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Journal articles on the topic 'Biochemical model'

Author: Grafiati

Published: 4 June 2021

Last updated: 8 February 2022

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1

Antoniotti, Marco, Alberto Policriti, Nadia Ugel, and Bud Mishra. "Model Building and Model Checking for Biochemical Processes." Cell Biochemistry and Biophysics 38, no. 3 (2003): 271–86. http://dx.doi.org/10.1385/cbb:38:3:271.

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2

Sahley, Tony L., and Richard H. Nodar. "A biochemical model of peripheral tinnitus." Hearing Research 152, no. 1-2 (February 2001): 43–54. http://dx.doi.org/10.1016/s0378-5955(00)00235-5.

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3

Appanna, Vasu D., Shawna L. Anderson, and Tamara Skakoon. "Biogenesis of calcite: A biochemical model." Microbiological Research 152, no. 4 (December 1997): 341–43. http://dx.doi.org/10.1016/s0944-5013(97)80049-3.

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4

Johnson, Mark A. "Biochemical bone fracture healing process model." IFAC Proceedings Volumes 36, no. 15 (August 2003): 335–40. http://dx.doi.org/10.1016/s1474-6670(17)33525-5.

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5

Elstner, Erich F., R. Adamczyk, A. Furch, and R. Kröner. "Biochemical Model Reactions for Cataract Research." Ophthalmic Research 17, no. 5 (1985): 302–7. http://dx.doi.org/10.1159/000265390.

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6

Craciun, Gheorghe, Jaejik Kim, Casian Pantea, and Grzegorz A. Rempala. "Statistical Model for Biochemical Network Inference." Communications in Statistics - Simulation and Computation 42, no. 1 (January 2013): 121–37. http://dx.doi.org/10.1080/03610918.2011.633200.

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7

Feliu, Elisenda, and Carsten Wiuf. "Simplifying biochemical models with intermediate species." Journal of The Royal Society Interface 10, no. 87 (October 6, 2013): 20130484. http://dx.doi.org/10.1098/rsif.2013.0484.

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Mathematical models are increasingly being used to understand complex biochemical systems, to analyse experimental data and make predictions about unobserved quantities. However, we rarely know how robust our conclusions are with respect to the choice and uncertainties of the model. Using algebraic techniques, we study systematically the effects of intermediate, or transient, species in biochemical systems and provide a simple, yet rigorous mathematical classification of all models obtained from a core model by including intermediates. Main examples include enzymatic and post-translational modification systems, where intermediates often are considered insignificant and neglected in a model, or they are not included because we are unaware of their existence. All possible models obtained from the core model are classified into a finite number of classes. Each class is defined by a mathematically simple canonical model that characterizes crucial dynamical properties, such as mono- and multistationarity and stability of steady states, of all models in the class. We show that if the core model does not have conservation laws, then the introduction of intermediates does not change the steady-state concentrations of the species in the core model, after suitable matching of parameters. Importantly, our results provide guidelines to the modeller in choosing between models and in distinguishing their properties. Further, our work provides a formal way of comparing models that share a common skeleton.

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8

Miskovic, Ljubisa, Jonas Béal, Michael Moret, and Vassily Hatzimanikatis. "Uncertainty reduction in biochemical kinetic models: Enforcing desired model properties." PLOS Computational Biology 15, no. 8 (August 20, 2019): e1007242. http://dx.doi.org/10.1371/journal.pcbi.1007242.

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9

Li, Shi, Xi Ju Zong, and Yan Hu. "Modeling and Control of Biochemical Reactor." Advanced Materials Research 791-793 (September 2013): 818–21. http://dx.doi.org/10.4028/www.scientific.net/amr.791-793.818.

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This paper is concerns with the study of modeling and control of biochemical reactor. Firstly, a mathematical model is established for a typical biochemical reactor, the mass balance equations are established individually for substrate concentration and biomass concentration. Then, the model is linearized at the steady-state point, two linear models are derived: state space model and transfer function model. The transfer function model is used in internal model control (IMC), where the filter parameter is selected and discussed. The state space model is applied in model predictive control (MPC), where controller parameters of control prediction horizon length and constraint of control variable variation are discussed.

