Cooperative [Ca]-Dependent Regulation of the Rate of Myosin Binding to Actin: Solution Data and the Tropomyosin Chain Model

The regulation of muscle contraction by calcium involves interactions among actin filaments, myosin-S1, tropomyosin (Tm), and troponin (Tn). We have extended our previous model in which the TmTn regulatory units are treated as a continuous flexible chain, and applied it to transient kinetic data. We have measured the time course of myosin-S1 binding to actin-Tm-Tn filaments in solution at various calcium levels with [actin]/[myosin] ratios of 10 and 0.1, which exhibit modest slowing as [Ca²⁺] is reduced and a lag phase at low calcium. These observations can be explained if myosin binds to actin in two steps, where the first step is rate-limiting and blocked by TmTnI at low calcium, and the second step is fast, reversible, and controlled by the neighboring configuration of coupled tropomyosin-troponin units. The model can describe the calcium dependence of the observed myosin binding reactions and predicts cooperative calcium binding to TnC with competition between actin and Ca-TnC for the binding of TnI. Implications for theories of thin-filament regulation in muscle are discussed.     

The structure of the amino terminus of tropomyosin is critical for binding to actin in the absence and presence of troponin

Analysis of two recombinant variants of chicken striated muscle alpha-tropomyosin has shown that the structure of the amino terminus is crucial for most aspects of tropomyosin function: affinity to actin, promotion of binding to actin by troponin, and regulation of the actomyosin MgATPase. Initial characterization of variants expressed and isolated from Escherichia coli has been published (Hitchcock-DeGregori, S. E., and Heald, R. W. (1987) J. Biol. Chem. 262, 9730-9735). Fusion tropomyosin contains 80 amino acids of a nonstructural influenza virus protein (NS1) on the amino terminus. Nonfusion tropomyosin is a variant because the amino-terminal methionine is not acetylated (unacetylated tropomyosin). The affinity of tropomyosin labeled at Cys190 with N-[14C]ethylmaleimide for actin was measured by cosedimentation in a Beckman Airfuge. Fusion tropomyosin binds to actin with an affinity slightly greater than that of chicken striated muscle alpha-tropomyosin (Kapp = 1-2 X 10(7) versus 0.5-1 X 10(7) M-1) and more strongly than unacetylated tropomyosin (Kapp = 3 X 10(5) M-1). Both variants bind cooperatively to actin. Troponin increases the affinity of unacetylated tropomyosin for actin (+Ca2+, Kapp = 6 X 10(6) M-1; +EGTA, Kapp = 2 X 10(7) M-1), but the affinity is still lower than that of muscle tropomyosin for actin in the presence of troponin (Kapp much greater than 10(8) M-1). Troponin has no effect on the affinity of fusion tropomyosin for actin indicating that binding of troponin T to the over-lap region of the adjacent tropomyosin, presumably sterically prevented by the fusion peptide in fusion tropomyosin, is required for troponin to promote the binding of tropomyosin to actin. The role of troponin T in regulation and the mechanisms of cooperative binding of tropomyosin to actin have been discussed in relation to this work.     

Cooperative [Ca²+]-dependent regulation of the rate of myosin binding to actin: solution data and the tropomyosin chain model

The regulation of muscle contraction by calcium involves interactions among actin filaments, myosin-S1, tropomyosin (Tm), and troponin (Tn). We have extended our previous model in which the TmTn regulatory units are treated as a continuous flexible chain, and applied it to transient kinetic data. We have measured the time course of myosin-S1 binding to actin-Tm-Tn filaments in solution at various calcium levels with [actin]/[myosin] ratios of 10 and 0.1, which exhibit modest slowing as [Ca(2+)] is reduced and a lag phase at low calcium. These observations can be explained if myosin binds to actin in two steps, where the first step is rate-limiting and blocked by TmTnI at low calcium, and the second step is fast, reversible, and controlled by the neighboring configuration of coupled tropomyosin-troponin units. The model can describe the calcium dependence of the observed myosin binding reactions and predicts cooperative calcium binding to TnC with competition between actin and Ca-TnC for the binding of TnI. Implications for theories of thin-filament regulation in muscle are discussed.     

