A comprehensive approach to the mathematical modeling of mass transport in biological systems: Fundamental concepts and models

Zaheri, Shadi; Hassanipour, Fatemeh

doi:10.1016/j.ijheatmasstransfer.2020.119777

Cited by 6 publications

(2 citation statements)

References 89 publications

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“…For instance, it is often assumed that specific steps in the enzyme mechanisms are slower than other steps, which generally allows removal of some terms in the equation. For information about enzyme mechanisms and kinetics see refs − , and for specific transport mechanisms see refs and .…”

Section: Dynamics and Modelingmentioning

confidence: 99%

Minimal Out-of-Equilibrium Metabolism for Synthetic Cells: A Membrane Perspective

et al. 2023

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Life-like systems need to maintain a basal metabolism, which includes importing a variety of building blocks required for macromolecule synthesis, exporting dead-end products, and recycling cofactors and metabolic intermediates, while maintaining steady internal physical and chemical conditions (physicochemical homeostasis). A compartment, such as a unilamellar vesicle, functionalized with membrane-embedded transport proteins and metabolic enzymes encapsulated in the lumen meets these requirements. Here, we identify four modules designed for a minimal metabolism in a synthetic cell with a lipid bilayer boundary: energy provision and conversion, physicochemical homeostasis, metabolite transport, and membrane expansion. We review design strategies that can be used to fulfill these functions with a focus on the lipid and membrane protein composition of a cell. We compare our bottom-up design with the equivalent essential modules of JCVI-syn3a, a top-down genome-minimized living cell with a size comparable to that of large unilamellar vesicles. Finally, we discuss the bottlenecks related to the insertion of a complex mixture of membrane proteins into lipid bilayers and provide a semiquantitative estimate of the relative surface area and lipid-to-protein mass ratios (i.e., the minimal number of membrane proteins) that are required for the construction of a synthetic cell.

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Section: Dynamics and Modelingmentioning

confidence: 99%

Minimal Out-of-Equilibrium Metabolism for Synthetic Cells: A Membrane Perspective

et al. 2023

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“…A mathematical model is a collection of equations that represents the mathematical representation of hypotheses (or assumptions). Mathematical modeling is widely used in ecological, epidemiological, and biological fields [1][2][3][4][5][6]. To gain a better understanding of patterns, modeling is widely utilized.…”

Section: Introductionmentioning

confidence: 99%

On Fractional-Order Discrete-Time Reaction Diffusion Systems

et al. 2023

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Reaction–diffusion systems have a broad variety of applications, particularly in biology, and it is well known that fractional calculus has been successfully used with this type of system. However, analyzing these systems using discrete fractional calculus is novel and requires significant research in a diversity of disciplines. Thus, in this paper, we investigate the discrete-time fractional-order Lengyel–Epstein system as a model of the chlorite iodide malonic acid (CIMA) chemical reaction. With the help of the second order difference operator, we describe the fractional discrete model. Furthermore, using the linearization approach, we established acceptable requirements for the local asymptotic stability of the system’s unique equilibrium. Moreover, we employ a Lyapunov functional to show that when the iodide feeding rate is moderate, the constant equilibrium solution is globally asymptotically stable. Finally, numerical models are presented to validate the theoretical conclusions and demonstrate the impact of discretization and fractional-order on system dynamics. The continuous version of the fractional-order Lengyel–Epstein reaction–diffusion system is compared to the discrete-time system under consideration.

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Numerical solution of a comprehensive form of convection–diffusion equation for binary isotopes in the gas centrifuge

Ghazanfari

Shadman

2022

Annals of Nuclear Energy

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A comprehensive approach to the mathematical modeling of mass transport in biological systems: Fundamental concepts and models

Cited by 6 publications

References 89 publications

Minimal Out-of-Equilibrium Metabolism for Synthetic Cells: A Membrane Perspective

Minimal Out-of-Equilibrium Metabolism for Synthetic Cells: A Membrane Perspective

On Fractional-Order Discrete-Time Reaction Diffusion Systems

Numerical solution of a comprehensive form of convection–diffusion equation for binary isotopes in the gas centrifuge

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