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10

Iqbal, Muhammad Asad, Syed Tauseef Mohyud-Din, and Bandar Bin-Mohsin. "A study of nonlinear biochemical reaction model." International Journal of Biomathematics 09, no. 05 (June 13, 2016): 1650071. http://dx.doi.org/10.1142/s1793524516500716.

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The present study deals with the introduction of an alteration in Legendre wavelets method by availing of the Picard iteration method for system of differential equations and named it Legendre wavelet-Picard method (LWPM). Convergence of the proposed method is also discussed. In order to check the competence of the proposed method, basic enzyme kinetics is considered. Systems of nonlinear ordinary differential equations are formed from the considered enzyme-substrate reaction. The results obtained by the proposed LWPM are compared with the numerical results obtained from Runge–Kutta method of order four (RK-4). Numerical results and those obtained by LWPM are in excellent conformance, which would be explained by the help of table and figures. The proposed method is easy and simple to implement as compared to the other existing analytical methods used for solving systems of differential equations arising in biology, physics and engineering.

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11

Schwarick, Martin, and Alexej Tovchigrechko. "IDD-based model validation of biochemical networks." Theoretical Computer Science 412, no. 26 (June 2011): 2884–908. http://dx.doi.org/10.1016/j.tcs.2010.06.030.

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12

FAWCETT, JAN, KATIE A. BUSCH, DOUGLAS JACOBS, HOWARD M. KRAVITZ, and LOUIS FOGG. "Suicide: A Four-pathway Clinical-Biochemical Model." Annals of the New York Academy of Sciences 836, no. 1 Neurobiology (December 1997): 288–301. http://dx.doi.org/10.1111/j.1749-6632.1997.tb52366.x.

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13

Schempp, Harald, Dieter Weiser, and Erich Elstner. "Biochemical Model Reactions Indicative of Inflammatory Processes." Arzneimittelforschung 50, no. 04 (December 27, 2011): 362–72. http://dx.doi.org/10.1055/s-0031-1300215.

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14

Ballarini, Paolo, Radu Mardare, and Ivan Mura. "Analysing Biochemical Oscillation through Probabilistic Model Checking." Electronic Notes in Theoretical Computer Science 229, no. 1 (February 2009): 3–19. http://dx.doi.org/10.1016/j.entcs.2009.02.002.

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15

COMEAU, Y., K. HALL, R. HANCOCK, and W. OLDHAM. "Biochemical model for enhanced biological phosphorus removal." Water Research 20, no. 12 (December 1986): 1511–21. http://dx.doi.org/10.1016/0043-1354(86)90115-6.

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16

Liu, Yen-Chang, Chun-Liang Lin, and Chia-Hua Chuang. "An Approach for Model Reduction of Biochemical Networks." Computational Biology Journal 2013 (May 8, 2013): 1–14. http://dx.doi.org/10.1155/2013/263973.

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Biochemical networks are not only complex but also extremely large. The dynamic biological model of great complexity resulting in a large number of parameters is a main difficulty for optimization and control processes. In practice, it is highly desirable to further simplify the structure of biological models for the sake of reducing computational cost or simplification for the task of system analysis. This paper considers the S-system model used for describing the response of biochemical networks. By introducing the technique of singular value decomposition (SVD), we are able to identify the major state variables and parameters and eliminate unimportant metabolites and the corresponding signal transduction pathways. The model reduction by multiobjective analysis integrates the criteria of reactive weight, sensitivity, and flux analyses to obtain a reduced model in a systematic way. The resultant model is closed to the original model in performance but with a simpler structure. Representative numerical examples are illustrated to prove feasibility of the proposed method.

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17

Palmisano, Alida, Stefan Hoops, Layne T. Watson, Thomas C. Jones Jr, John J. Tyson, and Clifford A. Shaffer. "Multistate Model Builder (MSMB): a flexible editor for compact biochemical models." BMC Systems Biology 8, no. 1 (2014): 42. http://dx.doi.org/10.1186/1752-0509-8-42.

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18

Xing, X., X. Zheng, and J. Liu. "AN INVERSION APPROACH FOR BIOCHEMICAL PARAMETERS OF VEGETATION BASED ON THE PROSPECT-5 MODEL." International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLIII-B3-2021 (June 29, 2021): 645–50. http://dx.doi.org/10.5194/isprs-archives-xliii-b3-2021-645-2021.

