Analysis and application of ADM1 for anaerobic methane production

An anaerobic model for the serum bottle test was developed and analyzed with sensitivities of stoichiometric and kinetic parameters to the components in order to establish a basis for appropriate application of the model. Anaerobic glucose degradation in a serum bottle was selected as an example. The anaerobic model was developed based on the anaerobic digestion model no. 1 (ADM1), which had five processes with 17 kinetic and stoichiometric parameters. Sensitivity analysis showed that the yield of product on the substrate (f) has high sensitivities to model components, and that the methane concentration was the most sensitive component. Important parameters including yield of product on the substrate (f), yield of biomass on the substrate (Y), and half-saturation values (K) were estimated using genetic algorithms, which optimized the parameters with experimental results. The Monod maximum specific uptake rate (k) was, however, so strongly associated with the concentration of biomass, that values could not be estimated individually. Simulation with estimated parameters showed good agreement with experimental results in the case of methane production. However, there were some differences in acetate and propionate concentrations.     

Comparative study of parameter sensitivity analyses of the TCR-activated Erk-MAPK signalling pathway

Parameter estimation is a major challenge for mathematical modelling of biological systems. Given the uncertainties associated with model parameters, it is important to understand how sensitive the model output is to variations in parameter values. A local sensitivity analysis determines the model sensitivity to parameter variations over a localised region around the nominal parameter values, whereas a global sensitivity analysis (GSA) investigates the sensitivity over the entire parameter space. Using a T-cell receptor-activated Erk-MAPK signalling pathway model as an example, the authors present a comparative study of a variety of different sensitivity analysis techniques. These techniques include: local sensitivity analysis, existing GSA methods of partial rank correlation coefficient, Sobol's, extended Fourier amplitude sensitivity test, as well as a weighted average of local sensitivities and a new GSA method to extract global parameter sensitivities from a parameter identification routine. Results of this study revealed critical reactions in the signalling pathway and their impact on the signalling dynamics and provided insights into embedded regulatory mechanisms such as feedback loops in the pathway. From this study, a recommendation emerges for a general sensitivity analysis strategy to efficiently and reliably infer quantitative, dynamic as well as topological properties from systems biology models.     

Metabolic control analysis. Sensitivity of control coefficients to elasticities

This paper illustrates a method to calculate the sensitivities of control coefficients to the elasticities which determine their values and it is shown that these sensitivities are systemic properties. We show, both theoretically and with a practical example, how they can be used to investigate: (a) the relative importance of a particular elasticity in the determination of the value of a control coefficient; (b) the effect of experimental error on the values of the control coefficients and (c) the construction of confidence limits around the values of the control coefficients.     

What Can We Learn from Global Sensitivity Analysis of Biochemical Systems?

Most biological models of intermediate size, and probably all large models, need to cope with the fact that many of their parameter values are unknown. In addition, it may not be possible to identify these values unambiguously on the basis of experimental data. This poses the question how reliable predictions made using such models are. Sensitivity analysis is commonly used to measure the impact of each model parameter on its variables. However, the results of such analyses can be dependent on an exact set of parameter values due to nonlinearity. To mitigate this problem, global sensitivity analysis techniques are used to calculate parameter sensitivities in a wider parameter space. We applied global sensitivity analysis to a selection of five signalling and metabolic models, several of which incorporate experimentally well-determined parameters. Assuming these models represent physiological reality, we explored how the results could change under increasing amounts of parameter uncertainty. Our results show that parameter sensitivities calculated with the physiological parameter values are not necessarily the most frequently observed under random sampling, even in a small interval around the physiological values. Often multimodal distributions were observed. Unsurprisingly, the range of possible sensitivity coefficient values increased with the level of parameter uncertainty, though the amount of parameter uncertainty at which the pattern of control was able to change differed among the models analysed. We suggest that this level of uncertainty can be used as a global measure of model robustness. Finally a comparison of different global sensitivity analysis techniques shows that, if high-throughput computing resources are available, then random sampling may actually be the most suitable technique.     

