Effect of Confinement on Titin Conformation and Elasticity

Abstract

Elasticity in muscle sarcomeres results largely from the mechanical properties of the giant protein titin. The I-band parts of titin molecules form filamentous connections between thick filaments and the Z-line, and behave as semi-flexible polymers, passively coiling and uncoiling during changes in sarcomere length. Important questions about titin mechanics in vivo concern effects of confinement, due to the surrounding actin filament lattice and to the high local concentration of titin. The actin lattice changes across the I-band, from hexagonal near the A-band to tetragonal towards the Z-line. At resting sarcomere length, a single hexagonal unit cell has radius ∼27 nm (Millman, 1998) and contains the six titin molecules that emerge from each thick filament, with a space of radius R ∼11 nm available to each molecule. The tetragonal lattice has average side length ∼24 nm and contains three titin molecules, with radius ∼7.8 nm for each molecule. Taking into account the condition for transition from weak to strong confinement 2R < RF (De Gennes, 1979), or 2R ∼ Lp (Cifra, 2009), and the average persistence length of titin (Lp, 9-19 nm), it can be concluded thatI-band titin is confined towards the Z-line. We analysed the effect of cylindrical confinement on the force-extension relationship of a polymer chain and showed it to lead to stiffening of the chain. This result, together with the above estimates, indicates that values of titin stiffness in situ derived from the interpolation formula for an unconfined worm-like chain (Marko & Siggia, 1995) are likely to be underestimates, even if titin molecules cross the I-band independently.