Modeling of cortical bone adaptation in a rat ulna: effect of frequency.

We employ a recently developed model for the adaptation of cortical bone in response to mechanical loading to study the effect of loading frequency on the computed response, and we compare our results to previous experimental measurements on rat ulnae. We represent the cortical bone as a poroelastic material with orthotropic permeability. Bone adaptation in the model is related to a mechanical stimulus derived from the dissipation energy of the poroelastic flow induced by deformation. We account for a non-locality in the mechanotransduction of osteocytes present in the lacunae by using a "zone of influence." Calculations are done using the finite element method applied to a rat ulna whose geometry is obtained from micro-computed tomography images. We show that the change in the second moment of inertia of the cross-section increases non-linearly and saturates at higher frequency range. The numerical results are then compared quantitatively to experimental data from the literature. Finally, we examine the role of local narrowing of intramedullary canal in our specific ulna in the development of local irregularities in growth.

A small-molecule inhibitor of skeletal muscle myosin II.

We screened a small-molecule library for inhibitors of rabbit muscle myosin II subfragment 1 (S1) actin-stimulated ATPase activity. The best inhibitor, N-benzyl-p-toluene sulphonamide (BTS), an aryl sulphonamide, inhibited the Ca2+-stimulated S1 ATPase, and reversibly blocked gliding motility. Although BTS does not compete for the nucleotide-binding site of myosin, it weakens myosin's interaction with F-actin. BTS reversibly suppressed force production in skinned skeletal muscle fibres from rabbit and frog skin at micromolar concentrations. BTS suppressed twitch production of intact frog fibres with minimum alteration of Ca2+ metabolism. BTS is remarkably specific, as it was much less effective in suppressing contraction in rat myocardial or rabbit slow-twitch muscle, and did not inhibit platelet myosin II. The isolation of BTS and the recently discovered Eg5 kinesin inhibitor, monastrol, suggests that motor proteins may be potential targets for therapeutic applications.

Phase field model for three-dimensional dendritic growth with fluid flow.

We study the effect of fluid flow on three-dimensional (3D) dendrite growth using a phase-field model on an adaptive finite-element grid. In order to simulate 3D fluid flow, we use an averaging method for the flow problem coupled to the phase-field method and the semi-implicit approximated projection method (SIAPM). We describe a parallel implementation for the algorithm, using the CHARM++ FEM framework, and demonstrate its efficiency. We introduce an improved method for extracting dendrite tip position and tip radius, facilitating accurate comparison to theory. We benchmark our results for 2D dendrite growth with solvability theory and previous results, finding them to be in good agreement. The physics of dendritic growth with fluid flow in three dimensions is very different from that in two dimensions, and we discuss the origin of this behavior.

The ADP release step of the smooth muscle cross-bridge cycle is not directly associated with force generation.

When smooth muscle myosin subfragment 1 (S1) is bound to actin filaments in vitro, the light chain domain tilts upon release of MgADP, producing a approximately 3.5-nm axial motion of the head-rod junction (Whittaker et al., 1995. Nature. 378:748-751). If this motion contributes significantly to the power stroke, rigor tension of smooth muscle should decrease substantially in response to cross-bridge binding of MgADP. To test this prediction, we monitored mechanical properties of permeabilized strips of chicken gizzard muscle in rigor and in the presence of MgADP. For comparison, we also tested psoas and soleus muscle fibers. Any residual bound ADP was minimized by incubation in Mg2+-free rigor solution containing 15 mM EDTA. The addition of 2 mM MgADP, while keeping ionic strength and free Mg2+ concentration constant, resulted in a slight increase in rigor tension in both gizzard and soleus muscles, but a decrease in psoas muscle. In-phase stiffness monitored during small (<0.1%) 500-Hz sinusoidal length oscillations decreased in all three muscle types when MgADP was added. The changes in force and stiffness with the addition of MgADP were similar at ionic strengths from 50 to 200 mM and were reversible. The results with gizzard muscle were similar after thiophosphorylation of the regulatory light chain of myosin. These results suggest that the axial motion of smooth muscle S1 bound to actin, upon dissociation of MgADP, is not associated with force generation. The difference between the present mechanical data and previous structural studies of smooth S1 may be explained if geometrical constraints of the intact contractile filament array alter the motions of the myosin heads.

Reversal of the cross-bridge force-generating transition by photogeneration of phosphate in rabbit psoas muscle fibres.

