8/10/2023 0 Comments Benchmark definition in math![]() ![]() A measured steady-state concentration, for instance, might merely provide information about the ratio k prod/ k deg of production and degradation rates. In such kind of settings, multiple parameter combinations can give rise to the same model response for experimentally investigated conditions. ![]() Since the evaluation of distinct experimental conditions is elaborate, the amount of available experimental data for parameter estimation is always limited. In contrast to phenomenological models which describe the empirical relationships in an abstract and simplified manner, the complexity of these so-called mechanistic models is dictated by the complexity of the investigated biological process.Įstimating the parameters of typical models in systems biology requires data that covers a broad set of experimental conditions such as multiple time points, genetic perturbations, and/or treatments. Moreover, biochemical interactions between the considered compounds are translated as rate equations into the model. To this end, molecular compounds such as proteins and spatial compartments such as cells are defined as model components. For simplicity, in the following, this task is sometimes briefly denoted as benchmarking of optimization approaches, although it always refers to the optimization for the fitting of parameters of ODE models which is also termed calibration or model calibration in the literature.Ī major characteristic of the mathematical models applied in systems biology is the intention to mirror the biological process of interest because this facilitates enhanced possibilities of interpretations and understanding. ![]() In this article, these aspects are discussed in the context of benchmarking of approaches for optimization-based fitting of mathematical models in systems biology. General guidelines have been provided recently for computational analysis of omics data, multiple alignment of protein sequences, and supervised classification methods as well as for periodic scientific benchmarking and general studies in computational biology. The importance of proper designs for benchmark studies in computational biology has been discussed in several publications. The absence of high-performing software implementations seems to be a major reason why ODE-based modeling is not yet a routinely applied computational approach for analyzing experimental data. Although parameter estimation is a central task of modeling, the lack of reliable computational approaches for fitting is still a bottleneck in systems biology. In addition, the optimization problem needs to be defined in terms of initialization, search space, termination criteria, and hyperparameters that set up and configure the numerical algorithms. Such optimization-based fitting of a model requires the selection of a generic numerical optimization approach as a core algorithm. Both approaches coincide with normally distributed measurement errors. In most cases, parameter estimation is performed by the optimization of a suitable objective function such as minimization of the sum of squared residuals for least squares estimation or maximization of the likelihood for maximum likelihood estimation. Application-specific calibration of the models is therefore required which corresponds to the estimation of these unknown parameters based on experimental data. Hence, they are represented as unknown parameters in mathematical models. Typical parameters in systems biology such as the abundances of compounds or the strengths and velocities of biochemical interactions are typically context-dependent, i.e., they vary between species, tissues, and cell types. In this article, I focus on the optimization-based fitting of these models although many aspects are general and also apply to other modeling types and approaches. In the BioModels Database, currently, 83% of all models which are uniquely assigned to a modeling approach are ODE models. Most frequently, ordinary differential equation models (ODEs) are applied because they enable a non-discretized description of the dynamics of a system and allow for quantitative evaluation of experimental data including statistical interpretations in terms of confidence and significance. Depending on the questions of interest and on the amount of available data, the type of models and the level of detail vary. A broad range of mathematical models is applied in systems biology. ![]()
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