Variable selection and multivariate methods for the identification of microorganisms by flow cytometry.

BACKGROUND: When exploited fully, flow cytometry can be used to provide multiparametric data for each cell in the sample of interest. While this makes flow cytometry a powerful technique for discriminating between different cell types, the data can be difficult to interpret. Traditionally, dual-parameter plots are used to visualize flow cytometric data, and for a data set consisting of seven parameters, one should examine 21 of these plots. A more efficient method is to reduce the dimensionality of the data (e.g., using unsupervised methods such as principal components analysis) so that fewer graphs need to be examined, or to use supervised multivariate data analysis methods to give a prediction of the identity of the analyzed particles. MATERIALS AND METHODS: We collected multiparametric data sets for microbiological samples stained with six cocktails of fluorescent stains. Multivariate data analysis methods were explored as a means of microbial detection and identification. RESULTS: We show that while all cocktails and all methods gave good accuracy of predictions (>94%), careful selection of both the stains and the analysis method could improve this figure (to > 99% accuracy), even in a data set that was not used in the formation of the supervised multivariate calibration model. CONCLUSIONS: Flow cytometry provides a rapid method of obtaining multiparametric data for distinguishing between microorganisms. Multivariate data analysis methods have an important role to play in extracting the information from the data obtained. Artificial neural networks proved to be the most suitable method of data analysis.     

Global parameter optimization for cardiac potassium channel gating models.

Quantitative ion channel model evaluation requires the estimation of voltage dependent rate constants. We have tested whether a unique set of rate constants can be reliably extracted from nonstationary macroscopic voltage clamp potassium current data. For many models, the rate constants derived independently at different membrane potentials are not unique. Therefore, our approach has been to use the exponential voltage dependence predicted from reaction rate theory (Stevens, C. F. 1978. Biophys. J. 22:295-306; Eyring, H., S. H. Lin, and S. M. Lin. 1980. Basic Chemical Kinetics. Wiley and Sons, New York) to couple the rate constants derived at different membrane potentials. This constrained the solution set of rate constants to only those that also obeyed this additional set of equations, which was sufficient to obtain a unique solution. We have tested this approach with data obtained from macroscopic delayed rectifier potassium channel currents in voltage-clamped guinea pig ventricular myocyte membranes. This potassium channel has relatively simple kinetics without an inactivation process and provided a convenient system to determine a globally optimized set of voltage-dependent rate constants for a Markov kinetic model. The ability of the fitting algorithm to extract rate constants from the macroscopic current data was tested using "data" synthesized from known rate constants. The simulated data sets were analyzed with the global fitting procedure and the fitted rate constants were compared with the rate constants used to generate the data. Monte Carlo methods were used to examine the accuracy of the estimated kinetic parameters. This global fitting approach provided a useful and convenient method for reliably extracting Markov rate constants from macroscopic voltage clamp data over a broad range of membrane potentials. The limitations of the method and the dependence on initial guesses are described.     

MCMC estimation of Markov models for ion channels

Ion channels are characterized by inherently stochastic behavior which can be represented by continuous-time Markov models (CTMM). Although methods for collecting data from single ion channels are available, translating a time series of open and closed channels to a CTMM remains a challenge. Bayesian statistics combined with Markov chain Monte Carlo (MCMC) sampling provide means for estimating the rate constants of a CTMM directly from single channel data. In this article, different approaches for the MCMC sampling of Markov models are combined. This method, new to our knowledge, detects overparameterizations and gives more accurate results than existing MCMC methods. It shows similar performance as QuB-MIL, which indicates that it also compares well with maximum likelihood estimators. Data collected from an inositol trisphosphate receptor is used to demonstrate how the best model for a given data set can be found in practice.     

Confidence intervals for the mean of diagnostic test charge data containing zeros

In this paper, we consider the problem of interval estimation for the mean of diagnostic test charges. Diagnostic test charge data may contain zero values, and the nonzero values can often be modeled by a log-normal distribution. Under such a model, we propose three different interval estimation procedures: a percentile-t bootstrap interval based on sufficient statistics and two likelihood-based confidence intervals. For theoretical properties, we show that the two likelihood-based one-sided confidence intervals are only first-order accurate and that the bootstrap-based one-sided confidence interval is second-order accurate. For two-sided confidence intervals, all three proposed methods are second-order accurate. A simulation study in finite-sample sizes suggests all three proposed intervals outperform a widely used minimum variance unbiased estimator (MVUE)-based interval except for the case of one-sided lower end-point intervals when the skewness is very small. Among the proposed one-sided intervals, the bootstrap interval has the best coverage accuracy. For the two-sided intervals, when the sample size is small, the bootstrap method still yields the best coverage accuracy unless the skewness is very small, in which case the bias-corrected ML method has the best accuracy. When the sample size is large, all three proposed intervals have similar coverage accuracy. Finally, we analyze with the proposed methods one real example assessing diagnostic test charges among older adults with depression.     

