Numerical methods for handling uncertainty in microarray data: an example analyzing perturbed mitochondrial function in yeast.
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Chloramphenicol↗
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Determination of the critical O2 delivery from experimental data: sensitivity to error.
Normally, metabolic need determines tissue O2 consumption (VO2). In states of reduced supply, VO2 declines sharply below a critical level of O2 delivery (QO2 = blood flow X arterial O2 content). Although several investigators have measured a critical O2 delivery in whole animals or in isolated tissues, there is no general agreement over how to determine the critical point from a collection of real data. In this study, we compare three algorithms for finding the critical O2 delivery from a set of experimental data. We also present a technique for estimating the effect of experimental error on the precision of these algorithms. Using 16 data sets collected in normal dogs, we compare single-line, dual-line, and polynomial regression algorithms for identifying the critical O2 delivery. The dual-line and polynomial regression techniques fit the data better (mean residual square deviation 0.024 and 0.031, respectively) than the single-regression line approach (0.110). To investigate the influence of experimental error on the derived critical QO2, we used a Monte Carlo technique, repeatedly perturbing the experimental data to simulate experimental error. We then calculated the variance of the critical QO2 frequency distribution obtained when the three algorithms were applied to the perturbed data. By this analysis, the dual-line regression technique was less sensitive to experimental error than the polynomial technique.
Algorithms↗
Artificial neural networks as a novel approach to integrated pharmacokinetic-pharmacodynamic analysis.
A novel model-independent approach to analyze pharmacokinetic (PK)-pharmacodynamic (PD) data using artificial neural networks (ANNs) is presented. ANNs are versatile computational tools that possess the attributes of adaptive learning and self-organization. The emulative ability of neural networks is evaluated with simulated PK-PD data, and the power of ANNs to extrapolate the acquired knowledge is investigated. ANNs of one architecture are shown to be flexible enough to accurately predict PD profiles for a wide variety of PK-PD relationships (e.g., effect compartment linked to the central or peripheral compartment and indirect response models). Also, an example is given of the ability of ANNs to accurately predict PD profiles without requiring any information regarding the active metabolite. Because structural details are not required, ANNs exhibit a clear advantage over conventional model-dependent methods. ANNs are proved to be robust toward error in the data and perturbations in the initial estimates. Moreover, ANNs were shown to handle sparse data well. Neural networks are emerging as promising tools in the field of drug discovery and development.
Mathematical Computing↗
A robust microcomputer routine for the identification of outlying and influential points in radioimmunoassay standard curves.
This paper describes a suite of robust logit-log optimization routines for the fitting of a linear relation to laboratory data. The microcomputer routines assign a weighting value to each data point corresponding to the relative importance of that point. This procedure ensures that the routines identify and deal with any outlying data points. The routines are designed to generate the results of both a standard, unweighted least-squares algorithm and a robust, weighted algorithm thus providing the laboratory analyst with invaluable information concerning the data and the fitted relation. The routines are thoroughly tested on "perfect" and perturbed laboratory data.
Biometry↗
A stability based method for discovering structure in clustered data.
We present a method for visually and quantitatively assessing the presence of structure in clustered data. The method exploits measurements of the stability of clustering solutions obtained by perturbing the data set. Stability is characterized by the distribution of pairwise similarities between clusterings obtained from sub samples of the data. High pairwise similarities indicate a stable clustering pattern. The method can be used with any clustering algorithm; it provides a means of rationally defining an optimum number of clusters, and can also detect the lack of structure in data. We show results on artificial and microarray data using a hierarchical clustering algorithm.
Algorithms↗
External validity of predictive models: a comparison of logistic regression, classification trees, and neural networks.
