Mark Schoenberg

Stiffness of skinned rabbit psoas fibers in MgATP and MgPPi solution

The stiffness of single skinned rabbit psoas fibers was measured during rapid length changes applied to one end of the fibers. Apparent fiber stiffness was taken as the initial slope when force was plotted vs. change in sarcomere length. In the presence of MgATP, apparent fiber stiffness increased with increasing speed of stretch. With the fastest possible stretches, the stiffness of relaxed fibers at an ionic strength of 20 mM reached more than 50% of the stiffness measured in rigor. However, it was not clear whether apparent fiber stiffness had reached a maximum, speed independent value. The same behavior was seen at several ionic strengths, with increasing ionic strength leading to a decrease in the apparent fiber stiffness measured at any speed of stretch. A speed dependence of apparent fiber stiffness was demonstrated even more clearly when stiffness was measured in the presence of 4 mM MgPPi. In this case, stiffness varied with speed of stretch over about four decades. This speed dependence of apparent fiber stiffness is likely due to cross-bridges detaching and reattaching during the stiffness measurement (Schoenberg, 1985. Biophys. J. 48:467). This means that obtaining an estimate of the maximum number of cross-bridges attached to actin in relaxed fibers at various ionic strengths is not straightforward. However, the data we have obtained are consistent with other estimates of cross-bridge affinity for actin in fibers (Brenner et al., 1986. Biophys. J. In press.) which suggest that ~60-90% of the cross-bridges attached in rigor are attached in relaxed fibers at an ionic strength of 20 mM and ~2-10% of this number of cross-bridges are attached in a relaxed fiber at an ionic strength of 170 mM.

Equilibrium muscle cross-bridge behavior: theoretical considerations

We have developed a model for the equilibrium attachment and detachment of myosin cross-bridges to actin that takes into account the possibility that a given cross-bridge can bind to one of a number of actin monomers, as seems likely, rather than to a site on only a single actin monomer, as is often assumed. The behavior of this multiple site model in response to constant velocity, as well as instantaneous stretches, was studied and the influence of system parameters on the force response explored. It was found that in the multiple site model the detachment rate constant has considerably greater influence on the mechanical response than the attachment rate constant. It is shown that one can obtain information about the detachment rate constants either by examining the relationship between the apparent stiffness and duration of stretch for constant velocity stretches or by examining the force-decay rate constants following an instantaneous stretch. The main effect of the attachment rate constant is to scale the mechanical response by influencing the number of attached cross-bridges. The significance of the modeling for the interpretation of experimental results is discussed.

Length-Force Relation of Calcium Activated Muscle Fibers

Calcium activated skinned frog muscle fibers develop a large relative force at a sarcomere length of 1.0 micrometer. Since the normal myofilament lattice is perturbed at this length, regularity of the lattice does not appear to be an important factor in the contraction mechanism.

Cross-Bridge Attachment in Relaxed Muscle

We have measured the stiffness of relaxed, skinned rabbit psoas fibers at 5 degrees C in low ionic strength relaxing solution (mu = 0.02 M) by stretching the fibers and measuring the resulting force and sarcomere length changes. This stiffness is very dependent upon the velocity of stretch. With very slow stretches (0.5% of fiber length in greater than 30 ms), it is almost negligible but with stretches as fast as 0.5% of fiber length in 150 microseconds, the stiffness approaches 1/3 that of the rigor fiber. This stiffness is also very sensitive to ionic strength, being reduced more than 20-fold at an ionic strength of 0.17 M. This ionic strength sensitive stiffness scales with the amount of overlap between the actin and myosin filaments which strongly suggests that it is due to attached cross-bridges. The speed dependence suggests that the attached cross-bridges are not statically attached but in rapid equilibrium between attached and detached states. Experiments with adenylyl-imido-diphosphate suggest that the rates of attachment and detachment depend upon nucleotide.