A new graphical method for determining parameters in Michaelis-Menten-type kinetics for enzymatic lactose hydrolysis

A new graphical method was developed to determine the kinetic parameters in the Michaelis-Menten-type equation. This method was then applied to studying the kinetics of lactose hydrolysis by Aspergillus niger beta-galactosidase. In this study, the reaction temperature ranged between 8 and 60 degrees C, and the initial lactose concentration ranged between 2.5 and 20%. A kinetic model similar to the conventional Michaelis-Menten equation with competitive product inhibition by galactose was tested using this graphical method as well as a nonlinear computer regression method. The experimental data and the model fit together fairly well at 50 degrees C. However, a relative large disparity was found for reactions at 30 degrees C. A three-parameter integrated model derived from the reversible reaction mechanism simulates the experimental data very well at all temperatures studied. However, this reversible reaction model does not follow the Arrhenius temperature dependence. Nevertheless, reaction rate constants for the proposed model involving the enzyme-galactose complex (in addition to the Michaelis complex) as an intermediate in lactose hydrolysis follow the Arrhenius temperature dependence fairly well, suggesting that this model can be best used for describing the enzymatic lactose hydrolysis. The lack of fit between the model predictions and data may be largely attributed to the effects of galactose mutarotation and oligosaccharide formation during lactose hydrolysis.     

Backpropagation Neural Network for Processing of Missing Data in Breast Cancer Detection

BackgroundA complete dataset is essential for biomedical implementation. Due to the limitation of objective or subjective factors, missing data often occurs, which exerts uncertainty in the subsequent data processing. Commonly used methods of interpolation are interpolating substitute values that keep minimum error. Some applications of statistics are usually used for handling this problem.MethodsWe are trying to find a higher performance interpolation method compared with the usual statistic methods, by using artificial intelligence which is in full swing today. The prediction and classification of backpropagation neural network are used in this paper, describes a missing data interpolation method to propose the interpolation model that mines association rules in the data. In the experiment, depending on a multi-layer network structure, the model is trained and tested by sample data, constantly revises network weights and thresholds. The error function decreases along the negative gradient direction and approaches the expected real output. The model is validated on the breast cancer dataset, and we select real samples from the data set for validation, moreover, add four traditional methods as a control group.ResultsThe proposed method has great performance improvement in the interpolation of missing data. Experimental results show that the interpolation accuracy of our proposed method (84%) is higher than four traditional methods (1.33%, 74.67%, 73.33%, 77.33%) as mentioned in this paper, BPNN stays low in MSE evaluation. Finally, we analyze the performance of various methods in processing missing data.ConclusionsThe study in this paper has estimated missing data with high accuracy as much as possible to reduce the negative impact in the diagnosis of real life. At the same time, it can also assist in missing data processing in the biomedical field.     

Optimal experiment selection for parameter estimation in biological differential equation models

ABSTRACT: BACKGROUND: Parameter estimation in biological models is a common yet challenging problem. In this work we explore the problem for gene regulatory networks modeled by differential equations with unknown parameters, such as decay rates, reaction rates, Michaelis-Menten constants, and Hill coefficients. We explore the question to what extent parameters can be efficiently estimated by appropriate experimental selection. RESULTS: A minimization formulation is used to find the parameter values that best fit the experiment data. When the data is insufficient, the minimization problem often has many local minima that fit the data reasonably well. We show that selecting a new experiment based on the local Fisher Information of one local minimum generates additional data that allows one to successfully discriminate among the many local minima. The parameters can be estimated to high accuracy by iteratively performing minimization and experiment selection. We show that the experiment choices are roughly independent of which local minima is used to calculate the local Fisher Information. CONCLUSIONS: We show that by an appropriate choice of experiments, one can, in principle, efficiently and accurately estimate all the parameters of gene regulatory network. In addition, we demonstrate that appropriate experiment selection can also allow one to restrict model predictions without constraining the parameters using many fewer experiments. We suggest that predicting model behaviors and inferring parameters represent two different approaches to model calibration with different requirements on data and experimental cost.     

