Hermann Riecke

Self-Sustained Activity in a Small-World Network of Excitable Neurons

We study the dynamics of excitable integrate-and-fire neurons in a small-world network. At low densities p of directed random connections, a localized transient stimulus results either in self-sustained persistent activity or in a brief transient followed by failure. Averages over the quenched ensemble reveal that the probability of failure changes from 0 to 1 over a narrow range in p; this failure transition can be described analytically through an extension of an existing mean-field result. Exceedingly long transients emerge at higher densities p; their activity patterns are disordered, in contrast to the mostly periodic persistent patterns observed at low p. The times at which such patterns die out follow a stretched-exponential distribution, which depends sensitively on the propagation velocity of the excitation.

A synaptic mechanism for retinal adaptation to luminance and contrast.

The gain of signaling in primary sensory circuits is matched to the stimulus intensity by the process of adaptation. Retinal neural circuits adapt to visual scene statistics, including the mean (background adaptation) and the temporal variance (contrast adaptation) of the light stimulus. The intrinsic properties of retinal bipolar cells and synapses contribute to background and contrast adaptation, but it is unclear whether both forms of adaptation depend on the same cellular mechanisms. Studies of bipolar cell synapses identified synaptic mechanisms of gain control, but the relevance of these mechanisms to visual processing is uncertain because of the historical focus on fast, phasic transmission rather than the tonic transmission evoked by ambient light. Here, we studied use-dependent regulation of bipolar cell synaptic transmission evoked by small, ongoing modulations of membrane potential (VM) in the physiological range. We made paired whole-cell recordings from rod bipolar (RB) and AII amacrine cells in a mouse retinal slice preparation. Quasi-white noise voltage commands modulated RB VM and evoked EPSCs in the AII. We mimicked changes in background luminance or contrast, respectively, by depolarizing the VM or increasing its variance. A linear systems analysis of synaptic transmission showed that increasing either the mean or the variance of the presynaptic VM reduced gain. Further electrophysiological and computational analyses demonstrated that adaptation to mean potential resulted from both Ca channel inactivation and vesicle depletion, whereas adaptation to variance resulted from vesicle depletion alone. Thus, background and contrast adaptation apparently depend in part on a common synaptic mechanism.

Mechanisms of pattern decorrelation by recurrent neuronal circuits

Decorrelation is a fundamental computation that optimizes the format of neuronal activity patterns. Channel decorrelation by adaptive mechanisms results in efficient coding, whereas pattern decorrelation facilitates the readout and storage of information. Mechanisms achieving pattern decorrelation, however, remain unclear. We developed a theoretical framework that relates high-dimensional pattern decorrelation to neuronal and circuit properties in a mathematically stringent fashion. For a generic class of random neuronal networks, we proved that pattern decorrelation emerges from neuronal nonlinearities and is amplified by recurrent connectivity. This mechanism does not require adaptation of the network, is enhanced by sparse connectivity, depends on the baseline membrane potential and is robust. Connectivity measurements and computational modeling suggest that this mechanism is involved in pattern decorrelation in the zebrafish olfactory bulb. These results reveal a generic relationship between the structure and function of neuronal circuits that is probably relevant for pattern processing in various brain areas.

Symmetry-breaking Hopf bifurcation in anisotropic systems

Abstract Symmetry-breaking Hopf bifurcation from a spatially uniform steady state of a spatially extended anisotropic system is considered. This work is motivated by the experimental observation of a Hopf bifurcation to oblique traveling rolls in electrohydrodynamic convection in planarly aligned nematic liquid crystals. Symmetry forces four traveling rolls to lose stability simultaneously. Four coupled complex ordinary differential equations describing the nonlinear interaction of the traveling rolls are analyzed using methods of equivariant bifurcation theory. Six branches of periodic solutions always bifurcate from the trivial state at the Hopf bifurcation. These correspond to traveling and standing wave patterns. In an open region of coefficient space there is a primary bifurcation to a quasiperiodic standing wave solution. The Hopf bifurcation can also lead directly to an aperiodic attractor in the form of an asymptotically stable, structurally stable heteroclinic cycle. The theory is applied to a model for the transition from normal to oblique traveling rolls.

Adaptation to Background Light Enables Contrast Coding at Rod Bipolar Cell Synapses

Rod photoreceptors contribute to vision over an ∼ 6-log-unit range of light intensities. The wide dynamic range of rod vision is thought to depend upon light intensity-dependent switching between two parallel pathways linking rods to ganglion cells: a rod → rod bipolar (RB) cell pathway that operates at dim backgrounds and a rod → cone → cone bipolar cell pathway that operates at brighter backgrounds. We evaluated this conventional model of rod vision by recording rod-mediated light responses from ganglion and AII amacrine cells and by recording RB-mediated synaptic currents from AII amacrine cells in mouse retina. Contrary to the conventional model, we found that the RB pathway functioned at backgrounds sufficient to activate the rod → cone pathway. As background light intensity increased, the RBs role changed from encoding the absorption of single photons to encoding contrast modulations around mean luminance. This transition is explained by the intrinsic dynamics of transmission from RB synapses.