Formation of ATP-insensitive weakly-binding crossbridges in single rabbit psoas fibers by treatment with phenylmaleimide or para-phenylenedimaleimide

Chaen et al. (1986. J. Biol. Chem. 261:13632-13636) showed that treatment of relaxed single muscle fibers with para-phenylenedimaleimide (pPDM) results in inhibition of a fibers ability to generate active force and a diminished ATPase activity. They postulated that the inhibition of force production was due to pPDMs ability to prevent crossbridges from participating in the normal ATP hydrolysis cycle. We find that the crossbridges produced by pPDM treatment of relaxed muscle cannot bind strongly to the actin filaments in rigor, but do bind weakly to the actin filaments in the presence and also absence of ATP. After pPDM treatment, fiber stiffness, as measured using ramp stretches of varying duration, is ATP-insensitive and identical to that of untreated relaxed fibers (both at high [165 mM] and low [40 mM] ionic strength). These results suggest that the pPDM-treated crossbridges, in both the presence and absence of ATP, are locked in a state that resembles the weakly-binding myosin ATP state of normal crossbridges. Their resemblance to the ATP-crossbridges of relaxed untreated fibers is quite strong; both bind to actin about equally tightly and have similar attachment and detachment rate constants. We also found that crossbridges are locked in a weakly-binding state after treatment with N-phenylmaleimide (NPM). In muscle fibers, this method of producing weakly-binding crossbridges appears preferable to pPDM treatment because, unlike treatment with pPDM, it does not increase the fibers resting tension and stiffness and it does not disrupt the titin band seen on SDS-PAGE.

Equilibrium muscle crossbridge behavior: The interaction of myosin crossbridges with actin

The interaction of myosin crossbridges with actin under equilibrium conditions is reviewed. Similarities and differences between the weakly- and strongly-binding interactions of myosin crossbridges with actin filaments are discussed. A precise, narrow definition of weakly-binding crossbridges is given. It is postulated that the fundamental difference between the weakly- and strongly-binding equilibrium interaction of crossbridges with actin is that the crossbridge heads are mobile after attachment in the first case but not in the second. It is argued that because the weakly-binding crossbridge heads are mobile after attachment, the heads appear to function independently of each other. The lack of head mobility in attached strongly-binding crossbridges makes the strongly-binding crossbridge heads appear to act cooperatively. This model of the strongly-binding crossbridge gives an explanation for two important and otherwise unexplained observations. It explains why the rate constant of force decay after a small stretch is a sigmoidal function of nucleotide analogue concentration, and why, in the presence of analogues or in rigor, the rate constant of force decay after a small stretch is often significantly slower than the rate constant for myosin subfragment-1 detachment from actin in solution. The model of the weakly-binding crossbridge accurately describes the behavior of the myosin-ATP crossbridge.

Graphical Evaluation of Alkylation of Myosin's SH1 and SH2: The N-Phenylmaleimide Reaction

Previous assertions about the effect of alkylation of SH1 and SH2 on the myosin high-salt calcium and EDTA ATPases have been summarized, and a simple procedure for obtaining the fractional labeling of SH1 and SH2 after treatment of myosin with alkylating agents has been derived. A simple graphical procedure for illustrating the degree of preference of a particular alkylating agent for SH1 over SH2 has also been developed. The procedures we developed were validated by applying them to two previously studied compounds, 4-(2-iodoacetamido)-TEMPO and 2,4-dinitrofluorobenzine, and then were used to determine a procedure for maximizing the extent of labeling of SH1 alone by N-phenylmaleimide, a compound not previously studied in this manner. It was found that approximately 80% of the SH1 sites could be alkylated without significant alkylation of SH2.

