Phase resetting and coupling of noisy neural oscillators

A number of experimental groups have recently computed Phase Response Curves (PRCs) for neurons. There is a great deal of noise in the data. We apply methods from stochastic nonlinear dynamics to coupled noisy phase-resetting maps and obtain the invariant density of phase distributions. By exploiting the special structure of PRCs, we obtain some approximations for the invariant distributions. Comparisons to Monte-Carlo simulations are made. We show how phase-dependence of the noise can move the peak of the invariant density away from the peak expected from the analysis of the deterministic system and thus lead to noise-induced bifurcations. B. Ermentrout supported in part by NIMH and NSF. Action Editor: Wulfram Gerstner     

Rapid Phase Resetting of a Mammalian Orcadian Rhythm by Brief Light Pulses

The phase-shift (Δψ) responses of the circadian rhythm in the field mouse Mus booduga to brief light pulses (LPs) of 15 minutes duration and 1000 lux intensity were measured in 90 experiments. In each experiment, a resetting light pulse LP₁ was administered at CT14 (CT, circadian time), and a scanning light pulse LP₂ was then variously administered in separate experiments at CT16, CT20, and CT22 in the same and in the next circadian cycle. The Δψ obtained in all these two-pulse experiments did not differ significantly from theoretical values computed on the assumption that LP₁ reset the phase response curve (PRC) rapidly. In each case, the steady-state Δψ observed after LP₁ and LP₂ differed significantly from the Δψ obtained at the same CT in determination of the single-pulse PRC (control) and also differed significantly from the values on the assumption of no Δψ in the PRC following LP₁. These results indicate that the circadian pacemaker of M. booduga, as measured by its PRC, is substantially reset within 2h after a light pulse at CT14. (Chronobiology International 14(6), 537–548, 1997)     

Phase resetting associated with changes of burst shape

Based on our stochastic approach to phase resetting of an ensemble of oscillators, in this article we investigate two stimulation mechanisms which exhibit qualitatively different dynamical behaviour as compared with the stimulation mechanism analysed in a previous study. Both the old as well as one of the new stimulation mechanisms give rise to a characteristic desynchronization behaviour: A stimulus of a given (non-vanishing) intensity administered at a critical initial ensemble phase for a critical duration T _crit annihilates the ensemble's synchronized oscillation. When the stimulation duration exceeds T _crit a transition from type 1 resetting to type 0 resetting occurs. The second new stimulation mechanism does not cause a desynchronization which is connected with a phase singularity. Correspondingly this mechanism only leads to type 1 resetting. In contrast to the stimulation mechanism analysed in a previous study, both new stimulation mechanisms cause burst splitting. According to our results, in this case peak or onset detection algorithms are not able to reveal a correct estimate of the ensemble phase. Thus, whenever stimulation induced burst splitting occurs, phase-resetting curves determined by means of peak or onset detection may be nothing but artifacts. Therefore it is necessary to understand burst splitting in order to develop reliable phase detection algorithms, which are e.g. based on detecting bursts' centers of mass. Our results are important for experimentalists: Burst splitting is, for instance, well-known from tremor resetting experiments. Thus, it often turned out to be at least rather difficult to derive reliable phase-resetting curves from experimental data.     

Existence and stability criteria for phase-locked modes in ring neural networks based on the spike time resetting curve method

We developed a systematic and consistent mathematical approach to predicting 1:1 phase-locked modes in ring neural networks of spiking neurons based on the open loop spike time resetting curve (STRC) and its almost equivalent counterpart—the phase resetting curve (PRC). The open loop STRCs/PRCs were obtained by injecting into an isolated model neuron a triangular shaped time-dependent stimulus current closely resembling an actual synaptic input. Among other advantages, the STRC eliminates the confusion regarding the undefined phase for stimuli driving the neuron outside of the unperturbed limit cycle. We derived both open loop PRC and STRC-based existence and stability criteria for 1:1 phase-locked modes developed in ring networks of spiking neurons. Our predictions were in good agreement with the closed loop numerical simulations. Intuitive graphical methods for predicting phase-locked modes were also developed both for half-centers and for larger ring networks.     

