Abstract
Passive forces in sarcomeres are mainly related to the giant protein titin. Titin’s extensible region consists of spring-like elements acting in series. In skeletal muscles these elements are the PEVK segment, two distinct immunoglobulin (Ig) domain regions (proximal and distal), and a N2A portion. While distal Ig domains are thought to form inextensible end filaments in intact sarcomeres, proximal Ig domains unfold in a force- and time-dependent manner. In length-ramp experiments of single titin strands, sequential unfolding of Ig domains leads to a typical saw-tooth pattern in force-elongation curves which can be simulated by Monte Carlo simulations. In sarcomeres, where more than a thousand titin strands are arranged in parallel, numerous Monte Carlo simulations are required to estimate the resultant force of all titin filaments based on the non-uniform titin elongations. To simplify calculations, the stochastic model of passive forces is often replaced by linear or non-linear deterministic and phenomenological functions. However, new theories of muscle contraction are based on the hypothesized binding of titin to the actin filament upon activation, and thereby on a prominent role of the structural properties of titin. Therefore, these theories necessitate a detailed analysis of titin forces in length-ramp experiments. In our study we present a simple and efficient alternative to Monte Carlo simulations. Based on a structural titin model, we calculate the exact probability distributions of unfolded Ig domains under length-ramp conditions needed for rigorous analysis of expected forces, distribution of unfolding forces, etc. Due to the generality of our model, the approach is applicable to a wide range of stochastic protein unfolding problems.
Highlights
Passive forces in sarcomeres or myofibrils are almost exclusively governed by the giant protein titin [1]
We provide a simple and stable algorithm to determine the exact solution of passive forces in a half sarcomere in length-ramp simulations
The comparison between Monte Carlo approximation based on the simulation of 200 titin strands and the exact solution reveals that mean forces of the Monte Carlo simulation and the exact solution correspond almost perfectly
Summary
Passive forces in sarcomeres or myofibrils are almost exclusively governed by the giant protein titin [1]. A titin strand spans the half sarcomere from Z-disk to M-band. While its section located in the thick filament is nearly inextensible, its I-band region functions as a molecular spring. The distal Ig domains (close to the AI-junction) are thought to form almost inextensible end-filaments [3, 4] (Fig 1). The proximal Ig domains (close to the Z-disk) are able to unfold in a force and time dependent manner [5]. Molecular dynamic simulations coincide with experimental data and provide new insight into the mechanics of unfolding at the atomic level; e.g. Molecular dynamic simulations coincide with experimental data and provide new insight into the mechanics of unfolding at the atomic level; e.g. [11,12,13,14]
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