Spontaneous Mechanical Oscillations Research Articles

Flagella-like beating of actin bundles driven by self-organized myosin waves.

Wave-like beating of eukaryotic cilia and flagella-threadlike protrusions found in many cells and microorganisms-is a classic example of spontaneous mechanical oscillations in biology. This type of self-organized active matter raises the question of the coordination mechanism between molecular motor activity and cytoskeletal filament bending. Here we show that in the presence of myosin motors, polymerizing actin filaments self-assemble into polar bundles that exhibit wave-like beating. Importantly, filament beating is associated with myosin density waves initiated at twice the frequency of the actin-bending waves. A theoretical description based on curvature control of motor binding to the filaments and of motor activity explains our observations in a regime of high internal friction. Overall, our results indicate that the binding of myosin to actin depends on the actin bundle shape, providing a feedback mechanism between the myosin activity and filament deformations for the self-organization of large motor filament assemblies.

Generation of mixed-mode stochastic oscillations in a hair bundle model

We consider a mathematical model of spontaneous mechanical oscillations of hair bundles in bullfrog saccular hair cells. This two-dimensional model describes dynamics of the positions of the bundle tip and molecular motors. The main control parameters of this model are the calcium feedback strength and the maximal force of molecular motors. The dynamics of hair bundles is subject to the random disturbances. We study noise-induced oscillations in the parametric zone where the equilibria are the only attractors of the system. We analyze the probabilistic mechanism of the generation of mixed-mode stochastic oscillations with the help of the stochastic sensitivity functions and confidence domains. The constructive abilities of this mathematical technique in the analysis of the stochastic effects in the hair bundle model are demonstrated.

Motor Mutants bring Wild-Type Motors to a Halt Stochastically

Motor Mutants bring Wild-Type Motors to a Halt Stochastically

Voltage oscillations and response dynamics in a model of sensory hair cells

Sensory hair cells in auditory and vestibular organs rely on active mechanisms to achieve high sensitivity and frequency selectivity with respect to weak stimuli. Self-sustained oscillations in hair cells occur on two very different levels. First, the mechano-sensory hair bundle itself can undergo spontaneous mechanical oscillations. Second, self-sustained electric voltage oscillations across the membrane of the hair cell have been documented in the inner ear of lower vertebrates. The functional significance of these self-sustained voltage oscillations is currently unknown. We used a Hodgkin-Huxley type model of the baso-lateral ionic currents of bullfrog sacculus to study genesis of spontaneous voltage oscillation patterns and how the spontaneous oscillations shape the response of the hair cell to external mechanical stimuli. To examine the influence of inevitable fluctuations on the dynamical regimes, we included a stochastic transduction current originating in the Brownian motion of the hair bundle and channel noise arising due to the finite number of mechano-electrical transduction channels [1]. We determined the bifurcation structure of the model in terms of two important ionic conductances, associated with the inwardly rectifier (K1) and Ca2+-activated (BK) potassium currents. We found that for large values of BK conductance the system is either at equilibrium or exhibit tonic oscillations. For small values of BK and large values of K1 conductances the dynamics of the model shows diverse patterns of activity including quasi-periodic oscillations, large-amplitude periodic spikes, and bursts of spikes. In particular we found a peculiar transition to bursting through quasiperiodic oscillations with two independent frequencies corresponding to a 2D torus in the phase space of the system. Within small patches of parameter space at the transition from spiking to bursting and at the spike adding transition, voltage dynamics are chaotic. Furthermore, we showed that thermal fluctuations of mechano-electrical transduction current can lead to chaos in a wide area of parameter space. We found a high sensitivity and frequency selectivity for the regime of regular spontaneous oscillations in response to sinusoidal stimuli with frequencies f > 5 Hz. Hence, an oscillatory voltage compartment might constitute a biophysical implementation of a high-gain amplifier. Cells poised in the chaotic regime of low BK and high K1 conductances showed poor tuning, but provided a high sensitivity to low-frequency variations of external stimuli. In summary, this study shows that the electrical oscillator found in saccular hair cells contributes significantly to nonlinear amplification of external mechanical stimuli. This further supports the idea of nonlinear oscillators playing a crucial role in the operation of the inner ear.

Mechano-electrical vibrations of microtubules—Link to subcellular morphology

Spontaneous mechanical oscillations were predicted and experimentally proven on almost every level of cellular structure. Besides morphogenetic potential of oscillatory mechanical force, oscillations may drive vibrations of electrically polar structures or these structures themselves may oscillate on their own natural frequencies. Vibrations of electric charge will generate oscillating electric field, role of which in morphogenesis is discussed in this paper. This idea is demonstrated in silico on the conformation of two growing microtubules.

Effects of the somatic ion channels upon spontaneous mechanical oscillations in hair bundles of the inner ear

Decoupled hair bundles of the bullfrog ( Lithobates catesbeianus) sacculus exhibit spontaneous oscillations in vitro. We examine the effect of the somatic electrical circuit upon active hair bundle motility. We found that innate bundle movements exhibit a complex profile with multiple periodicities. Inhibition of somatic ion channels using targeted neurotoxins and modified physiological solutions strongly affects the bundles’ mechanical behavior, modifying the amplitude and the temporal characteristics of the oscillation profile.

