Normalization of high dimensional genomics data where the distribution of the altered variables is skewed

Genome-wide analysis of gene expression or protein binding patterns using different array or sequencing based technologies is now routinely performed to compare different populations, such as treatment and reference groups. It is often necessary to normalize the data obtained to remove technical variation introduced in the course of conducting experimental work, but standard normalization techniques are not capable of eliminating technical bias in cases where the distribution of the truly altered variables is skewed, i.e. when a large fraction of the variables are either positively or negatively affected by the treatment. However, several experiments are likely to generate such skewed distributions, including ChIP-chip experiments for the study of chromatin, gene expression experiments for the study of apoptosis, and SNP-studies of copy number variation in normal and tumour tissues. A preliminary study using spike-in array data established that the capacity of an experiment to identify altered variables and generate unbiased estimates of the fold change decreases as the fraction of altered variables and the skewness increases. We propose the following work-flow for analyzing high-dimensional experiments with regions of altered variables: (1) Pre-process raw data using one of the standard normalization techniques. (2) Investigate if the distribution of the altered variables is skewed. (3) If the distribution is not believed to be skewed, no additional normalization is needed. Otherwise, re-normalize the data using a novel HMM-assisted normalization procedure. (4) Perform downstream analysis. Here, ChIP-chip data and simulated data were used to evaluate the performance of the work-flow. It was found that skewed distributions can be detected by using the novel DSE-test (Detection of Skewed Experiments). Furthermore, applying the HMM-assisted normalization to experiments where the distribution of the truly altered variables is skewed results in considerably higher sensitivity and lower bias than can be attained using standard and invariant normalization methods.     

Sampling of intracellular metabolites for stationary and non-stationary C metabolic flux analysis in Escherichia coli

The analysis of metabolic intermediates is a rich source of isotopic information for ¹³C metabolic flux analysis (¹³C-MFA) and extends the range of its applications. The sampling of labeled metabolic intermediates is particularly important to obtain reliable isotopic information. The assessment of the different sampling procedures commonly used to generate such data, therefore, is crucial. In this work, we thoroughly evaluated several sampling procedures for stationary and non-stationary ¹³C-MFA using Escherichia coli. We first analyzed the efficiency of these procedures for quenching metabolism and found that procedures based on cold or boiling solvents are reliable, in contrast to fast filtration, which is not. We also showed that separating the cells from the broth is not necessary in isotopic stationary state conditions. On the other hand, we demonstrated that the presence of metabolic intermediates outside the cells strongly affects the transient isotopic data monitored during non-stationary ¹³C-labeling experiments. Meaningful isotopic data can be obtained by recovering intracellular labeled metabolites from pellets of cells centrifuged in cold solvent. We showed that if the intracellular pools are not separated from the extracellular ones, accurate flux maps can be established provided that the contribution of exogenous compounds is taken into account in the metabolic flux model.     

Bidirectional reaction steps in metabolic networks: II. Flux estimation and statistical analysis

Metabolic carbon labelling experiments enable a large amount of extracellular fluxes and intracellular carbon isotope enrichments to be measured. Since the relation between the measured quantities and the unknown intracellular metabolic fluxes is given by bilinear balance equations, flux determination from this data set requires the numerical solution of a nonlinear inverse problem. To this end, a general algorithm for flux estimation from metabolic carbon labelling experiments based on the least squares approach is developed in this contribution and complemented by appropriate tools for statistical analysis. The linearization technique usually applied for the computation of nonlinear confidence regions is shown to be inappropriate in the case of large exchange fluxes. For this reason a sophisticated compactification transformation technique for nonlinear statistical analysis is developed. Statistical analysis is then performed by computing appropriate statistical quality measures like output sensitivities, parameter sensitivities and the parameter covariance matrix. This allows one to determine the order of magnitude of exchange fluxes in most practical situations. An application study with a large data set from lysine-producing Corynebacterium glutamicum demonstrates the power and limitations of the carbon-labelling technique. It is shown that all intracellular fluxes in central metabolism can be quantitated without assumptions on intracellular energy yields. At the same time several exchange fluxes are determined which is invaluable information for metabolic engineering. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 118-135, 1997.     

