Hystereses in the force-length relation and regulation of cross-bridge recruitment in tetanized rat trabeculae

Various mechanisms have been suggested to explain cardiac force-length Ca2+ relations. The existence of a cooperativity mechanism, whereby cross-bridge (XB) recruitment is affected by the number of active XBs, suggests that the force response to length oscillations should lag length oscillations. Consequently, the oscillatory force response should be larger during shortening than during lengthening. To test this prediction, force responses to large-sarcomere length (SL) oscillations (36.7 +/- 16.0 nm) at different SLs (n = 6) and frequencies (n = 7) were studied in intact tetanized trabeculae dissected from rat right ventricle (n = 13). Stable tetani were obtained by utilizing 30 microM cyclopiazonic acid in Krebs-Henseleit solution containing 6 mM extracellular Ca(2+) at 25 degrees C. SL was measured by laser diffraction techniques (Dalsa). Force was measured by silicone strain gauge. Instantaneous dynamic stiffness during large oscillations was measured by superimposing additional fast (50 or 200 Hz) and small-amplitude (2.25 +/- 0.25 nm) oscillations. The force responses lagged the SL oscillations at slow frequencies (112 +/- 41 ms at 1 Hz), and counterclockwise hystereses were obtained in the force-length plane: the force was higher during shortening than during lengthening. The delay in the force response decreased as the frequency of the SL oscillation was increased. Clockwise hysteresis, where the force preceded the SL, was obtained at frequencies >4 Hz. Similar hysteresis characteristics were obtained in the force-SL and stiffness-SL planes. Maximal lag was observed at the shortest SL, and the delay decreased with sarcomere elongation: 131.1 +/- 31.7 ms at 1.78 +/- 0.03 microm vs. 14.7 +/- 18.5 ms at 1.99 +/- 0.015 microm. The results establish the ability of cardiac fiber to adapt XB recruitment to changes in prevailing loading conditions. This study supports the stipulated existence of a cooperativity mechanism that regulates XB recruitment and highlights an additional method to characterize regulation of the force-length relation.     

Regulation of energy liberation during steady sarcomere shortening

Energy liberation rate (E) during steady muscle shortening is a monotonic increasing or biphasic function of the shortening velocity (V). The study examines three plausible hypotheses for explaining the biphasic E-V relationship (EVR): 1) the cross-bridge (XB) turnover rate from non-force-generating (weak) to force-generating (strong) conformation decreases as V increases; 2) XB kinetics is determined by the number of strong XBs (XB-XB cooperativity); and 3) the affinity of troponin for calcium is modulated by the number of strong XBs (XB-Ca cooperativity). The relative role of the various energy-regulating mechanisms is not well defined. The hypotheses were tested by coupling calcium kinetics with XB cycling. All three hypotheses yield identical steady-state characteristics: 1) hyperbolic force-velocity relationship; 2) quasi-linear stiffness-force relationship; and 3) biphasic EVR, where E declines at high V due to decrease in the number of cycling XBs or in the weak-to-strong transition rate. The hypotheses differ in the ability to describe the existence of both monotonic and biphasic EVRs and in the effect of intracellular free calcium concentration ([Ca2+]i) on the EVR peak. Monotonic and biphasic EVRs with a shift in EVR peak to higher velocity at higher [Ca2+]i are obtained only by XB-Ca cooperativity. XB-XB cooperativity provides only biphasic EVRs. A direct effect of V on XB kinetics predicts that EVR peak is obtained at the same velocity independently of [Ca2+]i. The study predicts that measuring the dependence of the EVR on [Ca2+]i allows us to test the hypotheses and to identify the dominant energy-regulating mechanism. The established XB-XB and XB-Ca mechanisms provide alternative explanations to the various reported EVRs.     

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.     

