Abstract
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.
Highlights
Many biological systems are irreducible meaning that they have more complicated properties than the structures of which they are composed
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
Even though the passive mechanical properties of the individual half-sarcomeres are invariant, the force produced by the multi-half-sarcomere framework rises progressively during the latter stages of the stretch whereas the force produced by the single half-sarcomere model remains almost constant after the muscle’s short-range response. This means that the simulations performed with the multi-halfsarcomere framework fit the experimental data better and they do so without requiring that the titin filaments become stiffer in the activating condition
Summary
Many biological systems are irreducible meaning that they have more complicated properties than the structures of which they are composed. Detailed understanding of a complete system requires knowledge both about how its individual components function and about how those components interact. A property of the complete system is described as emergent if it arises because of interactions between components and is not a property of a single component in isolation. The main strategy has been to try and explain the properties of an entire muscle fiber as the scaled behavior of a single half-sarcomere. This technique was pioneered by A.F.Huxley in 1957 [3] and it has been outstandingly successful. Reductionist halfsarcomere theories can explain virtually all of the mechanical effects that occur immediately after a muscle fiber is subjected to a very rapid length or tension perturbation [4,5]
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