A model for glucose-induced wave propagation in pancreatic islets of Langerhans

A reaction-diffusion type model is constructed, describing the spatio-temporal dynamics of the basic intracellular variables assumed to be involved in the initiation of the insulin secretion process by beta -cells in the pancreatic islets of Langerhans. The model includes equations for the electric membrane potential of the cells, with respective kinetics for ionic currents, for concentrations of both free and stored intracellular calcium, and for the intra- and extracellular concentrations of glucose. An empirical expression connecting the equation for the intracellular glucose concentration to the electrical equation is introduced. The model reproduces the events observed in experiments in vitro upon external glucose application to the islets of Langerhans, such as usual bursting oscillations of the membrane potential and corresponding oscillations of the intracellular calcium concentration. It also allows simulation of electric wave propagation through the islet, initiated by the spatial gradient of glucose concentration within the islet. The gradient emerges due to glucose diffusing into the islets from the external medium, being high at the edges. The latter results show that glucose diffusion presents a means for wave initiation in the islets, which supports our previous assumption (Aslanidi et al., 2001).     

Online optimization of surface plasmon resonance-based biosensor experiments for improved throughput and confidence

The emergence of surface plasmon resonance-based optical biosensors has facilitated the identification of kinetic parameters for various macromolecular interactions. Normally, these parameters are determined from experiments with arbitrarily chosen periods of macromolecule and buffer injections, and varying macromolecule concentrations. Since the choice of these variables is arbitrary, such experiments may not provide the required confidence in identified kinetic parameters expressed in terms of standard errors. In this work, an iterative optimization approach is used to determine the above-mentioned variables so as to reduce the experimentation time, while treating the required standard errors as constraints. It is shown using multiple experimental and simulated data that the desired confidence can be reached with much shorter experiments than those generally performed by biosensor users.     

Parameter estimation in models combining signal transduction and metabolic pathways: the dependent input approach

Biological complexity and limited quantitative measurements pose severe challenges to standard engineering methodologies for modelling and simulation of genes and gene products integrated in a functional network. In particular, parameter quantification is a bottleneck, and therefore parameter estimation, identifiability, and optimal experiment design are important research topics in systems biology. An approach is presented in which unmodelled dynamics are replaced by fictitious 'dependent inputs'. The dependent input approach is particularly useful in validation experiments, because it allows one to fit model parameters to experimental data generated by a reference cell type ('wild-type') and then test this model on data generated by a variation ('mutant'), so long as the mutations only affect the unmodelled dynamics that produce the dependent inputs. Another novel feature of the approach is in the inclusion of a priori information in a multi-objective identification criterion, making it possible to obtain estimates of parameter values and their variances from a relatively limited experimental data set. The pathways that control the nitrogen uptake fluxes in baker's yeast (Saccharomyces cerevisiae) have been studied. Well-defined perturbation experiments were performed on cells growing in steady-state. Time-series data of extracellular and intracellular metabolites were obtained, as well as mRNA levels. A nonlinear model was proposed and was shown to be structurally identifiable given data of its inputs and outputs. The identified model is a reliable representation of the metabolic system, as it could correctly describe the responses of mutant cells and different perturbations.     

ATP‐independent molecular chaperone activity generated under reducing conditions

Molecular chaperones are essential to maintain proteostasis. While the functions of intracellular molecular chaperones that oversee protein synthesis, folding and aggregation, are established, those specialized to work in the extracellular environment are less understood. Extracellular proteins reside in a considerably more oxidizing milieu than cytoplasmic proteins and are stabilized by abundant disulfide bonds. Hence, extracellular proteins are potentially destabilized and sensitive to aggregation under reducing conditions. We combine biochemical and mass spectrometry experiments and elucidate that the molecular chaperone functions of the extracellular protein domain Bri2 BRICHOS only appear under reducing conditions, through the assembly of monomers into large polydisperse oligomers by an intra‐ to intermolecular disulfide bond relay mechanism. Chaperone‐active assemblies of the Bri2 BRICHOS domain are efficiently generated by physiological thiol‐containing compounds and proteins, and appear in parallel with reduction‐induced aggregation of extracellular proteins. Our results give insights into how potent chaperone activity can be generated from inactive precursors under conditions that are destabilizing to most extracellular proteins and thereby support protein stability/folding in the extracellular space.SignificanceChaperones are essential to cells as they counteract toxic consequences of protein misfolding particularly under stress conditions. Our work describes a novel activation mechanism of an extracellular molecular chaperone domain, called Bri2 BRICHOS. This mechanism is based on reducing conditions that initiate small subunits to assemble into large oligomers via a disulfide relay mechanism. Activated Bri2 BRICHOS inhibits reduction‐induced aggregation of extracellular proteins and could be a means to boost proteostasis in the extracellular environment upon reductive stress.     