Heart muscle: mathematical modelling of the mechanical activity and modelling of mechanochemical uncoupling

A mechanical model of heart muscle is proposed which includes rheological equations and equations for Ca-troponin interaction, for the dependences of the number of myosin cross-bridges on the length of sarcomere and on the speed of motion. The main assumption of the model is the dependence of the troponin affinity to calcium ions on the number of myosin cross-bridges attached. The model successfully imitates isometric and isotonic contractions, the "length-force" relationships, load-dependent relaxation, and the group of mechanical phenomena known as mechanochemical uncoupling.     

Modulation of contractile activation in skeletal muscle by a calcium-insensitive troponin C mutant

Calcium controls the level of muscle activation via interactions with the troponin complex. Replacement of the native, skeletal calcium-binding subunit of troponin, troponin C, with mixtures of functional cardiac and mutant cardiac troponin C insensitive to calcium and permanently inactive provides a novel method to alter the number of myosin cross-bridges capable of binding to the actin filament. Extraction of skeletal troponin C and replacement with functional and mutant cardiac troponin C were used to evaluate the relationship between the extent of thin filament activation (fractional calcium binding), isometric force, and the rate of force generation in muscle fibers independent of the calcium concentration. The experiments showed a direct, linear relationship between force and the number of cross-bridges attaching to the thin filament. Further, above 35% maximal isometric activation, following partial replacement with mixtures of cardiac and mutant troponin C, the rate of force generation was independent of the number of actin sites available for cross-bridge interaction at saturating calcium concentrations. This contrasts with the marked decrease in the rate of force generation when force was reduced by decreasing the calcium concentration. The results are consistent with hypotheses proposing that calcium controls the transition between weakly and strongly bound cross-bridge states.     

Effect of vanadate on Ca++-activation in skeletal muscle

Vanadate (0.1 mM) reduces tension of glycerinated rabbit psoas muscle fibers, shifts tension--pCa curve to lower pCa, increases the rate constant of delayed tension development and changes dependence of this rate constant on the level of Ca2+-activation. Vanadate influence stops the increase of the rate constant with the rise of Ca++-activated tension. Since actin-myosin-ADP complex is dissociated by vanadate, the muscle performance at low activation levels is supposed to be conditioned largely by the cross-bridges interacting with actin of the actin blocks switched on by myosin-ADP. Kinetics of such cross-bridges differs from that of the cross bridges interacting with actin activated by Ca++ binding to troponin C.     

Effect of rigor and cycling cross-bridges on the structure of troponin C and on the Ca2+ affinity of the Ca2+-specific regulatory sites in skinned rabbit psoas fibers

Intrinsic troponin C (TnC) was extracted from small bundles of rabbit psoas fibers and replaced with TnC labeled with dansylaziridine (5-dimethylaminonaphthalene-1-sulfonyl). The flourescence of incorporated dansylaziridine-labeled TnC was enhanced by the binding of Ca2+ to the Ca2+-specific (regulatory) sites of TnC and was measured simultaneously with force (Zot, H.G., Güth, K., and Potter, J.D. (1986) J. Biol. Chem. 261, 15883-15890). Various myosin cross-bridge states also altered the fluorescence of dansylaziridine-labeled TnC in the filament, with cycling cross-bridges having a greater effect than rigor cross-bridges; and in both cases, there was an additional effect of Ca2+. The paired fluorescence and tension data were used to calculate the apparent Ca2+ affinity of the regulatory sites in the thin filament and were shown to increase at least 10-fold during muscle activation presumably due to the interaction of cycling cross-bridges with the thin filament. The cross-bridge state responsible for this enhanced Ca2+ affinity was shown to be the myosin-ADP state present only when cross-bridges are cycling. The steepness of the pCa force curves (where pCa represents the -log of the free Ca2+ concentration) obtained in the presence of ATP at short and long sarcomere lengths was the same, suggesting that cooperative interactions between adjacent troponin-tropomyosin units may spread along much of the actin filament when cross-bridges are attached to it. In contrast to the cycling cross-bridges, rigor bridges only increased the Ca2+ affinity of the regulatory sites 2-fold. Taken together, the results presented here indicate a strong coupling between the Ca2+ regulatory sites and cross-bridge interactions with the thin filament.     

