Fig 1.
Sketch of titin strands in a half sarcomere.
While a single titin strand spans the whole half sarcomere only a part of titin located in the half I-band is extensible.
Table 1.
Fig 2.
Solution of Eq (3) for stretches from 1μm to 2μm half sarcomere lengths.
Force [pN] of single titin strands at a given half sarcomere length is a discrete random variable with 51 states. The top curve represents the state in which all Ig domains are folded, the next curve the state in which exactly one Ig domain is unfolded, etc.
Fig 3.
Force-elongation behavior of a single titin strand with corresponding Monte Carlo simulations and force-elongation relation of a myofibril.
A When a single titin molecule is stretched it shows a typical saw-tooth pattern due to the unfolding of Ig domains [5, 9, 36, 38]. Three exemplar Monte Carlo simulations simulate that behavior. B Force-elongation curves of two myofibrils consisting of 7 and 8 sarcomeres respectivley. The shaded region indicates the standard error of the mean sarcomere length. Since over 1000 titin molecules are arranged in parallel in a single half sarcomere the saw tooth pattern observed in single molecule experiments is averaged out.
Fig 4.
Comparison between the two methods.
A Force-elongation curves of the Monte Carlo simulation. The red line indicates the mean value of force at a given half sarcomere length. The resulting curve is similar to the exact solution B. The small insert shows the difference between the two methods. The error of the Monte Carlo approximation rises with the first unfolding events but stays well within a 2pN range. The probability function and the normalized histograms (bin size based on the Freedman-Diaconis rule [44]) show similarities in shape.
Fig 5.
Forces at the first unfolding event.
A Histogram of forces at the first unfolding event (bin size based on the Freedman-Diaconis rule [44]) of 200 Monte Carlo simulation reveal a deviation (in terms of most likely unfolding forces) from the corresponding exact probability B.
Fig 6.
A Monte Carlo simulations and B exact solution of hysteresis loops based on one Ig cluster of the following setup: a half sarcomere was subject to two subsequent stretch-shortening cycles. After a resting period of 30s another stretch-shortening cycle was performed. We observed that while hysteresis was significantly reduced in the second cycle it fully recovered in the third cycle due to refolding of Ig domains in the resting period [5]. The effect of repeated stretch-shortening cycles on the unloading energy remains negligible.
Fig 7.
Hysteresis cycles of a single myofibril.
A A single myofibril consisting of 7 sarcomeres was stretched to an averaged sarcomere length of 3.7μm and subsequently cycled by approximately ± 2.5μm. The small insert shows the corresponding average sarcomere length (red line) ± standard error (black lines). The peak forces declined from the first to the second last peak. B The average force of Monte Carlo simulations based on 200 titin strands and a simplified half sarcomere length behavior (small insert) show a decline of peak forces based on the folding / unfolding behavior of Ig domains.
Fig 8.
Comparison of different Ig clusters.
The simulations are based on 50 Ig clusters (red) and 5 Ig clusters (black), respectively. The spontaneous unfolding rate constant (left panel) declines linearly but is perturbed by a Gaussian noise (SD = 0.2) in the case of 50 Ig clusters. The average force based on the Monte Carlo simulations of 50 titin strands (middle panel) as well as the probabilities of unfolding events as a function of half sarcomere length (right panel) are comparable between 50 Ig clusters (red) and 5 Ig clusters (black).