We discuss a two-dimensional model for the dynamics of axonemal deformations driven by internally generated forces of molecular motors. Our model consists of an elastic filament pair connected by active elements. We derive the dynamic equations for this system in presence of internal forces. In the limit of small deformations, a perturbative approach allows us to calculate filament shapes and the tension profile. We demonstrate that periodic filament motion can be generated via a self-organization of elastic filaments and molecular motors. Oscillatory motion and the propagation of bending waves can occur for an initially non-moving state via an instability termed Hopf bifurcation. Close to this instability, the behavior of the system is shown to be independent of microscopic details of the axoneme and the force-generating mechanism. The oscillation frequency however does depend on properties of the molecular motors. We calculate the oscillation frequency at the bifurcation point and show that a large frequency range is accessible by varying the axonemal length between 1 and 50µm. We calculate the velocity of swimming of a flagellum and discuss the effects of boundary conditions and externally applied forces on the axonemal oscillations.

We introduce the concept of self-tuned criticality as a general mechanism for signal detection in sensory systems. In the case of hearing, we argue that active amplification of faint sounds is provided by a dynamical system that is maintained at the threshold of an oscillatory instability. This concept can account for the exquisite sensitivity of the auditory system and its wide dynamic range as well as its capacity to respond selectively to different frequencies. A specific model of sound detection by the hair cells of the inner ear is discussed. We show that a collection of motor proteins within a hair bundle can generate oscillations at a frequency that depends on the elastic properties of the bundle. Simple variation of bundle geometry gives rise to hair cells with characteristic frequencies that span the range of audibility. Tension-gated transduction channels, which primarily serve to detect the motion of a hair bundle, also tune each cell by admitting ions that regulate the motor protein activity. By controlling the bundle's propensity to oscillate, this feedback automatically maintains the system in the operating regime where it is most sensitive to sinusoidal stimuli. The model explains how hair cells can detect sounds that carry less energy than the background noise. Detecting the sounds of the outside world imposes stringent demands on the design of the inner ear, where the transduction of acoustic stimuli to electrical signals takes place (1). Each of the hair cells within the cochlea, which act as mechanosensors, must be responsive to a particular frequency component of the auditory input. Moreover, these sensors need the utmost sensitivity, because the weakest audible sounds impart an energy, per cycle of oscillation, which is no greater than that of thermal noise (2). At the same time, they must operate over a wide range of volumes, responding and adapting to intensities that vary by many orders of magnitude. Clearly, some form of nonlinear amplification is necessary in sound detection. The familiar resonant gain of a passive elastic system is far from sufficient for the required demands because of the heavy viscous damping at microscopic scales (3). Instead, the cochlea has developed active amplificatory processes, whose precise nature remains to be discovered.There is strong evidence that the cochlea contains forcegenerating dynamical systems that are capable of executing oscillations of a characteristic frequency (4-10). In general, such a system exhibits a Hopf bifurcation (11): as the value of a control parameter is varied, the behavior abruptly changes from a quiescent state to self-sustained oscillations. When the system is in the immediate vicinity of the bifurcation, it can act as a nonlinear amplifier for sinusoidal stimuli close to the characteristic frequency. That such a phenomenon might occur in hearing was first proposed by Gold (3) more than 50 years ago. The idea was recently revived by Choe, Magnasco, and Hudspeth (12) in the context of a specific model of the hair cell. No gene...

We study a simple two-dimensional model for motion of an elastic filament subject to internally generated stresses and show that wavelike propagating shapes which can propel the filament can be induced by a self-organized mechanism via a dynamic instability. The resulting patterns of motion do not depend on the microscopic mechanism of the instability but only of the filament rigidity and hydrodynamic friction. Our results suggest that simplified systems, consisting only of molecular motors and filaments, could be able to show beating motion and self-propulsion. [S0031-9007(99)08456-2] PACS numbers: 87.10. + e, 02.30.Jr, 46.25.Cc, 47.15.Gf Cilia and flagella are hairlike appendages of many cells which generate motion and are used for self-propulsion and to stir the surrounding fluid. They all share the characteristic architecture of their core structure, the axoneme, a common structural motive that was developed early in evolution. It is characterized by nine parallel pairs of microtubules, which are long and rigid protein filaments, that are arranged in a circular fashion together with a large number of dynein molecular motors [1]. In the presence of adenosine triphosphate (ATP) which is a fuel, the dynein motors attached to the microtubules generate relative forces while acting on neighboring microtubules; the resulting internal stresses induce relative sliding motion of filaments which leads to the propagation of bending waves [1,2].These biological systems are complex; they consist of a large number of different components and various patterns of motion have been observed. Attempts to model their behavior are either based on the assumption that some unknown control system generates oscillatory motor activity [3] or that a self-organized mechanism is at work [4,5]. Generically, the latter involves a dynamical instability. Theoretical studies of simple models for collective action of molecular motors have demonstrated the possibility of such instabilities [4,[6][7][8]. Several examples of oscillatory motion of biological many-motor systems are known. Recently, it was suggested that spontaneous oscillations observed in muscles could be a property of the motor-filament system alone [7,9]. This idea is supported by the fact that the oscillations continue to exist after all regulatory systems are removed [9] but also by the observation that an in vitro motor-filament system shows the signature of a dynamic transition [10]. Furthermore, the observations that flagellar dyneins are able to generate oscillatory motion on microtubules [11] and that isolated and demembranated flagella in solution containing ATP above a threshold concentration swim with a simple wavelike motion [12] support the idea that basic types of flagellar beating could result from a dynamic instability. Eventually, the beating motion of flagella such as those of sea urchin sperms is planar, which suggests that basic properties can already be captured in a two-dimensional description [2].In this article, we introduce a simple two-dimensional mode...

