Journal of Applied Physiology Watch the video to learn how APS reaches out to developing nations.
HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
QUICK SEARCH:   [advanced]


     

J Appl Physiol 98: 1356-1365, 2005. First published November 19, 2004; doi:10.1152/japplphysiol.00834.2004
8750-7587/05 $8.00
This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF) Free
Right arrow All Versions of this Article:
98/4/1356    most recent
00834.2004v1
Right arrow Submit a response
Right arrow Alert me when this article is cited
Right arrow Alert me when eLetters are posted
Right arrow Alert me if a correction is posted
Right arrow Citation Map
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in Web of Science
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Citing Articles
Right arrow Citing Articles via HighWire
Right arrow Citing Articles via Web of Science (5)
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Hai, C.-M.
Right arrow Articles by Kim, H. R.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by Hai, C.-M.
Right arrow Articles by Kim, H. R.

An expanded latch-bridge model of protein kinase C-mediated smooth muscle contraction

Chi-Ming Hai and Hak Rim Kim

Department of Molecular Pharmacology, Physiology and Biotechnology, Brown University, Providence, Rhode Island

Submitted 3 August 2004 ; accepted in final form 17 November 2004


   ABSTRACT
TOP
 ABSTRACT
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 ACKNOWLEDGMENTS
 REFERENCES
 
A thin-filament-regulated latch-bridge model of smooth muscle contraction is proposed to integrate thin-filament-based inhibition of actomyosin ATPase activity with myosin phosphorylation in the regulation of smooth muscle mechanics. The model included two latch-bridge cycles, one of which was identical to the four-state model as proposed by Hai and Murphy (Am J Physiol Cell Physiol 255: C86–C94, 1988), whereas the ultraslow cross-bridge cycle has lower cross-bridge cycling rates. The model-fitted phorbol ester induced slow contractions at constant myosin phosphorylation and predicted steeper dependence of force on myosin phosphorylation in phorbol ester-stimulated smooth muscle. By shifting cross bridges between the two latch-bridge cycles, the model predicts that a smooth muscle cell can either maintain force at extremely low-energy cost or change its contractile state rapidly, if necessary. Depending on the fraction of cross bridges engaged in the ultraslow latch-bridge cycle, the model predicted biphasic kinetics of smooth muscle mechanics and variable steady-state dependencies of force and shortening velocity on myosin phosphorylation. These results suggest that thin-filament-based regulatory proteins may function as tuners of actomyosin ATPase activity, thus allowing a smooth muscle cell to have two discrete cross-bridge cycles with different cross-bridge cycling rates.

caldesmon; calponin; latch; mechanics; myosin

SMOOTH MUSCLE CELLS ARE THE contractile component of body passages, including blood vessels, airways, gastrointestinal tract, and others. Abnormal contractility of smooth muscle cells is an important cause of many diseases, such as hypertension and asthma. Much has been learned about the details of thin- and thick-filament-based regulatory proteins of smooth muscle contraction, but an integrative understanding of how the different regulatory proteins function together remains elusive. In this study, we propose a mathematical model of smooth muscle contraction that integrates thin-filament-based regulation of actomyosin ATPase activity and thick-filament-based myosin light chain phosphorylation.

It is well known that phosphorylation of the 20,000-Da myosin light chain is a central regulatory mechanism of smooth muscle contraction (26). However, myosin phosphorylation does not follow force during a smooth muscle contraction. Myosin phosphorylation typically increases to a peak level at the beginning of a contraction and then decreases to a lower steady-state level, whereas isometric force develops monotonically to the steady state (4, 5, 13, 18). In contrast, changes in myosin phosphorylation follow the changes in cross-bridge cycling rate, as measured by unloaded shortening velocity during smooth muscle contraction (4, 5). Therefore, steady-state force is maintained at relatively low levels of myosin light chain phosphorylation and cross-bridge cycling rates, which has been termed the "latch state" (5, 11). Hai and Murphy (9, 10) proposed a four-state cross-bridge model to explain the latch state in smooth muscle (Fig. 1A). The four-state model postulates the existence of attached, unphosphorylated latch bridges (AM) that are generated by dephosphorylation of attached phosphorylated cross bridges (AMp). The four-state model was able to predict the myosin phosphorylation transient during monotonic force development (9), linear dependence of cross-bridge cycling rate on myosin phosphorylation (10), and quasi-hyperbolic dependence of steady-state force on myosin phosphorylation (28). Using measurements of intracellular Ca2+ concentration ([Ca2+]), Rembold and Murphy (30) showed that the four-state model could quantitatively predict the force oscillations in response to intracellular [Ca2+] oscillations. By adding length dynamics, Yu et al. (43) showed that the four-state model could explain both isometric and nonisometric responses of vascular smooth muscle, airway smooth muscle, molluscan catch muscle, and Aplysia muscle. By including twitchin-dependent regulation of latch-bridge detachment, Butler et al. (3) showed that the four-state model could quantitatively explain the regulation of catch muscle contraction by twitchin phosphorylation. By incorporating Huxley's (15) model of strain-dependent cross-bridge cycling rates, Mijailovich et al. (23) showed that the four-state model could predict force fluctuation-induced lengthening of airway smooth muscle. These results show that the four-state model is robust in explaining smooth muscle mechanics.



View larger version (31K):
[in this window]
[in a new window]
  		Fig. 1. Schematic diagrams of four-state latch-bridge model as described by Hai and Murphy (9) (A) and thin-filament-regulated latch-bridge model (B). The regular latch-bridge cycle in B is the same as the four-state model in A. The ultraslow latch-bridge cycle in B has slower rate constants (K30, K40, K70) for cross-bridge cycling. K9 and K10 represent the rate constants for exchange between the regular and ultraslow latch-bridge cycles. A single pair of rate constants, K1 and K2, represents myosin light chain kinase (MLCK) and phosphatase (MLCP) activities in both models.

 
However, the four-state model is incomplete because it does not include thin-filament-based regulatory mechanisms such as calponin and caldesmon (8, 24, 38, 41), and it cannot explain phorbol ester-induced slow contractions when myosin phosphorylation has already reached steady state (1, 13, 31, 33, 35, 37). Calponin and caldesmon are actin-binding proteins that inhibit smooth muscle actomyosin ATPase activity in vitro. Phorbol esters are activators of PKC and have been shown to induce slow smooth muscle contractions with little or no increase in intracellular [Ca2+] and myosin phosphorylation. PKC-mediated inhibition of myosin light chain phosphatase (MLCP) activity could explain phorbol ester-induced contractions with small changes in intracellular [Ca2+] (2, 21, 22, 29, 36, 42). However, this mechanism cannot explain phorbol ester-induced contractions at constant myosin phosphorylation. The inclusion of MLCP inhibition in the four-state model also could not predict force development at constant myosin phosphorylation, because the model would predict the loss of latch bridges as a result of MLCP inhibition (12).

