Application of Global Sensitivity Analysis to Determine Goals for Design of Experiments: An Example Study on Antibody-Producing Cell Cultures (original) (raw)
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Global Sensitivity Analysis Challenges in Biological Systems Modeling
Industrial & Engineering Chemistry Research, 2009
Mammalian cell culture systems produce high-value biologics, such as monoclonal antibodies, which are increasingly being used clinically. A complete framework that interlinks model-based design of experiments (DOE) and model-based control and optimization to the actual industrial bioprocess could assist experimentation, hence reducing costs. However, high fidelity models have the inherent characteristic of containing a large number of parameters, which is further complicated by limitations in the current analytical techniques, thus resulting in the experimental validation of merely a small number of parameters. Sensitivity analysis techniques can provide valuable insight into model characteristics. Traditionally, the application of sensitivity analysis on models of biological systems has been treated more or less as a black box operation. In the present work, we elucidate the aspects of sensitivity analysis and identify, with reasoning, the most suitable group of sensitivity analysis methods for application to highly nonlinear dynamic models in the context of biological systems. Specifically, we perform computational experiments on antibody-producing mammalian cell culture models of different complexities and identify, as well as address, problems associated with such "real life" models. In conclusion, a novel global screening method (derivative based global sensitivity measures, DGSM) is proven to be the most time-efficient and robust alternative to the established variance-based Monte Carlo methods.
Optimal experimental design based on global sensitivity analysis
2007
The starting values considered for the model parameters strongly affect standard techniques for experimental design. When these values are far from the optimal ones, poor quality experiments are achieved or several steps are required resulting in a large experimental burden. Here, a novel criterion based on global sensitivity analysis, and therefore independent of the parameters values, is presented. In order to illustrate the performance of this methodology, a semicontinuous bioreactor is considered as a case study.
A tutorial on Sobol’ global sensitivity analysis applied to biological models
Networks in Systems Biology, 2020
Nowadays, in addition to traditional qualitative methods, quantitative techniques are also a standard tool to describe biological systems behavior. An example is the broad class of mathematical models, based on differential equations, used in ecology, biochemical kinetics, epidemiology, gene regulatory networks, etc. Independent of their simplicity or complexity, all these models have in common (generally unknown a priori) parameters that need to be identified from observations (data) of the real system, usually available on the literature, obtained by specific assays or surveyed by public health offices. Before using this data to calibrate the models, a good practice is to judge the most influential parameters. That can be done with aid of the Sobol’ indices, a variance-based statistical technique for global sensitivity analysis, which measures the individual importance of each parameter, as well as their joint-effect, on the model output (a.k.a. quantity of interest). These variance-based indexes may be computed using Monte Carlo simulation but, depending on the model, this task can be very costly. An alternative approach for this scenario is the use of surrogate models to speed-up the calculations. Using simple biological models, from different areas, we develop a tutorial that illustrates how practitioners can use Sobol’ indices to quantify, in a probabilistic manner, the relevance of the parameters of their models. This tutorial describes a very robust framework to compute Sobol’ indices employing a polynomial chaos surrogate model constructed with the UQLab package.
A guide to sensitivity analysis of quantitative models of gene expression dynamics
Methods, 2013
We provide a guide to performing a sensitivity analysis (SA) of quantitative models of gene expression dynamics appropriate to the levels of uncertainty in the model: spanning cases where parameters are relatively well-constrained to cases where they are poorly constrained. In the well-constrained case, we present methods to perform ''local'' SA (LSA), which considers small perturbations for a single set of model parameter values. In the poorly-constrained case, we present methods to perform ''global'' SA (GSA) as a means to evaluate the sensitivity of a model over large regions of parameter space. We apply these methods to quantitative models of increasing complexity. The models we consider are simple logistic growth, negative feedback in a mRNA-protein model, and two models of decision making within bacteriophage k. We discuss the best practices for how SA can be utilized in an iterative fashion to advance biological understanding.