Highly accurate computation of dynamic sensitivities in metabolic reaction systems by a Taylor series method

We have previously developed the software for calculation of dynamic sensitivities, SoftCADS, in which one can calculate dynamic sensitivities with high accuracy by just setting the differential equations for metabolite concentrations. However, SoftCADS did not always provide calculated values with the machine accuracy of a computer, although a Taylor series method was employed to numerically solve the differential equations. This is because numerical derivatives calculated from an approximate formula were directly used in the derivation of the differential equations for sensitivities from those for metabolite concentrations. The present work therefore attempts to further enhance the performance of SoftCADS, including not only the accuracies of the calculated values but also the calculation time. To overcome the problem, the approximate formula is expanded into a Taylor series in time and the first-term value of the series is replaced by the exact coefficient on the second term of the flux function expanded into a Taylor series in an independent or dependent variable. The result reveals that this replacement certainly provides not only numerical derivatives but also dynamic sensitivities with superhigh accuracies comparable to the machine accuracy, regardless of the degree of stiffness of the differential equations. Moreover, a comparison indicates that the improved SoftCADS shortens the calculation time of the dynamic sensitivities without reducing their accuracies, even when the simplest approximate derivative formula is used.     

The spectral sensitivity of single units in the nucleus rotundus of pigeon, Columba livia

Responses to diffuse monochromatic light were recorded from single units in the diencephalon of pigeon. Units were both excited and inhibited by light stimulation. Intensity-response functions based on latency measures to the first spike after stimulation were used to generate action spectra. One class of spectral sensitivity functions presumably from rods, showed peak sensitivities near 500 nm: these functions were unaffected by changing criterion values used to generate the functions. A second class of cone functions showed multiple peak sensitivities at 540 nm and 600–620 nm. These units shifted their peak sensitivities with a change in criterion values. Unit response types tended to be localized differentially in the nucleus rotundus. Excitatory units were located in the dorsal half of the nucleus, while inhibitory units were located in the ventral half, with a few exceptions. An attempt was made to integrate the present findings with previous behavioral, electrophysiological, photochemical, and anatomical data in the pigeon.     

Meta‐Analysis of Diagnostic Test Accuracy Studies with Multiple Thresholds using Survival Methods

Diagnostic tests play an important role in clinical practice. The objective of a diagnostic test accuracy study is to compare an experimental diagnostic test with a reference standard. The majority of these studies dichotomize test results into two categories: negative and positive. But often the underlying test results may be categorized into more than two, ordered, categories. This article concerns the situation where multiple studies have evaluated the same diagnostic test with the same multiple thresholds in a population of non‐diseased and diseased individuals. Recently, bivariate meta‐analysis has been proposed for the pooling of sensitivity and specificity, which are likely to be negatively correlated within studies. These ideas have been extended to the situation of diagnostic tests with multiple thresholds, leading to a multinomial model with multivariate normal between‐study variation. This approach is efficient, but computer‐intensive and its convergence is highly dependent on starting values. Moreover, monotonicity of the sensitivities/specificities for increasing thresholds is not guaranteed. Here, we propose a Poisson‐correlated gamma frailty model, previously applied to a seemingly quite different situation, meta‐analysis of paired survival curves. Since the approach is based on hazards, it guarantees monotonicity of the sensitivities/specificities for increasing thresholds. The approach is less efficient than the multinomial/normal approach. On the other hand, the Poisson‐correlated gamma frailty model makes no assumptions on the relationship between sensitivity and specificity, gives consistent results, appears to be quite robust against different between‐study variation models, and is computationally very fast and reliable with regard to the overall sensitivities/specificities.     

Predicted inactivation of viruses of relevance to biodefense by solar radiation

UV radiation from the sun is the primary germicide in the environment. The goal of this study was to estimate inactivation of viruses by solar exposure. We reviewed published reports on 254-nm UV inactivation and tabulated the sensitivities of a wide variety of viruses, including those with double-stranded DNA, single-stranded DNA, double-stranded RNA, or single-stranded RNA genomes. We calculated D(37) values (fluence producing on average one lethal hit per virion and reducing viable virus to 37%) from all available data. We defined "size-normalized sensitivity" (SnS) by multiplying UV(254) sensitivities (D(37) values) by the genome size, and SnS values were relatively constant for viruses with similar genetic composition. In addition, SnS values were similar for complete virions and their defective particles, even when the corresponding D(37) values were significantly different. We used SnS to estimate the UV(254) sensitivities of viruses for which the genome composition and size were known but no UV inactivation data were available, including smallpox virus, Ebola, Marburg, Crimean-Congo, Junin, and other hemorrhagic viruses, and Venezuelan equine encephalitis and other encephalitis viruses. We compiled available data on virus inactivation as a function of wavelength and calculated a composite action spectrum that allowed extrapolation from the 254-nm data to solar UV. We combined our estimates of virus sensitivity with solar measurements at different geographical locations to predict virus inactivation. Our predictions agreed with the available experimental data. This work should be a useful step to understanding and eventually predicting the survival of viruses after their release in the environment.     

