Protein kinase A changes calcium sensitivity but not crossbridge kinetics in human cardiac myofibrils

We investigated the effect of PKA treatment (1 U/ml) on the mechanical properties of isolated human cardiac myofibrils. PKA treatment was associated with significant incorporation of radiolabeled phosphate into several sarcomeric proteins including troponin I and myosin binding protein C and was also associated with a right shift in the tension-pCa relation (ΔpCa(50) = 0.2 ± 0.1). PKA treatment also caused right shifts in the pCa dependence of the rate of tension development, tension redevelopment, and the linear and exponential phases of myofibril relaxation. However, there was no change in the same measures of crossbridge turnover when expressed as a function of tension. We conclude that the changes in crossbridge kinetics as a function of calcium concentration reflect a reduced tension due to a lower calcium sensitivity and that the relationship between crossbridge kinetics and tension was unchanged, indicating no direct effect of PKA treatment on crossbridge cycling.     

A simple model with myofilament compliance predicts activation-dependent crossbridge kinetics in skinned skeletal fibers

The contribution of thick and thin filaments to skeletal muscle fiber compliance has been shown to be significant. If similar to the compliance of cycling cross-bridges, myofilament compliance could explain the difference in time course of stiffness and force during the rise of tension in a tetanus as well as the difference in Ca(2+) sensitivity of force and stiffness and more rapid phase 2 tension recovery (r) at low Ca(2+) activation. To characterize the contribution of myofilament compliance to sarcomere compliance and isometric force kinetics, the Ca(2+)-activation dependence of sarcomere compliance in single glycerinated rabbit psoas fibers, in the presence of ATP (5.0 mM), was measured using rapid length steps. At steady sarcomere length, the dependence of sarcomere compliance on the level of Ca(2+)-activated force was similar in form to that observed for fibers in rigor where force was varied by changing length. Additionally, the ratio of stiffness/force was elevated at lower force (low [Ca(2+)]) and r was faster, compared with maximum activation. A simple series mechanical model of myofilament and cross-bridge compliance in which only strong cross-bridge binding was activation dependent was used to describe the data. The model fit the data and predicted that the observed activation dependence of r can be explained if myofilament compliance contributes 60-70% of the total fiber compliance, with no requirement that actomyosin kinetics be [Ca(2+)] dependent or that cooperative interactions contribute to strong cross-bridge binding.     

Dynamic left ventricular elastance: a model for integrating cardiac muscle contraction into ventricular pressure-volume relationships.

To integrate myocardial contractile processes into left ventricular (LV) function, a mathematical model was built. Muscle fiber force was set equal to the product of stiffness and elastic distortion of stiffness elements, i.e., force-bearing cross bridges (XB). Stiffness dynamics arose from recruitment of XB according to the kinetics of myofilament activation and fiber-length changes. Elastic distortion dynamics arose from XB cycling and the rate-of-change of fiber length. Muscle fiber stiffness and distortion dynamics were transformed into LV chamber elastance and volumetric distortion dynamics. LV pressure equaled the product of chamber elastance and volumetric distortion, just as muscle-fiber force equaled the product of muscle-fiber stiffness and lineal elastic distortion. Model validation was in terms of its ability to reproduce cycle-time-dependent LV pressure response, DeltaP(t), to incremental step-like volume changes, DeltaV, in the isolated rat heart. All DeltaP(t), regardless of the time in the cycle at which DeltaP(t) was elicited, consisted of three phases: phase 1, concurrent with the leading edge of DeltaV; phase 2, a brief transient recovery from phase 1; and phase 3, sustained for the duration of systole. Each phase varied with the time in the cycle at which DeltaP(t) was elicited. When the model was fit to the data, cooperative activation was required to sustain systole for longer periods than was possible with Ca(2+) activation alone. The model successfully reproduced all major features of the measured DeltaP(t) responses, and thus serves as a credible indicator of the role of underlying contractile processes in LV function.     

