expressivity_paper

Publication

Principles of Computation by Competitive Protein Dimerization Networks

Authors

Jacob Parres

Gold, Matthew Levine, Ben Emert, Andrew Stuart, Michael B. Elowitz

Primary contact for code & data

: Jacob Parres

Gold,

jacobparresgold@gmail.com

This dataset is intended to

demonstrate how the data were generated

and how to re

analyze the

data if necessary.

All analysis was originally performed on an

Amazon Web Services (AWS)

c5.4xlarge instance and has been

further annotated for readability.

We tried to carefully implement

as few changes as possible; however, it is always possible that bugs may have been introduced,

such as in file

handing commands.

See the Methods section for details on the analysis.

Utilities

The following Python script provides functions that are used by other notebooks in the dataset:

•

dimer_network_u

tilities.

py

Resources

The following resources are available to simulate

the input

output functions of arbitrary networks:

simulate_individual_networks.ipynb

This notebook demonstrates simulations of

individual

one

and two

input

networks

with

schematics

the

network

architecture.

Interactive Google Colab

Interactive Google Colab notebook for

simulating one

and two

input networks.

Notebooks to Replot Figures

The following notebooks were used to plot the figures used in the paper.

They were created to

make re

plotting of the data as simple as possible. The data for these figures are drawn directly

from the

archived data folder.

These notebooks also include many plots not included in the main

or supplementary figures

;

such

plots have not been

aesthetically

cleaned up.

remake_GraphicalAbstract.ipynb

Plots for graphical abstract

remake_Fig1.ipynb

Plots for Figure 1

remake_Fig2.ipynb

Plots for Figure 2

remake_Fig3.ipynb

Plots for Figure 3

remake_Fig4.ipynb

Plots for Figure 4

and Figure S3

remake_Fig5.ipynb

Plots for Figure 5

and Figure S4

remake_Fig6.ipynb

Plots for Figure 6

and Figure S6

remake_FigS5.ipynb

Plots for Figure S5

remake_FigS7.ipynb

Plots for Figure S7

Notebooks to Demonstrate Analysis

Methods

The following notebooks were created from code that was used to perform

the majority of the

analysis for the paper

. Many of these notebooks use the ray package for parallelization, which is

not available for Windows. Thus, if you would like to re

run these notebooks, make sure to disable

the commands involving ray. It

may

also be necessary to change code relevant to

loading and

saving files.

analyze_1D_screen.ipynb

This notebook analyzes the responses

observed in the parameter screen of one

input network responses.

analyze_2D_screen.ipynb

This notebook analyzes the responses

observed in the parameter screen of

two

input network responses.

analyze_connectivity_trends.ipynb

Using the large screen of many networks,

this notebook assess

how various

network properties vary with network

connectivity.

analyze_equilibration_kinetics.ipynb

This

notebook

use

deterministic

simulations, via numerical integration of

ordinary differential equations (ODEs), to

estimate the time required for network re

equilibration after a perturbation of the

input monomer.

analyze_expression_noise_robustness.ipynb

This notebook simulate

various networks

(one for each unique function) under

random perturbations of monomer

expression levels (total abundances).

analyze_intrinsic_noise.ipynb

This

notebook

use

stochastic

stimulations, via Gillespie simulation, of

networks at steady state to estimate

stochastic

fluctuations

dimer

concentrations at equilibrium.

boolean_complexity

.ipynb

This notebook demonstrates how to

calculate the Boolean

complexity of the

Boolean functions used in this work.

generate_param_screen.ipynb

This notebook performs a parameter

screen of networks, considering 1 or 2

monomers as the input

optimizer_dualannealing.ipynb

This notebook demonstrates how a dual

annealing algorithm was used to optimize

dimerization networks to perform desired

functions.

separation_of_timescales

.ipynb

This

notebook

use

deterministic

simulations, via numerical integration of

ordinary differential equations (ODEs),

determine whether networks are at

equilibrium when an input monomer

oscillates over time.

v

ersatility_expression_changes

.ipynb

This notebook analyzes, from the results

of the optimization trials investigating

one

input versatility, the extent to which

accessory protein expression levels

changed to achieve versatility.

Data

: General

The full dataset is quite large

(~332 Gb)

. The data is

available as individual files

in an

AWS S3

bucket hosted by CaltechDATA.

We have also created a more user

friendly subset of the data

in a zip file called

parresgold_2023_dimer_networks_plotting_data.zip

. This file contains only the data

necessary to re

plot the figures

and is significantly smaller in size.

