Model of calcium diffusion, binding and membrane transport in the sarcomere of frog skeletal muscle

A model of calcium distribution in the sarcomere during activation of contraction was developed. It allows for diffusion and binding of calcium ions to various sarcoplasmic binding sites in the three dimensional spatial coordinate system. The model was used to analyze the influence of kinetic characteristic of binding processes on the temporal and spatial distribution of calcium in the sarcomere during activation of contraction by the action potential and by rectangular depolarizing pulses. The hypothesis concerning the calcium release control in the membrane of terminal cisternae was tested.     

Model of calcium movements during activation in the sarcomere of frog skeletal muscle

A model of calcium movement during activation of frog skeletal muscle is described. The model was based on the half sarcomere of a myofibril and included compartments representing the terminal cisternae, the longitudinal sarcoplasmic reticulum, the extramyofibrillar space, and the myofibrillar space. The calcium-binding proteins troponin, parvalbumin, and calsequestrin were present in appropriate locations and with realistic binding kinetics. During activation a time-dependent permeability in the terminal cisternal wall led to calcium release into the myoplasm and its diffusion through the myoplasm longitudinally and radially was computed. After adjustment of three parameters, the model produced a myoplasmic free-calcium concentration that was very similar to those recorded experimentally with calcium indicators. The model has been used to demonstrate the importance of parvalbumin in the relaxation of skeletal muscle, to describe the time course and magnitude of calcium gradients associated with diffusion across the sarcomere, and to estimate the errors associated with the use of aequorin as an intracellular calcium indicator in muscle.     

Relation of muscle cell contraction and calcium distribution in sarcomere

A model of activation of muscle contraction has been proposed. It is based on calcium diffusion and binding to specific regulatory sites in a sarcomere. Calcium ions activate interactions of contractile proteins and thus the generation of force. The model quantifies the relation between calcium released from intracellular stores and the elicited force.     

Distribution of calcium during contraction and relaxation of crayfish skeletal muscle fibre.

A model of activation of muscle contraction has been applied to the crayfish isolated skeletal muscle fibre. The model is based on calcium diffusion and binding to specific regulatory sites in a sarcomere. Calcium ions activate interactions of contractile proteins and thus the generation of force. The model quantifies the relation between calcium released from intracellular stores and force elicited. Experimental tension records from isolated crayfish skeletal muscle fibres under voltage clamp conditions are analyzed. Model parameters were determined either via approximation of the onset of tension by the model solution or from the model based relations between the tension maximum, and depolarizing pulse length and amplitude. This allowed to determine time changes of free and bound calcium distribution in the sarcomere and the calcium release from terminal cisternae. The steady state calcium concentration at terminal cisternae showed S-shaped voltage dependence with saturation below approx. 10 mumol/l at positive membrane potentials.     

Patterns of sarcomere activation, temperature dependence, and effect of ryanodine in chemically skinned cardiac fibers

Functionally skinned and electrochemically shunted myocytes were prepared by perfusing rat hearts with collagenase in order to obtain a technically improved measurement of sarcomere dynamics and to evaluate the role of sarcoplasmic reticulum in situ with respect to contractile activation. In the presence of micromolar calcium, the myocytes exhibited phasic and propagated contraction waves beginning at one end and proceeding along the myocyte. Beating rates, the propagation velocity of the activation wave, and single sarcomere shortening and relaxation velocities were obtained by manual or automated analysis of 16-mm film recorded at 170 frames/s from a camera attached to a microscope that was equipped with a temperature-controlled stage. In parallel experiments, calcium accumulation by the sarcoplasmic reticulum of the myocytes in situ was measured by direct isotopic tracer methods. The frequency (10-38 min-1) of spontaneous contractions, the velocity (1.9-7.4 microns . s-1) of sarcomere shortening, and the velocity (1.7-6.8 microns . s-1) of sarcomere relaxation displayed identical temperature dependences (Q10 = 2.2), which are similar to that of the calcium pump of sarcoplasmic reticulum and are consistent with a rate limit imposed by enzyme-catalyzed mechanisms on all these parameters. On the other hand, the velocity (77- 159 microns . s-1) of sequential sarcomere activation displayed a lower temperature dependence (Q10 = 1.5), which is consistent with a diffusion-limited and self-propagating release of calcium from one sarcomere to the other. The phasic contractile activity of the dissociated myocytes was inhibited by 10(-8)-10(6) M ryanodine (and not by myolemmal calcium blockers) under conditions in which calcium accumulation by sarcoplasmic reticulum in situ was demonstrated to proceed optimally. The effect of ryanodine is attributed to an interaction of this drug with sarcotubular structures, producing inhibition of calcium release from the sarcoplasmic reticulum. The consequent lack of sarcomere activation underlines the role of sarcoplasmic reticulum uptake and release in the phasic contractile activation of the electrochemically shunted myocytes.     

