Effect of sarcomere length on step size in relaxed rabbit psoas muscle
EKATERINA NAGORNYAK, FELIX BLYAKHMAN?and GERALD H. POLLACK*
Department of Bioengineering 357962, University of Washington, Seattle, WA 98195, USA
Received 20 July 2003; accepted in revised form 10 October 2003
Recent experiments have shown that shortening and stretching of sarcomeres in single activated and unactivated
myofibrils occur in stepwise fashion (Yang et al. (1998) Biophys J 74: 1473–1483; Blyakhman et al. (2001) Biophys J
81: 1093–1100; Yakovenko et al. (2002) Am J Physiol Cell Physiol 283: 735–742). Here, we carried out
measurements on single myofibrils from rabbit psoas muscle to investigate steps in unactivated specimens in more
detail. Activated and unactivated myofibrils were released and stretched in ramp-like fashion. The time course of
length change in the single sarcomere was consistently stepwise. We found that in the unactivated myofibrils, step
size depended on initial sarcomere length, diminishing progressively with increase of initial sarcomere length,
whereas in the case of activated sarcomeres, step size was consistently 2.7 nm.
Investigations of the mechanism of muscle contraction
and motility have focused on measurement of elemen-
tary molecular translation steps (Ishijima et al., 1996;
Kitamura et al., 1999; Yanagida et al., 2000; Murphy
et al., 2001). Measurements have yielded steps of a wide
range of sizes (Saito et al., 1994; Molloy et al., 1995;
Guildford et al., 1997). Recent myofibril experiments,
on the other hand, have shown that activated sarcomere
shortening occurs in steps consistently on the order of
2.7 nm or integer multiples thereof (Blyakhman et al.,
1999; Yakovenko et al., 2002). While the mechanism of
active stepping remains to be settled, steps in unactivat-
ed muscles seem inevitably associated with connecting
filaments, for it is only the connecting filaments that
change length in the relaxed state (Maruyama et al.,
1984; Fuerst et al., 1988; Horowits et al., 1989; Politou
et al., 1995; Improta et al., 1996). This conclusion is
supported by experiments on isolated titin molecules.
Rief et al. (1997) reported step sizes in isolated titin
molecules in the range from 25 to 30 nm, although
Tskhovrebova et al. (1997) noted a broader distribution,
5–25 nm. In experiments on single isolated myofibrils, in
which thin filaments had been functionally removed,
leaving the connecting (titin) filaments as sole agent
taking up the length change, step size was an integer
multiple of 2.3 nm (Blyakhman et al., 2001). The source
of the difference between our studies and those in
isolated titin molecules is unclear, although there is
some size overlap.
In the present experiments we employed a differen-
tially based algorithm that could suppress noise contri-
butions sufficiently to bring the detection limit down to
sub-nanometer levels (Sokolov et al., 2003). With this
high-resolution algorithm, we measured steps in acti-
vated and unactivated sarcomeres both during shorten-
sarcomeres, we confirmed that step size was invariant.
For relaxed myofibrils, however, step size was not
constant: it was a function of initial sarcomere length.
Single myofibrils were prepared from rabbit psoas
muscles (Linke et al., 1994). Briefly, muscles were
dissected bluntly along longitudinal cleavage planes into
thin strips, tied at both ends to small wooden sticks to
maintain native length, and placed in vials of rigor
solution. After 12 h, the specimens were transferred to
the glycerol solution and stored in a freezer at )20?C;
then, after 12 h the glycerol solution was changed again.
Muscles were kept at )80?C for longer-term storage for
a minimum of 9 days. To obtain single myofibrils,
glycerinated strips were kept in rigor solution for 60 min
at )20?C, further dissected into finer longitudinal strips,
and then strips were sliced into 2 mm segments. One
tissue piece was homogenized in a blender (Sorvall Omni
Mixer) in 7 ml of rigor solution using the following
protocol:twice · 5 s at
1800 rpm, once · 1 s at 2500 rpm, and once · 1 s at
3100 rpm. A drop of the blended muscle suspension was
placed on the cover-slip in the specimen chamber
(volume approximately 300 ll), and myofibrils were
1100 rpm, twice · 2 sat
?Present address: Department of Physics, Ural State University,
*To whom correspondence should be addressed: Tel.: +1-206-685-
1880; Fax: +1-206-685-3300; E-mail: email@example.com
Journal of Muscle Research and Cell Motility 25: 37–43, 2004.
? 2004 Kluwer Academic Publishers. Printed in the Netherlands.
allowed to settle and stick lightly to the chamber
bottom. Afterward, relaxing solution was used to flush
out free-floating particles. We were careful to select only
uniform specimens. Myofibril doublets were sometimes
selected, but mostly we used single myofibrils.
