Jens Timmer

Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood

MOTIVATION Mathematical description of biological reaction networks by differential equations leads to large models whose parameters are calibrated in order to optimally explain experimental data. Often only parts of the model can be observed directly. Given a model that sufficiently describes the measured data, it is important to infer how well model parameters are determined by the amount and quality of experimental data. This knowledge is essential for further investigation of model predictions. For this reason a major topic in modeling is identifiability analysis. RESULTS We suggest an approach that exploits the profile likelihood. It enables to detect structural non-identifiabilities, which manifest in functionally related model parameters. Furthermore, practical non-identifiabilities are detected, that might arise due to limited amount and quality of experimental data. Last but not least confidence intervals can be derived. The results are easy to interpret and can be used for experimental planning and for model reduction. AVAILABILITY An implementation is freely available for MATLAB and the PottersWheel modeling toolbox at http://web.me.com/andreas.raue/profile/software.html. SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.

WNT and DKK Determine Hair Follicle Spacing Through a Reaction-Diffusion Mechanism

Mathematical reaction-diffusion models have been suggested to describe formation of animal pigmentation patterns and distribution of epidermal appendages. However, the crucial signals and in vivo mechanisms are still elusive. Here we identify WNT and its inhibitor DKK as primary determinants of murine hair follicle spacing, using a combined experimental and computational modeling approach. Transgenic DKK overexpression reduces overall appendage density. Moderate suppression of endogenous WNT signaling forces follicles to form clusters during an otherwise normal morphogenetic program. These results confirm predictions of a WNT/DKK-specific mathematical model and provide in vivo corroboration of the reaction-diffusion mechanism for epidermal appendage formation.

Design principles of a bacterial signalling network

Cellular biochemical networks have to function in a noisy environment using imperfect components. In particular, networks involved in gene regulation or signal transduction allow only for small output tolerances, and the underlying network structures can be expected to have undergone evolution for inherent robustness against perturbations. Here we combine theoretical and experimental analyses to investigate an optimal design for the signalling network of bacterial chemotaxis, one of the most thoroughly studied signalling networks in biology. We experimentally determine the extent of intercellular variations in the expression levels of chemotaxis proteins and use computer simulations to quantify the robustness of several hypothetical chemotaxis pathway topologies to such gene expression noise. We demonstrate that among these topologies the experimentally established chemotaxis network of Escherichia coli has the smallest sufficiently robust network structure, allowing accurate chemotactic response for almost all individuals within a population. Our results suggest that this pathway has evolved to show an optimal chemotactic performance while minimizing the cost of resources associated with high levels of protein expression. Moreover, the underlying topological design principles compensating for intercellular variations seem to be highly conserved among bacterial chemosensory systems.

Testing for directed influences among neural signals using partial directed coherence

One major challenge in neuroscience is the identification of interrelations between signals reflecting neural activity. When applying multivariate time series analysis techniques to neural signals, detection of directed relationships, which can be described in terms of Granger-causality, is of particular interest. Partial directed coherence has been introduced for a frequency domain analysis of linear Granger-causality based on modeling the underlying dynamics by vector autoregressive processes. We discuss the statistical properties of estimates for partial directed coherence and propose a significance level for testing for nonzero partial directed coherence at a given frequency. The performance of this test is illustrated by means of linear and non-linear model systems and in an application to electroencephalography and electromyography data recorded from a patient suffering from essential tremor.

NONLINEAR DYNAMICAL SYSTEM IDENTIFICATION FROM UNCERTAIN AND INDIRECT MEASUREMENTS

We review the problem of estimating parameters and unobserved trajectory components from noisy time series measurements of continuous nonlinear dynamical systems. It is first shown that in parameter estimation techniques that do not take the measurement errors explicitly into account, like regression approaches, noisy measurements can produce inaccurate parameter estimates. Another problem is that for chaotic systems the cost functions that have to be minimized to estimate states and parameters are so complex that common optimization routines may fail. We show that the inclusion of information about the time-continuous nature of the underlying trajectories can improve parameter estimation considerably. Two approaches, which take into account both the errors-in-variables problem and the problem of complex cost functions, are described in detail: shooting approaches and recursive estimation techniques. Both are demonstrated on numerical examples.

