Input-output relations in biological systems: measurement, information and the Hill equation

Biology Direct

Steven A Frank¹ 

[1] Department of Ecology and Evolutionary Biology, University of California, Irvine, CA, 92697–2525, USA

关键词: Signal processing;    Natural selection;    Information theory;    Measurement theory;    Cellular sensors;    Cellular biochemistry;    Biological design;   

Others  :  793104
DOI  :  10.1186/1745-6150-8-31

 received in 2013-10-14, accepted in 2013-11-27,  发布年份 2013

【 摘 要 】

Biological systems produce outputs in response to variable inputs. Input-output relations tend to follow a few regular patterns. For example, many chemical processes follow the S-shaped Hill equation relation between input concentrations and output concentrations. That Hill equation pattern contradicts the fundamental Michaelis-Menten theory of enzyme kinetics. I use the discrepancy between the expected Michaelis-Menten process of enzyme kinetics and the widely observed Hill equation pattern of biological systems to explore the general properties of biological input-output relations. I start with the various processes that could explain the discrepancy between basic chemistry and biological pattern. I then expand the analysis to consider broader aspects that shape biological input-output relations. Key aspects include the input-output processing by component subsystems and how those components combine to determine the system’s overall input-output relations. That aggregate structure often imposes strong regularity on underlying disorder. Aggregation imposes order by dissipating information as it flows through the components of a system. The dissipation of information may be evaluated by the analysis of measurement and precision, explaining why certain common scaling patterns arise so frequently in input-output relations. I discuss how aggregation, measurement and scale provide a framework for understanding the relations between pattern and process. The regularity imposed by those broader structural aspects sets the contours of variation in biology. Thus, biological design will also tend to follow those contours. Natural selection may act primarily to modulate system properties within those broad constraints.

Reviewers

This article was reviewed by Eugene Koonin, Georg Luebeck and Sergei Maslov.

