Inferring Gene Expression Dynamics from Reporter Protein Levels

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We have presented a pair of simple mathematical models that relate the dynamics of gene expression to the accumulation of reporter proteins.  The models provide a straightforward way of reconstructing the approximate dynamics of gene expression from time series data for the reporter protein concentration and cell population.  While the models rely on several assumptions, they are ones commonly used in interpreting reporter protein data.  Moreover, our simulations indicate that the method is robust to moderate nonlinearities in the protein and population measurements, to uncertainty about the protein decay kinetics, and to realistic levels of experimental noise.

The models are simple and general because they are intended only to infer an unobserved process (gene expression) from an observed one (reporter protein accumulation).  They make no assumptions about the mechanisms regulating gene expression, allowing the dynamics to take on any pattern.  The result is a simple algorithm, implemented in a spreadsheet, that can be used to infer the dynamics of promoter activity or protein synthesis from standard time series data.  Nevertheless, the approach is sufficiently mechanistic to provide a more detailed analysis of gene expression than approaches based on linear regression [22, 23], and provides a much clearer picture of the dynamics than visual inspection of reporter protein data alone. 

In the scenarios that we simulated, knowing the protein half-life within a factor of two was usually sufficient for recovering the general pattern and approximate timing of gene expression.  However, subtle details may only be resolved with more precise knowledge of the decay rate, including how it changes over time.  While the general patterns are robust to variation in the decay rate or proteolytic saturation, uncertainty about the lifespan of reporter proteins in vivo may be an important limitation to precise inference about the dynamics of gene expression from reporter fusions.  To date, there does not appear to have been a major effort to determine these kinetics in a wide range of cell types and experimental conditions.

In principle, the reconstructed reporter protein synthesis produced by our models could be used as input to a model for predicting the dynamics of the functional protein or RNA of interest.  For example, suppose our model were applied to data from a transcriptional fusion.  The output would consist of the time course of the (relative) production of the target gene’s mRNA.  This could then be incorporated into a more complex model for simulating the target protein’s translation, folding, dimerization, decay, etc.  The result would be a prediction of the amount of functional target protein over time.  We have not pursued this in the current study because of the variety of possible scenarios and the number of parameter values that would be required.  However, it may be a promising avenue for future research, and it indicates the extent to which mathematical models can be used to extend the type of predictions made from gene fusion data.

More direct methods of measuring gene expression have been developed, including microarrays and quantitative reverse transcription PCR.  However, reporter gene fusions are likely to remain a popular method for inferring expression dynamics because of their relatively low cost and use in other applications [1, 24].  Model-based inference of gene expression dynamics from reporter fusions has the potential to increase the information provided by this important technology.