Troponin T modulates sarcomere length-dependent recruitment of cross-bridges in cardiac muscle

The heterogenic nature of troponin T (TnT) isoforms in fast skeletal and cardiac muscle suggests important functional differences. Dynamic features of rat cardiac TnT (cTnT) and rat fast skeletal TnT (fsTnT) reconstituted cardiac muscle preparations were captured by fitting the force response of small amplitude (0.5%) muscle length changes to the recruitment-distortion model. The recruitment of force-bearing cross-bridges (XBs) by increases in muscle length was favored by cTnT. The recruitment magnitude was approximately 1.5 times greater for cTnT- than for fsTnT-reconstituted muscle fibers. The speed of length-mediated XB recruitment (b) in cTnT-reconstituted muscle fiber was 0.50-0.57 times as fast as fsTnT-reconstituted muscle fibers (3.05 vs. 5.32 s(-1) at sarcomere length, SL, of 1.9 microm and 4.16 vs. 8.36 s(-1) at SL of 2.2 microm). Due to slowing of b in cTnT-reconstituted muscle fibers, the frequency of minimum stiffness (f(min)) was shifted to lower frequencies of muscle length changes (at SL of 1.9 microm, 0.64 Hz, and 1.16 Hz for cTnT- and fsTnT-reconstituted muscle fibers, respectively; at SL of 2.2 microm, 0.79 Hz, and 1.11 Hz for cTnT- and fsTnT-reconstituted muscle fibers, respectively). Our model simulation of the data implicates TnT as a participant in the process by which SL- and XB-regulatory unit cooperative interactions activate thin filaments. Our data suggest that the amino-acid sequence differences in cTnT may confer a heart-specific regulatory role. cTnT may participate in tuning the heart muscle by decreasing the speed of XB recruitment so that the heart beats at a rate commensurate with f(min).     

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.     

Sarcomere mechanics in uniform and non-uniform cardiac muscle: a link between pump function and arrhythmias

Starling's Law and the well-known end-systolic pressure-volume relationship (ESPVR) of the left ventricle reflect the effect of sarcomere length (SL) on stress (sigma) development and shortening by myocytes in the uniform ventricle. We show here that tetanic contractions of rat cardiac trabeculae exhibit a sigma-SL relationship at saturating [Ca2+] that depends on sarcomere geometry in a manner similar to skeletal sarcomeres and the existence of opposing forces in cardiac muscle shortened below slack length. The sigma-SL-[Ca2+]free relationships (sigma-SL-CaR) at submaximal [Ca2+] in intact and skinned trabeculae were similar, albeit that the sensitivity for Ca2+ of intact muscle was higher. We analyzed the mechanisms underlying the sigma-SL-CaR using a kinetic model where we assumed that the rates of Ca2+ binding by Troponin-C (Tn-C) and/or cross-bridge (XB) cycling are determined by SL, [Ca2+] or stress. We analyzed the correlation between the model results and steady state stress measurements at varied SL and [Ca2+] from skinned rat cardiac trabeculae to test the hypotheses that: (i) the dominant feedback mechanism is SL, stress or [Ca2+]-dependent; and (ii) the feedback mechanism regulates: Tn-C-Ca2+ affinity, XB kinetics or, unitary XB-force. The analysis strongly suggests that feedback of the number of strong XBs to cardiac Tn-C-Ca2+ affinity is the dominant mechanism that regulates XB recruitment. Application of this concept in a mathematical model of twitch-stress accurately reproduced the sigma-SL-CaR and the time course of twitch-stress as well as the time course of intracellular [Ca2+]i. Modeling of the response of the cardiac twitch to rapid stress changes using the above feedback model uniquely predicted the occurrence of [Ca2+]i transients as a result of accelerated Ca2+ dissociation from Tn-C. The above concept has important repercussions for the non-uniformly contracting heart in which arrhythmogenic Ca2+ waves arise from weakened areas in cardiac muscle. These Ca2+ waves can reversibly be induced in muscle with non-uniform excitation contraction coupling (ECC) by the cycle of stretch and release in the border zone between the damaged and intact regions. Stimulus trains induced propagating Ca2+ waves and reversibly induced arrhythmias. We hypothesize that rapid force loss by sarcomeres in the border zone during relaxation causes Ca2+ release from Tn-C and initiates Ca2+ waves propagated by the sarcoplasmic reticulum (SR). These observations suggest the unifying hypothesis that force feedback to Ca2+ binding by Tn-C is responsible for Starling's Law and the ESPVR in uniform myocardium and leads in non-uniform myocardium to a surge of Ca2+ released by the myofilaments during relaxation, which initiates arrhythmogenic propagating Ca2+ release by the SR.     

