Abstract
Computational modeling is a common tool to quantitatively describe biological processes. However, most model parameters are usually unknown because they cannot be directly measured. Therefore, a key issue in Systems Biology is model calibration, i.e. estimate parameters from experimental data. Existing methodologies for parameter estimation are divided in two classes: frequentist and Bayesian methods. The first ones optimize a cost function while the second ones estimate the parameter posterior distribution through different sampling techniques. Here, we present an innovative Bayesian method, called Conditional Robust Calibration (CRC), for nonlinear model calibration and robustness analysis using omics data. CRC is an iterative algorithm based on the sampling of a proposal distribution and on the definition of multiple objective functions, one for each observable. CRC estimates the probability density function of parameters conditioned to the experimental measures and it performs a robustness analysis, quantifying how much each parameter influences the observables behavior. We apply CRC to three Ordinary Differential Equations (ODE) models to test its performances compared to the other state of the art approaches, namely Profile Likelihood (PL), Approximate Bayesian Computation Sequential Monte Carlo (ABC-SMC) and Delayed Rejection Adaptive Metropolis (DRAM). Compared with these methods, CRC finds a robust solution with a reduced computational cost. CRC is developed as a set of Matlab functions (version R2018), whose fundamental source code is freely available at https://github.com/fortunatobianconi/CRC.
Highlights
In recent years omics technologies have tremendously advanced allowing the identification and quantification of molecules at the DNA, RNA and protein level [1, 2]
M1 is characterized by an oscillatory behavior of both output variables, M2 is used in synthetic biology and contains initial conditions and scale factors to estimate while M3 is a high-dimensional model based on experimental proteomics data
Profile Likelihood (PL) Results First of all, we estimate parameter values using three different optimization algorithms, available in the software D2D [13]: lsqnonlin, genetic algorithms (GA), and simulated annealing (SA). Both the default lsqnonlin and Genetic Algorithms (GA) correctly fit the model yielding the same results, while Simulated Annealing (SA) totally fails in parameter estimation
Summary
In recent years omics technologies have tremendously advanced allowing the identification and quantification of molecules at the DNA, RNA and protein level [1, 2] These high-throughput experiments produce huge amounts of data which need to be managed and analyzed in order to extract useful information [3]. The most used kinetic laws in ODE models can be divided into three types: the law of mass action, the Michaelis-Menten kinetic and the Hill function [7, 8] These equations contain unknown parameters which have to be estimated in order to properly simulate the model and represent the problem under study. A calibrated model can be used to predict the time evolution of substances for which enough information or measures are not available
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