Nonlinear dynamics and bifurcations of a coupled oscillator model for calling behavior of Japanese tree frogs (Hyla japonica)

Synchronization has been observed in various systems, including living beings. In a previous study, we reported a new phenomenon with antisynchronization in calling behavior of two interacting Japanese tree frogs. In this paper, we theoretically analyse nonlinear dynamics in a system of three coupled oscillators, which models three interacting frogs, where the oscillators of each pair have the property of antisynchronization; in particular, we perform bifurcation analysis and Lyapunov function analysis.     

On partial contraction analysis for coupled nonlinear oscillators

We describe a simple yet general method to analyze networks of coupled identical nonlinear oscillators and study applications to fast synchronization, locomotion, and schooling. Specifically, we use nonlinear contraction theory to derive exact and global (rather than linearized) results on synchronization, antisynchronization, and oscillator death. The method can be applied to coupled networks of various structures and arbitrary size. For oscillators with positive definite diffusion coupling, it can be shown that synchronization always occurs globally for strong enough coupling strengths, and an explicit upper bound on the corresponding threshold can be computed through eigenvalue analysis. The discussion also extends to the case when network structure varies abruptly and asynchronously, as in flocks of oscillators or dynamic elements.     

Transitory behaviors in diffusively coupled nonlinear oscillators

We study collective behaviors of diffusively coupled oscillators which exhibit out-of-phase synchrony for the case of weakly interacting two oscillators. In large populations of such oscillators interacting via one-dimensionally nearest neighbor couplings, there appear various collective behaviors depending on the coupling strength, regardless of the number of oscillators. Among others, we focus on an intermittent behavior consisting of the all-synchronized state, a weakly chaotic state and some sorts of metachronal waves. Here, a metachronal wave means a wave with orderly phase shifts of oscillations. Such phase shifts are produced by the dephasing interaction which produces the out-of-phase synchronized states in two coupled oscillators. We also show that the abovementioned intermittent behavior can be interpreted as in-out intermittency where two saddles on an invariant subspace, the all-synchronized state and one of the metachronal waves play an important role.     

Ancient gill and lung oscillators may generate the respiratory rhythm of frogs and rats

Though the mechanics of breathing differ fundamentally between amniotes and "lower" vertebrates, homologous rhythm generators may drive air breathing in all lunged vertebrates. In both frogs and rats, two coupled oscillators, one active during the inspiratory (I) phase and the other active during the preinspiratory (PreI) phase, have been hypothesized to generate the respiratory rhythm. We used opioids to uncouple these oscillators. In the intact rat, complete arrest of the external rhythm by opioid-induced suppression of the putative I oscillator, that is, pre-B?tzinger complex (PBC) oscillator, did not arrest the putative PreI oscillator. In the unanesthetized frog, the comparable PreI oscillator, that is, the putative buccal/gill oscillator, was refractory to opioids even though the comparable I oscillator, the putative lung oscillator, was arrested. Studies in en bloc brainstem preparations derived from both juvenile frogs and metamorphic tadpoles confirmed these results and suggested that opioids may play a role in the clustering of lung bursts into episodes. As the frog and rat respiratory circuitry produce functionally equivalent motor outputs during lung inflation, these data argue for a close homology between the frog and rat oscillators. We suggest that the respiratory rhythm of all lunged vertebrates is generated by paired coupled oscillators. These may have originated from the gill and lung oscillators of the earliest air breathers.     

Polyploids with different origins and ancestors form a single sexual polyploid species

Polyploidization is one of the few mechanisms that can produce instantaneous speciation. Multiple origins of tetraploid lineages from the same two diploid progenitors are common, but here we report the first known instance of a single tetraploid species that originated repeatedly from at least three diploid ancestors. Parallel evolution of advertisement calls in tetraploid lineages of gray tree frogs has allowed these lineages to interbreed, resulting in a single sexually interacting polyploid species despite the separate origins of polyploids from different diploids. Speciation by polyploidization in these frogs has been the source of considerable debate, but the various published hypotheses have assumed that polyploids arose through either autopolyploidy or allopolyploidy of extant diploid species. We utilized molecular markers and advertisement calls to infer the origins of tetraploid gray tree frogs. Previous hypotheses did not sufficiently account for the observed data. Instead, we found that tetraploids originated multiple times from extant diploid gray tree frogs and two other, apparently extinct, lineages of tree frogs. Tetraploid lineages then merged through interbreeding to result in a single species. Thus, polyploid species may have complex origins, especially in systems in which isolating mechanisms (such as advertisement calls) are affected directly through hybridization and polyploidy.     