On-line monitoring of PHB production by mixed microbial cultures using respirometry,titrimetry and chemometric modelling

This work describes a method for on-line monitoring of biomass production, acetate consumption and intracellular polyhydroxybutyrate (PHB) storage by mixed microbial cultures (MMC). The method is based on reliable and easily available on-line measurements, namely pH, dissolved oxygen, dissolved carbon dioxide, on-line respirometry and on-line titrimetric analysis. Biomass production refers to active biomass growth and also to the synthesis of extracellular polymeric substances (EPS). The composition and kinetics of EPS synthesis has high variability depending on the culture enrichment protocol. Since the metabolism for EPS production is rather difficult to define, it was not possible to develop a reliable estimation model based on metabolic principles only. Instead, projection of latent structures (PLS) linear regression constrained by steady state carbon balance was employed. PHB concentration and biomass production rate were directly estimated by the PLS model, whereas acetate concentration was indirectly estimated through the carbon balance. The method was validated experimentally with data of four experiments carried out in a SBR. Accurate on-line estimations were obtained with regression coefficients (r²) of 0.986 and 0.980 for biomass concentration, 0.976 and 0.999 for PHB and 0.992 and 0.999 for acetate concentration in calibration and validation, respectively. These results confirm the ability of the proposed methodology for on-line monitoring of the state variables in PHB production process by MMC.     

A Bayesian Alternative to Mutual Information for the Hierarchical Clustering of Dependent Random Variables

The use of mutual information as a similarity measure in agglomerative hierarchical clustering (AHC) raises an important issue: some correction needs to be applied for the dimensionality of variables. In this work, we formulate the decision of merging dependent multivariate normal variables in an AHC procedure as a Bayesian model comparison. We found that the Bayesian formulation naturally shrinks the empirical covariance matrix towards a matrix set a priori (e.g., the identity), provides an automated stopping rule, and corrects for dimensionality using a term that scales up the measure as a function of the dimensionality of the variables. Also, the resulting log Bayes factor is asymptotically proportional to the plug-in estimate of mutual information, with an additive correction for dimensionality in agreement with the Bayesian information criterion. We investigated the behavior of these Bayesian alternatives (in exact and asymptotic forms) to mutual information on simulated and real data. An encouraging result was first derived on simulations: the hierarchical clustering based on the log Bayes factor outperformed off-the-shelf clustering techniques as well as raw and normalized mutual information in terms of classification accuracy. On a toy example, we found that the Bayesian approaches led to results that were similar to those of mutual information clustering techniques, with the advantage of an automated thresholding. On real functional magnetic resonance imaging (fMRI) datasets measuring brain activity, it identified clusters consistent with the established outcome of standard procedures. On this application, normalized mutual information had a highly atypical behavior, in the sense that it systematically favored very large clusters. These initial experiments suggest that the proposed Bayesian alternatives to mutual information are a useful new tool for hierarchical clustering.     

Reverse smoothing: a model-free data smoothing algorithm

Biophysical chemistry experiments, such as sedimentation-equilibrium analyses, require computational techniques to reduce the effects of random errors of the measurement process. The existing approaches have primarily relied on assumption of polynomial models and least-squares approximation. Such models by constraining the data to remove random fluctuations may distort the data and cause loss of information. The better the removal of random errors the greater is the likely introduction of systematic errors through the constraining fit itself. An alternative technique, reverse smoothing, is suggested that makes use of a more model-free approach of exponential smoothing of the first derivative. Exponential smoothing approaches have been generally unsatisfactory because they introduce significant data lag. The approaches given here compensates for the lag defect and appears promising for the smoothing of many experimental data sequences, including the macromolecular concentration data generated by sedimentation-equilibria experiments. Test results on simulated sedimentation-equilibrium data indicate that a 4-fold reduction in error may be typical over standard analyses techniques.     

