Abstract
The signal processing through a chain of phosphorylation-dephosphorylations mediated by a pair of enzymes, Ca2+/calmodulin-dependent protein kinase II and the associated phosphatase, is formulated as a nonautonomous dynamical system in the framework of nonautocatalytic, intraholoenzyme reaction dynamics. A classification of switching characteristics of the system is made in the parameter space comprising the three controllable system parameters: an input-pulse intensity and initial concentrations of the two associated enzymes. It is found that a region of parameter space exists termed the transition zone, that exhibits a quasi-switching behaviour characterized by a signal storage time being prolonged by more than several orders of magnitude (104 times in certain cases) for the increase of two orders of magnitude in the input signal intensity. The effect of alterations of certain rate constants on the quasi-switching property is explored. It is numerically demonstrated that the Ca2+/calmodulin-dependent kinase II-related phosphatase is the most important key enzyme for regulating the signal storage time.
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Carlin RK, Grab DJ, Cohen RS, Siekevitz P (1980) Isolation and characterization of densities from various regions: enrichment of different types of postsynaptic densities. J Cell Biol 86:831–843
Carr DW, Stofko-hahn RE, Iaia DC, Fraser IDC, Cone RD, Scott JD (1992) Localization of the cAMP-dependent protein kinase to the postsynaptic densities by A-kinase anchoring proteins. J Biol Chem 267:16816–16823
Carter CA et al (1993) A divergence in the MAP kinase regulatory network defined by MEK kinase and raf. Science 260:315–319
Colbran RJ, Soderling TR (1990a) Calcium/calmodulin-dependent protein kinase II. Curr Top Cell Reg 31:181–221
Colbran RJ, Soldering TR (1990b) Calcium/calmodulin-independent autophosphorylation sites of calcium/calmodulin-dependent protein kinase II. J Biol Chem 265:11213–11219
Fersht A (1977) Enzyme structure and mechanism. Freeman, Reading
Fukunaga K, Stoppin L, Miyamato E, Muller D (1993) Longterm potentiation is associated with an increased activity of Ca2+/calmodulin-dependent protein kinase II. J Biol Chem 268:7863–7867
Griffith LC, Verselis LM, Aitken KM, Kyriacou CP, Danho W, Greenspan RJ (1993) Inhibition of calcium/calmodulin-dependent protein kinase in Drosophila disrupts behavioral plasticity. Neuron 10:501–509
Hanson PI, Schulman H (1992) Neuronal Ca2+/calmodulin-dependent protein kinases. Annu Rev Biochem 61:559–601
Hayashi K, Sakamoto N (1986) Dynamic analysis of enzyme systems. Japan Scientific Societies Press, Tokyo/Springer, Berlin Heidelberg New York
Hegde AN, Goldberg AL, Schwartz JH (1993) Regulatory subunits of cAMP-dependent protein kinases are degraded after conjugation to ubquitin: a molecular mechanism underlying long-term synaptic plasticity. Proc Natl Acad Sci USA 90:7436–7440
Ikeda A, Okuno S, Fujisawa H (1991) Studies on the generation of Ca2+/calmodulin independent activity of calmodulin-dependent protein kinase II by autophosphorylation. J Biol Chem 266:11582–11588
Kanaseki T, Ikeuchi Y, Sugiura H, Yamauchi T (1991) Structural features of Ca2+/calmodulin-dependent protein kinase II revealed by electron microscopy. J Cell Biol 115:1049–1060
Katoh T, Fujisawa H (1991a) Calmodulin-dependent protein kinase II. Kinetic studies on the interaction with substrates and calmodulin. Biochem Biophys Acta 1091:205–212
Katoh T, Fujisawa H (1991b) Autoactivation of calmodulin-dependent protein kinase II by autophosphorylation. J Biol Chem 266:3039–3044
Kuret J, Schulman H (1985) Mechanism of autophosphorylation of the multifunctional Ca2+/calmodulin-dependent protein kinase. J Biol Chem 260:6427–6433
Kwiatkowski AP, Huang CY, King MM (1990) Kinetic mechanism of the type II calmodulin-dependent protein kinase: studies of the forward and reverse reactions and observation of apparent rapidequilibrium ordered binding. Biochemistry 29:153–159
