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Nonlinear behavior of kinetics of calmodulin-calcium complexes

Experimental data obtained in last decade indicate that calcium concentration in postsynaptic intracellular solution can trigger long-term plasticity [1]. According to the "calcium control hypothesis", the low concentration of intracellular calcium [Ca2+]i does not change synaptic conductivity, whereas middle and high concentrations induce LTD and LTP respectively. Such dependence requires the sensitivity of synaptic modification to be nonlinearly related to peak calcium concentration [2]. However, the calcium ions penetrated into cell are mostly bound by calmodulin (CaM), a small (16.8 kDa) ubiquitous Ca2+ binding protein. A CaM molecule can bind four calcium ions by two sites in C-lobe and N-lobe [3, 4]. Stopped flow fluorescence studies [5, 6] showed that these two sites are quasi independent and have different association/dissociation reaction constants [3, 4]. Here, the minimalistic single compartment model of chemical kinetics of eight calmodulin-calcium complexes is presented.

The model is based on assumption that only double and single component reactions are going in system. The full graph of chemical reactions contains 24 association/dissociation reactions and is converted into system of nine ordinary differential equations (ODE). Free calcium concentration is presented as ODE for open system including first order, not zero intracellular calcium extrusion, square pulse calcium influx and all association and dissociation reactions with calmodulin. All simulations are performed using the interactive differential equation simulation package XPP [7]. The differential equations were integrated by fourth-order Runge-Kutta method with adaptive step built into XPP.

The simulation results show that each complex has unique dynamics. The amplitudes and moments of maximum concentrations and decay time constants vary for different complexes, and the curve of peak complex concentration to calcium injection obeyed the Michaelis-Menten-Henri law with different power coefficients. The time courses of complexes concentrations allow to separate complexes into five groups according to moment of maximal amplitude and decay time constant: early maximum moment and fast or middle decaying groups, belated maximum and fast or middle decaying groups and farther-slow group. This division and nonlinearity of peak concentrations show that different calmodulin-calcium complexes may be used as basic components for reconstruction of dependency curves of synaptic weight from free calcium concentration [2].


  1. Yang SN, Tang YG, Zucker RS: Selective induction of ltp and ltd by postsynaptic [Ca2+]i elevation. J Neurophysiol. 1999, 81: 781-787.

    CAS  PubMed  Google Scholar 

  2. Mizuno T, Kanazawa I, Sakurai M: Differential induction of LTP and LTD is not determined solely by instantaneous calcium concentration: an essential involvement of a temporal factor. J Neurosci. 2001, 14 (4): 701-708.

    CAS  Google Scholar 

  3. Keller DX, Franks KM, Bartol TM, Sejnowski TJ: Calmodulin activation by calcium transients in the postsynaptic density of dendritic spines. PLoS ONE. 2008, 4: e2045-10.1371/journal.pone.0002045.

    Article  Google Scholar 

  4. Kubota Y, Putkey JA, Shouval HZ, Waxham MN: IQ-motif proteins influence intracellular free Ca2+ in hippocampal neurons through their interactions with calmodulin. J Neurophysiol. 2008, 99: 264-276. 10.1152/jn.00876.2007.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  5. Putkey JA, Kleerekoper Q, Gaertner TR, Waxham MN: A new role for IQ motif protein in regulating calmodulin function. J Biol Chem. 2003, 278: 49667-49670. 10.1074/jbc.C300372200.

    Article  CAS  PubMed  Google Scholar 

  6. Martin SR, Teleman AA, Bayley PM, Drakenberg T, Forsen S: Kinetics of calcium dissociation from calmodulin and its tryptic fragments. A stopped-flow fluorescence study using Quin 2 reveals a two-domain structure. J Biochem. 1985, 151: 543-550.

    CAS  Google Scholar 

  7. Ermentrout B: Simulating, Analyzing, and Animating Dynamical Systems. A Guide to XPPAUT for Researchers and Students. 2002, Philadelphia, PA: SIAM

    Book  Google Scholar 

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Correspondence to Ruben A Tikidji-Hamburyan.

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Open Access This article is published under license to BioMed Central Ltd. This is an Open Access article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Tikidji-Hamburyan, R.A. Nonlinear behavior of kinetics of calmodulin-calcium complexes. BMC Neurosci 10 (Suppl 1), P223 (2009).

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