Circadian clocks optimally adapt to sunlight for reliable synchronization

Circadian oscillation provides selection advantages through synchronization to the daylight cycle. However, a reliable clock must be designed through two conflicting properties: entrainability to synchronize internal time with periodic stimuli such as sunlight, and regularity to oscillate with a precise period. These two aspects do not easily coexist because better entrainability favors higher sensitivity, which may sacrifice the regularity. To investigate conditions for satisfying the two properties, we analytically calculated the optimal phase-response curve with a variational method. Our result indicates an existence of a dead zone, i.e., a time period during which input stimuli neither advance nor delay the clock. A dead zone appears only when input stimuli obey the time course of actual solar radiation but a simple sine curve cannot yield a dead zone. Our calculation demonstrates that every circadian clock with a dead zone is optimally adapted to the daylight cycle.Comment: 24 pages, 7 figure

Fluctuating noise drives Brownian transport

The transport properties of Brownian ratchet was studied in the presence of stochastic intensity noise (SIN) in both overdamped and underdamped regimes. In the overdamped case, analytical solution using the matrix continued fraction method revealed the existence of a maximum current when the noise intensity fluctuates on intermediate time scale regions. Similar effects were observed for the underdamped case by Monte Carlo simulations. The optimal time-correlation for the Brownian transport coincided with the experimentally observed time-correlation of the extrinsic noise in Esherichia coli gene expression and implied the importance of environmental noise for molecular mechanisms.Comment: 22 pages, 8 figure

Enhanced entrainability of genetic oscillators by period mismatch

Biological oscillators coordinate individual cellular components so that they function coherently and collectively. They are typically composed of multiple feedback loops, and period mismatch is unavoidable in biological implementations. We investigated the advantageous effect of this period mismatch in terms of a synchronization response to external stimuli. Specifically, we considered two fundamental models of genetic circuits: smooth- and relaxation oscillators. Using phase reduction and Floquet multipliers, we numerically analyzed their entrainability under different coupling strengths and period ratios. We found that a period mismatch induces better entrainment in both types of oscillator; the enhancement occurs in the vicinity of the bifurcation on their limit cycles. In the smooth oscillator, the optimal period ratio for the enhancement coincides with the experimentally observed ratio, which suggests biological exploitation of the period mismatch. Although the origin of multiple feedback loops is often explained as a passive mechanism to ensure robustness against perturbation, we study the active benefits of the period mismatch, which include increasing the efficiency of the genetic oscillators. Our findings show a qualitatively different perspective for both the inherent advantages of multiple loops and their essentiality.Comment: 28 pages, 13 figure

Coherent oscillations of a levitated birefringent microsphere in vacuum driven by nonconservative rotation-translation coupling

Funding: UK Engineering and Physical Sciences Research Council (EP/P030017/1) and Czech Science Agency (GA19-17765S).We demonstrate an effect whereby stochastic, thermal fluctuations combine with nonconservative optical forces to break detailed balance and produce increasingly coherent, apparently deterministic motion for a vacuum-trapped particle. The particle is birefringent and held in a linearly polarized Gaussian optical trap. It undergoes oscillations that grow rapidly in amplitude as the air pressure is reduced, seemingly in contradiction to the equipartition of energy. This behavior is reproduced in direct simulations and captured in a simplified analytical model, showing that the underlying mechanism involves nonsymmetric coupling between rotational and translational degrees of freedom. When parametrically driven, these self-sustained oscillators exhibit an ultranarrow linewidth of 2.2 μHz and an ultrahigh mechanical quality factor in excess of 2 × 108 at room temperature. Last, nonequilibrium motion is seen to be a generic feature of optical vacuum traps, arising for any system with symmetry lower than that of a perfect isotropic microsphere in a Gaussian trap.Publisher PDFPeer reviewe

Stochastic Hopf bifurcations in vacuum optical tweezers

Funding: We acknowledge the support from the Engineering and Physical Sciences Research Council (Grant No. EP/P030017/1), the European Regional Development Fund (Grant No. CZ.02.1.01/0.0/0.0/15_003/0000476), the Czech Science Foundation (Grant No. GA19-17765S), and the Czech Academy of Sciences (Praemium Academiae, Grant No. RVO:68081731).The forces acting on an isotropic microsphere in optical tweezers are effectively conservative. However, reductions in the symmetry of the particle or trapping field can break this condition. Here we theoretically analyse the motion of a particle in a linearly non-conservative optical vacuum trap, concentrating on the case where symmetry is broken by optical birefringence, causing non-conservative coupling between rotational and translational degrees of freedom. Neglecting thermal fluctuations, we first show that the underlying deterministic motion can exhibit a Hopf bifurcation in which the trapping point destabilizes and limit cycles emerge whose amplitude grows with decreasing viscosity. When fluctuations are included, the bifurcation of the underlying deterministic system is expressed as a transition in the statistical description of the motion. For high viscosities, the probability distribution is normal, with a kurtosis of three, and persistent probability currents swirl around the stable trapping point. As the bifurcation is approached the distribution and currents spread out in phase space. Following the bifurcation the probability distribution function hollows out, reflecting the underlying limit cycle, and the kurtosis halves abruptly. The system is seen to be a noisy self sustained oscillator featuring a highly uneven limit cycle. A variety of applications, from autonomous stochastic resonance to synchronization, are discussed.Publisher PDFPeer reviewe

Dynamics of a levitated microparticle in vacuum trapped by a perfect vortex beam : three-dimensional motion around a complex optical potential

We trap a single silica microparticle in a complex three dimensional optical potential with orbital angular momentum in vacuum. The potential is formed by the generation of a ``perfect vortex' in vacuum which, upon propagation, evolves to a Bessel light field. The optical gradient and scattering forces interplay with the inertial and gravitational forces acting on the trapped particle, including the rotational degrees of freedom. As a result the particle undergoes a complex trajectory, part of which is rotational motion in the plane of the "perfect vortex". As the particle explores the whole three dimensional volume and not solely restricted to one anchor point, we are able to determine the three dimensional optical potential in situ by tracking the particle. This represents the first demonstration of trapping a microparticle within a complex three dimensional optical potential in vacuum. This may open up new perspectives in levitated optomechanics with particle dynamics on complex trajectories.PostprintPeer reviewe

Rotation of two trapped microparticles in vacuum : observation of optically mediated parametric resonances

Funding: Engineering and Physical Sciences Research Council (EPSRC) (EP/J01771X/1).We demonstrate trapping and rotation of two mesoscopic particles in vacuum using a spatial-light-modulator-based approach to trap more than one particle, induce controlled rotation of individual particles, and mediate interparticle separation. By trapping and rotating two vaterite particles, we observe intensity modulation of the scattered light at the sum and difference frequencies with respect to the individual rotation rates. This first demonstration of optical interference between two microparticles in vacuum leads to a platform to potentially explore optical binding and quantum friction effects.PostprintPeer reviewe