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Abstract. Accurate inversion of vegetation biochemicals using the PROSPECT model mostly depends on a proper inversion approach, including a suitable optimizing algorithm, appropriate dependent variables, and different properties from spectra of reflectance (R) and transmittance (T). In this paper, we propose a special inversion method using PROSPECT-5 and then explore its effectiveness in inverting chlorophyll, carotenoids, equivalent water thickness, and dry matter per area data from the ANGERS database. The inversion strategy includes (i) an optimal algorithm with constrained bounds (fminsearchbnd) to replace the common function fminsearch, (ii) and four parameters are considered together and separately as dependent variables of models, (iii) Using properties from the spectra of R, T and combined R&T to invert the above four biochemical parameters. The results show that fminsearchbnd can improve the model's R2 based on a field-measured database. Moreover, using the entire set of parameters together as the model inputs is more effective than using single parameters separately. T spectra are favoured for all parameter inversions in the model database while being inapplicable in the ANGERS database. These findings provide an appropriate inversion strategy for the PROSPECT-5 model in vegetation biochemical parameters analysis and suggest further research to develop an accurate inversion process for vegetation based on various physical models.

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19

Tomaso, Giulia Di, Cesar Pichardo-Almarza, and Vanessa Díaz-Zuccarini. "A COUPLED BIOCHEMICAL-CFD MULTISCALE MODEL OF ATHEROGENESIS." Journal of Biomechanics 45 (July 2012): S477. http://dx.doi.org/10.1016/s0021-9290(12)70478-5.

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20

Ballarini, Paolo, Michele Forlin, Tommaso Mazza, and Davide Prandi. "Efficient Parallel Statistical Model Checking of Biochemical Networks." Electronic Proceedings in Theoretical Computer Science 14 (December 15, 2009): 47–61. http://dx.doi.org/10.4204/eptcs.14.4.

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21

Comeau, Y., K. J. Hall, and W. K. Oldham. "A Biochemical Model for Biological Enhanced Phosphorus Removal." Water Science and Technology 17, no. 11-12 (November 1, 1985): 313–14. http://dx.doi.org/10.2166/wst.1985.0250.

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The limited understanding of the fundamental mechanisms involved in biological enhanced phosphorus (bio-P) removal has hindered the successful development of this technology for wastewater treatment. The major objective of this research (Comeau, 1984) was to propose a model that would explain the bio-P removal phenomena under both anaerobic and aerobic conditions. The model presented here is based on the observations made with bio-P removal processes and on principles of microbial biochemistry. Bio-P bacteria are defined as being responsible for bio-P removal and are proposed to be capable of both po1yphosphate (polyP) and po1y-β-hydroxybutyrate (PHB) storage. Under anaerobic conditions (absence of both free oxygen and nitrate - Fig. 1) available substrates such as acetate (HAc) will be transported across the membrane by facilitated diffusion. Under usual conditions of pH, most of the acetate will be in the anionic form (Ac− ) and one H+of the proton motive force1 will be required for Ac− intracellular transport. Once inside Ac− can then be stored as PHB. It is postulated that the mechanism by which polyP confers an advantage to bio-P bacteria for PHB accumulation is by re-estab1ishing the pmf in order to allow more Ac− to be transported across the membrane and be stored. If the pH gradient of the pmf was not re-estab1ished no more Ac− could be accumulated. The pmf is proposed to be re-estab1ished by polyP which provides a source of phosphate molecules that can be neutrally transported across the plasma membrane. Once outside, phosphate molecules will dissociate and the released protons (H+) will re-establish the pmf and H+ can be used again for acetate transport. The source of energy required to metabolize acetate into acetyl CoA could possibly come from polyP breakdown. For acetyl CoA to be stored as PHB, a source of NADH is required. NADH can be produced anaerobically from acetyl CoA utilization by the tricarboxylic acid (TCA) cycle which functions at a reduced rate under these conditions. Under subsequent aerobic conditions (Fig. 2) bio-P bacteria now have the advantage of a reserve of PHB that can be used for energy production while any available substrate in solution is heavily competed for by other aerobic bacteria. Energy is produced aerobically from PHB via acetyl CoA metabolized in the TCA cycle to produce NADH which is oxidized at the electron-transport chain (ETC) in the presence of oxygen (or nitrate) in order to expel protons and thus establish the pmf. The pmf is used to form ATP which can be converted to polyP for storage. The availability of PHB can result in a high intracellular ATP to ADP ratio. Thus polyP can be accumulated and bio-P bacteria can grow and multiply. Therefore, the proper sequencing of environmental conditions in the waste treatment reactors results in anaerobic exposure to simple substrates such as acetate which are stored with the assistance of polyP. This is followed by aerobic conditions where polyP accumulates and phosphorus is removed from the wastewater. The proposed models were found to provide not only very satisfactory explanations for the observed phenomena related to bio-P removal, but were also found to be of a very valuable predictive power to assess the pertinence of a design or of an operational modification for upgrading a bio-P treatment plant (Comeau, 1984). 1The proton motive force (pmf) is composed of a charge gradient and of a pH gradient across the plasma (inner) membrane of bacteria which is impermeable to ions (notably to H+). The major roles of the pmf are related to energy production (e.g. ATP), substrate transport and cellular movement (Harold, 1977). The sum of the gradients of the pmf should remain constant for a bacteria.

