we calculated helical crosslinking moments, parameters analogous to helical hydrophobic moments, as a quantitative way of condensing and utilizing a large body of crosslinking data. Crosslinking moments were used to define the relative separation and orientation of helical pairs, thus creating a quantitatively derived model for the transmembrane domain of Trg. Utilization of Fourier transforms to provide a quantitative indication of periodicity in data from analyses of transmembrane segments, in combination with helical crosslinking moments to position helical pairs should be useful in modeling other transmembrane domains.     

Harvesting on a stage-structured single population model with mature individuals in a polluted environment and pulse input of environmental toxin

In the natural world, there are many species whose individual members have a life history that they take them with two distinct stages: immaturity and maturity. In particular, we have in mind mammalian populations and some amphibious animals. We improve the assumption of a single population as a whole. It is assumed that the immature individuals and mature individuals are divided by a fixed period. This paper concentrates on the study of a stage-structured single population model with mature individuals in a polluted environment and pulse input of environmental toxin at fixed moments. Furthermore, the mature individuals are harvested continuously. We show that the population goes extinct if the harvesting rate is beyond a critical threshold. Conditions for the extended permanence of the population are also examined. From the biological point of view, it is easy to protect species by controlling the harvesting amount, impulsive period of the exogenous input of toxin and toxin impulsive input amount, etc. Our results provide reasonable tactics for biological resource management.     

A stochastic analysis of first-order reaction networks

A stochastic model for a general system of first-order reactions in which each reaction may be either a conversion reaction or a catalytic reaction is derived. The governing master equation is formulated in a manner that explicitly separates the effects of network topology from other aspects, and the evolution equations for the first two moments are derived. We find the surprising, and apparently unknown, result that the time evolution of the second moments can be represented explicitly in terms of the eigenvalues and projections of the matrix that governs the evolution of the means. The model is used to analyze the effects of network topology and the reaction type on the moments of the probability distribution. In particular, it is shown that for an open system of first-order conversion reactions, the distribution of all the system components is a Poisson distribution at steady state. Two different measures of the noise have been used previously, and it is shown that different qualitative and quantitative conclusions can result, depending on which measure is used. The effect of catalytic reactions on the variance of the system components is also analyzed, and the master equation for a coupled system of first-order reactions and diffusion is derived. All authors contributed equally to this work.     

Identification of passive elastic joint moments in the lower extremities.

Musculotendon actuators produce active and passive moments at the joints they span. Due to the existence of bi-articular muscles, the passive elastic joint moments are influenced by the angular positions of adjacent joints. To obtain quantitative information about this passive elastic coupling between lower limb joints, we examined the passive elastic joint properties of the hip, knee, and ankle joint of ten healthy subjects. Passive elastic joint moments were found to considerably depend on the adjacent joint angles. We present a simple mathematical model that describes these properties on the basis of a double-exponential expression. The model can be implemented in biomechanical models of the lower extremities, which are generally used for the simulation of multi-joint movements such as standing-up, walking, running, or jumping.     

The superposition principle applied to grasping an object producing moments outside anatomically-defined axes

The superposition principle suggests that motor commands can be divided into individually controlled components that summate to produce complex motor actions. Previous studies have examined the validity of this principle in human grasping by changing moments acting on an object about a single anatomically-defined axis and asking subjects to hold the object while their forearm was constrained. Superposition was reflected as separate control of the grip force and moments required to prevent object slip and maintain orientation. The objective of this study was to examine the robustness of this principle by: 1) expanding the range of tasks to include those where moments act on an object with respect to moment arms not necessarily in line with the anatomically-defined axes; 2) asking subjects to hold the object in an unconstrained manner. Ten subjects were asked to lift and hold an object vertically under eighteen moment conditions. Force and moment data from all digits were analysed using principal components analysis (PCA). Different PCAs were run for variable sets corresponding to moments about the long axis of the forearm (M(x)), the vertical (M(y)) and grip (M(z)) axes, and for the entire dataset (M(3D)). The PCA showed grip force and moment variables on separate PCs for the M(x), M(y), and M(3D) variable sets. The M(3D) PCA also showed a separation of variables corresponding to moments about each anatomically-defined axis. Thus, the present results show that the superposition principle holds during natural manipulation of an object experiencing external moments outside the anatomically-defined axes.     

Assessment of tibial stiffness by vibration testing in situ--I. Identification of mode shapes in different supporting conditions

Vibrational methods to monitor fracture healing, the BRA and the IFR, are compared under different supporting conditions, excitation technique and signal processing. Mode shapes are identified by modal analysis. A wet excised human tibia and an amputation specimen are investigated. Excitation technique and signal processing caused only minor differences in the resonance frequencies. The supporting conditions had an important influence on the single bending modes changing both mode-shapes and frequencies. Thus the BRA-splint imposed a node at the malleolus. Modal analysis revealed the following modes in the two supporting conditions: BRA-splint: A 'rigid body' mode of 165 Hz in the sagittal plane. A single bending mode of 315 Hz close to the sagittal plane. IFR-hanging leg: A 'rigid-body' mode of 167 Hz close to the sagittal plane. Two single bending modes ('free-free'), a mode of 303 Hz close to the frontal plane and a mode of 470 Hz in the sagittal plane.     