Lai Y, Nairn AC, Greengard P (1986) Autophosphorylation reversibly regulates the Ca2+/calmodulin-dependence of Ca2+/calmodulindependent protein kinase II. Proc Natl Acad Sci USA 83: 4253–4257
Lisman JE (1985) A mechanism for memory storage insensitive to molecular turnover: a bistable autophosphorylating kinase. Proc Natl Acad Sci USA 82:3055–3057
Lisman JE, Goldring MA (1988) Feasibility of long-term storage of graded information by the Ca2+/calmodulin-dependent protein kinase molecules of the postsynaptic density. Proc Natl Acad Sci USA 85:5320–5324
Lou LL, Lloyd SJ, Schulman H (1986) Activation of the multifunctional Ca2+/calmodulin-dependent protein kinase by autophosphorylation: ATP modulates production of an autonomous enzyme. Proc Natl Acad Sci USA 83:9497–9501
McGuinness TL, Lai Y, Greengard P (1985) Ca2+/calmodulin-dependent protein kinase II: isozymic forms from rat forebrain and cerebellum. J Biol Chem 260:1696–1704
Miller SG, Kennedy MB (1985) Distinct forebrain and cerebellar isozymes of type II Ca2+/calmodulin-dependent protein kinase associate differently with the postsynaptic density fraction. J Biol Chem 260:9039–9046
Miller SG, Kennedy MB (1986) Regulation of brain type II Ca2+/calmodulin-dependent protein kinase by autophosphorylation: a Ca2+-triggered molecular switch. Cell 44:861–871
Molloy SS, Kennedy MB (1991) Autophosphorylation of type II Ca2+/calmodulin-dependent protein kinase in cultures of postnatal rat hippocampal slices. Proc Natl Acad Sci USA 88:4756–4760
Murphy TH et al (1994) Differential regulation of calcium/calmodulindependent protein kinase II and p42 MAP kinase activity by synaptic transmission. J Neurosci 14:1320–1331
Nishida E, Gotoh Y (1993) The MAP kinase cascade is essential for diverse signal transduction pathways. Trends Biochem Sci 18:128–131
Patton BL, Miller SG, Kennedy MB (1990) Activation of type II calcium/calmodulin dependent protein kinase by Ca2+/calmodulin is inhibited by autophosphorylation of threonine within the calmodulin-binding domain. J Biol Chem 265:11204–11212
Pines J (1993) Cyclins and cyclin-depedent kinases: take your partners. Trends Biochem Sci 18:195–197
Sabe H, Okada M, Nakagawa H, Hanafusa H (1992) Activation of c-Src in cells bearing v-Crk and its suppression by Csk. Mol Cell Biol 12:4706–4713
Saitoh T, Schwartz JH (1985) Phosphorylation-dependent subcellular translocation of a Ca2+/calmodulin-dependent protein kinase produces an autonomous enzyme in Aplysia neurons. J Cell Biol 100:835–842
Schworer CM, Colbran RJ, Soderling TR (1986) Reversible generation f a Ca2+-independent form of Ca2+ (calmodulin)-dependent protein kinase II by an autophosphorylation mechanism. J Biol Chem 261:8581–8584
Silva AJ, Paylor R, Wehner JM, Tonegawa S (1992a) Impaired spatial learning in α-calcium-calmodulin kinase II mutant mice. Science 257:206–211
Silva AJ, Stevens CF, Tonegawa S, Wang Y (1992b) Deficient hippocampal long-term potentiation in α-calcium-calmodulin kinase II mutant mice. Science 257:201–206
Smith MK, Colbran RJ, Brickey DA, Soderling TR (1992) Functional determinants in the autoinhibitory domain of calcium/calmodulin-dependent protein kinase II. J Biol Chem 267:1761–1768
Uno I, Ueda T, Greengard P (1977) Adenosine 3′∶5′-monophosphateregulated phosphoprotein system of neuronal membranes. J Biol Chem 252:5164–5174
Waldmann R, Hanson PI, Schulman H (1990) Multifunctional Ca2+/calmodulin-independent protein kinase made Ca2+ independent for functional studies. Biochemistry 39:1679–1684
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Matsushita, T., Moriyama, S. & Fukai, T. Switching dynamics and the transient memory storage in a model enzyme network involving Ca2+/calmodulin-dependent protein kinase II in synapses. Biol. Cybern. 72, 497–509 (1995). https://doi.org/10.1007/BF00199892
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DOI: https://doi.org/10.1007/BF00199892