Excitable Units Research Articles

Universal behavior in populations composed of excitable and self-oscillatory elements

We study the robustness of self-sustained oscillatory activity in a globally coupled ensemble of excitable and oscillatory units. The critical balance to achieve collective self-sustained oscillations is analytically established. We also report a universal scaling function for the ensemble's mean frequency. Our results extend the framework of the "aging transition" [Phys. Rev. Lett. 93, 104101 (2004)] including a broad class of dynamical systems potentially relevant in biology.

Dynamics of three-state excitable units on Poisson vs. power-law random networks

The influence of the network topology on the dynamics of systems of coupled excitable units is studied numerically and demonstrates a lower dynamical variability for power-law networks than for Poisson ones. This effect which reflects a robust collective excitable behavior is however lower than that observed for diffusion processes or network robustness. Instead, the presence (and number) of triangles and larger loops in the networks appears as a parameter with strong influence on the considered dynamics.

Globally Coupled Resonate-and-Fire Models

We analyze globally coupled resonate-and-fire neuron models. We analytically explain the stability of asynchronous states in the limit of large number of neurons and calculate a phase diagram. The results of our theory coincide with those of numerical simulations. Our theory is applicable to any excitable units coupled with finite strength.

Found in translation: neural feedback from exercising muscles

In a recent Classical Perspectives article in The Journal of Physiology (Joyner, 2005), Mike Joyner summarizes his perspective of the contribution of a paper by McCloskey & Mitchell (1972). This does an excellent job of highlighting an area of research that continues to be important to this day and often throws up surprises. Unfortunately the account contains some inaccuracies and also overlooks key contributions from British scientists. An almost similar paper to the one above was published in 1971 in The Journal of Physiology (Coote et al. 1971). Our paper was the first to report the use of ventral root stimulation to evoke contraction of muscles and we did this in anaesthetized as well as in decerebrate cats (see also Coote et al. 1969). One particular difference in the paper by McCloskey and Mitchell was that they very elegantly showed that it was muscle afferent fibre Goup III and IV that were responsible but this was hardly surprising since with Perez-Gonzalez in 1970 I had published our studies on the effects on blood pressure and renal sympathetic nerve activity of stimulating muscle afferents of different sizes showing that only these small fibres were involved (Coote & Perez-Gonzalez, 1970). So I think Mike Joyner was going a little too far in implying that we didn't know these facts before the McCloskey and Mitchell paper. In tracing the history of what has subsequently occurred I think attention should have been drawn to an important study by Mike White and Richard Bull, which showed that similar blood pressure and heart rate effects can be evoked to voluntary contraction by electrically induced contraction of muscle (Bull et al. 1989). A significant finding in the latter paper was that in a post-contraction occlusion of the muscle circulation the blood pressure remained increased whilst the heart rate returned to base line, a phenomena that we have recently concluded can be explained by the differing actions of muscle Group III mechanoreceptors mainly affecting cardiac vagal tone whilst Group IV metaboreceptors mainly affect sympathetic tone (Gladwell & Coote, 2002; Gladwell et al. 2005). As to the way the afferent information converges Joyner does not draw attention to the beautiful studies of Peter McWilliams' group in Leeds, which in 1991–92, was already clearly demonstrating that the heart rate increase to muscle contraction was greater when cardiac vagal tone was increased by raising baroreceptor input. Furthermore, they showed that electrical stimulation of muscle nerves activated GABA neurones in the NTS and blocked baroreceptor excited units (McWilliam & Yang, 1991; McMahon & McWilliam, 1992; McMahon et al. 1992).We still do not know whether this is the primary site for interaction between muscle afferents and the baroreceptor reflex but the differential effect on heart rate and blood pressure of the muscle afferents might point to an influence in addition closer to the cardiac vagal neurones. I hope this sets the record straight although I accept that mine, like Mike Joyner's, is a biased viewpoint.

