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.     

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 analysis approaches applied to systems biology models

With the rising application of systems biology, sensitivity analysis methods have been widely applied to study the biological systems, including metabolic networks, signalling pathways and genetic circuits. Sensitivity analysis can provide valuable insights about how robust the biological responses are with respect to the changes of biological parameters and which model inputs are the key factors that affect the model outputs. In addition, sensitivity analysis is valuable for guiding experimental analysis, model reduction and parameter estimation. Local and global sensitivity analysis approaches are the two types of sensitivity analysis that are commonly applied in systems biology. Local sensitivity analysis is a classic method that studies the impact of small perturbations on the model outputs. On the other hand, global sensitivity analysis approaches have been applied to understand how the model outputs are affected by large variations of the model input parameters. In this review, the author introduces the basic concepts of sensitivity analysis approaches applied to systems biology models. Moreover, the author discusses the advantages and disadvantages of different sensitivity analysis methods, how to choose a proper sensitivity analysis approach, the available sensitivity analysis tools for systems biology models and the caveats in the interpretation of sensitivity analysis results.     

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.     

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].     

Random walk models in biology.

Mathematical modelling of the movement of animals, micro-organisms and cells is of great relevance in the fields of biology, ecology and medicine. Movement models can take many different forms, but the most widely used are based on the extensions of simple random walk processes. In this review paper, our aim is twofold: to introduce the mathematics behind random walks in a straightforward manner and to explain how such models can be used to aid our understanding of biological processes. We introduce the mathematical theory behind the simple random walk and explain how this relates to Brownian motion and diffusive processes in general. We demonstrate how these simple models can be extended to include drift and waiting times or be used to calculate first passage times. We discuss biased random walks and show how hyperbolic models can be used to generate correlated random walks. We cover two main applications of the random walk model. Firstly, we review models and results relating to the movement, dispersal and population redistribution of animals and micro-organisms. This includes direct calculation of mean squared displacement, mean dispersal distance, tortuosity measures, as well as possible limitations of these model approaches. Secondly, oriented movement and chemotaxis models are reviewed. General hyperbolic models based on the linear transport equation are introduced and we show how a reinforced random walk can be used to model movement where the individual changes its environment. We discuss the applications of these models in the context of cell migration leading to blood vessel growth (angiogenesis). Finally, we discuss how the various random walk models and approaches are related and the connections that underpin many of the key processes involved.     

Stability analysis of non-axisymmetric three-dimensional finite element rotor models with partial and full mass lumping

Unlike structural dynamics, the three-dimensional finite-element model of non-axisymmetric rotors on orthotropic bearings generates a large gyroscopic system with parametric stiffness. The present work explores the use of mass-lumping in stability analysis of such systems. Using a variant of Hill’s method, the problem reduces to a generalized Eigen value problem of order nm ×nm, with n as the order of the system in state vector representation and m as the number of terms in the assumed solution. The matrices in both the sides of the Eigen value problem are expressed in terms of Kronecker products where the mass-matrix appears twice as a sub-matrix in both the sides of the equation. A particular one or both of them can be made diagonal. Both options produce sufficiently accurate results with considerable savings, even with a coarse mesh.     

EUCLIS--an information system for circadian systems biology

A major barrier to progress in systems biology is the absence of suitable infrastructure for data and software integration, which would enable working biologists to use and manipulate the techniques directly. We describe the incremental development of key components of such an infrastructure for a research community focused on a specific (but important) biological system. EUCLOCK combines the expertise of 34 chronobiology laboratories from 29 institutions in 11 European countries in a 5-year effort to understand how circadian clocks are synchronised to their specific cyclic environment (entrainment). We envision that the EUCLOCK Information System (EUCLIS) will subsequently evolve to support the worldwide chronobiology community. The architecture of EUCLIS integrates a database for circadian systems biology, containing modules for experimental data (Clock Experiments) and models (Clock Models) with a digital library (Clock KnowledgeBase) for the research community. The digital library paradigm is superior to the simple 'access' or 'mining' as well as the 'data warehouse' approaches currently used in other systems as it provides a flexible framework for community information needs and the potential to use emerging reference models and standards, which will enable easier integration with other systems in the future. The main Clock KnowledgeBase components for EUCLIS V1.0, Clock Genes and Clock Library, are described in detail. An important aspect this work will need to address in the future is the integration of the database and digital library management functions.     

