Intersegmental coordination of the central pattern generator via interleaved electrical and chemical synapses in zebrafish spinal cord.

A significant component of the repetitive dynamics during locomotion in vertebrates is generated within the spinal cord. The legged locomotion of mammals is most likely controled by a hierarchical, multi-layer spinal network structure, while the axial circuitry generating the undulatory swimming motion of animals like lamprey is thought to have only a single layer in each segment. Recent experiments have suggested a hybrid network structure in zebrafish larvae in which two types of excitatory interneurons (V2a-I and V2a-II) both make first-order connections to the brain and last-order connections to the motor pool. These neurons are connected by electrical and chemical synapses across segments. Through computational modeling and an asymptotic perturbation approach we show that this interleaved interaction between the two neuron populations allows the spinal network to quickly establish the correct activation sequence of the segments when starting from random initial conditions, as needed for a swimming spurt, and to reduce the dependence of the intersegmental phase difference (ISPD) of the oscillations on the swimming frequency. The latter reduces the frequency dependence of the waveform of the swimming motion. In the model the reduced frequency dependence is largely due to the different impact of chemical and electrical synapses on the ISPD and to the significant spike-frequency adaptation that has been observed experimentally in V2a-II neurons, but not in V2a-I neurons. Our model makes experimentally testable predictions and points to a benefit of the hybrid structure for undulatory locomotion that may not be relevant for legged locomotion.

Structural spine plasticity: Learning and forgetting of odor-specific subnetworks in the olfactory bulb.

Learning to discriminate between different sensory stimuli is essential for survival. In rodents, the olfactory bulb, which contributes to odor discrimination via pattern separation, exhibits extensive structural synaptic plasticity involving the formation and removal of synaptic spines, even in adult animals. The network connectivity resulting from this plasticity is still poorly understood. To gain insight into this connectivity we present here a computational model for the structural plasticity of the reciprocal synapses between the dominant population of excitatory principal neurons and inhibitory interneurons. It incorporates the observed modulation of spine stability by odor exposure. The model captures the striking experimental observation that the exposure to odors does not always enhance their discriminability: while training with similar odors enhanced their discriminability, training with dissimilar odors actually reduced the discriminability of the training stimuli. Strikingly, this differential learning does not require the activity-dependence of the spine stability and occurs also in a model with purely random spine dynamics in which the spine density is changed homogeneously, e.g., due to a global signal. However, the experimentally observed odor-specific reduction in the response of principal cells as a result of extended odor exposure and the concurrent disinhibition of a subset of principal cells arise only in the activity-dependent model. Moreover, this model predicts the experimentally testable recovery of odor response through weak but not through strong odor re-exposure and the forgetting of odors via exposure to interfering odors. Combined with the experimental observations, the computational model provides strong support for the prediction that odor exposure leads to the formation of odor-specific subnetworks in the olfactory bulb.

Paradoxical phase response of gamma rhythms facilitates their entrainment in heterogeneous networks.

The synchronization of different γ-rhythms arising in different brain areas has been implicated in various cognitive functions. Here, we focus on the effect of the ubiquitous neuronal heterogeneity on the synchronization of ING (interneuronal network gamma) and PING (pyramidal-interneuronal network gamma) rhythms. The synchronization properties of rhythms depends on the response of their collective phase to external input. We therefore determine the macroscopic phase-response curve for finite-amplitude perturbations (fmPRC) of ING- and PING-rhythms in all-to-all coupled networks comprised of linear (IF) or quadratic (QIF) integrate-and-fire neurons. For the QIF networks we complement the direct simulations with the adjoint method to determine the infinitesimal macroscopic PRC (imPRC) within the exact mean-field theory. We show that the intrinsic neuronal heterogeneity can qualitatively modify the fmPRC and the imPRC. Both PRCs can be biphasic and change sign (type II), even though the phase-response curve for the individual neurons is strictly non-negative (type I). Thus, for ING rhythms, say, external inhibition to the inhibitory cells can, in fact, advance the collective oscillation of the network, even though the same inhibition would lead to a delay when applied to uncoupled neurons. This paradoxical advance arises when the external inhibition modifies the internal dynamics of the network by reducing the number of spikes of inhibitory neurons; the advance resulting from this disinhibition outweighs the immediate delay caused by the external inhibition. These results explain how intrinsic heterogeneity allows ING- and PING-rhythms to become synchronized with a periodic forcing or another rhythm for a wider range in the mismatch of their frequencies. Our results identify a potential function of neuronal heterogeneity in the synchronization of coupled γ-rhythms, which may play a role in neural information transfer via communication through coherence.