Dynamical systems and cognitive linguistics: toward an active morphodynamical semantics

We propose a novel dynamical system approach to cognitive linguistics based on cellular automata and spiking neural networks 1 1 An abbreviated version of some portions of this article appeared in Doursat & Petitot (2005), published under the IEEE copyright. . How can the same relationship ‘in’ apply to containers as different as ‘box’, ‘tree’ or ‘bowl’? Our objective is to categorize the infinite diversity of schematic visual scenes into a small set of grammatical elements and elucidate the topology of language. Gestalt-inspired semantic studies have shown that spatial prepositions such as ‘in’ or ‘above’ are neutral toward the shape and size of objects. We suggest that this invariance can be explained by introducing morphodynamical transforms, which erase image details and create virtual structures or singularities (boundaries, skeleton), and call this paradigm ‘active semantics’. Singularities arise from a large-scale lattice of coupled excitable units exhibiting spatiotemporal pattern formation, in particular traveling waves. This work addresses the crucial cognitive mechanisms of spatial schematization and categorization at the interface between vision and language and anchors them to expansion processes such as activity diffusion or wave propagation.

BIFURCATIONS DUE TO SMALL TIME-LAG IN COUPLED EXCITABLE SYSTEMS

A system of ODE's is used to attempt an approximation of the dynamics of two delayed coupled FitzHugh–Nagumo excitable units, described by delay-differential equations. It is shown that the codimension 2 generalized Hopf bifurcation acts as the organizing center for the dynamics of ODE's for small time-lags. Furthermore, this is used to explain important qualitative properties, like the phenomenon of oscillator death, of the exact dynamics for small time-delays.

Viscous Flow and Plastic Deformation of Glasses in the Model of Excited Atoms

The critical displacement of an atom (a group of atoms) Δrmax, which corresponds to the interatomic interaction force at the maximum, is treated as the atomic excitation in liquids and glasses. The formation and migration of excited atoms are governed by local fluctuations of the configurational entropy. In amorphous linear polymers, the role of an excited kinetic unit is played by a small-sized macromolecular segment (an atomic group in a monomer). The atomic excitation in silicate glasses corresponds to the critical displacement of a bridging oxygen atom in the Si–O–Si bridge upon switching of adjacent bridging bonds. The activation energy e h = Pmaxνh and the activation volume νh = πd2Δrmax of the atomic excitation are introduced. The activation energy e h is determined by the work done against the forces of the internal pressure Pmax. The formation of an excited kinetic unit in polymers and glasses is a small-scale low-energy process (e h = 10–20 kJ/mol, νh = 5–70 A3). The total activation volume of the system Vf = νhNh is termed the fluctuation volume, and the model under consideration is referred to as the fluctuation volume model (or the model of excited atoms). The viscosity equation and other relationships of the hole theory are interpreted in the framework of the proposed model. This model is also applied to analyze the plasticity of amorphous polymers and glasses. A relationship between the glass transition condition and the Lindemann melting criterion is established.

Chaotic spreading of epidemics in complex networks of excitable units

We explore the dynamics of an epidemiological disease spreading within a complex network of individuals. The local behavior of the epidemics is modelled by means of an excitable dynamics, and the individuals are connected in the network through a weighted small-world wiring. The global behavior of the epidemics can have stationary as well as chaotic states, depending upon the probability of substituting short-range with long-range interactions. We describe the bifurcation scenario leading to such latter states, and discuss the relevance of the observed chaotic dynamics for the description of the spreading mechanisms of epidemics inside complex networks.

Rhythmic Activity of Noisy Neural Circuits

Dynamical features of neural circuits generating different patterns of spike trains in the presence of noise are investigated: (i) We explore noise-induced multimode dynamics in excitable functional units. Multiple gain of regularity is found to be related to different frequency entrainments and to the appearance of additional time scales; (ii) We develop stochastic implementation of central pattern generator to show that excitable units can successfully replace pacemakers at the appropriate level of noise; (iii) We study the coexistence of beta and gamma rhythms in a local network of nerve cells. It is found that noise can cause coherent switchings between different oscillatory states.

