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.     

New interpretation of arterial stiffening due to cigarette smoking using a structurally motivated constitutive model

Cigarette smoking is the leading self-inflicted risk factor for cardiovascular diseases; it causes arterial stiffening with serious sequelea including atherosclerosis and abdominal aortic aneurysms. This work presents a new interpretation of arterial stiffening caused by smoking based on data published for rat pulmonary arteries. A structurally motivated "four fiber family" constitutive relation was used to fit the available biaxial data and associated best-fit values of material parameters were estimated using multivariate nonlinear regression. Results suggested that arterial stiffening caused by smoking was reflected by consistent increase in an elastin-associated parameter and moreover by marked increase in the collagen-associated parameters. That is, we suggest that arterial stiffening due to cigarette smoking appears to be isotropic, which may allow simpler phenomenological models to capture these effects using a single stiffening parameter similar to the approach in isotropic continuum damage mechanics. There is a pressing need, however, for more detailed histological information coupled with more complete biaxial mechanical data for a broader range of systemic arteries.     

Experimental validation of a time-domain-based wave propagation model of blood flow in viscoelastic vessels

Time-domain-based one-dimensional wave propagation models of the arterial system are preferable over one-dimensional wave propagation models in the frequency domain since the latter neglect the non-linear convection forces present in the physiological situation, especially when the vessel is tapered. Moreover, one-dimensional wave propagation models of the arterial system can be used to provide boundary conditions for fully three-dimensional fluid-structure interaction computations that are usually defined in the time domain. In this study, a time-domain-based one-dimensional wave propagation model in a cross-sectional area, flow and pressure (A,q,p)-formulation is developed. Using this formulation, a constitutive law that includes viscoelasticity based on the mechanical behaviour of a Kelvin body, is introduced. The resulting pressure and flow waves travelling through a straight and tapered vessel are compared to experimental data obtained from measurements in an in vitro setup. The model presented shows to be well suited to predict wave propagation through these straight and tapered vessels with viscoelastic wall properties and hereto can serve as a time-domain-based method to model wave propagation in the human arterial system.     

A comparison of the European Water Framework Directive physical typology and RIVPACS-type models as alternative methods of establishing reference conditions for benthic macroinvertebrates

The EU Water Framework Directive requires European Union Member States to establish ‘type-specific biological reference conditions’ for streams and rivers. Types can be defined by using either a fixed typology (System-A), defined by ecoregions and categories of altitude, catchment area and geology, or by means of an alternative characterisation (System-B) that can use a variety of physical and chemical factors. Several European countries also have existing RIVPACS-type models that give site (rather than stream type) specific predictions of benthic macroinvertebrate communities. In this paper we compare the Water Framework Directive (WFD) System-A physical typology and three existing European multivariate RIVPACS-type models as alternative methods of establishing reference conditions. This work is carried out in Great Britain – using RIVPACS, Sweden – using SWEPAC_SRI and the Czech Republic – using PERLA. We found that in all three countries, all seasons and season combinations, and for all biotic indices tested, RIVPACS-type models were more effective (lower standard deviations of O/E ratios) than models based solely on the WFD System-A variables or null models (based on a single expectation for all sites). We also investigated the explanatory power of whole groups of WFD System-A variables and RIVPACS-type model variables, and the explanatory power of individual variables. We found that variables used in the RIVPACS-type models were often better correlates of macroinvertebrate community variation than the WFD System-A variables. We conclude that this is primarily because while the latter use very broad categories of map-derived variables, the former are based on continuous variables selected for their ecological significance.     