A methodology for performing global uncertainty and sensitivity analysis in systems biology
Journal of Theoretical Biology, 2008
Extended Fourier amplitude sensitivity test (eFAST) Agent-based model (ABM) Sensitivity index Monte Carlo methods Aleatory uncertainty Epistemic uncertainty a b s t r a c t Accuracy of results from mathematical and computer models of biological systems is often complicated by the presence of uncertainties in experimental data that are used to estimate parameter values. Current mathematical modeling approaches typically use either single-parameter or local sensitivity analyses. However, these methods do not accurately assess uncertainty and sensitivity in the system as, by default, they hold all other parameters fixed at baseline values. Using techniques described within we demonstrate how a multi-dimensional parameter space can be studied globally so all uncertainties can be identified. Further, uncertainty and sensitivity analysis techniques can help to identify and ultimately control uncertainties. In this work we develop methods for applying existing analytical tools to perform analyses on a variety of mathematical and computer models. We compare two specific types of global sensitivity analysis indexes that have proven to be among the most robust and efficient. Through familiar and new examples of mathematical and computer models, we provide a complete methodology for performing these analyses, in both deterministic and stochastic settings, and propose novel techniques to handle problems encountered during these types of analyses.
Sensitivity analysis and robust experimental design of a signal transduction pathway system
International Journal of Chemical Kinetics, 2008
Experimental design for cellular networks based on sensitivity analysis is studied in this work. Both optimal and robust experimental design strategies are developed for the IκB-NF-κB signal transduction model. Based on local sensitivity analysis, the initial IKK intensity is calculated using an optimal experimental design process, and several scalarization measures of the Fisher information matrix are compared. Global sensitivity analysis and robust experimental design techniques are then developed to consider parametric uncertainties in the model. The modified Morris method is employed in global sensitivity analysis, and a semidefinite programming method is exploited to implement the robust experimental design for the problem of measurement set selection. The parametric impacts on the oscillatory behavior of NF-κB in the nucleus are also discussed.
A new strategy for assessing sensitivities in biochemical models
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2008
An integral part of any systems biology approach is the modelling and simulation of the respective system under investigation. However, the values of many parameters of the system have often not been determined or are not identifiable due to technical experimental difficulties or other constraints. Sensitivity analysis is often employed to quantify the importance of each of the model's parameters in the behaviour of the system. This approach can also be useful in identifying those parts of the system that are most sensitive with the potential of becoming drug targets. A problem of the commonly used methods of sensitivity analysis is that they constitute local methods meaning that they depend directly on the exact parameter space, which in turn is not known exactly. One way to circumvent this problem is to carry out sensitivity analysis over a wide range of values for all parameters, but this is handicapped by expensive computations when the systems are high dimensional. Another approach is to employ global sensitivity analysis, which in this context is mostly based on random sampling methods. In this paper we present an efficient approach that involves using numerical optimizing methods that search a wide region of parameter space for a given model to determine the maximum and minimum values of its metabolic control coefficients. A relevant example for drug development is presented to demonstrate the strategy using the software COPASI.
SIMULATION, 2003
Mathematical modeling and dynamic simulation of signal transduction pathways is a central theme in systems biology and is increasingly attracting attention in the postgenomic era. The estimation of model parameters from experimental data remains a bottleneck for a major breakthrough in this area. This study’s aim is to introduce a new strategy for experimental design based on parameter sensitivity analysis. The approach identifies key parameters/variables in a signal transduction pathway model and can thereby provide experimental biologists with guidance on which proteins to consider for measurement. The article focuses on applying this approach to the TNFα-mediated NF-κB pathway, which plays an important role in immunity and inflammation and in the control of cell proliferation, differentiation, and apoptosis. A mathematical model of this pathway is proposed, and the sensitivity analysis of model parameters is illustrated for this model by employing the Monte Carlo method over a br...
Sensitivity analysis of signaling pathway models based on discrete-time measurements
Archives of Control Sciences, 2017
The paper is focused on sensitivity analysis of large-scale models of biological systems that describe dynamics of the so called signaling pathways. These systems are continuous in time but their models are based on discrete-time measurements. Therefore, if sensitivity analysis is used as a tool supporting model development and evaluation of its quality, it should take this fact into account. Such models are usually very complex and include many parameters difficult to estimate in an experimental way. Changes of many of those parameters have little effect on model dynamics, and therefore they are called sloppy. In contrast, other parameters, when changed, lead to substantial changes in model responses and these are called stiff parameters. While this is a well-known fact, and there are methods to discern sloppy parameters from the stiff ones, they have not been utilized, so far, to create parameter rankings and quantify the influence of single parameter changes on system time responses. These single parameter changes are particularly important in analysis of signalling pathways, because they may pinpoint parameters, associated with the processes to be targeted at the molecular level in laboratory experiments. In the paper we present a new, original method of creating parameter rankings, based on an Hessian of a cost function which describes the fit of the model to a discrete experimental data. Its application is explained with simple dynamical systems, representing two typical dynamics exhibited by the signaling pathways.