Analyzing a randomized trial on breast self-examination with noncompliance and missing outcomes

Recently, instrumental variables methods have been used to address non-compliance in randomized experiments. Complicating such analyses is often the presence of missing data. The standard model for missing data, missing at random (MAR), has some unattractive features in this context. In this paper we compare MAR-based estimates of the complier average causal effect (CACE) with an estimator based on an alternative, nonignorable model for the missing data process, developed by Frangakis and Rubin (1999, Biometrika, 86, 365-379). We also introduce a new missing data model that, like the Frangakis-Rubin model, is specially suited for models with instrumental variables, but makes different substantive assumptions. We analyze these issues in the context of a randomized trial of breast self-examination (BSE). In the study two methods of teaching BSE, consisting of either mailed information about BSE (the standard treatment) or the attendance of a course involving theoretical and practical sessions (the new treatment), were compared with the aim of assessing whether teaching programs could increase BSE practice and improve examination skills. The study was affected by the two sources of bias mentioned above: only 55% of women assigned to receive the new treatment complied with their assignment and 35% of the women did not respond to the post-test questionnaire. Comparing the causal estimand of the new treatment using the MAR, Frangakis-Rubin, and our new approach, the results suggest that for these data the MAR assumption appears least plausible, and that the new model appears most plausible among the three choices.     

Network modeling of signal transduction: establishing the global view

Embryonic development and adult tissue homeostasis are controlled through activation of intracellular signal transduction pathways by extracellular growth factors. In the past, signal transduction has largely been regarded as a linear process. However, more recent data from large-scale and high-throughput experiments indicate that there is extensive cross-talk between individual signaling cascades leading to the notion of a signaling network. The behavior of such complex networks cannot be predicted by simple intuitive approaches but requires sophisticated models and computational simulations. The purpose of such models is to generate experimentally testable hypotheses and to find explanations for unexpected experimental results. Here, we discuss the need for, and the future impact of, mathematical models for exploring signal transduction in different biological contexts such as for example development.     

Estimation of Residual Valve Gradient from Incomplete Data with Outliers

An important indicator for the long-term recovery after valve replacement surgery is postoperative valve gradient. This information is available only for patients received catheterization or echocardiogram postoperatively. It is plausible that sicker patients are more inclined to undergo these postoperative procedures and their valve gradients tend to be higher. Under this situation, ignoring the missing values and using sample mean based on the available information as an estimate of the whole study population leads to overestimation. Regression estimator is a reasonable choice to eliminate this bias if independent (explanatory) variables closely associated with both residual valve gradient and non-response mechanism can be identified. Using a series of patients receiving St. Jude Medical prosthetic valves, we found that valve area index can be used as an independent variable in the regression estimator. Two digressions from the standard assumptions used in linear regression, heteroscedastic trend of the error term and outliers were found in the data set. Iteratively reweighted least square (IRLS) was adopted to handle heteroscedasticity. Influence function approach was used to evaluate the sensitivity of outliers in regression estimator. Under an equal response rate mechanism, IRLS not only solves the problem of heteroscedasticity, but is also less sensitive to outliers.     

Raw data graphing: an informative but under‐utilized tool for the analysis of multivariate abundances

Abstract In exploring the relationship between multivariate abundance data and environmental variables, a rarely used approach is to graph raw data separately for each different taxon. It is proposed that such raw data graphs become part of the standard toolset for graphing and analysing multivariate abundances. The key advantage of this approach is that axis scales have quantitative interpretations, enabling quantitative interpretation of patterns in abundance. In contrast, ordinations only present qualitative information. Ordinations are useful for inferring overall, qualitative patterns and raw data graphing is a complementary tool of greater use for answering more specific questions, aimed at a deeper understanding the ecology of a community. It is demonstrated using some well‐known examples that our understanding of the nature of associations can be considerably improved by using raw data graphs, even when only plotting a subset of variables. One example describes how an often‐cited dataset has been misinterpreted in key methodological papers, because data were interpreted from ordinations alone, with no consideration of plots of the raw data.     

Intracellular ethanol accumulation in yeast cells during aerobic fermentation: a Raman spectroscopic exploration

Aims: To investigate the intracellular ethanol accumulation in yeast cells by using laser tweezers Raman spectroscopy (LTRS). Methods and Results: Ethanol accumulation in individual yeast cells during aerobic fermentation triggered by excess glucose was studied using LTRS. Its amount was obtained by comparing intracellular and extracellular ethanol concentrations during initial process of ethanol production. We found that (i) yeasts start to produce ethanol within 3 min after triggering aerobic fermentation, (ii) average ratio of intracellular to extracellular ethanol is 1·54 ± 0·17 during the initial 3 h after addition of 10% (w/v) excess glucose and (iii) the accumulated intracellular ethanol is released when aerobic fermentation is stimulated with decreasing glucose concentration. Conclusions: Intracellular ethanol accumulation occurs in initial stage of a rapid aerobic fermentation and high glucose concentration may attribute to this accumulation process. Significance and Impact of the Study: This work demonstrates LTRS is a real‐time, reagent‐free, in situ technique and a powerful tool to study kinetic process of ethanol fermentation. This work also provides further information on the intracellular ethanol accumulation in yeast cells.     