The regulation of myosin binding to actin filaments by Lethocerus troponin

Lethocerus indirect flight muscle has two isoforms of troponin C, TnC-F1 and F2, which are unusual in having only a single C-terminal calcium binding site (site IV, isoform F1) or one C-terminal and one N-terminal site (sites IV and II, isoform F2). We show here that thin filaments assembled from rabbit actin and Lethocerus tropomyosin (Tm) and troponin (Tn) regulate the binding of rabbit myosin to rabbit actin in much the same way as the mammalian regulatory proteins. The removal of calcium reduces the rate constant for S1 binding to regulated actin about threefold, independent of which TmTn is used. This is consistent with calcium removal causing the TmTn to occupy the B or blocked state to about 70% of the total. The mid point pCa for the switch differed for TnC-F1 and F2 (pCa 6.9 and 6.0, respectively) consistent with the reported calcium affinities for the two TnCs. Equilibrium titration of S1 binding to regulated actin filaments confirms calcium regulated binding of S1 to actin and shows that in the absence of calcium the three actin filaments (TnC-F1, TnC-F2 and mammalian control) are almost indistinguishable in terms of occupancy of the B and C states of the filament. In the presence of calcium TnC-F2 is very similar to the control with approximately 80% of the filament in the C-state and 10-15% in the fully on M-State while TnC-F1 has almost 50% in each of the C and M states. This higher occupancy of the M-state for TnC-F1, which occurs above pCa 6.9, is consistent with this isoform being involved in the calcium activation of stretch activation. However, it leaves unanswered how a C-terminal calcium binding site of TnC can activate the thin filament.     

The effect of single residue substitutions of serine-283 on the strength of head-to-tail interaction and actin binding properties of rabbit skeletal muscle alpha-tropomyosin

Vertebrate skeletal muscle alpha-tropomyosin polymerizes in a head-to-tail manner and binds cooperatively to actin. It has been postulated that the cooperative actin binding is governed by the strength of the head-to-tail interaction. In order to know the relationship between the head-to-tail affinity and actin binding, we studied the properties of tropomyosin variants with single residue substitutions at serine-283, the penultimate residue at the carboxyl terminus that is involved in the head-to-tail interaction. It has been shown that the phosphorylation of serine-283 strengthens the head-to-tail interaction. Viscometry was employed to compare the head-to-tail affinity of tropomyosin variants. Variant S283E showed higher viscosity whereas variant S283K showed lower viscosity compared with the wild type non-phosphorylated alpha-tropomyosin. The results confirm the idea that the interaction is sensitive to the ionic properties of residue 283. The strength of the head-to-tail interaction was assessed directly by sedimentation equilibrium using two pairs of tropomyosin variants designed so that only dimeric interactions were allowed within each pair. From one pair of variants with serine-283, the association constant was determined to be 2.6 x 10(4) M(-1) (SD =1.0 x 10(4)), whereas for the second pair with glutamate-283, the affinity was 3.9 x 10(4) M(-1) (SD =1.6 x 10(4)), slightly stronger than the former, consistent with the results of viscometry. The results indicate that the head-to-tail association is weak as previously implicated from light scattering measurements. Cosedimentation was employed to measure the cooperative actin binding of tropomyosin variants. Although previous results indicated the phosphorylation has no significant influence on the actin affinity, variant S283E shows a lower affinity compared with the control. Variants S283K and S283A show even lower affinities to actin, although these species bind to actin more cooperatively than does variant S283E. The results indicate that the affinity of the head-to-tail interaction between adjacent tropomyosin molecules is weak, and is substantially influenced by an extra charge at residue 283. On the other hand, the interaction with actin, the affinity and the cooperativity in actin binding, is dependent on amino acid residues at 283 and is not simply correlated with the strength of the head-to-tail interaction between Tm molecules in solution.     

