Maximum Entropy Production and Maximum Shannon Entropy as Germane Principles for the Evolution of Enzyme Kinetics
There have been many attempts to use optimization approaches to study the biological evolution of enzyme kinetics. Our basic assumption here is that the biological evolution of catalytic cycle fluxes between enzyme internal functional states is accompanie
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Maximum Entropy Production and Maximum Shannon Entropy as Germane Principles for the Evolution of Enzyme Kinetics ˇ upanovic´, Milan Brumen Andrej Dobovišek, Paško Z and Davor Juretic´
Abstract There have been many attempts to use optimization approaches to study the biological evolution of enzyme kinetics. Our basic assumption here is that the biological evolution of catalytic cycle fluxes between enzyme internal functional states is accompanied by increased entropy production of the fluxes and increased Shannon information entropy of the states. We use simplified models of enzyme catalytic cycles and bioenergetically important free-energy transduction cycles to examine the extent to which this assumption agrees with experimental data. We also discuss the relevance of Prigogine’s minimal entropy production theorem to biological evolution.
19.1 Introduction During biological evolution, the earliest cells already contained complex macromolecules with a remarkable capacity to speed up chemical reactions. These macromolecules are proteins, called enzymes. The kinetic and structural properties of enzymes are outcomes of evolution. Are present-day enzymes optimized by evolution, and if so, what physical or statistical principles govern their optimization? A. Dobovišek (&) M. Brumen Natural Sciences and Mathematics, Medicine, and Health Sciences, University of Maribor, Slomškov trg 15, SI-2000 Maribor, Slovenia e-mail: [email protected] P. Zˇupanovic´ D. Juretic´ Department of Physics, Faculty of Science, University of Split, Teslina 12, 21000 Split, Croatia M. Brumen Jozˇef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia
R. C. Dewar et al. (eds.), Beyond the Second Law, Understanding Complex Systems, DOI: 10.1007/978-3-642-40154-1_19, Springer-Verlag Berlin Heidelberg 2014
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These are the questions that will be considered in this chapter, within the broader picture connecting enzymes to the energy conversions that are crucial to life. As a rule, biological processes are non-linear and take place far from the equilibrium. They require an input of free energy to operate and hence do not support blockages in the hierarchy of free-energy conversion. Energy conversion (also called transduction) is thus the central concept in bioenergetics. Many freeenergy transducers are integral membrane proteins, i.e. proteins embedded in biological membranes. For example, inner mitochondrial membranes and chloroplast thylakoid membranes convert redox and light energy, respectively, into a trans-membrane electrochemical potential difference. In this way, free-energy input from photons or from carbohydrates is converted into a ‘‘user-friendly’’ form, as gradients in ion concentration and potential, which cells or organelles can then use at their convenience. This primary step in energy conversion is performed by specialized membrane proteins that act as ion pumps. The next steps in the hierarchy of free-energy transduction are also performed by integral membrane proteins, which use e
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