Multirate method for co-simulation of electrical-chemical systems in multiscale modeling

Multiscale modeling by means of co-simulation is a powerful tool to address many vital questions in neuroscience. It can for example be applied in the study of the process of learning and memory formation in the brain. At the same time the co-simulation technique makes it possible to take advantage of interoperability between existing tools and multi-physics models as well as distributed computing. However, the theoretical basis for multiscale modeling is not sufficiently understood. There is, for example, a need of efficient and accurate numerical methods for time integration. When time constants of model components are different by several orders of magnitude, individual dynamics and mathematical definitions of each component all together impose stability, accuracy and efficiency challenges for the time integrator. Following our numerical investigations in Brocke et al. (Frontiers in Computational Neuroscience, 10, 97, 2016), we present a new multirate algorithm that allows us to handle each component of a large system with a step size appropriate to its time scale. We take care of error estimates in a recursive manner allowing individual components to follow their discretization time course while keeping numerical error within acceptable bounds. The method is developed with an ultimate goal of minimizing the communication between the components. Thus it is especially suitable for co-simulations. Our preliminary results support our confidence that the multirate approach can be used in the class of problems we are interested in. We show that the dynamics ofa communication signal as well as an appropriate choice of the discretization order between system components may have a significant impact on the accuracy of the coupled simulation. Although, the ideas presented in the paper have only been tested on a single model, it is likely that they can be applied to other problems without loss of generality. We believe that this work may significantly contribute to the establishment of a firm theoretical basis and to the development of an efficient computational framework for multiscale modeling and simulations.     

Hodgkin-Huxley type ion channel characterization: an improved method of voltage clamp experiment parameter estimation

The Hodgkin-Huxley formalism for quantitative characterization of ionic channels is widely used in cellular electrophysiological models. Model parameters for these individual channels are determined from voltage clamp experiments and usually involve the assumption that inactivation process occurs on a time scale which is infinitely slow compared to the activation process. This work shows that such an assumption may lead to appreciable errors under certain physiological conditions and proposes a new numerical approach to interpret voltage clamp experiment results. In simulated experimental protocols the new method was shown to exhibit superior accuracy compared to the traditional least squares fitting methods. With noiseless input data the error in gating variables and time constants was less than 1%, whereas the traditional methods generated upwards of 10% error and predicted incorrect gating kinetics. A sensitivity analysis showed that the new method could tolerate up to approximately 15% perturbation in the input data without unstably amplifying error in the solution. This method could also assist in designing more efficient experimental protocols, since all channel parameters (gating variables, time constants and maximum conductance) could be determined from a single voltage step.     

A method for determining a rate constant for biexponential processes using data on dynamics of accumulating the end product of a reaction

A new method the rate constant determination of some biexponential processes is suggested. The method is based on the asymptotic solution of transcendental irrational equations, described such processes. This method can be used when kinetics of the final product of reaction is known. The values of the rate constants obtained by suggested method are precise, if the data used for calculation are also precise. In the other case methods of mathematical statistics should be used for evaluation of the slopes of kinetics curves in the semi-logarithmic coordinates.     

Spectral displacement techniques for studying the binding of spectroscopically transparent ligands to cyclodextrins

A spectroscopic displacement method is used to determine association constants of beta-cyclodextrin with compounds that are spectroscopically transparent. These compounds are adamantanecarboxylate and structurally related compounds. Association constants obtained are compared to values obtained by other methods. It is shown that for all types of displacement techniques a distinction must be made between free and total concentrations of ligand in cases of strong binding.     

A new approach for efficient genotype imputation using information from relatives

Background

Genotype imputation can help reduce genotyping costs particularly for implementation of genomic selection. In applications entailing large populations, recovering the genotypes of untyped loci using information from reference individuals that were genotyped with a higher density panel is computationally challenging. Popular imputation methods are based upon the Hidden Markov model and have computational constraints due to an intensive sampling process. A fast, deterministic approach, which makes use of both family and population information, is presented here. All individuals are related and, therefore, share haplotypes which may differ in length and frequency based on their relationships. The method starts with family imputation if pedigree information is available, and then exploits close relationships by searching for long haplotype matches in the reference group using overlapping sliding windows. The search continues as the window size is shrunk in each chromosome sweep in order to capture more distant relationships.

Results

The proposed method gave higher or similar imputation accuracy than Beagle and Impute2 in cattle data sets when all available information was used. When close relatives of target individuals were present in the reference group, the method resulted in higher accuracy compared to the other two methods even when the pedigree was not used. Rare variants were also imputed with higher accuracy. Finally, computing requirements were considerably lower than those of Beagle and Impute2. The presented method took 28 minutes to impute from 6 k to 50 k genotypes for 2,000 individuals with a reference size of 64,429 individuals.

Conclusions

The proposed method efficiently makes use of information from close and distant relatives for accurate genotype imputation. In addition to its high imputation accuracy, the method is fast, owing to its deterministic nature and, therefore, it can easily be used in large data sets where the use of other methods is impractical.     

