Chimera states in the systems of nonlocally coupled phase oscillators are considered stable in the continuous limit of spatially distributed oscillators. However, it is reported that in the numerical simulations without taking such limit, chimera states are chaotic transient and finally collapse into the completely synchronous solution. In this Rapid Communication, we numerically study chimera states by using the coupling function different from the previous studies and obtain the result that chimera states can be stable even without taking the continuous limit, which we call the persistent chimera state. The behavior of coupled oscillator systems can describe various pattern formations in a wide range of scientific fields [1,2]. In the systems of nonlocally coupled identical oscillators, there often appears a strange phenomenon called the chimera state, which is characterized by the coexistence of coherent and incoherent domains, where the former domain consists of phase-locked oscillators and the latter domain consists of drifting oscillators with spatially changing frequencies . This interesting phenomenon was first discovered in the system of nonlocally coupled phase oscillators obeying the evolution equationwith 2π -periodic phases θ (x) on a finite interval x ∈ [0,1] under the periodic boundary condition, a smooth 2π -periodic coupling function , and the kernel G(y) = (κ/2) exp(−κ|y|), where a constant 1/κ denotes the coupling range [3]. Recently, similar spatiotemporal patterns have been found in various systems using, e.g., the logistic maps [14,15], Rössler systems [15], and FitzHugh-Nagumo oscillators [18].In the study of the chimera state, the system, Eq. (1), with the sine coupling [27]is particularly important because of its simplicity and generality. In fact, this coupling function was used also in the first discovery of the chimera state [3]. For numerical simulations, we usually discretize Eq. (1) into such form as Eq. (3). In the simulations of such discretized systems, we can confirm that chimera states are surely stable in the continuous limit N → ∞. However, the stability of chimera states in finitely discretized systems is questioned. In fact, it is reported that when N is finite, chimera states with the sine coupling are chaotic transient and finally collapse into the completely synchronous solution [12,13,26]. Recently, Ashwin and Burylko proposed the weak chimera similar to the chimera state, which is defined by the coexistence of frequency-synchronous and -asynchronous oscillators in the systems of coupled indistinguishable phase oscillators but is not necessarily spatially structured as coherent and incoherent domains [28]. They studied the weak chimera in some types of networks composed of the minimal number of oscillators with the Hansel-Mato-Meunier coupling, Eq. (4), and demonstrated that the weak chimera can be persistent (nontransient). In this Rapid Communication, we study chimera states in the systems of nonlocally coupled phase oscillators with the Hansel-MatoMeunier coupling b...

Chimera states for the one-dimensional array of nonlocally coupled phase oscillators in the continuum limit are assumed to be stationary states in most studies, but a few studies report the existence of breathing chimera states. We focus on multichimera states with two coherent and incoherent regions and numerically demonstrate that breathing multichimera states, whose global order parameter oscillates temporally, can appear. Moreover, we show that the system exhibits a Hopf bifurcation from a stationary multichimera to a breathing one by the linear stability analysis for the stationary multichimera.

Chimera states in one-dimensional nonlocally coupled phase oscillators are mostly assumed to be stationary, but breathing chimeras can occasionally appear, branching from the stationary chimeras via Hopf bifurcation. In this paper, we demonstrate two types of breathing chimeras: The type I breathing chimera looks the same as the stationary chimera at a glance, while the type II consists of multiple coherent regions with different average frequencies. Moreover, it is shown that the type I changes to the type II by increasing the breathing amplitude. Furthermore, we develop a self-consistent analysis of the local order parameter, which can be applied to breathing chimeras, and numerically demonstrate this analysis in the present system.

Gene delivery with nonviral vectors is a promising approach, due to its excellent safety profile in comparison to that of viral vectors. [1][2][3][4][5] However, low and transient transgene expression is a major concern for nonviral vectors. One of the keys to overcome this problem would be the establishment of an efficient and targeted delivery system, in which intracellular trafficking is considered. In addition, the controlled intranuclear disposition of the delivered plasmid would be quite important for achieving practical gene therapy.5) Indeed, analyses of the intranuclear disposition of plasmid DNA have indicated that the reasons for the low and transient transgene expression are the decreases in the amount of the exogenous DNA and the expression efficiency from one copy of the transgene over time. [6][7][8] Thus, the maintenance of both the plasmid DNA and its expression efficiency is essential for the controlled intranuclear disposition.We focused on a replicating plasmid, to prevent the decrease in the amount of the exogenous DNA. The SV40 origin-SV40 large T antigen system was used as a model. The large T antigen binds the origin, acts as helicase that unwinds DNA, and recruits DNA polymerase a-primase, which initiates replication.9,10) The plasmid with the origin and the large T antigen gene is replicated in dividing cells, and the replication of the plasmid is conducted in the S phase of the cell cycle, along with the endogenous chromosomal DNA. The replicating plasmid could alleviate the decrease in transgene expression by maintaining the amount of the exogenous DNA. This type of plasmid DNA was previously used in extrachromosomal replication and transgene expression. 11,12) In addition, we focused on the deoxyribonucleoside kinase from the fruit fly Drosophila melanogaster (Dm-dNK). Previously, we reported that the presence of the Dm-dNK gene on a plasmid enhanced the cytotoxicity of nucleoside analogs. 13) We expected that this gene on a replicating plasmid would be more effective than that on a non-replicating plasmid for nucleoside analog-induced cell death.In this study, we transfected replicating plasmid DNAs containing the luciferase and Dm-dNK genes into human cells. Our results confirmed that the replicating plasmid is an excellent tool for efficient protein production. We serendipitously discovered that the Dm-dNK gene on the replicating plasmid was highly cytotoxic and caused cell death without nucleoside analogs. MATERIALS AND METHODS MaterialsOligodeoxyribonucleotides were purchased from Sigma Genosys Japan (Ishikari, Japan) and Invitrogen Japan (Tokyo, Japan) in purified forms.Construction of Plasmid DNAs pYK-CMV-luc (8.5 kb) and pCMV-dNK (7.5 kb), containing the luciferase and dNK genes, respectively, under the cytomegalovirus (CMV) promoter were used as the parental plasmids in this study. 6,13)The pCMV-luc-T plasmid (11.5 kb), containing the SV40 origin/promoter and the SV40 large T antigen gene as well as the CMV promoter-luciferase gene, was constructed by ligating the SV40 origi...