The following solutions were used for preparation and
experimentation. Rigor solution had a composition (in
mM) of 50 Tris (pH 7.4), 100 NaCl, 2 KCl, 2 MgCl2,
and 10 EGTA. Normal relaxing solution (pH 7.0) had a
composition (in mM) of: 10 MOPS, 64.4 K+propio-
nate, 5.23 Mg2+propionate, 9.45 Na2SO4, 10 EGTA,
0.188 CaCl2, 7 ATP, and 10 creatine phosphate.
Activating solution (pH 7.0) had a composition (in
Mg2þpropionate, 9.27 Na2SO4, 10 EGTA, 9.91 CaCl2,
7.18 ATP, and 10 creatine phosphate. Glycerol solution:
half glycerol and half rigor solution.
Single myofibrils were isolated and mounted in a
specially constructed apparatus built around a Zeiss
Axiovert-35 microscope as previously described in detail
(Yang et al., 1998; Blyakhman et al., 1999) (Figure 1).
Briefly, the specimen in the experimental chamber was
held by a fixed glass needle at one end and the glass tip
of a piezomotor at the other end (Fauver et al., 1998).
The piezoelectric motor could impose linear length
changes on the specimen. These attachment fixtures
were in turn mounted on hydraulic micromanipulators
to facilitate positioning.
To obtain sarcomere lengths, the striation pattern
(Figure 2A) was projected onto a 1024-element photo-
diode array. The array was scanned every 50 ms (a
compromise between time resolution and integration
time needed to reduce noise) to produce a trace of
intensity vs. position along the myofibril. A-bands
produced positive-going signals, I-band negative-going
(Figure 2B). Figure 2C shows a display of successive
50 ms scans recorded during an imposed length change
similar to that used in the experiments. Images were also
obtained on video for visual inspection. Intensity
profiles were then acquired and converted to sarcomere
length by custom software (below) written in LabView.
All experiments were carried out at room temperature
(20–22?C). Two glass needles were positioned under low
magnification with one secured in place and the other
mounted onto a piezoelectric motor. Then the objective
was changed to an oil-immersion phase contrast lens
(Zeiss, 100·, NA 1.3). Once an isolated myofibril was
identified and detached from the cover-slip, several
wraps were made by moving one needle around the
other to ensure attachment of the myofibril to the glass
needles. All manipulations were done in relaxing solu-
The myofibril was positioned to lie in the plane of
focus, and to line up with the axis of the photodiode
array. Experiments were carried out in relaxing or
activating solution, and a trapezoidal length change was
imposed with the aid of the motor. Sometimes it was
necessary to readjust needle positions in order to assure
that the myofibril remained parallel to the array. Other
times it was necessary to readjust the lighting conditions
to assure that illumination remained uniform.
The stretch–release protocols were then carried out at
moderate length – 1.8 lm < SL < 3.3 lm for relaxed
Fig. 1. Schematic of apparatus.
Fig. 2. (A) Representative phase-contrast image of single myofibril.
(B) Intensity trace along myofibril. Large upward deflections represent
A-bands; small upward deflections correspond to Z lines. (C) Repe-
titive scans during motor-imposed length change, shown in grey scale.
Centroid computation shown as white, vertically oriented trace
running along the middle of the A-band.
muscles, and at 1.6 lm < SL < 2.7 lm for activated
muscles. Generally, the protocol consisted of imposing a
trapezoidal length change of 5–15% of initial length.
Motor-ramp speeds were selected to give two nominal
speeds of sarcomere-length change: ? 2 and ? 8 nm/s.
Because the exact speed of sarcomere-length change
depended on the number of sarcomeres in the specimen
and on the uniformity of the imposed length change,
appreciable speed variation resulted in individual sar-
comeres. Mostly, symmetrical trapezoids were used,
consisting of 13-s stretch, 2-s hold, and 13-s release. In
total, 412 sarcomeres from 34 relaxed myofibrils, and
112 sarcomeres from 11 activated myofibrils were
Calibration of the photodiode array revealed 8.17 pix-
els/lm. With sarcomere length around 2.5 lm, there
were 18–20 pixels/sarcomere.
Sarcomere length was calculated as the span between
centroids of contiguous A-bands. To calculate the
centroid we developed a peak-detection algorithm based
on the minimum average risk method proposed by
Kolmogorov (1931) (Sokolov et al., 2003). The algo-
rithm operates on repeated scans of an intensity peak,
precisely quantifying peak movement between scans.