Identification of mutants in inbred Xenopus tropicalis

Xenopus tropicalis offers the potential for genetic analysis in an amphibian. In order to take advantage of this potential, we have been inbreeding strains of frogs for future mutagenesis. While inbreeding a population of Nigerian frogs, we identified three mutations in the genetic background of this strain. These mutations are all recessive embryonic lethals. We show that multigenerational mutant analysis is feasible and demonstrate that mutations can be identified, propagated, and readily characterized using hybrid, dihybrid, and even trihybrid crosses. In addition, we are optimizing conditions to raise frogs rapidly and present our protocols for X. tropicalis husbandry. We find that males mature faster than females (currently 4 versus 6 months to sexual maturity). Here we document our progress in developing X. tropicalis as a genetic model organism and demonstrate the utility of the frog to study the genetics of early vertebrate development.     

Changes in the fluctuation of interbeat intervals in spontaneously beating cultured cardiac myocytes: experimental and modeling studies

 Isolated and cultured neonatal cardiac myocytes contract spontaneously and cyclically, and have the properties of a non-linear oscillator. In this study, we have analyzed the relationship between the fluctuation of contraction rhythm of spontaneously beating cultured cardiac myocytes, and the coupling strength among them. The coefficient of variation of contraction intervals increased transiently in the early stages of incubation, and then decreased almost monotonically with time. The contraction rhythm of the myocytes became synchronized in the late stage of the culture. The day on which synchronization occurred almost coincided with the day when the coefficient of variation reached its lowest value. In addition, we have performed a mathematical analysis using interacting Bonhoeffer–van der Pol oscillators to clarify the mechanisms underlying the changes in the fluctuation of contraction rhythm with time. As the coupling strength among oscillators increased, the coefficient of variation of oscillation periods increased temporarily, but then decreased rapidly when the oscillators showed synchronization. These results suggest that the changes in the fluctuation of beating rhythm result from the increase in strength of electrical coupling among spontaneously beating cardiac myocytes. Received: 10 August 2000 / Accepted in revised form: 19 August 2001     

Robust synchronization of coupled circadian and cell cycle oscillators in single mammalian cells

Circadian cycles and cell cycles are two fundamental periodic processes with a period in the range of 1 day. Consequently, coupling between such cycles can lead to synchronization. Here, we estimated the mutual interactions between the two oscillators by time‐lapse imaging of single mammalian NIH3T3 fibroblasts during several days. The analysis of thousands of circadian cycles in dividing cells clearly indicated that both oscillators tick in a 1:1 mode‐locked state, with cell divisions occurring tightly 5 h before the peak in circadian Rev‐Erbα‐YFP reporter expression. In principle, such synchrony may be caused by either unidirectional or bidirectional coupling. While gating of cell division by the circadian cycle has been most studied, our data combined with stochastic modeling unambiguously show that the reverse coupling is predominant in NIH3T3 cells. Moreover, temperature, genetic, and pharmacological perturbations showed that the two interacting cellular oscillators adopt a synchronized state that is highly robust over a wide range of parameters. These findings have implications for circadian function in proliferative tissues, including epidermis, immune cells, and cancer.     

