Molecular motors as an auto-oscillator

Complexus cordis

The science-based study of the heart has allowed us to know its structure and function deeply, through the fragmentation and analysis of its parts, following the guidelines that so many achievements have given to us. However, at the time of reassembling those analyzed fragments, we realize that something is missing; the simply sum of the parts is not equal to everything. Thus, for decades, numerous scientists have studied novel strategies that allow us understanding, every natural phenomena from a more inclusive, open and integrative models, which closely address to interactions rather than components. In this way, we can observe how, the behavior of many variables usually transgress the conventional plane and moves towards non-linearity and fractality, making a complex tissue that will maintain its structure while thermodynamically viable. Thus, this document shows the way how, the non-linear study of complex cardiovascular dynamics, begins to give us answers to many questions that the clinical cardiologist poses every day.

Spontaneous oscillatory contraction (SPOC) in cardiomyocytes

SPOC (spontaneous oscillatory contraction) is a characteristic state of the contractile system of striated (skeletal and cardiac) muscle that exists between the states of relaxation and contraction. For example, Ca-SPOCs occur at physiological Ca2+ levels (pCa ∼6.0), whereas ADP-SPOC occurs in the virtual absence of Ca2+ (pCa ≥ 8; relaxing conditions in the presence of MgATP), but in the presence of inorganic phosphate (Pi) and a high concentration of MgADP. The concentration of Mg-ADP necessary for SPOC is nearly equal to or greater than the MgATP concentration for cardiac muscle and is several times higher for skeletal muscle. Thus, the cellular conditions for SPOC are broader in cardiac muscle than in skeletal muscle. During these SPOCs, each sarcomere in a myofibril undergoes length oscillation that has a saw-tooth waveform consisting of a rapid lengthening and a slow shortening phase. The lengthening phase of one half of a sarcomere is transmitted to the adjacent half of the sarcomere successively, forming a propagating wave (termed a SPOC wave). The SPOC waves are synchronized across the cardiomyocytes resulting in a visible wave of successive contractions and relaxations termed the SPOC wave. Experimentally, the SPOC period (and therefore the velocity of SPOC wave) is observed in demembranated cardiomyocytes and can be prepared from a wide range of animal hearts. These periods correlate well with the resting heartbeats of a wide range of mammals (rat, rabbit, dog, pig and cow). Preliminary experiments showed that the SPOC properties of human cardiomyocytes are similar to the heartbeat of a large dog or a pig. This correlation suggests that SPOCs may play a fundamental role in the heart. Here, we briefly summarize a range of SPOC parameters obtained experimentally, and relate them to a theoretical model to explain those characteristics. Finally, we discuss the possible significance of these SPOC properties in each and every heartbeat.

Locally and globally coupled oscillators in muscle

At an intermediate activation level, striated muscle exhibits autonomous oscillations called SPOC, in which the basic contractile units, sarcomeres, oscillate in length, and various oscillatory patterns such as traveling waves and their disrupted forms appear in a myofibril. Here we show that these patterns are reproduced by mechanically connecting in series the unit model that explains characteristics of SPOC at the single-sarcomere level. We further reduce the connected model to phase equations, revealing that the combination of local and global couplings is crucial to the emergence of these patterns.

Temporal analysis of vascular smooth muscle cell elasticity and adhesion reveals oscillation waveforms that differ with aging

A spectral analysis approach was developed for detailed study of time-resolved, dynamic changes in vascular smooth muscle cell (VSMC) elasticity and adhesion to identify differences in VSMC from young and aged monkeys. Atomic force microscopy (AFM) was used to measure Young's modulus of elasticity and adhesion as assessed by fibronectin (FN) or anti-beta 1 integrin interaction with the VSMC surface. Measurements demonstrated that VSMC cells from old vs. young monkeys had increased elasticity (21.6 kPa vs. 3.5 kPa or a 612% increase in elastic modulus) and adhesion (86 pN vs. 43 pN or a 200% increase in unbinding force). Spectral analysis identified three major frequency components in the temporal oscillation patterns for elasticity (ranging from 1.7 × 10(-3) to 1.9 × 10(-2) Hz in old and 8.4 × 10(-4) to 1.5 × 10(-2) Hz in young) and showed that the amplitude of oscillation was larger (P < 0.05) in old than in young at all frequencies. It was also observed that patterns of oscillation in the adhesion data were similar to the elasticity waveforms. Cell stiffness was reduced and the oscillations were inhibited by treatment with cytochalasin D, ML7 or blebbistatin indicating the involvement of actin-myosin-driven processes. In conclusion, these data demonstrate the efficacy of time-resolved analysis of AFM cell elasticity and adhesion measurements and that it provides a uniquely sensitive method to detect real-time functional differences in biomechanical and adhesive properties of cells. The oscillatory behavior suggests that mechanisms governing elasticity and adhesion are coupled and affected differentially during aging, which may link these events to changes in vascular stiffness.

Biomechanical regulation of contractility: spatial control and dynamics

Cells are active materials; they can change shape using internal energy to build contractile networks of actin filaments and myosin motors. Contractility of the actomyosin cortex is tightly regulated in space and time to orchestrate cell shape changes. Conserved biochemical pathways regulate actomyosin networks in subcellular domains which drive cell shape changes. Actomyosin networks display complex dynamics, such as flows and pulses, which participate in myosin distribution and provide a more realistic description of the spatial distribution and evolution of forces during morphogenesis. Such dynamics are influenced by the mechanical properties of actomyosin networks. Moreover, actomyosin can self-organize and respond to mechanical stimuli through multiple types of biomechanical feedback. In this review we propose a framework encapsulating spatiotemporal regulation of contractility from established pathways with the dynamics and mechanics of actomyosin networks. Through the comparison of cytokinesis, cell migration and epithelial morphogenesis, we delineate emergent properties of contractile activity, including self-organization, adaptability and robustness.

Multicomponent analysis of junctional movements regulated by myosin II isoforms at the epithelial zonula adherens

The zonula adherens (ZA) of epithelial cells is a site of cell-cell adhesion where cellular forces are exerted and resisted. Increasing evidence indicates that E-cadherin adhesion molecules at the ZA serve to sense force applied on the junctions and coordinate cytoskeletal responses to those forces. Efforts to understand the role that cadherins play in mechanotransduction have been limited by the lack of assays to measure the impact of forces on the ZA. In this study we used 4D imaging of GFP-tagged E-cadherin to analyse the movement of the ZA. Junctions in confluent epithelial monolayers displayed prominent movements oriented orthogonal (perpendicular) to the ZA itself. Two components were identified in these movements: a relatively slow unidirectional (translational) component that could be readily fitted by least-squares regression analysis, upon which were superimposed more rapid oscillatory movements. Myosin IIB was a dominant factor responsible for driving the unilateral translational movements. In contrast, frequency spectrum analysis revealed that depletion of Myosin IIA increased the power of the oscillatory movements. This implies that Myosin IIA may serve to dampen oscillatory movements of the ZA. This extends our recent analysis of Myosin II at the ZA to demonstrate that Myosin IIA and Myosin IIB make distinct contributions to junctional movement at the ZA.