Handbook of Time Series Analysis

Handbook of time series analysis , Handbook of time series analysis , کتابخانه دیجیتال جندی شاپور اهواز

Dynamical modeling and multi-experiment fitting with PottersWheel

Motivation: Modelers in Systems Biology need a flexible framework that allows them to easily create new dynamic models, investigate their properties and fit several experimental datasets simultaneously. Multi-experiment-fitting is a powerful approach to estimate parameter values, to check the validity of a given model, and to discriminate competing model hypotheses. It requires high-performance integration of ordinary differential equations and robust optimization. Results: We here present the comprehensive modeling framework Potters-Wheel (PW) including novel functionalities to satisfy these requirements with strong emphasis on the inverse problem, i.e. data-based modeling of partially observed and noisy systems like signal transduction pathways and metabolic networks. PW is designed as a MATLAB toolbox and includes numerous user interfaces. Deterministic and stochastic optimization routines are combined by fitting in logarithmic parameter space allowing for robust parameter calibration. Model investigation includes statistical tests for model-data-compliance, model discrimination, identifiability analysis and calculation of Hessian- and Monte-Carlo-based parameter confidence limits. A rich application programming interface is available for customization within own MATLAB code. Within an extensive performance analysis, we identified and significantly improved an integrator–optimizer pair which decreases the fitting duration for a realistic benchmark model by a factor over 3000 compared to MATLAB with optimization toolbox. Availability: PottersWheel is freely available for academic usage at http://www.PottersWheel.de/. The website contains a detailed documentation and introductory videos. The program has been intensively used since 2005 on Windows, Linux and Macintosh computers and does not require special MATLAB toolboxes. Contact: maiwald@fdm.uni-freiburg.de Supplementary information: Supplementary data are available at Bioinformatics online.

Systems-level interactions between insulin-EGF networks amplify mitogenic signaling.

Crosstalk mechanisms have not been studied as thoroughly as individual signaling pathways. We exploit experimental and computational approaches to reveal how a concordant interplay between the insulin and epidermal growth factor (EGF) signaling networks can potentiate mitogenic signaling. In HEK293 cells, insulin is a poor activator of the Ras/ERK (extracellular signal‐regulated kinase) cascade, yet it enhances ERK activation by low EGF doses. We find that major crosstalk mechanisms that amplify ERK signaling are localized upstream of Ras and at the Ras/Raf level. Computational modeling unveils how critical network nodes, the adaptor proteins GAB1 and insulin receptor substrate (IRS), Src kinase, and phosphatase SHP2, convert insulin‐induced increase in the phosphatidylinositol‐3,4,5‐triphosphate (PIP3) concentration into enhanced Ras/ERK activity. The model predicts and experiments confirm that insulin‐induced amplification of mitogenic signaling is abolished by disrupting PIP3‐mediated positive feedback via GAB1 and IRS. We demonstrate that GAB1 behaves as a non‐linear amplifier of mitogenic responses and insulin endows EGF signaling with robustness to GAB1 suppression. Our results show the feasibility of using computational models to identify key target combinations and predict complex cellular responses to a mixture of external cues.

Systems biology: experimental design

Experimental design has a long tradition in statistics, engineering and life sciences, dating back to the beginning of the last century when optimal designs for industrial and agricultural trials were considered. In cell biology, the use of mathematical modeling approaches raises new demands on experimental planning. A maximum informative investigation of the dynamic behavior of cellular systems is achieved by an optimal combination of stimulations and observations over time. In this minireview, the existing approaches concerning this optimization for parameter estimation and model discrimination are summarized. Furthermore, the relevant classical aspects of experimental design, such as randomization, replication and confounding, are reviewed.

Clinical neurophysiology of tremor.

The neurophysiological analysis of tremor has a long tradition. These attempts were directed to understand the mechanisms underlying tremor, on the one hand, and to develop tools to better diagnose the different types of tremor, on the other. Meanwhile, reasonable criteria are available to distinguish between centrally and peripherally mediated tremors. However, no generally accepted means exist to differentiate the different forms of central tremors. Frequency is a useful classifier for cerebellar tremor, rubral tremor, and orthostatic tremor. Although the highest amplitudes are found in Parkinsons disease, this parameter does not well distinguish between the different tremors. Waveform analysis of tremor is a promising tool to separate between the different tremors. Polymyography is pathognomonic for some rare forms of tremor. New approaches to classify tremors are based on positron emission tomography scanning, analysis of ballistic movement, and reflex testing. The means to separate myoclonias from tremors include EEG/EMG correlation techniques, long-latency reflexes, and polymyography. Provided these techniques are applied in the setting of careful clinical analysis of tremor syndromes, they may prove to be helpful in clinical practice.