Sato et al. (31) have performed quick release experiments on KCl- and phorbol dibutyrate (PDBu)-stimulated smooth muscle strips. They observed similar force recoveries after shortening in KCl- and PDBu-stimulated muscle strips. Therefore, Sato et al. (31) concluded that PDBu-induced contractions were mediated by cycling cross bridges. The phorbol ester-induced slow contraction data suggest the appearance of a population of ultraslow cycling cross bridges at constant myosin phosphorylation. In the four-state model, the number of latch bridges is determined by the relative rates of latch-bridge detachment, latch-bridge phosphorylation, and dephosphorylation of attached cross bridges. Therefore, slowing of cross-bridge cycling rates, including latch-bridge detachment, could potentially lead to force development at constant myosin phosphorylation. Accordingly, we added an ultraslow latch-bridge cycle to the four-state model to create a thin-filament-regulated latch-bridge model, as shown in Fig. 1B. The regular and ultraslow latch-bridge cycles both have the four-state structure but different cross-bridge cycling rates. In this study, we tested the ability of the thin-filament-regulated latch-bridge model to fit the data of phorbol ester-induced slow force development at constant myosin phosphorylation. In addition, we performed model simulations to test the model's predictions of the steady-state dependencies of force and apparent cycling rate constants on myosin phosphorylation.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 ACKNOWLEDGMENTS
 REFERENCES
 
Mathematical Modeling

The system of differential equations was solved using WinSAAM, the Windows version of SAAM (Simulation, Analysis, and Modeling), run on a Pentium III-based microcomputer, as described by Wastney et al. (39). The earlier version of this software, SAAM, has been used previously in our laboratory's compartmental analysis of Ca2+ kinetics in vascular smooth muscle (27). Our laboratory's published data on PDBu-induced contraction (13) were used for modeling in this study because the cross-bridge cycling rate constants for bovine tracheal smooth muscle were already available (9). Because the primary goal in this study was model development, a model fit was considered acceptable when the model fits the mean data points within standard error bars. Tissues from slaughterhouse for normal food processing are exempted from institutional review.

Tissue Preparation

Bovine tracheae were collected from a local slaughterhouse and transported to the laboratory in cold (4°C) physiological salt solution (PSS) of the following composition (in mM): 140.1 NaCl, 4.7 KCl, 1.2 Na2HPO4, 2.0 MOPS (pH 7.4), 0.02 Na2EDTA, 1.2 MgSO4, 1.6 CaCl2, and 5.6 D-glucose. The smooth muscle layer, together with the adventitial and mucosal layers, were excised from the trachea by making longitudinal cuts along their attachments to the cartilage. The adventitial and mucosal layers were then carefully dissected away in cold PSS using microdissecting scissors and fine forceps under a dissecting microscope. Smooth muscle strips were prepared by making cuts along the direction of smooth muscle bundles, corresponding to the circumferential direction, in vivo.

Isometric Contractions

One end of each muscle strip was clamped to a stainless steel clip connected to a force transducer (Grass FT.03), and the other end was clamped to a stainless steel clip connected to a length manipulator (Narishige). Muscle strips were then equilibrated for 2 h in PSS (37°C, pH 7.4) bubbled with air and adjusted to optimal length for maximal active force development, as described previously (20). Muscle strips were then allowed to relax in PSS for 1 h before stimulation by 1 µM PDBu for 30 min.

Tissue Homogenization, Fractionation, SDS-PAGE, and Western Blotting

After 30 min of stimulation by carbachol, muscle strips were quickly homogenized in a cold (4°C) extraction buffer of the following composition: 20 mM Tris·HCl (pH 7.5), 2 mM EDTA, 2 mM EGTA, 6 mM mercaptoethanol, 50 µg/ml aprotinin, 50 µg/ml leupeptin, 0.1 mM Na3VO4, 1 mM PMSF, and 50 mM NaF. Tissue homogenates were centrifuged at 100,000 g for 1 h to separate the cytoskeletal-membrane and cytoplasmic fractions. The pellet represents the cytoskeletal-membrane fraction, whereas the supernatant represents the cytosolic fraction, as described previously (20). After ultracentrifugation, pellets were homogenized in a SDS buffer (1% SDS, 10% glycerol, and 20 mM dithiothreitol) at 20 mg/ml. The supernatant volume was measured, and an equal volume of 2x SDS buffer was added. The pellet and supernatant samples were stored at –80°C.

Proteins were separated by SDS-PAGE using a separating gel of 7.5% acrylamide. Pellet and supernatant samples from the same tissue were loaded next to each other to minimize variations during Western blotting. Equal volumes of pellet and supernatant samples were loaded onto the same gel. After SDS-PAGE, proteins were transferred electrophoretically to a nitrocellulose membrane (Transblot, Bio-Rad). The nitrocellulose membranes were blocked with 5% nonfat dry milk in Tris-buffered saline. After blocking, nitrocellulose membranes were incubated with primary antibodies against the conventional PKC isoforms {alpha}, {beta}, and {beta}II, and novel PKC isoforms {delta} and {epsilon} at 4°C with gentle shaking overnight. The conventional PKC isoforms {alpha}, {beta}, and {beta}II, and novel PKC isoforms {delta} and {epsilon} were selected for this study because PDBu, an analog of diacylglycerol, is expected to activate these two classes of PKC isoforms (14). Furthermore, bovine tracheal smooth muscle has been found to express predominantly PKC-{alpha}, -{beta}I, and -{beta}II, with very low expression levels of PKC-{delta} and -{epsilon} (40). Next, the nitrocellulose membranes were washed with Tris-buffered saline and then incubated with the appropriate horseradish peroxidase-conjugated secondary antibody for 1 h at room temperature. Primary antibodies against PKC isoforms were purchased from Santa Cruz. Secondary antibodies were purchased from Sigma.

Protein bands were detected by using enhanced chemiluminescence reagents (Amersham Biosciences, Piscataway, NJ) and XAR Autoradiography film (Kodak, Rochester, NY). Film images were captured and analyzed by the Kodak Electrophoresis Documentation and Analysis System 290 (EDAS 290) and Kodak 1D image analysis software. Because the loading volumes for pellet and supernatant samples were the same for each gel, we calculated the pellet-to-supernatant ratio (P/S) for each protein from pellet band density x pellet sample volume/supernatant band density x supernatant sample volume. P/S are presented as means ± SE; n represents the number of animals. Student's t-test was used for the comparison of two means (P < 0.05 was considered significant).