Spontaneous and propagated contractions in rat cardiac trabeculae

Sarcomere length measurement by microscopic and laser diffraction techniques in trabeculae of rat heart, superfused with Krebs-Henseleit solution at 21 degrees C, showed spontaneous local sarcomere shortening after electrically stimulated twitches. The contractions originated in a region of several hundred micrometers throughout the width of the muscle close to the end of the preparation that was damaged by dissection. The contractions propagated at a constant velocity along the trabeculae. The velocity of propagation increased from 0 to 10 mm/s in proportion to the number of stimuli (3-30) in a train of electrically evoked twitches at 2 Hz and at an external calcium ion concentration ([Ca++]o) of 1.5 mM. At a constant number of stimuli (n), the velocity of propagation increased from 0 to 15 mm/s with [Ca++]o increasing from 1 to 7 mM. In addition, increase of n and [Ca++]o led to an increase of the extent of local sarcomere shortening during the spontaneous contractions, and the occurrence of multiple contractions. Spontaneous contractions with much internal shortening and a high velocity of propagation frequently induced spontaneous synchronized contractions and eventually arrhythmias. Propagation of spontaneous contractions at low and variable velocity is consistent with the hypothesis that calcium leakage into damaged cells causes spontaneous calcium release from the overloaded sarcoplasmic reticulum in the damaged cells. This process propagates as a result of diffusion of calcium into adjacent cells, which triggers calcium release from their sarcoplasmic reticulum. We postulate that the propagation velocity depends on the intracellular calcium ion concentration, with increases with n and [Ca++]o.     

Effect of Ultrasound and Calcium Chloride on the Ultrastructure and the Warner-Bratzler Shear Force Value of Beef Shank Muscle Fibers

Meat tenderness is a major factor in consumer satisfaction. Tenderness may be quantified by changes in muscle sarcomere length, roughness (ultrastructure) and shear force. The ultrastructure and the Warner-Bratzler shear force value of beef shank muscle fibers were experimentally measured in controlled applications of ultrasound and calcium chloride. Uncooked beef samples were treated with ultrasound at 40 kHz at different intensities for 6 min, and then immersed in a range of calcium chloride solutions for 24 h. Warner–Bratzler shear analysis and atomic force microscopy (AFM) data collection were performed for each sample. AFM height derived data (the sarcomere length and roughness values) and the Warner–Bratzler shear force values indicate optimum ranges of ultrasound intensity and calcium chloride concentration for meat tenderization. While the effect of low intensity ultrasound alone was not significant, calcium chloride treatment increased the sarcomere length and decreased shear force values. Furthermore, the combination of ultrasound and calcium chloride increased the sarcomere length significantly and simultaneously reduced the Warner–Bratzler shear force tolerance of the sample. These data suggested that low intensity and frequency ultrasound alongside Calcium Chloride immersion can promote the transmembrane transport of calcium ions via the calpain system to improve meat tenderness.     