Development and binocular matching of orientation selectivity in visual cortex: a computational model.

In mouse visual cortex, right after eye opening binocular cells have different preferred orientations for input from the two eyes. With normal visual experience during a critical period, these preferred orientations evolve and eventually become well matched. To gain insight into the matching process, we developed a computational model of a cortical cell receiving orientation selective inputs via plastic synapses. The model captures the experimentally observed matching of the preferred orientations, the dependence of matching on ocular dominance of the cell, and the relationship between the degree of matching and the resulting monocular orientation selectivity. Moreover, our model puts forward testable predictions: 1) The matching speed increases with initial ocular dominance. 2) While the matching improves more slowly for cells that are more orientation selective, the selectivity increases faster for better matched cells during the matching process. This suggests that matching drives orientation selectivity but not vice versa. 3) There are two main routes to matching: the preferred orientations either drift toward each other or one of the orientations switches suddenly. The latter occurs for cells with large initial mismatch and can render the cells monocular. We expect that these results provide insight more generally into the development of neuronal systems that integrate inputs from multiple sources, including different sensory modalities.NEW & NOTEWORTHY Animals gather information through multiple modalities (vision, audition, touch, etc.). These information streams have to be merged coherently to provide a meaningful representation of the world. Thus, for neurons in visual cortex V1, the orientation selectivities for inputs from the two eyes have to match to enable binocular vision. We analyze the postnatal process underlying this matching using computational modeling. It captures recent experimental results and reveals interdependence between matching, ocular dominance, and orientation selectivity.

Top-down inputs drive neuronal network rewiring and context-enhanced sensory processing in olfaction.

Much of the computational power of the mammalian brain arises from its extensive top-down projections. To enable neuron-specific information processing these projections have to be precisely targeted. How such a specific connectivity emerges and what functions it supports is still poorly understood. We addressed these questions in silico in the context of the profound structural plasticity of the olfactory system. At the core of this plasticity are the granule cells of the olfactory bulb, which integrate bottom-up sensory inputs and top-down inputs delivered by vast top-down projections from cortical and other brain areas. We developed a biophysically supported computational model for the rewiring of the top-down projections and the intra-bulbar network via adult neurogenesis. The model captures various previous physiological and behavioral observations and makes specific predictions for the cortico-bulbar network connectivity that is learned by odor exposure and environmental contexts. Specifically, it predicts that-after learning-the granule-cell receptive fields with respect to sensory and with respect to cortical inputs are highly correlated. This enables cortical cells that respond to a learned odor to enact disynaptic inhibitory control specifically of bulbar principal cells that respond to that odor. For this the reciprocal nature of the granule cell synapses with the principal cells is essential. Functionally, the model predicts context-enhanced stimulus discrimination in cluttered environments ('olfactory cocktail parties') and the ability of the system to adapt to its tasks by rapidly switching between different odor-processing modes. These predictions are experimentally testable. At the same time they provide guidance for future experiments aimed at unraveling the cortico-bulbar connectivity.

Pulse-coupled mixed-mode oscillators: Cluster states and extreme noise sensitivity.