Cooperativity in mechano-calcium feedbacks in the myocardium: Some conceptual discrepancies and overcoming inconsistency within the framework of a mathematical model

Mechano-calcium feedbacks that provide fine tuning of electrical and calcium activation of the heart muscle to mechanical conditions of contractions are an important element of electromechanical coupling as a key mechanism of the autoregulation of the contractile activity of the myocardium. A large quantity of experimental and theoretical evidence supports the cooperative dependence of the calcium-troponin complex kinetics on the cross-bridge concentration as a principal mechanism that underlies the mechano-calcium feedback in the intact myocardium. At the same time, experiments performed using skinned myocardial preparations have demonstrated that mechanical conditions significantly affected only the calcium sensitivity of the Ca²⁺–force relationship rather than its Hill coefficient of cooperativity. These data make some investigators doubt the contribution of cooperativity to the mechano-calcium feedbacks. To overcome these arising discrepancies, we propose an improved conception of cooperativity that reveals the extent of intensity differently in the steady state and in transitional processes. The proposed conception enables us to reproduce and explain both the mechanodependence of calcium activation in the intact myocardium and the results with skinned muscle within the framework of a mathematical model.     

Force-velocity relationship and biochemical-to-mechanical energy conversion by the sarcomere

The intracellular control mechanism leading to the well-known linear relationship between energy consumption by the sarcomere and the generated mechanical energy is analyzed here by coupling calcium kinetics with cross-bridge cycling. A key element in the control of the biochemical-to-mechanical energy conversion is the effect of filament sliding velocity on cross-bridge cycling. Our earlier studies have established the existence of a negative mechanical feedback mechanism whereby the rate of cross-bridge turnover from the strong, force-generating conformation to the weak, non-force-generating conformation is a linear function of the filament sliding velocity. This feedback allows the analytic derivation of the experimentally established Hill's equation for the force-velocity relationship. Moreover, it allows us to derive the transient length response to load clamps and the transient force response to sarcomere shortening at constant velocity. The results are in agreement with experimental studies. The mechanical feedback regulates the generated power, maintains the linear relationship between energy liberated by the actomyosin-ATPase and the generated mechanical energy, and determines the efficiency of biochemical-to-mechanical energy conversion. The mechanical feedback defines three elements of the mechanical energy: 1) external work done; 2) pseudopotential energy, required for cross-bridge recruitment; and 3) energy dissipation caused by the viscoelastic property of the cross bridge. The last two elements dissipate as heat.     

Temperature-induced switching of the bacterial flagellar motor.

Chemotaxis signaling proteins normally control the direction of rotation of the flagellar motor of Escherichia coli. In their absence, a wild-type motor spins exclusively counterclockwise. Although the signaling pathway is well defined, relatively little is known about switching, the mechanism that enables the motor to change direction. We found that switching occurs in the absence of signaling proteins when cells are cooled to temperatures below about 10 degrees C. The forward rate constant (for counterclockwise to clockwise, CCW to CW, switching) increases and the reverse rate constant (for CW to CCW switching) decreases as the temperature is lowered. At about -2 degrees C, most motors spin exclusively CW. At temperatures for which reversals are frequent enough to generate a sizable data set, both CCW and CW interval distributions appear to be exponential. From the rate constants we computed equilibrium constants and standard free energy changes, and from the temperature dependence of the standard free energy changes we determined standard enthalpy and entropy changes. Using transition-state theory, we also calculated the activation free energy, enthalpy, and entropy. We conclude that the CW state is preferred at very low temperatures and that it is relatively more highly bonded and restricted than the CCW state.     

Spontaneous whole body rotations and classical dance expertise: How shoulder–hip coordination influences supporting leg displacements

The link between supporting leg stability and individual trunk strategies used during spontaneous whole-body rotations was studied according to visual and kinesthetic imagery styles for classical dancers and untrained female participants. Shoulders–hip angles in the horizontal plane and supporting leg (SL) displacements were analyzed with three-dimensional kinematic at the beginning and end of the four turns, identified according to their SL (left vs. right) and turn direction (clockwise, CW vs. counterclockwise, CCW). To begin a turn in CCW on left SL, all the participants turned shoulders before hips (?25° angle), p < 0.01. Untrained participants yielded the reverse (+30° angle) in CW – their non-preferred turn - whereas dancers maintained their trunk en bloc. In the turn slow down, in their preferred direction all the participants adopted en bloc behavior to avoid imbalance. Dancers kept this pattern in CCW but untrained participants separated shoulders and hips, p < 0.01; on left SL (+20° angle) hips finished before shoulders and on right SL (?25° angle), shoulders finished before hips. Both mental imagery styles and spatial context link reduction of shoulder–hip angle and stability of SL. Daily expertise, not only dance training, facilitates the en bloc shoulder–hip coordination to maintain equilibrium.     