Roles for the troponin tail domain in thin filament assembly and regulation. A deletional study of cardiac troponin T

Striated muscle contraction is regulated by Ca2+ binding to troponin, which has a globular domain and an elongated tail attributable to the NH2-terminal portion of the bovine cardiac troponin T (TnT) subunit. Truncation of the bovine cardiac troponin tail was investigated using recombinant TnT fragments and subunits TnI and TnC. Progressive truncation of the troponin tail caused progressively weaker binding of troponin-tropomyosin to actin and of troponin to actin-tropomyosin. A sharp drop-off in affinity occurred with NH2-terminal deletion of 119 rather than 94 residues. Deletion of 94 residues had no effect on Ca2+-activation of the myosin subfragment 1-thin filament MgATPase rate and did not eliminate cooperative effects of Ca2+ binding. Troponin tail peptide TnT1-153 strongly promoted tropomyosin binding to actin in the absence of TnI or TnC. The results show that the anchoring function of the troponin tail involves interactions with actin as well as with tropomyosin and has comparable importance in the presence or absence of Ca2+. Residues 95-153 are particularly important for anchoring, and residues 95-119 are crucial for function or local folding. Because striated muscle regulation involves switching among the conformational states of the thin filament, regulatory significance for the troponin tail may arise from its prominent contribution to the protein-protein interactions within these conformations.     

Structural changes in the muscle thin filament during contractions caused by single and double electrical pulses

In order to investigate the structural changes of the myofilaments involved in the phenomenon of summation in skeletal muscle contraction, we studied small-angle x-ray intensity changes during twitches of frog skeletal muscle elicited by either a single or a double stimulus at 16 °C. The separation of the pulses in the double-pulse stimulation was either 15 or 30 ms. The peak tension was more than doubled by the second stimulus. The equatorial (1,0) intensity, which decreased upon the first stimulus, further decreased with the second stimulus, indicating that more cross-bridges are formed. The meridional reflections from troponin at 1/38.5 and 1/19.2 nm^− 1 were affected only slightly by the second stimulus, showing that attachment of a small number of myosin heads to actin can make a cooperative structural change. In overstretched muscle, the intensity increase of the troponin reflection in response to the second stimulus was smaller than that to the first stimulus. These results show that the summation is not due to an increased Ca binding to troponin and further suggest a highly cooperative nature of the structural changes in the thin filament that are related to the regulation of contraction.     

Independent functions for the N- and C-termini in the overlap region of tropomyosin

Tropomyosin (TM) is a coiled-coil that binds head-to-tail along the helical actin filament. The ends of 284-residue tropomyosins are believed to overlap by about nine amino acids. The present study investigates the function of the N- and C-terminal overlap regions. Recombinant tropomyosins were produced in Escherichia coli in which nine amino acids were truncated from the N-terminal, C-terminal, or both ends of striated muscle alpha-tropomyosin (TM9a) and TM2 (TM9d), a nonmuscle alpha-tropomyosin expressed in many cells. The two isoforms are identical except for the C-terminal 27 amino acids encoded by exon 9a (striated) or exon 9d (TM2). Removal of either end greatly reduces the actin affinity of both tropomyosins in all conditions and the cooperativity with which myosin promotes tropomyosin binding to actin in the open state. N-Terminal truncations generally are more deleterious than C-terminal truncations. With TM9d, truncation of the N-terminus is as deleterious as both for myosin S1-induced binding. None of the TM9d variants binds well to actin with troponin (+/-Ca(2+)). TM9a with the truncated N-terminus binds more weakly to actin with troponin (-Ca(2+)) than when the C-terminus is removed but more strongly than when both ends are removed; the actin binding of all three forms is cooperative. The results show that the ends of TM9a, though important, are not required for cooperative function and suggest they have independent functions beyond formation of an overlap complex. The nonadditivity of the TM9d truncations suggests that the ends may primarily function as a complex in this isoform. A surprising result is that all variants bound with the same affinity, and noncooperatively, to actin saturated with myosin S1. Evidently, end-to-end interactions are not required for high-affinity binding to acto-myosin S1.     

