Yunfei Chu

Advances and selected recent developments in state and parameter estimation

Abstract This paper deals with two topics from state and parameter estimation. The first contribution of this work provides an overview of techniques used for determining which parameters of a model should be estimated. This is a question that commonly arises when fundamental models are used as these models often contain more parameters than can be reliably estimated from data. The decision of which parameters to estimate is independent of the observer/estimator design, however, it is directly affected by the structure of the model as well as the available data. The second contribution is an overview of recent developments regarding the design of nonlinear Luenberger observers, with special emphasis on exact error linearization techniques, but also discussing more general issues, including observer discretization, sampled data observers and the use of delayed measurements.

Necessary condition for applying experimental design criteria to global sensitivity analysis results

Abstract Conventional techniques for optimal experimental design are based on local sensitivity analysis to quantify parameter effects on the output. However, one of the key challenges for experimental design is that the local sensitivity is dependent on the unknown parameter values for a nonlinear model. This problem can be addressed if the sensitivity matrix, used in experimental design, could be computed by global sensitivity analysis techniques rather than local sensitivity analysis methods. However, not all existing global sensitivity analysis measures can compute such a sensitivity matrix. This paper presents a necessary condition for integrating global sensitivity analysis with experimental design criteria, i.e., the design criterion of the global sensitivity matrix reduces to the one applied to the local sensitivity matrix if the parameter uncertainty range tends to zero. Four different sensitivity measures are analyzed using this condition and the results are illustrated in a detailed case study where a comparison with local design and Bayesian design is made.

Determining transcription factor profiles from fluorescent reporter systems involving regularization of inverse problems

The availability and quality of experimental data pose challenges for identifying the role of individual proteins in signal transduction pathways. To address this issue, this paper formulates and solves an inverse problem to determine the dynamics of transcription factors, i.e., one important class of proteins, from fluorescence intensity measurements of green fluorescent protein (GFP) reporter systems. In the presented approach, a model describing transcription and translation of GFP is discretized and concentrations of transcription factor are estimated at discrete time points. Unlike previous works, this approach has no restrictions with regard to a particular shape of the profiles. However, the resulting inverse problem is ill-conditioned and requires the use of regularization techniques. Two regularization methods - truncated singular value decomposition and Tikhonov regularization - are investigated in this work and the characteristics of the results obtained are discussed in detail.

Generalisation of a procedure for computing transcription factor profiles

The limited amount of quantitative experimental data generated from life-science experiments poses a major challenge in systems biology. The reason for this is that many systems approaches, such as parameter estimation, simulation and sensitivity analysis make use of models or analyse quantitative data. However, these techniques are only of limited use if only qualitative or semi-quantitative information is available about a system. Therefore procedures that generate quantitative data from experiments in the life sciences can greatly expand the use of systems approaches to biological problems. This study addresses this issue as it introduces a procedure that computes quantitative transcription factor profiles from fluorescent microscopy data collected from green fluorescent protein (GFP) reporter cells. This technique forms a generalisation of a method that has recently been introduced for monitoring NF-B profiles. The contribution made in this work is that the assumption that the transcription factor profile exhibits damped oscillations is relaxed, as transcription factors, other than the previously investigated NF-B, may exhibit different profiles. This is achieved by investigating a variety of potential profiles and solving the inverse problem for the model describing transcription, translation and activation of GFP for each one. The transcription factor profile that results in the best fit among the potential candidates, for the measured fluorescent intensity data, is then chosen as the most likely concentration profile. The technique is illustrated in two detailed case studies, where one case study involves simulation data whereas the other one uses experimentally derived fluorescent intensity data.

Derivation of simplified signal transduction pathway models: Application to IL-6 signaling

Mathematical models of signal transduction pathways are characterized by a large number of proteins and uncertain parameters. One challenge involving these models is parameter identifiability as only a limited amount of quantitative data is generally available. One potential solution to this problem is model simplification, as the parts of the model that cannot be identified in experiments can be reduced. It is the main goal of the presented work to derive a model simplification procedure for signal transduction pathways such that: 1) the model size is significantly reduced such that the model can be validated using available experimental data, and 2) the physical interpretation of the remaining states and parameters is retained. The presented technique is used to derive a simplified version of an IL-6 signal transduction model. The number of equations and parameters in the model has been reduced from 68 to 13 and from 118 to 19, respectively. It is shown that the identifiability of the model has improved significantly. The new model is able to adequately predict the dynamic behavior of key proteins of the signal transduction pathway both in simulations but also when compared to available experimental data.