Building multivariate systems biology models

Systems biology methods using large-scale "omics" data sets face unique challenges: integrating and analyzing near limitless data space, while recognizing and removing systematic variation or noise. Herein we propose a complementary multivariate analysis workflow to both integrate "omics" data from disparate sources and analyze the results for specific and unique sample correlations. This workflow combines principal component analysis (PCA), orthogonal projections to latent structures discriminate analysis (OPLS-DA), orthogonal 2 projections to latent structures (O2PLS), and shared and unique structures (SUS) plots. The workflow is demonstrated using data from a study in which ApoE3Leiden mice were fed an atherogenic diet consisting of increasing cholesterol levels followed by therapeutic intervention (fenofibrate, rosuvastatin, and LXR activator T-0901317). The levels of structural lipids (lipidomics) and free fatty acids in liver were quantified via liquid chromatography-mass spectrometry (LC-MS). The complementary workflow identified diglycerides as key hepatic metabolites affected by dietary cholesterol and drug intervention. Modeling of the three therapeutics for mice fed a high-cholesterol diet further highlighted diglycerides as metabolites of interest in atherogenesis, suggesting a role in eliciting chronic liver inflammation. In particular, O2PLS-based SUS2 plots showed that treatment with T-0901317 or rosuvastatin returned the diglyceride profile in high-cholesterol-fed mice to that of control animals.     

Validation and invalidation of systems biology models using robustness analysis

Robustness, the ability of a system to function correctly in the presence of both internal and external uncertainty, has emerged as a key organising principle in many biological systems. Biological robustness has thus become a major focus of research in Systems Biology, particularly on the engineering-biology interface, since the concept of robustness was first rigorously defined in the context of engineering control systems. This review focuses on one particularly important aspect of robustness in Systems Biology, that is, the use of robustness analysis methods for the validation or invalidation of models of biological systems. With the explosive growth in quantitative modelling brought about by Systems Biology, the problem of validating, invalidating and discriminating between competing models of a biological system has become an increasingly important one. In this review, the authors provide a comprehensive overview of the tools and methods that are available for this task, and illustrate the wide range of biological systems to which this approach has been successfully applied.     

Proper lumping in systems biology models

An algorithm for automatic order reduction of models defined by large systems of differential equations is presented. The algorithm was developed with systems biology models in mind and the motivation behind it is to develop mechanistic pharmacokinetic/pharmacodynamic models from already available systems biology models. The approach used for model reduction is proper lumping of the system?s states and is based on a search through the possible combinations of lumps. To avoid combinatorial explosion, a heuristic, greedy search strategy is employed and comparison with the full exhaustive search provides evidence that it performs well. The method takes advantage of an apparent property of this kind of systems that lumps remain consistent over different levels of order reduction. Advantages of the method presented include: the variables and parameters of the reduced model retain a specific physiological meaning; the algorithm is automatic and easy to use; it can be used for nonlinear models and can handle parameter uncertainty and constraints. The algorithm was applied to a model of NF-kB signalling pathways in order to demonstrate its use and performance. Significant reduction was achieved for the example model, while agreement with the original model was proportional to the size of the reduced model, as expected. The results of the model reduction were compared with a published, intuitively reduced model of NF-kB signalling pathways and were found to be in agreement, in terms of the identified key species for the system?s kinetic behaviour. The method may provide useful insights which are complementary to the intuitive reduction approach, especially in large systems.     

Sensitivity analysis of multilayer perceptrons applied to focal-plane image compression

The authors previously considered the application of multilayer perceptrons (MLPs) to block coding at the sensor level of modern imaging systems, and have proposed analogue encoders with transistor-count complexity that is low enough to suit focal-plane implementation. In the paper, they extend the on-sensor block coding MLP study, to include a statistical analysis of the MLP sensitivity to implementation errors occuring in standard CMOS fabrication processes. Employing simple offset models, a comparison is made of the MLP with other block encoders based on full-search entropy-constrained vector quantisation (ECVQ) of the data, and it is verified that the MLPs are less sensitive over a wide range of rate-distortion compression points. By introducing a realistic linear model that takes into account sensitivity and the complexity performances for both systems, the authors verify that, for MLPs, the sensitivity becomes less dependent on the complexity as the expected quality loss is allowed to increase. Without setting a limit on the expected quality loss, the MLPs are consistently better than the ECVQs, both in terms of sensitivity and complexity for a precision equivalent to 6 bits     