Dynamics of individual sarcomeres during and after stretch in activated single myofibrils

It is generally assumed that sarcomere lengths (SLs) change in isometric fibres following activation and following stretch on the descending limb of the force-length relationship, because of an inherent instability. Although this assumption has never been tested directly, instability and SL non-uniformity have been associated with several mechanical properties, such as 'creep' and force enhancement. The aim of this study was to test directly the hypothesis that sarcomeres are unstable on the descending limb of the force-length relationship. We used single myofibrils, isolated from rabbit psoas, that were attached to glass needles that allowed for controlled stretching of myofibrils. Images of the sarcomere striation pattern were projected onto a linear photodiode array, which was scanned at 20 Hz to produce dark-light patterns corresponding to the A- and I-bands, respectively. Starting from a mean SL of 2.55 +/- 0.07 microm, stretches of 11.2 +/- 1.6% of SL at a speed of 118.9 +/- 5.9 nm s(-1) were applied to the activated myofibrils (pCa(2+) = 4.75). SLs along the myofibril were non-uniform before, during and after the stretch, but with few exceptions, they remained constant during the isometric period before stretch, and during the extended isometric period after stretch. Sarcomeres never lengthened to a point beyond thick and thin filament overlap. We conclude that sarcomeres are non-uniform but generally stable on the descending limb of the force-length relationship.     

Perturbed equilibria of myosin binding in airway smooth muscle: bond-length distributions, mechanics, and ATP metabolism

We carried out a detailed mathematical analysis of the effects of length fluctuations on the dynamically evolving cross-bridge distributions, simulating those that occur in airway smooth muscle during breathing. We used the latch regulation scheme of Hai and Murphy (Am. J. Physiol. Cell Physiol. 255:C86-C94, 1988) integrated with Huxley's sliding filament theory of muscle contraction. This analysis showed that imposed length fluctuations decrease the mean number of attached bridges, depress muscle force and stiffness, and increase force-length hysteresis. At frequencies >0.1 Hz, the bond-length distribution of slowly cycling latch bridges changed little over the stretch cycle and contributed almost elastically to muscle force, but the rapidly cycling cross-bridge distribution changed substantially and dominated the hysteresis. By contrast, at frequencies <0.033 Hz this behavior was reversed: the rapid cycling cross-bridge distribution changed little, effectively functioning as a constant force generator, while the latch bridge bond distribution changed substantially and dominated the stiffness and hysteresis. The analysis showed the dissociation of force/length hysteresis and cross-bridge cycling rates when strain amplitude exceeds 3%; that is, there is only a weak coupling between net external mechanical work and the ATP consumption required for cycling cross-bridges during the oscillatory steady state. Although these results are specific to airway smooth muscle, the approach generalizes to other smooth muscles subjected to cyclic length fluctuations.     

Handwriting: Hand–pen contact force synergies in circle drawing tasks

This study investigated synergistic actions of hand–pen contact forces during circle drawing tasks in three-dimensional (3D) space. Twenty-four right-handed participants drew thirty concentric circles in the counterclockwise (CCW) and clockwise (CW) directions. Three-dimensional forces acting on an instrumented pen as well as 3D linear and angular positions of the pen were recorded. These contact forces were then transformed into the 3D radial, tangential, and normal force components specific to circle drawing. Uncontrolled manifold (UCM) analysis was employed to calculate the magnitude of the hand–pen contact force synergy. Three hypotheses were tested. First, hand–pen contact force synergies during circle drawing are dependent on the angular position of the pen tip. Second, hand–pen contact force synergies are dependent on force components in circle drawing. Third, hand–pen contact force synergies are greater in CCW direction than CW direction. The results showed that the strength of the hand–pen contact force synergy increased during the initial phase of circle drawing and decreased during the final phase. The synergy strength was greater for the radial and tangential components as compared to the normal component. Also, the circle drawing in CW direction was associated with greater hand–pen contact force synergy than the CCW direction. The results of this study suggest that the central nervous system (CNS) prioritizes hand–pen contact force synergies for the force components (i.e., radial and tangential) that are critical for circle drawing. The CNS modulates hand–pen contact force synergies for preparation and conclusion of circle drawing, respectively.     

