Conservative deep neural networks for modeling competition of ribosomes with extended length

Abstract

We develop a network model that combines several ribosome flow models with extended objects (RFMEO) competing for the finite pool of ribosomes. This alleviates the need to systematically coarse-grain the mRNA molecules. The dynamics of the network is described by a system of non-linear ordinary differential equations. It is shown that the network always converges to a steady state for a fixed number of ribosomes. Our analysis shows that increasing any of the transition rates along an RFMEO increases its output rate and either the output rates of the other RFMEOs all increase or all decrease. Simulations also demonstrate a counterintuitive result that increasing the ribosomal footprint may sometimes lead to an increase in the network production rate. Next, we propose a conservative deep neural network (CDNN) framework to approximate the solution of the network. The proposed loss function also incorporates the term satisfying the first integral property of the network. Point-wise comparison of the solutions by CDNN is in good agreement with the Runge–Kutta based numerical solution. Also, the CDNN framework offers a closed-form solution of the RFMEONP as a function of free parameters, thus allowing evaluation of the solution at any parameter value without again simulating the system.