Filament Bending Research Articles

Actin Filament Dynamics in the Actomyosin VI Complex Is Regulated Allosterically by Calcium–Calmodulin Light Chain

The contractile and enzymatic activities of myosin VI are regulated by calcium binding to associated calmodulin (CaM) light chains. We have used transient phosphorescence anisotropy to monitor the microsecond rotational dynamics of erythrosin-iodoacetamide-labeled actin with strongly bound myosin VI (MVI) and to evaluate the effect of MVI-bound CaM light chain on actin filament dynamics. MVI binding lowers the amplitude but accelerates actin filament microsecond dynamics in a Ca2+- and CaM-dependent manner, as indicated from an increase in the final anisotropy and a decrease in the correlation time of transient phosphorescence anisotropy decays. MVI with bound apo-CaM or Ca2+–CaM weakly affects actin filament microsecond dynamics, relative to other myosins (e.g., muscle myosin II and myosin Va). CaM dissociation from bound MVI damps filament rotational dynamics (i.e., increases the torsional rigidity), such that the perturbation is comparable to that induced by other characterized myosins. Analysis of individual actin filament shape fluctuations imaged by fluorescence microscopy reveals a correlated effect on filament bending mechanics. These data support a model in which Ca2+-dependent CaM binding to the IQ domain of MVI is linked to an allosteric reorganization of the actin binding site(s), which alters the structural dynamics and the mechanical rigidity of actin filaments. Such modulation of filament dynamics may contribute to the Ca2+- and CaM-dependent regulation of myosin VI motility and ATP utilization.

Theory of crosslinked bundles of helical filaments: Intrinsic torques in self-limiting biopolymer assemblies

Inspired by the complex influence of the globular crosslinking proteins on the formation of biofilament bundles in living organisms, we study and analyze a theoretical model for the structure and thermodynamics of bundles of helical filaments assembled in the presence of crosslinking molecules. The helical structure of filaments, a universal feature of biopolymers such as filamentous actin, is shown to generically frustrate the geometry of crosslinking between the "grooves" of two neighboring filaments. We develop a coarse-grained model to investigate the interplay between the geometry of binding and mechanics of both linker and filament distortion, and we show that crosslinking in parallel bundles of helical filaments generates intrinsic torques, of the type that tend to wind the bundle superhelically about its central axis. Crosslinking mediates a non-linear competition between the preference for bundle twist and the size-dependent mechanical cost of filament bending, which in turn gives rise to feedback between the global twist of self-assembled bundles and their lateral size. Finally, we demonstrate that above a critical density of bound crosslinkers, twisted bundles form with a thermodynamically preferred radius that, in turn, increases with a further increase in crosslinking bonds. We identify the stiffness of crosslinking bonds as a key parameter governing the sensitivity of bundle structure and assembly to the availability and affinity of crosslinkers.

Force generation in bacteria without nucleotide-dependent bending of cytoskeletal filaments

Binary cell division in bacteria occurs via the formation and subsequent contraction of a polymeric ring, the so-called Z ring, at the middle of the cell. This ring is made of filamenting temperature-sensitive Z (FtsZ) proteins and it shrinks in radius to generate a contractile radial force on the cell membrane. Although a few models have been proposed, the ring contraction mechanism still remains a mystery. The models rely on various physical properties of the FtsZ filaments, some of which have been verified through in vitro experiments and some of which remain unclear. A feature common to all these models is the hydrolysis-driven transition of FtsZ filaments from straight to curved conformations. While the intrinsic curvature of FtsZ filaments has been experimentally established beyond doubt, evidence has been mounting against the existence of any transition between the straight FtsZ-GTP and the curved FtsZ-GDP conformations. Preliminary results from our earlier work [B. Ghosh and A. Sain, Phys. Rev. Lett. 101, 178101 (2008)] indicated that hydrolysis-induced bending is not necessary for Z-ring contraction. Since then many new experimental observations have been reported on this subject and in view of these here we argue that our model appears even more plausible than before. In addition, we have explored more realistic features, such as how the length distribution of FtsZ filaments in the cytoplasm may influence the contraction dynamics, and we have also demonstrated that the Z ring retains approximately the same number of monomers, although not the same monomers, during the course of contraction as reported by fluorescence experiments.