Pulse coupled oscillators and the phase resetting curve

Limit cycle oscillators that are coupled in a pulsatile manner are referred to as pulse coupled oscillators. In these oscillators, the interactions take the form of brief pulses such that the effect of one input dies out before the next is received. A phase resetting curve (PRC) keeps track of how much an input advances or delays the next spike in an oscillatory neuron depending upon where in the cycle the input is applied. PRCs can be used to predict phase locking in networks of pulse coupled oscillators. In some studies of pulse coupled oscillators, a specific form is assumed for the interactions between oscillators, but a more general approach is to formulate the problem assuming a PRC that is generated using a perturbation that approximates the input received in the real biological network. In general, this approach requires that circuit architecture and a specific firing pattern be assumed. This allows the construction of discrete maps from one event to the next. The fixed points of these maps correspond to periodic firing modes and are easier to locate and analyze for stability compared to locating and analyzing periodic modes in the original network directly. Alternatively, maps based on the PRC have been constructed that do not presuppose a firing order. Specific circuits that have been analyzed under the assumption of pulsatile coupling include one to one lockings in a periodically forced oscillator or an oscillator forced at a fixed delay after a threshold event, two bidirectionally coupled oscillators with and without delays, a unidirectional N-ring of oscillators, and N all-to-all networks.     

Rat Brain Synaptosomes Prepared by Phase Partition

Synaptosomes from rat forebrain can easily be isolated by combining centrifugation with partition in an aqueous two-phase system composed of dextran T500 and polyethylene glycol 4000 in which synaptosomes have an extreme affinity for the upper phase. The fraction thus obtained has been characterized by electron microscopy and biochemical markers for synaptosomes and some other cell components. The contamination by microsomes, free mitochondria, and myelin was 4.4, 3.2, and 0.1%, respectively. The morphometric analysis of the electron micrographs shows that greater than 60% of the structures are synaptosomes. This preparation of the isolation procedure is remarkably short (less than 1 h), formance as assayed by their respiratory activities and ATP level in the absence and presence of depolarizing agents. Synaptosomes prepared by phase partition release the neurotransmitter glutamate in a Ca2(+)-dependent manner. The duration of the isolation procedure is remarkably short (less than 1 h), no ultracentrifuge is required, and the method can be applied for small- or large-scale preparations.     

Phase locking of biological clocks

Radial isochron clocks (RICs) and their response to external signals and coupling with other RICs are studied. RICs are derived as phase approximations to self-sustained oscillators. Their response to single impulses (phase resetting) and to repetitive impulses is determined. This response may be harmonic or chaotic. Finally, the effect of coupling between clocks is studied. Simple coupling is shown to exhibit rhythm splitting like that observed in fish and small mammals. New phase locking results for general weakly coupled RIC systems are also derived.Supported in part by the National Science Foundation under grants MCS-80-15359 (FCH) and MCS-79-02505 (JPK)     

A Honey Bee (Apis mellifera) Light Phase Response Curve

The authors report a phase response curve (PRC) for individual honey bees (Apis mellifera) to single 1-h light pulses (1000 lux) using an Aschoff Type 1 protocol (n?=?134). The bee PRC is a weak (Type 1) PRC with a maximum advance of 1.5?h between circadian time (CT) 18 and 3 and a maximum delay of 1.5?h between CT 12 and 18. This is the first published honey bee light PRC and provides an important resource for chronobiologists and honey bee researchers. It may also have practical applications for what is an economically important species frequently transported across different time zones. (Author correspondence: G.warman@auckland.ac.nz)     

Phase structure of liposome in lipid mixtures

Gas microbubbles present in ultrasound imaging contrast agents are stabilized by lipid aggregates that typically contain a mixture of lipids. In this study, the phase structure of the lipid mixtures that contained two or three lipids was investigated using three different methods: dynamic light scattering, ¹H NMR, and microfluidity measurements with fluorescence probes. Three lipids that are commonly present in imaging agents (DPPC, DPPE-PEG, and DPPA) were used. Two types of systems, two-lipid model systems and simulated imaging systems were investigated. The results show that liposomes were the dominant aggregates in all the samples studied. The polar PEG side chains from the PEGylated lipid lead to the formation of micelles and micellar aggregates in small sizes. In the ternary lipid systems, almost all the lipids were present in bilayers with micelles absent and free lipids at very low concentration. These results suggest that liposomes, not micelles, contribute to the stabilization of microbubbles in an ultrasound imaging contrast agent.     

