Code

Executing The Code

This code was written to be executed in a particular file structure, diagrammed as follows:

With a GitHub account you can clone a repository with all data and code in place in the correct directory structure. Please follow the installation instructions on the GitHub repository.

Computational Environment

All analysis and data processing was performed with the following software configurations.

# Python Version
CPython 3.6.7
IPython 7.1.1

# Package Versions
bokeh==1.0.4
fcsparser==0.2.0
numpy==1.14.2
matplotlib==3.0.1
scipy==1.1.0
seaborn==0.9.0
pandas==0.23.4
tqdm==4.28.1
pystan==2.18.0.0
python_frontmatter==0.4.5
PyYAML==5.1

# System Information
compiler   : GCC 4.2.1 Compatible Clng 4.0.1 (tagss/RELEASE_401/final)
system     : Darwin
release    : 18.2.0
machine    : x86_64
processor  : i386
CPU cores  : 4
interpreter: 64bit

The mut Module

This work required a moderate amount of home-grown code. To ensure reproducibility, we have written it as a Python module that can be installed from the master branch of the GitHub repository. Please see the installation instructions for details. This module is required to execute all of the following scripts.

Figure Generation

All Figures in this work (save for Fig. 2) were generated programmatically.

Interactive Figures

The two interactive figures associated with this work (the model explorer and the data collapse figure) were generated using the Bokeh plotting framework using a combination of Python code and Javascript. The Python code (which includes the javascript) can be downloaded below.

• Model Explorer
  
• Interactive Data Collapse
  • Necessary Data Sets:
    1. Summarized fold-change data
    2. Data from Razo-Mejia et al. 2018
    3. Data from Garcia & Phillips 2011 and Brewster et al. 2014
       

Inferential Models

All parameter inference was performed using the Stan probabilistic programming language. The following Stan model files perform the described analysis.

• Inference of DNA Binding Energy
  Used to estimate the DNA binding energy and homoscedastic error for a single induction profile.
  

• Global Inference of DNA Binding Energy
  Used to estimate the DNA binding energy for a single mutant from multiple induction profiles

• Inference of Inducer Dissociation Constants
  Used to estimate the inducer dissociation constants Ka and Ki for a single induction profile, assuming the allosteric energy difference is unperturbed from the wild-type value.

• Inference of Allosteric Parameters
  Used to infer the inducer dissociation constants Ka and Ki along with the allosteric energy difference for a single induction profile.

• Global Inference of Allosteric Parameters
  Used to estimate the allosteric parameters for a single mutant from multiple induction profiles.

• Inference of Free Energy from Fold-Change Measurements
  Used to infer the mean fold-change, standard deviation, and free energy for a collection of fold-change measurements.

The following scripts were used to execute the inference models.

• Execution of parameter inference models
  Loads the data, calls the inferential models, and save statistics and samples to tidy .csv files.
  • Necessary Data Sets:
    1. Compiled fold-change measurements
       
• Execution of global parameter inference models
  Loads the data, estimates parameters for each mutant using all induction profiles, and saves samples and statistics.
  • Necessary Data Sets:
    1. Compiled fold-change measurements

Supplementary Materials

The following code was used to generate the supplementary figures as well as any data generated via simulation.

