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Computational singular perturbation analysis of brain lactate metabolism


Autoři: Dimitris G. Patsatzis aff001;  Efstathios-Al. Tingas aff001;  Dimitris A. Goussis aff004;  S. Mani Sarathy aff001
Působiště autorů: King Abdullah University of Science and Technology (KAUST), Clean Combustion Research Center (CCRC), Thuwal, Saudi Arabia aff001;  Department of Mechanics, School of Applied Mathematics and Physical Sciences, National Technical University of Athens (NTUA), Athens, Greece aff002;  Perth College, University of the Highlands and Islands, Crieff Rd, Perth PH1 2NX, United Kingdom aff003;  Department of Mechanical Engineering, Khalifa University of Science, Technology and Research (KUSTAR), Abu Dhabi, United Arab Emirates aff004
Vyšlo v časopise: PLoS ONE 14(12)
Kategorie: Research Article
doi: https://doi.org/10.1371/journal.pone.0226094

Souhrn

Lactate in the brain is considered an important fuel and signalling molecule for neuronal activity, especially during neuronal activation. Whether lactate is shuttled from astrocytes to neurons or from neurons to astrocytes leads to the contradictory Astrocyte to Neuron Lactate Shuttle (ANLS) or Neuron to Astrocyte Lactate Shuttle (NALS) hypotheses, both of which are supported by extensive, but indirect, experimental evidence. This work explores the conditions favouring development of ANLS or NALS phenomenon on the basis of a model that can simulate both by employing the two parameter sets proposed by Simpson et al. (J Cereb. Blood Flow Metab., 27:1766, 2007) and Mangia et al. (J of Neurochemistry, 109:55, 2009). As most mathematical models governing brain metabolism processes, this model is multi-scale in character due to the wide range of time scales characterizing its dynamics. Therefore, we utilize the Computational Singular Perturbation (CSP) algorithm, which has been used extensively in multi-scale systems of reactive flows and biological systems, to identify components of the system that (i) generate the characteristic time scale and the fast/slow dynamics, (ii) participate to the expressions that approximate the surfaces of equilibria that develop in phase space and (iii) control the evolution of the process within the established surfaces of equilibria. It is shown that a decisive factor on whether the ANLS or NALS configuration will develop during neuronal activation is whether the lactate transport between astrocytes and interstitium contributes to the fast dynamics or not. When it does, lactate is mainly generated in astrocytes and the ANLS hypothesis is realised, while when it doesn’t, lactate is mainly generated in neurons and the NALS hypothesis is realised. This scenario was tested in exercise conditions.

Klíčová slova:

Algorithms – Astrocytes – Evolutionary rate – Glucose – Glucose metabolism – Neurons – Reactants – Reaction dynamics


Zdroje

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99. Lam S, Goussis D. The CSP method for simplifying kinetics. International Journal of Chemical Kinetics. 1994;26(4):461–486. doi: 10.1002/kin.550260408

100. Lam S, Goussis D. Understanding complex chemical kinetics with computational singular perturbation. In: Symposium (International) on Combustion. 1989;22:931–941.

101. Hadjinicolaou M, Goussis DA. Asymptotic solution of stiff PDEs with the CSP method: the reaction diffusion equation. SIAM J. Sci. Comp., 1999;20:781–819. doi: 10.1137/S1064827596303995

102. Prager J, Najm HN, Valorani M, Goussis DA. Structure of n-heptane/air triple flames in partially-premixed mixing layers. Combustion and Flame. 2011;158(11):2128–44. doi: 10.1016/j.combustflame.2011.03.017

103. Goussis DA, Valorani M. An efficient iterative algorithm for the approximation of the fast and slow dynamics of stiff systems. Journal of Computational Physics. 2006;214(1):316–46. doi: 10.1016/j.jcp.2005.09.019

104. Neophytou MK, Goussis DA, Mastorakos E, Britter RE. The conceptual development of a simple scale-adaptive reactive pollutant dispersion model. Atmospheric Environment. 2005;39(15):2787–94. doi: 10.1016/j.atmosenv.2004.12.025

105. Kourdis PD, Goussis DA. Glycolysis in saccharomyces cerevisiae: algorithmic exploration of robustness and origin of oscillations. Mathematical biosciences. 2013;243(2):190–214. doi: 10.1016/j.mbs.2013.03.002 23517854

106. Surovtsova I, Simus N, Hübner K, Sahle S, Kummer U. Simplification of biochemical models: a general approach based on the analysis of the impact of individual species and reactions on the systems dynamics. BMC systems biology. 2012;6(1):14. doi: 10.1186/1752-0509-6-14 22390191

107. Samant A, Ogunnaike BA, Vlachos DG. A hybrid multiscale Monte Carlo algorithm (HyMSMC) to cope with disparity in time scales and species populations in intracellular networks. BMC bioinformatics. 2007;8(1):175. doi: 10.1186/1471-2105-8-175 17524148

108. Patsatzis DG, Goussis DA. A new Michaelis-Menten equation valid everywhere multi-scale dynamics prevails. Mathematical biosciences. 2019;315:108220. doi: 10.1016/j.mbs.2019.108220 31255632

109. Patsatzis DG, Maris DT, Goussis DA. Asymptotic analysis of a target-mediated drug disposition model: algorithmic and traditional approaches. Bulletin of mathematical biology, 2016;78(6):1121–1161. doi: 10.1007/s11538-016-0176-y 27271122

110. Michalaki LI, Goussis DA. Asymptotic analysis of a TMDD model: when a reaction contributes to the destruction of its product. Journal of mathematical biology. 2018:1–35.

