67 research outputs found

    Set-base dynamical parameter estimation and model invalidation for biochemical reaction networks

    Get PDF
    <p>Abstract</p> <p>Background</p> <p>Mathematical modeling and analysis have become, for the study of biological and cellular processes, an important complement to experimental research. However, the structural and quantitative knowledge available for such processes is frequently limited, and measurements are often subject to inherent and possibly large uncertainties. This results in competing model hypotheses, whose kinetic parameters may not be experimentally determinable. Discriminating among these alternatives and estimating their kinetic parameters is crucial to improve the understanding of the considered process, and to benefit from the analytical tools at hand.</p> <p>Results</p> <p>In this work we present a set-based framework that allows to discriminate between competing model hypotheses and to provide guaranteed outer estimates on the model parameters that are consistent with the (possibly sparse and uncertain) experimental measurements. This is obtained by means of exact proofs of model invalidity that exploit the polynomial/rational structure of biochemical reaction networks, and by making use of an efficient strategy to balance solution accuracy and computational effort.</p> <p>Conclusions</p> <p>The practicability of our approach is illustrated with two case studies. The first study shows that our approach allows to conclusively rule out wrong model hypotheses. The second study focuses on parameter estimation, and shows that the proposed method allows to evaluate the global influence of measurement sparsity, uncertainty, and prior knowledge on the parameter estimates. This can help in designing further experiments leading to improved parameter estimates.</p

    ADMIT: a toolbox for guaranteed model invalidation, estimation and qualitative–quantitative modeling

    Get PDF
    Summary: Often competing hypotheses for biochemical networks exist in the form of different mathematical models with unknown parameters. Considering available experimental data, it is then desired to reject model hypotheses that are inconsistent with the data, or to estimate the unknown parameters. However, these tasks are complicated because experimental data are typically sparse, uncertain, and are frequently only available in form of qualitative if–then observations. ADMIT (Analysis, Design and Model Invalidation Toolbox) is a MatLabTM-based tool for guaranteed model invalidation, state and parameter estimation. The toolbox allows the integration of quantitative measurement data, a priori knowledge of parameters and states, and qualitative information on the dynamic or steady-state behavior. A constraint satisfaction problem is automatically generated and algorithms are implemented for solving the desired estimation, invalidation or analysis tasks. The implemented methods built on convex relaxation and optimization and therefore provide guaranteed estimation results and certificates for invalidity

    ADMIT: a toolbox for guaranteed model invalidation, estimation and qualitative–quantitative modeling

    Get PDF
    Summary: Often competing hypotheses for biochemical networks exist in the form of different mathematical models with unknown parameters. Considering available experimental data, it is then desired to reject model hypotheses that are inconsistent with the data, or to estimate the unknown parameters. However, these tasks are complicated because experimental data are typically sparse, uncertain, and are frequently only available in form of qualitative if–then observations. ADMIT (Analysis, Design and Model Invalidation Toolbox) is a MatLabTM-based tool for guaranteed model invalidation, state and parameter estimation. The toolbox allows the integration of quantitative measurement data, a priori knowledge of parameters and states, and qualitative information on the dynamic or steady-state behavior. A constraint satisfaction problem is automatically generated and algorithms are implemented for solving the desired estimation, invalidation or analysis tasks. The implemented methods built on convex relaxation and optimization and therefore provide guaranteed estimation results and certificates for invalidity

    A state-space realization approach to set identification of biochemical kinetic parameters

    Get PDF
    This paper proposes a set-based parameter identification method for biochemical systems. The developed method identifies not a single parameter but a set of parameters that all explain time-series experimental data, enabling the systematic characterization of the uncertainty of identified parameters. Our key idea is to use a state-space realization that has the same input-output behavior as experimental data instead of the experimental data itself for the identification. This allows us to relax the originally nonlinear identification problem to an LMI feasibility problem validating the norm bound of an error system. We show that regions of parameters can be efficiently classified into consistent and inconsistent parameter sets by combining the LMI feasibility problems and a generalized bisection algorithm

    Numerical algebraic geometry for model selection and its application to the life sciences

    Full text link
    Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation, and model selection. These are all optimization problems, well-known to be challenging due to non-linearity, non-convexity and multiple local optima. Furthermore, the challenges are compounded when only partial data is available. Here, we consider polynomial models (e.g., mass-action chemical reaction networks at steady state) and describe a framework for their analysis based on optimization using numerical algebraic geometry. Specifically, we use probability-one polynomial homotopy continuation methods to compute all critical points of the objective function, then filter to recover the global optima. Our approach exploits the geometric structures relating models and data, and we demonstrate its utility on examples from cell signaling, synthetic biology, and epidemiology.Comment: References added, additional clarification

    On the performance of nonlinear dynamical systems under parameter perturbation

    Get PDF
    AbstractWe present a method for analysing the deviation in transient behaviour between two parameterised families of nonlinear ODEs, as initial conditions and parameters are varied within compact sets over which stability is guaranteed. This deviation is taken to be the integral over time of a user-specified, positive definite function of the difference between the trajectories, for instance the L2 norm. We use sum-of-squares programming to obtain two polynomials, which take as inputs the (possibly differing) initial conditions and parameters of the two families of ODEs, and output upper and lower bounds to this transient deviation. Equality can be achieved using symbolic methods in a special case involving Linear Time Invariant Parameter Dependent systems. We demonstrate the utility of the proposed methods in the problems of model discrimination, and location of worst case parameter perturbation for a single parameterised family of ODE models

    Control Theory: On the Way to New Application Fields

    Get PDF
    Control theory is an interdisciplinary field that is located at the crossroads of pure and applied mathematics with systems engineering and the sciences. Recently, deep interactions are emerging with new application areas, such as systems biology, quantum control and information technology. In order to address the new challenges posed by the new application disciplines, a special focus of this workshop has been on the interaction between control theory and mathematical systems biology. To complement these more biology oriented focus, a series of lectures in this workshop was devoted to the control of networks of systems, fundamentals of nonlinear control systems, model reduction and identification, algorithmic aspects in control, as well as open problems in control

    Parameter identification for biological models

    Full text link
    This thesis concerns the identification of dynamic models in systems biology. and is structured into two parts. Both parts concern building dynamic models from observed data, but are quite different in perspective, rationale and mathematics. The first part considers the development of novel identification techniques that are particularly tailored to (molecular) biology and considers two approaches. The first approach reformulates the parameter estimation problem as a feasibility problem. This reformulation allows the invalidation of models by analysing entire parameter regions. The second approach utilises nonlinear observers and a transformation of the model equations into parameter free coordinates. The parameter free coordinates allow the design of a globally convergent observer, which in turn estimates the parameter values, and further, allows to identify modelling errors or unknown inputs/influences. Both approaches are bottom up approaches that require a mechanistic understanding of the underlying processes (in terms of a biochemical reaction network) leading to complex nonlinear models. The second part is an example of what can be done with classical, well developed tools from systems identification when applied to hitherto unattended problems.In particular, part two of my thesis develops a modelling framework for rat movements in an experimental setup that it widely used to study learning and memory.The approach is a top down approach that is data driven resulting in simple linear models

    Verification of system properties of polynomial systems using discrete-time approximations and set-based analysis

    Get PDF
    Magdeburg, Univ., Fak. für Elektrotechnik und Informationstechnik, Diss., 2015von Philipp Rumschinsk
    corecore