The impact of measurement errors in the identification of regulatory networks

Background  

There are several studies in the literature depicting measurement error in gene expression data and also, several others about regulatory network models. However, only a little fraction describes a combination of measurement error in mathematical regulatory networks and shows how to identify these networks under different rates of noise.     

Application of macroscopic principles to microbial metabolism

General expressions for mass, elemental, energy, and entropy balances are derived and applied to microbial growth and product formation. The state of the art of the application of elemental balances to aerobic and heterotrophic growth is reviewed and extended somewhat to include the majority of the cases commonly encountered in biotechnology. The degree of reduction concept is extended to include nitrogen sources other than ammonia. The relationship between a number of accepted measures for the comparison of substrate yields is investigated. The theory is illustrated using a generalized correlation for oxygen yield data. The stoichiometry of anaerobic product formation is briefly treated, a limit to the maximum carbon conservation in product is derived, using the concept of elemental balance. In the treatment of growth energetics the correct statement of the second law of thermodynamics for growing organisms is emphasized. For aerobic heterotrophic growth the concept of thermodynamic efficiency is used to formulate a limit the substrate yield can never surpass. It is combined with a limit due to the fact that the maximum carbon conservation in biomass can obviously never surpass unity. It is shown that growth on substrates of a low degree of reduction is energy limited, for substrates of a high degree of reduction carbon limitation takes over. Based on a literature review concerning yield data some semiempirical notions useful for a preliminary evolution of aerobic heterotrophic growth are developed. The thermodynamic efficiency definition is completed by two other efficiency measures, which allow derivation of simple equations for oxygen consumption and heat production. The range of validity of the constancy of the rate of heat production to the rate of oxygen consumption is analyzed using these efficiency measures. The energetic of anaerobic growth are treated—it is shown that an approximate analysis in terms of an enthalpy balance is not valid for this case, the evaluation of the efficiency of growth has to be based on Gibbs free energy changes. A preliminary analysis shows the existence of regularities concerning the free energy conservation on anaerobic growth. The treatment is extended to include the effect of growth rate by the introduction of a linear relationship for substrate consumption. Aerobic and anaerobic growth are discussed using this relationship. A correlation useful in judging the potentialities for improvement in anaerobic product formation processes is derived. Finally the relevance of macroscopic principles to the modeling of bioengineering systems is discussed.     

Consequences of pH measurement errors

SUMMARY. 1. The pH range over which the effects of acidification on freshwater organisms become apparent may be quite narrow, in some cases less than half a pH unit. Therefore, accurate measurement is important, particularly in dilute surface waters near the biologically critical threshold of hydrogen ion activity.
2. A hypothetical example based on data from two species of fish illustrates the potential errors in predicting mean mortality when pH is measured by probes of varying accuracies, placing our results into an ecosystem management perspective. For a given error, there will be greater uncertainty in predicting mean mortality for species sensitive to increased hydrogen ion activity than for more tolerant species.
3. We review field pH measurement errors, and present unique laboratory (measurements at 1°C and under argon) and field comparisons of current instruments used for continuous, in situ pH monitoring, including the only instrument comparison in low conductivity waters during snow melt. Four operator or sampler-caused measurement errors and three electrode-caused pH measurement errors are illustrated with data from four common types of pH probes and meters.
4. Studies providing no confidence intervals for a set of pH measurements due to the lack of rigorous quality control and assurance procedures are of limited quantitative value to future investigators attempting to analyse temporal trends of surface water acidification. Management and policy decision attempts will remain seriously hampered until more interpretable results are routinely generated.     

Statistical mechanical estimation of the free energy of formation of E. coli biomass for use with macroscopic bioreactor balances

The need for the determination of the free energy of formation of biomass in bioreactor second law balances is well established. A statistical mechanical method for the calculation of the free energy of formation of E. coli biomass is introduced. In this method, biomass is modelled to consist of a system of biopolymer networks. The partition function of this system is proposed to consist of acoustic and optical modes of vibration. Acoustic modes are described by Tarasov's model, the parameters of which are evaluated with the aid of low-temperature calorimetric data for the crystalline protein bovine chymotrypsinogen A. The optical modes are described by considering the low-temperature thermodynamic properties of biological monomer crystals such as amino acid crystals. Upper and lower bounds are placed on the entropy to establish the maximum error associated with the statistical method. The upper bound is determined by endowing the monomers in biomass with ideal gas properties. The lower bound is obtained by limiting the monomers to complete immobility. On this basis, the free energy of formation is fixed to within 10%. Proposals are made with regard to experimental verification of the calculated value and extension of the calculation to other types of biomass.     