Sarcoplasmic reticulum calcium defect in Ras-induced hypertrophic cardiomyopathy heart

The small G protein Ras-mediated signaling pathway has been implicated in the development of hypertrophy and diastolic dysfunction in the heart. Earlier cellular studies have suggested that the Ras pathway is responsible for reduced L-type calcium channel current and sarcoplasmic reticulum (SR) calcium uptake associated with sarcomere disorganization in neonatal cardiomyocytes. In the present study, we investigated the in vivo effects of Ras activation on cellular calcium handling and sarcomere organization in adult ventricular myocytes using a newly established transgenic mouse model with targeted expression of the H-Ras-v12 mutant. The transgenic hearts expressing activated Ras developed significant hypertrophy and postnatal lethal heart failure. In adult ventricular myocytes isolated from the transgenic hearts, the calcium transient was significantly depressed but membrane L-type calcium current was unchanged compared with control littermates. The expressions of sarco(endo)plasmic reticulum Ca(2+)-ATPase (SERCA)2a and phospholamban (PLB) were significantly reduced at mRNA levels. The amount of SERCA2a protein was also modestly reduced. However, the expression of PLB protein and gross sarcomere organization remained unchanged in the hypertrophic Ras hearts, whereas Ser(16) phosphorylation of PLB was dramatically inhibited in the Ras transgenic hearts compared with controls. Hypophosphorylation of PLB was also associated with a significant induction of protein phosphatase 1 expression. Therefore, our results from this in vivo model system suggest that Ras-induced contractile defects do not involve decreased L-type calcium channel activities or disruption of sarcomere structure. Rather, suppressed SR calcium uptake due to reduced SERCA2a expression and hypophosphorylation of PLB due to changes in protein phosphatase expression may play important roles in the diastolic dysfunction of Ras-mediated hypertrophic cardiomyopathy.     

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.     

Ultrastructural and cytochemical localization of calcium in a rat cardiac muscle in normal and experimental conditions.

The experiment carried out by us on the, stimulated by adrenaline, cardiac muscle allowed the activation of calcium localized mainly in the mitochondria, MA and FA of the intercalated discs and SR to be translocated in the direction of the sarcomere myofilaments and this especially to the thin actin filaments. The authors' experimental proves, that during the contraction--relaxation function of the cardiac muscle there exists a circulation rythm or a oscillatory functional flow of calcium ions between the mitochondria, intercalated discs and SR and the contractile fibrillae of the sarcomere.     

Negative inotropic effects of high-mobility group box 1 protein in isolated contracting cardiac myocytes

High-mobility group box 1 (HMGB1) released from necrotic cells or macrophages functions as a late inflammatory mediator and has been shown to induce cardiovascular collapse during sepsis. Thus far, however, the effect(s) of HMGB1 in the heart are not known. We determined the effects of HMGB1 on isolated feline cardiac myocytes by measuring sarcomere shortening in contracting cardiac myocytes, intracellular Ca2+ transients by using fluo-3, and L-type calcium currents by using whole cell perforate configuration of the patch-clamp technique. Treatment of isolated myocytes with HMGB1 (100 ng/ml) resulted in a 70% decrease in sarcomere shortening and a 50% decrease in the height of the peak Ca2+ transient within 5 min (P < 0.01). The immediate negative inotropic effects of HMGB1 on cell contractility and calcium homeostasis were partially reversible upon washout of HMGB1. A significant inhibition of the inward l-type calcium currents was also documented by the patch-clamp technique. HMGB1 induced the PKC-epsilon translocation, and a PKC inhibitor significantly attenuated the negative inotropic effects of HMGB1. These studies show for the first time that HMGB1 impairs sarcomere shortening by decreasing calcium availability in cardiac myocytes through modulating membrane calcium influx and suggest that HMGB1 maybe acts as a novel myocardial depressant factor during cardiac injury.     

An activatable molecular spring reduces muscle tearing during extreme stretching

The purpose of this study was to determine failure stresses and failure lengths of actively and passively stretched myofibrils. As expected, myofibrils failed at average sarcomere lengths (about 6–7 μm) that vastly exceeded sarcomere lengths at which actin–myosin filament overlap ceases to exist (4 μm) and thus actin–myosin-based cross-bridge forces are zero at failure. Surprisingly, however, actively stretched myofibrils had much greater failure stresses and failure energies than passively stretched myofibrils, thereby providing compelling evidence for strong force production independent of actin–myosin-based cross-bridge forces. Follow-up experiments in which titin was deleted and cross-bridge formation was inhibited at high and low calcium concentrations point to titin as the regulator of this force, independent of calcium. The results of this study point to a mechanism of force production that reduces stretch-induced muscle damage at extreme length and limits injury and force loss within physiologically relevant ranges of sarcomere and muscle lengths.     

