Computing Average Passive Forces in Sarcomeres in Length-Ramp Simulations.
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.
Department for Mathematics and Computational Sciences, University of Graz, Graz, Austria.
Gudrun
G
Schappacher-Tilp
Human Performance Laboratory, University of Calgary, Calgary, Canada.
Timothy
0000-0003-0409-0069
T
Leonard
Department for Mathematics and Computational Sciences, University of Graz, Graz, Austria.
Gertrud
G
Desch
Human Performance Laboratory, University of Calgary, Calgary, Canada.
Walter
W
Herzog
D003198:Computer Simulation; D064211:Connectin / Q000737:chemistry* / Q000502:physiology* / Q000648:ultrastructure; D008954:Models, Biological; D008956:Models, Chemical; D008958:Models, Molecular; D012518:Sarcomeres / Q000737:chemistry* / Q000502:physiology* / Q000648:ultrastructure; D013314:Stress, Mechanical; D013329:Structure-Activity Relationship; D013718:Tensile Strength / Q000502:physiology
D064211:Connectin