Z band dynamics as a function of sarcomere length and the contractile state of muscle

The Z band in skeletal muscle has two distinct structural states--a relaxed (small square or ss) form and a maximally activated (basket weave or bw) form. We have examined by electron microscopy and optical diffraction Z lattice forms and dimensions and A band spacings in relaxed, tetanized, stretched, and stretched-and-tetanized rat soleus muscle. We have tested the independent contributions of passive load, active tension, and sarcomere length to Z band state. As the A band spacing decreased with increasing load and increasing sarcomere length in the untetanized muscles, the Z lattice remained in the ss form and the Z spacing changed only slightly. Computer-enhanced images from digitized electron micrographs showed that the ss Z lattice resisted deformation regardless of load or method of stretching. In contrast, when the muscle was tetanized at sarcomere lengths of up to 2.7 microns, the Z lattice assumed the bw form and the Z spacing was increased by 20%. Regardless of lattice form, Z spacing did not vary significantly with sarcomere length. Images from freeze-substituted preparations showed both lattice forms comparable to those in images from glutaraldehyde-fixed muscles. Thus, Z band state appears to be a function of the presence (or absence) of active tension. Our previous three-dimensional model is compatible with these observations and with the sub-structures revealed by computer-enhanced images of both lattice forms.     

Synchrony of sarcomeric movement regulates left ventricular pump function in the in vivo beating mouse heart

Sarcomeric contraction in cardiomyocytes serves as the basis for the heart’s pump functions. It has generally been considered that in cardiac muscle as well as in skeletal muscle, sarcomeres equally contribute to myofibrillar dynamics in myocytes at varying loads by producing similar levels of active and passive force. In the present study, we expressed α-actinin–AcGFP in Z-disks to analyze dynamic behaviors of sequentially connected individual sarcomeres along a myofibril in a left ventricular (LV) myocyte of the in vivo beating mouse heart. To quantify the magnitude of the contribution of individual sarcomeres to myofibrillar dynamics, we introduced the novel parameter “contribution index” (CI) to measure the synchrony in movements between a sarcomere and a myofibril (from −1 [complete asynchrony] to 1 [complete synchrony]). First, CI varied markedly between sarcomeres, with an average value of ∼0.3 during normal systole. Second, when the movements between adjacent sarcomeres were asynchronous (CI < 0), a sarcomere and the ones next to the adjacent sarcomeres and farther away moved in synchrony (CI > 0) along a myofibril. Third, when difference in LV pressure in diastole and systole (ΔLVP) was lowered to <10 mm Hg, diastolic sarcomere length increased. Under depressed conditions, the movements between adjacent sarcomeres were in marked asynchrony (CI, −0.3 to −0.4), and, as a result, average CI was linearly decreased in association with a decrease in ΔLVP. These findings suggest that in the left ventricle of the in vivo beating mouse heart, (1) sarcomeres heterogeneously contribute to myofibrillar dynamics due to an imbalance of active and passive force between neighboring sarcomeres, (2) the force imbalance is pronounced under depressed conditions coupled with a marked increase in passive force and the ensuing tug-of-war between sarcomeres, and (3) sarcomere synchrony via the distal intersarcomere interaction regulates the heart''s pump function in coordination with myofibrillar contractility.     

Cooperative activation in cardiac muscle: impact of sarcomere length

This study was undertaken to determine the impact of sarcomere length (SL) on the level of cooperative activation of the cardiac myofilament at physiological [Mg2+]. Active force development was measured in skinned rat cardiac trabeculae as a function of free [Ca2+] at five SLs (1.85-2.25 microm; 1 mM free [Mg2+]; 15 degrees C). Only muscle preparations with minimal force rundown during the entire protocol were included in the analysis (average 7.2 +/- 1.7%). Median SL was measured by on-line computer video micrometry and controlled within 0.01 microm. Care was taken to ensure a sufficient number of data points in the steep portion of the [Ca2+]-force relationship at every SL to allow for accurate fit of the data to a modified Hill equation. Multiple linear regression analysis of the fit parameters revealed that both maximum, Ca2+-saturated force and Ca2+ sensitivity were a significant function of SL (P < 0.001), whereas the level of cooperativity did not depend on SL (P = 0.2). Further analysis of the [Ca2+]-force relationships revealed a marked asymmetry that, also, was not affected by SL (P = 0.2-0.6). Finally, we found that the level of cooperativity in isolated skinned myocardium was comparable to that reported for intact, nonskinned myocardium. Our results suggest that an increase in SL induces an increase in the Ca2+ responsiveness of the cardiac sarcomere without affecting the level of cooperativity.     