Supramolecular fullerene architectures by quadruple hydrogen bonding

The synthesis and full characterization of a quadruple bonded fullerene dimer using self-complementary 2-ureido-4[1H]pyrimidinone units with high dimerization constants is described. The chemical integrity of the monomeric moiety in either compound is fully preserved, also with respect to its redox and UV-Vis behavior. Two novel supramolecular dyads consisting of an oligo(p-phenylene vinylene) (OPV) donor and fullerene (C-60) acceptor are created via quadruple hydrogen bonding upon mixing the fullerene dimer and an OPV dimer. In these supramolecular dyads, singlet-energy transfer from the excited OPV unit to the fullerene causes a strong quenching of the OPV fluorescence. The high association constant of the 2-ureido-4[1H]-pyrimidinone quadruple hydrogen-bonding unit results in high quenching factors (Q(max) greater than or equal to 90). The lower limit obtained for the rate constant for energy transfer (k(EN) greater than or equal to 6 x 10(10) s(-1)) is rationalized in terms of the Forster mechanism.

Dendrimers as ligands. Formation of a 2:1 luminescent complex between a dendrimer with a 1,4,8,11-tetraazacyclotetradecane (cyclam) core and Zn2+.

We have investigated the formation of metal complexes between Zn2+ and two derivatives, 1 and 2, of the well-known 1,4,8,11-tetraazacyclotetradecane (cyclam) ligand. Compound 1 is 1,4,8,11-tetrakis(naphthylmethyl) cyclam, and compound 2 is a dendrimer consisting of a cyclam core with appended 12 dimethoxybenzene and 16 naphthyl units. Compound 1 exhibits an emission band with a maximum around 480 nm, assigned to the formation of exciplexes between amine and excited naphthyl units. Dendrimer 2 exhibits three types of weak emission bands, assigned to naphthyl localized excited states (lambdamax = 337 nm), naphthyl excimers (lambdamax ca. 390 nm), and naphthyl-amine exciplexes (lambdamax = 480 nm). In CH3CN-CH2Cl2 1:1 v/v, titration of ligand 1 with Zn2+ causes the disappearance of the exciplex emission and the appearance of a strong naphthyl localized fluorescence; the titration plot is linear and reaches a plateau for a 1:1 stoichiometry, showing that a highly stable [Zn(1)]2+ complex is formed. In the case of 2, titration with Zn2+ causes the disappearance of the exciplex band, with a concomitant increase in the excimer and naphthyl localized emissions; the titration plot is again linear, but in this case it reaches a plateau for a 2:1 stoichiometric ratio, showing the unexpected formation of a [Zn(2)2]2+ complex. Such an unexpected stoichiometry for the complex of the dendritic ligand has been fully confirmed by 1H NMR titrations. The results obtained show that the dendrimer branches not only do not hinder, but in fact favor coordination of cyclam to Zn2+.

On the Temperature Profile of the Thermally Excited Resonant Silicon Micro Structural Pressure Sensor

AbstractAccording to the sensing structure of a practical silicon resonant pressure micro sensor whose preliminary sensing unit is a square silicon diaphragm and the final sensing unit is a silicon beam resonator, its operating mechanism is analyzed. The thermal resistor acts as the excited unit, and the piezoresistive unit acts as the detector, for the above micro sensor. By using the amplitude and phase conditions, the self-exciting closed loop system is investigated based on the operating mechanism for the above micro sensor. The temperature profile model and the thermal stress model are established for the beam resonator of the micro sensor. Moreover, the thermal feature is simulated and analyzed for the above micro sensor.

Noise-induced multimode behavior in excitable systems.

Based on experiments with electronic circuits, we show how a system of coupled excitable units can possess several noise-induced oscillatory modes. We characterize the multimode organization in terms of the coherence resonance effect. Multiple gain of regularity is found to be related to different frequency entrainments and to the appearance of additional time scales.