Use and abuse of the quasi-steady-state approximation

The transient kinetic behaviour of an open single enzyme, single substrate reaction is examined. The reaction follows the Van Slyke-Cullen mechanism, a spacial case of the Michaelis-Menten reaction. The analysis is performed both with and without applying the quasi-steady-state approximation. The analysis of the full system shows conditions for biochemical pathway coupling, which yield sustained oscillatory behaviour in the enzyme reaction. The reduced model does not demonstrate this behaviour. The results have important implications in the analysis of open biochemical reactions and the modelling of metabolic systems.     

EMG-Driven Forward-Dynamic Estimation of Muscle Force and Joint Moment about Multiple Degrees of Freedom in the Human Lower Extremity

This work examined if currently available electromyography (EMG) driven models, that are calibrated to satisfy joint moments about one single degree of freedom (DOF), could provide the same musculotendon unit (MTU) force solution, when driven by the same input data, but calibrated about a different DOF. We then developed a novel and comprehensive EMG-driven model of the human lower extremity that used EMG signals from 16 muscle groups to drive 34 MTUs and satisfy the resulting joint moments simultaneously produced about four DOFs during different motor tasks. This also led to the development of a calibration procedure that allowed identifying a set of subject-specific parameters that ensured physiological behavior for the 34 MTUs. Results showed that currently available single-DOF models did not provide the same unique MTU force solution for the same input data. On the other hand, the MTU force solution predicted by our proposed multi-DOF model satisfied joint moments about multiple DOFs without loss of accuracy compared to single-DOF models corresponding to each of the four DOFs. The predicted MTU force solution was (1) a function of experimentally measured EMGs, (2) the result of physiological MTU excitation, (3) reflected different MTU contraction strategies associated to different motor tasks, (4) coordinated a greater number of MTUs with respect to currently available single-DOF models, and (5) was not specific to an individual DOF dynamics. Therefore, our proposed methodology has the potential of producing a more dynamically consistent and generalizable MTU force solution than was possible using single-DOF EMG-driven models. This will help better address the important scientific questions previously approached using single-DOF EMG-driven modeling. Furthermore, it might have applications in the development of human-machine interfaces for assistive devices.     

Enzymatic multiplex DNA sequencing.

The problem of reading DNA sequence films has been reformulated using an easily implemented, multiplex version of enzymatic DNA sequencing. By utilizing a uniquely tagged primer for each base-specific sequencing reaction, the four reactions can be pooled and electrophoresed in a single lane. This approach has been previously proposed for use with fluorescently labelled probes (1), and is analogous to the principle used in four-dye fluorescence sequencing except that the signals are resolved following electrophoresis (2). After transfer to a nylon membrane, images are obtained separately for each of the four reactions by hybridization using oligonucleotide probes. The images can then be superimposed to reconstitute a complete sequence pattern. In this way the correction of gel distortion effects and accurate band registration are considerably simplified, as each of the four base-specific ladders require very similar corrections. The methods therefore provide the basis for a second generation of more accurate and reliable film reading programs, as well as being useful for conventional multiplex sequencing. Unlike the original multiplex protocol (3), the approach described is suitable for small projects, as multiple cloning vectors are not used. Although more than one vector can be utilized, only a library of fragments cloned into any single phage, phagemid or plasmid vector is actually required, together with a set of tagged oligonucleotide primers.     

Elution-band relaxation method. A method to analyze isomerization kinetics by HPLC and application to protein denaturation-renaturation

We present a novel method, the 'elution-band relaxation method', to analyze quantitatively reversible isomerization kinetics by elution chromatography, taking advantage of the high resolution and speed of high-performance liquid chromatography (HPLC). The kinetic information is obtained by measuring the first temporal moments of chromatograms of molecules undergoing isomerization and analyzing their dependence on the column length or flow rate. The major advantage of this method is that it is applicable to reactions as fast as the time of elution in HPLC, a speed which has not been attained previously in analysis of isomerization reactions based on the chromatographic property of molecules. We describe the method and report an experimental application to the denaturation-renaturation kinetics of bovine pancreatic ribonuclease A as an example.     

Fluctuation analysis in small chemically reacting systems

A theory of noise fluctuations is developed which is applicable to systems of any size in which unimolecular or bimolecular reactions are occurring. The main difference between small and large reacting systems is that in the former the probability of finding a particle in a particular state does not obey a Gaussian distribution, but satisfies a distribution which reflects the mechanism of the chemical reaction. This difference is reflected in the main result of the theory: an autocorrelation function that is expressible as a sum of exponentials, the amplitudes of which are explicit functions of the moments of the distribution. Thus, by using small systems, the autocorrelation function,in principle, allows the elucidation of reaction mechanisms. Numerical simulations indicate that for reacting systems having ten or fewer particles, the deviation of the autocorrelation function from a single exponential should be easily detectable, and that estimates of the first four moments of the distribution should be possible. Accurate inference of the distribution, however, will require further mathematical and experimental advances.     