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22

Lie, Pearl P. Y., C. Yan Cheng, and Dolores D. Mruk. "Coordinating cellular events during spermatogenesis: a biochemical model." Trends in Biochemical Sciences 34, no. 7 (July 2009): 366–73. http://dx.doi.org/10.1016/j.tibs.2009.03.005.

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23

Ortells, Marcelo O., and Georgina E. Barrantes. "Tobacco addiction: A biochemical model of nicotine dependence." Medical Hypotheses 74, no. 5 (May 2010): 884–94. http://dx.doi.org/10.1016/j.mehy.2009.11.004.

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24

Gerin, PA, PB Dengis, and PG Rouxhet. "Performance of XPS analysis of model biochemical compounds." Journal de Chimie Physique 92 (1995): 1043–65. http://dx.doi.org/10.1051/jcp/1995921043.

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25

Reid Sutton, V., Yanzhen Pan, Erica C. Davis, and William J. Craigen. "A mouse model of argininosuccinic aciduria: biochemical characterization." Molecular Genetics and Metabolism 78, no. 1 (January 2003): 11–16. http://dx.doi.org/10.1016/s1096-7192(02)00206-8.

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26

Lee, Chan-Won, and Seung-Yeon Weon. "BIOCHEMICAL MODEL AND MECHANISM FOR ACINETOBACTER NITRITE INHIBITION." Environmental Engineering Research 10, no. 1 (February 28, 2005): 22–30. http://dx.doi.org/10.4491/eer.2005.10.1.022.

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27

BUCKLEY, T. N., K. A. MOTT, and G. D. FARQUHAR. "A hydromechanical and biochemical model of stomatal conductance." Plant, Cell & Environment 26, no. 10 (September 3, 2003): 1767–85. http://dx.doi.org/10.1046/j.1365-3040.2003.01094.x.

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28

Linder, Daniel F., and Grzegorz A. Rempala. "Algebraic statistical model for biochemical network dynamics inference." Journal of Coupled Systems and Multiscale Dynamics 1, no. 4 (December 1, 2013): 468–75. http://dx.doi.org/10.1166/jcsmd.2013.1032.

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29

Christopher J. Portier, Frederick M. "COMMENTS ON A BIOCHEMICAL MODEL OF CYCLOPHOSPHAMIDE HEMATOTOXICITY." Journal of Toxicology and Environmental Health, Part A 61, no. 5-6 (November 10, 2000): 525–28. http://dx.doi.org/10.1080/00984100050166596.

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30

Rao, Shodhan, Arjan van der Schaft, Karen van Eunen, Barbara M. Bakker, and Bayu Jayawardhana. "A model reduction method for biochemical reaction networks." BMC Systems Biology 8, no. 1 (2014): 52. http://dx.doi.org/10.1186/1752-0509-8-52.

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31

Mason, Ian G., Robert I. McLachlan, and Daniel T. Gérard. "A double exponential model for biochemical oxygen demand." Bioresource Technology 97, no. 2 (January 2006): 273–82. http://dx.doi.org/10.1016/j.biortech.2005.02.042.

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32

Klika, Václav, Maria Angelés Pérez, José Manuel García-Aznar, František Maršík, and Manuel Doblaré. "A coupled mechano-biochemical model for bone adaptation." Journal of Mathematical Biology 69, no. 6-7 (November 12, 2013): 1383–429. http://dx.doi.org/10.1007/s00285-013-0736-9.