Titin visualization in real time reveals an unexpected level of mobility within and between sarcomeres

The giant muscle protein titin is an essential structural component of the sarcomere. It forms a continuous periodic backbone along the myofiber that provides resistance to mechanical strain. Thus, the titin filament has been regarded as a blueprint for sarcomere assembly and a prerequisite for stability. Here, a novel titin-eGFP knockin mouse provided evidence that sarcomeric titin is more dynamic than previously suggested. To study the mobility of titin in embryonic and neonatal cardiomyocytes, we used fluorescence recovery after photobleaching and investigated the contribution of protein synthesis, contractility, and calcium load to titin motility. Overall, the kinetics of lateral and longitudinal movement of titin-eGFP were similar. Whereas protein synthesis and developmental stage did not alter titin dynamics, there was a strong, inhibitory effect of calcium on titin mobility. Our results suggest a model in which the largely unrestricted movement of titin within and between sarcomeres primarily depends on calcium, suggesting that fortification of the titin filament system is activity dependent.     

Distribution of calcium differs in relaxed and contracted myocardial cells of the rat

Summary Myocardial cells from left ventricles of beating hearts of rats were fixed by immersion in an osmium tetroxide solution containing potassium pyroantimonate to study the electron-microscopic distribution of calcium, the cation being precipitated as an electron-opaque salt (calcium antimonate) by this cytochemical technique. The observed myocytes could be divided into two groups according to their contractile state, evaluated by sarcomere length measurements. In contracted cells (mean sarcomere length 1.43 m) the intramyoflbrillar precipitate was confined to areas of I-bands bordering the A-bands, the intermyofibrillar space showing scarce content in reaction product. Relaxed cells (mean sarcomere length 1.69 m) presented a heavy deposition of reaction product over the sarcomeres, the electron-opaque dots being absent on the H and Z bands. The sarcotubular system and mitochondria were also clearly marked by the reaction product. This second pattern of calcium distribution has not been previously described in heart muscle cells and is interpreted as corresponding to the phase of rise of intracellular calcium which is mediated by membrane depolarization. Our results suggest that different bands of heart sarcomeres show different abilities to bind calcium. The I bands retain the cation even in cells under sustained contraction, probably due to their content in calmodulin; Z and M bands are apparently not involved in calcium sequestration, whereas the content in calcium of the A bands seems to be dependent on the contraction-relaxation cycle of heart myocytes.Supported by Grant HL 06975 from the National Heart, Lung and Blood Institute and AM 18141 from the National Institute of Arthritis, Metabolism and Digestive DiseasesThe authors are grateful to Maria Kapuscinski, Luther B. Joseph, Elisabeth Lawson, Robert Linsmair and Miriam Alojipan for skilled technical assistance     

The positional stability of thick filaments in activated skeletal muscle depends on sarcomere length: evidence for the role of titin filaments

Electron microscopy was used to study the positional stability of thick filaments in isometrically contracting skinned rabbit psoas muscle as a function of sarcomere length at 7 degrees C. After calcium activation at a sarcomere length of 2.6 micron, where resting stiffness is low, sarcomeres become nonuniform in length. The dispersion in sarcomere length is complete by the time maximum tension is reached. A-bands generally move from their central position and continue moving toward one of the Z-discs after tension has reached a plateau at its maximum level. The lengths of the thick and thin filaments remain constant during this movement. The extent of A-band movement during contraction depends on the final length of the individual sarcomere. After prolonged activation, all sarcomeres between 1.9 and 2.5 micron long exhibit A-bands that are adjacent to a Z-disc, with no intervening I-band. Sarcomeres 2.6 or 2.7 micron long exhibit a partial movement of A-bands. At longer sarcomere lengths, where the resting stiffness exceeds the slope of the active tension-length relation, the A-bands remain perfectly centered during contraction. Sarcomere symmetry and length uniformity are restored upon relaxation. These results indicate that the central position of the thick filaments in the resting sarcomere becomes unstable upon activation. In addition, they provide evidence that the elastic titin filaments, which join thick filaments to Z-discs, produce almost all of the resting tension in skinned rabbit psoas fibers and act to resist the movement of thick filaments away from the center of the sarcomere during contraction.     