Intrinsic bursting of AII amacrine cells underlies oscillations in the rd1 mouse retina

In many forms of retinal degeneration, photoreceptors die but inner retinal circuits remain intact. In the rd1 mouse, an established model for blinding retinal diseases, spontaneous activity in the coupled network of AII amacrine and ON cone bipolar cells leads to rhythmic bursting of ganglion cells. Since such activity could impair retinal and/or cortical responses to restored photoreceptor function, understanding its nature is important for developing treatments of retinal pathologies. Here we analyzed a compartmental model of the wild-type mouse AII amacrine cell to predict that the cells intrinsic membrane properties, specifically, interacting fast Na and slow, M-type K conductances, would allow its membrane potential to oscillate when light-evoked excitatory synaptic inputs were withdrawn following photoreceptor degeneration. We tested and confirmed this hypothesis experimentally by recording from AIIs in a slice preparation of rd1 retina. Additionally, recordings from ganglion cells in a whole mount preparation of rd1 retina demonstrated that activity in AIIs was propagated unchanged to elicit bursts of action potentials in ganglion cells. We conclude that oscillations are not an emergent property of a degenerated retinal network. Rather, they arise largely from the intrinsic properties of a single retinal interneuron, the AII amacrine cell.

The mechanisms of repetitive spike generation in an axonless retinal interneuron.

Several types of retinal interneurons exhibit spikes but lack axons. One such neuron is the AII amacrine cell, in which spikes recorded at the soma exhibit small amplitudes (<10 mV) and broad time courses (>5 ms). Here, we used electrophysiological recordings and computational analysis to examine the mechanisms underlying this atypical spiking. We found that somatic spikes likely represent large, brief action potential-like events initiated in a single, electrotonically distal dendritic compartment. In this same compartment, spiking undergoes slow modulation, likely by an M-type K conductance. The structural correlate of this compartment is a thin neurite that extends from the primary dendritic tree: local application of TTX to this neurite, or excision of it, eliminates spiking. Thus, the physiology of the axonless AII is much more complex than would be anticipated from morphological descriptions and somatic recordings; in particular, the AII possesses a single dendritic structure that controls its firing pattern.

Structure and dynamics of modulated traveling waves in cellular flames

We describe the formation and evolution of spatial and temporal patterns in cylindrical premixed flames. We consider the cellular regime, Le < 1, where the Lewis number Le is the ratio of thermal to mass diffusivity of a deficient component of the combustible mixture. A transition from stationary, axisymmetric flames to stationary cellular flames is predicted analytically if Le is decreased below a critical value. We present the results of numerical computations to show that as Le is further decreased, with all other parameters fixed, traveling waves (TWs) along the flame front arise via an infinite-period bifurcation which breaks the reflection symmetry of the cellular array. Upon further decreasing Le we find the development of different kinds of periodically modulated traveling waves (MTWs) as well as a branch of quasiperiodically modulated traveling waves (QPMTWs). These transitions are accompanied by the development of different spatial and temporal symmetries including period doublings and period halvings in appropriate coordinate systems. We also observe the apparently chaotic temporal behavior of a disordered cellular pattern involving creation and annihilation of cells. We analytically describe the stability of the TW solution near its onset using suitable phase-amplitude equations. Within this framework one of the MTWs can be identified as a localized wave traveling through an underlying stationary, spatially periodic structure.

Localized Structures In Pattern-Forming Systems

A number of mechanisms that lead to the confinement of patterns to a small part of a translationally symmetric pattern-forming system are reviewed: nonadiabatic locking of fronts, global coupling and conservation laws, dispersion, and coupling to additional slow modes via gradients. Various connections with experimental results are made.

Oscillon-type structures and their interaction in a Swift-Hohenberg model

Abstract Motivated by the observation of localized circular excitations (‘oscillons’) in vertically vibrated granular layers [P. Umbanhowar, F. Melo, H. Swinney, Nature 382 (1996) 793], we numerically investigate an extension of a Swift–Hohenberg model that exhibits a subcritical transition to square patterns. For sufficiently strong damping of the basic state, stable oscillon structures are found. The localization mechanism is quite general and is due to non-adiabatic effects. Bound structures of oscillons of equal and opposite polarity are found with bound states of like polarity being less robust. Much of the phenomena are consistent with the experimental observations and suggest that oscillons are not specific to patterns in granular media or to parametrically driven systems. Experimental tests are suggested that would determine whether this minimal framework is sufficient to describe the phenomena.