   RESULTS
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 ACKNOWLEDGMENTS
 REFERENCES
 
The Thin-Filament-Regulated Latch-Bridge Model

Figure 1A shows the four-state model that was proposed by Hai and Murphy (9). A major assumption of this model was the postulated existence of latch bridges (AM) that were generated by dephosphorylation of attached, phosphorylated cross bridges (AMp). Figure 1B shows the thin-filament-regulated latch-bridge model that includes two latch-bridge cycles, both having the four-state structure but different cycling rates. The regular latch-bridge cycle, consisting of M, Mp, AMp, and AM, and the cycling rate constants K3, K4, and K7 were identical to the four-state model proposed by Hai and Murphy (Fig. 1A). The ultraslow latch-bridge cycle, consisting of M', Mp', A'Mp', A'M', and the cycling rate constants K30, K40, and K70 also have a four-state structure but slower cross-bridge cycling rates than the regular latch-bridge cycle. The specific assumptions and initial conditions for the model are as follows.

Assumption 1.   Myosin light chain kinase (MLCK) and MLCP activities are independent of cross-bridge states. This assumption was also included in the formulation of the four-state model by Hai and Murphy (9). This assumption implies that a single rate constant for MLCK activity (K1) governs the phosphorylation of all unphosphorylated cross-bridge species (M, AM, M', and A'M'). Similarly, a single rate constant for MLCP activity (K2) governs the dephosphorylation of all phosphorylated cross-bridge species (Mp, AMp, Mp', and A'Mp').

Assumption 2.   Attenuation of cross-bridge cycling rates in the ultraslow latch-bridge cycle is independent of cross-bridge states. This assumption was made to avoid bias in selecting specific rate constants for attenuation. This assumption implies proportional attenuation of all rate constants for cross-bridge cycling in the ultraslow latch-bridge cycle relative to the regular latch-bridge cycle. This assumption is described mathematically as follows.

where a < 1

Assumption 3.   A pair of transition rate constants (K9 and K10) governs the exchange between the regular and latch-bridge cycles. We took the minimalist approach to assume a single point of exchange between A + M and A' + M' in the thin-filament-regulated latch-bridge model.

Initial conditions.   We took the minimalist approach by assuming the following initial conditions before activation by PDBu.



The following system of differential equations describes the thin-filament-regulated latch-bridge model, as shown in Fig. 1B.








Fitting of PDBu Data by the Four-State Model and the Thin-Filament-Regulated Latch-Bridge Model

Figure 2A shows the time-dependent step functions of MLCK activity (K1) that fitted the time course of myosin phosphorylation (Fig. 2B) during PDBu-induced contractions of bovine tracheal smooth muscle, as published by Hai and Szeto (13). Step functions of MLCK activity were used to model the PDBu data because they required the minimum number of parameters. Basal myosin phosphorylation was not fitted because of the uncertainty on what mechanisms and artifacts contributed to basal myosin phosphorylation in the experimental data. Figure 2C shows the prediction of force by the four-state model using the same cross-bridge cycling rate constants (K3, K4, and K7), as published by Hai and Murphy (9) for bovine tracheal smooth muscle. Model prediction of force was calculated from the sum of AMp, AM, and basal force. As shown in Fig. 2C, the four-state model predicted the force data reasonably well up to 600 s of PDBu-induced contractions. The agreement between the model and data was remarkable because the rate constants for cross-bridge cycling (K3, K4, and K7) were constrained to be the same as those published by Hai and Murphy (9). However, the four-state model failed to predict force development after 600 s when myosin phosphorylation had already reached steady state. The failure of the four-state model to fit the later time points was to be expected because the rate constants for cross-bridge cycling, (K3, K4, and K7) were resolved previously from the fast contractions of electrically activated smooth muscle (9, 19, 34). Although Fig. 2C shows only one data point at 1,800 s, PDBu-induced slow-force development was continuous between 600 and 1,800 s (18, 33). Therefore, an important issue in modeling the PDBu data was whether a model could predict force development after myosin phosphorylation had already reached steady state.



View larger version (22K):
[in this window]
[in a new window]
  		Fig. 2. Fitting of experimental data of Hai and Szeto (13) ({bullet} and dashed lines) by four-state model of Hai and Murphy (9) (solid lines). A: time course of K1 (MLCK activity) that generated the model fit to the myosin phosphorylation (solid line; B). K1 (MLCK activity) was 4.5 x 10–3 s–1 between 0 and 60 s, 5 x 10–4 s–1 between 61 and 180 s, and 2.1 x 10–3 s–1 between 181 and 1,800 s. K2 (MLCP activity) was 8 x 10–3 s–1. C: model prediction of force (solid line) using the same cross-bridge cycling rate constants (K3, K4, and K7) as published by Hai and Murphy (9) for bovine tracheal smooth muscle. K3 was 0.44 s–1, K4 was 0.11 s–1, and K7 was 0.005 s–1. PDBu, phorbol dibutyrate; Fo, maximum isometric force.

 
Figure 3 shows fitting of the PDBu data by the thin-filament-regulated latch-bridge model. The same step functions of MLCK activity, as shown previously in Fig. 2A, were used to fit the myosin phosphorylation data. Changing the model did not change the fit to the myosin phosphorylation data (Fig. 3B) because MLCK (K1) and MLCP (K2) activities were modeled as independent of cross-bridge states. Figure 3C shows that the thin-filament-regulated latch-bridge model was able to fit PDBu-induced continuous force development after myosin phosphorylation had reached steady state. As shown in Fig. 4, analysis of the cross-bridge states indicated that accumulation of the latch bridges A'M' in the ultraslow latch-bridge cycle was primarily responsible for the slow-force development in PDBu-induced contractions.



View larger version (23K):
[in this window]
[in a new window]
  		Fig. 3. Fitting of experimental data by Hai and Szeto (13) ({bullet} and dashed lines) by the thin-filament-regulated latch-bridge model (solid lines). A: time course of K1 (MLCK activity) that generated the model fit to the myosin phosphorylation data (solid line; B). K1 (MLCK activity) was 4.5 x 10–3 s–1 between 0 and 60 s, 5 x 10–4 s–1 between 61 and 180 s, and 2.1 x 10–3 s–1 between 181 and 1,800 s. K2 (MLCP activity) was 8 x 10–3 s–1. C: model prediction of force by the thin-filament-regulated latch-bridge model (solid line) that fitted the experimental data (symbols). The cross-bridge cycling rate constants (K30, K40, and K70) for the ultraslow latch-bridge cycle were proportionally slower than the corresponding rate constants (K3, K4, and K7) in the regular latch-bridge cycle. K3, K4, and K7 were the same as those published by Hai and Murphy (9) for bovine tracheal smooth muscle. K3 was 0.44 s–1, K4 was 0.11 s–1, and K7 was 0.005 s–1. K30 was 0.012 s–1, K40 was 0.003 s–1, and K70 was 0.000136 s–1. For the exchange between the regular and ultraslow latch-bridge cycles, K9 was 3 x 10–3 s–1, and K10 was 10–3 s–1. TFR, thin-filament regulated.