Excitation energy density dependent fluorescence behaviour of a regioselectively functionalized tetraphenylporphyrin–cellulose conjugate

The fluorescence behaviour of tetraphenylporphyrin appended cellulose strands in chloroform is studied by weak cw excitation and intense picosecond laser pulse excitation (wavelength λ L=347.15 nm, duration Δt L=35 ps). With rising pump pulse energy density, a reduction of the fluorescence efficiency and a shortening of the fluorescence signal decay time are observed. The energy density dependent fluorescence quenching is analysed in terms of intra-strand singlet exciton–singlet exciton annihilation. The annihilation constant is determined and a critical singlet exciton number density ( N ex, ann =4.8×10 19 cm −3 ) as well as a critical fraction of excited repeat units ( f RU,ann=0.1) for annihilation are determined. Additionally the excited-state absorption cross-section, σ ex,L, at the pump laser wavelength, λ L, is determined by energy density dependent transmission measurements and is found to be approximately equal to the ground-state absorption, σ L, at λ L. The small-signal fluorescence quantum distribution, fluorescence quantum yield ( φ F=0.072), and degree of fluorescence polarisation ( P F=0.04) are determined by cw fluorimetry. The emitting exciton size is found to be equal to the repeat-unit size of the cellulose strands.

Solvatochromism as a mechanism for controlling intercomponent photoinduced processes in a bichromophoric complex containing [Ru(bpy)3]2+ and [Ru(bpy)(CN)4]2– units

The dinuclear complex [(bpy)2Ru(μ-L1)Ru(CN)4] (1) contains {Ru(bpy)3}2+-type (Ru-bpy) and {Ru(bpy)(CN)4}2−-type (Ru-CN) chromophores covalently linked by a short, saturated –CH2OCH2CH2OCH2– chain. Since the photophysical properties of the Ru-CN chromophore are strongly solvent-dependent, whereas those of the Ru-bpy chromophore are not, it follows that altering the solvent provides a means of altering the driving force for inter-component photoinduced energy- or electron transfer processes. At room temperature, in a mixed solvent system varying from pure water to pure dmso, the characteristic luminescence of the excited Ru-bpy unit is progressively quenched as the proportion of dmso in the mixture increases. This behaviour is consistent with both *Ru-bpy → Ru-CN energy transfer quenching and with Ru-CN → *Ru-bpy electron transfer quenching, because as the proportion of dmso in the solvent increases, the 3MLCT excited state of the Ru-CN unit drops in energy (which facilitates the energy transfer process) and its Ru(III)/Ru(II) reduction potential also becomes less positive (which facilitates the electron transfer process). Consideration of the solvent composition at which luminescence quenching of Ru-bpy by Ru-CN occurs, the saturated nature of the spacer, and the metal–metal separation, collectively point towards Forster energy transfer being the quenching process which is switched on by the change in solvent composition. In contrast, at 77 K (frozen solvent) the 3MLCT state of the Ru-CN unit is raised in energy above that of the Ru-bpy unit, such that the energy transfer gradient is reversed and *Ru-CN → Ru-bpy energy-transfer occurs with strong emission from the Ru-bpy terminus.

Singlet-energy transfer in quadruple hydrogen-bonded oligo(p-phenylenevinylene)–fullerene dyads

Two novel supramolecular dyads consisting of an oligo(p-phenylenevinylene) (OPV) donor and fullerene (C60) acceptor are created via quadruple hydrogen bonding using self-complementary 2-ureido-4[1H]-pyrimidinone units. In the dyads, singlet-energy transfer from the excited OPV unit to the fullerene causes a strong quenching of the OPV fluorescence. The high association constant of the 2-ureido-4[1H]-pyrimidinone quadruple hydrogen-bonding unit results in high quenching factors (Qmax ≥ 90). The lower limit obtained for the rate constant for energy transfer (kEN ≥ 6 × 1010 s−1) is rationalized in terms of the Forster mechanism. Photoinduced electron transfer does not occur in these hydrogen-bonded dimers, even in polar solvents. The absence of charge separation is ascribed to a low electronic coupling between the donor and acceptor in the excited state as result of the long distance between the chromophores.

Computing with excitable systems in a noisy environment.

In this work we show that excitable units with biologically inspired couplings are capable of performing any logic operation in a noisy environment without synchronization.

Photochemical and photophysical properties of poly(propylene amine) dendrimers with peripheral naphthalene and azobenzene groups.