The tricarboxylic acid cycle in Dictyostelium discoideum. II. Evaluation of model consistency and robustness.

When kinetic models of complex biochemical systems are reconstructed from knowledge of the component reactions that have been characterized in vitro, or when values must be assumed for some of the parameters, errors are invariably encountered, and, as a consequence, the resulting model is frequently internally inconsistent. The simplest and most basic manifestations of such logical inconsistency are the failure of the model to exhibit a steady state or to yield a steady state that is in agreement with the actual steady state of the integrated system, or to yield a steady state that is dynamically stable. Models that are consistent may nonetheless be lacking in robustness, which is manifested as a pathological sensitivity to small changes in the values of their parameters. In this paper, we examine the current model of the tricarboxylic acid cycle in Dictyostelium discoideum (see Shiraishi, F., and Savageau, M. A. (1992) J. Biol. Chem. 267, 22912-22918) with regard to these basic indicators of model quality. This may be viewed as a preliminary analysis; the object is to determine whether or not the model is reasonable and worthy of a more refined analysis and, if not, to diagnose the areas in need of modification before further analysis is undertaken. The results demonstrate that the current model of the tricarboxylic acid cycle is self-consistent and possesses a steady state that is in agreement with experimental evidence. However, the results also suggest that this model is not very robust. The high sensitivities of parameters influencing pyruvate metabolism indicate that the experimental characterization of these reactions might be fruitfully re-examined. These high sensitivities lead us to predict that this model of the tricarboxylic acid cycle should be accurate only over a very narrow range in variation of the independent variables. This is verified by the results presented in the following paper (Shiraishi, F., and Savageau, M. A. (1992) J. Biol. Chem. 267, 22926-22933).     

瓜实蝇不同寄主种群对4种杀虫剂的敏感性

为探索瓜实蝇Zeugodacus cucurbitae不同寄主种群对杀虫剂的敏感性,本研究在室内通过药膜法测定了瓜实蝇节瓜、黄瓜、丝瓜和苦瓜种群4日龄成虫对4种杀虫剂的敏感性,随后将瓜实蝇不同寄主种群致死中浓度LC50进行比较,计算抗性倍数。结果表明,4个寄主种群对甲维盐的敏感性为节瓜 > 苦瓜 > 丝瓜 > 黄瓜,其中节瓜、苦瓜种群对甲维盐最敏感,其次是丝瓜、黄瓜,LC50值分别为0.250、0.391、0.809和1.035 mg/L。4个寄主种群对灭多威的敏感性表现为节瓜 > 黄瓜 > 苦瓜 > 丝瓜,LC50值分别为0.302、0.318、0.652和0.804 mg/L。对多杀菌素的敏感性大小依次为黄瓜、节瓜、丝瓜、苦瓜,LC50值分别为1.157、1.198、1.232和2.029 mg/L。对啶虫脒的敏感性为苦瓜 > 节瓜 > 黄瓜 > 丝瓜,LC50值分别为17.946、20.166、20.190和21.986 mg/L,其中对甲维盐的敏感性差异幅度最大,为4.140倍,其次是灭多威,为2.654倍,对啶虫脒的敏感性差异幅度最小,为1.225倍。表明寄主植物可引起瓜实蝇对杀虫剂的敏感性变化。     

Parametric Sensitivity Analysis of Oscillatory Delay Systems with an Application to Gene Regulation

A parametric sensitivity analysis for periodic solutions of delay-differential equations is developed. Because phase shifts cause the sensitivity coefficients of a periodic orbit to diverge, we focus on sensitivities of the extrema, from which amplitude sensitivities are computed, and of the period. Delay-differential equations are often used to model gene expression networks. In these models, the parametric sensitivities of a particular genotype define the local geometry of the evolutionary landscape. Thus, sensitivities can be used to investigate directions of gradual evolutionary change. An oscillatory protein synthesis model whose properties are modulated by RNA interference is used as an example. This model consists of a set of coupled delay-differential equations involving three delays. Sensitivity analyses are carried out at several operating points. Comments on the evolutionary implications of the results are offered.     