Molecular motors stiffen non-affine semiflexible polymer networks

Reconstituted filamentous actin networks with myosin motor proteins form active gels, in which motor proteins generate forces that drive the network far from equilibrium. This motor activity can also strongly affect the network elasticity; experiments have shown a dramatic stiffening in in vitro networks with molecular motors. Here we study the effects of motor generated forces on the mechanics of simulated 2D networks of athermal stiff filaments. We show how heterogeneous internal motor stresses can lead to stiffening in networks that are governed by filament bending modes. The motors are modeled as force dipoles that cause muscle like contractions. These contractions "pull out" the floppy bending modes in the system, which induces a cross-over to a stiffer stretching dominated regime. Through this mechanism, motors can lead to a nonlinear network response, even when the constituent filaments are themselves purely linear. These results have implications for the mechanics of living cells and suggest new design principles for active biomemetic materials with tunable mechanical properties.

Origin of Twist-Bend Coupling in Actin Filaments

Actin filaments are semiflexible polymers that display large-scale conformational twisting and bending motions. Modulation of filament bending and twisting dynamics has been linked to regulatory actin-binding protein function, filament assembly and fragmentation, and overall cell motility. The relationship between actin filament bending and twisting dynamics has not been evaluated. The numerical and analytical experiments presented here reveal that actin filaments have a strong intrinsic twist-bend coupling that obligates the reciprocal interconversion of bending energy and twisting stress. We developed a mesoscopic model of actin filaments that captures key documented features, including the subunit dimensions, interaction energies, helicity, and geometrical constraints coming from the double-stranded structure. The filament bending and torsional rigidities predicted by the model are comparable to experimental values, demonstrating the capacity of the model to assess the mechanical properties of actin filaments, including the coupling between twisting and bending motions. The predicted actin filament twist-bend coupling is strong, with a persistence length of 0.15–0.4 μm depending on the actin-bound nucleotide. Twist-bend coupling is an emergent property that introduces local asymmetry to actin filaments and contributes to their overall elasticity. Up to 60% of the filament subunit elastic free energy originates from twist-bend coupling, with the largest contributions resulting under relatively small deformations. A comparison of filaments with different architectures indicates that twist-bend coupling in actin filaments originates from their double protofilament and helical structure.

The Antibacterial Cell Division Inhibitor PC190723 Is an FtsZ Polymer-stabilizing Agent That Induces Filament Assembly and Condensation

Cell division protein FtsZ can form single-stranded filaments with a cooperative behavior by self-switching assembly. Subsequent condensation and bending of FtsZ filaments are important for the formation and constriction of the cytokinetic ring. PC190723 is an effective bactericidal cell division inhibitor that targets FtsZ in the pathogen Staphylococcus aureus and Bacillus subtilis and does not affect Escherichia coli cells, which apparently binds to a zone equivalent to the binding site of the antitumor drug taxol in tubulin (Haydon, D. J., Stokes, N. R., Ure, R., Galbraith, G., Bennett, J. M., Brown, D. R., Baker, P. J., Barynin, V. V., Rice, D. W., Sedelnikova, S. E., Heal, J. R., Sheridan, J. M., Aiwale, S. T., Chauhan, P. K., Srivastava, A., Taneja, A., Collins, I., Errington, J., and Czaplewski, L. G. (2008) Science 312, 1673-1675). We have found that the benzamide derivative PC190723 is an FtsZ polymer-stabilizing agent. PC190723 induced nucleated assembly of Bs-FtsZ into single-stranded coiled protofilaments and polymorphic condensates, including bundles, coils, and toroids, whose formation could be modulated with different solution conditions. Under conditions for reversible assembly of Bs-FtsZ, PC190723 binding reduced the GTPase activity and induced the formation of straight bundles and ribbons, which was also observed with Sa-FtsZ but not with nonsusceptible Ec-FtsZ. The fragment 2,6-difluoro-3-methoxybenzamide also induced Bs-FtsZ bundling. We propose that polymer stabilization by PC190723 suppresses in vivo FtsZ polymer dynamics and bacterial division. The biochemical action of PC190723 on FtsZ parallels that of the microtubule-stabilizing agent taxol on the eukaryotic structural homologue tubulin. Both taxol and PC190723 stabilize polymers against disassembly by preferential binding to each assembled protein. It is yet to be investigated whether both ligands target structurally related assembly switches.

