Acellular matrix derived from rat liver improves the functionality of rat pancreatic islets before or after vitrification.

Cryopreservation of pancreatic islets can overcome the severe shortage of islet donors in clinical islet transplantation, but the impaired quality of post-warm islets need improvement. This present study was conducted to investigate whether the pre- or post-treatment of rat islets with liver decellularized matrix (LDM) for vitrification can improve the viability (FDA/PI double staining) and the functionality (glucose-stimulated insulin secretion [GSIS] assay). Rat LDM was prepared by high-hydrostatic pressure, lyophilization, and re-suspension in saline. Co-culturing of isolated islets with 0 (control), 30, 60, or 90 µg/ml LDM for 24 h resulted in the comparable viability among the 4 groups (98.7-99.6%) and the higher insulin secretion potential in 30 and 60 µg/ml LDM treatment groups than the control group (stimulation index [SI]: 12.1 and 12.7, respectively, vs. 6.5 in the control group, P < 0.05). When the islets co-cultured with 60 µg/ml LDM were vitrified-warmed on a nylon mesh cryodevice, the viability and the GSIS of the post-warm islets were not improved. Post-treatment of vitrified-warmed islets with 60 µg/ml LDM during the recovery culture for 12 h resulted in the comparable clearance of degenerating cell debris from the post-warm islets, while their insulin secretion potential was improved (SI: 5.0 vs. 3.5 in the control group, P < 0.05). These findings indicate that the components in LDM can enhance the insulin secretion potential of rat islets suffering damage by enzymatic stress during the islet isolation process or by cryoinjuries during the vitrification-warming process.

Large-scale vortex lattice emerging from collectively moving microtubules.

Spontaneous collective motion, as in some flocks of bird and schools of fish, is an example of an emergent phenomenon. Such phenomena are at present of great interest and physicists have put forward a number of theoretical results that so far lack experimental verification. In animal behaviour studies, large-scale data collection is now technologically possible, but data are still scarce and arise from observations rather than controlled experiments. Multicellular biological systems, such as bacterial colonies or tissues, allow more control, but may have many hidden variables and interactions, hindering proper tests of theoretical ideas. However, in systems on the subcellular scale such tests may be possible, particularly in in vitro experiments with only few purified components. Motility assays, in which protein filaments are driven by molecular motors grafted to a substrate in the presence of ATP, can show collective motion for high densities of motors and attached filaments. This was demonstrated recently for the actomyosin system, but a complete understanding of the mechanisms at work is still lacking. Here we report experiments in which microtubules are propelled by surface-bound dyneins. In this system it is possible to study the local interaction: we find that colliding microtubules align with each other with high probability. At high densities, this alignment results in self-organization of the microtubules, which are on average 15 µm long, into vortices with diameters of around 400 µm. Inside the vortices, the microtubules circulate both clockwise and anticlockwise. On longer timescales, the vortices form a lattice structure. The emergence of these structures, as verified by a mathematical model, is the result of the smooth, reptation-like motion of single microtubules in combination with local interactions (the nematic alignment due to collisions)--there is no need for long-range interactions. Apart from its potential relevance to cortical arrays in plant cells and other biological situations, our study provides evidence for the existence of previously unsuspected universality classes of collective motion phenomena.

Arnold tongue of electrochemical nonlinear oscillators.

We study the Arnold tongue of a nonlinear electrochemical oscillator entrained to an electrical periodic forcing. In our system, the width of the 1:3 entrainment region was broader than that of the 1:2 region. The 1:1 and 1:3 regions became monotonically broad when the conductance of the electrode cell was increased by the electrochemical redox reaction of Fe(CN)(6)(4-) <==> Fe(CN)(6)(3-) + e. In contrast, the 1:2 region changed nonmonotonically. In particular, the rate of change in the 1:2 region was greater than those of the 1:1 and 1:3 regions. These experimental results were qualitatively reproduced by the use of phase response curves of a corresponding mathematical model. We also discuss higher harmonics included in a limit cycle describing the isolated oscillator, dependence on the redox reaction, and hysteresis due to a bistability.

Global structure in spatiotemporal chaos of the Matthews-Cox equations.

We find that an amplitude death state and a spatiotemporally chaotic state coexist spontaneously in the Matthews-Cox equations and this coexistence is robust. Although the entire system is far from equilibrium, the domain wall between the two states is stabilized by a negative-feedback effect due to a conservation law. This is analogous to the phase separation in conserved systems that exhibit spinodal decompositions. We observe similar phenomena also in the Nikolaevskii equation, from which the Matthews-Cox equations were derived. A Galilean invariance of the former equation corresponds to the conservation law of the latter equations.