Modelling the mechanical properties of cardiac muscle

A model of passive and active cardiac muscle mechanics is presented, suitable for use in continuum mechanics models of the whole heart. The model is based on an extensive review of experimental data from a variety of preparations (intact trabeculae, skinned fibres and myofibrils) and species (mainly rat and ferret) at temperatures from 20 to 27°C. Experimental tests include isometric tension development, isotonic loading, quick-release/restretch, length step and sinusoidal perturbations. We show that all of these experiments can be interpreted with a four state variable model which includes (i) the passive elasticity of myocardial tissue, (ii) the rapid binding of Ca²⁺ to troponin C and its slower tension-dependent release, (iii) the kinetics of tropomyosin movement and availability of crossbridge binding sites and the length dependence of this process and (iv) the kinetics of crossbridge tension development under perturbations of myofilament length.     

Why exercise builds muscles: titin mechanosensing controls skeletal muscle growth under load

Muscles sense internally generated and externally applied forces, responding to these in a coordinated hierarchical manner at different timescales. The center of the basic unit of the muscle, the sarcomeric M-band, is perfectly placed to sense the different types of load to which the muscle is subjected. In particular, the kinase domain of titin (TK) located at the M-band is a known candidate for mechanical signaling. Here, we develop a quantitative mathematical model that describes the kinetics of TK-based mechanosensitive signaling and predicts trophic changes in response to exercise and rehabilitation regimes. First, we build the kinetic model for TK conformational changes under force: opening, phosphorylation, signaling, and autoinhibition. We find that TK opens as a metastable mechanosensitive switch, which naturally produces a much greater signal after high-load resistance exercise than an equally energetically costly endurance effort. Next, for the model to be stable and give coherent predictions, in particular for the lag after the onset of an exercise regime, we have to account for the associated kinetics of phosphate (carried by ATP) and for the nonlinear dependence of protein synthesis rates on muscle fiber size. We suggest that the latter effect may occur via the steric inhibition of ribosome diffusion through the sieve-like myofilament lattice. The full model yields a steady-state solution (homeostasis) for muscle cross-sectional area and tension and, a quantitatively plausible hypertrophic response to training, as well as atrophy after an extended reduction in tension.     

Dynamic actin interaction of crossbridges: A general principle and its implications for crossbridge action in muscle

The oar-like crossbridge cycle, developed up to the mid-1970's, was shown to be inconsistent with more recent biochemical results. In crossbridge theories developed on the basis of the more recent kinetic schemes of the actomyosin ATPase in solution (Eisenberg and co-workers), however, the key elements proposed by Huxley (1957) were retained, one of which is the assumption that detachment of a force-generating crossbridge can only occur via completion of the ATPase cycle (release of ADP and rebinding of ATP). Furthermore, in these theories regulation is assumed to act by blocking/unblocking of a step subsequent to crossbridge attachment (e.g., P_i-release step). Both concepts, however, were recently shown to be in conflict with studies on skinned muscle fibers (still low ATPase activity at high-speed isotonic shortening, regulation acts via turnover kinetics and not recruitment (39)). By incorporation of the observed reversible actin interaction of crossbridges in all states, including the force-generating states, a working hypothesis can be developed (Fig. 5) which can account for the isotonic data. A mechanism by which such a scheme can also account for regulation via turnover kinetics was previously discussed (39).     

A model to account for the elastic element in muscle crossbridges in terms of a bending myosin rod