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33

Galvanauskas, V., R. Simutis, N. Volk, and A. Lübbert. "Model based design of a biochemical cultivation process." Bioprocess Engineering 18, no. 3 (1998): 227. http://dx.doi.org/10.1007/s004490050435.

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34

Schroeder, Y., J. M. Huyghe, C. C. van Donkelaar, and K. Ito. "A biochemical/biophysical 3D FE intervertebral disc model." Biomechanics and Modeling in Mechanobiology 9, no. 5 (March 13, 2010): 641–50. http://dx.doi.org/10.1007/s10237-010-0203-0.

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35

Gupta, Soma, Diya Bhaduri, Smarajit Bose, Saswati Nath, and H. N. Das. "Development of a Model with a Panel of Biochemical Parameters to Identify Major Depressive Disorder." Annals of Applied Bio-Sciences 5, no. 2 (June 2018): A49–54. http://dx.doi.org/10.21276/aabs.2105.

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36

Yang, Bin, Chuan Zhu Liao, Ming Yan Jiang, and Dong Feng Yuan. "Delayed Stochastic Biochemical Reactions Reconstruction Based on Additive Reaction Model." Advanced Materials Research 894 (February 2014): 280–83. http://dx.doi.org/10.4028/www.scientific.net/amr.894.280.

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Stochastic dynamics and delayed time of biochemical reactions play an important role in the biological networks such as gene regulatory and metabolic networks. This paper presents a new model, called additive reaction model (ARM), to capture the stochastic dynamical and delayed behavior. The new evolutionary strategy is used to search the optimal biochemical model, in which genetic algorithm (GA) and particle swarm optimization (PSO) are employed to evolve the architecture and parameters of biochemical reactions, respectively. The results reveal that the delayed biochemical reaction modeling problems could be solved effectively and efficiently using our proposed new model and new evolutionary strategy.

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37

Dulf, Eva-H., Dan C. Vodnar, Alex Danku, Cristina-I. Muresan, and Ovidiu Crisan. "Fractional-Order Models for Biochemical Processes." Fractal and Fractional 4, no. 2 (April 10, 2020): 12. http://dx.doi.org/10.3390/fractalfract4020012.

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Biochemical processes present complex mechanisms and can be described by various computational models. Complex systems present a variety of problems, especially the loss of intuitive understanding. The present work uses fractional-order calculus to obtain mathematical models for erythritol and mannitol synthesis. The obtained models are useful for both prediction and process optimization. The models present the complex behavior of the process due to the fractional order, without losing the physical meaning of gain and time constants. To validate each obtained model, the simulation results were compared with experimental data. In order to highlight the advantages of fractional-order models, comparisons with the corresponding integer-order models are presented.

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38

Gawthrop, Peter J., Joseph Cursons, and Edmund J. Crampin. "Hierarchical bond graph modelling of biochemical networks." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2184 (December 2015): 20150642. http://dx.doi.org/10.1098/rspa.2015.0642.

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The bond graph approach to modelling biochemical networks is extended to allow hierarchical construction of complex models from simpler components. This is made possible by representing the simpler components as thermodynamically open systems exchanging mass and energy via ports. A key feature of this approach is that the resultant models are robustly thermodynamically compliant: the thermodynamic compliance is not dependent on precise numerical values of parameters. Moreover, the models are reusable owing to the well-defined interface provided by the energy ports. To extract bond graph model parameters from parameters found in the literature, general and compact formulae are developed to relate free-energy constants and equilibrium constants. The existence and uniqueness of solutions is considered in terms of fundamental properties of stoichiometric matrices. The approach is illustrated by building a hierarchical bond graph model of glycogenolysis in skeletal muscle.

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39

Mohan, T. R. Krishna. "Bifurcations and Chaos in a Model Biochemical Reaction Pathway." International Journal of Bifurcation and Chaos 08, no. 02 (February 1998): 381–94. http://dx.doi.org/10.1142/s0218127498000231.

