Biological Rhythms Generated by a Single Activator-Repressor Loop with Inhomogeneity and Diffusion.

Common models of circadian rhythms are typically constructed as compartmental reactions of well-mixed biochemicals, incorporating a negative-feedback loop consisting of several intermediate reaction steps essentially required to produce oscillations. Spatial transport of each reactant is often represented as an extra compartmental reaction step. Contrary to this traditional understanding, in this Letter we demonstrate that a single activation-repression biochemical reaction pair is sufficient to generate sustained oscillations if the sites of both reactions are spatially separated and molecular transport is mediated by diffusion. Our proposed scenario represents the simplest configuration in terms of the participating chemical reactions and offers a conceptual basis for understanding biological oscillations and inspiring in vitro assays aimed at constructing minimal clocks.

Information, Coding, and Biological Function: The Dynamics of Life.

In the mid-20th century, two new scientific disciplines emerged forcefully: molecular biology and information-communication theory. At the beginning, cross-fertilization was so deep that the term genetic code was universally accepted for describing the meaning of triplets of mRNA (codons) as amino acids. However, today, such synergy has not taken advantage of the vertiginous advances in the two disciplines and presents more challenges than answers. These challenges not only are of great theoretical relevance but also represent unavoidable milestones for next-generation biology: from personalized genetic therapy and diagnosis to Artificial Life to the production of biologically active proteins. Moreover, the matter is intimately connected to a paradigm shift needed in theoretical biology, pioneered a long time ago, that requires combined contributions from disciplines well beyond the biological realm. The use of information as a conceptual metaphor needs to be turned into quantitative and predictive models that can be tested empirically and integrated in a unified view. Successfully achieving these tasks requires a wide multidisciplinary approach, including Artificial Life researchers, to address such an endeavour.

The fluid mechanics of poohsticks.

The year 2019 marked the bicentenary of George Gabriel Stokes, who in 1851 described the drag-Stokes drag-on a body moving immersed in a fluid, and 2020 is the centenary of Christopher Robin Milne, for whom the game of poohsticks was invented; his father A. A. Milne's The House at Pooh Corner, in which it was first described in print, appeared in 1928. So this is an apt moment to review the state of the art of the fluid mechanics of a solid body in a complex fluid flow, and one floating at the interface between two fluids in motion. Poohsticks pertains to the latter category, when the two fluids are water and air. This article is part of the theme issue 'Stokes at 200 (part 2)'.

Geometric mixing.

Mixing fluids often involves a periodic action, like stirring one's tea. But reciprocating motions in fluids at low Reynolds number, in Stokes flows where inertia is negligible, lead to periodic cycles of mixing and unmixing, because the physics, molecular diffusion excepted, is time reversible. So how can fluid be mixed in such circumstances? The answer involves a geometric phase. Geometric phases are found everywhere in physics as anholonomies, where after a closed circuit in the parameters, some system variables do not return to their original values. We discuss the geometric phase in fluid mixing: geometric mixing. This article is part of the theme issue 'Stokes at 200 (part 2)'.

Three-dimensional structure of the Z-ring as a random network of FtsZ filaments.

The spatial organization of the Z-ring, the central element of the bacterial division machinery, is not yet fully understood. Using optical tweezers and subpixel image analysis, we have recently shown that the radial width of the Z-ring in unconstricted Escherichia coli is about 100 nm. The relatively large width is consistent with the observations of others. Moreover, simulation of the experimental FtsZ distribution using the theoretical three-dimensional (3D) point spread function was strongly in favour of a toroidal rather than a thin cylindrical model of the Z-ring. Here, we show that the low density of FtsZ filaments in the ring coincides within experimental uncertainty with the critical density of a 3D random network of cylindrical sticks. This suggests that the Z-ring may consist of a percolating network of FtsZ filaments. Several factors that are expected to affect the polymerization state and the extent of self-interaction of FtsZ within the Z-ring, as well as the functional implications of its sparse toroidal structure, are discussed in terms of percolation theory.

Excitability and optical pulse generation in semiconductor lasers driven by resonant tunneling diode photo-detectors.

We demonstrate, experimentally and theoretically, excitable nanosecond optical pulses in optoelectronic integrated circuits operating at telecommunication wavelengths (1550 nm) comprising a nanoscale double barrier quantum well resonant tunneling diode (RTD) photo-detector driving a laser diode (LD). When perturbed either electrically or optically by an input signal above a certain threshold, the optoelectronic circuit generates short electrical and optical excitable pulses mimicking the spiking behavior of biological neurons. Interestingly, the asymmetric nonlinear characteristic of the RTD-LD allows for two different regimes where one obtain either single pulses or a burst of multiple pulses. The high-speed excitable response capabilities are promising for neurally inspired information applications in photonics.