Equilibrium muscle cross-bridge behavior. Theoretical considerations. II. Model describing the behavior of strongly-binding cross-bridges when both heads of myosin bind to the actin filament

A model has been developed for characterizing the interaction between strongly-binding myosin cross-bridges and actin in muscle fibers under equilibrium conditions where both heads of the myosin cross-bridge bind to actin. The model, that of Anderson and Schoenberg (1987. Biophys. J. 52:1077-1082) is quite similar to that of Schoenberg (1985. Biophys. J. 48:467-475), except that explicit account is taken of the fact that each crossbridge has two heads which can bind to actin. The key assumption that allows this model to explain a large body of data unexplained by the Schoenberg (1985) model is that the two crossbridge heads are not totally independent of one another after attachment. After the first head attaches, the second head is then free to attach only to an actin site distal to the first head. This means that when the more distally attached head subsequently detaches and reattaches (as the heads continually do), it will not reattach in a position of lesser strain and reduce the force it supports, but instead will remain attached in its strained position until the proximally attached head also detaches. This model gives an explanation for two important and otherwise unexplained observations made previously: it explains why at ionic strengths in the range of 50-120 mM, (a) the rate constant of force decay after a small stretch is a sigmoidal function of nucleotide analogue concentration, and (b) why in the presence of analogues or in rigor the rate constant of force decay after a small stretch is significantly slower than the rate constant for myosin subfragment-1 detachment from actin in solution.

Behavior of N-Phenylmaleimide-Reacted Muscle Fibers in Magnesium-Free Rigor Solution

Using x-ray diffraction and mechanical stiffness, the response of N-phenylmaleimide (NPM)-reacted cross-bridges to solutions containing different amounts of ATP and Mg2+ has been studied. In relaxing solution containing greater than millimolar amounts of ATP and Mg2+, NPM-treated muscle fibers give x-ray diffraction patterns and stiffness records, which are nearly indistinguishable from those of untreated relaxed fibers. In a solution devoid of added ATP, but with Mg2+ (rigor(+Mg) solution), the muscle fibers still give x-ray diffraction patterns and mechanical responses characteristic of relaxed muscle. The new finding reported here is that in a solution devoid of both ATP and Mg2+ (rigor(-Mg) solution containing EDTA with no added ATP), NPM-reacted cross-bridges do give rigor-like behavior. This is the first report that NPM-reacted cross-bridges, at least in the presence of EDTA, are capable of going into a strongly binding conformation.

Crossbridge Head Detachment Rate Constants Determined from a Model that Explains the Behavior of Both Weakly-and Strongly-Binding Crossbridges

Experimentally it is observed that the head regions of weakly-binding myosin crossbridges (crossbridges with ATP or ADP.Pi at the nucleotide binding site) are mobile while attached to actin, while strongly-binding crossbridge heads, such as those with PPi or AMP-PNP at the nucleotide binding site, are immobile (Pate and Cooke, Biophys. J., 1988; Fajer et al., Biophys. J., 1988). I postulate that the fundamental difference between weakly- and strongly-binding crossbridges is not their difference in affinity for actin, but the difference in mobility of the myosin heads attached to actin. Because the heads of weakly-binding crossbridges are mobile while attached to actin, the heads function independently and their behavior can be described by a simple independent-head model. With strongly-binding crossbridges, when one head detaches, it cannot re-attach in a position of lesser strain while the other is attached immobile; both heads must be detached concurrently before the crossbridge can relocate to a position of less strain and relax any tension it supports. This makes the heads appear to act cooperatively. A double-headed crossbridge model is presented which takes into account the difference between weakly- and strongly-binding crossbridges. The model is quite successful at describing the experimental data. In particular, for weakly-binding crossbridges the time constant of the response to stretch is shown to be relatively insensitive to ionic strength and for strongly-binding crossbridges, the model predicts with great accuracy the large ionic strength dependence of the rate constant for force decay. When the experimental results are interpreted according to the model, an important conclusion that emerges is that in all cases (for both weakly- and strongly-binding crossbridges) unstrained crossbridge heads in the muscle fiber detach from actin with approximately the same rate constant as myosin subfragment-1 detaches from actin in solution.