 


View larger version (18K):
[in this window]
[in a new window]
  		Fig. 4. Model predictions of the time courses of force and attached cross-bridge species during PDBu-induced contractions. AMp and AM represent the attached, phosphorylated cross bridges and latch bridges in the regular latch-bridge cycle (Fig. 1B). A'Mp' and A'M' represent the attached, phosphorylated cross bridges and latch bridges in the ultraslow latch-bridge cycle. Model prediction of suprabasal force was calculated from the sum of AMp, AM, A'Mp', and A'M'.

 
Sensitivity Analysis

In the thin-filament-regulated latch-bridge model, proportional slowing of cross-bridge cycling rates was represented by the slowing factor ("a"), which equals the ratios of K30/K3, K40/K4, and K70/K7. As shown in Fig. 3C, the PDBu-induced contraction data were fitted with a slowing factor a of 0.027, implying that the rate constants for cross-bridge cycling in the ultraslow cross-bridge cycle were 2.7% of the corresponding rate constants in the regular cross-bridge cycle. Fig. 5A shows the sensitivity analysis of the predicted force to changes in the slowing factor a. The solid line, labeled "a = 0.027" in Fig. 5A, represents the model's fit to the PDBu-induced force development. The dashed line, labeled "a = 1" in Fig. 5A, represents the special case of identical cross-bridge cycling rates in the two latch-bridge cycles. In this special case, the thin-filament-regulated latch-bridge cycle becomes the same as the four-state model. Therefore, the thin-filament-regulated latch-bridge model represents a general model that includes the four-state model as a special case when the two latch-bridge cycles have identical cross-bridge cycling rates. As shown in Fig. 5A, as the value of the slowing factor a decreases, the model predicts force development at constant myosin phosphorylation.



View larger version (25K):
[in this window]
[in a new window]
  		Fig. 5. Sensitivity analysis of model predictions to changes in slowing factor a (A) and transition rate constant K9 (B). A: the slowing factor a represents the ratio of cross-bridge cycling rate constants between the ultraslow and regular latch-bridge cycles (a = K30/K3 = K40/K4 = K70/K7). Solid line represents the model's fit to the force data (symbols) with a value of 0.027 for the slowing factor a. Dashed lines represent model predictions using other values of slowing factor a, ranging from 0.01 to 1. B: the transition rate constant K9 governs the shifting of cross bridges from the regular latch-bridge cycle to the ultraslow latch-bridge cycle. Solid line represents the model's fit to the force data (symbols) with a value of 3 x 10–3 s–1 for K9. Dashed lines represent model predictions using other values of K9, ranging from 3 x 10–4 to 3 x 10–2 s–1.

 
As shown in Fig. 1B, the rate constant K9 governs the transition from the regular latch-bridge cycle to the ultraslow latch-bridge cycle. Figure 5B shows the sensitivity analysis of the predicted force to changes in the transition rate constant K9. The solid line, labeled "3E-3" in Fig. 5B, represents the model's fit to PDBu-induced force development. As shown in the dashed lines in Fig. 5B, other values of K9 failed to fit the rate of force development in PDBu-induced contractions.

Steady-State Analysis

Using the set of rate constants that fitted the PDBu data (Fig. 3), steady-state solutions of the cross-bridge states were computed for different values of myosin phosphorylation. Figure 6A shows the model's prediction of the dependence of steady-state force on myosin phosphorylation, and the steady-state distribution of the four attached cross-bridge states as functions of myosin light chain phosphorylation. As shown in Fig. 6A, the model predicted a quasi-hyperbolic dependence of force on myosin phosphorylation, such that steady-state force reached 90% of maximum force at ~30% myosin phosphorylation (Fig. 6A, solid line). A'Mp' and A'M' in the ultraslow latch-bridge cycle were the major attached cross bridges that contributed to force development (Fig. 6A). AMp in the regular latch-bridge cycle also increased with myosin phosphorylation, but [AMp] was only one-third or less of [A'Mp'] at a given level of myosin phosphorylation. [A'Mp'] was approximately threefold of [AMp] at a given level of myosin phosphorylation due to the 3:1 ratio of K9/K10. The accumulation of A'M' at low levels of myosin phosphorylation was due to the slow rate constant of latch-bridge detachment for A'M' (K70 = 0.00014 s–1) relative to MLCK activity (K1) and MLCP activity (K2). In the steady-state analysis, K1 ranged from 0.001 s–1 at 11% myosin phosphorylation to 0.1 s–1 at 92% myosin phosphorylation, whereas K2 was 0.008 s–1. As shown in the thin-filament-regulated latch-bridge model (Fig. 1B), when the latch-bridge detachment rate constant K70 becomes negligible relative to K1, [A'M'] is determined primarily by the exchanges with A'Mp', via MLCK (K1) and phosphatase (K2) activities. Therefore, except at a very low value of MLCK activity (K1), the [A'M']/[A'Mp'] could be approximated by the MLCP-to-MLCK ratio. As a result, [A'M'] was higher than [A'Mp'] when myosin phosphorylation was <50%. Conversely, [A'M'] was lower than [A'Mp'] when myosin phosphorylation was >50%.



View larger version (23K):
[in this window]
[in a new window]
  		Fig. 6. Steady-state solutions of dependencies of attached cross-bridge species and suprabasal force on myosin phosphorylation, using rate constants that fitted the PDBu data in Fig. 3 (A) and variable force-phosphorylation relations as function of K9 (B). AMp, AM, A'Mp', and A'M' are as described in Fig. 4 legend. Model prediction of force was calculated from the sum of AMp, AM, A'Mp', and A'M'. Model prediction of myosin phosphorylation was calculated from the sum of Mp, AMp, Mp', and A'Mp'. Solid lines in both panels represent the steady-state solutions using rate constants that fitted the PDBu data in Fig. 3. In B, dashed lines represent model predictions of steady-state force-phosphorylation relations using other values of K9. LC20, 20,000-Da myosin light chain.

 
Figure 6B shows the effect of changing the transition rate constant K9 on the steady-state force-myosin phosphorylation relation. As shown in Fig. 6B, a 10-fold decrease in K9 from 3 x 10–3 to 3 x 10–4 s–1 substantially decreased the slope of the steady-state phosphorylation-force relation. In contrast, a 10-fold increase in K9 from 3 x 10–3 to 3 x 10–2 s–1 had a relatively small effect on the slope of the steady-state phosphorylation-force relation. The differential sensitivities of the force-myosin phosphorylation relation to the increase and decrease in K9 can be explained in terms of the fraction of total cross-bridge population that is engaged in the ultraslow cross-bridge cycle. At the value of K9 that fitted the PDBu data (Fig. 3), the K9-to-K10 ratio was 3:1, implying that ~75% of the cross-bridge population was engaged in the ultraslow latch-bridge cycle during PDBu-induced contractions. A 10-fold decrease in K9 would decrease the K9-to-K10 ratio to 0.3:1, decreasing the cross-bridge population engaged in the ultraslow latch-bridge cycle to 23%. This represents a relatively large loss (69%) of the original cross-bridge population and results in a relatively large decrease in the slope of the force-phosphorylation relation. In contrast, a 10-fold increase in K9 from 3 x 10–3 to 3 x 10–2 s–1 would increase the K9-to-K10 ratio to 30:1, increasing the cross-bridge population engaged in the ultraslow latch-bridge cycle to 97%. This represents a relatively small gain (29%) of the original cross-bridge population and results in a relatively small increase in the slope of the force-myosin phosphorylation relation.

