Analysis of the modal hypothesis of Ca 2+ -dependent inactivation of L-type Ca 2+ channels Nick I. Markevich a,b, * , Oleg Y. Pimenov a , Yury M. Kokoz a a Institute of Theoretical and Experimental Biophysics, Russian Academy of Sciences, Pushchino, Moscow 142290, Russia b Department of Pathology, Anatomy and Cell Biology, Thomas Jefferson University, Room 233, JAH, 1020 Locust St., Philadelphia, PA 19107, USA Received 25 April 2005; received in revised form 28 April 2005; accepted 28 April 2005 Available online 4 June 2005 Abstract A kinetic model of Ca 2+ -dependent inactivation (CDI) of L-type Ca 2+ channels was developed. The model is based on the hypothesis that postulates the existence of four short-lived modes with lifetimes of a few hundreds of milliseconds. Our findings suggest that the transitions between the modes is primarily determined by the binding of Ca 2+ to two intracellular allosteric sites located in different motifs of the CI region, which have greatly differing binding rates for Ca 2+ (different k on ). The slow-binding site is controlled by local Ca 2+ near a single open channel that is consistent with the ‘‘domain’’ CDI model, and Ca 2+ binding to the fast-binding site(s) depends on Ca 2+ arising from distant sources that is consistent with the ‘‘shell’’ CDI model. The model helps to explain numerous experimental findings that are poorly understood so far. D 2005 Elsevier B.V. All rights reserved. Keywords: Ca 2+ -dependent inactivation; Gating mode; Mathematical model 1. Introduction High-threshold voltage-dependent L-type Ca 2+ channels play a key role in the contraction of smooth and cardiac muscles, neuroendocrine secretion, and many other vital functions of the organisms. They are regulated by a great number of factors of different physicochemical nature [1,2]. Among the most important are hormones and neurotrans- mitters, which bring about a relatively slow regulation (up to a few tens of seconds), and membrane potential (V) and intracellular calcium, which accomplish a fast regulation (of the order of hundreds of milliseconds). The slow regulation is mainly related to chemical modification, including (de)phosphorylation of channels, which is associated with cascades of enzymes whose activity is modulated by hormones and neurotransmitters [1]. The fast regulation is determined by voltage- and Ca 2+ -dependent conformational transitions in the channel. The L-type Ca 2+ current that develops in response to membrane depolarization can be divided into the following components: voltage-dependent activation, Ca 2+ -dependent inactivation (CDI), voltage-dependent inactivation (VDI), and residual current [1,3]. The inactivation of the channel with time t is usually described by the double-exponential function I (t )= A Ca I exp( t /s Ca )+ A V Iexp( t /s V )+ I 0 , where A Ca and A V are the amplitudes, s Ca and s V are the time constants of CDI and VDI, respectively, and I 0 is the residual current. Despite the simple kinetics of the L-type Ca 2+ current and abundant experimental evidence that has accumulated over a period of more than 25 years, both the molecular and kinetic mechanisms of regulation of the current are not yet completely understood to explain the dependencies of amplitudes and time constants of different inactivation components on V and intracellular Ca 2+ concentration. In the last decade, considerable progress has been made towards understanding the molecular mechanism of CDI. 0301-4622/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.bpc.2005.04.017 * Corresponding author. Department of Pathology, Anatomy and Cell Biology, Thomas Jefferson University, Room 233, JAH, 1020 Locust St., Philadelphia, PA 19107, USA. Tel.: +1 215 503 4794; fax: +1 215 923 2218. E-mail address: Nikolai.Markevitch@jefferson.edu (N.I. Markevich). Biophysical Chemistry 117 (2005) 173 – 190 http://www.elsevier.com/locate/biophyschem