Phase transition and lateral phase separation in planar lipid membranes as sensed by the lipophilic ion dipicrylamine

The permeation of the lipophilic ion dipicrylamine through planar lipid membranes formed from dipalmitoylphosphatidylcholine in n-decane shows an anomaly near the main phase transition of this system. Both the rate constant, k_i, of ion translocation across the membrane interior and the interfacial concentration, N, of this ion have a maximum at about 36°C. Analogous experiments were performed with tetraphenylborate. A considerably lesser effect of the phase transition was found. The addition of cholesterol leads to a broadening of the maxima for k_i and N. The time course of the current following a voltage jump shows a characteristic change below a temperature of about 45°C, if the molar ratio cholesterol/ phosphatidylcholine in the membrane forming solution exceeds 1. While the current transient decays exponentially above 45°C, a sum of two exponential terms yields an adequate fit below that temperature. This is regarded as evidence for a lateral phase separation below 45°C into structurally different domains, which provide two different pathways for dipicrylamine.     

Phase variable restriction-modification systems in Moraxella catarrhalis

A repetitive DNA motif was used as a marker to identify novel genes in the mucosal pathogen Moraxella catarrhalis. There is a high prevalence of such repetitive motifs in virulence genes that display phase variable expression. Two repeat containing loci were identified using a digoxigenin-labelled 5'-(CAAC)6-3' oligonucleotide probe. The repeats are located in the methylase components of two distinct type III restriction-modification (R-M) systems. We suggest that the phase variable nature of these R-M systems indicates that they have an important role in the biology of M. catarrhalis.     

湖北海棠阶段转变过程中几种同工酶变化研究

采用聚丙烯酰胺凝胶电泳法、研究了湖北海棠1年生实生菌（S1）、4年生（S4）、14年生（S14）实生树及4年生成年芽嫁接树（G4）不同高度叶片的过氧化物酶（POX）、细胞色素氧化酶（COD）、酯酶（EST）、乙醇脱氢酶（ADH）同工酶的变化。结果表明：多年生实生树随着高度的增加,POX Rf 0.56、0.60,COD Rf0.50,EST Rf0.09、0.15、0.75、0.77,ADH Rf0.76等几条酶带呈现,邮童区和成年区各自特有的同工酶带,随高度童区特征酶带消失或成年区特征酶带的高度均保持在150－200cm之间,同当年植株开花最低位置相同,S4、S14童区与S1同工酶谱带完全一致,S4、S14成年区与G4同工酶谱基本保持一致,G4同工酶谱并未随高度增加而发生变化,四种同工酶可以作为阶段转变的指标。S4、S14童区与成年区谱带的差异是高度的结果,高度是湖北海棠阶段转变的重要因子。     

Phase Delaying the Human Circadian Clock with Blue-Enriched Polychromatic Light

The human circadian system is maximally sensitive to short-wavelength (blue) light. In a previous study we found no difference between the magnitude of phase advances produced by bright white versus bright blue-enriched light using light boxes in a practical protocol that could be used in the real world. Since the spectral sensitivity of the circadian system may vary with a circadian rhythm, we tested whether the results of our recent phase-advancing study hold true for phase delays. In a within-subjects counterbalanced design, this study tested whether bright blue-enriched polychromatic light (17000 K, 4000 lux) could produce larger phase delays than bright white light (4100 K, 5000 lux) of equal photon density (4.2×10¹⁵ photons/cm²/sec). Healthy young subjects (n?=?13) received a 2 h phase delaying light pulse before bedtime combined with a gradually delaying sleep/dark schedule on each of 4 consecutive treatment days. On the first treatment day the light pulse began 3 h after the dim light melatonin onset (DLMO). An 8 h sleep episode began at the end of the light pulse. Light treatment and the sleep schedule were delayed 2 h on each subsequent treatment day. A circadian phase assessment was conducted before and after the series of light treatment days to determine the time of the DLMO and DLMOff. Phase delays in the blue-enriched and white conditions were not significantly different (DLMO: ?4.45±2.02 versus ?4.48±1.97 h; DLMOff: ?3.90±1.97 versus ?4.35±2.39 h, respectively). These results indicate that at light levels commonly used for circadian phase shifting, blue-enriched polychromatic light is no more effective than the white polychromatic lamps of a lower correlated color temperature (CCT) for phase delaying the circadian clock. (Author correspondence: ceastman@rush.edu)     

Phase behavior of freeze-dried phospholipid-cholesterol mixtures stabilized with trehalose

A study is presented of the role of cholesterol content on the gel-to-liquid crystalline phase transition of freeze-dried liposomes stabilized with trehalose, a well known lyoprotectant. The phospholipids considered in this work, DPPC and DPPE, belong to the two predominant phospholipid species found in numerous biological membranes. Cholesterol is found in abundance in mammalian plasma membranes. DSC measurements reveal that cholesterol-containing liposomes exhibit multiple phase transitions upon dehydration. Addition of trehalose to these systems lowers the phase transition temperature and limits the phase separation of the lipidic components upon freeze-drying. This work provides strong evidence for the effectiveness of trehalose in stabilizing cholesterol-containing membranes upon lyophilization.     

