Mathematical model for the effects of adhesion and mechanics on cell migration speed.

Migration of mammalian blood and tissue cells over adhesive surfaces is apparently mediated by specific reversible reactions between cell membrane adhesion receptors and complementary ligands attached to the substratum. Although in a number of systems these receptors and ligand molecules have been isolated and identified, a theory capable of predicting the effects of their properties on cell migration behavior currently does not exist. We present a simple mathematical model for elucidating the dependence of cell speed on adhesion-receptor/ligand binding and cell mechanical properties. Our model can be applied to propose answers to questions such as: does an optimal adhesiveness exist for cell movement? How might changes in receptor and ligand density and/or affinity affect the rate of migration? Can cell rheological properties influence movement speed? This model incorporates cytoskeletal force generation, cell polarization, and dynamic adhesion as requirements for persistent cell movement. A critical feature is the proposed existence of an asymmetry in some cell adhesion-receptor property, correlated with cell polarity. We consider two major alternative mechanisms underlying this asymmetry: (a) a spatial distribution of adhesion-receptor number due to polarized endocytic trafficking and (b) a spatial variation in adhesion-receptor/ligand bond strength. Applying a viscoelastic-solid model for cell mechanics allows us to represent one-dimensional locomotion with a system of differential equations describing cell deformation and displacement along with adhesion-receptor dynamics. In this paper, we solve these equations under the simplifying assumption that receptor dynamics are at a quasi-steady state relative to cell locomotion. Thus, our results are strictly valid for sufficiently slow cell movement, as typically observed for tissue cells such as fibroblasts. Numerical examples relevant to experimental systems are provided. Our results predict how cell speed might vary with intracellular contractile force, cell rheology, receptor/ligand kinetics, and receptor/ligand number densities. A biphasic dependence is shown to be possible with respect to some of the system parameters, with position of the maxima essentially governed by a balance between transmitted contractile force and adhesiveness. We demonstrate that predictions for the two alternative asymmetry mechanisms can be distinguished and could be experimentally tested using cell populations possessing different adhesion-receptor numbers.     

Measurement of thoracoabdominal asynchrony: importance of sensor sensitivity to cross section deformations.

Discrepancies in the assessment of thoracoabdominal asynchrony are observed depending on the choice of respiratory movement sensors. We test the hypothesis that these discrepancies are due to a different dependence of the sensors on cross-sectional perimeter and area variations of the chest wall. First, we study the phase shift between perimeter and area (Phi(PA)) for an elliptical model, which is deformed by sinusoidal changes of its principal axes. We show that perimeter and area vary sinusoidally in the physiological range of deformations, and we discuss how Phi(PA) depends on the ellipticity of the cross section, on the ratio of transverse and dorsoventral movement amplitudes, and on their phase difference. Second, we compute the relationship between perimeter, area, and the output of the inductive sensor, and we proceed by comparing inductive plethysmography with strain gauges for several cross section deformations. We demonstrate that both sensors can provide different phase information for identical cross section deformations and, hence, can estimate thoracoabdominal asynchrony differently. Furthermore, the complex dependence of the inductive sensor on perimeter and area warns against this sensor for the evaluation of thoracoabdominal asynchrony.     

A Dynamic Analysis of IRS-PKR Signaling in Liver Cells: A Discrete Modeling Approach

A major challenge in systems biology is to develop a detailed dynamic understanding of the functions and behaviors in a particular cellular system, which depends on the elements and their inter-relationships in a specific network. Computational modeling plays an integral part in the study of network dynamics and uncovering the underlying mechanisms. Here we proposed a systematic approach that incorporates discrete dynamic modeling and experimental data to reconstruct a phenotype-specific network of cell signaling. A dynamic analysis of the insulin signaling system in liver cells provides a proof-of-concept application of the proposed methodology. Our group recently identified that double-stranded RNA-dependent protein kinase (PKR) plays an important role in the insulin signaling network. The dynamic behavior of the insulin signaling network is tuned by a variety of feedback pathways, many of which have the potential to cross talk with PKR. Given the complexity of insulin signaling, it is inefficient to experimentally test all possible interactions in the network to determine which pathways are functioning in our cell system. Our discrete dynamic model provides an in silico model framework that integrates potential interactions and assesses the contributions of the various interactions on the dynamic behavior of the signaling network. Simulations with the model generated testable hypothesis on the response of the network upon perturbation, which were experimentally evaluated to identify the pathways that function in our particular liver cell system. The modeling in combination with the experimental results enhanced our understanding of the insulin signaling dynamics and aided in generating a context-specific signaling network.     