Runaway electrification of friable self-replicating granular matter.

We establish that the nonlinear dynamics of collisions between particles favors the charging of an insulating, friable, self-replicating granular material that undergoes nucleation, growth, and fission processes; we demonstrate with a minimal dynamical model that secondary nucleation produces a positive feedback in an electrification mechanism that leads to runaway charging. We discuss ice as an example of such a self-replicating granular material: We confirm with laboratory experiments in which we grow ice from the vapor phase in situ within an environmental scanning electron microscope that charging causes fast-growing and easily breakable palmlike structures to form, which when broken off may form secondary nuclei. We propose that thunderstorms, both terrestrial and on other planets, and lightning in the solar nebula are instances of such runaway charging arising from this nonlinear dynamics in self-replicating granular matter.

Modeling the resonant release of synaptic transmitter by hair cells as an example of biological oscillators with cooperative steps.

The initial synapses of the auditory system, which connect hair cells to afferent nerve fibers, display two unusual features. First, synaptic transmission occurs in a multiquantal fashion: the contents of multiple synaptic vesicles are discharged simultaneously. Second, synaptic transmission may be tuned to specific frequencies of stimulation. We developed a minimal theoretical model to explore the possibility that hair-cell synapses achieve both multiquantal release and frequency selectivity through a cooperative mechanism for the exocytotic release of neurotransmitter. We first characterized vesicle release as a four-step cycle at each release site, then generalized the result to an arbitrary number of steps. The cyclic process itself induces some degree of resonance, and may display a stable, underdamped fixed point of the release dynamics associated with a pair of complex eigenvalues. Cooperativity greatly enhances the frequency selectivity by moving the eigenvalues toward the imaginary axis; spontaneously oscillatory release can arise beyond a Hopf bifurcation. These phenomena occur both in the macroscopic limit, when the number of release sites involved is very large, and in the more realistic stochastic regime, when only a limited number of release sites participate at each synapse. It is thus possible to connect multiquantal release with frequency selectivity through the mechanism of cooperativity.

Ice polyamorphism in the minimal Mercedes-Benz model of water.

We investigate ice polyamorphism in the context of the two-dimensional Mercedes-Benz model of water. We find a first-order phase transition between a crystalline phase and a high-density amorphous phase. Furthermore, we find a reversible transformation between two amorphous structures of high and low density; however, we find this to be a continuous and not an abrupt transition, as the low-density amorphous phase does not show structural stability. We discuss the origin of this behavior and its implications with regard to the minimal generic modeling of polyamorphism.

Chemosensing versus mechanosensing in nodal and Kupffer's vesicle cilia and in other left-right organizer organs.

How is sensing carried out by cilia in the mouse node, zebrafish Kupffer's vesicle and similar left-right (LR) organizer organs in other species? Two possibilities have been put forward. In the former, cilia would detect some chemical species in the fluid; in the latter, they would detect fluid flow. In either case, the hypothesis is that an imbalance would be detected between this signalling coming from cilia on the left and right sides of the organizer, which would initiate a cascade of signals leading ultimately to the breaking of LR symmetry in the developing body plan of the organism. We review the evidence for both hypotheses. This article is part of the Theo Murphy meeting issue 'Unity and diversity of cilia in locomotion and transport'.

Fluid dynamics of establishing left-right patterning in development.

How does the clockwise motion of tens of monocilia drive a leftward flow in the node? And, as the observed flow is leftward, how is the fluid recirculating within the node, as it must, because the node is a closed structure? How does the nodal flow lead to left-right symmetry breaking in the embryo? These questions are within the realm of fluid physics, whose application to the problem of left-right symmetry breaking in vertebrates has led to important advances in the field.

Dynamics of tidal synchronization and orbit circularization of celestial bodies.

We take a dynamical-systems approach to study the qualitative dynamical aspects of the tidal locking of the rotation of secondary celestial bodies with their orbital motion around the primary. We introduce a minimal model including the essential features of gravitationally induced elastic deformation and tidal dissipation that demonstrates the details of the energy transfer between the orbital and rotovibrational degrees of freedom. Despite its simplicity, our model can account for both synchronization into the 1:1 spin-orbit resonance and the circularization of the orbit as the only true asymptotic attractors, together with the existence of relatively long-lived metastable orbits with the secondary in p:q synchronous rotation.

Embryonic nodal flow and the dynamics of nodal vesicular parcels.