Tearin' up my heart: proteolysis in the cardiac sarcomere

Proteolysis within the cardiac sarcomere is a constantly evolving area of research. Three major pathways of proteolysis have been identified as being active within the cardiac sarcomere, namely the ubiquitin-proteasome system, autophagy, and the calpain system. The role of ubiquitin-proteasome system-mediated proteolysis in cardiovascular health and disease has been known for some time; however, it is now apparent that other proteolytic systems also aid in the stabilization of cardiac sarcomere structure and function. This minireview focuses on the individual as well as cooperative involvement of each of these three major pathways of proteolysis within the cardiac sarcomere.     

Myofilament lattice spacing as a function of sarcomere length in isolated rat myocardium

The Frank-Starling relationship of the heart has, as its molecular basis, an increase in the activation of myofibrils by calcium as the sarcomere length increases. It has been suggested that this phenomenon may be due to myofilaments moving closer together at longer lengths, thereby enhancing the probability of favorable acto-myosin interaction, resulting in increased calcium sensitivity. Accordingly, we have developed an apparatus so as to obtain accurate measurements of myocardial interfilament spacing (by synchrotron X-ray diffraction) as a function of sarcomere length (by video microscopy) over the working range of the heart, using skinned as well as intact rat trabeculas as model systems. In both these systems, lattice spacing decreased significantly as sarcomere length was increased. Furthermore, lattice spacing in the intact muscle was significantly smaller than that in the skinned muscle at all sarcomere lengths studied. These observations are consistent with the hypothesis that lattice spacing underlies length-dependent activation in the myocardium.     

Modulation of mouse cardiac function in vivo by eNOS and ANP

To study the role of endothelial nitric oxide synthase (eNOS) in cardiac function, we compared eNOS expression, contractility, and relaxation in the left ventricles of wild-type and eNOS-deficient mice. eNOS immunostaining is localized to the macro- and microvascular endothelium throughout the myocardium in wild-type mice and is absent in eNOS-/- mice. Whereas blood pressure is elevated in eNOS-/- mice, baseline cardiac contractility (dP/dt(max)) is similar in wild-type and eNOS-/- mice (9,673 +/- 2, 447 and 9,928 +/- 1,566 mmHg/s, respectively). The beta-adrenergic agonist isoproterenol (Iso) at doses of >/=1 ng causes enhanced increases in dP/dt(max) in eNOS-/- mice compared with wild-type controls in vivo (P < 0.01) as well as in Langendorff isolated heart preparations (P < 0.02). beta-Adrenergic receptor binding (B(max)) is not significantly different in the two groups of animals (B(max) = 41.4 +/- 9.4 and 36.1 +/- 5.1 fmol/mg for wild-type and eNOS-/-). Iso-stimulated ventricular relaxation is also enhanced in the eNOS-/- mice, as measured by dP/dt(min) in the isolated heart. However, baseline ventricular relaxation is normal in eNOS-/- mice (tau = 5.2 +/- 1.0 and 5.6 +/- 1.5 ms for wild-type and eNOS-/-, respectively), whereas it is impaired in wild-type mice after NOS inhibition (tau = 8.3 +/- 2.4 ms). cGMP levels in the left ventricle are unaffected by eNOS gene deletion (wild-type: 3.1 +/- 0.8 pmol/mg, eNOS-/-: 3.1 +/- 0.6 pmol/mg), leading us to examine the level of another physiological regulator of cGMP. Atrial natriuretic peptide (ANP) expression is markedly upregulated in the eNOS-/- mice, and exogenous ANP restores ventricular relaxation in wild-type mice treated with NOS inhibitors. These results suggest that eNOS attenuates both inotropic and lusitropic responses to beta-adrenergic stimulation, and it also appears to regulate baseline ventricular relaxation in conjunction with ANP.     

