Inferring Gene Expression Dynamics from Reporter Protein Levels
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.
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