Entropy production and lumping of species can effectively reduce complex cell signaling pathways

Khoshnaw, Sarbaz H. A.; Rasool, Hemn Mohammed

doi:10.1088/1402-4896/ac6211

Cited by 3 publications

(4 citation statements)

References 34 publications

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“…Furthermore, we have also applied the proposed method to the ERK signaling pathways, which include 11 variables and 11 parameters. This model's reduction process is illustrated in Figure (2). This model has reduced from 11 to 8 parameters, and the deviation value is only 1.76%.…”

Section: Discussionmentioning

confidence: 99%

“…There are many methods and technique for model reduction, readers can see more applied techniques in [1][2][3][4]. Lumping of parameter technique is suggested to simplified the number of parameters in this study, and to evaluate the difference between the original and reduced models at each stage we use function of deviation, for more detail of this formulas readers can see [5].…”

Section: Introductionmentioning

confidence: 99%

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Model Reduction and Analysis for ERK Cell Signalling Pathway Using Implicit-Explicit Rung-Kutta Methods

Rasool

Pirdawood

Sabawi

et al. 2022

PJBAS

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Many complex cell signalling pathways and chemical reaction networks include many variables and parameters; this is sometimes a big issue for identifying critical model elements and describing the model dynamics. Therefore, model reduction approaches can be employed as a mathematical tool to reduce the number of elements. In this study, we use a new technique for model reduction: the Lumping of parameters for the simple linear chemical reaction network and the complex cell signalling pathway that is extracellular-signal-regulated kinase (ERK) pathways. Moreover, we propose a high-order and accurate method for solving stiff nonlinear ordinary differential equations. The curtail idea of this scheme is based on splitting the problem into stiff and non-stiff terms. More specifically, stiff discretization uses the implicit method, and nonlinear discretization uses the explicit method. This is consequently leading to a reduction in the computational cost of the scheme.The main aim of this study is to reduce the complex cell signalling pathway models by proposing an accurate numerical approximation Runge-Kutta method. This improves one's understanding of such behaviour of these systems and gives an accurate approximate solution. Based on the suggested technique, the simple model's parameters are minimized from 6 to 3, and the complex models from 11 to 8. Resultsshow that there is a good agreement between the original models and the simplified models.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Model Reduction and Analysis for ERK Cell Signalling Pathway Using Implicit-Explicit Rung-Kutta Methods

Rasool

Pirdawood

Sabawi

et al. 2022

PJBAS

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“…Information is relayed in the form of complex and dynamic signaling events translating into various cellular functions in cells, and signaling networks are also complex considering both the chemical and biophysical events underlying them as well as the sheer number of interactions. One study deals with the complicated issue in many of the cell signaling pathways concerned with the number of state variables and parameters [6]. Prediction of their model dynamics is computationally expensive and sometimes difficult.…”

Section: Work In Progressmentioning

confidence: 99%

Advanced fractional calculus, differential equations and neural networks: analysis, modeling and numerical computations

Baleanu,

Karaca,

Vázquez

et al. 2023

Phys. Scr.