Motivated by rhythms in the olfactory system of the brain, we investigate the synchronization of all-to-all pulse-coupled neuronal oscillators exhibiting various types of mixed-mode oscillations (MMOs) composed of sub-threshold oscillations (STOs) and action potentials ("spikes"). We focus particularly on the impact of the delay in the interaction. In the weak-coupling regime, we reduce the system to a Kuramoto-type equation with non-sinusoidal phase coupling and the associated Fokker-Planck equation. Its linear stability analysis identifies the appearance of various cluster states. Their type depends sensitively on the delay and the width of the pulses. Interestingly, long delays do not imply slow population rhythms, and the number of emerging clusters only loosely depends on the number of STOs. Direct simulations of the oscillator equations reveal that for quantitative agreement of the weak-coupling theory the coupling strength and the noise have to be extremely small. Even moderate noise leads to significant skipping of STO cycles, which can enhance the diffusion coefficient in the Fokker-Planck equation by two orders of magnitude. Introducing an effective diffusion coefficient extends the range of agreement significantly. Numerical simulations of the Fokker-Planck equation reveal bistability and solutions with oscillatory order parameters that result from nonlinear mode interactions. These are confirmed in simulations of the full spiking model.

Chimera States in Continuous Media: Existence and Distinctness.

The defining property of chimera states is the coexistence of coherent and incoherent domains in systems that are structurally and spatially homogeneous. The recent realization that such states might be common in oscillator networks raises the question of whether an analogous phenomenon can occur in continuous media. Here, we show that chimera states can exist in continuous systems even when the coupling is strictly local, as in many fluid and pattern forming media. Using the complex Ginzburg-Landau equation as a model system, we characterize chimera states consisting of a coherent domain of a frozen spiral structure and an incoherent domain of amplitude turbulence. We show that in this case, in contrast with discrete network systems, fluctuations in the local coupling field play a crucial role in limiting the coherent regions. We suggest these findings shed light on new possible forms of coexisting order and disorder in fluid systems.

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 cell's 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.

Adult Neurogenesis Reconciles Flexibility and Stability of Olfactory Perceptual Memory.

In brain regions featuring ongoing plasticity, the task of quickly encoding new information without overwriting old memories presents a significant challenge. In the rodent olfactory bulb, which is renowned for substantial structural plasticity driven by adult neurogenesis and persistent turnover of dendritic spines, we show that such plasticity is vital to overcoming this flexibility-stability dilemma. To do so, we develop a computational model for structural plasticity in the olfactory bulb and show that the maturation of adult-born neurons facilitates the abilities to learn quickly and forget slowly. Particularly important to achieve this goal are the transient enhancement of the plasticity, excitability, and susceptibility to apoptosis that characterizes young neurons. The model captures many experimental observations and makes a number of testable predictions. Overall, it identifies memory consolidation as an important role of adult neurogenesis in olfaction and exemplifies how the brain can maintain stable memories despite ongoing extensive plasticity.

Chromatin endogenous cleavage provides a global view of RNA polymerase II transcription kinetics.

Chromatin immunoprecipitation (ChIP-seq) is the most common approach to observe global binding of proteins to DNA in vivo. The occupancy of transcription factors (TFs) from ChIP-seq agrees well with an alternative method, chromatin endogenous cleavage (ChEC-seq2). However, ChIP-seq and ChEC-seq2 reveal strikingly different patterns of enrichment of yeast RNA polymerase II. We hypothesized that this reflects distinct populations of RNAPII, some of which are captured by ChIP-seq and some of which are captured by ChEC-seq2. RNAPII association with enhancers and promoters - predicted from biochemical studies - is detected well by ChEC-seq2 but not by ChIP-seq. Enhancer/promoter bound RNAPII correlates with transcription levels and matches predicted occupancy based on published rates of enhancer recruitment, preinitiation assembly, initiation, elongation and termination. The occupancy from ChEC-seq2 allowed us to develop a stochastic model for global kinetics of RNAPII transcription which captured both the ChEC-seq2 data and changes upon chemical-genetic perturbations to transcription. Finally, RNAPII ChEC-seq2 and kinetic modeling suggests that a mutation in the Gcn4 transcription factor that blocks interaction with the NPC destabilizes promoter-associated RNAPII without altering its recruitment to the enhancer.

Neurogenesis drives stimulus decorrelation in a model of the olfactory bulb.