Actin filament remodeling by actin depolymerization factor/cofilin

We investigate, using molecular dynamics, how the severing protein, actin depolymerization factor (ADF)/cofilin, modulates the structure, conformational dynamics, and mechanical properties of actin filaments. The actin and cofilactin filament bending stiffness and corresponding persistence lengths obtained from all-atom simulations are comparable to values obtained from analysis of thermal fluctuations in filament shape. Filament flexibility is strongly affected by the nucleotide-linked conformation of the actin subdomain 2 DNase-I binding loop and the filament radial mass density distribution. ADF/cofilin binding between subdomains 1 and 3 of a filament subunit triggers reorganization of subdomain 2 of the neighboring subunit such that the DNase-I binding loop (DB-loop) moves radially away from the filament. Repositioning of the neighboring subunit DB-loop significantly weakens subunit interactions along the long-pitch helix and lowers the filament bending rigidity. Lateral filament contacts between the hydrophobic loop and neighboring short-pitch helix monomers in native filaments are also compromised with cofilin binding. These works provide a molecular interpretation of biochemical solution studies documenting the disruption of filament subunit interactions and also reveal the molecular basis of actin filament allostery and its linkage to ADF/cofilin binding.

Effects of molecular-scale processes on observable growth properties of actin networks.

The properties of actin network growth against a flat obstacle are studied using several different sets of molecular-level assumptions regarding filament growth and nucleation. These assumptions are incorporated into a multifilament methodology which treats both the distribution of filament orientations and bending of filaments. Three single-filament force-generation mechanisms in the literature are compared within this framework. Each mechanism is treated using two different filament nucleation modes, namely, spontaneous nucleation and branching off pre-existing filaments. We find that the shape of the force-velocity relation depends mainly on the ratio of the thermodynamic and mechanical stall forces of the filaments. If the thermodynamic stall force greatly exceeds the mechanical stall force, the velocity drops abruptly to zero when the mechanical stall force is reached; otherwise, it goes more gradually to zero. In addition, branching nucleation gives a steeper increase in the filament number with opposing force than spontaneous nucleation does. Finally, the zero-force velocity of the obstacle as a function of the detachment and capping rates differs significantly between the different single-filament growth mechanisms. Experiments are proposed to use these differences to discriminate between the network growth models.

Subdiffraction‐Resolution Fluorescence Microscopy of Myosin–Actin Motility

Subdiffraction-resolution imaging by subsequent localization of single photoswitchable molecules can achieve a spatial resolution in the range of approximately 20 nm with moderate excitation intensities, but have so far been too slow for imaging faster dynamics in biology. Herein, we introduce a novel approach for video-like subdiffraction microscopy based on rapid and reversible photoswitching of commercially available organic carbocyanine fluorophores. With the present concept, we demonstrate in vitro studies on the motility of fluorophore-labeled actin filaments along myosin II. Actin filaments were densely labeled with carbocyanine fluorophores, and the gliding velocity adjusted by the concentration of ATP. At imaging frame rates of approximately 100 Hz, only 100 consecutive frames are sufficient to generate a single high-resolution image of moving actin filaments with a lateral resolution of approximately 30 nm. A video-like sequence is generated from individual reconstructed images by additionally applying a sliding window algorithm. We measured velocities of individual actin filaments of up to approximately 0.18 microm s(-1), observed strong bending and disruption of filaments as well as locally immobile fragments.

Proposed role of the M-band in sarcomere mechanics and mechano-sensing: a model study

In sarcomeres of striated muscles the middle parts of adjacent thick filaments are connected to each other by the M-band proteins. To understand the role of the M-band in sarcomere mechanics a model of forces which pull a thick filament to opposite Z-disks of a sarcomere is considered. Forces of actin-myosin cross-bridges, I-band titin segments and the M-band are accounted for. A continual expression for the M-band force is obtained assuming that the M-band proteins which connect neighbor thick filaments have nonlinear elastic properties. On the ascending and descending limbs of the force-length diagram cross-bridge forces tend to destabilize sarcomere while titin tries to restore its symmetric configuration. When destabilizing cross-bridge force exceeds a critical limit, symmetric configuration of a sarcomere becomes unstable and the M-band buckles. Stiffness of the M-band increases stability only if the M-band is anchored to the extra-sarcomere cytoskeleton. Realistic magnitudes of the M-band buckling require that the M-band proteins have essentially nonlinear elasticity. The buckling may explain the M-band bending and axial misalignment of the thick filaments observed in contracting muscle. We hypothesize that the buckling stretches the titin protein kinase domain localized in the M-band being the signal for mechanical control of gene expression and protein turnover in striated muscle.

