Nonnormal amplification in random balanced neuronal networks

In dynamical models of cortical networks, the recurrent connectivity can amplify the input given to the network in two distinct ways. One is induced by the presence of near-critical eigenvalues in the connectivity matrix W, producing large but slow activity fluctuations along the corresponding eigenvectors (dynamical slowing). The other relies on W being nonnormal, which allows the network activity to make large but fast excursions along specific directions. Here we investigate the tradeoff between nonnormal amplification and dynamical slowing in the spontaneous activity of large random neuronal networks composed of excitatory and inhibitory neurons. We use a Schur decomposition of W to separate the two amplification mechanisms. Assuming linear stochastic dynamics, we derive an exact expression for the expected amount of purely nonnormal amplification. We find that amplification is very limited if dynamical slowing must be kept weak. We conclude that, to achieve strong transient amplification with little slowing, the connectivity must be structured. We show that unidirectional connections between neurons of the same type together with reciprocal connections between neurons of different types, allow for amplification already in the fast dynamical regime. Finally, our results also shed light on the differences between balanced networks in which inhibition exactly cancels excitation, and those where inhibition dominates.Comment: 13 pages, 7 figure

Extracting non-linear integrate-and-fire models from experimental data using dynamic I–V curves

The dynamic I–V curve method was recently introduced for the efficient experimental generation of reduced neuron models. The method extracts the response properties of a neuron while it is subject to a naturalistic stimulus that mimics in vivo-like fluctuating synaptic drive. The resulting history-dependent, transmembrane current is then projected onto a one-dimensional current–voltage relation that provides the basis for a tractable non-linear integrate-and-fire model. An attractive feature of the method is that it can be used in spike-triggered mode to quantify the distinct patterns of post-spike refractoriness seen in different classes of cortical neuron. The method is first illustrated using a conductance-based model and is then applied experimentally to generate reduced models of cortical layer-5 pyramidal cells and interneurons, in injected-current and injected- conductance protocols. The resulting low-dimensional neuron models—of the refractory exponential integrate-and-fire type—provide highly accurate predictions for spike-times. The method therefore provides a useful tool for the construction of tractable models and rapid experimental classification of cortical neurons

Use of substratum ripples for flow refuging by Atlantic cod, Gadus morhua

The ability to maintain position in a current without actively swimming (station-holding) was measured on substratum ripples for Atlantic cod, Gadus morhua, a bentho-pelagic fusiform species. The current velocities tested ranged from 0–111 cm sec -1 . Ripples were sinusoidal, with twelve combinations of ripple wavelength (10, 25, 50, 125 cm) and ripple amplitude (1.0, 2.5, 5.0 cm). Ripple wavelengths were chosen to approximate 0.5, 1.0, 2.0 and 5.0 times fish total length. The potential of ripples to locally retard current and thereby provide a refuge from the flow was measured as a velocity ratio, u trough /u free-stream , where u trough is the flow velocity measured at a height of 0.5 cm from the bottom of a trough and u free-stream the flow velocity measured at a height of 10 cm above ripple crests. Cod usually swam steadily above substratum ripple crests in the free-stream flow. They used substratum ripples to hold station on only 3 of the 12 ripples tested by refuging from the flow in the ripple troughs (flow refuging). These ripples had wavelengths approaching twice the body length, with ripple amplitudes that produced velocity ratios of 0.44–0.65, thus providing at least a 35% flow reduction in the troughs. In addition, these ripples were only used at intermediate velocities starting at 49–78 cm sec -1 and ending at 81–109 cm sec -1 depending on the ripple morphology, suggesting there may be costs involved in flow refuging, probably in stability control. Flow refuging on substratum ripples could dramatically impact the physiology and ecology of cod in high current velocities by providing areas of retreat for energetic savings, but also offering opportunities for enhanced feeding and migration.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42640/1/10641_2004_Article_153122.pd

Generalized Rate-Code Model for Neuron Ensembles with Finite Populations

We have proposed a generalized Langevin-type rate-code model subjected to multiplicative noise, in order to study stationary and dynamical properties of an ensemble containing {\it finite} $N$ neurons. Calculations using the Fokker-Planck equation (FPE) have shown that owing to the multiplicative noise, our rate model yields various kinds of stationary non-Gaussian distributions such as gamma, inverse-Gaussian-like and log-normal-like distributions, which have been experimentally observed. Dynamical properties of the rate model have been studied with the use of the augmented moment method (AMM), which was previously proposed by the author with a macroscopic point of view for finite-unit stochastic systems. In the AMM, original $N$-dimensional stochastic differential equations (DEs) are transformed into three-dimensional deterministic DEs for means and fluctuations of local and global variables. Dynamical responses of the neuron ensemble to pulse and sinusoidal inputs calculated by the AMM are in good agreement with those obtained by direct simulation. The synchronization in the neuronal ensemble is discussed. Variabilities of the firing rate and of the interspike interval (ISI) are shown to increase with increasing the magnitude of multiplicative noise, which may be a conceivable origin of the observed large variability in cortical neurons.Comment: 19 pages, 9 figures, accepted in Phys. Rev. E after minor modification

Learning navigational maps through potentiation and modulation of hippocampal place cells

We analyze a model of navigational map formation based on correlation-based, temporally asymmetric potentiation and depression of synapses between hippocampal place cells. We show that synaptic modification during random exploration of an environment shifts the location encoded by place cell activity in such a way that it indicates the direction from any location to a fixed target avoiding walls and other obstacles. Multiple maps to different targets can be simultaneously stored if we introduce target-dependent modulation of place cell activity. Once maps to a number of target locations in a given environment have been stored, novel maps to previously unknown target locations are automatically constructed by interpolation between existing maps

Competing synapses with two timescales: a basis for learning and forgetting

Competitive dynamics are thought to occur in many processes of learning involving synaptic plasticity. Here we show, in a game theory-inspired model of synaptic interactions, that the competition between synapses in their weak and strong states gives rise to a natural framework of learning, with the prediction of memory inherent in a timescale for `forgetting' a learned signal. Among our main results is the prediction that memory is optimized if the weak synapses are really weak, and the strong synapses are really strong. Our work admits of many extensions and possible experiments to test its validity, and in particular might complement an existing model of reaching, which has strong experimental support.Comment: 7 pages, 3 figures, to appear in Europhysics Letter

Topological Speed Limits to Network Synchronization

We study collective synchronization of pulse-coupled oscillators interacting on asymmetric random networks. We demonstrate that random matrix theory can be used to accurately predict the speed of synchronization in such networks in dependence on the dynamical and network parameters. Furthermore, we show that the speed of synchronization is limited by the network connectivity and stays finite, even if the coupling strength becomes infinite. In addition, our results indicate that synchrony is robust under structural perturbations of the network dynamics.Comment: 5 pages, 3 figure

The spike train statistics for consonant and dissonant musical accords

The simple system composed of three neural-like noisy elements is considered. Two of them (sensory neurons or sensors) are stimulated by noise and periodic signals with different ratio of frequencies, and the third one (interneuron) receives the output of these two sensors and noise. We propose the analytical approach to analysis of Interspike Intervals (ISI) statistics of the spike train generated by the interneuron. The ISI distributions of the sensory neurons are considered to be known. The frequencies of the input sinusoidal signals are in ratios, which are usual for music. We show that in the case of small integer ratios (musical consonance) the input pair of sinusoids results in the ISI distribution appropriate for more regular output spike train than in a case of large integer ratios (musical dissonance) of input frequencies. These effects are explained from the viewpoint of the proposed theory.Comment: 22 pages, 6 figure