BACKGROUND AND OBJECTIVE: The utility of predictive models depends on their external validity, that is, their ability to maintain accuracy when applied to patients and settings different from those on which the models were developed. We report a simulation study that compared the external validity of standard logistic regression (LR1), logistic regression with piecewise-linear and quadratic terms (LR2), classification trees, and neural networks (NNETs). METHODS: We developed predictive models on data simulated from a specified population and on data from perturbed forms of the population not representative of the original distribution. All models were tested on new data generated from the population. RESULTS: The performance of LR2 was superior to that of the other model types when the models were developed on data sampled from the population (mean receiver operating characteristic [ROC] areas 0.769, 0.741, 0.724, and 0.682, for LR2, LR1, NNETs, and trees, respectively) and when they were developed on nonrepresentative data (mean ROC areas 0.734, 0.713, 0.703, and 0.667). However, when the models developed using nonrepresentative data were compared with models developed from data sampled from the population, LR2 had the greatest loss in performance. CONCLUSION: Our results highlight the necessity of external validation to test the transportability of predictive models.
Classification↗
Proliferation kinetics of perturbed cell populations determined by the bromodeoxyuridine-33258 technique: radiotoxic effects of incorporated [3H]thymidine.
A simple analytical method is described for the evaluation of flow cytometric data of perturbed cell populations obtained by applying the BrdUrd-33258 Hoechst technique. This procedure allows for determining the growth curve, the efflux from and the influx into G2 + M as well as the transit characteristics of cell cohorts through the G2 + M phase. As an example of the application of the method, the radiotoxic effects of incorporated 3H-thymidine on the proliferation of L-929 cells in vitro are described.
Animals↗
Gene regulatory network structure informs the distribution of perturbation effects.
Gene regulatory networks (GRNs) govern many core developmental and biological processes underlying human complex traits. Even with broad-scale efforts to characterize the effects of molecular perturbations and interpret gene coexpression, it remains challenging to infer the architecture of gene regulation in a precise and efficient manner. Key properties of GRNs, like hierarchical structure, modular organization, and sparsity, provide both challenges and opportunities for this objective. Here, we seek to better understand properties of GRNs using a new approach to simulate their structure and model their function. We produce realistic network structures with a novel generating algorithm based on insights from small-world network theory, and we model gene expression regulation using stochastic differential equations formulated to accommodate modeling molecular perturbations. With these tools, we systematically describe the effects of gene knockouts within and across GRNs, finding a subset of networks that recapitulate features of a recent genome-scale perturbation study. With deeper analysis of these exemplar networks, we consider future avenues to map the architecture of gene expression regulation using data from cells in perturbed and unperturbed states, finding that while perturbation data are critical to discover specific regulatory interactions, data from unperturbed cells may be sufficient to reveal regulatory programs.
Gene Regulatory Networks↗
Various strategies of using residual dipolar couplings in NMR-driven protein docking: application to Lys48-linked di-ubiquitin and validation against 15N-relaxation data.
When classical, Nuclear Overhauser Effect (NOE)-based approaches fail, it is possible, given high-resolution structures of the free molecules, to model the structure of a complex in solution based solely on chemical shift perturbation (CSP) data in combination with orientational restraints from residual dipolar couplings (RDCs) when available. RDCs can be incorporated into the docking following various strategies: as direct restraints and/or as intermolecular intervector projection angle restraints (Meiler et al., J Biomol NMR 2000;16:245-252). The advantage of the latter for docking is that they directly define the relative orientation of the molecules. A combined protocol in which RDCs are first introduced as intervector projection angle restraints and at a later stage as direct restraints is shown here to give the best performance. This approach, implemented in our information-driven docking approach HADDOCK (Dominguez et al., J Am Chem Soc 2003;125:1731-1737), is used to determine the solution structure of the Lys48-linked di-ubiquitin, for which chemical shift mapping, RDCs, and (15)N-relaxation data have been previously obtained (Varadan et al., J Mol Biol 2002;324:637-647). The resulting structures, derived from CSP and RDC data, are cross-validated using (15)N-relaxation data. The solution structure differs from the crystal structure by a 20 degrees rotation of the two ubiquitin units relative to each other.
Algorithms↗
Global analysis of the acid-induced and urea-induced unfolding of staphylococcal nuclease and two of its variants.