The reshaping and decorrelation of similar activity patterns by neuronal networks can enhance their discriminability, storage, and retrieval. How can such networks learn to decorrelate new complex patterns, as they arise in the olfactory system? Using a computational network model for the dominant neural populations of the olfactory bulb we show that fundamental aspects of the adult neurogenesis observed in the olfactory bulb--the persistent addition of new inhibitory granule cells to the network, their activity-dependent survival, and the reciprocal character of their synapses with the principal mitral cells--are sufficient to restructure the network and to alter its encoding of odor stimuli adaptively so as to reduce the correlations between the bulbar representations of similar stimuli. The decorrelation is quite robust with respect to various types of perturbations of the reciprocity. The model parsimoniously captures the experimentally observed role of neurogenesis in perceptual learning and the enhanced response of young granule cells to novel stimuli. Moreover, it makes specific predictions for the type of odor enrichment that should be effective in enhancing the ability of animals to discriminate similar odor mixtures.

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 (V(M)) 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 V(M) and evoked EPSCs in the AII. We mimicked changes in background luminance or contrast, respectively, by depolarizing the V(M) or increasing its variance. A linear systems analysis of synaptic transmission showed that increasing either the mean or the variance of the presynaptic V(M) 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.

Pattern orthogonalization via channel decorrelation by adaptive networks.

The early processing of sensory information by neuronal circuits often includes a reshaping of activity patterns that may facilitate further processing in the brain. For instance, in the olfactory system the activity patterns that related odors evoke at the input of the olfactory bulb can be highly similar. Nevertheless, the corresponding activity patterns of the mitral cells, which represent the output of the olfactory bulb, can differ significantly from each other due to strong inhibition by granule cells and peri-glomerular cells. Motivated by these results we study simple adaptive inhibitory networks that aim to separate or even orthogonalize activity patterns representing similar stimuli. Since the animal experiences the different stimuli at different times it is difficult for the network to learn the connectivity based on their similarity; biologically it is more plausible that learning is driven by simultaneous correlations between the input channels. We investigate the connection between pattern orthogonalization and channel decorrelation and demonstrate that networks can achieve effective pattern orthogonalization through channel decorrelation if they simultaneously equalize their output levels. In feedforward networks biophysically plausible learning mechanisms fail, however, for even moderately similar input patterns. Recurrent networks do not have that limitation; they can orthogonalize the representations of highly similar input patterns. Even when they are optimized for linear neuronal dynamics they perform very well when the dynamics are nonlinear. These results provide insights into fundamental features of simplified inhibitory networks that may be relevant for pattern orthogonalization by neuronal circuits in general.

Synchronization by uncorrelated noise: interacting rhythms in interconnected oscillator networks.

Oscillators coupled in a network can synchronize with each other to yield a coherent population rhythm. How do multiple such rhythms interact with each other? Do these collective oscillations synchronize like individual oscillators? We show that this is not the case: for strong, inhibitory coupling rhythms can become synchronized by noise. In contrast to stochastic synchronization, this new mechanism synchronizes the rhythms even if the noisy inputs to different oscillators are completely uncorrelated. Key for the synchrony across networks is the reduced synchrony within the networks: it substantially increases the frequency range across which the networks can be entrained by other networks or by periodic pacemaker-like inputs. We demonstrate this type of robust synchronization for different classes of oscillators and network connectivities. The synchronization of different population rhythms is expected to be relevant for brain rhythms.

Hexagons and spiral defect chaos in non-Boussinesq convection at low Prandtl numbers.

We study the stability and dynamics of non-Boussinesq convection in pure gases (CO2 and SF6) with Prandtl numbers near Pr approximately 1 and in a H2-Xe mixture with Pr=0.17. Focusing on the strongly nonlinear regime we employ Galerkin stability analyses and direct numerical simulations of the Navier-Stokes equations. For Pr approximately 1 and intermediate non-Boussinesq effects we find reentrance of stable hexagons as the Rayleigh number is increased. For stronger non-Boussinesq effects the usual, transverse side-band instability is superseded by a longitudinal side-band instability. Moreover, the hexagons do not exhibit any amplitude instability to rolls. Seemingly, this result contradicts the experimentally observed transition from hexagons to rolls. We resolve this discrepancy by including the effect of the lateral walls. Non-Boussinesq effects modify the spiral defect chaos observed for larger Rayleigh numbers. For convection in SF6 we find that non-Boussinesq effects strongly increase the number of small, compact convection cells and with it enhance the cellular character of the patterns. In H2-Xe, closer to threshold, we find instead an enhanced tendency toward roll-like structures. In both cases the number of spirals and of targetlike components is reduced. We quantify these effects using recently developed diagnostics of the geometric properties of the patterns.