We advance a structural model to account for the rapid elastic element seen in mechanical transient experiments on vertebrate skeletal muscle (A.F. Huxley & Simmons 1971 Nature, Lond. 233, 533-538). In contrast to other crossbridge models, ours does not envisage a myosin rod made up of two rigid portions connected by a hinge, but rather a gradually bending rod portion connecting the heads to the thick filament shaft. We propose that, in relaxed muscle, the subfragment 2 (S2) portion of the myosin rod is bound to the thick filament shaft by ionic interactions analogous to those between the light meromyosin (LMM) portions of the rod that constitute the body of the shaft. These interactions probably involve the alternating zones of positive and negative charge seen in myosin rod amino acid sequences. As the crossbridge cycle that generates tension begins, we propose that part of S2 detaches from the thick filament shaft and bends to enable the myosin head to attach to actin. When tension develops in the crossbridge, the S2 is straightened and more of it becomes detached from the shaft so that the junction between S2 and the myosin heads moves 3-4 nm axially. As tension declines at the end of the crossbridge stroke, we propose that S2 rebinds to the thick filament shaft and that this provides the restoring force to return the junction of the heads and S2 to its original axial position. Thus this movement would have the characteristics of an elastic element; detailed calculations indicate that it would have properties similar to those observed experimentally. Furthermore, this model can account for the radial attractive force seen in rigor and in contracting muscle, the decrease in stiffness when interfilament spacing is increased in skinned muscle, and the increased rate of proteolysis observed at the S2-LMM junction in contracting muscle.     

Force suppression and the crossbridge cycle in swine carotid artery

Cyclic nucleotides can relax arterial smooth muscle without reductions in crossbridge phosphorylation, a process termed force suppression. There are two potential mechanisms for force suppression: 1) phosphorylated crossbridges binding to thin filaments could be inhibited or 2) the attachment of thin filaments to anchoring structures could be disrupted. These mechanisms were evaluated by comparing histamine-stimulated swine arterial smooth muscle with and without forskolin-induced force suppression and with and without latrunculin-A-induced actin filament disruption. At matched force, force suppression was associated with higher crossbridge phosphorylation and shortening velocity at low loads when compared with tissues without force suppression. Shortening velocity at high loads, noise temperature, hysteresivity, and stiffness did not differ with and without force suppression. These data suggest that crossbridge phosphorylation regulates the crossbridge cycle during force suppression. Actin disruption with latrunculin-A was associated with higher crossbridge phosphorylation when compared with tissues without actin disruption. Shortening velocity, noise temperature, hysteresivity, and stiffness did not differ with and without actin disruption. These data suggest that actin disruption interferes with regulation of crossbridge cycling by crossbridge phosphorylation. Stiffness was linearly dependent on stress, suggesting that the force per attached crossbridge was not altered with force suppression or actin disruption. These data suggest a difference in the mechanical characteristics observed during force suppression and actin disruption, implying that force suppression does not mechanistically involve actin disruption. These data are most consistent with a model where force suppression involves the inhibition of phosphorylated crossbridge binding to thin filaments. force suppression; heat shock protein 20; vascular smooth muscle     

Thin filament protein dynamics in fully differentiated adult cardiac myocytes: toward a model of sarcomere maintenance.

Sarcomere maintenance, the continual process of replacement of contractile proteins of the myofilament lattice with newly synthesized proteins, in fully differentiated contractile cells is not well understood. Adenoviral-mediated gene transfer of epitope-tagged tropomyosin (Tm) and troponin I (TnI) into adult cardiac myocytes in vitro along with confocal microscopy was used to examine the incorporation of these newly synthesized proteins into myofilaments of a fully differentiated contractile cell. The expression of epitope-tagged TnI resulted in greater replacement of the endogenous TnI than the replacement of the endogenous Tm with the expressed epitope-tagged Tm suggesting that the rates of myofilament replacement are limited by the turnover of the myofilament bound protein. Interestingly, while TnI was first detected in cardiac sarcomeres along the entire length of the thin filament, the epitope-tagged Tm preferentially replaced Tm at the pointed end of the thin filament. These results support a model for sarcomeric maintenance in fully differentiated cardiac myocytes where (a) as myofilament proteins turnover within the cell they are rapidly exchanged with newly synthesized proteins, and (b) the nature of replacement of myofilament proteins (ordered or stochastic) is protein specific, primarily affected by the structural properties of the myofilament proteins, and may have important functional consequences.     

