Gerald H. Pollack

Passive and active tension in single cardiac myofibrils

Single myofibrils were isolated from chemically skinned rabbit heart and mounted in an apparatus described previously (Fearn et al., 1993; Linke et al., 1993). We measured the passive length-tension relation and active isometric force, both normalized to cross sectional area. Myofibrillar cross sectional area was calculated based on measurements of myofibril diameter from both phase-contrast images and electron micrographs. Passive tension values up to sarcomere lengths of approximately 2.2 microns were similar to those reported in larger cardiac muscle specimens. Thus, the element responsible for most, if not all, passive force of cardiac muscle at physiological sarcomere lengths appears to reside within the myofibrils. Above 2.2 microns, passive tension continued to rise, but not as steeply as reported in multicellular preparations. Apparently, structures other than the myofibrils become increasingly important in determining the magnitude of passive tension at these stretched lengths. Knowing the myofibrillar component of passive tension allowed us to infer the stress-strain relation of titin, the polypeptide thought to support passive force in the sarcomere. The elastic modulus of titin is 3.5 x 10(6) dyn cm-2, a value similar to that reported for elastin. Maximum active isometric tension in the single myofibril at sarcomere lengths of 2.1-2.3 microns was 145 +/- 35 mN/mm2 (mean +/- SD; n = 15). This value is comparable with that measured in fixed-end contractions of larger cardiac specimens, when the amount of nonmyofibrillar space in those preparations is considered. However, it is about 4 times lower than the maximum active tension previously measured in single skeletal myofibrils under similar conditions (Bartoo et al., 1993).

Long-range forces extending from polymer-gel surfaces.

Aqueous suspensions of microspheres were infused around gels of varying composition. The solutes were excluded from zones on the order of 100 microm from the gel surface. We present evidence that this finding is not an artifact, and that solute-repulsion forces exist at distances far greater than conventional theory predicts. The observations imply that solutes may interact over an unexpectedly long range.

Maximum Velocity as an Index of Contractility in Cardiac Muscle: A CRITICAL EVALUATION

The use of maximum velocity of shortening (Vmax) as an index of contractility has been based on the assumption that Vmax of muscle fibers is equivalent to Vmax of the contractile element. It is shown here that such equivalence applies to the two-element model of skeletal muscle but not to three-element models of cardiac muscle. Analysis of published data in terms of the Voigt and Maxwell three-element models shows that the Vmax of the contractile element, unlike that of the muscle fibers, is not independent of fiber length but increases at least 50% for a 25% increase of fiber length. Moreover, Vmax of the contractile element is seen to be even more highly dependent on fiber length when correction is made for the nonuniform contribution of levels of active state to the force-velocity curves giving rise to Vmax of the contractile element. It appears that in cardiac muscle an inotropic shift of Vmax of the contractile element cannot be distinguished from a shift due to change in fiber length, thus invalidating it as an index of contractility.

Mechanics of F-Actin Characterized with Microfabricated Cantilevers

In this report we characterized the longitudinal elasticity of single actin filaments manipulated by novel silicon-nitride microfabricated levers. Single actin filaments were stretched from zero tension to maximal physiological tension, P(0). The obtained length-tension relation was nonlinear in the low-tension range (0-50 pN) with a resultant strain of approximately 0.4-0.6% and then became linear at moderate to high tensions (approximately 50-230 pN). In this region, the stretching stiffness of a single rhodamine-phalloidin-labeled, 1-microm-long F-actin is 34.5 +/- 3.5 pN/nm. Such a length-tension relation could be characterized by an entropic-enthalpic worm-like chain model, which ascribes most of the energy consumed in the nonlinear portion to overcoming thermal undulations arising from the filaments interaction with surrounding solution and the linear portion to the intrinsic stretching elasticity. By fitting the experimental data with such a worm-like chain model, an estimation of persistence length of approximately 8.75 microm was derived. These results suggest that F-actin is more compliant than previously thought and that thin filament compliance may account for a substantial fraction of the sarcomeres elasticity.

Microfabricated cantilevers for measurement of subcellular and molecular forces

We present two new microfabricated cantilever-beam force transducers. The transducers were fabricated from thin silicon-nitride films, and were used respectively to measure forces generated by two small-muscle preparations: the single myofibril, and the single actin filament in contact with a myosin-coated surface. A simple resonance method was developed to characterize the transducers. Because of the high reproducibility of lever dimensions and the consistency of the modulus of elasticity, few calibration measurements sufficed to characterize the stiffness of all the levers on a single wafer.

Dynamics of individual sarcomeres during and after stretch in activated single myofibrils

It is generally assumed that sarcomere lengths (SLs) change in isometric fibres following activation and following stretch on the descending limb of the force–length relationship, because of an inherent instability. Although this assumption has never been tested directly, instability and SL non–uniformity have been associated with several mechanical properties, such as ‘creep’ and force enhancement. The aim of this study was to test directly the hypothesis that sarcomeres are unstable on the descending limb of the force–length relationship. We used single myofibrils, isolated from rabbit psoas, that were attached to glass needles that allowed for controlled stretching of myofibrils. Images of the sarcomere striation pattern were projected onto a linear photodiode array, which was scanned at 20 Hz to produce dark–light patterns corresponding to the A– and I–bands, respectively. Starting from a mean SL of 2.55±0.07 &mgr;m, stretches of 11.2± 1.6% of SL at a speed of 118.9± 5.9 nm s–1 were applied to the activated myofibrils (pCa2+ = 4.75). SLs along the myofibril were non–uniform before, during and after the stretch, but with few exceptions, they remained constant during the isometric period before stretch, and during the extended isometric period after stretch. Sarcomeres never lengthened to a point beyond thick and thin filament overlap. We conclude that sarcomeres are non–uniform but generally stable on the descending limb of the force–length relationship.

