Analyzing and Constraining Signaling Networks: Parameter Estimation for the User

Abstract

The behavior of most dynamical models not only depends on the wiring but also on the kind and strength of interactions which are reflected in the parameter values of the model. The predictive value of mathematical models therefore critically hinges on the quality of the parameter estimates. Constraining a dynamical model by an appropriate parameterization follows a 3-step process. In an initial step, it is important to evaluate the sensitivity of the parameters of the model with respect to the model output of interest. This analysis points at the identifiability of model parameters and can guide the design of experiments. In the second step, the actual fitting needs to be carried out. This step requires special care as, on the one hand, noisy as well as partial observations can corrupt the identification of system parameters. On the other hand, the solution of the dynamical system usually depends in a highly nonlinear fashion on its parameters and, as a consequence, parameter estimation procedures get easily trapped in local optima. Therefore any useful parameter estimation procedure has to be robust and efficient with respect to both challenges. In the final step, it is important to access the validity of the optimized model. A number of reviews have been published on the subject. A good, nontechnical overview is provided by Jaqaman and Danuser (Nat Rev Mol Cell Biol 7(11):813-819, 2006) and a classical introduction, focussing on the algorithmic side, is given in Press (Numerical recipes: The art of scientific computing, Cambridge University Press, 3rd edn., 2007, Chapters 10 and 15). We will focus on the practical issues related to parameter estimation and use a model of the TGFβ-signaling pathway as an educative example. Corresponding parameter estimation software and models based on MATLAB code can be downloaded from the authors's web page ( http://www.bsse.ethz.ch/cobi ).

Inter-dependent tissue growth and Turing patterning in a model for long bone development

“…Moreover, the model reproduces the observed gene expression patterns as well as key mutant phenotypes. Further quantitative comparisons and data-based parameter estimation procedures as are common for ordinary differential equation-based models [23,54], however, are not yet possible, given the available data.…”

Estimasi Parameter Model Nonlinear Menggunakan Analisis Sensitivitas dan Pengoptimalan Berbasis Turunan

“…Pada teknik pengoptimalan ini, nilai solusi optimal di setiap iterasi diperbarui berdasarkan nilai gradien suatu fungsi residu R ij (p). Lebih spesifik, kandidat nilai solusi optimal ditentukan sebagai nilai parameter yang menghasilkan perubahan gradien fungsi residu terkecil atau kurang dari kriteria nilai toleransi kesalahan yang ditentukan sejak awal pada algoritme pengoptimalan [6]- [7], [11]- [13].…”

“…Makalah ini meninjau metode estimasi parameter di model (3) berdasarkan data pengukuran variabel keadaan x(t). Karena keterbatasan alat ataupun kesulitan dalam proses pengukuran, data pengukuran seringkali hanya diperoleh untuk sebagian dari variabel keadaan x(t) [9]- [11]. Data pengukuran yang diperoleh juga umumnya tidak langsung dalam bentuk nilai masing-masing variabel keadaan, tetapi merupakan nilai kombinasi atau fungsi beberapa variabel keadaan.…”

“…Dalam hal ini, model pengukuran untuk sistem pada (3) untuk waktu 0 ≥ t dapat dituliskan sebagai berikut [10], [11]…”

Global optimization using Gaussian processes to estimate biological parameters from image data

“…The behaviour of the model, and hence the predictions derived from it, can differ depending on the parameter set used. Consequently, parameter estimation is an important problem in computational modeling, see [2][3][4][5] and the references therein.…”