Mechanical transients of single toad stomach smooth muscle cells. Effects of lowering temperature and extracellular calcium

Smooth muscle's slow, economical contractions may relate to the kinetics of the crossbridge cycle. We characterized the crossbridge cycle in smooth muscle by studying tension recovery in response to a small, rapid length change (i.e., tension transients) in single smooth muscle cells from the toad stomach (Bufo marinus). To confirm that these tension transients reflect crossbridge kinetics, we examined the effect of lowering cell temperature on the tension transient time course. Once this was confirmed, cells were exposed to low extracellular calcium [( Ca2+]o) to determine whether modulation of the cell's shortening velocity by changes in [Ca2+]o reflected the calcium sensitivity of one or more steps in the crossbridge cycle. Single smooth muscle cells were tied between an ultrasensitive force transducer and length displacement device after equilibration in temperature-controlled physiological saline having either a low (0.18 mM) or normal (1.8 mM) calcium concentration. At the peak of isometric force, after electrical stimulation, small, rapid (less than or equal to 1.8% cell length in 3.6 ms) step stretches and releases were imposed. At room temperature (20 degrees C) in normal [Ca2+]o, tension recovery after the length step was described by the sum of two exponentials with rates of 40-90 s-1 for the fast phase and 2-4 s-1 for the slow phase. In normal [Ca2+]o but at low temperature (10 degrees C), the fast tension recovery phase slowed (apparent Q10 = 1.9) for both stretches and releases whereas the slow tension recovery phase for a release was only moderately affected (apparent Q10 = 1.4) while unaffected for a stretch. Dynamic stiffness was determined throughout the time course of the tension transient to help correlate the tension transient phases with specific step(s) in the crossbridge cycle. The dissociation of tension and stiffness, during the fast tension recovery phase after a release, was interpreted as evidence that this recovery phase resulted from both the transition of crossbridges from a low- to high-force producing state as well as a transient detachment of crossbridges. From the temperature studies and dynamic stiffness measurements, the slow tension recovery phase most likely reflects the overall rate of crossbridge cycling. From the tension transient studies, it appears that crossbridges cycle slower and have a longer duty cycle in smooth muscle. In low [Ca2+]o at 20 degrees C, little effect was observed on the form or time course of the tension transients.(ABSTRACT TRUNCATED AT 400 WORDS)     

Dynamic stiffness and crossbridge action in muscle

Small sinusoidal vibrations at 300 HZ were applied to frog sartorius muscle to measure the dynamic stiffness (Young's modulus) throughout the course of tetanus. For a peak-to-peak amplitude of 0.4% the dynamic Young's modulus increased from 1.5 X 10(5) Nm-2 in the resting state to 2 X 10(7) Nm-2 in tetanus. After correction for the external connective tissue, the dynamic Young's modulus of the muscle was almost directly proportional to the tension throughout the development of tetanus. The ratio of dynamic Young's modulus to tensile stress thus remained constant (with a value at 300 Hz of approximately 100), consistently with Huxley and Simmon's identification of the crossbridges as the source of both tension and stiffness. For a single crossbridge the ratio of stiffness to tension was 8.2 X 10(7) m-1 at 300 Hz; it is deduced from literature data that the limiting value at high frequencies is about 1.6 X 10(8) m-1. This ratio is interpreted on Harrington's (1971) model to show that crossbridge action can be explained by a helix-coil transition of about 80 out of the 260 residues in each S-2 myosin strand. It is also shown that a helix-coil model can account for the observed rapid relaxation of muscle without invoking any complex behaviour of the crossbridge head.     

Effects of PKA phosphorylation of cardiac troponin I and strong crossbridge on conformational transitions of the N-domain of cardiac troponin C in regulated thin filaments