Sensitivity analysis techniques applied to a revised model of molybdenum biokinetics

A revised model of molybdenum biokinetics in humans was recently developed on the basis of experimental data gathered in specific investigations conducted with stable tracers. The model can be used for radiation protection purposes, and it is also a suitable working tool for designing new investigations aimed at further improvements to the model. For the latter goal, a sensitivity analysis was performed in order to determine the most significant model parameters in relation to output measurements performed in studies of molybdenum metabolism. A typical sensitivity analysis approach was adopted, considering the effects in variation of model parameters on the time courses of model outputs such as urinary excretion and blood clearance. A recent new sensitivity technique was considered too, based on the calculation of the so-called generalised sensitivity functions. This combines the sensitivities of the model output with respect to model parameters (as in the typical sensitivity analysis method), with the sensitivities of parameter estimates with respect to changes in model outputs. The results obtained in this analysis suggests that data collected in the first 7 h are critical for the definition of the process of blood clearance and related parameters, whereas reliable information at later times is required for a proper characterisation of urinary excretion.     

Family tree of Markov models in systems biology

Motivated by applications in systems biology, a probabilistic framework based on Markov processes is proposed to represent intracellular processes. The formal relationships between different stochastic models referred to in the systems biology literature are reviewed. As part of this review, a novel derivation of the differential Chapman-Kolmogorov equation for a general multidimensional Markov process made up of both continuous and jump processes, is presented. First, the definition of a time-derivative for a probability density is focused, but placing no restrictions on the probability distribution, in particular, it is not assumed to be to be confined to a region that has a surface (on which the probability is zero). In this derivation, the master equation gives the jump part of the Markov process and the Fokker-Planck equation gives the continuous part. As a result, a 'family tree' for stochastic models in systems biology is sketched, providing explicit derivations of their formal relationship and clarifying assumptions involved.     

Sensitivity based reduced approaches for structural reliability analysis

In the reliability analysis of a complex engineering structures a very large number of system parameters can be considered to be random variables. The difficulty in computing the failure probability increases rapidly with the number of variables. In this paper, a few methods are proposed whereby the number of variables can be reduced without compromising the accuracy of the reliability calculation. Based on the sensitivity of the failure surface, three new reduction methods, namely (a) gradient iteration method, (b) dominant gradient method, and (c) relative importance variable method, have been proposed. Numerical examples are provided to illustrate the proposed methods.     

Sensitivity analysis for non-linear constrained elastostatic systems

Adjoint and direct differentiation methods are used to formulate design sensitivities for non-linear constrained elastostatic systems. Variations of a general response functional are expressed in explicit form with respect to all design field variations, including shape. The response functional is expressed over the undeformed configuration; however, the displacement gradient is included so that field quantities that are defined over the deformed configuration, such as Cauchy stress, may be modelled. The finite element method is used to evaluate the sensitivities in an example problem.     

Systems biology approaches to understanding stem cell fate choice

Stem cells have the capability to self-renew and maintain their undifferentiated state or to differentiate into one or more specialised cell types. Stem cell expansion and manipulation ex vivo is a promising approach for engineering cell replacement therapies, and endogenous stem cells represent potential drugable targets for tissue repair. Before we can harness stem cells' therapeutic potential, we must first understand the intracellular mechanisms controlling their fate choices. These mechanisms involve complex signal transduction and gene regulation networks that feature, for example, intricate feed-forward loops, feedback loops and cross-talk between multiple signalling pathways. Systems biology applies computational and experimental approaches to investigate the emergent behaviour of collections of molecules and strives to explain how these numerous components interact to regulate molecular, cellular and organismal behaviour. Here we review systems biology, and in particular computational, efforts to understand the intracellular mechanisms of stem cell fate choice. We first discuss deterministic and stochastic models that synthesise molecular knowledge into mathematical formalism, enable simulation of important system behaviours and stimulate further experimentation. In addition, statistical analyses such as Bayesian networks and principal components analysis (PCA)/partial least squares (PLS) regression can distill large datasets into more readily managed networks and principal components that provide insights into the critical aspects and components of regulatory networks. Collectively, integrating modelling with experimentation has strong potential for enabling a deeper understanding of stem cell fate choice and thereby aiding the development of therapies to harness stem cells' therapeutic potential.     