Population dynamics of the cactus Mammillaria gaumeri: an integral projection model approach

The Cactaceae family in Mexico is particularly important because members of this family exhibit a high degree of endemism. Unfortunately, many species of the Cactaceae are threatened or endangered. We employed an integral projection model for studies of the population dynamics of Mammillaria gaumeri, an endemic cactus of the Yucatán characterized by a small population size. The integral projection model provides estimates of the asymptotic growth rate, stable size distribution, reproductive values, and sensitivities and elasticities of the growth rate to changes in vital rates. Nine locations of this species were studied along the Yucatan coast over a 9-year period. Individuals were classified by plant volume. Most population growth rate (λ) values were below unity. The highest elasticity values corresponded to the survival of intermediate size individuals. The percentage of germination in the field was low, and consequently, fecundity values were also low. Reproductive values were observed to increase with plant volume. The stable size distribution of M. gaumeri was skewed toward small individuals. For all years, the kernel showed that individual survival determined the population growth rate.     

Sensitivity to values of the rate constants in a neurochemical metabolic model

Equations were derived for the instantaneous relative sensitivities of reaction rates (controllability indices) and metabolite concentrations (response indices) to perturbations in the values of rate constants and were used to analyze the behavior of a model of in vivo glutamate metabolism in rat brain. Controllabilities of reversible reactions were found to increase as the values of the corresponding rate constants (i.e., the rate of approach to equilibrium) increased. Response indices generally declined with the metabolic distance between the metabolite and the rate constant, but they were unexpectedly high for reversible reactions with high controllabilities. The transient response of a given metabolite is most sensitive to reactions involving metabolites which are changing most rapidly relative to their respective pool sizes. Rapidly reversible reactions are most important for communication between metabolite pools.     

Universally sloppy parameter sensitivities in systems biology models

Quantitative computational models play an increasingly important role in modern biology. Such models typically involve many free parameters, and assigning their values is often a substantial obstacle to model development. Directly measuring in vivo biochemical parameters is difficult, and collectively fitting them to other experimental data often yields large parameter uncertainties. Nevertheless, in earlier work we showed in a growth-factor-signaling model that collective fitting could yield well-constrained predictions, even when it left individual parameters very poorly constrained. We also showed that the model had a “sloppy” spectrum of parameter sensitivities, with eigenvalues roughly evenly distributed over many decades. Here we use a collection of models from the literature to test whether such sloppy spectra are common in systems biology. Strikingly, we find that every model we examine has a sloppy spectrum of sensitivities. We also test several consequences of this sloppiness for building predictive models. In particular, sloppiness suggests that collective fits to even large amounts of ideal time-series data will often leave many parameters poorly constrained. Tests over our model collection are consistent with this suggestion. This difficulty with collective fits may seem to argue for direct parameter measurements, but sloppiness also implies that such measurements must be formidably precise and complete to usefully constrain many model predictions. We confirm this implication in our growth-factor-signaling model. Our results suggest that sloppy sensitivity spectra are universal in systems biology models. The prevalence of sloppiness highlights the power of collective fits and suggests that modelers should focus on predictions rather than on parameters.     

Influence of parameter values on the oscillation sensitivities of two p53–Mdm2 models

Biomolecular networks that present oscillatory behavior are ubiquitous in nature. While some design principles for robust oscillations have been identified, it is not well understood how these oscillations are affected when the kinetic parameters are constantly changing or are not precisely known, as often occurs in cellular environments. Many models of diverse complexity level, for systems such as circadian rhythms, cell cycle or the p53 network, have been proposed. Here we assess the influence of hundreds of different parameter sets on the sensitivities of two configurations of a well-known oscillatory system, the p53 core network. We show that, for both models and all parameter sets, the parameter related to the p53 positive feedback, i.e. self-promotion, is the only one that presents sizeable sensitivities on extrema, periods and delay. Moreover, varying the parameter set values to change the dynamical characteristics of the response is more restricted in the simple model, whereas the complex model shows greater tunability. These results highlight the importance of the presence of specific network patterns, in addition to the role of parameter values, when we want to characterize oscillatory biochemical systems.

Electronic supplementary material

The online version of this article (doi:10.1007/s11693-015-9173-y) contains supplementary material, which is available to authorized users.     