Regulation of cardiac muscle function is initiated by binding of Ca2+ to troponin C (cTnC) which induces a series of structural changes in cTnC and other thin filament proteins. These structural changes are further modulated by crossbridge formation and fine-tuned by phosphorylation of cTnI. The objective of the present study is to use a new F?rster resonance energy transfer-based structural marker to distinguish structural and kinetic effects of Ca2+ binding, crossbridge interaction, and protein kinase A phosphorylation of cTnI on the conformational changes of the cTnC N-domain. The FRET-based structural marker was generated by attaching AEDANS to one cysteine of a double-cysteine mutant cTnC(13C/51C) as a FRET donor and attaching DDPM to the other cysteine as the acceptor. The doubly labeled cTnC mutant was reconstituted into the thin filament by adding cTnI, cTnT, tropomyosin, and actin. Changes in the distance between Cys13 and Cys51 induced by Ca2+ binding/dissociation were determined by FRET-sensed Ca2+ titration and stopped-flow studies, and time-resolved fluorescence measurements. The results showed that the presence of both Ca2+ and strong binding of myosin head to actin was required to achieve a fully open structure of the cTnC N-domain in regulated thin filaments. Equilibrium and stopped-flow studies suggested that strongly bound myosin head significantly increased the Ca2+ sensitivity and changed the kinetics of the structural transition of the cTnC N-domain. PKA phosphorylation of cTnI impacted the Ca2+ sensitivity and kinetics of the structural transition of the cTnC N-domain but showed no global structural effect on cTnC opening. These results provide an insight into the modulation mechanism of strong crossbridge and cTnI phosphorylation in cardiac thin filament activation/relaxation processes.     

Filament compliance influences cooperative activation of thin filaments and the dynamics of force production in skeletal muscle

Striated muscle contraction is a highly cooperative process initiated by Ca²⁺ binding to the troponin complex, which leads to tropomyosin movement and myosin cross-bridge (XB) formation along thin filaments. Experimental and computational studies suggest skeletal muscle fiber activation is greatly augmented by cooperative interactions between neighboring thin filament regulatory units (RU-RU cooperativity; 1 RU = 7 actin monomers+1 troponin complex+1 tropomyosin molecule). XB binding can also amplify thin filament activation through interactions with RUs (XB-RU cooperativity). Because these interactions occur with a temporal order, they can be considered kinetic forms of cooperativity. Our previous spatially-explicit models illustrated that mechanical forms of cooperativity also exist, arising from XB-induced XB binding (XB-XB cooperativity). These mechanical and kinetic forms of cooperativity are likely coordinated during muscle contraction, but the relative contribution from each of these mechanisms is difficult to separate experimentally. To investigate these contributions we built a multi-filament model of the half sarcomere, allowing RU activation kinetics to vary with the state of neighboring RUs or XBs. Simulations suggest Ca²⁺ binding to troponin activates a thin filament distance spanning 9 to 11 actins and coupled RU-RU interactions dominate the cooperative force response in skeletal muscle, consistent with measurements from rabbit psoas fibers. XB binding was critical for stabilizing thin filament activation, particularly at submaximal Ca²⁺ levels, even though XB-RU cooperativity amplified force less than RU-RU cooperativity. Similar to previous studies, XB-XB cooperativity scaled inversely with lattice stiffness, leading to slower rates of force development as stiffness decreased. Including RU-RU and XB-RU cooperativity in this model resulted in the novel prediction that the force-[Ca²⁺] relationship can vary due to filament and XB compliance. Simulations also suggest kinetic forms of cooperativity occur rapidly and dominate early to get activation, while mechanical forms of cooperativity act more slowly, augmenting XB binding as force continues to develop.     

Use of distraction loading to estimate subject-specific knee ligament slack lengths

Knee ligaments guide and restrain joint motion, and their properties influence joint mechanics. Inverse modeling schemes have been used to estimate specimen-specific ligament properties, where external joint forces are assumed to balance with internal ligament and contact forces. This study simplifies this assumption by adjusting experimental loads to remove internal contact forces. The purpose of this study was to use novel experimental loading in an inverse modeling scheme to estimate ligament slack lengths, perform validation using additional loading scenarios, and evaluate sensitivity to the applied loading. Joint kinematics and kinetics were experimentally measured for a set of load cases. An optimization scheme used a specimen-specific forward kinematics model to estimate ligament slack lengths by minimizing the residual between model and experimentally measured kinetics. The calibrated model was used for a form of validation by evaluating non-optimized load cases. Additionally, uncertainty analysis related kinetic errors to previously reported kinematic errors. The six DOF tibial reactions realized RMS errors less than 23 N and 0.75 Nm for optimized load cases, and 33 N and 2.25 Nm for the non-optimized load cases. The uncertainty analysis, which was performed using the optimized load cases, showed average kinetic RMS errors less than 26 N and 0.45 Nm. The model’s recruitment patterns were similar to those found in clinical and cadaveric studies. This study demonstrated that experimental distraction loading can be used in an inverse modeling scheme to estimate ligament slack lengths with a forward kinematics model.     