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Most physical systems in nature display inherently nonlinear and dynamical properties; hence, it would be difficult for nonlinear equations to be solved merely by analytical methods, which has given rise to the emerging of engrossing phenomena such as bifurcation and chaos. Conjointly, due to nonlinear systems’ exhibiting more exotic behavior than harmonic distortion, it becomes compelling to test, classify and interpret the results in an accurate way. For this reason, avoiding preconceived ideas of the way the system is likely to respond is of pivotal importance since this facet would have effect on the type of testing run and processing techniques used in nonlinear systems. Paradigms of nonlinear science may suggest that it is ‘the study of every single phenomenon’ due to its interdisciplinary nature, which is another challenge encountered and needs to be addressed by generating and designing a systematic mathematical framework where the complexity of natural phenomena hints the requirement of identifying their commonalties and classifying their various manifestations in different nonlinear systems. Studying such common properties, concepts or paradigms can enable one to gain insight into nonlinear problems, their essence and consequences in a broad range of disciplines all forthwith. Fractional differential equations associated with non-local phenomena in physics have arisen as a powerful mathematical tool within a multidisciplinary research framework. Fractional differential equations, as one extension of the fractional calculus theory, can yield the evolution of various systems properly, which reinforces its position in mathematics and science while setting stage for the description of dynamic, complicated and nonlinear events. Through the reflection of the systems’ actual properties, fractional calculus manifests unforeseeable and hidden variations, and thus, enables integration and differentiation, with the solutions to be approximated by numerical methods along with modeling and predicting the dynamics of multiphysics, multiscale and physical systems. Neural Networks (NNs), consisting of hidden layers with nonlinear functions that have vector inputs and outputs, are also considerably employed owing to their versatile and efficient characteristics in classification problems as well as their sophisticated neural network architectures, which make them capable of tackling complicated governing partial differential equation problems. Furthermore, partial differential equations are used to provide comprehensive and accurate models for many scientific phenomena owing to the advancements of data gathering and machine learning techniques which have raised opportunities for data-driven identification of governing equations derived from experimentally observed data. Given these considerations, while many problems are solvable and have been solved, efforts are still needed to be able to respond to the remaining open questions in the fields that have a broad range of spectrum ranging from mathematics, physics, biology, virology, epidemiology, chemistry, engineering, social sciences to applied sciences. With a view of different aspects of such questions, our special issue provides a collection of recent research focusing on the advances in the foundational theory, methodology and topical applications of fractals, fractional calculus, fractional differential equations, differential equations (PDEs, ODEs, to name some), delay differential equations (DDEs), chaos, bifurcation, stability, sensitivity, machine learning, quantum machine learning, and so forth in order to expound on advanced fractional calculus, differential equations and neural networks with detailed analyses, models, simulations, data-driven approaches as well as numerical computations.

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“…This path of reduced dimensions is known as a slow invariant manifold (SIM). Many techniques have been developed to find the SIM [1][2][3], including methods for obtaining initial approximations and refining them. The present work applies only two MRTs to a complex reaction mechanism.…”

Section: Introductionmentioning

confidence: 99%

Simplified modeling of butane dehydrogenation: deeper understanding of the system’s dynamics

Hamad,

Khoshnaw,

Shahzad

2024

Phys. Scr.

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The dehydrogenation of butane is a catalytic process that involves the separation of hydrogen atoms from an organic molecule, and it relies on the presence of a catalyst Z, such as Ni, Pt, Pd, Fe, ZnO, Cr 2 O 3, or Fe 2 O 3. In this paper, we introduce two highly effective mathematical techniques known as Lumping Compartments (LC) and Intrinsic Low Dimensional Manifold (ILDM) to simplify the complexity of the dehydrogenation of butane. Initially, the model consists of seven nonlinear differential equations with eight parameters. To streamline the model, we applied LC to ten different cases, considering various initial states and parameters. As a result, the number of compartments significantly decreased from seven to three. The obtained computational results and total differences reveal a remarkable agreement between the complete model and the simplified version, demonstrating a high degree of predictive accuracy. Additionally, ILDM is employed to enhance the initial estimation of the slow invariant manifold. This enables us to easily distinguish between the fast and slow variations at each point, with the variations acting as chemical kinetics attractors. Fast chemical reactions are drawn towards these attractors, while slow chemical reactions occur within the manifolds.

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Entropy production and lumping of species can effectively reduce complex cell signaling pathways

Cited by 3 publications

References 34 publications

Model Reduction and Analysis for ERK Cell Signalling Pathway Using Implicit-Explicit Rung-Kutta Methods

Model Reduction and Analysis for ERK Cell Signalling Pathway Using Implicit-Explicit Rung-Kutta Methods

Advanced fractional calculus, differential equations and neural networks: analysis, modeling and numerical computations

Simplified modeling of butane dehydrogenation: deeper understanding of the system’s dynamics

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