We address with fluid-dynamical simulations using direct numerical techniques three important and fundamental questions with respect to fluid flow within the mouse node and left-right development. First, we consider the differences between what is experimentally observed when assessing cilium-induced fluid flow in the mouse node in vitro and what is to be expected in vivo. The distinction is that in vivo, the leftward fluid flow across the mouse node takes place within a closed system and is consequently confined, while this is no longer the case on removing the covering membrane and immersing the embryo in a fluid-filled volume to perform in vitro experiments. Although there is a central leftward flow in both instances, we elucidate some important distinctions about the closed in vivo situation. Second, we model the movement of the newly discovered nodal vesicular parcels (NVPs) across the node and demonstrate that the flow should indeed cause them to accumulate on the left side of the node, as required for symmetry breaking. Third, we discuss the rupture of NVPs. Based on the biophysical properties of these vesicles, we argue that the morphogens they contain are likely not delivered to the surrounding cells by their mechanical rupture either by the cilia or the flow, and rupture must instead be induced by an as yet undiscovered biochemical mechanism.

Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach.

Mixing fluid in a container at low Reynolds number--in an inertialess environment--is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the "belly phase," peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing.

Bailout embeddings, targeting of invariant tori, and the control of Hamiltonian chaos.

We introduce a technique, which we term bailout embedding, that can be used to target orbits having particular properties out of all orbits in a flow or map. We explicitly construct a bailout embedding for Hamiltonian systems so as to target invariant tori. We show how the bailout dynamics are able to lock onto extremely small regular islands in a chaotic sea.

Experimental evidence of van der Pol-Fitzhugh-Nagumo dynamics in semiconductor optical amplifiers.

Thermo-optical pulsing in semiconductor amplifiers is experimentally shown to correspond to a very common excitable scenario (the van der Pol-Fitzhugh-Nagumo system). Self-sustained oscillations appear in the sequence predicted by this simple dynamical model as we change either the injection level or the bias current. Periodic modulation of these parameters leads to the characteristic phase-locking structure. Furthermore, coherence resonance is observed when external noise is added to the system.

Effective dimensions and percolation in hierarchically structured scale-free networks.

We introduce appropriate definitions of dimensions in order to characterize the fractal properties of complex networks. We compute these dimensions in a hierarchically structured network of particular interest. In spite of the nontrivial character of this network that displays scale-free connectivity among other features, it turns out to be approximately one dimensional. The dimensional characterization is in agreement with the results on statistics of site percolation and other dynamical processes implemented on such a network.

Bubbling and on-off intermittency in bailout embeddings.

We establish and investigate the conceptual connection between the dynamics of the bailout embedding of a Hamiltonian system and the dynamical regimes associated with the occurrence of bubbling and blowout bifurcations. The roles of the invariant manifold and the dynamics restricted to it, required in bubbling and blowout bifurcating systems, are played in the bailout embedding by the embedded Hamiltonian dynamical system. The Hamiltonian nature of the dynamics is precisely the distinctive feature of this instance of a bubbling or blowout bifurcation. The detachment of the embedding trajectories from the original ones can thus be thought of as transient on-off intermittency, and noise-induced avoidance of some regions of the embedded phase space can be recognized as Hamiltonian bubbling.

Excitable media in open and closed chaotic flows.

We investigate the response of an excitable medium to a localized perturbation in the presence of a two-dimensional smooth chaotic flow. Two distinct types of flows are numerically considered: open and closed. For both of them three distinct regimes are found, depending on the relative strengths of the stirring and the rate of the excitable reaction. In order to clarify and understand the role of the many competing mechanisms present, simplified models of the process are introduced. They are one-dimensional baker-map models for the flow and a one-dimensional approximation for the transverse profile of the filaments observed in the concentration patterns.

Subharmonic stochastic synchronization and resonance in neuronal systems.

We study the response of a model neuron, driven simultaneously by noise and at least two weak periodic signals. We focus on signals with frequencies components kf(0),(k+1)f(0),...(k+n)f(0) with k>1. The neuron's output is a sequence of pulses spaced at random interpulse intervals. We find an optimum input noise intensity for which the output pulses are spaced approximately 1/f(0), i.e., there is a stochastic resonance (SR) at a frequency missing in the input. Even higher noise intensities uncover additional, but weaker, resonances at frequencies present in the input. This is a different form of SR whereby the most robust resonance is the one enhancing a frequency, which is absent in the input, and which is not possible to recover via any linear processing. This can be important in understanding sensory systems including the neuronal mechanism for perception of complex tones.