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Review
. 2010 Sep 27;11(9):3540-99.
doi: 10.3390/ijms11093540.

Quantitative Analysis of Cellular Metabolic Dissipative, Self-Organized Structures

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Free PMC article
Review

Quantitative Analysis of Cellular Metabolic Dissipative, Self-Organized Structures

Ildefonso Martínez de la Fuente. Int J Mol Sci. .
Free PMC article

Abstract

One of the most important goals of the postgenomic era is understanding the metabolic dynamic processes and the functional structures generated by them. Extensive studies during the last three decades have shown that the dissipative self-organization of the functional enzymatic associations, the catalytic reactions produced during the metabolite channeling, the microcompartmentalization of these metabolic processes and the emergence of dissipative networks are the fundamental elements of the dynamical organization of cell metabolism. Here we present an overview of how mathematical models can be used to address the properties of dissipative metabolic structures at different organizational levels, both for individual enzymatic associations and for enzymatic networks. Recent analyses performed with dissipative metabolic networks have shown that unicellular organisms display a singular global enzymatic structure common to all living cellular organisms, which seems to be an intrinsic property of the functional metabolism as a whole. Mathematical models firmly based on experiments and their corresponding computational approaches are needed to fully grasp the molecular mechanisms of metabolic dynamical processes. They are necessary to enable the quantitative and qualitative analysis of the cellular catalytic reactions and also to help comprehend the conditions under which the structural dynamical phenomena and biological rhythms arise. Understanding the molecular mechanisms responsible for the metabolic dissipative structures is crucial for unraveling the dynamics of cellular life.

Keywords: dissipative structures; metabolic dynamics; metabolic self-organization; quantitative biology; systems biology.

Figures

Figure 1
Figure 1
Diversity dynamic behaviors emerge in the simple dissipative metabolic subsystem. (a) Periodic pattern. (b) Hard excitation, the integral solutions depending on the initial conditions settle on two regimens: a stable steady state and a stable periodic oscillation. (c) Chaotic oscillations. (d) Complex periodic behaviors. The substrate concentration α is represented as a function of the time in seconds. Reproduced with permission from PNAS [198].
Figure 2
Figure 2
Molecular processes for M-phase control in eukaryotic cells. (a) Cdc2 protein kinase monomers combine with cyclin subunits to form dimers. Subunits of kinase Cdc2 can be phosphorylated and desphosphorylated at an activatory threonine (Thr) residue or/and an inhibitory tyrosine (Tyr) residue. All cyclin subunits can be degraded by an ubiquitin pathway. (b) Active MPF stimulates its own production, which is positive feedback. (c) But active MPF also stimulates the destruction of cyclin, which is negative feedback. Reproduced with permission from the Company of Biologistd Ltd. [218].
Figure 3
Figure 3
Quantitative analysis of the M-phase control system showing spontaneous periodic oscillations in the metabolic intermediaries. The total cyclin concentrations (blue), active form of MPF (red), tyrosine-phosphorylated dimers, YP, (green) and total phosphorylated cdc2 monomers (orange) are represented as a function of the time in minute. The bar graphs indicate the periods during which the active forms exceed 50% of the total amount. Reproduced with permission from the Company of Biologists Ltd. [218].
Figure 4
Figure 4
A limit cycle attractor governs the cell cycle. The cell cycle is controlled by a dynamical structure called “limit cycle” which is a closed orbit corresponding to the oscillations with a period of 80 minutes. The numbers along the limit cycle represent time in minutes after exit from mitosis. Reproduced with permission from the Company of Biologists Ltd. [218].
Figure 5
Figure 5
Numerical oscillatory responses of glycolysis under periodic substrate input flux showing a transition sequence to chaos through quasiperiodicity. In the first column are represented the corresponding attractors (projections in two dimensions for the α concentration, x-axis, and the β concentrations, y-axis), power spectra in the second column and Poincaré sections in the α, β plane (third column). Reproduced with permission from Elsevier [283].
Figure 6
Figure 6
Quasiperiodicity route to chaos under constant substrate input flux. Evolution of (a) periodic oscillation, (bc) quasiperiodic motion, (d) complex quasiperiodic oscillations and (e) chaotic responses. (The β concentrations are represented as a function of time). Also shown are the corresponding power spectra (second column) and Poincaré sections (α, β plane). Reproduced with permission from ScienceDirect [281].
Figure 7
Figure 7
Molecular model for circadian oscillations during genetic expression based on negative self-regulation of the PER gene by its protein product PER. The model incorporates gene transcription into PER mRNA, transport of PER mRNA (MP) into the cytosol as well as mRNA degradation, synthesis of the PER protein at a rate proportional to the PER mRNA level, reversible phosphorylation and degradation of PER (P0, P1 and P2), as well as transport of PER into the nucleus (PN) where it represses the transcription of the PER gene. Reproduced with permission from PNAS [342].
Figure 8
Figure 8
Effect of molecular noise on circadian oscillations during genetic expression. (a) Periodic behaviors obtained by numerical integration of the deterministic model in absence of noise. (Left) The oscillatory patterns correspond to mRNA (MP), nuclear protein (PN) and total clock protein (Pt). (Right) Limit cycle obtained as a projection onto the PN – MP phase plane. (b) Robust circadian oscillations with a period of 24.4 h produced by the metabolic model in presence of noise. (Left) The number of mRNA molecules oscillates between a few and 1,000, whereas nuclear and total clock proteins oscillate in the ranges of 200–4,000 and 800–8,000, respectively. (Right) Stochastic simulations of the model yield oscillations that correspond, in the phase plane (PN – MP) to the evolution of a noisy limit cycle. Reproduced with permission from PNAS [342].
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References

    1. Jeong H, Tombor B, Albert R, Oltvai ZN, Barabási AL. The large-scale organization of metabolic networks. Nature. 2000;407:651–654. - PubMed
    1. Sear RP. The cytoplasm of living cells: a functional mixture of thousands of components. J. Phys. Condens. Matter. 2005;17:S3587–S3595.
    1. Goldbeter A. Biological rhythms as temporal dissipative structures. Adv. Chem. Phys. 2007;135:253–295.
    1. Nicolis G, Prigogine I. From dissipative structures to order through fluctuations. Wiley; New York, NY, USA: 1977. Self-organization in nonequilibrium systems.
    1. Gavin AC, Bosche M, Krause R, Grandi P, Marzioch M, Bauer A, Schultz J, Rick JM, Michon AM, Cruciat CM, Remor M, Höfert C, Schelder M, Brajenovic M, Ruffner H, Merino A, Klein K, Hudak M, Dickson D, Rudi T, Gnau V, Bauch A, Bastuck S, Huhse B, Leutwein C, Heurtier MA, Copley R, Edelmann A, Querfurth E, Rybin V, Drewes G, Raida M, Bouwmeester T, Bork P, Seraphin B, Kuster B, Neubauer G, Superti-Furga G. Functional organization of the yeast proteome by systematic analysis of protein complexes. Nature. 2002;415:141–147. - PubMed
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