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

Title data

Pande, Naman Krishna ; Jain, Aditi ; Kumar, Arun ; Gupta, Arvind Kumar:
Conservative deep neural networks for modeling competition of ribosomes with extended length.
In: Physica D: Nonlinear Phenomena. Vol. 470 (2024) Issue Part A . - 134415.
ISSN 0167-2789
DOI: https://doi.org/10.1016/j.physd.2024.134415

Review:

Project information

Project financing: Andere
DST-SERB, Govt. of India (Grant CRG/2019/004669)
FIST program of the Department of Science and Technology, Government of India (reference no. SR/FST/MS-I/2018/22(C))

Abstract in another language

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.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: ribosome flow model with extended objects; ordinary differential equations; first integral; contraction theory; deep neural networks
Subject classification: Mathematics Subject Classification Code: 92C37 92C40 34A34 76Z05 92B20 68T07
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Profile Fields > Advanced Fields > Nonlinear Dynamics
Research Institutions > Central research institutes > Bayreuth Research Center for Modeling and Simulation - MODUS
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
500 Science > 570 Life sciences, biology
Date Deposited: 11 Mar 2025 12:39
Last Modified: 11 Mar 2025 12:39
URI: https://eref.uni-bayreuth.de/id/eprint/92623