Computational analysis of viscoelastic properties of crosslinked actin networks.

Mechanical force plays an important role in the physiology of eukaryotic cells whose dominant structural constituent is the actin cytoskeleton composed mainly of actin and actin crosslinking proteins (ACPs). Thus, knowledge of rheological properties of actin networks is crucial for understanding the mechanics and processes of cells. We used Brownian dynamics simulations to study the viscoelasticity of crosslinked actin networks. Two methods were employed, bulk rheology and segment-tracking rheology, where the former measures the stress in response to an applied shear strain, and the latter analyzes thermal fluctuations of individual actin segments of the network. It was demonstrated that the storage shear modulus (G′) increases more by the addition of ACPs that form orthogonal crosslinks than by those that form parallel bundles. In networks with orthogonal crosslinks, as crosslink density increases, the power law exponent of G′ as a function of the oscillation frequency decreases from 0.75, which reflects the transverse thermal motion of actin filaments, to near zero at low frequency. Under increasing prestrain, the network becomes more elastic, and three regimes of behavior are observed, each dominated by different mechanisms: bending of actin filaments, bending of ACPs, and at the highest prestrain tested (55%), stretching of actin filaments and ACPs. In the last case, only a small portion of actin filaments connected via highly stressed ACPs support the strain. We thus introduce the concept of a ‘supportive framework,’ as a subset of the full network, which is responsible for high elasticity. Notably, entropic effects due to thermal fluctuations appear to be important only at relatively low prestrains and when the average crosslinking distance is comparable to or greater than the persistence length of the filament. Taken together, our results suggest that viscoelasticity of the actin network is attributable to different mechanisms depending on the amount of prestrain.

Buckling-induced zebra stripe patterns in nematic F-actin

Rather than forming a simple and uniform nematic liquid crystal, concentrated solutions of semiflexible polymers, such as F-actin, have been observed to display a spatially periodic switching of the nematic director. When observed with polarization microscopy, these patterns appear as alternating light and dark bands, often referred to as zebra stripe patterns. Zebra stripe patterns, although not fully characterized, are due to periodic orientation distortions in the nematic order. We characterize such patterns by using a combination of two techniques. Using polarization microscopy, we quantify the periodic orientation distortions and show that the magnitude of the order parameter also varies periodically in the striped domains. When using fluorescently labeled filaments as markers, filaments spanning the striped domains are seen to undergo large angle bends. With fluorescence, clear density differences between adjacent stripes are also observed with domains of lesser density corresponding to strongly bent filaments. By directly comparing patterned areas with both polarization and fluorescence techniques, we show that periodic variation in the orientation, order parameter, filament bending, and density are correlated. We propose that these effects originate from the coupling of orientation and density that occurs for highly concentrated solutions of long semiflexible polymers subject to shear flows, as previously proposed [P. de Gennes, Mol. Cryst. Liq. Cryst. (Phila. Pa.) 34, 177 (1977)]. After cessation of shearing, strong interfilament interactions and high compressibility can lead to periodic buckling from the relaxation of filaments stretched during flows. The characterization of zebra stripe patterns presented here provides evidence that buckling in confined F-actin nematics produces strong periodic bending that is responsible for the observed features.

Nonlinear elasticity of stiff filament networks: strain stiffening, negative normal stress, and filament alignment in fibrin gels.

Many biomaterials formed by cross-linked semiflexible or rigid filaments exhibit nonlinear theology in the form of strain-stiffening and negative normal stress when samples are deformed in simple shear geometry. Two different classes of theoretical models have been developed to explain this nonlinear elastic response, which is neither predicted by rubber elasticity theory nor observed in elastomers or gels formed by flexible polymers. One model considers the response of isotropic networks of semiflexible polymers that have nonlinear force-elongation relations arising from their thermal fluctuations. The other considers networks of rigid filaments with linear force-elongation relations in which nonlinearity arises from nonaffine deformation and a shift from filament bending to stretching at increasing strains. Fibrin gels are a good experimental system to test these theories because the fibrin monomer assembles under different conditions to form either thermally fluctuating protofibrils with persistence length on the order of the network mesh size, or thicker rigid fibers. Comparison of rheologic and optical measurements shows that strain stiffening and negative normal stress appear at smaller strains than those at which filament orientation is evident from birefringence. Comparisons of shear to normal stresses and the strain-dependence of shear moduli and birefringence suggest methods to evaluate the applicability of different theories of rod-like polymer networks. The strain-dependence of the ratio of normal stress to shear stress is one parameter that distinguishes semiflexible and rigid filament models, and comparisons with experiments reveal conditions under which specific theories may be applicable.