Statistical analyses of repeated measures in physiological research: a tutorial

Experimental designs involving repeated measurements on experimental units are widely used in physiological research. Often, relatively many consecutive observations on each experimental unit are involved and the data may be quite nonlinear. Yet evidently, one of the most commonly used statistical methods for dealing with such data sets in physiological research is the repeated-measurements ANOVA model. The problem herewith is that it is not well suited for data sets with many consecutive measurements; it does not deal with nonlinear features of the data, and the interpretability of the model may be low. The use of inappropriate statistical models increases the likelihood of drawing wrong conclusions. The aim of this article is to illustrate, for a reasonably typical repeated-measurements data set, how fundamental assumptions of the repeated-measurements ANOVA model are inappropriate and how researchers may benefit from adopting different modeling approaches using a variety of different kinds of models. We emphasize intuitive ideas rather than mathematical rigor. We illustrate how such models represent alternatives that 1) can have much higher interpretability, 2) are more likely to meet underlying assumptions, 3) provide better fitted models, and 4) are readily implemented in widely distributed software products.     

Compound Regression Models for Ordered Categorical Data

A general class of sequential models for the analysis of ordered categorical variables is developed and discussed. The models apply if the ordinal response may be subdivided into two or more meaningful sets of response categories. The parametrization explicitly makes use of this subdivision. The models furnish a linear alternative to non-linear models which incorporate a scale parameter. They are shown to be special cases of multivariate generalized linear models. Applications are discussed with the use of several examples.     

Multivariate data analysis in empirical research. A look on the bright side

The interpretive benefits of employing multivariate analysis methods on experimental data with more than one dependent variable are described heuristically and illustrated on a set of data from a simply designed experiment in physiological psychology. Multivariate analysis of variance (MANOVA) is performed on the 9 dependent variables contained in the sample data and on the four composites derived from a principal components analysis (PCA) of the variability of the nine. A linear discriminant analysis (LDA) is conducted following both MANOVA results, and 5 methods of determining the "important" dependent variables in the experimental-control group difference are presented and discussed in terms of the data at hand.     

Identification of vascular territory resistances in one-dimensional hemodynamics simulations

The present work deals with the parameter identification problem in outflow models used in one-dimensional simulations of arterial blood flow. Specifically, the resistive elements that define the models used to account for the blood supply to the vascular territories in arterial networks are computed by solving a system of non-linear equations using a Broyden method. This strategy is employed to compute the terminal parameters in the vascular territories of an anatomically detailed model of the arm comprising 67 arterial segments and 16 vascular territories. A comparison with a simple analytical approach, in terms of vascular territory resistances, average blood flows and time-dependent hemodynamic quantities, is performed. Also, a sensitivity analysis is presented to assess the performance of this new approach in normal and abnormal cardiovascular scenarios. This identification procedure allows to correctly set up hemodynamics simulations in highly detailed arterial networks making possible to gain insight in the aspects related to the blood circulation in arterial vessels.     

An exhaustive analysis of heuristic methods for variable selection in ecological niche modeling and species distribution modeling

Ecological niche models and species distribution models are used in many fields of science. Despite their popularity, only recently have important aspects of the modeling process like model selection been developed. Choosing environmental variables with which to create these models is another critical part of the process, but methods currently in use are not consistent in their results and no comprehensive approach exists by which to perform this step. Here, we compared seven heuristic methods of variable selection against a novel approach that proposes to select best sets of variables by evaluating performance of models created with all combinations of variables and distinct parameter settings of the algorithm in concert. Our results were that—except for the jackknife method for one of the 12 species and fluctuation index for two of the 12 species—none of the heuristic methods for variable selection coincided with the exhaustive one. Performance decreased in models created using variables selected with heuristic methods and both underfitting and overfitting were detected when comparing their geographic projections with the ones of models created with variables selected with the exhaustive method. Using the exhaustive approach could be time consuming, so a two-step exercise may be necessary. However, using this method identifies adequate variable sets and parameter settings in concert that are associated with increased model performance.     

A comparison of models of the isometric force of locust skeletal muscle in response to pulse train inputs

Muscle models are an important tool in the development of new rehabilitation and diagnostic techniques. Many models have been proposed in the past, but little work has been done on comparing the performance of models. In this paper, seven models that describe the isometric force response to pulse train inputs are investigated. Five of the models are from the literature while two new models are also presented. Models are compared in terms of their ability to fit to isometric force data, using Akaike’s and Bayesian information criteria and by examining the ability of each model to describe the underlying behaviour in response to individual pulses. Experimental data were collected by stimulating the locust extensor tibia muscle and measuring the force generated at the tibia. Parameters in each model were estimated by minimising the error between the modelled and actual force response for a set of training data. A separate set of test data, which included physiological kick-type data, was used to assess the models. It was found that a linear model performed the worst whereas a new model was found to perform the best. The parameter sensitivity of this new model was investigated using a one-at-a-time approach, and it found that the force response is not particularly sensitive to changes in any parameter.     