Functions of tropomyosin's periodic repeats

Tropomyosin binds along actin filaments and regulates actin-myosin interaction in muscle and nonmuscle cells. Seven periodic amino acid repeats are proposed to correspond to actin binding sites, and the middle periods are important for cooperative activation of actin by myosin. The functional contributions of individual periods were studied in mutants in which periods 2-6 were individually deleted from rat striated muscle alphaalpha-tropomyosin or replaced with a leucine zipper sequence. Unacetylated recombinant tropomyosins were assayed for actin binding, regulation of the actomyosin ATPase with troponin, cooperative myosin S1-induced binding to actin, and thermal stability. Tropomyosin function is relatively insensitive to deletion of period 2, but loss increases as the deletion is shifted toward the C-terminus. Retention of function upon deletion of the periodic repeats is in the order of 2 > 3 approximately 4 approximately 6 > 5. Internal periods are important for specific functions and are not quasiequivalent. Deletion of period 5 (residues 166-207), and especially deletion or replacement of residues 166-188, a constitutively expressed region encoded by exon 5, had severe consequences on actin affinity and cooperative myosin S1-induced binding to actin. Period 6, residues 208-242, part of the troponin binding site, is required for full inhibition of the actomyosin ATPase in the absence of calcium. The effect of the deletion can depend on its context, suggesting that sequence alone is not the only factor important for function. We propose that the local structure and stability, and consequent flexibility, of the coiled coil are major determinants of actin affinity.     

Structure–function relationships of molluscan troponin T revealed by limited proteolysis

Molluscan troponin regulates muscle contraction through a novel Ca²⁺-dependent activating mechanism associated with Ca²⁺-binding to the C-terminal domain of troponin C. To elucidate the further details of this regulation, we performed limited chymotryptic digestion of the troponin complex from akazara scallop striated muscle. The results indicated that troponin T is very susceptible to the protease, compared to troponin C or troponin I. The cleavage occurred at the C-terminal extension, producing an N-terminal 33-kDa fragment and a C-terminal 6-kDa fragment. This extension is conserved in various invertebrate troponin T proteins, but not in vertebrate troponin T. A ternary complex composed of the 33-kDa fragment of troponin T, troponin I, and troponin C could be separated from the 6-kDa troponin T fragment by gel filtration. This complex did not show any Ca²⁺-dependent activation of the Mg-ATPase activity of rabbit-actomyosin–scallop-tropomyosin. In addition, the actin–tropomyosin-binding affinity of this complex was significantly decreased with increasing Ca²⁺ concentration. These results indicate that the C-terminal extension of molluscan troponin T plays a role in anchoring the troponin complex to actin–tropomyosin filaments and is essential for regulation.     

Actin filaments in muscle: Pattern of myosin and tropomyosin/troponin attachments

X-ray patterns from lobster and crayfish muscles show very clear layer lines from the thin filaments, well separated from the myosin layer lines. The intensities in patterns from relaxed muscles include an important contribution from the regulatory proteins, and allow the arrangement of the troponin complexes to be deduced. Moreover, the troponin diffraction indirectly provides an accurate value for the pitch of the actin helix in relaxed muscle.In rigor, the attachment of cross-bridges modifies the intensities. These X-ray patterns support Reedy's (1968) concept that cross-bridges in rigor attach only to certain azimuths on the actin filaments (“target areas”); the 145 Å repeat of their origins on the thick filaments is not reflected in the pattern of attachment. Our calculations show that the observed intensities agree quantitatively with those expected for models based on such attachment, but depend significantly on the locations of the troponin complexes. The arrangement of the filament components is discussed in terms of design requirements. Our conclusions may be applicable to many other muscles, especially insect flight muscle and other invertebrate muscles.     