哈士蟆油的形态结构观察和化学成分测定

在不同的文献中对“哈士蟆油”存在着完全不同的解释,主要有三种观点：哈士蟆油是“哈士蟆的脂肪”,“雌性哈士蟆的卵巢和输卵管外的脂肪”,“雌性哈士蟆的输卵管”。本研究通过对哈士蟆油干品形态结构的观察、显微切片的观察和化学成分的分析,否定了上述的前两种解释。形态结构、组织化学和成分分析的结果均表明：哈士蟆油是雌性哈士蟆（中国桂蛙Ｒａｎａ ｔｅｍｐｏｒａｒｉａ ｃｈｅｎｓｉｎｅｎｓｉｓ或黑龙江林蛙Ｒ．ａｍ     

Modeling of a bipedal robot using mutually coupled Rayleigh oscillators

The objective of the work presented here was the modeling of a bipedal robot using a central pattern generator (CPG) formed by a set of mutually coupled Rayleigh oscillators. We analyzed a 2D model, with the three most important determinants of gait, that performs only motions parallel to the sagittal plane. Using oscillators with integer relation of frequency, we determined the transient motion and the stable limit cycles of the network formed by the three oscillators, showing the behavior of the knee angles and the hip angle. A comparison of the plotted graphs revealed that the system provided excellent results when compared to experimental analysis. Based on the results of the study, we come to the conclusion that the use of mutually coupled Rayleigh oscillators can represent an excellent method of signal generation, allowing their application for feedback control of a walking machine.Acknowledgements The authors would like to express their gratitude to CNPq and CAPES for the financial support provided during the course of this research.     

Dynamics and bifurcations of two coupled neural oscillators with different connection types

In this paper we present an oscillatory neural network composed of two coupled neural oscillators of the Wilson-Cowan type. Each of the oscillators describes the dynamics of average activities of excitatory and inhibitory populations of neurons. The network serves as a model for several possible network architectures. We study how the type and the strength of the connections between the oscillators affect the dynamics of the neural network. We investigate, separately from each other, four possible connection types (excitatory→excitatory, excitatory→inhibitory, inhibitory→excitatory, and inhibitory→inhibitory) and compute the corresponding bifurcation diagrams. In case of weak connections (small strength), the connection of populations of different types lead to periodicin-phase oscillations, while the connection of populations of the same type lead to periodicanti-phase oscillations. For intermediate connection strengths, the networks can enter quasiperiodic or chaotic regimes, and can also exhibit multistability. More generally, our analysis highlights the great diversity of the response of neural networks to a change of the connection strength, for different connection architectures. In the discussion, we address in particular the problem of information coding in the brain using quasiperiodic and chaotic oscillations. In modeling low levels of information processing, we propose that feature binding should be sought as a temporally coherent phase-locking of neural activity. This phase-locking is provided by one or more interacting convergent zones and does not require a central “top level” subcortical circuit (e.g. the septo-hippocampal system). We build a two layer model to show that although the application of a complex stimulus usually leads to different convergent zones with high frequency oscillations, it is nevertheless possible to synchronize these oscillations at a lower frequency level using envelope oscillations. This is interpreted as a feature binding of a complex stimulus.     

The evolution of jumping in frogs: Morphological evidence for the basal anuran locomotor condition and the radiation of locomotor systems in crown group anurans

Our understanding of the evolution of frog locomotion follows from the work of Emerson in which anurans are proposed to possess one of three different iliosacral configurations: 1) a lateral‐bending system found in walking and hopping frogs; 2) a fore‐aft sliding mechanism found in several locomotor modes; and 3) a sagittal‐hinge‐type pelvis posited to be related to long‐distance jumping performance. The most basal living (Ascaphus) and fossil (Prosalirus) frogs are described as sagittal‐hinge pelvic types, and it has been proposed that long‐distance jumping with a sagittal‐hinge pelvis arose early in frog evolution. We revisited osteological traits of the pelvic region to conduct a phylogenetic analysis of the relationships between pelvic systems and locomotor modes in frogs. Using two of Emerson's diagnostic traits from the sacrum and ilium and two new traits from the urostyle, we resampled the taxa originally studied by Emerson and key paleotaxa and conducted an analysis of ancestral‐character state evolution in relation to locomotor mode. We present a new pattern for the evolution of pelvic systems and locomotor modes in frogs. Character analysis shows that the lateral‐bender, walker/hopper condition is both basal and generally conserved across the Anura. Long‐distance jumping frogs do not appear until well within the Neobatrachia. The sagittal‐hinge morphology is correlated with long‐distance jumping in terrestrial frogs; however, it evolved convergently multiple times in crown group anurans with the same four pelvic traits described herein. Arboreal jumping has appeared in multiple crown lineages as well, but with divergent patterns of evolution involving each of the three pelvic types. The fore‐aft slider morph appears independently in three different locomotor modes and, thus, is a more complex system than previously thought. Finally, it appears that the advent of a bicondylar sacro‐urostylic articulation was originally related to providing axial rigidity to lateral‐bending behaviors rather than sagittal bending. J. Morphol., 2011. © 2010 Wiley‐Liss, Inc.     