Electron microscopic study of actin polymerization in airway smooth muscle

Actin polymerization as part of the normal smooth muscle response to various stimuli has been reported. The actin dynamics are believed to be necessary for cytoskeletal remodeling in smooth muscle in its adaptation to external stress and strain and for maintenance of optimal contractility. We have shown in our previous studies in airway smooth muscle that myosins polymerized in response to contractile activation as well as to adaptation at longer cell lengths. We postulated that the same response could be elicited from actins under the same conditions. In the present study, actin filament formation was quantified electron microscopically in cell cross sections. Nanometer resolution allowed us to examine regional distribution of filaments in a cell cross section. Airway smooth muscle bundles were fixed in relaxed and activated states at two lengths; muscle preparations were also fixed after a period of oscillatory strain, a condition known to cause depolymerization of myosin filaments. The results indicate that contractile activation and increased cell length nonsynergistically enhanced actin polymerization; the extent of actin polymerization was substantially less than that of myosin polymerization. Oscillatory strain increased thin filament formation. Although thin filament density was found higher in cytoplasmic areas near dense bodies, contractile activation did not preferentially enhance actin polymerization in these areas. It is concluded that actin thin filaments are dynamic structures whose length and number are regulated by the cell in response to changes in extracellular environment and that polymerization and depolymerization of thin filaments occur uniformly across the whole cell cross section.     

Co-ordinated expression of contractile and non-contractile features of control equine muscle fibre types characterised by immunostaining of myosin heavy chains

Combined methodologies of immunohistochemistry, histochemistry and photometric image analysis were applied: (1) to characterise control equine skeletal muscle fibres according to their myosin heavy chain (MyHC) composition and (2) to determine on a fibre-to-fibre basis the correlation between contractile [i.e. MyHC(s), myofibrillar ATPase (mATPase) and sarco(endo)plasmic reticulum Ca(2+)-ATPase (SERCA) isoforms], metabolic [i.e. succinate dehydrogenase (SDH) and alpha-glycerophosphate dehydrogenase (GPD) activities, glycogen and phospholamban (PLB) contents], and morphological [i.e. cross-sectional area (CSA), capillary and nuclear densities] features of individual myofibres. An accurate delineation of MyHC-based fibre types was obtained with the immunohistochemical method developed. This protocol showed a high sensitivity and objectivity to delineate hybrid fibres with overwhelming dominance of one MyHC isoform and, furthermore, it allowed a semiquantitative delineation of fast hybrid fibres according to the predominant MyHC isoform expressed. The phenotypic differences in contractile, metabolic and morphological properties seen between fibre types were related to MyHC content. Slow fibres had the lowest mATPase activity (related to shortening velocity), the highest SDH activity (oxidative capacity), the lowest GPD activity (glycolytic metabolism) and glycogen content, the smallest CSA, the greatest capillary and nuclear densities, and expressed slow SERCA isoform and PLB, but not the fast SERCA isoform. The reverse pattern was true for pure IID/X fibres, and type IIA fibres had intermediate properties. Hybrid IIAD/X fibres had mean values intermediate to those of their respective pure phenotypes. Discrimination of fibres according to their MyHC content was possible on the basis of their contractile and non-contractile profiles. These intrafibre interdependencies suggest that, even when controlled by different mechanisms, myofibres of control horses exhibit a high degree of co-ordination in their physiological, biochemical and anatomical features.     