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Control mechanisms in the form of positive and negative feedback loops are responsible for the sensitivity and stability in the coherent behavior of the spatio-temporal organization in living cells. Models of these networks involving such feedback mechanisms have been shown to exhibit a rich spectrum of dynamical behaviors. A network involving both positive and negative feedbacks was earlier investigated by Sinha and Ramaswamy [1987]. We obtain a phase diagram of the possible dynamical behaviors for this model. Further, we investigate the origin and properties of the complex oscillations in the model. A simpler system is derived and shown to possess similar dynamical behaviors. Avenues for further investigation of the system with respect to relevant variations in some of the parameter values are suggested.

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40

Warne, David J., Ruth E. Baker, and Matthew J. Simpson. "Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art." Journal of The Royal Society Interface 16, no. 151 (February 2019): 20180943. http://dx.doi.org/10.1098/rsif.2018.0943.

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Stochasticity is a key characteristic of intracellular processes such as gene regulation and chemical signalling. Therefore, characterizing stochastic effects in biochemical systems is essential to understand the complex dynamics of living things. Mathematical idealizations of biochemically reacting systems must be able to capture stochastic phenomena. While robust theory exists to describe such stochastic models, the computational challenges in exploring these models can be a significant burden in practice since realistic models are analytically intractable. Determining the expected behaviour and variability of a stochastic biochemical reaction network requires many probabilistic simulations of its evolution. Using a biochemical reaction network model to assist in the interpretation of time-course data from a biological experiment is an even greater challenge due to the intractability of the likelihood function for determining observation probabilities. These computational challenges have been subjects of active research for over four decades. In this review, we present an accessible discussion of the major historical developments and state-of-the-art computational techniques relevant to simulation and inference problems for stochastic biochemical reaction network models. Detailed algorithms for particularly important methods are described and complemented with Matlab ® implementations. As a result, this review provides a practical and accessible introduction to computational methods for stochastic models within the life sciences community.

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41

Tominaga, Kazuto, Yoshikazu Suzuki, Keiji Kobayashi, Tooru Watanabe, Kazumasa Koizumi, and Koji Kishi. "Modeling Biochemical Pathways Using an Artificial Chemistry." Artificial Life 15, no. 1 (January 2009): 115–29. http://dx.doi.org/10.1162/artl.2009.15.1.15108.

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Artificial chemistries are candidates for methodologies that model and design biochemical systems. If artificial chemistries can deal with such systems in beneficial ways, they may facilitate activities in the new area of biomolecular engineering. In order to explore such possibilities, we illustrate four models of biochemical pathways described in our artificial chemistry based on string pattern matching and recombination. The modeled pathways are the replication of DNA, transcription from DNA to mRNA, translation from mRNA to protein, and the oxidation of fatty acids. The descriptions show that the present approach has good modularity and scalability that will be useful for modeling a huge network of pathways. Moreover, we give a procedure to perform reasoning in the artificial chemistry, which checks whether a specified collection of molecules can be generated in a given model, and we demonstrate that it works on a model that describes a natural biochemical pathway.

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42

Anand, M., K. Rajagopal, and K. R. Rajagopal. "A Model Incorporating Some of the Mechanical and Biochemical Factors Underlying Clot Formation and Dissolution in Flowing Blood." Journal of Theoretical Medicine 5, no. 3-4 (2003): 183–218. http://dx.doi.org/10.1080/10273660412331317415.

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Multiple interacting mechanisms control the formation and dissolution of clots to maintain blood in a state of delicate balance. In addition to a myriad of biochemical reactions, rheological factors also play a crucial role in modulating the response of blood to external stimuli. To date, a comprehensive model for clot formation and dissolution, that takes into account the biochemical, medical and rheological factors, has not been put into place, the existing models emphasizing either one or the other of the factors. In this paper, after discussing the various biochemical, physiologic and rheological factors at some length, we develop a model for clot formation and dissolution that incorporates many of the relevant crucial factors that have a bearing on the problem. The model, though just a first step towards understanding a complex phenomenon, goes further than previous models in integrating the biochemical, physiologic and rheological factors that come into play.

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43

Smith, Stephen, and Neil Dalchau. "Model reduction enables Turing instability analysis of large reaction–diffusion models." Journal of The Royal Society Interface 15, no. 140 (March 2018): 20170805. http://dx.doi.org/10.1098/rsif.2017.0805.