Biochemical investigation of the Rana esculenta complex in the Kis-Balaton Nature Reserve, Hungary

In this study it has been proved by PAGE of serum proteins that all the three members of the Rana esculenta complex occur in the Kis-Balaton Nature Reserve (Hungary). On the basis of the LDH isoenzyme pattern which is characteristic in green frogs we could distinguish all three variations of R. ridibunda and R. lessonae and one type of R. esculenta. The mobility of serum albumins on SDS-PAGE implies that the R. esculenta comes from hybridization of the two other species. The PAGE methods provide a reliable basis for the rapid taxonomic identification of both adults and immature speciments of the three forms of frogs.     

Modeling of signaling networks

Biochemical networks, including those containing signaling pathways, display a wide range of regulatory properties. These include the ability to propagate information across different time scales and to function as switches and oscillators. The mechanisms underlying these complex behaviors involve many interacting components and cannot be understood by experiments alone. The development of computational models and the integration of these models with experiments provide valuable insight into these complex systems-level behaviors. Here we review current approaches to the development of computational models of biochemical networks and describe the insights gained from models that integrate experimental data, using three examples that deal with ultrasensitivity, flexible bistability and oscillatory behavior. These types of complex behavior from relatively simple networks highlight the necessity of using theoretical approaches in understanding higher order biological functions.     

Extremely abundant antimicrobial peptides existed in the skins of nine kinds of Chinese odorous frogs

Peptide agents are regarded as hopeful candidates to solve life-threatening resistance of pathogenic microorganisms to classic antibiotics due to their unique action mechanisms. Peptidomic and genomic investigation of natural antimicrobial peptides (AMPs) from amphibian skin secretions can provide a large amount of structure-functional information to design peptide antibiotics with therapeutic potential. In the present study, we identified a large number of AMPs from the skins of nine kinds of Chinese odorous frogs. Eighty AMPs were purified from three different odorous frogs and confirmed by peptidomic analysis. Our results indicated that post-translational modification of AMPs rarely happened in odorous frogs. cDNAs encoding precursors of 728 AMPs, including all the precursors of the confirmed 80 native peptides, were cloned from the constructed AMP cDNA libraries of nine Chinese odorous frogs. On the basis of the sequence similarity of deduced mature peptides, these 728 AMPs were grouped into 97 different families in which 71 novel families were identified. Out of these 728 AMPs, 662 AMPs were novel and 28 AMPs were reported previously in other frog species. Our results revealed that identical AMPs were widely distributed in odorous frogs; 49 presently identified AMPs could find their identical molecules in different amphibian species. Purified peptides showed strong antimicrobial activities against 4 tested microbe strains. Twenty-three deduced peptides were synthesized and their bioactivities, including antimicrobial, antioxidant, hemolytic, immunomodulatory and insulin-releasing activities, were evaluated. Our findings demonstrate the extreme diversity of AMPs in amphibian skins and provide plenty of templates to develop novel peptide antibiotics.     

Three New Ranidae Mitogenomes and the Evolution of Mitochondrial Gene Rearrangements among Ranidae Species

Various types of gene rearrangements have been discovered in the mitogenoes of the frog family Ranidae.In this study,we determined the complete mitogenome sequence of three Rana frogs.By combining the available mitogenomic data sets from Gen Bank,we evaluated the phylogenetic relationships of Ranidae at the mitogenome level and analyzed mitogenome rearrangement cases within Ranidae.The three frogs shared an identical mitogenome organization that was extremely similar to the typical Neobatrachian-type arrangement.Except for the genus Babina,the monophyly of each genus was well supported.The genus Amnirana occupied the most basal position among the Ranidae.The[Lithobates+Rana]was the closest sister group of Odorrana.The diversity of mitochondrial gene arrangements in ranid species was unexpectedly high,with 47 mitogenomes from 40 ranids being classified into 10 different gene rearrangement types.Some taxa owned their unique gene rearrangement characteristics,which had significant implication for their phylogeny analysis.All rearrangement events discovered in the Ranidae mitogenomes can be explained by the duplication and random loss model.     

