reconstruction.ecoli.dataclasses.process.rna_decay

SimulationData for rna decay process

class reconstruction.ecoli.dataclasses.process.rna_decay.RnaDecay(raw_data, sim_data)[source]

Bases: object

_buildRnaDecayData(raw_data, sim_data)[source]
km_loss_function(vMax, rnaConc, kDeg, isEndoRnase, alpha)[source]

Generates the functions used for estimating the per-RNA affinities (Michaelis-Menten constants) to the endoRNAses.

The optimization problem is formulated as a multidimensional root-finding problem; the goal is to find a set of Michaelis-Menten constants such that the endoRNAse-mediated degradation under basal concentrations is consistent with the experimentally observed half-lives, thus

(nonlinear rate) = (linear rate)

where the nonlinear rate is the rate as predicted from some kinetic rate law, and the linear rate is proportional to the inverse of the observed half-life. Then, reordering,

0 = (nonlinear rate) - (linear rate)

is (for the moment) the root we wish to find, for each RNA species, giving us the multidimensional function

R_aux = (nonlinear rate) - (linear rate)

This is the unnormalized residual function; the normalized residuals are

R = (nonlinear rate)/(linear rate) - 1

In addition to matching our half-lives we also desire the Michaelis-Menten constants to be non-negative (negative values have no physical meaning). Thus we introduce a penalty term for negative values. TODO (John): explain penalty term

The two terms (the residuals R and the negative value penalty Rneg) are combined into one ‘loss’ function L (alpha is the weighting on the negative value penalty):

L = ln((exp(R) + exp(alpha*Rneg))/2)

= ln(exp(R) + exp(alpha*Rneg)) - ln(2)

The loss function has one element for each RNA. This functional form is a soft (continuous and differentiable) approximation to

L = max(R, alpha*Rneg)

The root finder, provided with L, will attempt to make each element of L as close to zero as possible, and therefore minimize both R and Rneg.

The third-party package Aesara (formerly Theano) creates the functions and finds an analytic expression for the Jacobian.

Parameters:

  • vMax (scalar) – The total endoRNAse capacity, in dimensions of amount per volume per time.

  • rnaConc (1-D array, float) – Concentrations of RNAs (that will be degraded), in dimensions of amount per volume.

  • kDeg (1-D array, float) – Experimentally observed degradation rates (computed from half-lives), in dimensions of per unit time.

  • isEndoRnase (1-D array, bool) – A vector that is True everywhere that an RNA corresponds to an endoRNAse; that is, an endoRNAse (or endoRNAse subunit) mRNA.

  • alpha (scalar, >0) – Regularization weight, used to penalize for negative Michaelis-Menten value predictions during the course of the optimization. Typical value is 0.5.

Returns:

  • L (function) – The ‘loss’ function.

  • Rneg (function) – The negative Michaelis-Menten constant penalty terms.

  • R (function) – The residual error (deviation from steady-state).

  • Lp (function) – The Jacobian of the loss function L with respect to the Michaelis-Menten constants.

  • R_aux (function) – Unnormalized ‘residual’ function.

  • L_aux (function) – Unnormalized ‘loss’ function.

  • Lp_aux (function) – Jacobian of the unnormalized ‘loss’ function.

  • Jacob (function) – Duplicate with Lp.

  • Jacob_aux (function) – Duplicate with Lp_aux.

Notes

The regularization term also includes a penalty for the endoRNAse residuals, as well as a fixed weighting (WFendoR = 0.1). TODO (John): Why is this needed? It seems redundant. TODO (John): How do we know this weight is sufficient?

All of the outputs are Aesara functions, and take a 1-D array of Michaelis-Menten constants as their sole inputs. All of the functions return a 1-D array, with the exception of the Jacobians, which return matrices.

TODO (John): Remove the redundant outputs.

TODO (John): Consider redesigning this as an objective minimization problem rather than a root finding problem.

TODO (John): Consider replacing the Michaelis-Menten constants with logarithmic equivalents, thereby eliminating the requirement for the negative value penalty.

TODO (John): Consider moving this method out of this class, as it is, in fact, a static method, and isn’t utilized anywhere within this class.