We have studied the equilibrium unfolding staphylococcal nuclease and two of its variants, V66W and V66W', over two perturbation axes (acid-induced unfolding as a function of urea concentration and urea-induced unfolding as a function of pH). The transitions were monitored by simultaneous measurements of circular dichroism and fluorescence. With this multidimensional array of data (2 perturbation axes and 2 signals), we present a strategy of performing a global analysis, over as many as 12 individual data sets, to test various models for the unfolding process, to determine with greater confidence the pertinent thermodynamic parameters, and to characterize unfolding intermediates. For example, wildtype nuclease shows a cooperative two-state transition with either urea or pH as denaturant, but the global fits are improved when the model is expanded to include a pH dependence of the urea m value or when two distinct classes of protonic groups are considered. The best fit for wild-type nuclease is with delta G degree 0,UN = 6.4 kcal/mol at pH 7, with the acid-induced unfolding being triggered by protonation of three to five carboxylate groups (with possible contribution from His121), and with the urea m = 2.5 kcal mol-1 M-1. V66W' lacks the last 13 amino acids on the C-terminus, has a tryptophan at position 66, has a predominantly beta-sheet structure, and is less stable than the wild type. For V66W', delta G degree 0,UN = 1.6 kcal/mol, m = 1.2 kcal mol-1 M-1, and there are two or three groups responsible for acid unfolding. V66W, a full-length mutant with two tryptophan residues, unfolds via a three-state mechanism: native reversible intermediate reversible unfolded. It appears that its beta-barrel subdomain retains structure in the intermediate state. Assuming that the unfolding of V66W' and the beta-barrel subdomain of V66W can be described by the same thermodynamic parameters, a global analysis enabled a description of the alpha subdomain of V66W with delta G degree 0,IN = 2.7 kcal/mol, mIN = 1.1 kcal mol-1 M-1, and with the acid unfolding being triggered by protonation of a single group. This group has a pKa around 6 in the unfolded state, suggesting that the state of protonation of a histidine residue may contribute significantly to the stability of V66W.
Circular Dichroism↗
Estimation of uncertainties in X-ray refinement results by use of perturbed structures.
The uncertainties in the refined parameters for a 1.5-A X-ray structure of carbon-monoxy (FeII) myoglobin are estimated by combining energy minimization with least-squares refinement against the X-ray data. The energy minimizations, done without reference to the X-ray data, provide perturbed structures which are used to restart conventional X-ray refinement. The resulting refined structures have the same, or better, R-factor and stereochemical parameters as the original X-ray structure, but deviate from it by 0.13 A rms for the backbone atoms and 0.31 A rms for the sidechain atoms. Atoms interacting with a disordered sidechain, Arg 45 CD3, are observed to have larger positional uncertainties. The uncertainty in the B-factors, within the isotropic harmonic motion approximation, is estimated to be 15%. The resulting X-ray structures are more consistent with the energy parameters used in simulations.
Arginine↗
Models to interpret kinetic data in stable isotope tracer studies.
In contrast to "weightless" radioactive tracers, stable isotope tracers have nonnegligible mass and are naturally present in the system, and the measured variable is a ratio of two isotopic species. These features do not allow stable isotopic tracer data analysis using straightforward analogy with radioactive tracer approaches, even though this practice is common. In this study, we present kinetic variables, models, and measurements for the analysis and interpretation of stable isotope tracer data. Assumptions and mathematical techniques for modeling the data when perturbation is both nonnegligible and negligible are discussed. Emphasis is placed on the rich information content of the dynamic portion of a stable isotope tracer curve and on the role of compartmental and noncompartmental modeling approaches for its interpretation. A presumed and commonly used analogy between the radioactive specific activity and stable isotopic enrichment is shown to be incorrect. We show that the proper analogue of specific activity is the tracer-to-tracee molar ratio. This variable is not a directly measurable one, but a formula is derived that allows its computation from the data. A method for reconstructing the time course in blood of the concentration component due to endogenous synthesis is presented. This allows measurement of the extent of the perturbation in the case where a nonweightless tracer is used. Special attention is given to data analysis originating from a multiple tracer experiment, a configuration necessary for studying more complex systems, e.g., the kinetics of interacting substrates.