Critical exponents of Nikolaevskii turbulence.

We study the spatial power spectra of Nikolaevskii turbulence in one-dimensional space. First, we show that the energy distribution in wave-number space is extensive in nature. Then, we demonstrate that, when varying a particular parameter, the spectrum becomes qualitatively indistinguishable from that of Kuramoto-Sivashinsky turbulence. Next, we derive the critical exponents of turbulent fluctuations. Finally, we argue that in some previous studies, parameter values for which this type of turbulence does not appear were mistakenly considered, and we resolve inconsistencies obtained in previous studies.

Chemical turbulence equivalent to Nikolavskii turbulence.

We find evidence that a certain class of reaction-diffusion (RD) systems can exhibit chemical turbulence equivalent to Nikolaevskii turbulence. We study an extended complex Ginzburg-Landau (CGL) equation derived from this class of RD systems. First, we show numerically that the power spectrum of this CGL equation, in the neighborhood of a codimension-two Turing-Benjamin-Feir point, is qualitatively quite similar to that of the Nikolaevskii equation. Then, we demonstrate that the Nikolaevskii equation can in fact be obtained from this CGL equation through a phase reduction procedure.

Complex Ginzburg-Landau equation with nonlocal coupling.

A Ginzburg-Landau-type equation with nonlocal coupling is derived systematically as a reduced form of a universal class of reaction-diffusion systems near the Hopf bifurcation point and in the presence of another small parameter. The reaction-diffusion systems to be reduced are such that the chemical components constituting local oscillators are nondiffusive or hardly diffusive, so that the oscillators are almost uncoupled, while there is an extra diffusive component which introduces effective nonlocal coupling over the oscillators. Linear stability analysis of the reduced equation about the uniform oscillation is also carried out. This revealed that new types of instability which can never arise in the ordinary complex Ginzburg-Landau equation are possible, and their physical implication is briefly discussed.

Juggling motion in a system of motile coupled oscillators.

A particular dynamic steady state emerging in the swarm oscillator model--a system of interacting motile elements with an internal degree of freedom--is presented. In the state, elements form a rotating triangle whose corners appear to catch and throw elements. This motion is referred to as "juggling motion" in this paper. How this motion is maintained is studied theoretically. In particular, the five-element system, the minimum system that exhibits the motion, is investigated. With the help of the analysis of the two-element system, several factors essential to maintaining this motion are obtained.

Dimensionality of clusters in a swarm oscillator model.

We investigate what is called swarm oscillator model where interacting motile oscillators form various kinds of ordered structures. We particularly focus on the dimensionality of clusters which oscillators form. In two-dimensional space, oscillators spontaneously form one-dimensional clusters or two-dimensional clusters. By studying the three-oscillator system, we analytically find the conditions of the appearance of those patterns. The validity of those conditions in applying to systems of more oscillators is demonstrated by numerically investigating a system of twenty oscillators.

Hierarchical cluster structures in a one-dimensional swarm oscillator model.

Swarm oscillator model derived by one of the authors (Tanaka), where interacting motile elements form various kinds of patterns, is investigated. We particularly focus on the cluster patterns in one-dimensional space. We mathematically derive all static and stable configurations in final states for a particular but a large set of parameters. In the derivation, we introduce renormalized expression of this model. We find that the static final states are hierarchical cluster structures in which a cluster consists of smaller clusters in a nesting manner.

General chemotactic model of oscillators.

We propose a general chemotactic model describing a system of interacting elements. Each element in this model exhibits internal dynamics, and there exists a nonlinear coupling between elements that depends on their internal states. From this model, we derive a simpler model describing the phases and positions of the chemotactic elements by means of center-manifold and phase-reduction methods. We find that, despite its simplicity, the model obtained through this reduction exhibits a rich variety of patterns.

Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators.

We show that a wide class of uncoupled limit-cycle oscillators can be in-phase synchronized by common weak additive noise. An expression of the Lyapunov exponent is analytically derived to study the stability of the noise-driven synchronizing state. The result shows that such a synchronization can be achieved in a broad class of oscillators with little constraint on their intrinsic property. On the other hand, the leaky integrate-and-fire neuron oscillators do not belong to this class, generating intermittent phase slips according to a power law distribution of their intervals.