Abstract
Bayesian and non-Bayesian moment-based inference methods are commonly used to estimate the parameters defining stochastic models of gene regulatory networks from noisy single cell or population snapshot data. However, a systematic investigation of the accuracy of the predictions of these methods remains missing. Here, we present the results of such a study using synthetic noisy data of a negative auto-regulatory transcriptional feedback loop, one of the most common building blocks of complex gene regulatory networks. We study the error in parameter estimation as a function of (i) number of cells in each sample; (ii) the number of time points; (iii) the highest-order moment of protein fluctuations used for inference; (iv) the moment-closure method used for likelihood approximation. We find that for sample sizes typical of flow cytometry experiments, parameter estimation by maximizing the likelihood is as accurate as using Bayesian methods but with a much reduced computational time. We also show that the choice of moment-closure method is the crucial factor determining the maximum achievable accuracy of moment-based inference methods. Common likelihood approximation methods based on the linear noise approximation or the zero cumulants closure perform poorly for feedback loops with large protein–DNA binding rates or large protein bursts; this is exacerbated for highly heterogeneous cell populations. By contrast, approximating the likelihood using the linear-mapping approximation or conditional derivative matching leads to highly accurate parameter estimates for a wide range of conditions.
Highlights
In recent years, it has been shown that a significant percentage of genes in bacteria and yeast are auto-regulated [1 –3], i.e. a transcription factor activates or represses the expression of its own gene
In electronic supplementary material figure S1, we reconstruct the time-dependent distribution of molecule numbers based on 3MA and conditional derivative matching (CDM) inferred kinetic parameters reported in table 1. We find that both methods lead to a distribution that is visually close to that generated using the true parameter values, with the accuracy being highest for the CDM-reconstructed distribution which is virtually indistinguishable from the true distribution
We have reported the results of an exhaustive study of the factors influencing the accuracy of momentbased MCMC and MLE methods for an auto-regulatory transcriptional feedback loop
Summary
It has been shown that a significant percentage of genes in bacteria and yeast are auto-regulated [1 –3], i.e. a transcription factor activates or represses the expression of its own gene. Given the widespread availability of experimental data on the number of mRNAs and proteins at the single cell level [8,9,10,11], a natural question is how can we use these data to infer the rate constants and other relevant parameters of negative auto-regulatory transcriptional feedback loops. Approximate Bayesian computing approaches perform exhaustive stochastic simulations using the stochastic simulation algorithm (SSA) [23] and accept parameter values if the differences between simulation and experimental data are sufficiently small [19,24,25] These methods are asymptotically exact, but they suffer from poor computational efficiency due to the very large number of required SSA runs. Our results show that for cases where large bursts in protein production are evident and/or where strong feedback is suspected, approximation of the likelihood using the LNA and 2MA leads to large errors in the parameter estimates; this can be avoided by the use of more sophisticated moment-closure techniques
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