Two attached non-rigor crossbridge forms in insect flight muscle

We have performed thin-section electron microscopy on muscle fibers fixed in different mechanically monitored states, in order to identify structural changes in myosin crossbridges associated with force production and maintenance. Tension and stiffness of fibers from glycerinated Lethocerus flight muscle were monitored during a sequence of conditions using AMPPNP and then AMPPNP plus increasing concentrations of ethylene glycol, which brought fibers through a graded sequence from rigor relaxation. Two intermediate crossbridge forms distinct from the rigor or relaxed forms were observed. The first was produced by AMPPNP at 20 degrees C, which reduced isometric tension 60 to 70% below rigor level without reducing rigor stiffness. Electron microscopy of these fibers showed that, in spite of the drop in tension, no obvious change from the 45 degrees crossbridge angle characteristic of rigor occurred. However, the thick filament ends of the crossbridges were altered from their rigor positions, so that they now marked a 14.5 nm repeat, and formed four separate origins at each crossbridge level. The bridges were also less slewed and bent than rigor bridges, as seen in transverse sections. The second crossbridge form was seen in glycol-AMPPNP at 4 degrees C, just below the glycol concentration that produced mechanical relaxation. These fibers retained 90% of rigor stiffness at 40 Hz oscillation, but would not bear sustained tension. Stiffness was also high in the presence of calcium at room temperature under similar conditions. Electron microscopy showed crossbridges projecting from the thick filaments at an angle that centered around 90 degrees, rather than the 45 degree angle familiar from rigor. This coupling of relaxed appearance with persistent stiffness suggests that the 90 degree form may represent a weakly attached crossbridge state like that proposed to precede force development in current models of the crossbridge power stroke.     

Electron and proton transport in chloroplasts taking into account lateral heterogeneity of thylakoids. Mathematical model]

A mathematical model of a chloroplast was constructed, which takes into account the inhomogeneous distribution of complexes of photosystems I and II between granal and intergranal thylakoids. The structural and functional complexes of photosystems I and II, which are localized in intergranal and granal thylakoids, respectively, and the b/f complex, which is uniformly distributed in thylakoid membranes, are assumed to be immobile. The interactions between spatially distant electron transport complexes are provided by plastoquinone and plastocyanine, which diffuse in the thylakoid membrane and intrathylakoid space, respectively. The main stages of proton transport associated with the functioning of photosystem II and oxidation-reduction transformations of plastoquinone are considered. The model takes into account the interactions of protons with membrane-bound buffer groups, the lateral diffusion of hydrogen ions in the intrathylakoid space and in the lumen between adjacent granal thylakoids, and the transmembrane proton transport associated with the function of ATP synthase and passive leakage of protons from thylakoids outside. The numerical integration of two systems of differential equations describing the behavior of some variables in two different regions: granal and intergranal thylakoids was performed. The model describes adequately the kinetics of processes being studied and predicts the occurrence of inhomogeneous lateral profiles of proton potentials and redox state of electron carriers. Modeling the electron and proton transport with allowance for the topological features of chloroplasts (lateral heterogeneity of thylakoids) is important for correct interpretation of "power-flux" interactions and the experimentally measured kinetic parameters averaged over the entire spatially inhomogeneous thylakoid system.     