Adaptive wavelets applied to the analysis of nonlinear systems with chaotic dynamics

We consider an approach to the analysis of nonstationary processes based on the application of wavelet basis sets constructed using segments of the analyzed time series. The proposed method is applied to the analysis of time series generated by a nonlinear system with and without noise.     

Mechanical and geometrical approaches applied to composite fabric forming

In this paper, we are interested in the forming of composite fabric by deep-drawing. Two approaches (geometrical and mechanical) are proposed for the simulation of the composite fabric forming. The geometrical approach is based on a fishnet model. It is well adapted to preliminary design phase and to give a suitable estimate of the resulting flat patterns. The mechanical approach is based on a meso-structural approach. It allows us to take into account the mechanical properties of composite fabric (fibres and resin) and the various dominant modes of deformation of fabrics during the forming process. During simulation of composite fabric forming, where large displacement and relative rotation of fibres are possible, severe mesh distortions occur after a few incremental steps. Hence an automatic mesh generation with remeshing capabilities is essential to carry out the finite element analysis. Some numerical simulations of forming process are proposed and compared with the experimental results in order to demonstrate the efficiency of the proposed approaches.     

Design approaches to power-over-optical local-area-network systems

This paper discusses fiber optic power and signal transmission systems considering the application of dc powering to information tools such as personal computers. We discuss system requirements and technical issues for the system components, including high-power laser diodes and photovoltaic cells. It is clarified that the conversion efficiencies of photovoltaic cells are kept constant with heat radiation and improve with extremely small series resistance. The transmittable optical powers through the optical fiber limited by a nonlinear optical effect are estimated. We also discuss the system designs for the use of single- and multi-mode optical fibers.     

Sensitivity analysis of entropy-constrained designs of water distribution systems

A study of the relationship between the statistical entropy and hydraulic reliability of water distribution systems (WDS) was carried out by assessing the effects of layout, flow direction, and pipe costs. Because of an invariance property of the entropy function, different WDS layouts can have identical maximum entropy values. The properties of designs that have identical maximum entropy values were also compared. The results reinforce previous observations that entropy is a potential surrogate measure for hydraulic reliability and suggest that any influences due to the design factors mentioned above are negligible. Maximum entropy designs are shown to be more reliable than other designs, while designs with different layouts but equal maximum entropy values have very similar levels of reliability. The head-dependent analysis method was used and revealed the correlation between entropy and reliability more clearly than hitherto achieved using demand-driven analysis.     

Sensitivity analysis for dynamic mechanical systems with finite rotations

This paper presents a sensitivity analysis for dynamic systems with large rotations using a semi‐analytical direct differentiation technique. The choice of a suitable time integration strategy for the rotation group appears to be critical for the development of an efficient sensitivity analysis. Three versions of the generalized‐α time integration scheme are considered: a residual form, a linear form, and a geometric form. Their consistency is discussed, and we show that the residual form, which is the most direct extension of the generalized‐α algorithm defined in structural dynamics, should not be used for problems with large rotations. The sensitivity analysis is performed and close connections are highlighted between the structure of the sensitivity equations and of the linearized dynamic equations. Hence, algorithms developed for the original problem can be directly reused for the sensitivities. Finally, a numerical example is analysed in detail. Copyright © 2007 John Wiley & Sons, Ltd.     

Teaching systems biology

Advances in systems biology are increasingly dependent upon the integration of various types of data and different methodologies to reconstruct how cells work at the systemic level. Thus, teams with a varied array of expertise and people with interdisciplinary training are needed. So far this training was thought to be more productive if aimed at the Masters or PhD level. At this level, multiple specialised and in-depth courses on the different subject matters of systems biology are taught to already well-prepared students. This approach is mostly based on the recognition that systems biology requires a wide background that is hard to find in undergraduate students. Nevertheless, and given the importance of the field, the authors argue that exposition of undergraduate students to the methods and paradigms of systems biology would be advantageous. Here they present and discuss a successful experiment in teaching systems biology to third year undergraduate biotechnology students at the University of Lleida in Spain. The authors' experience, together with that from others, argues for the adequateness of teaching systems biology at the undergraduate level. [Includes supplementary material].