Moving mitochondria: establishing distribution of an essential organelle

Mitochondria form a dynamic network responsible for energy production, calcium homeostasis and cell signaling. Appropriate distribution of the mitochondrial network contributes to organelle function and is essential for cell survival. Highly polarized cells, including neurons and budding yeast, are particularly sensitive to defects in mitochondrial movement and have emerged as model systems for studying mechanisms that regulate organelle distribution. Mitochondria in multicellular eukaryotes move along microtubule tracks. Actin, the primary cytoskeletal component used for transport in yeast, has more subtle functions in other organisms. Kinesin, dynein and myosin isoforms drive motor-based movement along cytoskeletal tracks. Milton and syntabulin have recently been identified as potential organelle-specific adaptor molecules for microtubule-based motors. Miro, a conserved GTPase, may function with Milton to regulate transport. In yeast, Mmr1p and Ypt11p, a Rab GTPase, are implicated in myosin V-based mitochondrial movement. These potential adaptors could regulate motor activity and therefore determine individual organelle movements. Anchoring of stationary mitochondria also contributes to organelle retention at specific sites in the cell. Together, movement and anchoring ultimately determine mitochondrial distribution throughout the cell.     

Resistance to radial expansion limits muscle strain and work

The collagenous extracellular matrix (ECM) of skeletal muscle functions to transmit force, protect sensitive structures, and generate passive tension to resist stretch. The mechanical properties of the ECM change with age, atrophy, and neuromuscular pathologies, resulting in an increase in the relative amount of collagen and an increase in stiffness. Although numerous studies have focused on the effect of muscle fibrosis on passive muscle stiffness, few have examined how these structural changes may compromise contractile performance. Here we combine a mathematical model and experimental manipulations to examine how changes in the mechanical properties of the ECM constrain the ability of muscle fibers and fascicles to radially expand and how such a constraint may limit active muscle shortening. We model the mechanical interaction between a contracting muscle and the ECM using a constant volume, pressurized, fiber-wound cylinder. Our model shows that as the proportion of a muscle cross section made up of ECM increases, the muscle’s ability to expand radially is compromised, which in turn restricts muscle shortening. In our experiments, we use a physical constraint placed around the muscle to restrict radial expansion during a contraction. Our experimental results are consistent with model predictions and show that muscles restricted from radial expansion undergo less shortening and generate less mechanical work under identical loads and stimulation conditions. This work highlights the intimate mechanical interaction between contractile and connective tissue structures within skeletal muscle and shows how a deviation from a healthy, well-tuned relationship can compromise performance.     

Coordination of cell differentiation and migration in mathematical models of caudal embryonic axis extension

Vertebrate embryos display a predominant head-to-tail body axis whose formation is associated with the progressive development of post-cranial structures from a pool of caudal undifferentiated cells. This involves the maintenance of active FGF signaling in this caudal region as a consequence of the restricted production of the secreted factor FGF8. FGF8 is transcribed specifically in the caudal precursor region and is down-regulated as cells differentiate and the embryo extends caudally. We are interested in understanding the progressive down-regulation of FGF8 and its coordination with the caudal movement of cells which is also known to be FGF-signaling dependent. Our study is performed using mathematical modeling and computer simulations. We use an individual-based hybrid model as well as a caricature continuous model for the simulation of experimental observations (ours and those known from the literature) in order to examine possible mechanisms that drive differentiation and cell movement during the axis elongation. Using these models we have identified a possible gene regulatory network involving self-repression of a caudal morphogen coupled to directional domain movement that may account for progressive down-regulation of FGF8 and conservation of the FGF8 domain of expression. Furthermore, we have shown that chemotaxis driven by molecules, such as FGF8 secreted in the stem zone, could underlie the migration of the caudal precursor zone and, therefore, embryonic axis extension. These mechanisms may also be at play in other developmental processes displaying a similar mode of axis extension coupled to cell differentiation.     