Estimation in capture-recapture models when covariates are subject to measurement errors

We consider estimation problems in capture-recapture models when the covariates or the auxiliary variables are measured with errors. The naive approach, which ignores measurement errors, is found to be unacceptable in the estimation of both regression parameters and population size: it yields estimators with biases increasing with the magnitude of errors, and flawed confidence intervals. To account for measurement errors, we derive a regression parameter estimator using a regression calibration method. We develop modified estimators of the population size accordingly. A simulation study shows that the resulting estimators are more satisfactory than those from either the naive approach or the simulation extrapolation (SIMEX) method. Data from a bird species Prinia flaviventris in Hong Kong are analyzed with and without the assumption of measurement errors, to demonstrate the effects of errors on estimations.     

A test of homogeneity of distributions when observations are subject to measurement errors

When the observed data are contaminated with errors, the standard two-sample testing approaches that ignore measurement errors may produce misleading results, including a higher type-I error rate than the nominal level. To tackle this inconsistency, a nonparametric test is proposed for testing equality of two distributions when the observed contaminated data follow the classical additive measurement error model. The proposed test takes into account the presence of errors in the observed data, and the test statistic is defined in terms of the (deconvoluted) characteristic functions of the latent variables. Proposed method is applicable to a wide range of scenarios as no parametric restrictions are imposed either on the distribution of the underlying latent variables or on the distribution of the measurement errors. Asymptotic null distribution of the test statistic is derived, which is given by an integral of a squared Gaussian process with a complicated covariance structure. For data-based calibration of the test, a new nonparametric Bootstrap method is developed under the two-sample measurement error framework and its validity is established. Finite sample performance of the proposed test is investigated through simulation studies, and the results show superior performance of the proposed method than the standard tests that exhibit inconsistent behavior. Finally, the proposed method was applied to real data sets from the National Health and Nutrition Examination Survey. An R package MEtest is available through CRAN.     

Application of the macroscopic electric charge balance in fermentation modeling

This article treats the application of the macroscopic electric charge balance in fermentation modeling. From the presented calculations it follows that the definition formula of the so-called degree of reduction is changed due to the ionic character of the fermentation reactants. It is also shown that the macroscopic electric charge balance, together with the ionic equilibria between fermentation reactants, leads to an expression for the calculation of the pH during fermentation. Finally it is concluded that one should be very careful in the estimation of biomass production from the acid or base feed rates which are necessary for pH control.     

Delay time adjustments to minimize errors in breath-by-breath measurement of VO2 during exercise

Proctor, David N., and Kenneth C. Beck. Delay timeadjustments to minimize errors in breath-by-breath measurement of O₂ during exercise.J. Appl. Physiol. 81(6):2495-2499, 1996.If the delay time between gas concentration andflow signals is not adequately corrected during breath-by-breathanalysis of expired gas, an error in calculation of oxygen consumption(O₂) will result. Toexamine the frequency and delay time dependences of errors inO₂ measurement, six healthymen exercised at 100, 200, and 250 W on a cycle ergometer whilebreath-by-breath assessment ofO₂ was made simultaneouslywith collection of expired air. Subjects breathed first at normal rates(15-30 breaths/min) and then at 70 breaths/min. Each subjectperformed each level of exercise twice by using erroneous values forthe delay time between gas concentration and flow signals. At normalbreathing frequencies, errors inO₂ measurement were±10% over the full range of delay times used, and the errors werenot tightly correlated with variations in delay times from optimum.However, at 70 breaths/min, errors approached ±30% as thevariations in delay times deviated ±0.1 s from the optimal, and theerrors were highly correlated with the variations in delay times. Weconclude that there is greater potential for errors inO₂ measurement withincorrect delay time at higher breathing frequencies. These findingssuggest that the optimal delay time for breath-by-breath systems shouldbe adjusted by using high breathing frequencies.