Elevated atmospheric CO2 does not affect per se the preference for symbiotic nitrogen as opposed to mineral nitrogen of Trifolium repens L.

The objective of this investigation was to examine the effect of an elevated atmospheric CO₂ partial pressure ( p CO₂) on the N-sink strength and performance of symbiotic N₂ fixation in Trifolium repens L. cv. Milkanova. After initial growth under ambient p CO₂ in a nitrogen-free nutrient solution, T. repens in the exponential growth stage was exposed to ambient and elevated p CO₂ (35 and 60 Pa) and two levels of mineral N (N-free and 7·5 mol m^–3 N) for 36 d in single pots filled with silica sand in growth chambers. Elevated p CO₂ evoked a significant increase in biomass production from day 12 after the start of CO₂ enrichment. For plants supplied with 7·5 mol m^–3 N, the relative contribution of symbiotically fixed N (%N_sym) as opposed to N assimilated from mineral sources (¹⁵N-isotope-dilution method), dropped to 40%. However, in the presence of this high level of mineral N, %N_sym was unaffected by atmospheric p CO₂ over the entire experimental period. In plants fully dependent on N₂ fixation, the increase in N yield reflects a stimulation of symbiotic N₂ fixation that was the result of the formation of more nodules rather than of higher specific N₂ fixation. These results are discussed with regard to physiological processes governing symbiotic N₂ fixation and to the response of symbiotic N₂ fixation to elevated p CO₂ in field-grown T. repens .     

Roles of polymerization dynamics, opposed motors, and a tensile element in governing the length of Xenopus extract meiotic spindles

Metaphase spindles assemble to a steady state in length by mechanisms that involve microtubule dynamics and motor proteins, but they are incompletely understood. We found that Xenopus extract spindles recapitulate the length of egg meiosis II spindles, by using mechanisms intrinsic to the spindle. To probe these mechanisms, we perturbed microtubule polymerization dynamics and opposed motor proteins and measured effects on spindle morphology and dynamics. Microtubules were stabilized by hexylene glycol and inhibition of the catastrophe factor mitotic centromere-associated kinesin (MCAK) (a kinesin 13, previously called XKCM) and destabilized by depolymerizing drugs. The opposed motors Eg5 and dynein were inhibited separately and together. Our results are consistent with important roles for polymerization dynamics in regulating spindle length, and for opposed motors in regulating the relative stability of bipolar versus monopolar organization. The response to microtubule destabilization suggests that an unidentified tensile element acts in parallel with these conventional factors, generating spindle shortening force.     

Rheology of myocardium. The relation between force, velocity, sarcomere length and activation in rat cardiac muscle

The relations between force, shortening velocity and sarcomere length (F-V-SL) during cardiac contraction, underlie Starling's Law of the Heart. F-V-SL were investigated in isolated, intact and skinned trabeculae and myocytes from rat heart. SL and V were measured with laser diffraction techniques; F was measured with a silicon strain gauge. The "ascending" F-SL relation appeared to result from both length dependent sensitivity of the contractile system to activator calcium ions and the presence of restoring forces (Fr), residing in the collagen skeleton of the muscle. Fr increased exponentially with decreasing SL below slack length to 25% of maximal twitch force (Ft) at SL = 1.60 microns. V was inversely proportional to the load and attained a maximum at zero load (Vo). Vo increased with factors that increased F: [Ca++], SL, and time during the twitch. Vo reached a maximum and remained constant (13.5 microns/s) when F attained or exceeded 50% of its maximum value. Viscous force in the passive muscle increased with V to a maximum of 4% of Ft at V = 40 microns/s. The relation between Vo and these factors could be predicted by a model of contraction in which the measured visco-elastic properties of myocardium were incorporated, while the truly unloaded maximal velocity of sarcomere shortening was assumed to be independent of the level of activation of the contractile filaments. A model of the cardiac cycle which explains the relation between Frank's and Starling's laws is presented.     