O-GlcNAcylation is a key modulator of skeletal muscle sarcomeric morphometry associated to modulation of protein–protein interactions

BackgroundThe sarcomere structure of skeletal muscle is determined through multiple protein–protein interactions within an intricate sarcomeric cytoskeleton network. The molecular mechanisms involved in the regulation of this sarcomeric organization, essential to muscle function, remain unclear. O-GlcNAcylation, a post-translational modification modifying several key structural proteins and previously described as a modulator of the contractile activity, was never considered to date in the sarcomeric organization.MethodsC2C12 skeletal myotubes were treated with Thiamet-G (OGA inhibitor) in order to increase the global O-GlcNAcylation level.ResultsOur data clearly showed a modulation of the O-GlcNAc level more sensitive and dynamic in the myofilament-enriched fraction than total proteome. This fine O-GlcNAc level modulation was closely related to changes of the sarcomeric morphometry. Indeed, the dark-band and M-line widths increased, while the I-band width and the sarcomere length decreased according to the myofilament O-GlcNAc level. Some structural proteins of the sarcomere such as desmin, αB-crystallin, α-actinin, moesin and filamin-C have been identified within modulated protein complexes through O-GlcNAc level variations. Their interactions seemed to be changed, especially for desmin and αB-crystallin.ConclusionsFor the first time, our findings clearly demonstrate that O-GlcNAcylation, through dynamic regulations of the structural interactome, could be an important modulator of the sarcomeric structure and may provide new insights in the understanding of molecular mechanisms of neuromuscular diseases characterized by a disorganization of the sarcomeric structure.General significanceIn the present study, we demonstrated a role of O-GlcNAcylation in the sarcomeric structure modulation.     

Interplay of Protein Binding Interactions,DNA Mechanics,and Entropy in?DNA Looping Kinetics

DNA looping plays a key role in many fundamental biological processes, including gene regulation, recombination, and chromosomal organization. The looping of DNA is often mediated by proteins whose structural features and physical interactions can alter the length scale at which the looping occurs. Looping and unlooping processes are controlled by thermodynamic contributions associated with mechanical deformation of the DNA strand and entropy arising from thermal fluctuations of the conformation. To determine how these confounding effects influence DNA looping and unlooping kinetics, we present a theoretical model that incorporates the role of the protein interactions, DNA mechanics, and conformational entropy. We show that for shorter DNA strands the interaction distance affects the transition state, resulting in a complex relationship between the looped and unlooped state lifetimes and the physical properties of the looped DNA. We explore the range of behaviors that arise with varying interaction distance and DNA length. These results demonstrate how DNA deformation and entropy dictate the scaling of the looping and unlooping kinetics versus the J-factor, establishing the connection between kinetic and equilibrium behaviors. Our results show how the twist-and-bend elasticity of the DNA chain modulates the kinetics and how the influence of the interaction distance fades away at intermediate to longer chain lengths, in agreement with previous scaling predictions.     

Load-dependent kinetics of force production by smooth muscle myosin measured with optical tweezers

Muscle contraction is driven by the cyclical interaction of myosin with actin, coupled with ATP hydrolysis. Myosin attaches to actin, forming a crossbridge that produces force and movement as it tilts or rocks into subsequent bound states before finally detaching. It has been hypothesized that the kinetics of one or more of these mechanical transitions are dependent on load, allowing muscle to shorten quickly under low load, but to sustain tension economically, with slowly cycling crossbridges under high load conditions. The idea that muscle biochemistry depends on mechanical output is termed the 'Fenn effect'. However, the molecular details of how load affects the kinetics of a single crossbridge are unknown. Here, we describe a new technique based on optical tweezers to rapidly apply force to a single smooth muscle myosin crossbridge. The crossbridge produced movement in two phases that contribute 4 nm + 2 nm of displacement. Duration of the first phase depended in an exponential manner on the amplitude of applied load. Duration of the second phase was much less affected by load, but was significantly shorter at high ATP concentration. The effect of load on the lifetime of the bound crossbridge is to prolong binding when load is high, but to accelerate release when load is low or negative.