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allow non-rate-equation-based kinetic models
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"""Demonstration of how to make a Bayesian kinetic model with enzax.""" | ||
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import functools | ||
import logging | ||
import warnings | ||
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import arviz as az | ||
import jax | ||
from jax import numpy as jnp | ||
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from enzax.examples import methionine | ||
from enzax.mcmc import ( | ||
ObservationSet, | ||
AllostericMichaelisMentenPriorSet, | ||
get_idata, | ||
ind_prior_from_truth, | ||
posterior_logdensity_amm, | ||
run_nuts, | ||
) | ||
from enzax.steady_state import get_kinetic_model_steady_state | ||
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SEED = 1234 | ||
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jax.config.update("jax_enable_x64", True) | ||
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def main(): | ||
"""Demonstrate How to make a Bayesian kinetic model with enzax.""" | ||
structure = methionine.structure | ||
rate_equations = methionine.rate_equations | ||
true_parameters = methionine.parameters | ||
true_model = methionine.model | ||
default_state_guess = jnp.full((5,), 0.01) | ||
true_states = get_kinetic_model_steady_state( | ||
true_model, default_state_guess | ||
) | ||
prior = AllostericMichaelisMentenPriorSet( | ||
log_kcat=ind_prior_from_truth(true_parameters.log_kcat, 0.1), | ||
log_enzyme=ind_prior_from_truth(true_parameters.log_enzyme, 0.1), | ||
log_drain=ind_prior_from_truth(true_parameters.log_drain, 0.1), | ||
dgf=ind_prior_from_truth(true_parameters.dgf, 0.1), | ||
log_km=ind_prior_from_truth(true_parameters.log_km, 0.1), | ||
log_conc_unbalanced=ind_prior_from_truth( | ||
true_parameters.log_conc_unbalanced, 0.1 | ||
), | ||
temperature=ind_prior_from_truth(true_parameters.temperature, 0.1), | ||
log_ki=ind_prior_from_truth(true_parameters.log_ki, 0.1), | ||
log_transfer_constant=ind_prior_from_truth( | ||
true_parameters.log_transfer_constant, 0.1 | ||
), | ||
log_dissociation_constant=ind_prior_from_truth( | ||
true_parameters.log_dissociation_constant, 0.1 | ||
), | ||
) | ||
# get true concentration | ||
true_conc = jnp.zeros(methionine.structure.S.shape[0]) | ||
true_conc = true_conc.at[methionine.structure.balanced_species].set( | ||
true_states | ||
) | ||
true_conc = true_conc.at[methionine.structure.unbalanced_species].set( | ||
jnp.exp(true_parameters.log_conc_unbalanced) | ||
) | ||
# get true flux | ||
true_flux = true_model.flux(true_states) | ||
# simulate observations | ||
error_conc = 0.03 | ||
error_flux = 0.05 | ||
error_enzyme = 0.03 | ||
key = jax.random.key(SEED) | ||
obs_conc = jnp.exp(jnp.log(true_conc) + jax.random.normal(key) * error_conc) | ||
obs_enzyme = jnp.exp( | ||
true_parameters.log_enzyme + jax.random.normal(key) * error_enzyme | ||
) | ||
obs_flux = true_flux + jax.random.normal(key) * error_conc | ||
obs = ObservationSet( | ||
conc=obs_conc, | ||
flux=obs_flux, | ||
enzyme=obs_enzyme, | ||
conc_scale=error_conc, | ||
flux_scale=error_flux, | ||
enzyme_scale=error_enzyme, | ||
) | ||
pldf = functools.partial( | ||
posterior_logdensity_amm, | ||
obs=obs, | ||
prior=prior, | ||
structure=structure, | ||
rate_equations=rate_equations, | ||
guess=default_state_guess, | ||
) | ||
samples, info = run_nuts( | ||
pldf, | ||
key, | ||
true_parameters, | ||
num_warmup=200, | ||
num_samples=200, | ||
initial_step_size=0.0001, | ||
max_num_doublings=10, | ||
is_mass_matrix_diagonal=False, | ||
target_acceptance_rate=0.95, | ||
) | ||
idata = get_idata( | ||
samples, info, coords=methionine.coords, dims=methionine.dims | ||
) | ||
print(az.summary(idata)) | ||
if jnp.any(info.is_divergent): | ||
n_divergent = info.is_divergent.sum() | ||
msg = f"There were {n_divergent} post-warmup divergent transitions." | ||
warnings.warn(msg) | ||
else: | ||
logging.info("No post-warmup divergent transitions!") | ||
print("True parameter values vs posterior:") | ||
for param in true_parameters.__dataclass_fields__.keys(): | ||
true_val = getattr(true_parameters, param) | ||
model_low = jnp.quantile(getattr(samples.position, param), 0.01, axis=0) | ||
model_high = jnp.quantile( | ||
getattr(samples.position, param), 0.99, axis=0 | ||
) | ||
print(f" {param}:") | ||
print(f" true value: {true_val}") | ||
print(f" posterior 1%: {model_low}") | ||
print(f" posterior 99%: {model_high}") | ||
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if __name__ == "__main__": | ||
main() |
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"""Demonstration of how to find a steady state and its gradients with enzax.""" | ||
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import time | ||
from enzax.kinetic_model import RateEquationModel | ||
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import jax | ||
from jax import numpy as jnp | ||
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from enzax.examples import methionine | ||
from enzax.steady_state import get_kinetic_model_steady_state | ||
from jaxtyping import PyTree | ||
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BAD_GUESS = jnp.full((5,), 0.01) | ||
GOOD_GUESS = jnp.array( | ||
[ | ||
4.233000e-05, # met-L | ||
3.099670e-05, # amet | ||
2.170170e-07, # ahcys | ||
3.521780e-06, # hcys | ||
6.534400e-06, # 5mthf | ||
] | ||
) | ||
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def main(): | ||
"""Function for testing the steady state solver.""" | ||
model = methionine.model | ||
# compare good and bad guess | ||
for guess in [BAD_GUESS, GOOD_GUESS]: | ||
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def get_steady_state_from_params(parameters: PyTree): | ||
"""Get the steady state from just parameters. | ||
This lets us get the Jacobian wrt (just) the parameters. | ||
""" | ||
_model = RateEquationModel( | ||
parameters, model.structure, model.rate_equations | ||
) | ||
return get_kinetic_model_steady_state(_model, guess) | ||
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# solve once for jitting | ||
get_kinetic_model_steady_state(model, GOOD_GUESS) | ||
jax.jacrev(get_steady_state_from_params)(model.parameters) | ||
# timer on | ||
start = time.time() | ||
conc_steady = get_kinetic_model_steady_state(model, guess) | ||
jac = jax.jacrev(get_steady_state_from_params)(model.parameters) | ||
# timer off | ||
runtime = (time.time() - start) * 1e3 | ||
sv = model.dcdt(jnp.array(0.0), conc=conc_steady) | ||
flux = model.flux(conc_steady) | ||
print(f"Results with starting guess {guess}:") | ||
print(f"\tRun time in milliseconds: {round(runtime, 4)}") | ||
print(f"\tSteady state concentration: {conc_steady}") | ||
print(f"\tFlux: {flux}") | ||
print(f"\tSv: {sv}") | ||
print(f"\tLog Km Jacobian: {jac.log_km}") | ||
print(f"\tDgf Jacobian: {jac.dgf}") | ||
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if __name__ == "__main__": | ||
main() |
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from jax import config | ||
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config.update("jax_enable_x64", True) |
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