Temperature dependence of switching of the bacterial flagellar motor by the protein CheY(13DK106YW).

The behavior of the bacterium Escherichia coli is controlled by switching of the flagellar rotary motor between the two rotational states, clockwise (CW) and counterclockwise (CCW). The molecular mechanism for switching remains unknown, but binding of the response regulator CheY-P to the motor component FliM enhances CW rotation. This effect is mimicked by the unphosphorylated double mutant CheY13DK106YW (CheY**). To learn more about switching, we measured the fraction of time that a motor spends in the CW state (the CW bias) at different concentrations of CheY** and at different temperatures. From the CW bias, we computed the standard free energy change of switching. In the absence of CheY, this free energy change is a linear function of temperature (. Biophys. J. 71:2227-2233). In the presence of CheY**, it is nonlinear. However, the data can be fit by models in which binding of each molecule of CheY** shifts the difference in free energy between CW and CCW states by a fixed amount. The shift increases linearly from approximately 0.3kT per molecule at 5 degrees C to approximately 0.9kT at 25 degrees C, where k is Boltzmann's constant and T is 289 Kelvin (= 16 degrees C). The entropy and enthalpy contributions to this shift are about -0. 031kT/ degrees C and 0.10kT, respectively.     

Direction of flagellar rotation in bacterial cell envelopes

Cell envelopes with functional flagella, isolated from wild-type strains of Escherichia coli and Salmonella typhimurium by formation of spheroplasts with penicillin and subsequent osmotic lysis, demonstrate counterclockwise (CCW)-biased rotation when energized with an electron donor for respiration, DL-lactate. Since the direction of flagellar rotation in bacteria is central to the expression of chemotaxis, we studied the cause of this bias. Our main observations were: (i) spheroplasts acquired a clockwise (CW) bias if instead of being lysed they were further incubated with penicillin; (ii) repellents temporarily caused CW rotation of tethered bacteria and spheroplasts but not of their derived cell envelopes; (iii) deenergizing CW-rotating cheV bacteria by KCN or arsenate treatment caused CCW bias; (iv) cell envelopes isolated from CW-rotating cheC and cheV mutants retained the CW bias, unlike envelopes isolated from cheB and cheZ mutants, which upon cytoplasmic release lost this bias and acquired CCW bias; and (v) an inwardly directed, artificially induced proton current rotated tethered envelopes in CCW direction, but an outwardly directed current was unable to rotate the envelopes. It is concluded that (i) a cytoplasmic constituent is required for the expression of CW rotation (or repression of CCW rotation) in strains which are not defective in the switch; (ii) in the absence of this cytoplasmic constituent, the motor is not reversible in such strains, and it probably is mechanically constricted so as to permit CCW sense of rotation only; (iii) the requirement of CW rotation for ATP is not at the level of the motor or the switch but at one of the preceding functional steps of the chemotaxis machinery; (iv) the cheC and cheV gene products are associated with the cytoplasmic membrane; and (v) direct interaction between the switch-motor system and the repellent sensors is improbable.     

Cardiac length dependence of force and force redevelopment kinetics with altered cross-bridge cycling

We examined the influence of cross-bridge cycling kinetics on the length dependence of steady-state force and the rate of force redevelopment (k(tr)) during Ca(2+)-activation at sarcomere lengths (SL) of 2.0 and 2.3 microm in skinned rat cardiac trabeculae. Cross-bridge kinetics were altered by either replacing ATP with 2-deoxy-ATP (dATP) or by reducing [ATP]. At each SL dATP increased maximal force (F(max)) and Ca(2+)-sensitivity of force (pCa(50)) and reduced the cooperativity (n(H)) of force-pCa relations, whereas reducing [ATP] to 0.5 mM (low ATP) increased pCa(50) and n(H) without changing F(max). The difference in pCa(50) between SL 2.0 and 2.3 microm (Delta pCa(50)) was comparable between ATP and dATP, but reduced with low ATP. Maximal k(tr) was elevated by dATP and reduced by low ATP. Ca(2+)-sensitivity of k(tr) increased with both dATP and low ATP and was unaffected by altered SL under all conditions. Significantly, at equivalent levels of submaximal force k(tr) was faster at short SL or increased lattice spacing. These data demonstrate that the SL dependence of force depends on cross-bridge kinetics and that the increase of force upon SL extension occurs without increasing the rate of transitions between nonforce and force-generating cross-bridge states, suggesting SL or lattice spacing may modulate preforce cross-bridge transitions.     