Breath-by-breath interactions between inspiratory and expiratory duration in occlusive sleep apnea

We examined interactions between inspiratory duration (TI), expiratory duration (TE), and inspiratory (esophageal) pressure (Pes) generation in seven subjects with confirmed occlusive sleep apnea. Breath-by-breath values of TI, TE, and Pes were identified by digital computer during 21 260-s epochs of repetitive occlusive apnea during non-rapid-eye-movement sleep. The control theory of interacting nonlinear oscillators was used to categorize the interaction between TI and TE for each epoch as either 1) synchronization, the strongest possible interaction between biological oscillators; 2) relative entrainment, a moderate interaction between oscillators; or 3) relative coordination, a weak interaction. The latter two interactions were characterized by systemic oscillations in the moving cross-correlation between TI and TE. The relationship between TI and Pes was analyzed in a similar fashion. Significant oscillations were present in all three parameters (P less than 0.0001 for each). We observed significant negative correlations between TI and TE and between TI and Pes (P less than 0.001 for each) when all breaths for all epochs were pooled. In no epoch was there a significant positive correlation between TI and TE or Pes. All three interactions were observed between TI and TE: five epochs of synchronization, nine of relative entrainment, and seven of relative coordination. In contrast, 19 of 21 epochs exhibited synchronization between TI and Pes, with 2 epochs of relative entrainment. The relative frequency of TI vs. Pes synchronization was significantly greater than TI vs. TE synchronization (P less than 0.005).(ABSTRACT TRUNCATED AT 250 WORDS)     

Range position and climate sensitivity: The structure of among‐population demographic responses to climatic variation

Species’ distributions will respond to climate change based on the relationship between local demographic processes and climate and how this relationship varies based on range position. A rarely tested demographic prediction is that populations at the extremes of a species’ climate envelope (e.g., populations in areas with the highest mean annual temperature) will be most sensitive to local shifts in climate (i.e., warming). We tested this prediction using a dynamic species distribution model linking demographic rates to variation in temperature and precipitation for wood frogs (Lithobates sylvaticus) in North America. Using long‐term monitoring data from 746 populations in 27 study areas, we determined how climatic variation affected population growth rates and how these relationships varied with respect to long‐term climate. Some models supported the predicted pattern, with negative effects of extreme summer temperatures in hotter areas and positive effects on recruitment for summer water availability in drier areas. We also found evidence of interacting temperature and precipitation influencing population size, such as extreme heat having less of a negative effect in wetter areas. Other results were contrary to predictions, such as positive effects of summer water availability in wetter parts of the range and positive responses to winter warming especially in milder areas. In general, we found wood frogs were more sensitive to changes in temperature or temperature interacting with precipitation than to changes in precipitation alone. Our results suggest that sensitivity to changes in climate cannot be predicted simply by knowing locations within the species’ climate envelope. Many climate processes did not affect population growth rates in the predicted direction based on range position. Processes such as species‐interactions, local adaptation, and interactions with the physical landscape likely affect the responses we observed. Our work highlights the need to measure demographic responses to changing climate.     

Crab Clockwork: The Case for Interactive Circatidal and Circadian Oscillators Controlling Rhythmic Locomotor Activity of Carcinus Maenas

The circalunidian hypothesis that tidal rhythms in coastal animals are controlled by two lunar-day (c. 24.8 h) oscillators coupled in antiphase is challenged. Rhythmic locomotor activity patterns of the shore crab Carcinus maenas, and probably of some other species too, are more economically explained by interacting circadian (c. 24 h) and true circatidal (c. 12.4 h) physiological oscillators. A testable hypothesis is proposed that combines a circadian promotor and a circatidal inhibitor of locomotor activity.