Modular regulation analysis of heart contraction: application to in situ demonstration of a direct mitochondrial activation by calcium in beating heart

Heart contraction is characterized by the absence of changes in energetic intermediates in response to a large increase of activity. Until now no experimental approach could address this question concerning the intact beating heart. Ca(2+) plays a crucial role in the excitation-contraction coupling, and in vitro studies have evidenced that Ca(2+) may also directly activate mitochondrial oxidative phosphorylation. We applied our new in situ modular control and regulation analysis on isolated beating rat heart perfused under two different calcium concentrations with pyruvate or glucose as the substrate. Modular control analysis demonstrated experimentally that, although control by energy production was slightly higher under glucose conditions compared with pyruvate, most of the control of heart contraction resides in energy utilization. This behavior is the direct consequence of the high sensitivity (elasticity) of the energy producer processes to ATP utilization. Interestingly, the increase in heart metabolic rate by Ca(2+) did not significantly change the pattern of control distribution. The regulation analysis performed under the two calcium conditions demonstrated a balanced activation of myofibrils ATPases, and mitochondrial ATP synthesis in response to Ca(2+) increase. This first study demonstrates in situ the hypothesis that the energetic adequation in heart contraction is mediated by a parallel activation of both processes of energy production and utilization by Ca(2+). The results presented here show that modular control and regulation analyses allow in situ study of internal regulations in intact beating heart energetics and function and may now be applied to heart dysfunctions and therapeutic effects.     

In vivo assessment of neurocardiovascular regulation in the mouse: principles, progress, and prospects

A growing body of evidence indicates that a number of common complex diseases, including hypertension, heart failure, and obesity, are characterized by alterations in central neurocardiovascular regulation. However, our understanding of how changes within the central nervous system contribute to the development and progression of these and other diseases remains unclear. As with many areas of cardiovascular research, the mouse has emerged as a key species for investigations of neuroregulatory processes because of its amenability to highly specific genetic manipulations. In parallel with the development of increasingly sophisticated murine models has come the miniaturization and advancement in methodologies for in vivo assessment of neurocardiovascular end points in the mouse. The following brief review will focus on a number of key direct and indirect experimental approaches currently in use, including measurement of arterial blood pressure, assessment of cardiovascular autonomic control, and evaluation of arterial baroreflex function. The advantages and limitations of each methodology are highlighted to allow for a critical evaluation by the reader when considering these approaches.     

Neonatal mouse testis-derived multipotent germline stem cells improve the cardiac function of acute ischemic heart mouse model

Multipotent germline stem (mGS) cells have been established from neonatal mouse testes. We previously reported that undifferentiated mGS cells are phenotypically similar to embryonic stem cells and that fetal liver kinase 1 (Flk1)⁺ mGS cells have a similar potential to differentiate into cardiomyocytes and endothelial cells compared with Flk1⁺ embryonic stem cells. Here, we transplanted these Flk1⁺ mGS cells into an ischemic heart failure mouse model to evaluate the improvement in cardiac function. Significant increase in left ventricular wall thickness of the infarct area, left ventricular ejection fraction and left ventricular maximum systolic velocity was observed 4 weeks after when sorted Flk1⁺ mGS cells were transplanted directly into the hearts of the acute ischemic model mice. Although the number of cardiomyocytes derived from Flk1⁺ mGS cells were too small to account for the improvement in cardiac function but angiogenesis around ischemic area was enhanced in the Flk1⁺ mGS cells transplanted group than the control group and senescence was also remarkably diminished in the early phase of ischemia according to β-galactosidase staining assay. In conclusion, Flk1⁺ mGS cell transplantation can improve the cardiac function of ischemic hearts by promoting angiogenesis and by delaying host cell death via senescence.     

