Date last updated: 3/8/2022
This repo implements a kinetic proofreading model of protein degradation via the ubiquitin-proteasome system (UPS) motivated by the work of Bartlett et al. (2020)1. Given an initial state of species amounts, this repo can perform the following functions:
- solve a system of ODEs for the system state over time
- calculate target protein degradation, ternary complex formation, Dmax (percent maximum degradation)
- compute species totals over time
For mathematical details, see technical document here.
Dependencies can be found in environment.yml. To create an environment satisfying all the dependencies with Anaconda, make sure that the current working directory contains
environment.yml, then run the following command:
conda env create
Activate the created environment with:
conda activate kinetic-degradation
We maintain a similar notation as used by Bartlett et al. and denote the amounts of species involved in the UPS as follows. Ensure that all initial values and model parameters have consistent units. We will use micromolar for concentration, liter for volume, and hour for time.
Model species notation
- BPD_ec: extracellular Bispecific Protein Degrader.
- BPD_ic: intracellular Bispecific Protein Degrader.
- T: unbound Target protein.
- E3: unbound E3 ligase.
- BPD_T: BPD-T binary complex.
- BPD_E3: BPD-E3 binary complex.
- Ternary: T-BPD-E3 ternary complex.
- T_Ub_i: Target protein with i ubiquitin molecules attached.
- BPD_T_Ub_i: BPD-T binary complex with i ubiquitin molecules attached.
- Ternary_Ub_i: ternary complex with i ubiquitin molecules attached.
To model a target protein degradation system, you must provide a config file in a format such as YAML that can be read into a Python dictionary data structure and save it to the ./data/ folder.
The config file must contain the following keys (with units in parentheses):
Kinetic rate constants and Binding affinity
- alpha: ternary complex cooperativity
- Kd_T_binary (uM): equilibrium dissociation constant of BPD-T binary complex
- kon_T_binary (1/uM/h): kon of BPD + T -> BPD-T
- koff_T_binary (1/h): koff of BPD-T -> BPD + T
- Kd_T_ternary (uM): equilibrium dissociation constant of T in ternary complex
- kon_T_ternary (1/uM/h): kon of BPD-E3 + T -> T-BPD-E3
- koff_T_ternary (1/h): koff of T-BPD-E3 -> BPD-E3 + T
- Kd_E3_binary (uM): equilibrium dissociation constant of BPD-E3 binary complex
- kon_E3_binary (1/uM/h): kon of BPD + E3 -> BPD-E3
- koff_E3_binary (1/h): koff of BPD-E3 -> BPD + E3
- Kd_E3_ternary (uM): equilibrium dissociation constant of E3 in ternary complex
- kon_E3_ternary (1/uM/h): kon of BPD-T + E3 -> T-BPD-E3
- koff_E3_ternary (1/h): koff of T-BPD-E3 -> BPD-T + E3Other parameters
- n: number of ubiquitination steps before proteasomal degradation
- kub (1/h): rate of ubiquitination
- kde_ub (1/h): rate of de-ubiquitination
- kdeg_UPS (1/h): rate of proteasomal degradation for poly-ubiquitinated T and BPD-T
- kdeg_Ternary (1/h): rate of proteasomal degradation for poly-ubiquitinated Ternary
- fu_ec: fraction unbound extracellular BPD
- fu_ic: fraction unbound intracellular BPD
- PS_cell (L/h): permeability-surface area product
- kprod_T (umol/h): [Optional] intrinsic target protein production rate. Will be calculated and set to Conc_T_base * Vic * kdeg_T
- kdeg_T (1/h): intrinsic target protein degradation rate
- Conc_T_base (uM): baseline target protein concentration
- Conc_E3_base (uM): baseline E3 concentration
- num_cells: number of cells in system
- Vic (L): intracellular volume
- Vec (L): extracellular volumeA sufficient number of kinetic rate parameters must be defined and those that are provided must be consistent. That is, a config is sufficient and consistent if all kinetic rate constants can either be derived from or satisfy the following ratios:
Kd = koff / kon
alpha = Kd_binary / Kd_ternary
Ternary complex formation is just a special case of the kinetic proofreading model wherein target protein ubiquitination and proteasomal degradation is prevented. This is equivalent to setting the following parameters to 0 in the config file:
- n
- kub
- kde_ub
- kdeg_UPS
- kdeg_Ternary
It is possible to model entirely intracellular systems by setting the following parameters to 0 in the config file:
- PS_cell
This repo implements a mechanistic mathematical model as a system of ordinary differential equations that describe the change in amounts of species involved in a UPS over time given an initial condition.
See files in bin/ for examples of how to simulate a UPS.
run_kinetic_model.py: simulates a UPS for- fixed initial concentration of degrader over time
- fixed time point over initial concentrations of degrader
Kd_vs_alpha.py: analyzes effect of cooperativity across binary targetKdon degradation for fixed initial concentration of degrader and time pointktransit_vs_alpha.py: analyzes effect of cooperativity across ubiquitination ratekubon degradation for fixed initial concentration of degrader and time point
- Add
srcto thePYTHONPATHenvironment variable to make the modules there accessible.
Linux
export PYTHONPATH="$(pwd)/src/"
Windows
set PYTHONPATH=%cd%\src\;%PYTHONPATH%
-
In your current working directory, create a folder named
saved_objects. This is where simulations results are saved to in the examples inbin. -
In your current working directory, create a folder named
dataand store simulation config.ymlfiles there.
Example
./data/unit_test_config.yml
- Run a simulation script from the command line.
Example
python bin/deg_vs_time.py
- In your current working directory, create a folder named
plotsand visualize the simulation results.
Example
python make_plots/plot_deg_vs_time.py