3-Hydroxybutyric Acid↗
Quantitative evaluation of the electromyographic responses to multidirectional load perturbations of the human arm.
1. Force perturbations consisting of a random train of pulses were applied to the forearms of human subjects, the direction of the force being varied +/- 60 degrees from vertical in the sagittal plane in different trials. 2. Both forearm and upper arm were free to move, and the perturbations resulted in angular motion and torque at both joints. By varying the direction of the force, different combinations of these variables could be obtained. 3. Average angular motion and net torque at the shoulder and elbow joints and electromyographic activity of shoulder and elbow muscles due to a single pulse of force were computed by cross-correlation methods. 4. The pattern of responses in biceps, brachio-radialis, and anterior deltoid was not related uniquely to angular motion at the shoulder or elbow joints. Furthermore, the responses appeared to consist of two distinct components, an "early" one with a latency less than 40 ms and a "late" one with a latency of approximately 80 ms. 5. The average amplitude of the early response was best correlated with the average change in angular velocities, whereas that of the late one was best correlated with average changes in torque resulting from the perturbation. The data are consistent with the hypothesis that the two components have different anatomical substrates and that they have different functional implications for the stabilization of the limb in the face of perturbations.
Arm↗
Deceleration affects anticipatory and reactive components of triggered postural responses.
Understanding the physiological and psychological factors that contribute to healthy and pathological balance control in man has been made difficult by the confounding effects of the perturbations used to test balance reactions. The present study examined how postural responses were influenced by the acceleration-deceleration interval of an unexpected horizontal translation. Twelve adult males maintained balance during unexpected forward and backward surface translations with two different acceleration-deceleration intervals and presentation orders (serial or random). "SHORT" perturbations consisted of an initial acceleration (peak acceleration 1.3 m s(-2); duration 300 ms) followed 100 ms later by a deceleration. "LONG" perturbations had the same acceleration as SHORT perturbations, followed by a 2-s interval of constant velocity before deceleration. Surface and intra-muscular electromyography (EMG) from the leg, trunk, and shoulder muscles were recorded along with motion and force plate data. LONG perturbations induced larger trunk displacements compared to SHORT perturbations when presented randomly and larger EMG responses in proximal and distal muscles during later (500-800 ms) response intervals. During SHORT perturbations, activity in some antagonist muscles was found to be associated with deceleration and not the initial acceleration of the support surface. When predictable, SHORT perturbations facilitated the use of anticipatory mechanisms to attenuate early (100-400 ms) EMG response amplitudes, ankle torque change and trunk displacement. In contrast, LONG perturbations, without an early deceleration effect, did not facilitate anticipatory changes when presented in a predictable order. Therefore, perturbations with a short acceleration-deceleration interval can influence triggered postural responses through reactive effects and, when predictable with repeated exposure, through anticipatory mechanisms.
Acceleration↗
Gait analysis and motor point block in dynamic varus of the rear foot in a head injured adult.
This clinical note describes a typical case of dynamic varus deformity of the hind part of the foot in a head injured adult. Gait analysis objectified, by kinematic data, the perturbed movement of the rear foot in the frontal plane and identified, by dynamic electromyography, the overactive muscle (posterior tibialis) involved in the deformity. The diagnosis was confirmed by a motor point block of the posterior tibialis muscle with functional improvement. Kinematic data also showed improvement after the block. This case report illustrates the usefulness of gait analysis in diagnosis and management of gait disturbances in adult patients.
Adult↗
Variance of estimated DTI-derived parameters via first-order perturbation methods.
