A modelized distribution of actomyosin interactions in the vertebrate cardiac muscle

Preliminary assumption of this model is that interactions between actin and myosin presupposes an exact three-dimensional geometrical correspondence between sites, due to the very short time constants present under physiological conditions. Only small and controlled torsions of the actin filaments are accepted. The model uses geometrical information concerning orientations and dimensions of myosin crossbridges and actin monomeres to modelize the distribution of their inter-actions. An orientation map of actin sites in the cross-section perpendicular to the filament axis is proposed, adapted to the specific filament array of vertebrate muscle. Orientation of myosin crossbridges follows Luther's rules. According to the model, any interaction between actin and myosin implies the superimposition of their respective cross-sectional planes. The axial length of actin monomere is 55 A; the distance between two crossbridges along the myosin filament axis is 143 A. The following properties are derived: 1) The shortening step of the sliding actin filament must be a multiple of 11 A (highest common factor). Taking into account the staggered disposition of the two actin strands and the presence of two heads for each cross-bridge, the most probable value for this shortening step is equal to 99 A. A specific scheme is proposed to describe the shortening process. The behavior of the modelized crossbridge does not need any elastic structure--2) Planes situated at 715 A (lowest common multiple) of actin and myosin coinciding planes are also in coincidence. In a hemi-sarcomere the maximal number of these planes, referred to as simultaneously activable planes, is 10 (20 if both myosin heads are considered). The proportion of interactions authorized by the site orientations is 1/12. In the model, the concept of randomly recruited crossbridges is replaced by a discretized recruitment, based on geometrical properties at an ultrastructural level. The proposed distribution is homogeneous: it can be extended radially in the sarcomere and authorizes the actin filament sliding in the whole physiological range under the control of a dual activation function, reproducing Ca++ temporal and spatial distribution.