111. Fenichel N. Geometric singular perturbation theory for ordinary differential equations. Journal of differential equations. 1979;31(1):53–98. doi: 10.1016/0022-0396(79)90152-9

112. Kaper TJ. An introduction to geometric methods and dynamical systems theory for singular perturbation problems. In: Cronin J, Robert J, O’Malley E (eds) Analyzing multiscale phenomena using singular perturbation methods. Proceedings of symposia in applied mathematics. 1999;56(1):85–131.

113. Kuehn C. Multiple time scale dynamics. Springer; 2015.

114. Zagaris A, Kaper HG, Kaper TJ. Analysis of the computational singular perturbation reduction method for chemical kinetics. Journal of Nonlinear Science. 2004;14(1):59–91. doi: 10.1007/s00332-003-0582-9

115. Zagaris A, Kaper HG, Kaper TJ. Fast and slow dynamics for the computational singular perturbation method. Multiscale Modeling & Simulation. 2004;2(4):613–638. doi: 10.1137/040603577

116. Zagaris A, Kaper HG, Kaper TJ. Two perspectives on reduction of ordinary differential equations. Mathematische Nachrichten. 2005;278(12-13):1629–1642. doi: 10.1002/mana.200410328

117. Kaper HG, Kaper TJ, Zagaris A. Geometry of the computational singular perturbation method. Mathematical modelling of natural phenomena. 2015;10(3):16–30. doi: 10.1051/mmnp/201510303

118. Hek G. Geometric singular perturbation theory in biological practice. Journal of mathematical biology. 2010;60(3):347–386. doi: 10.1007/s00285-009-0266-7 19347340

119. Auger P, de La Parra RB, Poggiale J-C, Sánchez E, Sanz L. Aggregation methods in dynamical systems and applications in population and community dynamics. Physics of Life Reviews. 2008;5(2):79–105. doi: 10.1016/j.plrev.2008.02.001

120. Kosiuk I, Szmolyan P. Geometric analysis of the Goldbeter minimal model for the embryonic cell cycle. Journal of mathematical biology. 2016;72(5):1337–1368. doi: 10.1007/s00285-015-0905-0 26100376

121. Popović N, Marr C, Swain PS. A geometric analysis of fast-slow models for stochastic gene expression. Journal of mathematical biology. 2016;72(1-2):87–122. doi: 10.1007/s00285-015-0876-1 25833185

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125. Lam S, Goussis D. Conventional asymptotics and computational singular perturbation for simplified kinetics modelling. In: Reduced kinetic mechanisms and asymptotic approximations for methane-air flames; 1991. p. 227–242.

126. Tingas EA, Kyritsis DC, Goussis DA. Ignition delay control of DME/air and EtOH/air homogeneous autoignition with the use of various additives. Fuel. 2016;169:15–24. doi: 10.1016/j.fuel.2015.11.081

127. Goussis DA, Najm HN. Model reduction and physical understanding of slowly oscillating processes: the circadian cycle. Multiscale Modeling & Simulation. 2006;5(4):1297–1332. doi: 10.1137/060649768

128. Valorani M, Najm HN, Goussis DA. CSP analysis of a transient flame-vortex interaction: time scales and manifolds. Combustion and Flame. 2003;134(1):35–53. doi: 10.1016/S0010-2180(03)00067-1

129. Goussis DA, Skevis G. Nitrogen chemistry controlling steps in methane-air premixed flames. In: Bathe KJ, editor. Computational Fluid and Solid Mechanics. Elsevier, Amsterdam; 2005. p. 650–653.

130. Diamantis DJ, Mastorakos E, Goussis DA. H2/air autoignition: The nature and interaction of the developing explosive modes. Combustion Theory and Modelling. 2015;19(3):382–433. doi: 10.1080/13647830.2015.1027273

131. Goussis D, Lam S. A study of homogeneous methanol oxidation kinetics using CSP. In: Symposium (International) on Combustion. vol. 24. Elsevier; 1992. p. 113–120.

132. Goussis DA. Quasi steady state and partial equilibrium approximations: their relation and their validity. Combustion Theory and Modelling. 2012;16(5):869–926. doi: 10.1080/13647830.2012.680502

133. Kourdis PD, Palasantza AG, Goussis DA. Algorithmic asymptotic analysis of the NF-κB signaling system. Computers & Mathematics with Applications. 2013;65(10):1516–1534. doi: 10.1016/j.camwa.2012.11.004

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