Additive hazards models in repairable systems reliability

The paper is concerned with the analysis of a repairable system's failure behaviour. In a brief survey the shortcomings of commonly used probabilistic models are mentioned. Appearing to be more appropriate, a regression type of analysis is followed, with explanatory variables acting additively on the hazard function. As repairable systems may experience multiple failures, the hazard function modelling is continued beyond a system's first failure to second and subsequent failures. In this way a kind of additive variant of the model developed by Prentice, Williams and Peterson (which is an extension of Cox's proportional hazards model) is formulated. The techniques are illustrated in an example.     

Glassy models for granular systems

We briefly review some simple lattice models, introduced recently to study granular systems based on the similarities with glassy systems. The basic common ingredient, partially responsible for the complex behavior shown, is geometric frustration due to steric hindrance. Received: 30 March 2000     

Network integration and graph analysis in mammalian molecular systems biology

Abstraction of intracellular biomolecular interactions into networks is useful for data integration and graph analysis. Network analysis tools facilitate predictions of novel functions for proteins, prediction of functional interactions and identification of intracellular modules. These efforts are linked with drug and phenotype data to accelerate drug-target and biomarker discovery. This review highlights the currently available varieties of mammalian biomolecular networks, and surveys methods and tools to construct, compare, integrate, visualise and analyse such networks.     

Detection of distortions in models of stochastic systems

Objects described by stochastic differential equations and the associated control systems under the conditions of possible distortions in models generating these systems are considered. A solution of problems of detecting and diagnostics of distortions which utilizes sequential decision rules and the maximum of posterior probability criterion is validated. As an application, and efficient algorithm of the fastest detection of a maneuver of a moving object which assesses the given probabilities of the type I and type II errors is developed. The necessary programming system is established and positive results of computational experiments are obtained. Translated from Izmeritel'naya Tekhnika, No. 3, pp. 9–11, March, 1996.     

Continuous models in nonlinear thermomechanics of binary systems

We study some general problems connected with the construction of thermodynamic models in the mechanics of two-component elastic bodies. Principal relations of the model are established on the basis of fundamental concepts and approaches of nonlinear continuum mechanics and nonequilibrium thermodynamics. We also demonstrate that systems of this sort can be described without using chemical potentials in the explicit form.Center of Mathematical Simulation. Pidstryhach Institute for Applied Problems in Mathematics and Mechanics, Ukrainian Academy of Sciences, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 31, No. 4, pp. 7–15, July – August, 1995.     

On ARMA models for vibrating systems

The paper considers the possible ARMA models which can be derived from the discrete-time state space model. This is achieved by the definition of the regular observation matrix. ARMA models of different order are obtained and the number of identified parameters of these models is determined. The almost sure existence of the minimal parameter ARMA model is shown. On this basis, the classification of ARMA models for vibrating systems is presented.     

Engineering challenges of BioNEMS: the integration of microfluidics, micro- and nanodevices, models and external control for systems biology

Systems biology, i.e. quantitative, postgenomic, postproteomic, dynamic, multiscale physiology, addresses in an integrative, quantitative manner the shockwave of genetic and proteomic information using computer models that may eventually have 10(6) dynamic variables with non-linear interactions. Historically, single biological measurements are made over minutes, suggesting the challenge of specifying 10(6) model parameters. Except for fluorescence and micro-electrode recordings, most cellular measurements have inadequate bandwidth to discern the time course of critical intracellular biochemical events. Micro-array expression profiles of thousands of genes cannot determine quantitative dynamic cellular signalling and metabolic variables. Major gaps must be bridged between the computational vision and experimental reality. The analysis of cellular signalling dynamics and control requires, first, micro- and nano-instruments that measure simultaneously multiple extracellular and intracellular variables with sufficient bandwidth; secondly, the ability to open existing internal control and signalling loops; thirdly, external BioMEMS micro-actuators that provide high bandwidth feedback and externally addressable intracellular nano-actuators; and, fourthly, real-time, closed-loop, single-cell control algorithms. The unravelling of the nested and coupled nature of cellular control loops requires simultaneous recording of multiple single-cell signatures. Externally controlled nano-actuators, needed to effect changes in the biochemical, mechanical and electrical environment both outside and inside the cell, will provide a major impetus for nanoscience.