Accuracy of parameter estimation for auto-regulatory transcriptional feedback loops from noisy data

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.