Flat leaf formation realized by cell-division control and mutual recessive gene regulation.

Most of the land plants generally have dorsoventrally flat leaves, maximizing the surface area of both upper (adaxial) side and lower (abaxial) side. The former is specialized for light capturing for photosynthesis and the latter is specialized for gas exchange. From findings of molecular genetics, it has been considered that the coupled dynamics between tissue morphogenesis and gene regulation for cell identity is responsible for making flat leaves. The hypothesis claims that a flat leaf is generated under two assumptions, (i) two mutually recessive groups of genes specify adaxial and abaxial sides of a leaf, (ii) cell divisions are induced at the limited region in the leaf margin where both of two groups are expressed. We examined the plausibility and possibility of this hypothesis from the dynamical point of view. We studied a mathematical model where two processes are coupled, tissue morphogenesis induced by cell division and deformation, and dynamics of gene regulations. From the analysis of the model we found that the classically believed hypothesis is not sufficient to generate flat leaves with high probability. We examined several different modifications and revision of the model. Then we found that a simple additional rule of polarized cell division facilitates flat leaf formation. The result of our analysis gives prediction of possible mechanism, which can be easily verified in experiments.

Mathematical study for the mechanism of vascular and spot patterns by auxin and pin dynamics in plant development.

Inhomogeneous distribution of auxin is essential in various differentiation processes of plant development. Auxin transfer between cells by efflux carrier protein called PINFORMED (PIN) has been considered to be responsible for inhomogeneous distribution of auxin. Two major types of auxin distribution patterns are "spot" patterns and "passage" patterns, which are responsible for determining the position of the primordia of a leaf or flower in shoot apical meristem and formation of leaf veins, respectively. In this study, we studied the pattern formation of auxin distribution mediated by polarization of PIN using mathematical methods. We developed several different models which show possible interaction mechanisms between auxin and PIN on 2-dimentional hexagonal cellular lattice, (1) Basic auxin flux model, (2) auxin-dependent PIN degradation model and (3) auxin self-feedback model. We analyzed these models by numerical calculation and mathematical analysis. From intensive numerical calculations under different conditions, we found that some models show three different types of pattern formations in dynamics, (a) homogeneous, (b) passage and (c) spot pattern depending on parameter condition. We analyzed these models mathematically using approximation of 1-dimensional periodic space. We determined the conditions that passage and spot patterns are generated in each model, respectively. After these analyses, we propose possible mechanisms by which plants switch passage and spot patterns in different organs by small modification.

Spatio-temporal structure of hooded gull flocks.

We analyzed the spatio-temporal structure of hooded gull flocks with a portable stereo camera system. The 3-dimensional positions of individuals were reconstructed from pairs of videos. The motions of each individual were analyzed, and both gliding and flapping motions were quantified based on the velocity time series. We analyzed the distributions of the nearest neighbor's position in terms of coordinates based on each individual's motion. The obtained results were consistent with the aerodynamic interaction between individuals. We characterized the leader-follower relationship between individuals by a delay time to mimic the direction of a motion. A relation between the delay time and a relative position was analyzed quantitatively, which suggested the basic properties of the formation flight that maintains order in the flock.

Group-size distribution of skeins of wild geese.

In appropriate situations, large populations of geese exhibit dynamical rearrangements by repeated mergers and splits among the groups. We describe the grouping process in terms of a mean-field model based on the Smoluchowski equation of coagulation with fragmentation and observationally plausible kernels. To verify our model, we conducted field observations on skeins of airborne geese, noting both the group-size distribution and the group-forming processes. We found that the group-size distribution we obtained in our field measurements could be represented by a fractional power function with an exponential cutoff. This function matches the asymptotic form of the steady-state solution of our model. Furthermore, we estimated the effective number of individuals involved in interactions by comparison of the model to our field data.

Oscillatory instability in slow crack propagation in rubber under large deformation.

We performed experiments to investigate slow fracture in thin rubber films under uniaxial tension using high-viscosity oils. In this system we observed an oscillating instability in slowly propagating cracks for small applied strains. The transition between oscillatory and straight patterns occurred near the characteristic strain at which rubber exhibits a nonlinear stress-strain relation. This suggests that nonlinear elasticity plays an important role in the formation of the observed pattern. This was confirmed by numerical simulation for neo-Hookean and linear elasticity models.

A quorum-sensing factor in vegetative Dictyostelium discoideum cells revealed by quantitative migration analysis.

BACKGROUND: Many cells communicate through the production of diffusible signaling molecules that accumulate and once a critical concentration has been reached, can activate or repress a number of target genes in a process termed quorum sensing (QS). In the social amoeba Dictyostelium discoideum, QS plays an important role during development. However little is known about its effect on cell migration especially in the growth phase. METHODS AND FINDINGS: To investigate the role of cell density on cell migration in the growth phase, we use multisite timelapse microscopy and automated cell tracking. This analysis reveals a high heterogeneity within a given cell population, and the necessity to use large data sets to draw reliable conclusions on cell motion. In average, motion is persistent for short periods of time (t ≤ 5 min), but normal diffusive behavior is recovered over longer time periods. The persistence times are positively correlated with the migrated distances. Interestingly, the migrated distance decreases as well with cell density. The adaptation of cell migration to cell density highlights the role of a secreted quorum sensing factor (QSF) on cell migration. Using a simple model describing the balance between the rate of QSF generation and the rate of QSF dilution, we were able to gather all experimental results into a single master curve, showing a sharp cell transition between high and low motile behaviors with increasing QSF. CONCLUSION: This study unambiguously demonstrates the central role played by QSF on amoeboid motion in the growth phase.