Towards Custom-topology Tracks For Probing Myosin Motor Dynamics

An important part of cellular transportation infrastructure is formed by myosin motors that use actin filaments as their tracks. Many questions concerning the mechano-chemistry of those motors and the degree of evolutionary adaption to the track topology remain elusive because we cannot tailor the geometric properties of F-actin.Here, we employ three-dimensional DNA origami to construct hybrid DNA-actin filaments with precisely controlled geometric properties. We engineered building blocks exhibiting custom-shaped cavities that host F-actin tetramers such that myosin motors may still access their usual binding site on actin. We describe triggering the formation of filaments from those building blocks that grow to lengths above 10 microns and that have periodically aligned cavities for hosting actin segments. Binding-site orientation can be rotated by 90 degrees with respect to the filament axis to probe myosin's ability to take sidesteps. We propose the following strategy for hosting actin fragments: F-actin is labeled with thiol-modified oligos, followed by capture of this oligo by the DNA track building blocks, followed by filament bending into the custom shaped cavity on each building block, followed by filament breaking fueled by DNA hybridization.Figure 1Upper panels: TEM micrographs and schematics of actin-hosting DNA track building blocks. Bottom: TEM micrograph of a synthetic filament with periodically spaced actin hosting cavities.View Large Image | View Hi-Res Image | Download PowerPoint Slide

Rods-on-string idealization captures semiflexible filament dynamics

We present an approach to modeling the two-dimensional Brownian dynamics of semiflexible filaments in the worm-model description as uniform, isotropic, and continuously flexible. Experimental observations increasingly show that the mechanical behavior of semiflexible filament networks departs from conventional knowledge. A force-balance-based dynamic simulation of the filament networks has multiple advantages as an approach to understanding their anomalous mechanics. However, a major disadvantage is the difficulty of capturing filament hydrodynamics and bending mechanics in a computationally efficient and physically consistent manner. To that end, we propose a strategy for modeling semiflexible filaments which involves idealizing a semiflexible filament as a contiguous string of flexible rods, and considering the Brownian forces on it as Einsteinian-like point normal and tangential forces. By idealizing the filament as a string of rods, we avoid the complex hydrodynamic treatment involved in beads-on-string idealizations, and implement large-deflection beam mechanics and filament inextensibility in a natural manner, while reducing the computational size of the problem. By considering the Brownian forces as point normal and tangential forces, we decompose the Brownian forces on straight and curved segments into a combination of classical resultant forces and couples whose distribution is shown to be governed by the rod diffusion coefficients. The decomposition allows solution of the Euler beam equations to second-order continuity between segments and fifth-order continuity within segments. We show that the approach is physically consistent by capturing multiple Brownian phenomena ranging from the rigid to the semiflexible limit: the translational and rotational diffusion of rigid rods; the thermal fluctuation of semirigid cantilever filaments; and the shape, bending, and time relaxation of freely diffusing, semiflexible actin filaments.

Three-dimensional spiral waves in an excitable reaction system: Initiation and dynamics of scroll rings and scroll ring pairs

We report experimental results on spiral and scroll waves in the 1,4-cyclohexanedione Belousov-Zhabotinsky reaction. The propagating concentration waves are detected by two-dimensional photometry and optical tomography. Wave pulses can disappear in front-to-front and front-to-back collisions. This anomaly causes the nucleation of vortices from collisions of three nonrotating waves. In three-dimensional systems, these vortices are scroll rings that rotate around initially circular filaments. Depending on reactant concentrations, the filaments shrink or expand indicating positive and negative filament tensions, respectively. Shrinkage results in vortex annihilation. Expansion is accompanied by filament buckling and bending, which is interpreted as developing Winfree turbulence. We also describe the initiation of scroll ring pairs in four-wave collisions. The two filaments are stacked on top of each other and their motion suggests filament repulsion.