Model Simulations

Modeling of PDBu data predicts that shifting cross bridges from the regular latch-bridge cycle to the ultraslow latch-bridge cycle will lead to force development at constant myosin phosphorylation. To test this model prediction directly, we performed the following model simulations. First, a step increase in MLCK activity (K1) was simulated to induce a relatively fast increase in myosin phosphorylation that reached steady state within 1,000 s (Fig. 7A). All other rate constants were constrained to be the same as those that fitted the PDBu data (Fig. 3). Figure 7B shows the three model simulations of changing K9 and the predicted time courses of force development. It is important to note that changing K9 has no effect on myosin phosphorylation because the rate constants for MLCK and MLCP activities were modeled as independent of cross-bridge states. When K9 was held at 3 x 10–3 s–1 at all times between 0 and 7,000 s, the model predicted monotonic development of force to ~70% of total cross bridges (Fig. 7B, "K9 = 3E-3"). When K9 was held at 3 x 10–4 s–1 at all times between 0 and 7,000 s, the model predicted monotonic development of force to ~50% of total cross bridges (Fig. 7B, "K9 = 3E-4"). When K9 was held at 3 x 10–4 s–1 from 0 to 1,880 s and then increased to 3 x 10–3 s–1 at 1,881 s, the model predicted the following. As shown in Fig. 7B (solid line), the predicted force first followed the curve for K9 = 3 x 10–4 s–1 up to 1,880 s, then decreased slightly, and finally increased to the level for K9 = 3 x 10–3 s–1 while myosin phosphorylation remained constant at all times.



View larger version (18K):
[in this window]
[in a new window]
  		Fig. 7. Model simulations of changing K9 and the predicted effects on force and myosin phosphorylation. A: model prediction of myosin phosphorylation when K1 (MLCK) was 2.1 x 10–3 s–1 between 0 and 7,000 s. All other rate constants, except K9, were the same as those that fitted the PDBu data in Fig. 3. B: the two dotted lines represented model predictions of force when K9 was held at 3 x 10–4 or 3 x 10–3 s–1 at all times between 0 and 7,000 s. B: the solid line represented the model prediction of force when K9 was held at 3 x 10–4 s–1 from 0 to 1,880 s, and then increased from 3 x 10–4 to 3 x 10–3 s–1 at 1,881 s. LC, 20,000 Da myosin light chain.

 
Figure 8 shows the predicted time courses of phosphorylated and attached cross-bridge states during the shifting of cross bridges from regular latch-bridge cycle to ultraslow latch-bridge cycle. As shown in Fig. 8A, an increase in K9 led to the even exchange of the phosphorylated cross bridges Mp and AMp in the regular latch-bridge cycle, with the phosphorylated cross bridges Mp' and A'Mp' in the ultraslow latch-bridge cycle, without changing the level of myosin phosphorylation. This exchange was even because the rate constants for MLCK and MLCP activities were modeled as independent of cross-bridge states. As shown in Fig. 8B, an increase in K9 led to the exchange of the attached cross bridges A'Mp' and A'M' in the ultraslow latch-bridge cycle, with the attached cross bridges AMp and AM in the regular latch-bridge cycle. However, the exchange of attached cross bridges between the two latch-bridge cycles was uneven, resulting in the net gain of attached cross bridges in the ultraslow latch-bridge cycle and force development.



View larger version (25K):
[in this window]
[in a new window]
  		Fig. 8. Model predictions of the effect of changing K9 on phosphorylated cross-bridge states (A) and attached cross-bridge states (B). K9 was held at 3 x 10–4 s–1 from 0 to 1,880 s, and then increased to 3 x 10–3 s–1 at 1,881 s. A: exchange of the phosphorylated cross bridges Mp and AMp in the regular latch-bridge cycle (dotted lines) with the phosphorylated cross bridges Mp' and A'Mp' in the ultraslow latch-bridge cycle (solid lines) as a result of increasing K9. B: exchange of the attached cross bridges AMp and AM in the regular latch-bridge cycle (dotted lines) with the attached cross bridges A'Mp' and A'M' in the ultraslow latch-bridge cycle (solid lines) as a result of increasing K9.

 
Apparent Cross-Bridge Cycling Rate Constants

Apparent attachment and detachment rate constants were calculated from the steady-state solutions (Fig. 9). As described previously by Hai and Murphy (10), the apparent cross-bridge attachment rate constant (F) was defined as follows: (total flux of cross-bridge attachment)/(total detached cross bridges). In a steady state, the flux along a given pathway equals mass x rate constant (39). Accordingly, the following equation calculates the apparent attachment rate constant.



View larger version (21K):
[in this window]
[in a new window]
  		Fig. 9. Model predictions of variable dependencies of apparent attachment rate constant (F) (A) and apparent detachment rate constant (G) on myosin phosphorylation as a function of K9 (B). Apparent attachment and detachment rate constants were calculated using the rate constants and steady-state solutions shown in Fig. 6 (see text).

 
The apparent detachment rate constant (G) was defined as follows: (total flux of cross-bridge detachment)/(total attached cross bridges). The following equation calculates the apparent detachment rate constant.

Figure 9 shows the dependencies of apparent attachment and detachment rate constants on myosin phosphorylation at different values of K9. At a given value of K9, the increase in apparent cycling rate constants with myosin phosphorylation reflected the conversion of latch bridges to the cycling phosphorylated cross bridges within each of the two latch-bridge cycles. The K9-dependent changing of the dependence of apparent cycling rate constants on myosin phosphorylation (Fig. 9) reflects the shifting of cross bridges from the regular latch-bridge cycle to the ultraslow latch-bridge cycle.

PDBu-Induced Translocation of PKC Isoforms

Figure 10 shows the Western blots of PKC-{alpha}, -{beta}, and -{beta}II in the pellet and supernatant fractions of unstimulated (PSS) and 1 µM PDBu-stimulated (PDBu) tissues. We observed extremely low expression levels of PKC-{delta} and -{epsilon} that were indistinguishable from background signals. This observation is consistent with the findings of Webb et al. (40). As shown in Fig. 10, in unstimulated tissues (PSS), band densities for PKC-{alpha}, -{beta}, and -{beta}II were stronger in the supernatant than the pellet, whereas the reverse is true for PDBu-stimulated tissues (PDBu). As shown in Fig. 11, PDBu stimulation significantly increased the P/S of PKC-{alpha} and -{beta} by 3.0- and 5.9-fold, respectively. However, the increase in the P/S of PKC-{beta}II was statistically insignificant.