Cardiac Muscle Activation Blunted by a Mutation to the Regulatory Component,Troponin T

The striated muscle thin filament comprises actin, tropomyosin, and troponin. The Tn complex consists of three subunits, troponin C (TnC), troponin I (TnI), and troponin T (TnT). TnT may serve as a bridge between the Ca²⁺ sensor (TnC) and the actin filament. In the short helix preceding the IT-arm region, H1(T2), there are known dilated cardiomyopathy-linked mutations (among them R205L). Thus we hypothesized that there is an element in this short helix that plays an important role in regulating the muscle contraction, especially in Ca²⁺ activation. We mutated Arg-205 and several other amino acid residues within and near the H1(T2) helix. Utilizing an alanine replacement method to compare the effects of the mutations, the biochemical and mechanical impact on the actomyosin interaction was assessed by solution ATPase activity assay, an in vitro motility assay, and Ca²⁺ binding measurements. Ca²⁺ activation was markedly impaired by a point mutation of the highly conserved basic residue R205A, residing in the short helix H1(T2) of cTnT, whereas the mutations to nearby residues exhibited little effect on function. Interestingly, rigor activation was unchanged between the wild type and R205A TnT. In addition to the reduction in Ca²⁺ sensitivity observed in Ca²⁺ binding to the thin filament, myosin S1-ADP binding to the thin filament was significantly affected by the same mutation, which was also supported by a series of S1 concentration-dependent ATPase assays. These suggest that the R205A mutation alters function through reduction in the nature of cooperative binding of S1.     

Tropomyosin ends determine the stability and functionality of overlap and troponin T complexes

Tropomyosin binds end to end along the actin filament. Tropomyosin ends, and the complex they form, are required for actin binding, cooperative regulation of actin filaments by myosin, and binding to the regulatory protein, troponin T. The aim of the work was to understand the isoform and structural specificity of the end-to-end association of tropomyosin. The ability of N-terminal and C-terminal model peptides with sequences of alternate alpha-tropomyosin isoforms, and a troponin T fragment that binds to the tropomyosin overlap, to form complexes was analyzed using circular dichroism spectroscopy. Analysis of N-terminal extensions (N-acetylation, Gly, AlaSer) showed that to form an overlap complex between the N-terminus and the C-terminus requires that the N-terminus be able to form a coiled coil. Formation of a ternary complex with the troponin T fragment, however, effectively takes place only when the overlap complex sequences are those found in striated muscle tropomyosins. Striated muscle tropomyosins with N-terminal modifications formed ternary complexes with troponin T that varied in affinity in the order: N-acetylated > Gly > AlaSer > unacetylated. The circular dichroism results were corroborated by native gel electrophoresis, and the ability of the troponin T fragment to promote binding of full-length tropomyosins to filamentous actin.     

Effects of cardiac thin filament Ca2+: statistical mechanical analysis of a troponin C site II mutant.

Cardiac thin filaments contain many troponin C (TnC) molecules, each with one regulatory Ca2+ binding site. A statistical mechanical model for the effects of these sites is presented and investigated. The ternary troponin complex was reconstituted with either TnC or the TnC mutant CBMII, in which the regulatory site in cardiac TnC (site II) is inactivated. Regardless of whether Ca2+ was present, CBMII-troponin was inhibitory in a thin filament-myosin subfragment 1 MgATPase assay. The competitive binding of [3H]troponin and [14C]CBMII-troponin to actin.tropomyosin was measured. In the presence of Mg2+ and low free Ca2+ they had equal affinities for the thin filament. When Ca274+ was added, however, troponin's affinity for the thin filament was 2.2-fold larger for the mutant than for the wild type troponin. This quantitatively describes the effect of regulatory site Ca2+ on troponin's affinity for actin.tropomyosin; the decrease in troponin-thin filament binding energy is small. Application of the theoretical model to the competitive binding data indicated that troponin molecules bind to interdependent rather than independent sites on the thin filament. Ca2+ binding to the regulatory site of TnC has a long-range rather than a merely local effect. However, these indirect TnC-TnC interactions are weak, indicating that the cooperativity of muscle activation by Ca2+ requires other sources of cooperativity.     

