8 Evaluating the Robustness to Noise of NETISCE

This section contains the results of evaluating NETISCE’s robustness to noisy initial states data. We evaluated this metric in the von Dassow ODE model of Drosophila Segment Polarity Genes and the Zhou model of pancreatic cell fate differentiation.

The original study of controlling Drosophila development using the FVS Control theory was performed by Zanudo et al. inStructure-based control of complex networks with nonlinear dynamics using the von Dassow Segment Polarity genes ODE model, originally published in The segment polarity network is a robust developmental module.. The ODE model was obtained form xyz, and the initial states were extracted from the supplementary material of Zanudo et al.. The study of pancreatic cell fate differentiation was performed by Zhou et al. in “Predicting Pancreas Cell Fate Decisions and Reprogramming with a Hierarchical Multi-Attractor Model”. The model and parameters were extracted from Zhou et al.

The input data, COPASI files, nextflow pipeline, and results of this simulation can be found in the noise_studies folder in the NETISCE github repository.

Our approach to these noise studies uses COPASI to simulate two differential equation models of cell reprogramming and add different noise levels into some initial states. We use these generated initial states to simulate 1,000 triplicates of the desired and undesired phenotype normalized gene expression data per noise level varying from 0% to 50%

8.1 COPASI simualtions of mathematical models

In COPASI, we simulated the Differential Equation (DE) DE models using the Time Course function for the undesired and desired phenotypes. We additionally simulate the time course for the undesired initial condition when a perturbation on FVS nodes is applied to ensure the system still arrives at the desired attractor. We injected seven levels of noise (1%, 5%, 10%, 20%, 30%, 40%, 50%) in the undesired and desired initial conditions using the Random Distribution item in the COPASI’s Parameter Scan function. For each node with a nonzero initial concentration, the noisy initial condition was generated using a normal distribution, where the mean was the initial state of the node, and the standard deviation was .1, .5, .10, .20, .30, .40, or .50, to simulate 1%, 5%, 10%, 20%, 30%, 40%, or 50% noise, respectively. We generated 1,000 initial states for each noise level for the desired initial and undesired initial states.

8.1.1 von Dassow’s Drosophila Segment Polarity Gene model

In COPASI, von Dassow’s Drosophila Segment Polarity Gene model simulations were computed using the deterministic LSODA Solver for 500 seconds when a steady-state was reached. The COPASI file containing the model, parameters, and Time Course functions for both the wild type and unpatterned initial states can be found in https://github.com/VeraLiconaResearchGroup/Netisce/tree/main/noise_studies/drosophila/copasi.

8.1.2 Zhou Cell Fate Specification model

The SDE model was extracted from Zhou et al. and simulated using the SDE solver. To implement the time-delay perturbations of MafA, Pdx1, Ngn3, Pax4 overexpression, and Ptf1a knockout in exocrine cells, we used the Event function to increase the production or degradation rates as performed in Zhou et al. he COPASI file containing the model, parameters, and Time Course functions can be found in https://github.com/VeraLiconaResearchGroup/Netisce/tree/main/noise_studies/pancreas/copasi.

8.2 Noisy initial states files

The above COPASI files automatically export the initial states of the network nodes with noise to a csv file (found in https://github.com/VeraLiconaResearchGroup/Netisce/tree/main/noise_studies/drosophila/noise-initial-states or https://github.com/VeraLiconaResearchGroup/Netisce/blob/main/noise_studies/pancreas/noise-initial-states/expressions-10percent.csv). The generate_triplicates.py script can split the generated initial states into separate files, each containing 3 undesired and 3 desired initial states. You can find examples in the pancreas and (drosophila)[https://github.com/VeraLiconaResearchGroup/Netisce/tree/main/noise_studies/drosophila/NETISCE/40-percentnoise/input_data/noise] subfolders.

8.3 Running the NETISCE simulations

Due to space constraints on github, we have provided the entire folder for one level of noise for the Drosophila and Pancreas examples.

8.3.1 Drosophila noise studies at 40% noise in initial states

The relevant input files and nextflorw pipeline can be found in https://github.com/VeraLiconaResearchGroup/Netisce/tree/main/noise_studies/drosophila/NETISCE/40-percentnoise. We provide the shell script which will loop through all initial states files to run NETISCE for each set of wild type and unpatterened initial states.

If you are interested in running this analysis with a different noise level, you can use the generate_triplicates.py to create triplicates of initial states from the appropriate noisy initial states. Then, in the run.sh shell script, set the --expressions flag to the directory that contains your noisy initial states.

8.3.2 Pancreas cell fate specification at 10% noise in initial states

The relevant input files and nextflorw pipeline can be found in https://github.com/VeraLiconaResearchGroup/Netisce/tree/main/noise_studies/pancreas/NETISCE/10percent/input_data. We provide the shell script which will loop through all initial states files to run NETISCE for each set of exocrine and beta cell initial states.