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

Spatial control of membrane receptor function using ligand nanocalipers

The spatial organization of membrane-bound ligands is thought to regulate receptor-mediated signaling. However, direct regulation of receptor function by nanoscale distribution of ligands has not yet been demonstrated, to our knowledge. We developed rationally designed DNA origami nanostructures modified with ligands at well-defined positions. Using these 'nanocalipers' to present ephrin ligands, we showed that the nanoscale spacing of ephrin-A5 directs the levels of EphA2 receptor activation in human breast cancer cells. Furthermore, we found that the nanoscale distribution of ephrin-A5 regulates the invasive properties of breast cancer cells. Our ligand nanocaliper approach has the potential to provide insight into the roles of ligand nanoscale spatial distribution in membrane receptor mediated signaling