Titin determines the Frank-Starling relation in early diastole

Titin, a giant protein spanning half the sarcomere, is responsible for passive and restoring forces in cardiac myofilaments during sarcomere elongation and compression, respectively. In addition, titin has been implicated in the length-dependent activation that occurs in the stretched sarcomere, during the transition from diastole to systole. The purpose of this study was to investigate the role of titin in the length-dependent deactivation that occurs during early diastole, when the myocyte is shortened below slack length. We developed a novel in vitro assay to assess myocyte restoring force (RF) by measuring the velocity of recoil in Triton-permeabilized, unloaded rat cardiomyocytes after rigor-induced sarcomere length (SL) contractions. We compared rigor-induced SL shortening to that following calcium-induced (pCa) contractions. The RF-SL relationship was linearly correlated, and the SL-pCa curve displayed a characteristic sigmoidal curve. The role of titin was defined by treating myocytes with a low concentration of trypsin, which we show selectively degrades titin using mass spectroscopic analysis. Trypsin treatment reduced myocyte RF as shown by a decrease in the slope of the RF-SL relationship, and this was accompanied by a downward and leftward shift of the SL-pCa curve, indicative of sensitization of the myofilaments to calcium. In addition, trypsin digestion did not alter the relationship between SL and interfilament spacing (assessed by cell width) after calcium activation. These data suggest that as the sarcomere shortens below slack length, titin-based restoring forces act to desensitize the myofilaments. Furthermore, in contrast to length-dependent activation at long SLs, length-dependent deactivation does not depend on interfilament spacing. This study demonstrates for the first time the importance of titin-based restoring force in length-dependent deactivation during the early phase of diastole.     

Elastic behavior of connectin filaments during thick filament movement in activated skeletal muscle

Connectin (also called titin) is a huge, striated muscle protein that binds to thick filaments and links them to the Z-disc. Using an mAb that binds to connectin in the I-band region of the molecule, we studied the behavior of connectin in both relaxed and activated skinned rabbit psoas fibers by immunoelectron microscopy. In relaxed fibers, antibody binding is visualized as two extra striations per sarcomere arranged symmetrically about the M-line. These striations move away from both the nearest Z-disc and the thick filaments when the sarcomere is stretched, confirming the elastic behavior of connectin within the I- band of relaxed sarcomeres as previously observed by several investigators. When the fiber is activated, thick filaments in sarcomeres shorter than 2.8 microns tend to move from the center to the side of the sarcomere. This translocation of thick filaments within the sarcomere is accompanied by movement of the antibody label in the same direction. In that half-sarcomere in which the thick filaments move away from the Z-disc, the spacings between the Z-disc and the antibody and between the antibody and the thick filaments both increase. Conversely, on the side of the sarcomere in which the thick filaments move nearer to the Z-line, these spacings decrease. Regardless of whether I-band spacing is varied by stretch of a relaxed sarcomere or by active sliding of thick filaments within a sarcomere of constant length, the spacings between the Z-line and the antibody and between the antibody and the thick filaments increase with I-band length identically. These results indicate that the connectin filaments remain bound to the thick filaments in active fibers, and that the elastic properties of connectin are unaltered by calcium ions and cross-bridge activity.     

In silico identification of potential calcium dynamics and sarcomere targets for recovering left ventricular function in rat heart failure with preserved ejection fraction