We report the preparation, the absorption spectra, and the photophysical and photochemical properties in dichloromethane solution of four dendrimers of the poly(propylene amine) family (indicated by POPAM or PPI) functionalised with naphthalene and trans-azobenzene units. Each dendrimer Gn, where n = 1 to 4 is the generation number, comprises 2(n+1)-2 (i.e., 30 for G4) tertiary amine units in the interior and 2(n1) (i.e., 32 for G4) naphthalene and trans-azobenzene units in the periphery. For comparison purposes, the photophysical and photochemical properties of model compounds of the peripheral units have also been investigated. We have found that the fluorescence of the naphthalene units is quenched by the tertiary amines (via electron transfer) as well as by the trans-azobenzene units (via energy transfer). The quantum yields of the trans-->cis and cis-->trans photoisomerisation of the azobenzene units have been measured at various excitation wavelengths. Quenching of the fluorescence of the excited naphthalene unit by the trans- and cis-azobenzene units is accompanied by the sensitisation of the cis-->trans (but not of the trans-->cis) isomerisation. The rate constant of the thermal cis-->trans isomerisation of the azobenzene units has also been measured. Comparison of the results obtained for model compounds and for the G4 dendrimer shows that the dendritic structure favours the trans configuration of the azobenzene units ("dendritic effect"), presumably because it is less demanding in terms of space and causes less crowding on the dendrimer surface.

Background noise improves gap detection in tonically inhibited inferior colliculus neurons.

Single units in the inferior colliculus (IC) in the C57Bl/6 inbred mouse strain were tested for their temporal processing ability as measured by their minimum gap threshold (MGT), the shortest silent interval in an ongoing white-noise stimulus which a unit could encode. After ascertaining the MGT in quiet, units were re-tested in various levels of background noise. The focus of this report is on two types of tonically responding units found in the IC. Tonically inhibited (TI) units encoded gaps poorly in quiet and low levels of background noise as compared with tonically excited (TE) units. In quiet, the MGTs of TI units were about an order of magnitude longer than the MGTs typical of TE units. Paradoxically, gap encoding was improved in high levels of background noise for TI units. This result is unexpected from the traditional viewpoint that noise necessarily degrades signal processing and is inconsistent with psychophysical observations of diminished speech and gap detection processing in noisy environments. We believe the improved feature detection described here is produced by the adaptation of inhibitory input. Continuous background noise would diminish the inhibitory efficacy of the gap stimulus by increasing the latency to the onset of inhibition and decreasing its duration. This would allow more spontaneous activity to "bleed through" the silent gap, thus signaling its presence. Improved feature detection in background noise resulting from inhibitory adaptation would seem an efficient neural mechanism and one that might be generally useful in other signal detection tasks.

Two-Photon Absorption and Excited-State Energy-Transfer Properties of a New Multibranched Molecule

This paper presents a molecular design for a two-photon absorbing structure, which contains a two-dimensional molecular architecture with four arms and one bridging unit, each of these segments having an extended π-conjugation and capable of producing two-photon absorption in different spectral ranges. Two chromophore units of a triphenylamine derivative dye, (N, N-di[4-{4-(5-[4-tert-butylphenyl]-1,3,4-oxadiazol-2-yl)styryl}phenyl]amino)benzene, were linked with a π-conjugated di-2-thienylethenylene bridging unit to form a new multibranched compound, bis(5-[4-{N,N-di(4-[4-{5-(4-tert-butylphenyl)-1,3,4-oxadiazol-2-yl}styryl]phenyl)amino}styryl]thien-2-yl)ethenylene. Linear absorption spectra and luminescence spectra of the component and the multibranched chromophores revealed a hypochromic effect for the multibranched dye. A very effective energy transfer from the excited arm units to the π-conjugated bridging unit is observed. The two-photon cross-sections were measured using the femtosecond Z-scan technique at several excitation wavelengths in the 620−800 nm range. Comparing the nonlinear absorption coefficients observed for the constituent chromophore dyes with that for the multibranched compound, we found that the arm units make the dominant contribution to the two-photon absorption when the wavelength of excitation is longer than 720 nm.