Dynamic State and Compressive Nonlinearity of Coupled Hair Cells in the Frog Sacculus

Auditory and vestibular organs of non-mammals lack outer hair cells yet the organs all exhibit signs of an active process. Active hair bundle mobility has been proposed as the cellular basis for this amplification. Uncoupled hair cells in the bullfrog sacculus exhibit spontaneous mechanical oscillations and a compressive nonlinearity that agrees with theoretical predictions. Using a high-speed CMOS camera we are able to record the motion of many hair bundles in parallel in an in vitro preparation of the bullfrog sacculus. Spontaneous mechanical oscillations are not observed when the hair bundles are coupled to the otolithic membrane implying that the cells are in a quiescent rather than oscillatory regime. We explore the compressive nonlinearity of arrays of cells under native coupling conditions.

Spontaneous Oscillations of a Minimal Acto-Myosin System Under Elastic Loading

Spontaneous mechanical oscillations occur in various types of biological systems where groups of motor molecules are elastically coupled to their environment. By using an optical trap to oppose the gliding motion of a single bead-tailed actin filament over a substrate densely coated with heavy meromyosin molecules, we mimicked this condition in vitro. We show that this minimal acto-myosin system can oscillate spontaneously. Our finding accords quantitatively with a general theoretical framework where oscillatory instabilities emerge generically from the collective dynamics of molecular motors under load.

Spontaneous Oscillations of a Minimal Actomyosin System under Elastic Loading

Spontaneous mechanical oscillations occur in various types of biological systems where groups of motor molecules are elastically coupled to their environment. By using an optical trap to oppose the gliding motion of a single bead-tailed actin filament over a substrate densely coated with myosin motors, we mimicked this condition in vitro. We show that this minimal actomyosin system can oscillate spontaneously. Our finding accords quantitatively with a general theoretical framework where oscillatory instabilities emerge generically from the collective dynamics of molecular motors under load.

Stability of split Stirling refrigerators

In many thermal systems spontaneous mechanical oscillations are generated under the influence of large temperature gradients. Well-known examples are Taconis oscillations in liquid-helium cryostats and oscillations in thermoacoustic systems. In split Stirling refrigerators the compressor and the cold finger are connected by a flexible tube. The displacer in the cold head is suspended by a spring. Its motion is pneumatically driven by the pressure oscillations generated by the compressor. In this paper we give the basic dynamic equations of split Stirling refrigerators and investigate the possibility of spontaneous mechanical oscillations if a large temperature gradient develops in the cold finger, e.g. during or after cool down. These oscillations would be superimposed on the pressure oscillations of the compressor and could ruin the cooler performance.

Study of the mechanisms of hydrogen peroxide and hydroxyl free radical-induced cellular injury and calcium overload in cardiac myocytes

There is evidence that myocardial injury, as would occur on post-ischemic reperfusion, may be caused by the generation of oxygen radicals, as well as by the induction of intracellular calcium overload; however, the relationship between these two mechanisms of injury is not known. To test the hypothesis that oxidants and oxygen radicals can cause cardiac myocyte injury and intracellular calcium overload, isolated adult rat ventricular myocytes were exposed to H2O2 (1-10 mM) and Fe3(+)-nitrilotriacetate. EPR measurements confirmed the production of the highly reactive .OH radical by this system. The oxygen radical generating system initially caused a transient augmentation of twitch amplitude in single field stimulated myocytes. This was followed by contractile oscillations occurring during the twitch prior to full cell relaxation, and spontaneous mechanical oscillations occurring between electrically stimulated contractions. Eventually, cells became inexcitable and abruptly underwent contracture. In the presence of lower bathing calcium concentrations, these oxidant-induced alterations were prevented or delayed. However, cells exposed to the radical generating system in the absence of extracellular calcium still eventually underwent contracture but stimulated contractions or mechanical oscillations were not seen. Measurements in single myocytes loaded with the fluorescent probe of intracellular calcium, Indo-1, demonstrated a rise in both systolic and diastolic fluorescence ratio, as well as oscillations and widening of the fluorescence transient, suggestive of cellular calcium loading, following exposure to the radical generating system. Injured myocytes did not take up trypan blue dye. Contractile dysfunction and calcium channel blocker, nitrendipine. NMR measurements of cellular [ATP] demonstrated that these alterations in cellular calcium preceded the depletion of ATP. Subsequent depletion of ATP was accompanied by the appearance of increased concentrations of sugar phosphates indicative of a block in glycolysis and ATP depletion correlated with cellular rigor. Thus, oxygen free radicals can cause cardiac myocyte injury with contractile abnormalities which occur due to myocyte calcium loading. The mechanism of oxidant-induced calcium loading is not due to nonspecific membrane damage, or energy depletion, but rather due to increased calcium influx through voltage gated calcium channels. This early calcium overload state as well as oxidant induced block of glycolysis result in cellular energy depletion and cell death with the induction of contracture.