1. Orthophosphate (P(i), 0.1-2.0 mM) was photogenerated within the filament lattice of isometrically contracting glycerinated fibres of rabbit psoas muscle at 10 and 20 degrees C. The P(i) was produced by laser flash photolysis of the photolabile compound 1-(2-nitrophenyl)ethylphosphate (caged P(i)). Caged P(i) caused a depression of tension that was much smaller than that caused by P(i). 2. Photolysis of caged P(i) produced a decline in isometric force composed of four phases: phase I, a lag phase (e.g. 1-4 ms at 10 degrees C) during which force did not change; phase II, an exponential decline by as much as 20% of the pre-pulse force; phase III, a partial force recovery (0-3% of the pre-pulse force); and phase IV, a further slow (0.5-3 s) decline to the steady value. Phases I, III and IV were largely independent of [P(i)] and are likely to be indirect effects caused by the caged P(i) photolysis. 3. Both the rate and amplitude of phase II depended markedly on [P(i)]. The amplitude of phase II was similar to the reduction of steady-state force by P(i). The rate of phase II increased with increasing temperature and [P(i)]. At high [P(i)] the rate began to saturate, and approached limits of 123 s-1 at 10 degrees C and 194 s-1 at 20 degrees C. 4. The rate of phase II was independent of sarcomere overlap, while the amplitude was proportional to tension at partial filament overlap. A control experiment using caged ATP showed that phase II was not produced by the photolytic by-products or the light pulse. The results suggest that phase II is associated with the force-generating transition of the cross-bridge cycle. 5. Sinusoidal length oscillations at 0.5 and 2 kHz were used to measure muscle stiffness during phase II. Stiffness declined in a single exponential phase, with the same time course as phase II of the tension transient. The change in stiffness was 83 +/- 6% (mean +/- S.E.M., n = 10, 0.5 kHz) of the change in tension when both signals were normalized to their pre-flash values. 6. Analysis of the data shows that two steps are involved in force generation and P(i) release. The non-force exerting AM-ADP-P(i) cross-bridge state first isomerizes to form a force-exerting cross-bridge state (AM'-ADP-P(i)). P(i) is then released to form a second force-generating state, AM'-ADP.(ABSTRACT TRUNCATED AT 400 WORDS)

Cross-bridge kinetics in the presence of MgADP investigated by photolysis of caged ATP in rabbit psoas muscle fibres.

1. The interaction between MgADP and rigor cross-bridges in glycerol-extracted single fibres from rabbit psoas muscle has been investigated using laser pulse photolysis of caged ATP (P3-1(2-nitrophenyl)ethyladenosine 5'-triphosphate) in the presence of MgADP and following small length changes applied to the rigor fibre. 2. Addition of 465 microM-MgADP to a rigor fibre caused rigor tension to decrease by 15.3 +/- 0.7% (S.E.M., n = 24 trials in thirteen fibres). The half-saturation value for this tension reduction was 18 +/- 4 microM (n = 23, thirteen fibres). 3. Relaxation from rigor by photolysis of caged ATP in the absence of Ca2+ was markedly slowed by inclusion of 20 microM-2 mM-MgADP in the photolysis medium. 4. Four phases of tension relaxation occurred with MgADP in the medium: at, a quick partial relaxation (in pre-stretch fibres); bt, a slowing of relaxation or a rise in tension for 50-100 ms; ct, a sudden acceleration of relaxation; and dt, a final, nearly exponential relaxation. 5. Experiments at varied MgATP and MgADP concentrations suggested that phase at is due to MgATP binding to nucleotide-free cross-bridges. 6. Phase bt was abbreviated by including 1-20 mM-orthophosphate (Pi) in the photolysis medium, or by applying quick stretches before photolysis or during phase bt. These results suggest that phases bt and ct are complex processes involving ADP dissociation, cross-bridge reattachment and co-operative detachment involving filament sliding and the Ca(2+)-regulatory system. 7. Stretching relaxed muscle fibres to 3.2-3.4 microns striation spacing followed by ATP removal and release of the rigor fibre until tension fell below the relaxed level allowed investigation of the strain dependence of relaxation in the regions of negative cross-bridge strain. In the presence of 50 microM-2 mM-MgADP and either 10 mM-Pi or 20 mM-2,3-butanedione monoxime, relaxation following photolysis of caged ATP was 6- to 8-fold faster for negatively strained cross-bridges than for positively strained ones. This marked strain dependence of cross-bridge detachment is predicted from the model of A. F. Huxley (1957). 8. In the presence of Ca2+, activation of contraction following photolysis of caged ATP was slowed by inclusion of 20-500 microM-MgADP in the medium. An initial decrease in tension related to cross-bridge detachment by MgATP was markedly suppressed in the presence of MgADP. 9. Ten millimolar Pi partly suppressed active tension generation in the presence of MgADP.(ABSTRACT TRUNCATED AT 400 WORDS)