     

Evaluating outlier loci and their effect on the identification of pedigree errors

Homozygosity outlier loci, which show patterns of variation that are extremely divergent from the rest of the genome, can be evaluated by comparison of the homozygosity under Hardy-Weinberg proportions (the sum of the squares of allele frequencies) with the expected homozygosity under neutrality. Such outlier loci are potentially under selection (balancing selection or directional selection) when genome-wide effects (such as bottleneck and rapid population growth) are excluded. Outlier loci show skewed allele frequencies with respect to neutrality and may therefore affect the identification of pedigree errors. However, choosing neutral markers (excluding outlier loci) for the identification of pedigree errors has been neglected thus far. Our results showed that 4.1%, 5.5%, and 1.5% of the microsatellite markers, Illumina single-nucleotide polymorphisms (SNPs), and Affymetrix SNPs, respectively, on the autosomes appear to be under balancing selection (p or=40%) appear to be under balancing selection. Pedigree structure errors in 15 of 143 pedigrees were detected using microsatellite markers from the autosomes and/or selected SNPs from chromosomes 1 to 18 of the Illumina and/or selected SNPs from chromosomes 1 to 16 of the Affymetrix. Outlier loci did not make a major difference to the identification of pedigree errors. The Collaborative Study on the Genetics of Alcoholism data has pedigree errors and some of them may be due to sample mix up.     

A macroscopic ansatz to deduce the Hill relation

In this study, we derive the hyperbolic force-velocity relation of concentric muscular contraction, first formulated empirically by A.V. Hill in 1938, from three essential model assumptions: (1) the structural assembly of three well-known elements - i.e. active, parallel damping, and serial - fulfilling a force equilibrium, (2) the parallel damping coefficient explicitly depending on muscle force output and three parameters, and (3) the kinematic gearing ratio between active and serial element being assigned to a parameter. The energy source within the muscle represented by the force of the active element is an additional fifth parameter. As a result we find the Hill “constants” A and B as functions of our five model parameters. Using A and B values from literature on experimental data, we predict heat power release of our model. By calculating enthalpy rate and mechanical efficiency, we compare the model heat power to predictions from another Hill-type model, to Hill's original findings, and to findings from modern muscle heat measurements. We reconsider why the biggest share of heat rate during isometric contractions (maintenance heat) and the velocity-dependent heat rate during concentric contractions in addition to maintenance heat rate (shortening heat rate) may be traced back to the same mechanism represented by the kinematic gearing ratio. Namely, we suggest that the serial element transfers attachment-detachment fluctuations of actin-myosin crossbridges within one sarcomere to others in the same sarcomere and to those in parallel and in series. Numerically, in case of negligible passive muscular damping, we find the ratio between A and isometric force (relative A) to depend exclusively on the kinematic gearing ratio, whereas the maintenance heat rate scales with the square of relative A. Moreover, this mechanical coupling internal to the muscle fibres may also be behind the macroscopic force dependency of the overall parallel damping coefficient.     

Systematic identification of gene annotation errors in the widely used yeast mutation collections

The baker's yeast mutation collections are extensively used genetic resources that are the basis for many genome-wide screens and new technologies. Anecdotal evidence has previously pointed to the putative existence of a neighboring gene effect (NGE) in these collections. NGE occurs when the phenotype of a strain carrying a particular perturbed gene is due to the lack of proper function of its adjacent gene. Here we performed a large-scale study of NGEs, presenting a network-based algorithm for detecting NGEs and validating software predictions using complementation experiments. We applied our approach to four datasets uncovering a similar magnitude of NGE in each (7-15%). These results have important consequences for systems biology, as the mutation collections are extensively used in almost every aspect of the field, from genetic network analysis to functional gene annotation.     

Application of the dual-micropipet technique to the measurement of tumor cell locomotion

The objective of this work was to characterize tumor cell locomotion in response to chemotactic stimulation using a dual-micropipet assay. The assay involves two micropipets. An individual A2058 human melanoma cell was retained, without pressure gradient, in a pipet of approximately 14 micrometers i.d. A solution of type IV collagen, chosen as the chemotactic source, was placed in another pipet (approximately 10 micrometers o.d.) with zero pressure at the pipet tip. The smaller pipet was then inserted into the larger one containing the melanoma cell. The initial chemoattractant concentration (C0) and the distance between the tip of the small pipet and the cell surface (delta) provided a gradient (C0/delta) for tumor cell locomotion toward stimulation. This novel assay provides a direct measure of cell movement: cyclic pseudopod protrusion (Lp) and subsequent cell locomotion (Lc). The influences of different adhesion substrates on cell locomotion were also studied. The peak length in Lp precedes the highest locomotion velocity (dLc/dt) by an apparent lag time. C0/delta influences pseudopod protrusion frequency (fp) and dLc/dt, but not significantly on Lp. Substrate adhesions affect dLc/dt, but apparently not Lp or fp. In conclusion, pseudopod protrusion and substrate adhesion are two necessary but mutually independent factors in tumor cell locomotion. dLc/dt correlates with changes in C0/delta, which is in significant correlation with fp but not Lp.