Interactions between Connected Half-Sarcomeres Produce Emergent Mechanical Behavior in a Mathematical Model of Muscle

Most reductionist theories of muscle attribute a fiber's mechanical properties to the scaled behavior of a single half-sarcomere. Mathematical models of this type can explain many of the known mechanical properties of muscle but have to incorporate a passive mechanical component that becomes ∼300% stiffer in activating conditions to reproduce the force response elicited by stretching a fast mammalian muscle fiber. The available experimental data suggests that titin filaments, which are the mostly likely source of the passive component, become at most ∼30% stiffer in saturating Ca2+ solutions. The work described in this manuscript used computer modeling to test an alternative systems theory that attributes the stretch response of a mammalian fiber to the composite behavior of a collection of half-sarcomeres. The principal finding was that the stretch response of a chemically permeabilized rabbit psoas fiber could be reproduced with a framework consisting of 300 half-sarcomeres arranged in 6 parallel myofibrils without requiring titin filaments to stiffen in activating solutions. Ablation of inter-myofibrillar links in the computer simulations lowered isometric force values and lowered energy absorption during a stretch. This computed behavior mimics effects previously observed in experiments using muscles from desmin-deficient mice in which the connections between Z-disks in adjacent myofibrils are presumably compromised. The current simulations suggest that muscle fibers exhibit emergent properties that reflect interactions between half-sarcomeres and are not properties of a single half-sarcomere in isolation. It is therefore likely that full quantitative understanding of a fiber's mechanical properties requires detailed analysis of a complete fiber system and cannot be achieved by focusing solely on the properties of a single half-sarcomere.Author Summary: Quantitative muscle biophysics has been dominated for the last 60 years by reductionist theories that try to explain the mechanical properties of an entire muscle fiber as the scaled behavior of a single half-sarcomere (typical muscle fibers contain ∼106 such structures). This work tests the hypothesis that a fiber's mechanical properties are irreducible, meaning that the fiber exhibits more complex behavior than the half-sarcomeres do. The key finding is that a system composed of many interacting half-sarcomeres has mechanical properties that are very different from that of a single half-sarcomere. This conclusion is based on the results of extensive computer modeling that reproduces the mechanical behavior of a fast mammalian muscle fiber during an imposed stretch without requiring that titin filaments become more than 3-fold stiffer in an activated muscle. This work is significant because it shows that it is probably not sufficient to attribute functional properties of whole muscle fibers solely to the behavior of a single half-sarcomere. Systems-level approaches are therefore likely to be required to explain how known structural and biochemical heterogeneities influence function in normal and diseased muscle tissue.