View larger version (31K):
[in this window]
[in a new window]
  		Fig. 10. Western blots of PKC-{alpha}, -{beta}, and -{beta}II in the pellet (P) and supernatant (S) fractions of unstimulated [physiological salt solution (PSS)] and 1 µM PDBu-stimulated bovine tracheal smooth muscle.

 


View larger version (8K):
[in this window]
[in a new window]
  		Fig. 11. Pellet-to-supernatant ratios (P/S) of PKC-{alpha}, -{beta}, and -{beta}II in unstimulated and 1 µM PDBu-stimulated bovine tracheal smooth muscle. Identical volumes of pellet (P) and supernatant (S) samples were loaded into adjacent lanes of the same gel to minimize variations during Western blotting. Total pellet and supernatant volumes from a given tissue were similar. The P/S were calculated from pellet band density x pellet sample volume/supernatant band density x supernatant sample volume. Data are presented as means ± SE (n = 3). P/S represents the partition of a given protein between the cytoskeletal/membrane complex and cytoplasm. *Significant difference between P/S in unstimulated and PDBu-stimulated tissues (P < 0.05).

 

   DISCUSSION
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
ACKNOWLEDGMENTS
 REFERENCES
 
Four-State Model vs. Thin-Filament-Regulated Latch-Bridge Model

In this study, a new model of smooth muscle contraction (Fig. 1B) has been developed to address some experimental data that could not be explained by the four-state model (Fig. 1A). Thin-filament-based regulation of actomyosin ATPase activity was absent in the four-state model because the four-state model assumed that myosin light chain phosphorylation was the only regulatory mechanism (9, 10). Phorbol ester-induced force development at constant myosin phosphorylation could not be explained by the four-state model because the rate constants for cross-bridge cycling were derived from fast contractions of electrically stimulated smooth muscle (9, 19). The proposed thin-filament-regulated latch-bridge model included two latch-bridge cycles, one of which was identical to the four-state model, whereas the ultraslow cross-bridge cycle had lower cross-bridge cycling rates. To avoid bias in selecting specific rate constants for attenuation, we assumed proportional slowing of all cross-bridge cycling rate constants in the ultraslow latch-bridge cycle. The thin-filament-regulated latch-bridge model was able to fit phorbol ester-induced ultraslow contractions at constant myosin phosphorylation by shifting cross bridges from the regular latch-bridge cycle to the ultraslow cross-bridge cycle. This modeling result was counterintuitive because proportional slowing of cross-bridge attachment and detachment rates was not expected to change the number of attached cross bridges in a two-state cross-bridge model. Modeling the phorbol ester data indicated that the rate constants for cross-bridge cycling in the ultraslow cross-bridge cycle were only 2.7% of those in the regular cross-bridge cycle. Therefore, adding the ultraslow latch-bridge cycle to the four-state model would increase the dynamic range of cross-bridge cycling rate by 37-fold without losing the capacity to generate force. Functionally, having the regular and ultraslow cross-bridge cycles would allow a smooth muscle cell to have the flexibility of either maintaining force at extremely low-energy cost or changing its contractile state rapidly, if necessary.

Implications for PKC-Mediated Smooth Muscle Contraction

A large amount of data derived from phorbol ester experiments suggest the existence of mechanisms that can generate ultraslow contractions without changing myosin phosphorylation in smooth muscle (7, 13, 18, 29, 31, 33). PKC-mediated phosphorylation of CPI-17 has been postulated as a mechanism of PKC-mediated inhibition of MLCP (17). This mechanism can potentially explain the initial increase in myosin light chain phosphorylation with a modest increase in intracellular [Ca2+] in PDBu-induced contractions. However, this mechanism cannot explain the continued force development after myosin phosphorylation has already reached steady state. Fulginiti et al. (7) found that the stress-stiffness relationship was not significantly different between K+-depolarized and phorbol ester-activated smooth muscle, suggesting that cross bridges are the basic force-bearing element in phorbol ester-activated smooth muscle. Therefore, a challenge to explaining the phorbol ester data is to develop a cross-bridge model that can predict phosphorylation-independent smooth muscle contractions.

In this study, we modeled the PDBu data by adding an ultraslow cross-bridge cycle to the four-state model, with the implicit assumption that PKC activation leads to the inhibition of actomyosin ATPase activity. This assumption is consistent with the findings of Nishikawa et al. (25) and Ikebe et al. (16) that PKC phosphorylates smooth muscle myosin, leading to the inhibition of actin-activated myosin ATPase activity. Several studies have confirmed that the PKC-specific sites on smooth muscle myosin were indeed phosphorylated in PDBu-activated arterial smooth muscle (1, 32, 35). In this study, we studied the translocation of conventional and novel PKC isoforms in PDBu-induced contractions. The observed PDBu-induced significant increases in the P/S of PKC-{alpha} and -{beta} suggest that these two conventional PKC isoforms are involved in PDBu-induced contractions (Figs. 10 and 11). The relatively small and insignificant change in the PKC-{beta}II P/S could not explain the 5.9-fold increase in the P/S of PKC-{beta} in response to PDBu stimulation, suggesting that other PKC-{beta} isoforms, possibly PKC-{beta}I, are involved in PDBu-induced contractions. These results are consistent with the hypothesis that PDBu-induced airway smooth muscle contraction is mediated by the activation of conventional PKC isoforms.

Therefore, it is conceivable that PDBu inhibits actomyosin ATPase activity in intact smooth muscle. Although myosin is the postulated target of PKC in phorbol ester-induced contractions, the thin-filament-regulated latch-bridge model remains applicable because, mathematically, the model only assumes attenuation of actomyosin ATPase activity in the ultraslow latch-bridge cycle without specifying the target of regulation. As shown in this study, the thin-filament-regulated latch-bridge model fitted the PDBu-induced slow contractions at constant myosin phosphorylation. Furthermore, steady-state solutions of the model predicted steeper dependence of force on myosin phosphorylation in PDBu-stimulated smooth muscle, consistent with the findings by Bremerich et al. (2). These modeling results suggest that PKC-mediated inhibition of actomyosin ATPase activity may be an important mechanism of phorbol ester-induced smooth muscle contractions.