相转移催化与微波技术用于苯丙氨酸合成

采用微波辐射技术结合固液相转移催化进行有机合成，明显地加速了有机反应速率甚至提高了合成产率。以苯甲基叉亚胺的苄基化反应为例，仅用１ｍｉｎ时间便能完成反应。然后经酸性水解得苯丙氨酸消旋体。整个合成路线全程总产率达６２．５％，操作简便。     

Altitudinal Variation In Phase Response Curves For The Himalayan Strains Of Drosophila Helvetica

In previous research, it was determined that the altitude of origin altered the parameters of photic entrainment and free‐running rhythmicity of adult locomotor activity of the high‐altitude Himalayan (haH) strain (Hemkund‐Sahib, 4121 m above sea level) of Drosophila helvetica compared to the low‐altitude Himalayan (laH) strain (Birahi, 1132 m above sea level) of the same species. The present study investigated whether the altitude of origin also affects the parameters of the light pulse phase response curve (PRC) of the adult locomotor activity rhythm of the haH strain. Light pulse PRCs were determined for both strains against the background of constant darkness. Although both were “weak” or type 1 PRCs, the PRC for the haH strain differed from that of the laH strain in three basic parameters. The PRC for the haH strain was of low amplitude, had a protracted dead zone, and showed a ratio of the advance to delay region (A/D>1), while the PRC of the laH strain was characterized by high amplitude, absence of dead zone, and a A/D ratio<1. The asymmetric PRCs of these strains might explain the process of photic entrainment to 24 h light‐dark cycles, as the long period of the free‐running rhythm (τ) of the haH strain is complemented with a larger advance portion of its PRC (A/D>1), whereas the short τ of the laH strain is matched with a larger delay portion of its PRC (A/D<1). Prolonged dead zone and low amplitude in the PRC of the haH strain imply that the photic sensitivity of this strain has been drastically diminished as an adaptation to environmental conditions at the altitude of its origin. While adults of this strain begin activity in very bright light in the forenoon due to non‐permissible low temperature in the morning, the converse is true for the laH strain.     

Phase variation in meningococcal lipooligosaccharide biosynthesis genes

Neisseria meningitidis expresses a range of lipooligosaccharide (LOS) structures, comprising of at least 13 immunotypes (ITs). Meningococcal LOS is subject to phase variation of its terminal structures allowing switching between ITs, which is proposed to have functional significance in disease. The objectives of this study were to investigate the repertoire of structures that can be expressed in clinical isolates, and to examine the role of phase-variable expression of LOS genes during invasive disease. Southern blotting was used to detect the presence of LOS biosynthetic genes in two collections of meningococci, a global set of strains previously assigned to lineages of greater or lesser virulence, and a collection of local clinical isolates which included paired throat and blood isolates from individual patients. Where the phase-variable genes lgtA, lgtC or lgtG were identified, they were amplified by PCR and the homopolymeric tracts, responsible for their phase-variable expression, were sequenced. The results revealed great potential for variation between alternate LOS structures in the isolates studied, with most strains capable of expressing several alternative terminal structures. The structures predicted to be currently expressed by the genotype of the strains agreed well with conventional immunotyping. No correlation was observed between the structural repertoire and virulence of the isolate. Based on the potential for LOS phase variation in the clinical collection and observations with the paired patient isolates, our data suggest that phase variation of LOS structures is not required for translocation between distinct compartments in the host.     

Phase changes of cardiolipin vesicles mediated by divalent cations

Small unilamellar vesicles were prepared from cardiolipin and produced the hexagonal II phase when dialyzed against CaCl₂ or MgCl₂. Upon removal of the cation by dialysis against EDTA large unilamellar vesicles were formed. The events of the transition from the lamellar to hexagonal phase and back to the lamellar phase are described.