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<p>This paper presents an intelligent computational framework for modeling nonlinear irreversible biochemical reactions (NIBR) using artificial neural networks (ANNs). The biochemical reactions are modeled using an extended Michaelis-Menten kinetic scheme involving enzyme-substrate and enzyme-product complexes, expressed through a system of nonlinear ordinary differential equations (ODEs). Datasets were generated using the Runge-Kutta 4th order (RK4) method and used to train a multilayer feedforward ANN employing the Backpropagation Levenberg-Marquardt (BLM) algorithm. The proposed BLM-ANN model is compared with two other training algorithms: Bayesian Regularization (BR) and Scaled Conjugate Gradient (SCG). Six kinetic scenarios, each with four cases of varying reaction rate constants <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_13146_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="126" /> </InlineMediaObject> <EquationSource Format="TEX">\(k_1, k_{-1}, k_2, k_{-2}, k_3\)</EquationSource> </InlineEquation>, were used to validate the models. Performance was evaluated using mean squared error (MSE), absolute error (AE), regression coefficients (R), error histograms, and auto-correlation analysis. Results show that the BLM-ANN model outperforms BR and SCG in terms of accuracy (with MSE as low as <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_13146_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="TEX">\(10^{-13}\)</EquationSource> </InlineEquation>), convergence speed, and robustness across diverse kinetic profiles. Regression plots confirm high correlation with RK4 solutions, and error distributions validate the model’s predictive capability. The comparison between the solution of BLM-ANN and RK4 method of the proposed model. These results demonstrate the high accuracy, reliability, and generalization capability of the proposed framework.</p>

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An intelligent framework for modeling nonlinear irreversible biochemical reactions using artificial neural networks

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  • 出版模式：

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  • 发表日期：

    2025年8月4日

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  • Hazrat Bilal,
  • Rehan Ali Shah,
  • Hijaz Ahmad,
  • Akhter Jan,
  • Taha Radwan

摘要

This paper presents an intelligent computational framework for modeling nonlinear irreversible biochemical reactions (NIBR) using artificial neural networks (ANNs). The biochemical reactions are modeled using an extended Michaelis-Menten kinetic scheme involving enzyme-substrate and enzyme-product complexes, expressed through a system of nonlinear ordinary differential equations (ODEs). Datasets were generated using the Runge-Kutta 4th order (RK4) method and used to train a multilayer feedforward ANN employing the Backpropagation Levenberg-Marquardt (BLM) algorithm. The proposed BLM-ANN model is compared with two other training algorithms: Bayesian Regularization (BR) and Scaled Conjugate Gradient (SCG). Six kinetic scenarios, each with four cases of varying reaction rate constants \(k_1, k_{-1}, k_2, k_{-2}, k_3\) , were used to validate the models. Performance was evaluated using mean squared error (MSE), absolute error (AE), regression coefficients (R), error histograms, and auto-correlation analysis. Results show that the BLM-ANN model outperforms BR and SCG in terms of accuracy (with MSE as low as \(10^{-13}\) ), convergence speed, and robustness across diverse kinetic profiles. Regression plots confirm high correlation with RK4 solutions, and error distributions validate the model’s predictive capability. The comparison between the solution of BLM-ANN and RK4 method of the proposed model. These results demonstrate the high accuracy, reliability, and generalization capability of the proposed framework.