Stabilizing PID controllers for a single-link biomechanical model with position, velocity, and force feedback

In this paper we address the problem of PID stabilization of a single-link inverted pendulum-based biomechanical model with force feedback, two levels of position and velocity feedback, and with delays in all the feedback loops. The novelty of the proposed model lies in its physiological relevance, whereby both small and medium latency sensory feedbacks from muscle spindle (MS), and force feedback from Golgi tendon organ (GTO) are included in the formulation. The biomechanical model also includes active and passive viscoelastic feedback from Hill-type muscle model and a second-order low-pass function for muscle activation. The central nervous system (CNS) regulation of postural movement is represented by a proportional-integral-derivative (PID) controller. Padé approximation of delay terms is employed to arrive at an overall rational transfer function of the biomechanical model. The Hermite-Biehler theorem is then used to derive stability results, leading to the existence of stabilizing PID controllers. An algorithm for selection of stabilizing feedback gains is developed using the linear matrix inequality (LMI) approach.     

Interaction between myosin heavy chain and troponin isoforms modulate cardiac myofiber contractile dynamics

Coordinated expression of species-specific myosin heavy chain (MHC) and troponin (Tn) isoforms may bring about a dynamic complementarity to match muscle contraction speed with species-specific heart rates. Contractile system function and dynamic force-length measurements were made in muscle fibers from mouse and rat hearts and in muscle fibers after reconstitution with either recombinant homologous Tn or orthologous Tn. The rate constants of length-mediated cross-bridge (XB) recruitment (b) and tension redevelopment (k(tr)) of mouse fibers were significantly faster than those of rat fibers. Both the tension cost (ATPase/tension) and rate constant of length-mediated XB distortion (c) were higher in the mouse than in the rat. Thus the mouse fiber was faster in all dynamic and functional aspects than the rat fiber. Mouse Tn significantly increased b and k(tr) in rat fibers; conversely, rat Tn significantly decreased b and k(tr) in mouse fibers. Thus the length-mediated recruitment of force-bearing XB occurs much more rapidly in the presence of mouse Tn than in the presence of rat Tn, demonstrating that the speed of XB recruitment is regulated by Tn. There was a significant interaction between Tn and MHC such that changes in either Tn or MHC affected the speed of XB recruitment. Our data demonstrate that the dynamics of myocardial contraction are different in the mouse and rat hearts because of sequence heterogeneity in MHC and Tn. At the myofilament level, coordinated expression of complementary regulatory contractile proteins produces a functional dynamic phenotype that allows the cardiovascular systems to function effectively at different heart rates.     

Noise underlies switching behavior of the bacterial flagellum

We report the switching behavior of the full bacterial flagellum system that includes the filament and the motor in wild-type Escherichia coli cells. In sorting the motor behavior by the clockwise bias, we find that the distributions of the clockwise (CW) and counterclockwise (CCW) intervals are either exponential or nonexponential with long tails. At low bias, CW intervals are exponentially distributed and CCW intervals exhibit long tails. At intermediate CW bias (0.5) both CW and CCW intervals are mainly exponentially distributed. A simple model suggests that these two distinct switching behaviors are governed by the presence of signaling noise within the chemotaxis network. Low noise yields exponentially distributed intervals, whereas large noise yields nonexponential behavior with long tails. These drastically different motor statistics may play a role in optimizing bacterial behavior for a wide range of environmental conditions.     

Spiral growth in the radially-expanding piloboloid mutants ofPhycomyces blakesleeanus

The growth zone of the sporangiophore of a piloboloid mutant,pil, ofPhycomyces expands radially at an increased rate until the growth zone becomes nearly spherical, in sharp contrast to that of the wild-type sporangiophore which exhibits longitudinal elongation only and is conical. The rotation of thepil sporangiophore reverses its direction from clockwise (CW) to counterclockwise (CCW) during the period of increased radial expansion, and the CCW rotation continues as long as does the radial expansion. The direction of rotation and the time of reversal are correlated with the relative rates of cell-wall expansion in the longitudinal and transverse directions. The CCW rotation of the sporangiophore of this mutant can be explained by the behavior of the microfibrils, as previously proposed to explain the rotation of the wild-type sporangiophore.Abbreviations CW clockwise - CCW counterclockwise — both as viewed from above