Contractile Torque as a Steering Mechanism for Orientation of Adherent Cells

It is well established that adherent cells change their orientation in response to non-uniform substrate stretching. Most observations indicate that cells orient away from the direction of the maximal substrate strain, whereas in some cases cells also align with the direction of the maximal strain. Previous studies suggest that orientation and steering of the cell may be closely tied to cytoskeletal contractile stress but they could not explain the mechanisms that direct cell reorientation. This led us to develop a simple, mechanistic theoretical model that could predict a direction of cell orientation in response to mechanical nonuniformities of the substrate. The model leads to a simple physical mechanism -- namely the contractile torque -- that directs the cell toward a new orientation in response to anisotropic substrate stretching or substrate material anisotropy. A direction of the torque is determined by a dependence of the contractile stress on substrate strain. Model predictions are tested in the case of simple elongation of the substrate and found to be consistent with experimental data from the literature.     

Myosin localization during meiosis I of crane-fly spermatocytes gives indications about its role in division

We showed previously that in crane-fly spermatocytes myosin is required for tubulin flux [Silverman-Gavrila and Forer, 2000a: J Cell Sci 113:597-609], and for normal anaphase chromosome movement and contractile ring contraction [Silverman-Gavrila and Forer, 2001: Cell Motil Cytoskeleton 50:180-197]. Neither the identity nor the distribution of myosin(s) were known. In the present work, we used immunofluorescence and confocal microscopy to study myosin during meiosis-I of crane-fly spermatocytes compared to tubulin, actin, and skeletor, a spindle matrix protein, in order to further understand how myosin might function during cell division. Antibodies to myosin II regulatory light chain and myosin II heavy chain gave similar staining patterns, both dependent on stage: myosin is associated with nuclei, asters, centrosomes, chromosomes, spindle microtubules, midbody microtubules, and contractile rings. Myosin and actin colocalization along kinetochore fibers from prometaphase to anaphase are consistent with suggestions that acto-myosin forces in these stages propel kinetochore fibres poleward and trigger tubulin flux in kinetochore fibres, contributing in this way to poleward chromosome movement. Myosin and actin colocalization at the cell equator in cytokinesis, similar to studies in other cells [e.g., Fujiwara and Pollard, 1978: J Cell Biol 77:182-195], supports a role of actin-myosin interactions in contractile ring function. Myosin and skeletor colocalization in prometaphase spindles is consistent with a role of these proteins in spindle formation. After microtubules or actin were disrupted, myosin remained in spindles and contractile rings, suggesting that the presence of myosin in these structures does not require the continued presence of microtubules or actin. BDM (2,3 butanedione, 2 monoxime) treatment that inhibits chromosome movement and cytokinesis also altered myosin distributions in anaphase spindles and contractile rings, consistent with the physiological effects, suggesting also that myosin needs to be active in order to be properly distributed.     

Microtubule polarity in Sertoli cells: a model for microtubule-based spermatid transport

Bundles of microtubules occur adjacent to ectoplasmic specializations (ESs) that line Sertoli cell crypts and support developing spermatids. These microtubules are oriented parallel to the direction of spermatid movement during spermatogenesis. We propose a model in which ESs function as vehicles, and microtubules as tracks, for microtubule-based transport of spermatids through the seminiferous epithelium. Microtubule polarity provides the basis for the direction of force generation by available mechanoenzymes. As part of a more general study designed to investigate the potential role of microtubule-based transport during spermatogenesis, we have studied the polarity of cytoplasmic microtubules of Sertoli cells. Rat testis blocks were incubated in a lysis/decoration buffer, with and without exogenous purified bovine brain tubulin. This treatment results in the decoration of endogenous microtubules with curved tubulin protofilament sheets (seen as hooks in cross section). The direction of curvature of the hooks indicates microtubule polarity; that is, clockwise hooks are seen when viewing microtubules from the plus to the minus end. We found that, in Sertoli cells, most of the hooks were orientated in the same direction. Significantly, when viewed from the base of the epithelium, hooks pointed in a clockwise direction. The clockwise direction of dynein arms on axonemes of sperm tails, in the same section, provided an internal check of the section orientation. Electron micrographs of fields of seminiferous epithelium were assembled into montages for quantitative analysis of microtubule polarity. Our data indicate that Sertoli cell cytoplasmic microtubules are of uniform polarity and are orientated with their minus ends toward the cell periphery. These observations have significant implications for our proposed model of microtubule-based transport of spermatids through the seminiferous epithelium.     