Minimal Conductance-Based Model of Auditory Coincidence Detector Neurons

Sound localization is a fundamental sensory function of a wide variety of animals. The interaural time difference (ITD), an important cue for sound localization, is computed in the auditory brainstem. In our previous modeling study, we introduced a two-compartment Hodgkin-Huxley type model to investigate how cellular and synaptic specializations may contribute to precise ITD computation of the barn owl''s auditory coincidence detector neuron. Although our model successfully reproduced fundamental physiological properties observed in vivo, it was unsuitable for mathematical analyses and large scale simulations because of a number of nonlinear variables. In the present study, we reduce our former model into three types of conductance-based integrate-and-fire (IF) models. We test their electrophysiological properties using data from published in vivo and in vitro studies. Their robustness to parameter changes and computational efficiencies are also examined. Our numerical results suggest that the single-compartment active IF model is superior to other reduced models in terms of physiological reproducibility and computational performance. This model will allow future theoretical studies that use more rigorous mathematical analysis and network simulations.     

Temperature effects on circadian clocks

Periodic temperature changes represent one of the most effective entraining (Zeitgeber) signals for circadian clocks in many organisms. Different constant temperatures affect the circadian amplitude and ultimately the expression of circadian clocks, while the circadian period length (tau) remains approximately constant (temperature compensation). Experimental results and theoretical models are presented that may serve to explain these effects. After introducing the physico-chemical basis of temperature on enzyme-catalyzed and physiological reactions, and after describing mechanisms for temperature adaptation of physiological reactions to different thermal environments, general effects of temperature on chemical and biological oscillators are described. Kinetic models for circadian clocks and temperature compensation are presented and compared with experimental results. Special attention is given to the question how constant but different temperature levels affect clock amplitude, period length and phase. Influences of single and periodic temperature variations (steps or pulses) on circadian clocks are presented together with models which may explain the resulting phase response curves and entrainment patterns. Because temperature compensation is only one aspect of a general homeostatic mechanism that keeps the circadian period rather constant, the influence of other environmental variables and their relationship to temperature are discussed.     

Categorical variables with many categories are preferentially selected in bootstrap‐based model selection procedures for multivariable regression models

Automated variable selection procedures, such as backward elimination, are commonly employed to perform model selection in the context of multivariable regression. The stability of such procedures can be investigated using a bootstrap‐based approach. The idea is to apply the variable selection procedure on a large number of bootstrap samples successively and to examine the obtained models, for instance, in terms of the inclusion of specific predictor variables. In this paper, we aim to investigate a particular important problem affecting this method in the case of categorical predictor variables with different numbers of categories and to give recommendations on how to avoid it. For this purpose, we systematically assess the behavior of automated variable selection based on the likelihood ratio test using either bootstrap samples drawn with replacement or subsamples drawn without replacement from the original dataset. Our study consists of extensive simulations and a real data example from the NHANES study. Our main result is that if automated variable selection is conducted on bootstrap samples, variables with more categories are substantially favored over variables with fewer categories and over metric variables even if none of them have any effect. Importantly, variables with no effect and many categories may be (wrongly) preferred to variables with an effect but few categories. We suggest the use of subsamples instead of bootstrap samples to bypass these drawbacks.     

