We investigate the instability and subsequent dynamics of a closed rod with twist and bend in a viscous, incompressible fluid. A new version of the immersed boundary (IB) method is used in which the immersed boundary applies torque as well as force to the surrounding fluid and in which the equations of motion of the immersed boundary involve the local angular velocity as well as the local linear velocity of the fluid. An important feature of the IB method in this context is that self-crossing of the rod is automatically avoided because the rod moves in a continuous (interpolated) velocity field. A rod with a uniformly distributed twist that has been slightly perturbed away from its circular equilibrium configuration is used as an initial condition, with the fluid initially at rest. If the twist in the rod is sufficiently small, the rod simply returns to its circular equilibrium configuration, but for larger twists that equilibrium configuration becomes unstable, and the rod undergoes large excursions before relaxing to a stable coiled configuration.

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SUMMARY Circadian clock-gated cell division cycles are observed from cyanobacteria to mammals via intracellular molecular connections between these two oscillators. Here we demonstrate WNT-mediated intercellular coupling between the cell cycle and circadian clock in 3D murine intestinal organoids (enteroids). The circadian clock gates a population of cells with heterogeneous cell-cycle times that emerge as 12-hr synchronized cell division cycles. Remarkably, we observe reduced-amplitude oscillations of circadian rhythms in intestinal stem cells and progenitor cells, indicating an intercellular signal arising from differentiated cells governing circadian clock-dependent synchronized cell division cycles. Stochastic simulations and experimental validations reveal Paneth cell-secreted WNT as the key intercellular coupling component linking the circadian clock and cell cycle in enteroids.

Abstract. When an elastic filament spins in a viscous incompressible fluid it may undergo a whirling instability, as studied asymptotically by Wolgemuth, Powers, and Goldstein [Phys. Rev. Lett., 84 (2000), pp. [16][17][18][19][20][21][22][23]. We use the immersed boundary (IB) method to study the interaction between the elastic filament and the surrounding viscous fluid as governed by the incompressible Navier-Stokes equations. This allows the study of the whirling motion when the shape of the filament is very different from the unperturbed straight state.Key words. twirling, whirling, overwhirling, immersed boundary method AMS subject classifications. 65-04, 65M06, 76D05, 76M20 DOI. 10.1137/S10648275024174771. Introduction. Dynamics of a rotationally forced filament with twist and bend elasticity at zero Reynolds number has been studied in [1]. These authors consider a slender elastic filament in a fluid of viscosity µ, rotated at one end with the other end free, and assume that its centerline is inextensible. Analytical and numerical methods reveal two dynamical regimes of motion depending on the rotation rate: twirling, in which the straight but twisted rod rotates about its centerline, and whirling, in which the centerline of the rod writhes and crankshafts around the rotation axis in a steady state. A critical frequency, ω c , separates whirling from twirling. In this paper, we present simulations of the same physical situation by the immersed boundary (IB) method. The IB method is useful for biofluid mechanical problems to simulate fluid-structure interaction in a viscous incompressible fluid. No approximations such as slender body theory [2] or small deformation are needed when the IB method is used. The IB method was developed to study flow patterns around heart valves [3,4,5] and has been applied to many problems of computational fluid dynamics [6,7,8,9,10,11].The computational model we are dealing with here is an elastic and neutrally buoyant filament having microarchitecture motivated by bacterial flagella [12,13]. It is composed of inner and outer layers with motors on the outer layer at the bottom. We assume that the fluid is governed by the Navier-Stokes equations [14,15,16] at a very low but nonzero Reynolds number.As in [1], we find a critical rotation frequency ω c , below which the straight state of the filament is stable. When the rotation rate of the filament is above ω c , however, we find a new phenomenon, which we call overwhirling. Overwhirling is the motion in which the tip of filament "falls down" and rotates around its rotation axis in a steady state. We notice that the behavior of filament is very sensitive to the spinning rate

Circadian clock mechanisms have been extensively investigated but the main rate-limiting step that determines circadian period remains unclear. Formation of a stable complex between clock proteins and CK1 is a conserved feature in eukaryotic circadian mechanisms. Here we show that the FRQ-CK1 interaction, but not FRQ stability, correlates with circadian period in Neurospora circadian clock mutants. Mutations that specifically affect the FRQ-CK1 interaction lead to severe alterations in circadian period. The FRQ-CK1 interaction has two roles in the circadian negative feedback loop. First, it determines the FRQ phosphorylation profile, which regulates FRQ stability and also feeds back to either promote or reduce the interaction itself. Second, it determines the efficiency of circadian negative feedback process by mediating FRQ-dependent WC phosphorylation. Our conclusions are further supported by mathematical modeling and in silico experiments. Together, these results suggest that the FRQ-CK1 interaction is a major rate-limiting step in circadian period determination.