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. Interpreting cardiac muscle force-length dynamics using a novel functional model. Am J Physiol Heart Circ Physiol 286: H1535-H1545, 2004; 10.1152/ ajpheart.01029.2003.-To describe the dynamics of constantly activated cardiac muscle, we propose that length affects force via both recruitment and distortion of myosin cross bridges. This hypothesis was quantitatively tested for descriptive and explanative validity. Skinned cardiac muscle fibers from animals expressing primarily ␣-myosin heavy chain (MHC) (mouse, rat) or ␤-MHC (rabbit, ferret) were activated with solutions from pCa 6.1 to 4.3. Activated fibers were subjected to small-amplitude length perturbations [⌬L(t)] rich in frequency content between 0.1 and 40 Hz. In descriptive validation tests, the model was fit to the ensuing force response [⌬F(t)] in the time domain. In fits to 118 records, the model successfully accounted for most of the measured variation in ⌬F(t) (R 2 range, 0.997-0.736; median, 0.981). When some residual variations in ⌬F(t) were not accounted for by the model (as at low activation), there was very little coherence (Ͻ0.5) between these residual force variations and the applied ⌬L(t) input function, indicating that something other than ⌬L(t) was causing the measured variation in ⌬F(t). With one exception, model parameters were estimated with standard errors on the order of 1% or less. Thus parameters of the recruitment component of the model could be uniquely separated from parameters of the distortion component of the model and parameters estimated from any given fiber could be considered unique to that fiber. In explanative validation tests, we found that recruitment and distortion parameters were positively correlated with independent assessments of the physiological entity they were assumed to represent. The recruitment distortion model was judged to be valid from both descriptive and explanative perspectives and is, therefore, a useful construct for describing and explaining dynamic force-length relationships in constantly activated cardiac muscle. muscle stiffness; cross-bridge recruitment; cross-bridge distortion; model validation; mouse; rat; ferret; rabbit MUSCLE LENGTH modulates cardiac muscle force development, and the resultant force-length relationship (FLR) is basic to the Frank-Starling mechanism of the heart. In general, however, muscle FLRs extend beyond the typical isometric twitching conditions under which force-length data are commonly collected to also include the force response to any length change during contraction. Thus descriptors of muscle FLR should also depict the dynamic force response to length changes that occur during contraction. One often-studied aspect of the dynamic FLR is the force response to sinusoidal length change in a constantly activated muscle fiber. Under these dynamic conditions, the amplitude and phase of the force response depends on both the frequency and amplitude of the sinusoidal length change. Dividing the steady-state sinusoidal force response by the sinusoidal length change yields...

Multiple linear regression, in which several predictor variables are related to a response variable, is a powerful statistical tool for gaining quantitative insight into complex in vivo physiological systems. For these insights to be correct, all predictor variables must be uncorrelated. However, in many physiological experiments the predictor variables cannot be precisely controlled and thus change in parallel (i.e., they are highly correlated). There is a redundancy of information about the response, a situation called multicollinearity, that leads to numerical problems in estimating the parameters in regression equations; the parameters are often of incorrect magnitude or sign or have large standard errors. Although multicollinearity can be avoided with good experimental design, not all interesting physiological questions can be studied without encountering multicollinearity. In these cases various ad hoc procedures have been proposed to mitigate multicollinearity. Although many of these procedures are controversial, they can be helpful in applying multiple linear regression to some physiological problems.

Chandra M, Tschirgi ML, Ford SJ, Slinker BK, Campbell KB. Interaction between myosin heavy chain and troponin isoforms modulate cardiac myofiber contractile dynamics. Am J Physiol Regul Integr Comp Physiol 293: R1595-R1607, 2007. First published July 11, 2007; doi:10.1152/ajpregu.00157.2007.-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 lengthmediated 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. myofiber dynamics; contraction speed; heart rate THERE IS SUBSTANTIAL PROTEIN sequence heterogeneity among orthologous cardiac myosin heavy chain (MHC) and troponin (Tn) isoforms across different animal species (30). This sequence heterogeneity in regulatory contractile proteins significantly affects myofilament dynamics, as assessed by the force response to muscle length change in constantly activated cardiac myofibers, which exhibits two clearly separable processes (3,5,20,30,35): 1) a relatively fast force dynamic associated with myosin cross-bridge (XB) distortion and 2) a relatively slow force dynamic associated with recruitment of additional XB into force-bearing states. The dynamics of XB distortion are principally determined by the enzymatic kinetics of MHC, and the dynamics of XB recruitment are affected greatly by cooperative interactions between Tn actions and XB cycling kinetics (3, 5, 6, 30).Our group (9) recently showed that differences in troponin T (TnT), a subunit of the Tn regulatory protein complex, affected the slow XB recruitment dynamic (9), whereas a shift f...

The inverse relationship between track rebound rate and negative acceleration peaks for all hooves reflects the most important dynamic property of a track. Any factor that reduces negative acceleration of the hooves will increase stride efficiency by allowing smoother transition from retardation to propulsion and therefore may be important in determining the safety of racing surfaces.