Implications for Thin-Filament-Based Regulation of Smooth Muscle Contraction

Calponin and caldesmon are thin-filament-based regulatory proteins that inhibit actomyosin ATPase activity in vitro. Calponin knockout mice studies indicated that calponin attenuated maximum shortening velocity independent of myosin phosphorylation in intact smooth muscle (38). On the contrary, Facemire et al. (6) did not observe a significant difference in shortening velocity between smooth muscles naturally expressing different amounts of calponin. Therefore, the physiological role of calponin in regulating smooth muscle mechanics remains controversial. The model described in this study provides a specific and mechanistic framework for integrating thin-filament-based inhibition of actomyosin ATPase activity with myosin light chain phosphorylation in the regulation of smooth muscle mechanics. The model postulates the existence of two latch-bridge cycles with different cross-bridge cycling rates. This postulate is compatible with the biochemistry of calponin and caldesmon because both proteins can exist in the unphosphorylated and phosphorylated form. Mechanistically, the ultraslow latch-bridge cycle may represent the interaction between myosin cross bridges and calponin-inhibited thin filament, and the regular latch-bridge cycle may represent the interaction between myosin cross bridges and uninhibited thin filament. The postulate of two latch-bridge cycles leads to the following implications for thin-filament-based regulation. First, the model predicts biphasic kinetics of smooth muscle mechanics as illustrated by phorbol ester-induced contractions. Second, the model predicts variable steady-state dependencies of force and shortening velocity on myosin phosphorylation, depending on the fraction of total cross bridges engaged in the calponin-inhibited ultraslow latch-bridge cycle. These model predictions highlight the importance of considering biphasic kinetics, calponin phosphorylation, and myosin phosphorylation in studying the effect of calponin and caldesmon on smooth muscle mechanics. Finally, modeling results from this study suggest the novel concept that thin-filament-based regulatory proteins may function as tuners of actomyosin ATPase activity, thus allowing a smooth muscle cell to have two discrete cross-bridge cycles with substantially different cross-bridge cycling rates.


   ACKNOWLEDGMENTS
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 ACKNOWLEDGMENTS
REFERENCES
 
This study was supported by National Heart, Lung, and Blood Institute Grant HL-52714.


   FOOTNOTES
 

Address for reprint requests and other correspondence: C.-M. Hai, Brown University, Box G-B3, Providence, RI 02912 (E-mail: Chi-Ming_Hai{at}brown.edu)

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.


   REFERENCES
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 ACKNOWLEDGMENTS
 REFERENCES
 