Prospective inference of bioprocess cell viability through chemometric modeling of fluorescence multiway data

In this investigation, the fermentation step of a standard mammalian cell-based industrial bioprocess for the production of a therapeutic protein was studied, with particular emphasis on the evolution of cell viability. This parameter constitutes one of the critical variables for bioprocess monitoring since it can affect downstream operations and the quality of the final product. In addition, when the cells experiment an unpredictable drop in viability, the assessment of this variable through classic off-line methods may not provide information sufficiently in advance to take corrective actions. In this context, Process Analytical Technology (PAT) framework aims to develop novel strategies for more efficient monitoring of critical variables, in order to improve the bioprocess performance. Thus, in this work, a set of chemometric tools were integrated to establish a PAT strategy to monitor cell viability, based on fluorescence multiway data obtained from fermentation samples of a particular bioprocess, in two different scales of operation. The spectral information, together with data regarding process variables, was integrated through chemometric exploratory tools to characterize the bioprocess and stablish novel criteria for the monitoring of cell viability. These findings motivated the development of a multivariate classification model, aiming to obtain predictive tools for the monitoring of future lots of the same bioprocess. The model could be satisfactorily fitted, showing the non-error rate of prediction of 100%.     

Intraphagosomal oxygen in stimulated macrophages

A new electron paramagnetic resonance (EPR)-based method was developed to obtain selective information on pO₂ in a specific intracellular compartment (phagosomes). This method did not require the use of a broadening agent thereby eliminating one of the potential sources of experimental error with EPR oximetry. An oxygen-sensitive probe (4-(Trimethylammonium) 2,2,6,6-tetramethylpiperidine-d₁₇-1-oxyl iodide (d-Cat₁)) which has a net positive charge, was incorporated selectively into the phagosomes of macrophages stimulated with zymosan. Extracellular oxygen was measured by addition of a neutral nitroxide (4-oxo-2,2,6,6-tetramethylpiperidine-d₁₆-1-oxyl (¹⁵N PDT)) to this same sample. Measurements based on EPR linewidths showed the average intraphagosomal oxygen concentration to be 11.2 ± 3.4 μM lower than that measured from the extracellular compartment when the sample was perfused with air, and this was increased on stimulation of mitochondrial consumption or by increasing the oxygen concentration in the extracellular compartment. These experiments provide what we believe to be the first reported measurements of the oxygen concentration in a specific intracellular location (intraphagosomal) and its comparison with the oxygen concentration in the extracellular space. The observed gradient cannot be explained in terms of known coefficients of diffusion, and these results are consistent with previous reports that a gradient in oxygen concentration can occur between the average intracellular and extracellular concentration of oxygen. © 1995 Wiley-Liss, Inc.     

Is intracellular Ca2+ the trigger for oxygen radical production by polymorphonuclear leucocytes?

The aim of this paper is critically to evaluate the existing evidence for the role of intracellular Ca2+ in polymorphonuclear leucocyte (PMN) activation and in particular in oxygen radical production. Indirect experiments are based on the manipulation of extracellular Ca2+, measurement of 45Ca fluxes, employing pharmacological agents such as Ca2+-ionophores and intracellular Ca2+ antagonists and monitoring chlortetracycline fluorescence. Experiments of this type do not provide the necessary definitive evidence that an increase in intracellular Ca2+ is the trigger for PMN activation. Recent direct measurements of intracellular free Ca2+ using the Ca2+-activated photoprotein, obelin, and the Ca2+-sensitive fluorescent indicator, quin 2, have provided evidence for the existence of two distinct mechanisms of activation, one triggered by a rise in intracellular Ca2+ and the other independent of a rise in intracellular Ca2+. The source of the Ca2+ for the former mechanism is mainly extracellular but can also come from an intracellular Ca2+ store.