Memory effects on scale-free dynamics in foraging Drosophila.

The fruit fly, Drosophila melanogaster, displays a scale-free behavior in foraging, i.e., the dwell time on food exhibits a power law distribution. The scaling exponent is generally believed to be stable and the significance of the exponent itself with respect to the scale-free behavior remains elusive. We propose a model whereby the scaling exponent of the scale-free behavior of an animal depends on the memory of the individual. The proposed model is based on the premise that animal behaviors are associated with internal states of the animal. The changes in the scaling exponent are derived by considering losing memory as increasing uncertainty, which is expressed in terms of information entropy of the internal states. Predicted model behaviors agree with experimental results of foraging behavior in wild-type and learning/memory Drosophila mutants. The concept of changes in the scaling exponent due to the amount of memory provides a novel insight into the emergence of a scale-free behavior and the meaning of the scaling exponent.

Bending-filament model for the buckling and coiling instability of a viscous fluid rope.

A simple model is proposed for the buckling and coiling instability of a viscous "fluid rope" falling on a plane. By regarding a fluid rope as a one-dimensional flow, this model accounts for only the axial and shared viscous forces. Our model successfully reproduces several experiments with no adjustable parameters, such as the existence of three distinct coiling regimes reported in the paper by Maleki [Phys. Rev. Lett. 93, 214502 (2004)]. Our model allows for the discussion of unsteady motion. An expression for the critical fall height at which the coiling frequency changes from a decrease to increase was phenomenologically derived. It was found that the coil-uncoil transition shows remarkable hysteresis only for weak gravity condition.

Coevolutionary networks with homophily and heterophily.

We have investigated a simple coevolutionary network model incorporating three processes-changes of opinions, homophily, and heterophily. In this model, each node holds one of G opinions and changes its opinion, as in the voter model. Homophily is the tendency for connections to form between individuals of the same opinions and heterophily is the opposite effect. If there is no heterophily, this model corresponds to the Holme and Newman model [Phys. Rev. E 74, 056108 (2006)]. We show that the behavior of this model without heterophily can be understood in terms of a mean field approximation. We also find that this model with heterophily exhibits topologically complicated behaviors such as the small-world property.

Adaptation-induced collective dynamics of a single-cell protozoan.

We investigate the behavior of a single-cell protozoan in a narrow tubular ring. This environment forces them to swim under a one-dimensional periodic boundary condition. Above a critical density, single-cell protozoa aggregate spontaneously without external stimulation. The high-density zone of swimming cells exhibits a characteristic collective dynamics including translation and boundary fluctuation. We analyzed the velocity distribution and turn rate of swimming cells and found that the regulation of the turing rate leads to a stable aggregation and that acceleration of velocity triggers instability of aggregation. These two opposing effects may help to explain the spontaneous dynamics of collective behavior. We also propose a stochastic model for the mechanism underlying the collective behavior of swimming cells.

Waveform simulation based on 3D dose distribution for acoustic wave generated by proton beam irradiation.

A pulsed proton beam is capable of generating an acoustic wave when it is absorbed by a medium. This phenomenon suggests that the acoustic waveform produced may well include information on the three-dimensional (3D) dose distribution of the proton beam. We simulated acoustic waveforms by using a transmission model based on the Green function and the 3D dose distribution. There was reasonable agreement between the calculated and measured results. The results obtained confirm that the acoustic waveform includes information on the dose distribution.

Theoretical and numerical approach to "magic angle" of stone skipping.

We investigate the condition for the bounce of circular disks which obliquely impacts on the fluid surface. An experiment [C. Clanet, F. Hersen, and L. Bocquet, Nature (London) 427, 29 (2004)] revealed that there exists a "magic angle" of 20 degrees between a disk's face and water surface in which the condition of the lowest impact speed necessary for a bounce is minimized. We perform a three-dimensional simulation of the disk-water impact by means of the smoothed particle hydrodynamics. Furthermore, we analyze the impact with a model of the ordinary differential equation (ODE). Our simulation is in good agreement with the experiment. The analysis with the ODE model gives us a theoretical insight into the "magic angle" of stone skipping.

Collision of one-dimensional nonlinear chains.

We investigate one-dimensional collisions of unharmonic chains and a rigid wall. We find that the coefficient of restitution (COR) is strongly dependent on the velocity of colliding chains and has a minimum value at a certain velocity. The relationship between COR and collision velocity is derived for low-velocity collisions using perturbation methods. We found that the velocity dependence is characterized by the exponent of the lowest unharmonic term of interparticle potential energy.