The theory for current fluctuations in ac-driven transport through nanoscale systems is put forward. By use of a generalized, non-Hermitian Floquet theory we derive novel explicit expressions for the time-averaged current and the zero-frequency component of the power spectrum of current fluctuations. A distinct suppression of both the zero-frequency noise and the dc-current occurs for suitably tailored ac-fields. The relative level of transport noise, being characterized by a Fano factor, can selectively be manipulated by ac-sources; in particular, it exhibits both characteristic maxima and minima near current suppression.PACS numbers: 05.60. Gg, 85.65.+h, 72.40.+w Recent experimental successes in the coherent coupling of quantum dots [1] and in the reproducible measurement of electronic currents through molecules [2,3] have given rise to renewed theoretical interest in the transport properties of nanoscale systems [4,5]. Thereby, new ideas in order to exploit the quantum coherence of such systems for the construction of novel electronic devices [5] have emerged. One possible construction element is based on the manipulation of quantum dots or single molecules by use of an oscillating gate voltage or an infrared laser, respectively. A prominent effect of such ac-fields consists in the adiabatic [6,7,8,9] and nonadiabatic [10, 11] pumping of electrons. Moreover, laser irradiated molecular wires provide novel devices such as coherent quantum rectifiers [12] and optically controlled transistors [13]. However, such time-dependent control schemes can be valuable in practice only if they operate at tolerable noise levels. Thus, the question whether noise properties of nanoscale systems can be selectively manipulated becomes of foremost interest.Electron transport through time-independent, mesoscopic systems is commonly described within the framework of a scattering formalism. Both the average current [14] and the transport noise characteristics [15,16] can be expressed in terms of the quantum transmission coefficients for the corresponding transport channels. By contrast, the theory for driven quantum transport is much less developed. Expressions for the spectral density of the current fluctuations have been derived for the low-frequency ac-conductance [17] and the scattering by a slowly time-dependent potential [18]. However, the situation becomes more opaque in the presence of rapidly varying time-dependent fields. Within a Green function approach, a formal expression for the current through a time-dependent conductor has been presented in Refs. [19,20]. Here, we derive explicit expressions for both the current and the noise properties of electron transport through a nanoscale conductor under the influence of time-dependent forces at arbitrary frequency and strength. The dynamics of the electrons is solved by integrating the Heisenberg equations of motion for the electron creation/annihilation operators within a generalized Floquet approach. We then use the resulting expressions to explore the possibility of an ...

We investigate the possibility of optical current control through single molecules which are weakly coupled to leads. A master equation approach for the transport through a molecule is combined with a Floquet theory for the timedependent molecule. This yields an efficient numerical approach to the evaluation of the current through time-dependent nano-structures in the presence of a finite external voltage. We propose tunable optical current switching in two-and three-terminal molecular electronic devices driven by properly adjusted laser fields, i.e., a novel class of molecular transistors.

We derive within a time-dependent scattering formalism expressions for both the current through ac-driven nanoscale conductors and its fluctuations. The results for the time-dependent current, its time average, and, above all, the driven shot noise properties assume an explicit and serviceable form by relating the propagator to a non-Hermitian Floquet theory. The driven noise cannot be expressed in terms of transmission probabilities. The results are valid for a driving of arbitrary strength and frequency. The connection with commonly known approximation schemes such as the Tien-Gordon approach or a high-frequency approximation is elucidated together with a discussion of the corresponding validity regimes. Within this formalism, we study the coherent suppression of current and noise caused by properly chosen electromagnetic fields.

We study the current and the associated noise for the transport through a two-site molecule driven by an external oscillating field. Within a high-frequency approximation, the time-dependent Hamiltonian is mapped to a static one with effective parameters that depend on the driving amplitude and frequency. This analysis allows an intuitive physical picture explaining the nontrivial structure found in the noise properties as a function of the driving amplitude. The presence of dips in the Fano factor permits a control of the noise level by means of an appropriate external driving.

Bundles of polar filaments which interact via active elements can exhibit complex dynamic behaviors. By using a simple and general description for the bundle dynamics, we find regimes for which density profiles propagate as solitary waves with a characteristic velocity along the bundle. These behaviors emerge from an interplay of local contractions in the bundle and relative sliding of oppositely oriented filaments. By introducing filament binding to and detachment from a substrate, the system is able to generate net motion as a self-organization phenomenon.