• Fig. S2: Prior Predictive Checks for DNA Binding Energy and Homoscedastic Error
  Used to generate Figure S2 illustrating the prior distributions for the DNA binding energy and homoscedastic error as well as visualize the percentiles of the prior predictive checks.
  • Necessary Data Sets and Auxiliary Scripts:
    1. DNA binding energy prior predictive check data
    2. DNA binding energy prior predictive check generation
• Fig. S3: Prior Distribution Recovery for DNA Binding Energy and Homoscedastic Error
  Used to generate Figure S3 which shows that the prior distributions of the parameters can be recovered through repeated inferential runs on simulated data.
  • Necessary Data Sets and Auxiliary Scripts:
    1. DNA binding energy prior predictive check data
    2. DNA binding energy simulation based calibration results
    3. DNA binding energy simulation based calibration generation
• Fig. S3 - Fig. S5: Simulation Based Calibration of DNA Binding Energy Inference
  Used to generate three figures (Fig. S3 - S5) which use simulation based calibration to assess the sensitivity and computational tractability of the statistical model for estimating the DNA binding energy.
  • Necessary Data Sets and Auxiliary Scripts
    1. DNA binding energy simulation based calibration samples
    2. DNA binding energy simulation based calibration generation
    3. Stan model for inference of DNA binding energy
• Fig. S6: DNA Binding Energy Posterior Predictive Checks
  Used to generate Fig. S6 which shows the MCMC sampling output and corresponding posterior predictive checks for DNA binding mutant Q21M.
  • Necessary Data Sets
    1. Compiled fold-change measurements
    2. DNA binding energy samples
• Fig. S7: Prior Predictive Checks for Free Energy Inference
  Used to generate Fig. S7 which plots the percentiles of the prior predictive checks for estimation of the free energy from fold-change measurements.
  • Necessary Data Sets and Auxiliary Scripts
    1. Empirical free energy prior predictive checks
    2. Empirical free energy prior predictive check generation
• Fig. S8: Simulation Based Calibration for Free Energy Inference
  Used to generate Fig. S8 which shows z-scores, shrinkage, and rank distribution for model that infers the free energy from a collection of fold-change measurements.
  • Necessary Data Sets and Auxiliary Scripts
    1. Empirical free energy simulation based calibration samples
    2. Empirical free energy simulation based calibration generation
    3. Stan model for inference of free energy
• Fig. S9: Empirical Free Energy Posterior Predictive Checks
  Used to generate Fig. S9 which shows the MCMC samples and the posterior predictive checks for estimating the mean fold-change for Y20I-Q294K with operator O2 at 50 µM IPTG.
  • Necessary Data Sets and Auxiliary Scripts
    1. Compiled fold-change measurements
    2. Stan model for inference of empirical free energy from fold-change measurements
• Fig. S10: Sensitivity Limits for Inferring Empirical Free Energy
  Used to generate Fig S9 which shows the sensitivity limits for inferring the free energy from simulated and real fold-change measurements.
  • Necessary Data Sets and Auxiliary Scripts
    1. Simulated fold-change data
    2. Generation of simulated fold-change data
    3. Inference statistics for simulated fold-change data
    4. Inference statistics of free energy from wild-type data
    5. Stan model for inference of free energy from fold-change measurements
    6. Fold-change measurements from Razo-Mejia et al. 2018
• Fig. S11: Comparison of DNA Binding Energy Inference to Other Repressor Copy Numbers
  Used to generate Fig. S11 which shows the influence of the choice of fit strain on predictions of induction profiles for other DNA binding mutants.
  • Necessary Data Sets
    1. Summarized fold-change measurements
    2. DNA binding energy inference statistics
• Fig. S12: Effect of DNA Binding Energy Fit Strain on ∆F Predictions
  Used to generate Fig. S12 which shows how the choice of fitting strain influences the predicted change in free energy for DNA binding mutants.
  • Necessary Data Sets
    1. Empirical free energy inference statistics
    2. DNA binding energy inference statistics
• Fig. S13: Prior Predictive checks for Inference of Allosteric Parameters
  Used to plot percentiles of prior predictive checks for two hypotheses for inducer binding domain mutants.
  • Necessary Data Sets and Auxiliary Scripts:
    1. Prior predictive samples for inducer binding mutant models
    2. Generation of prior predictive samples for inducer binding mutant models
• Fig. S14: Simulation Based Calibration of Inducer Binding Mutant Statistical Models
  Used to plot z-scores, shrinkage, and rank distributions for inducer binding domain models.
  • Necessary Data Sets and Auxiliary Scripts:
    1. Simulation based calibration samples
    2. Generation of simulation based calibration samples
    3. Stan model for inference of inducer binding constants
    4. Stan model for inference of all allosteric parameters
• Fig. S15 - Fig. S16: Posterior Predictive Checks For Inducer Binding Domain Models
  Plots the MCMC samples and posterior predictive checks for both inducer binding domain statistical models for the mutant Q294K paired with the O2 operator.
  • Necessary Data Sets and Auxiliary Scripts:
    1. Generation of posterior predictive samples for inducer binding domain models
• Fig. S17 - Fig. S18: Comparison of Fit Strain Choice on Prediction of Inducer Binding Domain Mutants
  Compares the effect of the choice of fit strain under both inducer binding domain statistical models on predicting induction profiles.
  • Necessary Data Sets:
    1. Summarized fold-change measurements
    2. MCMC samples from inference of inducer binding constants
    3. MCMC samples from inference of all allosteric parameters
• Fig. S19: Influence of Choice of Fit Strain on ∆F Predictions for Inducer Binding Domain Mutants
  Shows the predicted change in free energy for all choices of fit strain for inference of allosteric parameters.
  • Necessary Data Sets:
    1. Empirical free energy inference statistics
    2. MCMC samples from inference of all allosteric parameters
• Fig. S20: Global DNA Binding Energy Inference Induction Profiles and ∆F
  Shows the fits of the induction profiles for each DNA binding mutant after global estimation of the DNA binding energy. It also shows the predicted ∆F along with the inferred free energies.
  • Necessary Data Sets and Auxiliary Scripts:
    1. Summarized fold-change measurements
    2. Empirical free energy inference statistics
    3. Global DNA binding energy inference statistics
    4. Global inference of DNA binding energy
    5. Stan model for global inference of DNA binding energy
• Fig. S21: Global Allosteric Parameter Inference Induction Profiles and ∆F
  Shows the fits of the induction profiles for each inducer binding mutant after global estimation of the allosteric parameters. It also shows the predicted ∆F along with the inferred free energies.
  • Necessary Data Sets and Auxiliary Scripts:
    1. Summarized fold-change measurements
    2. Empirical free energy inference statistics
    3. Global allosteric parameter inference samples
    4. [Global inference of allosteric parameters ](/mwc_mutants/code/Chure2019_pooled_parameter_inference.py
    5. Stan model for global inference of allosteric parameters