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Synthesizing a genetic network which generates stable Turing patterns is one of the great challenges of synthetic biology, but a significant obstacle is the disconnect between the mathematical theory and the biological reality. Current mathematical understanding of patterning is typically restricted to systems of two or three chemical species, for which equations are tractable. However, when models seek to combine descriptions of intercellular signal diffusion and intracellular biochemistry, plausible genetic networks can consist of dozens of interacting species. In this paper, we suggest a method for reducing large biochemical systems that relies on removing the non-diffusible species, leaving only the diffusibles in the model. Such model reduction enables analysis to be conducted on a smaller number of differential equations. We provide conditions to guarantee that the full system forms patterns if the reduced system does, and vice versa. We confirm our technique with three examples: the Brusselator, an example proposed by Turing, and a biochemically plausible patterning system consisting of 17 species. These examples show that our method significantly simplifies the study of pattern formation in large systems where several species can be considered immobile.

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44

Gasparyan, Manvel, Arnout Van Messem, and Shodhan Rao. "An Automated Model Reduction Method for Biochemical Reaction Networks." Symmetry 12, no. 8 (August 7, 2020): 1321. http://dx.doi.org/10.3390/sym12081321.

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We propose a new approach to the model reduction of biochemical reaction networks governed by various types of enzyme kinetics rate laws with non-autocatalytic reactions, each of which can be reversible or irreversible. This method extends the approach for model reduction previously proposed by Rao et al. which proceeds by the step-wise reduction in the number of complexes by Kron reduction of the weighted Laplacian corresponding to the complex graph of the network. The main idea in the current manuscript is based on rewriting the mathematical model of a reaction network as a model of a network consisting of linkage classes that contain more than one reaction. It is done by joining certain distinct linkage classes into a single linkage class by using the conservation laws of the network. We show that this adjustment improves the extent of applicability of the method proposed by Rao et al. We automate the entire reduction procedure using Matlab. We test our automated model reduction to two real-life reaction networks, namely, a model of neural stem cell regulation and a model of hedgehog signaling pathway. We apply our reduction approach to meaningfully reduce the number of complexes in the complex graph corresponding to these networks. When the number of species’ concentrations in the model of neural stem cell regulation is reduced by 33.33%, the difference between the dynamics of the original model and the reduced model, quantified by an error integral, is only 4.85%. Likewise, when the number of species’ concentrations is reduced by 33.33% in the model of hedgehog signaling pathway, the difference between the dynamics of the original model and the reduced model is only 6.59%.

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45

Singh, Urvasini, Vandana Sharma, Shruti Bhandari, Jayashri Vajpai, and Sunita Kumbhat. "Absorbance Based Model for Determination of Biochemical Oxygen Demand." British Journal of Applied Science & Technology 4, no. 31 (January 10, 2014): 4408–19. http://dx.doi.org/10.9734/bjast/2014/12372.

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46

Kim, Jinkyung, Younghee Lee, and Il Moon. "Automatic Verification of Biochemical Network Using Model Checking Method." Chinese Journal of Chemical Engineering 16, no. 1 (February 2008): 90–94. http://dx.doi.org/10.1016/s1004-9541(08)60043-9.

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47

Goh, S. M., M. S. M. Noorani, and I. Hashim. "Introducing variational iteration method to a biochemical reaction model." Nonlinear Analysis: Real World Applications 11, no. 4 (August 2010): 2264–72. http://dx.doi.org/10.1016/j.nonrwa.2009.06.015.

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48

Zhu, Shengdong, Yuanxin Wu, and Ziniu Yu. "An extended model for biochemical kinetic resolution of enantiomers." Process Biochemistry 41, no. 7 (July 2006): 1688–91. http://dx.doi.org/10.1016/j.procbio.2006.02.017.

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49

Dorfmueller, Helge C., Andrew T. Ferenbach, Vladimir S. Borodkin, and Daan M. F. van Aalten. "A Structural and Biochemical Model of Processive Chitin Synthesis." Journal of Biological Chemistry 289, no. 33 (June 18, 2014): 23020–28. http://dx.doi.org/10.1074/jbc.m114.563353.

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Holland, David O., Nicholas C. Krainak, and Jeffrey J. Saucerman. "Graphical Approach to Model Reduction for Nonlinear Biochemical Networks." PLoS ONE 6, no. 8 (August 25, 2011): e23795. http://dx.doi.org/10.1371/journal.pone.0023795.

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