Effects of the amino-terminal regions of tropomyosin and troponin T on thin filament assembly.

Bacterially expressed alpha-tropomyosin lacks the amino-terminal acetylation present in muscle tropomyosin and binds poorly to actin (Hitchcock-DeGregori, S. E., and Heald, R. W. (1987) J. Biol. Chem. 262, 9730-9735). Using a linear lattice model, we determined the affinity (Ko) of unacetylated tropomyosin or troponin-unacetylated tropomyosin for an isolated site on the actin filament and the fold increase in affinity (y) when binding is to an adjacent site. The absence of tropomyosin acetylation decreased Ko 2 orders of magnitude in the absence of troponin. Tropomyosin acetylation also enhanced troponin-tropomyosin binding to actin, not by increasing cooperativity (y), but rather by increasing Ko. These results suggest that the amino-terminal region of tropomyosin is a crucial actin binding site. Troponin promoted unacetylated tropomyosin binding to actin, increasing Ko more than 1,000-fold. Troponin70-259, which lacks the troponin T peptide (1-69) spanning the overlap between adjacent tropomyosins, behaved similarly to intact troponin. Cooperative interactions between adjacent troponin-tropomyosin complexes remained strong despite the use of a nonpolymerizable tropomyosin and a troponin unable to bridge neighboring tropomyosins physically. The Ko for troponin70-259-unacetylated tropomyosin was 500-fold greater than for troponin159-259-unacetylated tropomyosin, indicating that troponin T residues 70-158 are critical for anchoring troponin-tropomyosin to F-actin. The mechanism of cooperative thin filament assembly is discussed.     

A Spatially Detailed Model of Isometric Contraction Based on Competitive Binding of Troponin I Explains Cooperative Interactions between Tropomyosin and Crossbridges

Biophysical models of cardiac tension development provide a succinct representation of our understanding of force generation in the heart. The link between protein kinetics and interactions that gives rise to high cooperativity is not yet fully explained from experiments or previous biophysical models. We propose a biophysical ODE-based representation of cross-bridge (XB), tropomyosin and troponin within a contractile regulatory unit (RU) to investigate the mechanisms behind cooperative activation, as well as the role of cooperativity in dynamic tension generation across different species. The model includes cooperative interactions between regulatory units (RU-RU), between crossbridges (XB-XB), as well more complex interactions between crossbridges and regulatory units (XB-RU interactions). For the steady-state force-calcium relationship, our framework predicts that: (1) XB-RU effects are key in shifting the half-activation value of the force-calcium relationship towards lower [Ca²⁺], but have only small effects on cooperativity. (2) XB-XB effects approximately double the duty ratio of myosin, but do not significantly affect cooperativity. (3) RU-RU effects derived from the long-range action of tropomyosin are a major factor in cooperative activation, with each additional unblocked RU increasing the rate of additional RU’s unblocking. (4) Myosin affinity for short (1–4 RU) unblocked stretches of actin of is very low, and the resulting suppression of force at low [Ca²⁺] is a major contributor in the biphasic force-calcium relationship. We also reproduce isometric tension development across mouse, rat and human at physiological temperature and pacing rate, and conclude that species differences require only changes in myosin affinity and troponin I/troponin C affinity. Furthermore, we show that the calcium dependence of the rate of tension redevelopment k_tr is explained by transient blocking of RU’s by a temporary decrease in XB-RU effects.