New insights into skeletal muscle fibre types in the dog with particular focus towards hybrid myosin phenotypes

Electrophoresis, immunoblots, immunohistochemistry and image analysis methods were applied to characterise canine trunk and appendicular muscle fibres according to their myosin heavy chain (MyHC) composition and to determine, on a fibre-to-fibre basis, the correlation between contractile [MyHC (s), myofibrillar ATPase (mATPase) and sarco(endo)plasmic reticulum Ca²⁺-ATPase (SERCA) isoforms], metabolic [succinate dehydrogenase (SDH) and glycerol-3-phosphate dehydrogenase (GPDH) activities and glycogen and phospholamban (PLB) content] and morphological (cross-sectional area and capillary and nuclear densities) features of individual myofibres. An accurate delineation of MyHC-based fibre types was obtained with the developed immunohistochemical method, which showed high sensitivity and objectivity to delineate hybrid fibres with overwhelming dominance of one MyHC isoform. Phenotypic differences in contractile, metabolic and morphological properties seen between fibre types were related to MyHC content. All canine skeletal muscle fibre types had a relatively high histochemical SDH activity but significant differences existed in the order IIA>I>IIX. Mean GPDH was ranked according to fibre type such that I<IIA<IIX. Type IIA fibres were the smallest, type IIX fibres the largest and type I of intermediate size. Capillary and nuclear density decreased in the order IIA>I>IIX. Hybrid fibres, which represented nearly one third of the whole pool of skeletal muscle fibres analysed, had mean values intermediate between their respective pure phenotypes. Slow fibres expressed the slow SERCA isoform and PLB, whereas type II fibres expressed the fast SERCA isoform. Discrimination of myofibres according to their MyHC content was possible on the basis of their contractile, metabolic and morphological features. These intrafibre interrelationships suggest that myofibres of control dogs exhibit a high degree of co-ordination in their physiological, biochemical and morphological characteristics. This study demonstrates that canine skeletal muscle fibres have been misclassified in numerous previous studies and offers useful baseline data and new prospects for future work on muscle-fibre-typing in canine experimental studies.     

The consequence of substrates of large-scale rigidity on actin network tension in adherent cells

Abstract

There is compelling evidence that substrate stiffness affects cell adhesion as well as cytoskeleton organization and contractile activity. This work was designed to study the cytoskeletal contractile activity of single cells plated on micropost substrates of different stiffness using a numerical model simulating the intracellular tension of individual cells. We allowed cells to adhere onto micropost substrates of various rigidities and used experimental traction force data to infer cell contractility using a numerical model. The model shows that higher substrate stiffness leads to an increase in intracellular tension. The strength of this model is its ability to calculate the mechanical state of each cell in accordance to its individual cytoskeletal structure. This is achieved by regenerating a numerical cytoskeleton based on microscope images of the actin network of each cell. The resulting numerical structure consequently represents pulling characteristics on its environment similar to those generated by the cell in-vivo. From actin imaging we can calculate and better understand how forces are transmitted throughout the cell.     