Cofilin Increases the Bending Flexibility of Actin Filaments: Implications for Severing and Cell Mechanics

We determined the flexural (bending) rigidities of actin and cofilactin filaments from a cosine correlation function analysis of their thermally driven, two-dimensional fluctuations in shape. The persistence length of actin filaments is 9.8 μm, corresponding to a flexural rigidity of 0.040 pN μm 2. Cofilin binding lowers the persistence length ∼5-fold to a value of 2.2 μm and the filament flexural rigidity to 0.0091 pN μm 2. That cofilin-decorated filaments are more flexible than native filaments despite an increased mass indicates that cofilin binding weakens and redistributes stabilizing subunit interactions of filaments. We favor a mechanism in which the increased flexibility of cofilin-decorated filaments results from the linked dissociation of filament-stabilizing ions and reorganization of actin subdomain 2 and as a consequence promotes severing due to a mechanical asymmetry. Knowledge of the effects of cofilin on actin filament bending mechanics, together with our previous analysis of torsional stiffness, provide a quantitative measure of the mechanical changes in actin filaments associated with cofilin binding, and suggest that the overall mechanical and force-producing properties of cells can be modulated by cofilin activity.

Comparison between predictions and measurements of the superconducting performance ofNb3Sn cable in conduit conductors with transverse load degradation

Nb3Sn cable in conduit type conductors (CICC) are a popular choice for high current conductorsoperating in steady or slowly changing current/field conditions. They provide a low costway of bundling strands together to achieve large conductor currents at high field(up to 13 T), allowing a reduction in coil voltage requirements. The extensivestrand contact, although giving relatively high AC losses, gives resilience againstcurrent non-uniformity and local strand damage, and there is good stability toelectromagnetic disturbances due to the extensive helium contact area with the strands.In the last 5–6 years there has been clear evidence ofNb3Sn CICC performance degradation compared to expectations based on strand measurements.Investigations have linked this to filament bending and fracture under the mechanicalloads, and particularly their accumulation from top to bottom of a cable. These effects werenot widely expected to occur in small cables, and even in large ones their extent wasexpected to be limited. However, in 2006 testing of a small 15 kA conductor intended for adipole showed severe degradation that continuously increased with cycling andsome large 70 kA CICC have also shown a higher than expected performancedrop. Experimental evidence strongly suggests that the degradation is dependentnot only on the cable pattern but also on the sensitivity of different types ofNb3Sn strands to bending and pinching. The variability of results, with some strand–cablecombinations giving a satisfactory performance, has provided an incentive to improve themodelling of the degradation to provide better predictions at the strand level of thecharacteristics needed for successful cable performance.Modelling was being developed as early as 2005 with an analytic cable mechanical modelbut a simplified and non-physical procedure to then derive the superconductingperformance. The mechanical model was successfully benchmarked against overallmechanical property measurements on cables. This paper continues the developmenttowards a complete predictive cable degradation model, this time covering the linkbetween filament bending and damage (available from the earlier mechanical modeland also increasingly from more sophisticated numerical simulations) and theoverall superconducting performance, benchmarked using data from strand tests.

Effective Medium Theory of Semiflexible Filamentous Networks

We develop an effective medium approach to the mechanics of disordered, semiflexible polymer networks and study the response of such networks to uniform and nonuniform strain. We identify distinct elastic regimes in which the contributions of either filament bending or stretching to the macroscopic modulus vanish. We also show that our effective medium theory predicts a crossover between affine and nonaffine strain, consistent with both prior numerical studies and scaling theory.

Dynamics of a transmural scroll wave in ground squirrel myocardium

A study was made of tachyarrhythmia evoked by a premature stimulus (4 ms at 4–5 diastolic thresholds) following a train of rectangular pulses (4 ms at 2 diastolic thresholds, repetition rate of 0.5 or 2 s−1). The spatiotemporal distribution of the potential over the endo- and epicardial surfaces of a thin (∼1 mm) specimen of ground squirrel ventricular myocardium was monitored with two arrays of 32 unipolar electrodes each. The electrographic data were processed into isochrone maps reflecting the spread of activation over the surfaces. These maps were further analyzed to infer the 3D structure and dynamics of the vortex (scroll) wave. During the evolution of a transmural scroll, (i) the filament could be normal to the myocardial surfaces as well as oblique at varying angles (down to 12°); (ii) the scroll could drift as a whole, whereby the filament remained self-parallel or changed its inclination; in other cases, one (endocardial) core was anchored while the other changed its position (precession of the filament); (iii) the vortex cores on both or only one surface changed in size and shape; (iv) the filament could be repeatedly twisted through various angles and untwisted. Scroll rotation was attended with excitation breakthroughs that might have originated from filament bending as well as from focal sources.