In typical applications of diffusion tensor imaging (DTI), DT-derived quantities are used to make a diagnostic, therapeutic, or scientific determination. In such cases it is essential to characterize the variability of these tensor-derived quantities. Parametric and empirical methods have been proposed to estimate the variance of the estimated DT, and quantities derived from it. However, the former method cannot be generalized since a parametric distribution cannot be found for all DT-derived quantities. Although powerful empirical methods, such as the bootstrap, are available, they require oversampling of the diffusion-weighted imaging (DWI) data. Statistical perturbation methods represent a hybrid between parametric and empirical approaches, and can overcome the primary limitations of both methods. In this study we used a first-order perturbation method to obtain analytic expressions for the variance of DT-derived quantities, such as the trace, fractional anisotropy (FA), eigenvalues, and eigenvectors, for a given experimental design. We performed Monte Carlo (MC) simulations of DTI experiments to test and validate these formulae, and to determine their range of applicability for different experimental design parameters, including the signal-to-noise ratio (SNR), diffusion gradient sampling scheme, and number of DWI acquisitions. This information should be useful for designing DTI studies and assessing the quality of inferences drawn from them.
Algorithms↗
Influence of electric dichroism on the temperature-jump relaxation study of proflavine-DNA complexes.
The temperature-jump relaxation kinetics of proflavine-DNA complexes has been reinvestigated with a standard apparatus equipped for absorption detection of plane-polarized light in order to discriminate between chemical relaxation and transient orientation effects. Under low ionic strength conditions (0.015 M Na+), these effects may represent the major contribution to the signal when the T-jump apparatus is used without a polarizer. They have been improperly assigned to chemical relaxation in previous work. The actual relaxation times are smaller than 30 musec at 10 degrees C. Under medium ionic strength conditions (0.2 M Na+) it is shown that: (i) the "instantaneous" change of transmission reported in earlier work (Li, H. J., and Crothers, D. M. (1969), J. Mol. Biol. 39, 461-477; Schmechel, D. E. V., and Crothers, D. M. (1971), Biopolymers 10, 465-480) is due to orientation effects; (ii) an intermediate exists whose absorption spectrum resembles somewhat that of proflavine aggregates on a linear polyanion; (iii) the rate constants for outside binding may be significantly larger than previously reported. The new kinetic data are consistent with a modified mechanism derived from equilibrium studies (Ramstein, J., Hogrel, J. F., Dourlent, M., Leng, M., an Hélène, C. 1973), in Dynamic Aspects of Conformation Changes in Biological Macromolecules, Sadron, C., Ed., Dordrecht, Holland, Reidel Publisher, pp 333-347; Dourlent, M., and Hogrel, J. F. (1976), Biopolymers (in press)), but, however, do not unambiguously prove it. From these studies, it is inferred that orientation effects can perturb relaxation data on systems containing linear polymers in many cases.
Acridines↗
Identification of small scale biochemical networks based on general type system perturbations.
New technologies enable acquisition of large data-sets containing genomic, proteomic and metabolic information that describe the state of a cell. These data-sets call for systematic methods enabling relevant information about the inner workings of the cell to be extracted. One important issue at hand is the understanding of the functional interactions between genes, proteins and metabolites. We here present a method for identifying the dynamic interactions between biochemical components within the cell, in the vicinity of a steady-state. Key features of the proposed method are that it can deal with data obtained under perturbations of any system parameter, not only concentrations of specific components, and that the direct effect of the perturbations does not need to be known. This is important as concentration perturbations are often difficult to perform in biochemical systems and the specific effects of general type perturbations are usually highly uncertain, or unknown. The basis of the method is a linear least-squares estimation, using time-series measurements of concentrations and expression profiles, in which system states and parameter perturbations are estimated simultaneously. An important side-effect of also employing estimation of the parameter perturbations is that knowledge of the system's steady-state concentrations, or activities, is not required and that deviations from steady-state prior to the perturbation can be dealt with. Time derivatives are computed using a zero-order hold discretization, shown to yield significant improvements over the widely used Euler approximation. We also show how network interactions with dynamics that are too fast to be captured within the available sampling time can be determined and excluded from the network identification. Known and unknown moiety conservation relationships can be processed in the same manner. The method requires that the number of samples equals at least the number of network components and, hence, is at present restricted to relatively small-scale networks. We demonstrate herein the performance of the method on two small-scale in silico genetic networks.
Cell Physiological Phenomena↗