A simulation study comparing the impact of experimental error on the performance of experimental designs and artificial neural networks used for process screening

Many variables and their interactions can affect a biotechnological process. Testing a large number of variables and all their possible interactions is a cumbersome task and its cost can be prohibitive. Several screening strategies, with a relatively low number of experiments, can be used to find which variables have the largest impact on the process and estimate the magnitude of their effect. One approach for process screening is the use of experimental designs, among which fractional factorial and Plackett–Burman designs are frequent choices. Other screening strategies involve the use of artificial neural networks (ANNs). The advantage of ANNs is that they have fewer assumptions than experimental designs, but they render black-box models (i.e., little information can be extracted about the process mechanics). In this paper, we simulate a biotechnological process (fed-batch growth of bakers yeast) to analyze and compare the effect of random experimental errors of different magnitudes and statistical distributions on experimental designs and ANNs. Except for the situation in which the error has a normal distribution and the standard deviation is constant, it was not possible to determine a clear-cut rule for favoring one screening strategy over the other. Instead, we found that the data can be better analyzed using both strategies simultaneously.     

Temperature profiles with respect to inhomogeneity and geometry of the human body

Temperature profiles within the human body are highly dependent on the geometry and inhomogeneity of the body. Physical parameters such as density and heat conductivity of the various tissues and variables such as blood flow and metabolic heat production of different organs are spatially distributed and thereby influence the temperature profiles within the human body. Actual physiological knowledge allows one to take into account up to 54 different spatially distributed values for each parameter. An adequate representation of the anatomy of the body requires a spatial three-dimensional grid of at least 0.5-1.0 cm. This is achieved by photogrammetric treatment of three-dimensional anatomic models of the human body. As a first essential result, the simulation system has produced a realistic picture of the topography of temperatures under neutral conditions. Compatibility of reality and simulation was achieved solely on the basis of physical considerations and physiological data base. Therefore the simulation is suited to the extrapolation of temperature profiles that cannot be obtained experimentally.     

Mathematical modeling and optimization of cellulase protein production using Trichoderma reesei RL-P37

The enzyme cellulase, a multienzyme complex made up of several proteins, catalyzes the conversion of cellulose to glucose in an enzymatic hydrolysis-based biomass-to-ethanol process. Production of cellulase enzyme proteins in large quantities using the fungus Trichoderma reesei requires understanding the dynamics of growth and enzyme production. The method of neural network parameter function modeling, which combines the approximation capabilities of neural networks with fundamental process knowledge, is utilized to develop a mathematical model of this dynamic system. In addition, kinetic models are also developed. Laboratory data from bench-scale fermentations involving growth and protein production by T. reesei on lactose and xylose are used to estimate the parameters in these models. The relative performances of the various models and the results of optimizing these models on two different performance measures are presented. An approximately 33% lower root-mean-squared error (RMSE) in protein predictions and about 40% lower total RMSE is obtained with the neural network-based model as opposed to kinetic models. Using the neural network-based model, the RMSE in predicting optimal conditions for two performance indices, is about 67% and 40% lower, respectively, when compared with the kinetic models. Thus, both model predictions and optimization results from the neural network-based model are found to be closer to the experimental data than the kinetic models developed in this work. It is shown that the neural network parameter function modeling method can be useful as a "macromodeling" technique to rapidly develop dynamic models of a process.     

The use of gene knockout mice in thermoregulation studies

As the use of gene knockout models in thermoregulation studies has gained popularity, the reported incidence of redundant or discrepant phenotypes between studies has also increased. Several gene knockout models mimic human processes and have provided valuable insight into the role of endogenous mediators in thermoregulatory processes. There are also many examples of mutant strains expressing virtually identical phenotypes as their wild-type controls, causing concern regarding the appropriateness of these models for the study of physiological processes. In some cases, discrepancies in results are being reported from different laboratories that are studying the same gene knockout model. While mutant strains provide a powerful tool for analysis of gene function in vivo, the breeding strategies used to generate the strain may have a profound impact on the expressed phenotype. This review examines the intricacies of working with a small rodent such as the mouse and discusses the advantages and disadvantages of using gene knockout models for thermoregulatory research. A number of experimental strategies that can be used to minimize the occurrence of redundant phenotypes are presented. The influence of background strain effects is also considered, since this may be one of the most important factors influencing a mutant phenotype. A future perspective is provided in which more advanced technologies using conditional gene inactivation and the production of rat knockout strains will improve current experimental design.