Heart failure with preserved ejection fraction (HFpEF) is a complex disease associated with multiple co-morbidities, where impaired cardiac mechanics are often the end effect. At the cellular level, cardiac mechanics can be pharmacologically manipulated by altering calcium signalling and the sarcomere. However, the link between cellular level modulations and whole organ pump function is incompletely understood. Our goal is to develop and use a multi-scale computational cardiac mechanics model of the obese ZSF1 HFpEF rat to identify important biomechanical mechanisms that underpin impaired cardiac function and to predict how whole-heart mechanical function can be recovered through altering cellular calcium dynamics and/or cellular contraction. The rat heart was modelled using a 3D biventricular biomechanics model. Biomechanics were described by 16 parameters, corresponding to intracellular calcium transient, sarcomere dynamics, cardiac tissue and hemodynamics properties. The model simulated left ventricular (LV) pressure-volume loops that were described by 14 scalar features. We trained a Gaussian process emulator to map the 16 input parameters to each of the 14 outputs. A global sensitivity analysis was performed, and identified calcium dynamics and thin and thick filament kinetics as key determinants of the organ scale pump function. We employed Bayesian history matching to build a model of the ZSF1 rat heart. Next, we recovered the LV function, described by ejection fraction, peak pressure, maximum rate of pressure rise and isovolumetric relaxation time constant. We found that by manipulating calcium, thin and thick filament properties we can recover 34%, 28% and 24% of the LV function in the ZSF1 rat heart, respectively, and 39% if we manipulate all of them together. We demonstrated how a combination of biophysically based models and their derived emulators can be used to identify potential pharmacological targets. We predicted that cardiac function can be best recovered in ZSF1 rats by desensitising the myofilament and reducing the affinity to intracellular calcium concentration and overall prolonging the sarcomere staying in the active force generating state.     

A mechanism for sarcomere breathing: volume change and advective flow within the myofilament lattice

During muscle contraction, myosin motors anchored to thick filaments bind to and slide actin thin filaments. These motors rely on energy derived from ATP, supplied, in part, by diffusion from the sarcoplasm to the interior of the lattice of actin and myosin filaments. The radial spacing of filaments in this lattice may change or remain constant during contraction. If the lattice is isovolumetric, it must expand when the muscle shortens. If, however, the spacing is constant or has a different pattern of axial and radial motion, then the lattice changes volume during contraction, driving fluid motion and assisting in the transport of molecules between the contractile lattice and the surrounding intracellular space. We first create an advective-diffusive-reaction flow model and show that the flow into and out of the sarcomere lattice would be significant in the absence of lattice expansion. Advective transport coupled to diffusion has the potential to substantially enhance metabolite exchange within the crowded sarcomere. Using time-resolved x-ray diffraction of contracting muscle, we next show that the contractile lattice is neither isovolumetric nor constant in spacing. Instead, lattice spacing is time varying, depends on activation, and can manifest as an effective time-varying Poisson ratio. The resulting fluid flow in the sarcomere lattice of synchronous insect flight muscles is even greater than expected for constant lattice spacing conditions. Lattice spacing depends on a variety of factors that produce radial force, including cross-bridges, titin-like molecules, and other structural proteins. Volume change and advective transport varies with the phase of muscle stimulation during periodic contraction but remains significant at all conditions. Although varying in magnitude, advective transport will occur in all cases in which the sarcomere is not isovolumetric. Akin to “breathing,” advective-diffusive transport in sarcomeres is sufficient to promote metabolite exchange and may play a role in the regulation of contraction itself.     

Muscle active force-length curve explained by an electrophysical model of interfilament spacing

The active isometric force-length relation (FLR) of striated muscle sarcomeres is central to understanding and modeling muscle function. The mechanistic basis of the descending arm of the FLR is well explained by the decreasing thin:thick filament overlap that occurs at long sarcomere lengths. The mechanistic basis of the ascending arm of the FLR (the decrease in force that occurs at short sarcomere lengths), alternatively, has never been well explained. Because muscle is a constant-volume system, interfilament lattice distances must increase as sarcomere length shortens. This increase would decrease thin and thick-filament electrostatic interactions independently of thin:thick filament overlap. To examine this effect, we present here a fundamental, physics-based model of the sarcomere that includes filament molecular properties, calcium binding, sarcomere geometry including both thin:thick filament overlap and interfilament radial distance, and electrostatics. The model gives extremely good fits to existing FLR data from a large number of different muscles across their entire range of measured activity levels, with the optimized parameter values in all cases lying within anatomically and physically reasonable ranges. A local first-order sensitivity analysis (varying individual parameters while holding the values of all others constant) shows that model output is most sensitive to a subset of model parameters, most of which are related to sarcomere geometry, with model output being most sensitive to interfilament radial distance. This conclusion is supported by re-running the fits with only this parameter subset being allowed to vary, which increases fit errors only moderately. These results show that the model well reproduces existing experimental data, and indicate that changes in interfilament spacing play as central a role as changes in filament overlap in determining the FLR, particularly on its ascending arm.