Production and characterization of bifunctional enzymes. Substrate channeling in the aspartate pathway

The direct channeling of an intermediate between enzymes that catalyze consecutive reactions in a pathway offers the possibility of an efficient, exclusive, and protected means of metabolite delivery. Aspartokinase-homoserine dehydrogenase I (AK-HDH I) from Escherichia coli is an unusual bifunctional enzyme in that it does not catalyze consecutive reactions. The potential channeling of the intermediate beta-aspartyl phosphate between the aspartokinase of this bifunctional enzyme and aspartate semialdehyde dehydrogenase (ASADH), the enzyme that catalyzes the intervening reaction, has been examined. The introduction of increasing levels of inactivated ASADH has been shown to compete against enzyme-enzyme interactions and direct intermediate channeling, leading to a decrease in the overall reaction flux through these consecutive enzymes. These same results are obtained whether these experiments are conducted with aspartokinase III, a naturally occurring monofunctional isozyme, with an artificially produced monofunctional aspartokinase I, or with a fusion construct of AK I-ASADH. These results provide definitive evidence for the channeling of beta-aspartyl phosphate between aspartokinase and aspartate semialdehyde dehydrogenase in E. coli and suggest that ASADH may provide a bridge to channel the intermediates between the non-consecutive reactions of AK-HDH I.     

Optical rotatory properties of L-cystine conformational isomers. Theoretical analysis

The near ultraviolet chiroptical properties of L -cystine conformational isomers are examined on a static, “one-electron” model in which the disulfide moiety is the chromophoric group and the atoms of the L -alanyl fragments are treated as perturbers. The zeroth order chromophoric wave functions are calculated on a semiempirical molecular orbital model in which excited states are constructed in the virtual orbital-configuration interaction approximation. The perturbing environment is represented by point charges located at the atomic centers of the L -alanyl fragments. Chromophore–perturber interactions are expressed as charge–multipole moments with only the charge–dipole and charged–quadrupole terms being retained in the calculations. Vicinal contributions to the rotatory strengths of the five lowest energy disulfide transitions are computed for 30 conformational isomers of the L -cystine dizwitterion. The results provide support for the view that vicinal or peripheral effects can account entirely for the observed near ultraviolet (λ > 230 nm) chiroptical properties of L -cystine and its derivatives and that these properties are diagnostic of conformational features external to the disulfide moiety.     

Evolution of patterns of gene expression in Hawaiian picture-wingedDrosophila

Summary The tissue and stage specificity of expression of five enzymes was examined by electrophoretic analysis of relative enzyme levels in extracts of 13 larval and adult tissues in 27 species of Hawaiian picture-wingedDrosophila. The developmentally regulated patterns of enzyme expression thus characterized were compared to a modal standard phenotype. About 30% of the pattern features analyzed differed significantly from the standard in one or more species. Many of these regulatory differences are essentially qualitative, with tissue specific differences in enzyme activity in excess of 100 fold for some species pairs. The adaptive significance of these pattern differences is unknown, but the results provide strong direct evidence for rapid evolution of new patterns of gene regulation in this group of organisms.     

Band centrifugation of macromolecules in self-generating density gradients. II. Sedimentation and diffusion of macromolecules in bands

Three approaches to the simultaneous sedimentation and diffusion of hands or zones of noninteracting homogeneous macromolecules are examined: (1) The authors' method of moments: (2) the transport me of Sehumaker and Rosenbloom; and (3) the stochastic solution of the Lamm equation due to Gehatia and Katehalski. All three methods indicate that the motion of the maximum of the hand may be used to evaluate the sedimentation coefficient. The moment, method provides relations which appear to be useful for measuring diffusion coefficients. Relations are given for the analysis of resolved components. The problem of measuring sedimentation coefficients of macromolecules with concentration-dependent sedimentation coefficients is examined. Methods are described for evaluating the sedimentation coefficient in these systems and for obtaining the sedimentation coefficient at infinite dilution. Methods are described for determining the weight-average sedimentation coefficient in Multi-component systems, and the differential and integral distribution of sedimentation coefficients of macromolecules with low-diffusion coefficients.     

Assessment of tibial stiffness by vibration testing in situ--II. Influence of soft tissues, joints and fibula

The influence of soft tissues and joints on the vibration of the human tibia was examined by modal analysis on amputated lower limbs, where the soft tissues and the fibula were dissected gradually. Measurements were made in two different set ups, IFR and BRA, which were both designed to monitor fracture healing. In IFR, vibrations are generated by hammer impact on a relaxed hanging lower leg, with the knee flexed. Resonant frequencies are determined by a computer Fourier transform procedure. In BRA, a steady state vibration is induced in a lower leg, supported near the ankle and the tibial tuberosity, using an electromagnetic shaker. Resonant frequencies are determined from the maxima in vibration amplitudes. In both set ups the soft tissues have a similar influence on the vibration of the tibia: the skin hardly influences the determined modal parameter. The mass of the muscles influences both the resonant frequency and the damping. The fibula has a stiffening effect on the tibia. The influence of the joints is small in the IFR-set up: the tibia vibrates in conditions close to those for the free-free vibration. In the BRA-set up, the supports determine the boundary conditions.