assesses the stability of the estimated support values. To translate bootstrap support values to false discovery rates we run the same pipeline with shuffled data as input. This provides a general method to control the false discovery rate of GRN inference that can be applied to any setting of inference parameters, noise level, or data properties. We evaluated nested bootstrapping on a simulated dataset spanning a range of such properties, using the LASSO, Least Squares, and RNI inference methods. An improved inference accuracy was observed in almost all situations. Nested bootstrapping was incorporated into the GeneSPIDER package, which was also used for generating the simulated networks and data, as well as running and analyzing the inferences.
Fig. 2. Bootstrap support by overlap and frequency. Illustration for user- defined FDR cutoff (here 5%) for link
inclusion. The blue line depicts link fre- quency as a function of bootstrap support when using measured data, and the red line when using shuffled data. The black vertical bar defines a boot- strap cutoff above which the measured data links are in the blue area and the shuffled data links are in the red area. In this illustration we set the FDR level for inferred links by finding the cutoff that makes the red area 5% of the total area under the measured data. The overlap is the intersection of links in the bootstrap runs divided by their union. This indicates what level of overlap is expected by chance, and what level is observed in the measured data (Color version of this figure is available at Bioinformatics online.)
Fig. 1. FDR estimation via NestBoot algorithm for a given sparsity. Data is sampled at each bootstrap iteration and a bootstrap network is inferred. After Q iterations, bootstrap support for each link is saved as the frequency at which it was inferred, keeping direction and sign of the link as separate events. This process is repeated for R runs, which are later used to evaluate stability. The distribution of bootstrap support for all runs is compared with the distribution for shuffled expression data, and this is used to locate the bootstrap support cutoff at the desired FDR level. Links are then extracted which are present in each run above this cutoff
Fig. 3: GRNaccuracies under native and NestBoot-enhanced inference on 10-gene synthetic data. The distribution of scores across all datasets is presented in grey where native inference configuration is used and in blue where NestBoot-enhanced inference is enabled for methods LASSO, LSCO and RNICO.
The accuracy was measured as median MCC across a range of sparsities for each of the 200 datasets of 10 genes.
Fig. 4: GRNaccuracies under native and NestBoot-enhanced inference on 45-gene synthetic data. The distribution of scores across all datasets is presented in grey where native inference configuration is used and in blue where NestBoot-enhanced inference is enabled for methods LASSO, LSCO, and RNICO.
The accuracy was measured as median MCC across a range of sparsities for each of the 200 datasets of 45 genes.
Fig. 5: Experimental NestBoot performance at 5% FDR cutoff Comparison of native methods to those enhanced with NestBoot on three biological datasets. The measured SNR levels of the three datasets are shown below.
Fig. 6: Comparison of inference methods utilizing bootstrapping on 10-gene networks. Methods enhanced with NestBoot for LASSO, LSCO and RNICO, and native bootstrap usages for Genie3 are compared.
Modelling of the GAL1 Genetic Circuit in Yeast Using Three Equations.
Authors: Chi-Ching Hsu, Yu-Heng Wu, Filippo Menolascina, and Torbjörn E M Nordling.
In 10th IFAC Symposium on Advanced Control of Chemical Processes (ADCHEM2018), Shenyang, China, july 2018. International Federation of Automatic Control (IFAC)
Synthetic gene circuits can be used to modify and control existing biological processes and thus e.g. increase drug yields. Currently their use is hampered by the, largely, trial and error approach used to design them. Lack of reliable quantitative dynamical models of genetic circuits e.g. prevents the use of well established control design methods. We aim toward creation of a pipeline for automated closed-loop identification of dynamic models of synthetically engineered genetic circuits in microorganisms. As a step towards this aim, we here study modelling of the input-output behaviour of the yGIL337 strain of S. cerevisiae. In this strain expression of the fluorescent reporter can be turned on by growing the yeast in galactose and off by glucose. We perform parameter estimation on a system of three ordinary differential equations of Michaelis-Menten type based on in vivo data from a microfluidic experiment by Fiore et al. (2013) after redoing the data preprocessing. The parameter estimation is done using AMIGO2–a state of the art Matlab toolbox for iterative identification of dynamical models. We show that the goodness-of-fit of our model is comparable to the five models proposed by Fiore et al. and we hypothesise that the system is an adaptive feedback system.
Fig. 1. GAL1 promoter construct: GAL1 and GFP, the code of Gal1 and Gfp, are integrated downstream of the GAL1 promoter (Fiore et al., 2013)
.
Fig. 2. Data and predictions: The input (red x), output (green x), and smoothed standard deviation of the fluorescence of the cell population (green lines). The predicted output of all the six models in Scenario B
stays within one standard deviation of the output except at the final two time points. In practice all these models can explain the data.