Moving forward moving backward: directional sorting of chemotactic cells due to size and adhesion differences

Differential movement of individual cells within tissues is an important yet poorly understood process in biological development. Here we present a computational study of cell sorting caused by a combination of cell adhesion and chemotaxis, where we assume that all cells respond equally to the chemotactic signal. To capture in our model mesoscopic properties of biological cells, such as their size and deformability, we use the Cellular Potts Model, a multiscale, cell-based Monte Carlo model. We demonstrate a rich array of cell-sorting phenomena, which depend on a combination of mescoscopic cell properties and tissue level constraints. Under the conditions studied, cell sorting is a fast process, which scales linearly with tissue size. We demonstrate the occurrence of “absolute negative mobility”, which means that cells may move in the direction opposite to the applied force (here chemotaxis). Moreover, during the sorting, cells may even reverse the direction of motion. Another interesting phenomenon is “minority sorting”, where the direction of movement does not depend on cell type, but on the frequency of the cell type in the tissue. A special case is the cAMP-wave-driven chemotaxis of Dictyostelium cells, which generates pressure waves that guide the sorting. The mechanisms we describe can easily be overlooked in studies of differential cell movement, hence certain experimental observations may be misinterpreted.     

Transmission of forces within mammalian skeletal muscles

Most models of in vivo musculoskeletal function fail to take into account the diversity of force trajectories defined by muscle fiber architecture. It has been shown for many muscles, across species, that muscle fibers commonly end within muscle fascicles without reaching a myotendinous junction, and that many of these fibers show a progressive decline in cross-sectional area along the length of the muscle. The significance of these anatomical observations is that the tapering would seem to preclude forces generated at the largest cross-sectional area of the fibers being transmitted to the sarcomeres toward the ends of the tapered fiber. If all of the forces are transmitted via the sarcomeres arranged in series, those few sarcomeres at the smaller ends of the fibers must tolerate the stress exerted by the more numerous sarcomeres arranged in parallel at the portions of the fiber with larger cross-sectional areas. A logical alternative would be for forces to be transmitted laterally along the length of a fiber to the cell membrane and the extracellular matrix. Such a structural arrangement would permit an alternative force transmission vector and minimize the necessity for a precise level of force to be generated along the entire length of a fiber. There are cytoarchitectural and biochemical data demonstrating the presence of a subcellular network which is appropriately located to transmit forces from the active intracellular contractile elements to the extracellular intramuscular connective tissues. However, to fully comprehend how forces are transmitted from individual cross bridges to the tendon, it will be necessary to understand the interactions of all of the components of the muscle tendon complex from the molecular to the multicellular level. It is insufficient to know the physiology of the individual components in a restricted experimental paradigm and assume that these conditions account for the functional characteristics in vivo. Thus, the challenge is to understand how the sarcomeres and all of the associated structures transmit the forces of the whole muscle to its attachments.     

Fibre organization and reorganization in the retinotectal projection of Xenopus

This study concerns the retinotopic organization of the ganglion cell fibres in the visual system of the frog Xenopus laevis. HRP was used to trace the pathways taken by fibres from discrete retinal positions as they pass from the retina, along the optic nerve and into the chiasma. The ganglion cell fibres in the retina are arranged in fascicles which correspond with their circumferential positions of origin. Within the fascicles the fibres show little age-related layering and do not have a strict radial organization. As the fascicles of fibres pass into the optic nerve head there is some exchange of position resulting in some loss of the retinal circumferential organization. The poor radial organization of the fibres in the retinal fascicles persists as the fibres pass through the intraocular part of the nerve. At a position just behind the eye there is a major fibre reorganization in which fibres arising from cells of increasingly peripheral retinal locations are found to have passed into increasingly peripheral positions in the nerve. Thus, fibres from peripheral-most retina are located at the nerve perimeter, whilst fibres from central retina are located in the nerve core. It is at this point that the radial, chronotopic, ordering of the ganglion cell axons, found throughout the rest of the optic pathway, is established. This annular organization persists along the length of the nerve until a position just before the nerve enters the brain. Here, fibres from each annulus move to form layers as they pass into the optic chiasma. This change in the radial organization appears to be related to the pathway followed by all newly growing fibres, in the most superficial part of the optic tract, adjacent to the pia. Just behind the eye, where fibres become radially ordered, the circumferential organization of the projection is largely lost. Fibres from every circumferential retinal position, which are of similar radial position, are distributed within the same annulus of the nerve. At the nerve-chiasma junction where each annulus forms a single layer as it enters the optic tract, there is a further mixing of fibres from all circumferential positions. However, as the fibres pass through the chiasma some active pathway selection occurs, generating the circumferential organization of the fibres in the optic tract. Additional observations of the organization of fibres in the optic nerve of Rana pipiens confirm previous reports of a dual representation of fibres within the nerve. The difference in the organization of fibres in the optic nerve of Xenopus and Rana pipiens is discussed.     