Cardiac Muscle Models An Overextension of Series Elasticity

Quick-stretch and quick-release experiments were performed on right ventricular cat papillary muscles to test the applicability of the Hill model to cardiac mechanics. Series elastic component (SEC) force-length curves were calculated from stretches and releases carried out at various times during the contractile cycle. At any SEC force, the SEC elastic modulus depended on the time during the contractile cycle at which it was measured. When measured at the same time and at the same SEC force, elastic moduli obtained by releases of less than 1% of muscle length differed from those obtained by corresponding stretches. Larger stretches, in fact, appeared to yield negative elastic moduli. Thus, a unique SEC modulus could not be identified at any level of SEC force. It is concluded that the concept of the SEC as a passive elasticity appears unsatisfactory and, as a consequence, that the quantitative validity of the Hill model for cardiac muscle is questionable. Moreover, since an anatomical counterpart of the SEC has not been identified, the Hill model also appears unsatisfactory from a structural point of view.

Active tension generation in isolated skeletal myofibrils

SummarySingle or double myofibrils isolated from rabbit psoas muscle were suspended between a fine needle and an optical force transducer. By using a photodiode array, the length of every sarcomere along the specimen could be measured. Relaxed specimens exhibited uniform sarcomere lengths and their passive length-tension curve was comparable to that of larger specimens. Most specimens could be activated and relaxed four to five times before active force levels began to decline; some specimens lasted for 10–15 activation cycles. Active tension (20–22°C) was reproducible from contraction to contraction. The contractile response was dependent on initial sarcomere length. If initially activated at sarcomere lengths of ≥2.7 μm, one group of sarcomeres usually shortened to sarcomere lengths of 1.8–2.0 μm, while the remaining sarcomeres were stretched to longer lengths. Myofibrils that were carefully activated at shorter initial sarcomere lengths usually contracted homogeneously. Both homogeneous and inhomogeneous contractions produced high levels of active tension. Calcium sensitivity was found to be comparable to that in larger preparations; myofibrils immersed in pCa 6.0 solution generated 30% of maximal tension, while pCa 5.5–4.5 resulted in full activation. Active tension at full overlap of thick and thin filaments ranged from 0.34 to 0.94 N mm-2 (mean of 0.59 N mm-2±0.13 sd. n=65). Even allowing for a maximum of 20% nonmyofibrillar space in skinned or intact muscle fibres, the mean tension generated by isolated myofibrils per cross-sectional area is higher than by fibre preparations.

Elastic properties of the titin filament in the Z-line region of vertebrate striated muscle.

SummaryThe characteristics of the titin filament in the vicinity of the Z-line were investigated using immunoelectron microscopy. We used monoclonal titin antibodies T-11 and T-12 on single fibres of frog skeletal muscle, and on Z-line-extracted fibres. It is well established that the I-band region of titin is elastic. We find, however, that the elastic properties are not uniform. The T-12 epitope, which binds near the Z-line at the N1-line level, hardly changes position relative to the Z-line as the sarcomere is stretched. This demonstrates the functional inextensibility of the N1-Z-line region. After extreme stretch (above 6-μm sarcomere length), this zone finally does elongate; thus, the titin molecule in this region is intrisically elastic. The functional inextensibility seen at shorter sarcomere lengths may, therefore, be a result of binding of titin to the actin filament in the zone near the Z-line. When the Z-line was extracted, the T-12 epitope remained in the same position as in the unextracted fibres; it did not retract from the Z-line. Failure to retract implies that functional anchoring of titin is not exclusive to the Z-line, but includes some site closer to the A-band. Combined with the results of the above-mentioned stretch experiment, this result implies a likely binding of titin to the thin filament either focally at the N1 line or all along the entire N1-Z region. Thus, this region of titin is functionally stiff, but intrinsically elastic.

The role of aqueous interfaces in the cell.

The cell is rich with biopolymeric surfaces. Yet, the role of these surfaces and attendant surface-water interfaces has received little attention among biologists, most of whom consider water as a neutral carrier. This review aims to begin bridging the gap between biology and interface science-to show that a surface-oriented approach has power to bring fresh insights into an otherwise impenetrably complex maze. In this approach the cell is treated as a polymer gel. If the cell is a gel, then a logical approach to the understanding of cell function is through an understanding of gel function. Great strides have been made recently in understanding the principles of polymer-gel dynamics, and particularly the role of the polymer-water interface. It has become clear that a central mechanism in biology is the phase-transition-a major structural change prompted by a subtle change of environment. Phase-transitions are capable of doing work and such work could be responsible for much of the work of the cell. Here, we pursue this approach. We set up a polymer-gel-based foundation for cell behavior, and explore the extent to which this foundation explains how the cell achieves its everyday tasks.