Comparisons of predictive values of binary medical diagnostic tests for paired designs

Positive and negative predictive values of a diagnostic test are key clinically relevant measures of test accuracy. Surprisingly, statistical methods for comparing tests with regard to these parameters have not been available for the most common study design in which each test is applied to each study individual. In this paper, we propose a statistic for comparing the predictive values of two diagnostic tests using this paired study design. The proposed statistic is a score statistic derived from a marginal regression model and bears some relation to McNemar's statistic. As McNemar's statistic can be used to compare sensitivities and specificities of diagnostic tests, parameters that condition on disease status, our statistic can be considered as an analog of McNemar's test for the problem of comparing predictive values, parameters that condition on test outcome. We report on the results of a simulation study designed to examine the properties of this test under a variety of conditions. The method is illustrated with data from a study of methods for diagnosis of coronary artery disease.     

Estimation of genetic variance for macro- and micro-environmental sensitivity using double hierarchical generalized linear models

Background

Genetic variation for environmental sensitivity indicates that animals are genetically different in their response to environmental factors. Environmental factors are either identifiable (e.g. temperature) and called macro-environmental or unknown and called micro-environmental. The objectives of this study were to develop a statistical method to estimate genetic parameters for macro- and micro-environmental sensitivities simultaneously, to investigate bias and precision of resulting estimates of genetic parameters and to develop and evaluate use of Akaike’s information criterion using h-likelihood to select the best fitting model.

Methods

We assumed that genetic variation in macro- and micro-environmental sensitivities is expressed as genetic variance in the slope of a linear reaction norm and environmental variance, respectively. A reaction norm model to estimate genetic variance for macro-environmental sensitivity was combined with a structural model for residual variance to estimate genetic variance for micro-environmental sensitivity using a double hierarchical generalized linear model in ASReml. Akaike’s information criterion was constructed as model selection criterion using approximated h-likelihood. Populations of sires with large half-sib offspring groups were simulated to investigate bias and precision of estimated genetic parameters.

Results

Designs with 100 sires, each with at least 100 offspring, are required to have standard deviations of estimated variances lower than 50% of the true value. When the number of offspring increased, standard deviations of estimates across replicates decreased substantially, especially for genetic variances of macro- and micro-environmental sensitivities. Standard deviations of estimated genetic correlations across replicates were quite large (between 0.1 and 0.4), especially when sires had few offspring. Practically, no bias was observed for estimates of any of the parameters. Using Akaike’s information criterion the true genetic model was selected as the best statistical model in at least 90% of 100 replicates when the number of offspring per sire was 100. Application of the model to lactation milk yield in dairy cattle showed that genetic variance for micro- and macro-environmental sensitivities existed.

Conclusion

The algorithm and model selection criterion presented here can contribute to better understand genetic control of macro- and micro-environmental sensitivities. Designs or datasets should have at least 100 sires each with 100 offspring.     

Response of diatom indices to simulated water quality improvements in a river

Various diatom indices are routinely used in European countries to monitor water quality in waterways. In order to assess their sensitivities and their integration interval after a sudden and lasting environmental change, epilithic diatom biofilms were transferred from several polluted rivers to an unpolluted stream. To monitor the changes of the index values, the biofilms were sampled in a first experiment 20 and 40 days after transfer, and in a second experiment 30 and 60 days after transfer. Sensitivities of the indices to the water quality improvement were assessed calculating the differences between the index values of the reference and the transferred assemblages. Some indices have intermediate sensitivities (BDI, GDI, ILM, SLA), others higher sensitivities (CEE, EPI, ROT, SPI, TDI). The integration interval of these indices was 40–60 days. Some differences were observed between the indices, but their results were homogeneous when compared to those obtained with other metrics such as Bray-Curtis or Chord distances, used to assess the difference between the transferred and the reference diatom assemblages. These other metrics showed that even after 60 days, the transferred assemblages still differed from the reference. This underlines that metrics do not have the same integration intervals and do not assess the same stresses; the choice of the metric used to assess water quality is of prime importance.     

Statistical Assessment of Jointly Observed Screening Tests

In this article, Lindley and Novick criteria of screening usefulness is applied to the statistical assessment of jointly observed screening test. Posterior probabilities comparing screening sensitivities and specificities, and posterior probability bounds to comparing screening predictive values are obtained.