  1. Barany K, Polyak E, and Barany M. Protein phosphorylation in arterial muscle contracted by high concentration of phorbol dibutyrate in the presence and absence of Ca2+. Biochim Biophys Acta 1134: 233–241, 1992.[Medline]
  2. Bremerich DH, Kai T, Warner DO, and Jones KA. Effect of phorbol esters on Ca2+ sensitivity and myosin light-chain phosphorylation in airway smooth muscle. Am J Physiol Cell Physiol 274: C1253–C1260, 1998.[Abstract/Free Full Text]
  3. Butler TM, Mooers SU, Li C, Narayan S, and Siegman MJ. Regulation of catch muscle by twitchin phosphorylation: effects on force, ATPase, and shortening. Biophys J 75: 1904–1914, 1998.[Web of Science][Medline]
  4. Dillon PF, Aksoy MO, Driska SP, and Murphy RA. Myosin phosphorylation and the cross bridge cycle in arterial smooth muscle. Science 211: 495–497, 1981.[Abstract/Free Full Text]
  5. Dillon PF and Murphy RA. Tonic force maintenance with reduced shortening velocity in arterial smooth muscle. Am J Physiol Cell Physiol 242: C102–C108, 1982.[Abstract/Free Full Text]
  6. Facemire C, Brozovich FV, and Jin JP. The maximal velocity of vascular smooth muscle shortening is independent of the expression of calponin. J Muscle Res Cell Motil 21: 367–373, 2000.[CrossRef][Web of Science][Medline]
  7. Fulginiti J, Singer HA 3rd, and Moreland RS. Phorbol ester-induced contractions of swine carotid artery are supported by slowly cycling crossbridges which are not dependent on calcium or myosin light chain phosphorylation. J Vasc Res 30: 315–322, 1993.[CrossRef][Web of Science][Medline]
  8. Haeberle JR. Calponin decreases the rate of cross-bridge cycling and increases maximum force production by smooth muscle myosin in an in vitro motility assay. J Biol Chem 269: 12424–12431, 1994.[Abstract/Free Full Text]
  9. Hai CM and Murphy RA. Regulation of shortening velocity by cross-bridge phosphorylation in smooth muscle. Am J Physiol Cell Physiol 255: C86–C94, 1988.[Abstract/Free Full Text]
  10. Hai CM and Murphy RA. Cross-bridge phosphorylation and regulation of latch state in smooth muscle. Am J Physiol Cell Physiol 254: C99–C106, 1988.[Abstract/Free Full Text]
  11. Hai CM and Murphy RA. Ca2+, crossbridge phosphorylation, and contraction. Annu Rev Physiol 51: 285–298, 1989.[Web of Science][Medline]
  12. Hai CM and Murphy RA. Crossbridge phosphorylation and regulation of vascular smooth muscle contraction. Am J Hypertens 3: 235S–237S, 1990.[Medline]
  13. Hai CM and Szeto B. Agonist-induced myosin phosphorylation during isometric contraction and unloaded shortening in airway smooth muscle. Am J Physiol Lung Cell Mol Physiol 262: L53–L62, 1992.[Abstract/Free Full Text]
  14. Horowitz A, Menice CB, Laporte R, and Morgan KG. Mechanisms of smooth muscle contraction. Physiol Rev 76: 967–1003, 1996.[Abstract/Free Full Text]
  15. Huxley AF. Muscle structure and theories of contraction. Prog Biophys Mol Biol 7: 255–318, 1957.[Web of Science]
  16. Ikebe M, Hartshorne DJ, and Elzinga M. Phosphorylation of the 20,000-dalton light chain of smooth muscle myosin by the calcium-activated, phospholipid-dependent protein kinase. J Biol Chem 262: 9569–9573, 1987.[Abstract/Free Full Text]
  17. Ito M, Nakano T, Erdodi F, and Hartshorne DJ. Myosin phosphatase: structure, regulation and function. Mol Cell Biochem 259: 197–209, 2004.[CrossRef][Web of Science][Medline]
  18. Jiang MJ and Morgan KG. Agonist-specific myosin phosphorylation and intracellular calcium during isometric contractions of arterial smooth muscle. Pflügers Arch 413: 637–643, 1989.[CrossRef][Web of Science][Medline]
  19. Kamm KE and Stull JT. Myosin phosphorylation, force and maximal shortening velocity in neurally stimulated tracheal smooth muscle. Am J Physiol Cell Physiol 249: C238–C247, 1985.[Abstract/Free Full Text]
  20. Kim HR, Hoque M, and Hai CM. Cholinergic receptor-mediated differential cytoskeletal recruitment of actin- and integrin-binding proteins in intact airway smooth muscle. Am J Physiol Cell Physiol 287: C1375–C1383, 2004.[Abstract/Free Full Text]
  21. Kitazawa T, Polzin A, and Eto M. CPI-17-deficient smooth muscle of chicken. J Physiol 557: 515–528, 2004.[Abstract/Free Full Text]
  22. Li L, Eto M, Lee MR, Morita F, Yazawa M, and Kitazawa T. Possible involvement of the novel CPI-17 protein in protein kinase C signal transduction of rabbit arterial smooth muscle. J Physiol 508: 871–881, 1998.[Abstract/Free Full Text]
  23. Mijailovich SM, Butler JP, and Fredberg JJ. Perturbed equilibria of myosin binding in airway smooth muscle: bond-length distributions, mechanics, and ATP metabolism. Biophys J 79: 2667–2681, 2000.[Web of Science][Medline]
  24. Morgan KG and Gangopadhyay SS. Invited review: Cross-bridge regulation by thin filament-associated proteins. J Appl Physiol 91: 953–962, 2001.[Abstract/Free Full Text]
  25. Nishikawa M, Sellers JR, Adelstein RS, and Hidaka H. Protein kinase C modulates in vitro phosphorylation of the smooth muscle meromyosin by myosin light chain kinase. J Biol Chem 259: 8808–8814, 1984.[Abstract/Free Full Text]
  26. Ogut O and Brozovich FV. Regulation of force in vascular smooth muscle. J Mol Cell Cardiol 35: 347–355, 2003.[CrossRef][Web of Science][Medline]
  27. Phair RD and Hai CM. Resolution of intracellular calcium metabolism in intact segments of rabbit aorta. Circ Res 59: 74–84, 1986.[Abstract/Free Full Text]
  28. Ratz PH, Hai CM, and Murphy RA. Dependence of stress on cross-bridge phosphorylation in vascular smooth muscle. Am J Physiol Cell Physiol 256: C96–C100, 1989.[Abstract/Free Full Text]
  29. Rembold CM and Murphy RA. [Ca2+]-dependent myosin phosphorylation in phorbol diester stimulated smooth muscle contraction. Am J Physiol Cell Physiol 255: C719–C723, 1988.[Abstract/Free Full Text]
  30. Rembold CM and Murphy RA. Latch-bridge model in smooth muscle: [Ca2+]i can quantitatively predict stress. Am J Physiol Cell Physiol 259: C251–C257, 1990.[Abstract/Free Full Text]
  31. Sato K, Hori M, Ozaki H, Takano-Ohmuro H, Tsuchiya T, Sugi H, and Karaki H. Myosin phosphorylation-independent contraction induced by phorbol ester in vascular smooth muscle. J Pharmacol Exp Ther 261: 497–505, 1992.[Abstract/Free Full Text]
  32. Singer HA. Protein kinase C activation and myosin light chain phosphorylation in 32P-labeled arterial smooth muscle. Am J Physiol Cell Physiol 259: C631–C639, 1990.[Abstract/Free Full Text]
  33. Singer HA and Baker KM. Calcium dependence of phorbol 12, 13-dibutyrate-induced force and myosin light chain phosphorylation in arterial smooth muscle. J Pharmacol Exp Ther 243: 814–821, 1987.[Abstract/Free Full Text]
  34. Singer HA and Murphy RA. Maximal rates of activation in electrically stimulated swine carotid media. Circ Res 60: 438–445, 1987.[Abstract/Free Full Text]
  35. Singer HA, Oren JW, and Benscoter HA. Myosin light chain phosphorylation in 32P-labeled rabbit aorta stimulated by phorbol 12, 13-dibutyrate and phenylephrine. J Biol Chem 264: 21215–21222, 1989.[Abstract/Free Full Text]
  36. Somlyo AP and Somlyo AV. Ca2+ sensitivity of smooth muscle and nonmuscle myosin II: modulated by G proteins, kinases, and myosin phosphatase. Physiol Rev 83: 1325–1358, 2003.[Abstract/Free Full Text]
  37. Tajimi M, Hori M, Ozaki H, and Karaki H. Effect of phorbol esters on cytosolic Ca2+ level, myosin phosphorylation and muscle tension in high K+-stimulated bovine tracheal smooth muscle. Jap J Pharmacol 74: 195–201, 1997.
  38. Takahashi K, Yoshimoto R, Fuchibe K, Fujishige A, Mitsui-Saito M, Hori M, Ozaki H, Yamamura H, Awata N, Taniguchi S, Katsuki M, Tsuchiya T, and Karaki H. Regulation of shortening velocity by calponin in intact contracting smooth muscles. Biochem Biophys Res Commun 279: 150–157, 2000.[CrossRef][Web of Science][Medline]
  39. Wastney ME, Patterson BH, Linares OA, Greif PC, and Boston RC. Investigating Biological Systems Using Modeling. San Diego, CA: Academic, 1999, p. 95–138.
  40. Webb BLJ, Lindsay MA, Barnes PJ, and Giembycz MA. Protein kinase C isoenzymes in airway smooth muscle. Biochem J 324: 167–175, 1997.
  41. Winder SJ, Allen BG, Clement-Chomienne O, and Walsh MP. Regulation of smooth muscle actin-myosin interaction and force by calponin. Acta Physiol Scand 164: 415–426, 1998.[Web of Science][Medline]
  42. Woodsome TP, Eto M, Everett A, Brautigan DL, and Kitazawa T. Expression of CPI-17 and myosin phosphatase correlates with Ca2+ sensitivity of protein C-induced contraction in rabbit smooth muscle. J Physiol 535: 553–564, 2001.[Abstract/Free Full Text]
  43. Yu SN, Crago PE, and Chiel HJ. A nonisometric kinetic model for smooth muscle. Am J Physiol Cell Physiol 272: C1025–C1039, 1997.[Abstract/Free Full Text]



This article has been cited by other articles:


Home page
 Am. J. Physiol. Cell Physiol.Home page
Z. M. Goeckeler, P. C. Bridgman, and R. B. Wysolmerski
Nonmuscle myosin II is responsible for maintaining endothelial cell basal tone and stress fiber integrity
Am J Physiol Cell Physiol, October 1, 2008; 295(4): C994 - C1006.
[Abstract] [Full Text] [PDF]

This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF) Free
Right arrow All Versions of this Article:
98/4/1356    most recent
00834.2004v1
Right arrow Submit a response
Right arrow Alert me when this article is cited
Right arrow Alert me when eLetters are posted
Right arrow Alert me if a correction is posted
Right arrow Citation Map
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in Web of Science
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Citing Articles
Right arrow Citing Articles via HighWire
Right arrow Citing Articles via Web of Science (5)
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Hai, C.-M.
Right arrow Articles by Kim, H. R.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by Hai, C.-M.
Right arrow Articles by Kim, H. R.

HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
Visit Other APS Journals Online
Copyright © 2005 by the American Physiological Society.