Identifiability analysis for models of the translation kinetics after mRNA transfection

Abstract

Mechanistic models are a powerful tool to gain insights into biological processes. The parameters of such models, e.g. kinetic rate constants, usually cannot be measured directly but need to be inferred from experimental data. In this article, we study dynamical models of the translation kinetics after mRNA transfection and analyze their parameter identifiability. Previous studies have considered ordinary differential equation (ODE) models of the process, and here we formulate a stochastic differential equation (SDE) model. For both model types, we consider structural identifiability based on the model equations and practical identifiability based on simulated as well as experimental data and find that the SDE model provides better parameter identifiability than the ODE model. Moreover, our analysis shows that even for those parameters of the ODE model that are considered to be identifiable, the obtained estimates are sometimes unreliable. Overall, our study clearly demonstrates the relevance of considering different modeling approaches and that stochastic models can provide more reliable and informative results.

An amortized approach to non-linear mixed-effects modeling based on neural posterior estimation

“…Here, we again considered the processes of mRNA transfection, but described by a stochastic differential equation (SDE) as proposed by (Pieschner et al, 2022) (detailed model specification in Supplement A.1). This model is superior for the description of individual cells and improves parameter identifiability (Pieschner et al, 2022), but has not been used so far in an NLME modeling framework.…”

“…The simple ODE model can be easily extended to the SDE model from (Pieschner et al, 2022) with ϕ = ( δ, γ, k, m 0 , scale, offset, σ ), where B t is a two-dimensional standard Brownian motion, m ( t 0 ) = 1 and p (0) = 0. To compare the model to the previous one we take as observable mapping The priors assumed for the variables are This SDE system is simulated based on an Euler-Maruyama scheme with a step size of 0.01 and using just in time compilation from (Lam et al, 2015).…”

“…However, for such models, the likelihood function -which our purely simulation-based approach does not need -is often unavailable, requiring computationally demanding techniques such as approximate Bayesian computation or a Metropolis-within-Gibbs algorithm, which can handle the unavailable likelihood function via correlated particle filters [23,24,40]. Here, we again considered the processes of mRNA transfection, but described by a stochastic differential equation (SDE) as proposed by [41] (see the model specification in Supplement A.1). This model has been shown to be superior for the description of individual cells and to improve parameter identifiability [41], but has not been used so far in an NLME modeling framework.…”

“…from [41], where B t is a two-dimensional standard Brownian motion, m(t 0 ) = 1 and p(0) = 0. To compare the model to the previous one we take as observable mapping…”