Mathematical Modeling of the Relation between Myosin Phosphorylation and Stress Development in Smooth Muscles

Abstract

In this paper the 4-state latch bridge model proposed by Rembold and Murphy is expanded; first by incorporation of the analytical expression of Ca2+ dependent MLCK activation from the work of Kato et al. and second, by inclusion of the myosin dephosphorylation based on the Michaelis-Menten kinetics. The analysis of the proposed model and the comparison with the original model results as well as with the experimental data is presented. The model is able to predict the steady-state isometric stress and the myosin phosphorylation in dependence on steady cytosolic [Ca2+] as well as the temporal evolution of the system in dependence on the input Ca2+ signal in the form of biphasic transient, whereby our model results are in several aspects in better agreement with experimental observations.

Role of Protein Kinase Network in Excitation-Contraction Coupling in Smooth Muscle Cell

“…Moreover, the half saturation time for achieving the final active MLCK form for [Ca 2+ ] i = 0.1 µM is 1.5 s and for [Ca 2+ ] i = 0.5 µM it is 0.5 s. These results of the eight-state model show that the processes of activation/deactivation of MLCK are not as fast as proposed by earlier models (Kato et al, 1984) and some in vitro experiments on isolated CaM and MLCK (Kasturi et al, 1993;Torok et al, 1994). Moreover, the half-saturation time of MLCK activation/deactivation is of the same order of magnitude as the typical periods of oscillatory Ca 2+ signals in smooth muscle cells (Mbikou et al, 2006;Perez et al, 2005), thus the processes of MLCK activation significantly contribute to decoding of oscillatory Ca 2+ signal into a rather steady developed force already at the cellular level (Fajmut et al, 2008;Fajmut et al, 2005b;Mbikou et al, 2011;Mbikou et al, 2006) and add a small delay in force development after [Ca 2+ ] i increase.…”

“…In our models (Fajmut et al, 2008;Fajmut et al, 2005b;Mbikou et al, 2011;Mbikou et al, 2006) we showed that the transduction of the Ca 2+ signal from its appearance in the cytosol as a time-dependent variation of concentration to the development of force in smooth muscle cells is decoded mainly by the interactions between Ca 2+ , CaM and MLCK, and is further translated to force by the balance between the phosphorylation and dephosphorylation of MLC, whereby both processes are regulated by MLCK and MLCP, respectively. The abundance of actomyosin crossbridges either phosphorylated or in the latch state is reflected in the magnitude of developed force.…”

“…In the following sections, we will present the concepts of our recent mathematical modelling of isometric contraction and force development in airway smooth muscle cells based on the 4-state latch bridge model (Hai et al, 1988a) and upgraded by the unique description of MLCK and www.intechopen.com MLCP regulatory pathways (Fajmut et al, 2008;Fajmut et al, 2005a;Fajmut et al, 2005b;Fajmut et al, 2005c;Mbikou et al, 2011;Mbikou et al, 2006).…”

“…In general, an increase in [Ca 2+ ] i is considered to initiate the binding of four Ca 2+ ions to CaM, which is finally followed by association of complex Ca 4 CaM with MLCK (Dabrowska et al, 1982;Smith et al, 2000). In this chapter we will present three different approaches to deal with interactions between Ca 2+ , CaM and MLCK: a three-state model proposed by Kato et al in 1984(Kato et al, 1984, our eight-state model proposed by Fajmut et al in 2005(Fajmut et al, 2005b) and a semi-theoretical approach proposed by Rembold andMurphy in 1990 (Rembold et al, 1990). The kinetic scheme of a three-state model is presented in Figure 4.…”

“…In our first models (Fajmut et al, 2008;Fajmut et al, 2005b;Mbikou et al, 2006) we treated dephosphorylation process with two parallel enzymatic reactions of Michaelis-Menten type with AMP and MP as the substrates for MLCP and with MLCP·MP and MLCP·AMP as the intermediate complexes. All these models considered constant total amount of the enzyme and one Ca 2+ independent catalytic activity of MLCP.…”