The method is differential; it compares the respective A-
band intensity peak with that of the one immediately
previous. The algorithm is implemented by finding the
optimal position of a scan relative to the first derivative
of the immediately previous scan. The optimal registra-
tion determined as the minimum of their integrated
product. The amount of shift required to achieve
optimal registration is equal to the amount of feature
As implemented, a two-sarcomere-wide sub-section of
each successive digitized scan of a myofibril is selected to
bracket a given A-band. The shift required to obtain
the best fit, relative to the previous scan, is determined.
The change of sarcomere length can be computed from
the relative shift between two A-bands. By repeating this
computation for each successive scan, the time course of
each A-band position, and thus of sarcomere length, can
be obtained. Because the method is differential, high
resolution is achieved.
An example of the result of A-band-centroid compu-
tation is displayed in Figure 2B. The horizontal span
between contiguous centroids is taken as sarcomere
length. Through successive sarcomere-length computa-
tions, we could follow the time course of the length
changes in single sarcomeres.
Analytical details follow largely along lines already
presented (Yang et al., 1998, Blyakhman et al., 2001).
To identify a step it was necessary to define the pair of
pauses surrounding the step. The pause was taken
provisionally as a region of the trace whose estimated
best-fit by eye was nominally parallel to the horizontal
axis. The region had to contain a minimum of five
consecutive sample points to qualify; most contained
more. After assigning beginning and end points of the
pause, a best-fit line was computed. This fit provided a
guide for slight adjustment of the break points to yield
pauses with slope closest to zero. Step size was then
computed as the vertical span between centers of two
successive best-fit line segments. The procedure was
repeated for other pauses and steps.
Although considerable attention was paid to precision
of sarcomere-length-change, the absolute values of
sarcomere length were measured with accuracy no better
A representative trace of sarcomere-length vs. time in a
relaxed specimen is shown in Figure 3. In this experi-
ment the myofibril was stretched, held, and then released
following imposition of the symmetric trapezoid. Sar-
comere-length-change traces contain multiple pause
periods during which the sarcomere-length change was
indistinguishable from zero. Between pauses, the sarco-
mere shortened or lengthened in steps of several
To analyze these shortening and lengthening steps, an
algorithm computed the vertical spacing between suc-
cessive pauses, which gave the size of the step. Sizes
obtained from many steps were plotted as a continuous
histogram. An example of the results obtained from
shortening steps is shown in Figure 4. The light curve
shows a primary peak at 2.5 nm. An additional peak is
seen at an approximate integer multiple of the primary
value (5 nm). The dark curve represents the histogram
obtained for lengthening steps. Again, two histogram
peaks are observed: a primary one at 2.5 nm and
Fig. 3. Representative trace of sarcomere-length change during motor-
imposed trapezoid in rabbit psoas muscle. Inset shows part of the trace
with representative pauses denoted.
secondary one at 5 nm. The histogram illustrates in a
single figure that the size of the shortening step is similar
to the size of lengthening step, and is equal to an integer
multiple of 2.5 nm.
Experiments were also carried out to determine the
effect of ramp speed. This was done both for stretch and
for release. Figure 5 shows results for high-speed ramp
(dark line) and for low-speed ramp (dotted line). For the
high-speed ramp, the range of sarcomere speeds was 6–
11 nm/s, and for the low-speed ramp it was 1–4 nm/s.
Lower speed increased the fraction of smaller steps
relative to larger ones. Otherwise, the effect of speed was
modest. Extending the range of speeds beyond these
values was impractical because of high noise/signal ratio
on the low end, and because of scan-time resolution on
the high end.
To determine the effect of sarcomere length on step
size, all experimental data for relaxed muscles were
separated into four groups, depending on initial sarco-
mere length. The groups were: (1) 1.8 lm < SL < 2.4
lm; (2) 2.4 lm < SL < 2.7 lm; (3) 2.7 lm < SL <
3.0 lm; (4) 3.0 lm < SL < 3.3 lm. For low-velocity
ramps (nominally 2 nm/sarc/s) and for higher velocity
ramps (nominally 8 nm/sarc/s) the histograms show that
as initial SL decreased, step size increased. This trend is
shown in Figure 6 (low velocity) and even more clearly
in Figure 7 (high velocity).
All histograms show higher order peaks, which are
integer multiples of the lower order ones.
The main finding of these studies was that minimum
step size in relaxed muscle was not constant. We found
an inverse relation between step size and initial sarco-
mere length, which was revealed both for low speed and
Fig. 4. Histograms of shortening-step size (shaded line; 320 steps from
73 traces) and lengthening-step size (dark line; 309 steps from 74
traces) in relaxed specimens. In both histograms, peaks are situated at
approximate integer multiples of 2.5 nm.
