Abstract
Kinetic models of metabolism can be constructed to predict cellular regulation and devise metabolic engineering strategies, and various promising computational workflows have been developed in recent years for this. Due to the uncertainty in the kinetic parameter values required to build kinetic models, these workflows rely on ensemble modeling (EM) principles for sampling and building populations of models describing observed physiologies. Sensitivity coefficients from metabolic control analysis (MCA) of kinetic models can provide important insight about cellular control around a given physiological steady state. However, despite considering populations of kinetic models and their model outputs, current approaches do not provide adequate tools for statistical inference. To derive conclusions from model outputs, such as MCA sensitivity coefficients, it is necessary to rank/compare populations of variables with each other. Currently existing workflows consider confidence intervals (CIs) that are derived independently for each comparable variable. Hence, it is important to derive simultaneous CIs for the variables that we wish to rank/compare. Herein, we used an existing large-scale kinetic model of Escherichia Coli metabolism to present how univariate CIs can lead to incorrect conclusions, and we present a new workflow that applies three different multivariate statistical approaches. We use the Bonferroni and the exact normal methods to build symmetric CIs using the normality assumptions. We then suggest how bootstrapping can compute asymmetric CIs whilst relaxing this normality assumption. We conclude that the Bonferroni and the exact normal methods can provide simple and efficient ways for constructing reliable CIs, with the exact normal method favored over the Bonferroni when the compared variables present dependencies. Bootstrapping, despite its significantly higher computational cost, is recommended when comparing non-normal distributions of variables. Additionally, we show how the Bonferroni method can readily be used to estimate required sample numbers to attain a certain CI size.
Highlights
Kinetic models are becoming essential computational tools for studying the metabolism of organisms and for understanding the dynamics of their cellular biochemical interactions [1]
We studied four different operational configurations— referred to as flux directionality profiles (FDPs) in their publication [12]—that were able to characterize the physiology of aerobically grown E. coli
As our study focused on comparing statistical methods for deriving confidence intervals (CIs) around the outputs of populations of kinetic models, we do not discuss the differences in these four operational configurations
Summary
Kinetic models are becoming essential computational tools for studying the metabolism of organisms and for understanding the dynamics of their cellular biochemical interactions [1]. The construction of kinetic models remains a challenging endeavor as there are large uncertainties in the rate expressions describing all the reactions making up these cellular interactions [2]. This is often because reaction mechanisms are rarely fully characterized for an organism, making it difficult to select appropriate rate expressions for reactions, and information on the parameter values required by these expressions is very scarce. Several ensemble modeling (EM) approaches that assign kinetic mechanisms to reactions, incorporate experimental data, and sample unknown kinetic parameter values have emerged for generating populations of kinetic models [3,4,5,6]. Despite originating from statistical mechanics, EM has only been employed in systems biology for two decades [8], and its use of statistical methods for managing uncertainty remains, to our knowledge, untapped
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