Speckle variance optical coherence tomography of blood flow in the beating mouse embryonic heart

Efficient separation of blood and cardiac wall in the beating embryonic heart is essential and critical for experiment‐based computational modelling and analysis of early‐stage cardiac biomechanics. Although speckle variance optical coherence tomography (SV‐OCT) relying on calculation of intensity variance over consecutively acquired frames is a powerful approach for segmentation of fluid flow from static tissue, application of this method in the beating embryonic heart remains challenging because moving structures generate SV signal indistinguishable from the blood. Here, we demonstrate a modified four‐dimensional SV‐OCT approach that effectively separates the blood flow from the dynamic heart wall in the beating mouse embryonic heart. The method takes advantage of the periodic motion of the cardiac wall and is based on calculation of the SV signal over the frames corresponding to the same phase of the heartbeat cycle. Through comparison with Doppler OCT imaging, we validate this speckle‐based approach and show advantages in its insensitiveness to the flow direction and velocity as well as reduced influence from the heart wall movement. This approach has a potential in variety of applications relying on visualization and segmentation of blood flow in periodically moving structures, such as mechanical simulation studies and finite element modelling. Picture : Four‐dimensional speckle variance OCT imaging shows the blood flow inside the beating heart of an E8.5 mouse embryo.     

Response of equatorial x-ray reflections and stiffness to altered sarcomere length and myofilament lattice spacing in relaxed skinned cardiac muscle

Low angle x-ray diffraction measurements of myofilament lattice spacing (D(1,0)) and equatorial reflection intensity ratio (I(1,1)/I(1,0)) were made in relaxed skinned cardiac trabeculae from rats. We tested the hypothesis that the degree of weak cross-bridge (Xbr) binding, which has been shown to be obligatory for force generation in skeletal muscle, is modulated by changes in lattice spacing in skinned cardiac muscle. Altered weak Xbr binding was detected both by changes in I(1,1)/I(1,0) and by measurements of chord stiffness (chord K). Both measurements showed that, similar to skeletal muscle, the probability of weak Xbr binding at 170-mM ionic strength was significantly enhanced by lowering temperature to 5 degrees C. The effects of lattice spacing on weak Xbr binding were therefore determined under these conditions. Changes in D(1,0), I(1,1)/I(1,0), and chord K by osmotic compression with dextran T500 were determined at sarcomere lengths (SL) of 2.0 and 2.35 micro m. At each SL increasing [dextran] caused D(1,0) to decrease and both I(1,1)/I(1,0) and chord K to increase, indicating increased weak Xbr binding. The results suggest that in intact cardiac muscle increasing SL and decreasing lattice spacing could lead to increased force by increasing the probability of initial weak Xbr binding.     

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.     

MRI/MRS assessment of in vivo murine cardiac metabolism, morphology, and function at physiological heart rates

Transgenic mice are increasingly used to probe genetic aspects of cardiovascular pathophysiology. However, the small size and rapid rates of murine hearts make noninvasive, physiological in vivo studies of cardiac bioenergetics and contractility difficult. The aim of this report was to develop an integrated, noninvasive means of studying in vivo murine cardiac metabolism, morphology, and function under physiological conditions by adapting and modifying noninvasive cardiac magnetic resonance imaging (MRI) with image-guided (31)P magnetic resonance spectroscopy techniques used in humans to mice. Using spatially localized, noninvasive (31)P nuclear magnetic resonance spectroscopy and MRI at 4.7 T, we observe mean murine in vivo myocardial phosphocreatine-to-ATP ratios of 2.0 +/- 0.2 and left ventricular ejection fractions of 65 +/- 7% at physiological heart rates ( approximately 600 beats/min). These values in the smallest species studied to date are similar to those reported in normal humans. Although these observations do not confirm a degree of metabolic scaling with body size proposed by prior predictions, they do suggest that mice can serve, at least at this level, as a model for human cardiovascular physiology. Thus it is now possible to noninvasively study in vivo myocardial bioenergetics, morphology, and contractile function in mice under physiological conditions.     