【 授权许可】

   
2013 Frank; licensee BioMed Central Ltd.

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【 参考文献 】

• [1]Tyson JJ, Chen KC, Novak B: Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell. Curr Opin Cell Biol 2003, 15:221-231.
• [2]Zhang Q, Bhattacharya S, Andersen ME: Ultrasensitive response motifs: basic amplifiers in molecular signalling networks. Open Biol 2013, 3:130031. doi:10.1098/rsob.130031
• [3]Frank SA: The common patterns of nature. J Evol Biol 2009, 22:1563-1585.
• [4]Kauffman SA: The Origins of Order. Oxford: Oxford University Press; 1993.
• [5]Hand DJ: Measurement Theory and Practice. London: Arnold; 2004.
• [6]Stevens SS: On the psychophysical law. Psychol Rev 1957, 64:153-181.
• [7]Cornish-Bowden A: Fundamentals of Enzyme Kinetics. Hoboken, NJ: Wiley-Blackwell; 2012.
• [8]Gescheider GA: Psychophysics: The Fundamentals. Mahwah, NJ: Lawrence Erlbaum Associates; 1997.
• [9]Krantz DH, Luce RD, Suppes P, Tversky A: Foundations of Measurement: Volume 1: Additive and Polynomial Representations. New York: Dover; 2006.
• [10]Krantz DH, Luce RD, Suppes P, Tversky A: Foundations of Measurement. Volume II: Geometrical, Threshold, and Probabilistic Representations. New York: Dover; 2006.
• [11]Suppes P, Krantz DH, Luce RD, Tversky A: Foundations of Measurement. Volume III: Representation, Axiomatization, and Invariance. New York: Dover; 2006.
• [12]Rabinovich SG: Measurement Errors and Uncertainty: Theory and Practice. New York: Springer; 2005.
• [13]Sarpeshkar R: Ultra Low Power Bioelectronics. Cambridge, UK: Cambridge University Press; 2010.
• [14]Goldbeter A, Koshland DE: An amplified sensitivity arising from covalent modification in biological systems. Proc Nat Acad Sci USA 1981, 78:6840-6844.
• [15]Kim SY, Ferrell JE: Substrate competition as a source of ultrasensitivity in the inactivation of Wee1. Cell 2007, 128:1133-1145.
• [16]Ferrell JE: Signaling motifs and Weber’s law. Mol Cell 2009, 36:724-727.
• [17]Cohen-Saidon C, Cohen AA, Sigal A, Liron Y, Alon U: Dynamics and variability of ERK2 response to EGF in individual living cells. Mol Cell 2009, 36:885-893.
• [18]Goentoro L, Kirschner MW: Evidence that fold-change, and not absolute level, of β-catenin dictates Wnt signaling. Mol Cell 2009, 36:872-884.
• [19]Goentoro L, Shoval O, Kirschner MW, Alon U: The incoherent feedforward loop can provide fold-change detection in gene regulation. Mol Cell 2009, 36:894-899.
• [20]Alon U: An Introduction to Systems Biology: Design Principles of Biological Circuits. Boca Raton, Florida: CRC press; 2007.
• [21]DeLean A, Munson P, Rodbard D: Simultaneous analysis of families of sigmoidal curves: application to bioassay, radioligand assay, and physiological dose-response curves. Am J Physiol-Endocrinol Metab 1978, 235:97-102.
• [22]Weiss JN: The Hill equation revisited: uses and misuses. FASEB J 1997, 11:835-841.
• [23]Rang HP: The receptor concept: pharmacology’s big idea. Br J Pharmacol 2006, 147:9-16.
• [24]Bindslev N: Drug-Acceptor Interactions, Chapter 10: Hill in Hell. Jarfalla, Sweden: Co-Action Publishing; 2008. doi:10.3402/bindslev.2008.14
• [25]Walker JS, Li X, Buttrick PM: Analysing force–pCa curves. J Muscle Res Cell Motil 2010, 31:59-69.
• [26]Hoffman A, Goldberg A: The relationship between receptor-effector unit heterogeneity and the shape of the concentration-effect profile: pharmacodynamic implications. J Pharmacokinet Biopharm 1994, 22:449-468.
• [27]Getz WM, Lansky P: Receptor dissociation constants and the information entropy of membrane coding ligand concentration. Chem Senses 2001, 26:95-104.
• [28]Kolch W, Calder M, Gilbert D: When kinases meet mathematics: the systems biology of MAPK, signalling. FEBS Lett 2005, 579:1891-1895.
• [29]Tkačik G, Walczak AM: Information transmission in genetic regulatory networks: a review. J Phys: Condens Matter 2011, 23:153102.
• [30]Marzen S, Garcia HG, Phillips R: Statistical mechanics of Monod-Wyman-Changeux (MWC) models. J Mol Biol 2013, 425:1433-1460.
• [31]Savageau MA: Michaelis-Menten mechanism reconsidered: implications of fractal kinetics. J Theor Biol 1995, 176:115-124.
• [32]Savageau MA: Development of fractal kinetic theory for enzyme-catalysed reactions and implications for the design of biochemical pathways. Biosystems 1998, 47:9-36.
• [33]Andrews SS, Bray D: Stochastic simulation of chemical reactions with spatial resolution and single molecule detail. Phys Biol 2004, 1:137-151.
• [34]ben-Avraham D, Havlin S: Diffusion and Reactions in Fractals and Disordered Systems. Cambridge, UK: Cambridge Univerity Press; 2000.
• [35]Schnell S, Turner TE: Reaction kinetics in intracellular environments with macromolecular crowding: simulations and rate laws. Prog Biophys Mol Biol 2004, 85:235-260.
• [36]Dieckmann U, Law R, Metz JAJ: The Geometry of Ecological Interactions: Simplifying Spatial Complexity. Cambridge, UK: Cambridge University Press; 2000.
• [37]Ellner SP: Pair approximation for lattice models with multiple interaction scales. J Theor Biol 2001, 210:435-447.
• [38]Marro J, Dickman R: Nonequilibrium Phase Transitions in Lattice Models. Cambridge, UK: Cambridge University Press; 2005.
• [39]Kholodenko BN, Hoek JB, Westerhoff HV, Brown GC: Quantification of information transfer via cellular signal transduction pathways. FEBS Lett 1997, 414:430-434.
• [40]Jaynes ET: Probability Theory: The Logic of Science. New York: Cambridge University Press; 2003.
• [41]Frank SA, Smith E: Measurement invariance, entropy, and probability. Entropy 2010, 12:289-303.
• [42]Frank SA, Smith E: A simple derivation and classification of common probability distributions based on information symmetry and measurement scale. J Evol Biol 2011, 24:469-484.
• [43]Das S, Vikalo H, Hassibi A: On scaling laws of biosensors: a stochastic approach. J Appl Phys 2009, 105:102021.
• [44]Andrews SS, Addy NJ, Brent R, Arkin AP: Detailed simulations of cell biology with Smoldyn 2.1. PLoS Comput Biol 2010, 6:1000705.
• [45]Blühgen N, Herzel H: How robust are switches in intracellular signaling cascades? J Theor Biol 2003, 225:293-300.
• [46]Aparicio FM, Estrada J: Empirical distributions of stock returns: European securities markets, 1990-95. Eur J Finance 2001, 7(1):1-21.
• [47]Dragulescu AA, Yakovenko VM: Exponential and power-law probability distributions of wealth and income in the United Kingdom and the United States. Phys A 2001, 299:213-221.
• [48]Feynman RP: The Character of Physical Law. Cambridge, MA: MIT Press; 1967.
• [49]Anderson P: More is different. Science 1972, 177:393-396.
• [50]Weyl H: Symmetry. Princeton, NJ: Princeton University Press; 1983.
• [51]Frank SA: Measurement scale in maximum entropy models of species abundance. J Evol Biol 2011, 24:485-496.