Fig. 5. Histograms of step size obtained by imposing stretch ramps at
different speed. Low-velocity ramps are shown by broken line (604
steps from 109 traces); high-velocity ramps are shown by solid line (611
steps from 63 traces).
Fig. 6. Histograms of step size obtained during applied low-speed
ramp. Step size increases with decrease of initial sarcomere length. (1)
604 steps from 109 traces; (2) 518 steps from 101 traces; (3) 603 steps
from 109 traces; (4) 544 steps from 102 traces.
Fig. 7. Histograms of step size obtained during high-speed ramp for
both stretch and release. Peaks shift to lower values with increase of
initial sarcomere length. (1) 611 steps from 63 traces; (2) 792 steps from
140 traces; (3) 742 steps from 80 traces; (4) 539 steps from 58 traces.
high-speed deformations. Therefore, some feature of the
relaxed sarcomere generates steps of variable size.
Measurements of sarcomere-length change at high
resolution are subject to various potential sources of
artifact. To check for artifact, many controls have
previously been carried out (Yang et al., 1998; Blyakh-
man et al., 1999, 2001). The effect of discreteness of the
photodiode array was checked using two methods:
replacing the photodiode array with a non-discrete
sensor; and, using two different magnifications on the
photodiode array (Yang et al., 1998). Results were
indistinguishable. Analytical procedures were checked
by testing whether each of two independent algorithms
yielded similar step distributions (Blyakhman et al.,
2001). Also checked was whether steps might arise out
of specimen translation along the photodiode array
(Yang et al., 1998): displacement of the A-band closest
to the motor was tracked as it translated along the
array, and no step-like behavior was present. Sub-
nanometer precision was tested by imposing a motor
waveform that forced sarcomeres to step at a size
slightly different from that of naturally occurring steps;
step-size distributions could be discerned with peaks
separated by 0.4 nm or less (Blyakhman et al., 2001). To
check the effects of noise, the power-spectrum of
simulated step-free shortening was analyzed; it showed
only noise, with no features of significance near the step
size obtained in the experiments (Blyakhman et al.,
Thus, all previous tests were negative for artifact.
As an additional control, we examined the influence
of initial SL on step size in activated specimens. Figure 8
shows histograms plotted for each of three different
initial sarcomere-length ranges (1.6–2.0, 2.0–2.4, and
2.4–2.8 lm). For all histograms the primary peak was
seen at 2.68–2.71 nm, with additional peaks at integer
multiples of this quantal value. Results, therefore, show
no dependence of step-size on initial SL in specimens
that were activated. Hence the SL dependence observed
for relaxed myofibrils apparently does not arise out of
some instrument artifact. A summary of the above
results is shown in Figure 9.
As a supplementary control, we restricted the data set
to include only those records with relatively low noise.
Thus, records in which peak-to-peak noise during the
pause exceeded 2 nm were discarded. Although the
number of counts decreased, the shapes of the histo-
grams did not change significantly, and step sizes
remained unchanged (Figure 10).
Possible source of passive steps
Given their connecting-filament origin, the steps have at
least two possible origins. One is the folding/unfolding
of compound structures due to a state change: each
filament has a primary, secondary and tertiary structure,
and the step could arise from a transition between
structural states. Another possible mechanism is the
transition within a structure – progressive unfolding/
folding of folded/unfolded proteins (Zocchi, 1997). For
example, structures with many folds could unfold in
stages, each unfolding event giving a slightly different
step size, and thereby accounting for the non-constancy
of step size. One such candidate is the sevenfold b-barrel
structure of the connecting filament’s Ig-domain (Erick-
son, 1994; Improta et al., 1996, 1998). Each turn could
unfold, giving steps of 2.3–2.5 nm (Blyakhman et al.,
Dependence of step size on initial sarcomere length
One possible explanation of the sarcomere-length de-
pendence is that distinct structures give rise to distinct
step sizes, some elicited at low tension, others at high
tension (Rief et al., 1999). The steps, then, would result
from folding/unfolding of these structures. Larger steps
are seen at low levels of tension, and vice versa. For
Fig. 8. Histograms of step size obtained in the activated state.
Multiple peaks appear at approximate integer multiples of 2.7 nm.
(1) 606 steps from 86 traces; (2) 670 steps from 78 traces; (3) 588 steps
from 74 traces.
Fig. 9. Comparison of effects of initial sarcomere length in activated
and relaxed state. Numbers on the abscissa correspond to different SL
groups. Step size in activated specimens (gray lines) is invariant,
whereas in the unactivated state, step size decreases progressively with
increase of initial sarcomere length (black lines). In total, 412
sarcomeres from 34 relaxed myofibrils, and 112 sarcomeres from 11
activated myofibrils were analyzed.