Data from Parameter Screens

param_screen_1D

Raw data from

one

input parameter

screen.

param_screen_1D_limited_param_range

Raw data from one

input parameter

screen with a more limited parameter

range.

param_screen_2D

Raw data from two

input parameter

screen.

param_screen_analysis_1D

Results of downstream analysis of the

one

input parameter screens.

param_screen_analysis_1D_limited_param_range

Results of downstream analysis of the

one

input parameter screens with a

more limited parameter range.

param_screen_analysis_2D

Results of downstream analysis of the

two

input parameter screens.

Data from

Annealing Optimizations for Multi

Input Logic Gates

optimization_trials_dualannealing_3D_4D

Optimization results, based on the dual

annealing optimizer,

for three

and four

input optimization trials.

Data on Transcription Factor Co

Expression

transcription_factor_coexpression

expression data for nuclear receptor (NR)

and bZIP transcription factors in mouse and

humans.

Code

and Data

for Versatility Analysis

The code for the versatility analysis, in which genetic algorithm

optimization was used to optimize

accessory expression levels

of networks to perform desired functions, was primarily written by

Matthew Levine.

This code was not condensed like the above notebooks were; instead, they have

been

directly

included

is.

The

code

can

found

randomK_versatility_optimization_trials

, and the results

can be found in the folders listed

below

This code, rather than being run in a notebook, was run as a series of batch scripts.

understand that this code is not as easily

parsed

as the rest; if you have questions, please reach out

to the authors.

optimization_trials_randomK_1D

Versatility results

for the general one

input functions.

•

targets.csv

This file has columns

"m","targetID","used","0","1",..."29"

where

"m" is the network size, "targetID" is the name

of the m

dependent index of the target

function, "used" is True if the target was used

in the experiment, and the other columns are

the 30 val

ues of the target.

•

summary.csv

This file has columns "m",

"targetID", "KID", "dimerID", "Linf", "MSE",

"goodenough", where "m" is the network size,

"targetID" is the name of the m

dependent

index of the target function, "KID" is the name

of the m

dependent index of the network

parameter

K, "dimerID" is the name of the

index of the dimer, "Linf" is the Linf error of

the target fit, "MSE" is the MSE error of the

target fit, and "goodenough" is True if Linf <=

1.0.

•

a_opt.pkl

This file is a dictionary with keys

"m" and a value of a 4D numpy array of shape

(N K's x N Dimers x N targets x N accessories).

The first index is the index of the KID, the

second index is the index of the dimer, the third

index is the index of the target

, and the fourth

index is the index of the accessory. The value

is the optimal accessory parameter a as

determined by the optimization experiment.

•

K_random.pkl

This file is a dictionary with

keys "m" and a value of a 2D numpy array of

shape (N K's x N Dimers). The first index is the

index of the KID, and the second index is the

index of the dimer. The value is the random K

value used in the experiment.

•

name_dict.pkl

This file is a dictionary with

keys "K_names" and "a_names" and values of

dictionaries with keys "m" and values of lists

of names. The "K_names" dictionary has keys

"m" and values of lists of names of the KID's.

The "a_names" dictionary has keys "m" and

lues of lists of names of the dimerID's.

optimization_trials_

randomK_

1D_testing_connectivity

Versatility results for an experiment in which we

tested networks of 8 monomers while explicitly

varying network connectivity.

The filenames follow

the same conventions as above.

optimization_trials_randomK_

2

D

Versatility results for a select set of 2

input functions.

Note that data is included for networks of 8, 16, and 20

monomers, although the analys

s shown in Figure 6

and Figure S6 come from the 20

monomer dataset.

The 20

monomer dataset was optimized much more

deeply than the other two datasets were, so we caution

against directly comparing the results.

Optimization

results are provided as a

.pkl

file for a dictionary. The

first level of keys specify:

•

Network size

m

•

Target name

targetID

•

Index of the random K

KID

E.g., a first

level key could be

’m

-

20_targetID

-

XNOR_KID

-

9_dimerID

-

Non

e’

The second level of keys specify

properties associated

with the

optimized solution:

['MSE','MSE

-

per

-

target','Linf','a', 

'theta','logK','K','f_fit','f_target']

•

a

gives the optimized accessory concentrations

•

theta

is a binary vector with many 0’s and

exactly one 1 (the location of this 1 indicates

the optimally selected output dimer ID).

•

logK

and

K

represent the binding affinities for

this

KID

•

f_fit

is the

optimized

2D function (in log

space) un

rolled into a vector. To get the 2D

grid, you can do .reshape(12,12).

•

f_target

is the

target

2D function (in log

space) un

rolled into a vector. To get the 2D

grid, you can do .reshape(12,12)

There is also a summary

.csv

file that provides a

bunch of metrics comparing how well

f_fit

matches

f_target

.