A marginal model approach for analysis of multi-reader multi-test receiver operating characteristic (ROC) data

The receiver operating characteristic curve is a popular tool to characterize the capabilities of diagnostic tests with continuous or ordinal responses. One common design for assessing the accuracy of diagnostic tests involves multiple readers and multiple tests, in which all readers read all test results from the same patients. This design is most commonly used in a radiology setting, where the results of diagnostic tests depend on a radiologist's subjective interpretation. The most widely used approach for analyzing data from such a study is the Dorfman-Berbaum-Metz (DBM) method (Dorfman et al., 1992) which utilizes a standard analysis of variance (ANOVA) model for the jackknife pseudovalues of the area under the ROC curves (AUCs). Although the DBM method has performed well in published simulation studies, there is no clear theoretical basis for this approach. In this paper, focusing on continuous outcomes, we investigate its theoretical basis. Our result indicates that the DBM method does not satisfy the regular assumptions for standard ANOVA models, and thus might lead to erroneous inference. We then propose a marginal model approach based on the AUCs which can adjust for covariates as well. Consistent and asymptotically normal estimators are derived for regression coefficients. We compare our approach with the DBM method via simulation and by an application to data from a breast cancer study. The simulation results show that both our method and the DBM method perform well when the accuracy of tests under the study is the same and that our method outperforms the DBM method for inference on individual AUCs when the accuracy of tests is not the same. The marginal model approach can be easily extended to ordinal outcomes.     

Bayesian Hierarchical Model for Estimating Gene Expression Intensity Using Multiple Scanned Microarrays

We propose a method for improving the quality of signal from DNA microarrays by using several scans at varying scanner sen-sitivities. A Bayesian latent intensity model is introduced for the analysis of such data. The method improves the accuracy at which expressions can be measured in all ranges and extends the dynamic range of measured gene expression at the high end. Our method is generic and can be applied to data from any organism, for imaging with any scanner that allows varying the laser power, and for extraction with any image analysis software. Results from a self-self hybridization data set illustrate an improved precision in the estimation of the expression of genes compared to what can be achieved by applying standard methods and using only a single scan.     

Exact computation of coalescent likelihood for panmictic and subdivided populations under the infinite sites model

Coalescent likelihood is the probability of observing the given population sequences under the coalescent model. Computation of coalescent likelihood under the infinite sites model is a classic problem in coalescent theory. Existing methods are based on either importance sampling or Markov chain Monte Carlo and are inexact. In this paper, we develop a simple method that can compute the exact coalescent likelihood for many data sets of moderate size, including real biological data whose likelihood was previously thought to be difficult to compute exactly. Our method works for both panmictic and subdivided populations. Simulations demonstrate that the practical range of exact coalescent likelihood computation for panmictic populations is significantly larger than what was previously believed. We investigate the application of our method in estimating mutation rates by maximum likelihood. A main application of the exact method is comparing the accuracy of approximate methods. To demonstrate the usefulness of the exact method, we evaluate the accuracy of program Genetree in computing the likelihood for subdivided populations.     

A new procedure for refining force constants in normal coordinate calculations on large molecules

We develop a force-constant refinement procedure which we believe capable of being used in problems of large molecules and biopolymers. The procedure is based on a Green-function expression which relates changes in frequency to changes in force constants. The method does not require that assignments be made before refinment (although they may be). An expansion of this expression gives rise to a set of linear algebraic equations for the force-constant corrections, rather than an equation involving residuals to minimize. The resulting calculations are considerably simpler. This approximate is iterated to find the final refined force-constants. We discuss several methods of improving the convergence of the procedure which take into account the experimental information which may be available. Of particular interest is a scheme to select the force constants to be refined by imposing a criterion for selecting those which will fit the experimental data with the smallest changes of the force constants from their expected values. We discuss some limitations which occur for all methods of refinement applied to large molecules.     

On the development of protein pKa calculation algorithms

Protein pK(a) calculation methods are developed partly to provide fast non-experimental estimates of the ionization constants of protein side chains. However, the most significant reason for developing such methods is that a good pK(a) calculation method is presumed to provide an accurate physical model of protein electrostatics, which can be applied in methods for drug design, protein design, and other structure-based energy calculation methods. We explore the validity of this presumption by simulating the development of a pK(a) calculation method using artificial experimental data derived from a human-defined physical reality. We examine the ability of an RMSD-guided development protocol to retrieve the correct (artificial) physical reality and find that a rugged optimization landscape and a huge parameter space prevent the identification of the correct physical reality. We examine the importance of the training set in developing pK(a) calculation methods and investigate the effect of experimental noise on our ability to identify the correct physical reality, and find that both effects have a significant and detrimental impact on the physical reality of the optimal model identified. Our findings are of relevance to all structure-based methods for protein energy calculations and simulation, and have large implications for all types of current pK(a) calculation methods. Our analysis furthermore suggests that careful and extensive validation on many types of experimental data can go some way in making current models more realistic.