Multiresonant forcing of the complex Ginzburg-Landau equation: pattern selection.

We study spatial patterns excited by resonant, multifrequency forcing of systems near a Hopf bifurcation to spatially homogeneous oscillations. Our third-order, weakly nonlinear analysis shows that for small amplitudes only stripe patterns or hexagons (up and down) are linearly stable; for larger amplitudes rectangles and super-hexagons may become stable. Numerical simulations show, however, that in the latter regime the third-order analysis is insufficient: superhexagons are unstable. Instead large-amplitude hexagons can arise and be bistable with the weakly nonlinear hexagons.

Persistent Structural Plasticity Optimizes Sensory Information Processing in the Olfactory Bulb.

In the mammalian brain, the anatomical structure of neural circuits changes little during adulthood. As a result, adult learning and memory are thought to result from specific changes in synaptic strength. A possible exception is the olfactory bulb (OB), where activity guides interneuron turnover throughout adulthood. These adult-born granule cell (GC) interneurons form new GABAergic synapses that have little synaptic strength plasticity. In the face of persistent neuronal and synaptic turnover, how does the OB balance flexibility, as is required for adapting to changing sensory environments, with perceptual stability? Here we show that high dendritic spine turnover is a universal feature of GCs, regardless of their developmental origin and age. We find matching dynamics among postsynaptic sites on the principal neurons receiving the new synaptic inputs. We further demonstrate in silico that this coordinated structural plasticity is consistent with stable, yet flexible, decorrelated sensory representations. Together, our study reveals that persistent, coordinated synaptic structural plasticity between interneurons and principal neurons is a major mode of functional plasticity in the OB.

Rotating convection in an anisotropic system.

We study the stability of patterns arising in rotating convection in weakly anisotropic systems using a modified Swift-Hohenberg equation. The anisotropy, either an endogenous characteristic of the system or induced by external forcing, can stabilize periodic rolls in the Küppers-Lortz chaotic regime. We apply this to the particular case of rotating convection with time-modulated rotation where recently, in experiment, spiral and target patterns have been observed in otherwise Küppers-Lortz-unstable regimes. We show how the underlying base flow breaks the isotropy, thereby affecting the linear growth rate of convection rolls in such a way as to stabilize spirals and targets. Throughout we compare analytical results to numerical simulations of the Swift-Hohenberg equation.

Tunable front interaction and localization of periodically forced waves.

In systems that exhibit a bistability between nonlinear traveling waves and the basic state, pairs of fronts connecting these two states can form localized wave pulses whose stability depends on the interaction between the fronts. We investigate wave pulses within the framework of coupled Ginzburg-Landau equations describing the traveling-wave amplitudes. We find that the introduction of resonant temporal forcing results in a tunable mechanism for stabilizing such wave pulses. In contrast to other localization mechanisms the temporal forcing can achieve localization by a repulsive as well as by an attractive interaction between the fronts. Systems for which the results are expected to be relevant include binary-mixture convection and electroconvection in nematic liquid crystals.

Instabilities and spatio-temporal chaos of long-wave hexagon patterns in rotating Marangoni convection.

We consider surface-tension driven convection in a rotating fluid layer. For nearly insulating boundary conditions we derive a long-wave equation for the convection planform. Using a Galerkin method and direct numerical simulations we study the stability of the steady hexagonal patterns with respect to general side band instabilities. In the presence of rotation, steady and oscillatory instabilities are identified. One of them leads to stable, homogeneously oscillating hexagons. For sufficiently large rotation rates the stability balloon closes, rendering all steady hexagons unstable and leading to spatio-temporal chaos. (c) 2002 American Institute of Physics.