Effective Single-Step Posttranscriptional Dynamics Allowing for a Direct Maximum Likelihood Estimation of Transcriptional Activity and the Quantification of Sources of Gene Expression Variability with an Illustration for the Hypoxia and TNFα Regulated Inflammatory Pathway

Data analysis methods for estimating promoter activity from gene reporter data frequently involve the reconstruction of the dynamics of unobserved species and numerical search algorithms for determining optimal model parameters. In contrast, we argue that posttranscriptional dynamics effectively behave like a singlestep stochastic process when gene expression variability is relatively low and, half-lives of the unobserved species are relatively small compared to characteristic observation time scales. In this case, by means of maximum likelihood estimators, for which analytical expressions exist, transcriptional activity of gene promoters can be estimated directly from observed gene reporter data without the need for numerical search algorithms and the reconstruction of unobserved variables. In addition, the model-based data analysis approach yields a single variable that measures the effective strength of the sources that give rise to gene expression variability. The approach is applied to conduct a model-based analysis of the inflammatory pathway under hypoxia condition and stimulation with tumor necrosis factor alpha in HEK293 cells. 1. Introduction A problem in the field of computational biology is how to model and determine quantitatively promoter activity from observed reporter data. Deterministic approaches suggest that when the activity of a promoter is constant over a period of time, then reporter data should be linearly increasing (see Section 2.1). The steepness of the increase is proportional to the activity of the promoter. Linear regression analysis may be applied to determine the rate of increase [1]. This deterministic perspective is limited in its scope, which becomes clear when considering stochastic approaches as alternatives. For example, deterministic approaches regard gene expression fluctuations as errors. In contrast, according to stochastic approaches gene expression fluctuations indicate that the transcriptional machinery functions properly because the machinery is based on biochemical reactions that are stochastic in the very nature. Stochastic accounts, for example, based on chemical Langevin equations, provide a mathematical framework to address both the deterministic and stochastic components of promoter activity [2]. In the literature, modeling of gene transcription often starts at the promoter level with the transcription event [3–6]. Accordingly, mRNA is produced at a certain rate . Subsequently, mRNA is translated into proteins at a rate . The proteins are finally exported out of the cell with an export rate .