Fiber-type morphology and function of the triads in frog (Rana esculenta) skeletal muscle)]

1. Owing to differing structural characteristics of the contractile substance, the muscle fibres have been divided into the three types A, B and C in former papers. This distinction seems to be corroborated by our investigations into the different structure regarding the traids. As for the A-fibres, they are structured in terms of the T-system being connected in its entire length with the SR-cisternae and circling the myofibrils at the level of the Z-layer. In the B-fibres, this permanent couping of the two membrane systems is partially interrupted so that the T-tubules are arranged round the myofibrils in such a way that they are isolated or only coupled on one side with the SR-cisternae. Apart from the triads we also find diads. There is a totally different arrangement of the membrane systems in the C-fibres. In this instance the T-tubules are not only arranged transversally but also vertically along the contractile elements. They are surrounded by an "SR-labyrinth" which forms individual minor cisternae which are lateraly coupled with the T-tubules. So the axis of these triads is turned by 90 degrees as compared to the A and B fibres. As a result of this different arrangement, these triads always appear in cross-sections, not however, in longitudinal sections as is the case with the A and B fibres. The tirads have a varying shape in the cross-sections depending on the level of the section and due to the fact that the cisternae are not always coupled congruently with the T-tubules. 2. In our discussion we have tried to related these differing shapes and arrangements of the triads in the fibre types A, B and C to known physiological findings. Therefore we deduced that the excitation transmittance and calcium release can be correlated with the anomal rectification of the triads, which has been localized in the region where the T-tubules and SR-cisternae are coupled. However, we can only reckon with a solution once the morphology and function of the "feet" and the eletronmicroscopically "blank" spaces which fill the gap-junction between the T-tubules and the SR-cisternae have been explained. Whatever function the free surface of the T-tubules has remains open. It is directly adjoining the sarcoplasm and we are tryping to relate it to the delayed rectification which appears on the fibre membrane. 3. Moreover from the arrangement of the SR-cisternae i- the individual fibre types we can deduce th intrafibrillar directions of expansion of the calcium after its release and thus the process of the excitation in the A, B and C fibres. It appears that calcium is being directed homogeneously from the SR-cisternae of the A-fibres to the actinfilaments. here the morphological appearance of the twitch fibre presents itself to us. In principle this pattern of expansion of calcium in the B-fibres remains consistent. Owing to the interruption between the T-system and the SR-cisternae we may assume that the process of contraction is delayed in contrast to the A-fibres...     

The myosin motor: muscle contraction and in vitro movement

The molecular mechanism of in vitro movement is assumed, by most investigators, to be identical to that of muscle contraction. We discuss this view, which raises various problems. We believe there are mechanisms for muscle contraction (in this case considerable forces are developed, with small displacements) and other mechanisms for in vitro movement (giving large displacements, without necessarily generating substantial forces). Hybrid models may explain muscle contraction. The traditional swinging-crossbridge model may explain in vitro movement. For muscle contraction, movement may result partly from the swinging-crossbridge mechanism and partly from other factors. Comparisons of different fibres at different moments of the Mg-ATPase cycle suggest that both the value of the isometric force in muscle and in vitro and that of the Mg-ATPase activity used in vitro need to be reconsidered. The recently reported dependence of the isometric active tension of smooth skinned fibres on temperature appears to be weaker than predicted by the swinging-crossbridge theory alone. This recent observation is compatible with the existence of other forces (electrostatic repulsions) decreasing with temperature as has been known for some years. From recent experimental data, we think the biochemistry of myosin and actomyosin should be reassessed, to try to find new details of the mechanisms of muscle contraction and in vitro motility.