Establishment of cardiac cytoarchitecture in the developing mouse heart

Cardiomyocytes are characterized by an extremely well-organized cytoarchitecture. We investigated its establishment in the developing mouse heart with particular reference to the myofibrils and the specialized types of cell-cell contacts, the intercalated discs (ICD). Early embryonic cardiomyocytes have a polygonal shape with cell-cell contacts distributed circumferentially at the peripheral membrane and myofibrils running in a random orientation in the sparse cytoplasm between the nucleus and the plasma membrane. During fetal development, the cardiomyocytes elongate, and the myofibrils become aligned. The restriction of the ICD components to the bipolar ends of the cells is a much slower process and is achieved for adherens junctions and desmosomes only after birth, for gap junctions even later. By quantifying the specific growth parameters of prenatal cardiomyocytes, we were able to identify a previously unknown fetal phase of physiological hypertrophy. Our results suggest (1) that myofibril alignment, bipolarization and ICD restriction happen sequentially in cardiomyocytes, and (2) that increase of heart mass in the embryo is not only achieved by hyperplasia alone but also by volume increase of the individual cardiomyocytes (hypertrophy). These observations help to understand the mechanisms that lead to the formation of a functional heart during development at a cellular level.     

Activated Met signalling in the developing mouse heart leads to cardiac disease

Background

The Hepatocyte Growth Factor (HGF) is a pleiotropic cytokine involved in many physiological processes, including skeletal muscle, placenta and liver development. Little is known about its role and that of Met tyrosine kinase receptor in cardiac development.

Methodology/Principal Findings

In this study, we generated two transgenic mice with cardiac-specific, tetracycline-suppressible expression of either Hepatocyte Growth Factor (HGF) or the constitutively activated Tpr-Met kinase to explore: i) the effect of stimulation of the endogenous Met receptor by autocrine production of HGF and ii) the consequence of sustained activation of Met signalling in the heart. We first showed that Met is present in the neonatal cardiomyocytes and is responsive to exogenous HGF. Exogenous HGF starting from prenatal stage enhanced cardiac proliferation and reduced sarcomeric proteins and Connexin43 (Cx43) in newborn mice. As adults, these transgenics developed systolic contractile dysfunction. Conversely, prenatal Tpr-Met expression was lethal after birth. Inducing Tpr-Met expression during postnatal life caused early-onset heart failure, characterized by decreased Cx43, upregulation of fetal genes and hypertrophy.

Conclusions/Significance

Taken together, our data show that excessive activation of the HGF/Met system in development may result in cardiac damage and suggest that Met signalling may be implicated in the pathogenesis of cardiac disease.     

Functional design of tentacles in squid: linking sarcomere ultrastructure to gross morphological dynamics

This paper offers a quantitative analysis of tentacle extension in squid that integrates several levels of structural organization. The muscular stalks of the two tentacles of squid are rapidly elongated by 70 per cent of resting length during prey capture. A typical duration of the extension is 30 ms in Loligo pealei (with a contracted tentacle length of 93 mm and a strike distance of about 37 mm). In a successful strike, the terminal clubs hit the prey and attach to it via arrays of suckers.A forward dynamics model is proposed for the extension of the tentacular stalk and the forward motion of the terminal club. The stalk is modelled as a longitudinal array of thin muscular discs with extensor muscle fibres oriented parallel to the disc planes. As a disc contracts radially, it lengthens because its volume is constant. The equations of motion for the linked system of discs were formulated and solved numerically. The inputs of the model are the dimensions of the tentacle, passive and active muscle properties such as Hill''s force–velocity relationship, myofilament lengths and activation of the muscle fibres. The model predicts the changing geometry of the tentacle, the pressure and stress distribution inside the tentacle and the velocity and kinetic energy distribution of the stalk and club. These predictions are in agreement with kinematic observations from high-speed films of prey capture. The model demonstrates also that the unusually short myosin filaments (reported range 0.5–0.9 micrometre) that characterize the extensor muscles are necessary for the observed extension performance. Myosin filament lengths typical for vertebrate sarcomeres (1.58 micrometre) would lead to a significant reduction in performance. In addition, the model predicts that, to maximize peak velocity of the terminal club, the myosin filaments should be longer at the base and shorter at the tip of the stalk (0.97 micrometre at the base and 0.50 micrometre at the tip for the tentacle size above). This results from differences in dynamic loading along the stalk. Finally, the model allows exploration of the effects of changes in the dimensions and mass of the tentacle and intrinsic speed of the myofilaments on the optimum myosin filament lengths.