Relaxation of muscle fibers with adenosine 5'-[gamma-thio]triphosphate (ATP[gamma S]) and by laser photolysis of caged ATP[gamma S]: evidence for Ca2+-dependent affinity of rapidly detaching zero-force cross-bridges.

The relationship between the mechanical and biochemical states of the muscle cross-bridge cycle and the control of contraction were investigated by using the nucleotide analogs adenosine 5'-[gamma-thio]triphosphate (ATP[gamma S]) and caged ATP[gamma S] [the O-1(2-nitrophenyl)ethyl P3-ester of ATP[gamma S]]. ATP[gamma S] interacts with actomyosin in a manner similar to ATP but is hydrolyzed (by a factor of 500) more slowly. Generation of ATP[gamma S] by photolysis of caged ATP[gamma S] within a permeabilized fiber in rigor in the absence of Ca2+ relaxed tension and stiffness as occurs with ATP. The transient rise in tension prior to final relaxation observed with photolysis of caged ATP was absent with caged ATP[gamma S]. This result suggests that following detachment of a cross-bridge, ATP is normally hydrolyzed before force generation. In the presence of Ca2+, photolysis of caged ATP[gamma S] within rigor fibers caused tension to relax fully but significant stiffness remained. Stiffness also developed without concomitant tension when Ca2+ concentration was raised from less than 1 nM to 30 microM in the presence of ATP[gamma S]. The amplitude of the tension response to ramp stretches in the presence of Ca2+ and ATP[gamma S] increased with ramp stretch velocity, suggesting that the cross-bridges have detachment rate constants extending into the 10(3) s-1 range. The results provide evidence that the Ca2+-regulatory system can directly control attachment of cross-bridges into states before the power stroke.

Suppression of muscle contraction by vanadate. Mechanical and ligand binding studies on glycerol-extracted rabbit fibers.

The suppression of tension development by orthovanadate (Vi) was studied in mechanical experiments and by measuring the binding of radioactive Vi and nucleotides to glycerol-extracted rabbit muscle fibers. During active contractions, Vi bound to the cross-bridges and suppressed tension with an apparent second-order rate constant of 1.34 X 10(3) M-1s-1. The half-saturation concentration for tension suppression was 94 microM Vi. The incubation of fibers in Vi relaxing or rigor solutions prior to initiation of active contractions had little effect on the initial rise of active tension. The addition of adenosine diphosphate (ADP) and Vi to fibers in rigor did not cause relaxation. Suppression of tension only developed during cross-bridge cycling. After slow relaxation from rigor in 1 mM Vi and low (50 microM) MgATP concentration (0 Ca2+), radioactive Vi and ADP were trapped within the fiber. This finding indicated the formation of a stable myosin X ADP X Vi complex, as has been reported in biochemical experiments with isolated myosin. Vi and ADP trapped within the fibers were released only by subsequent cross-bridge attachment. Vi and ADP were preferentially trapped under conditions of cross-bridge cycling in the presence of ATP rather than in relaxed fibers or in rigor with ADP. These results indicate that in the normal cross-bridge cycle, inorganic phosphate (Pi) is released from actomyosin before ADP. The resulting actomyosin X ADP intermediate can bind Vi and Pi. This intermediate probably supports force. Vi behaves as a close analogue of Pi in muscle fibers, as it does with isolated actomyosin.

Phosphate release and force generation in skeletal muscle fibers.

Rapid laser pulse-induced photolysis of an adenosine triphosphate precursor in muscle fibers abruptly initiated cycling of the cross-bridges. The accompanying changes in tension and stiffness were related to elementary mechanochemical events of the energy-transducing mechanism. When inorganic phosphate was present at millimolar concentrations during liberation of adenosine triphosphate in the absence of calcium, relaxation was accelerated. Steady active tension in the presence of calcium was decreased but the approach to final tension was more rapid. These results suggest that, during energy transduction, formation of the dominant force-generating cross-bridge state is coupled to release of inorganic phosphate in a reaction that is readily reversible.