Comparing models with one versus multiple myosin-binding sites per actin target zone: The power of simplicity

Abstract

Mechanokinetic statistical models describe the mechanisms of muscle contraction on the basis of the average behavior of a large ensemble of actin–myosin motors. Such models often assume that myosin II motor domains bind to regularly spaced, discrete target zones along the actin-based thin filaments and develop force in a series of strain-dependent transitions under the turnover of ATP. The simplest models assume that there is just one myosin-binding site per target zone and a uniform spatial distribution of the myosin motor domains in relation to each site. However, most of the recently developed models assume three myosin-binding sites per target zone, and some models include a spatially explicit 3-D treatment of the myofilament lattice and thereby of the geometry of the actin–myosin contact points. Here, I show that the predictions for steady-state contractile behavior of muscle are very similar whether one or three myosin-binding sites per target zone is assumed, provided that the model responses are appropriately scaled to the number of sites. Comparison of the model predictions for isometrically contracting mammalian muscle cells suggests that each target zone contains three or more myosin-binding sites. Finally, I discuss the strengths and weaknesses of one-site spatially inexplicit models in relation to three-site models, including those that take into account the detailed 3-D geometry of the myofilament lattice. The results of this study suggest that single-site models, with reduced computational cost compared with multisite models, are useful for several purposes, e.g., facilitated molecular mechanistic insights.

Single molecule turnover of fluorescent ATP by myosin and actomyosin unveil elusive enzymatic mechanisms

“…Notably, the actin-activated ATP turnover rate is slower than 10–17 s −1 for isometrically contracting muscle fibers (ref. 51 and references therein), but quite similar to the rate (4 s −1 ) of the slow phase of isometric relaxation upon removal of calcium from a muscle cell 52 . Because detachment from actin of high-force myosin heads dominates the latter process, it is reasonable to presume that our single-molecule data primarily report turnover of high-force heads.…”

“…Under these conditions, the ADP-release rate (and thereby the cross-bridge detachment rate) is 100–1000-fold slower than at zero strain (ref. 51 and references therein, ref. 52 ), thus becoming rate limiting for the ATP turnover cycle.…”

The effects of inorganic phosphate on muscle force development and energetics: challenges in modelling related to experimental uncertainties

“…S2). This discrepancy is similar if only one site per target zone is assumed (Månsson 2019). Furthermore, the discrepancy is appreciably enhanced if the assumed binding strength in the weak-binding AMDP state is reduced within an experimentally observed range (see Månsson 2016 and references therein), i.e.…”

“…However, the rate of rise of active isometric force following rapid length changes to zero tension (Månsson 2016) or following rapid perturbations of the Pi-concentration (Rahman et al 2018) also seem to be accounted for. Furthermore, arguments have also been put forward (Månsson 2019) to suggest that the tension transient in response to fast length steps, with the T1 and T2 relationships (Huxley and Simmons 1971), should be consistent with the model. Eccentric contractions however, seem to involve complexities that require additional assumptions in the models which do not follow directly from experimental findings of isolated proteins (Campbell et al 2011;Rahman et al 2018;Rassier and Pavlov 2012).…”

“…Despite the perceived need for increasingly complex models, it was found recently (Månsson 2016 , 2019 ; Månsson et al 2018 , 2019 ; Rahman et al 2018 ) that assignment of parameter values as described in the preceding paragraph, allow models to account surprisingly well for a range of critical aspects of muscle contraction. Both isometric contraction and shortening contractions are thus accounted for without the need to invoke cooperative transitions (Huxley and Tideswell 1997 ; Månsson 2010a ), inter-site slippage (Caremani et al 2013 ), effects of accessory proteins (Tanner et al 2007 ), branched pathways (Caremani et al 2013 ; Debold et al 2013 ), 3D order (Mijailovich et al 2016 ) or emergent phenomena due to higher order sarcomere behaviour (Campbell et al 2011 ).…”