Subthreshold membrane-potential resonances shape spike-train patterns in the entorhinal cortex.

Many neurons exhibit subthreshold membrane-potential resonances, such that the largest voltage responses occur at preferred stimulation frequencies. Because subthreshold resonances are known to influence the rhythmic activity at the network level, it is vital to understand how they affect spike generation on the single-cell level. We therefore investigated both resonant and nonresonant neurons of rat entorhinal cortex. A minimal resonate-and-fire type model based on measured physiological parameters captures fundamental properties of neuronal firing statistics surprisingly well and helps to shed light on the mechanisms that shape spike patterns: 1) subthreshold resonance together with a spike-induced reset of subthreshold oscillations leads to spike clustering and 2) spike-induced dynamics influence the fine structure of interspike interval (ISI) distributions and are responsible for ISI correlations appearing at higher firing rates (> or =3 Hz). Both mechanisms are likely to account for the specific discharge characteristics of various cell types.

Dynamics of rat entorhinal cortex layer II and III cells: characteristics of membrane potential resonance at rest predict oscillation properties near threshold.

Neurones generate intrinsic subthreshold membrane potential oscillations (MPOs) under various physiological and behavioural conditions. These oscillations influence neural responses and coding properties on many levels. On the single-cell level, MPOs modulate the temporal precision of action potentials; they also have a pronounced impact on large-scale cortical activity. Recent studies have described a close association between the MPOs of a given neurone and its electrical resonance properties. Using intracellular sharp microelectrode recordings we examine both dynamical characteristics in layers II and III of the entorhinal cortex (EC). Our data from EC layer II stellate cells show strong membrane potential resonances and oscillations, both in the range of 5-15 Hz. At the resonance maximum, the membrane impedance can be more than twice as large as the input resistance. In EC layer III cells, MPOs could not be elicited, and frequency-resolved impedances decay monotonically with increasing frequency or has only a small peak followed by a subsequent decay. To quantify and compare the resonance and oscillation properties, we use a simple mathematical model that includes stochastic components to capture channel noise. Based on this model we demonstrate that electrical resonance is closely related though not equivalent to the occurrence of sag-potentials and MPOs. MPO frequencies can be predicted from the membrane impedance curve for stellate cells. The model also explains the broad-band nature of the observed MPOs. This underscores the importance of intrinsic noise sources for subthreshold phenomena and rules out a deterministic description of MPOs. In addition, our results show that the two identified cell classes in the superficial EC layers, which are known to target different areas in the hippocampus, also have different preferred frequency ranges and dynamic characteristics. Intrinsic cell properties may thus play a major role for the frequency-dependent information flow in the hippocampal formation.

Representation of acoustic communication signals by insect auditory receptor neurons.

Despite their simple auditory systems, some insect species recognize certain temporal aspects of acoustic stimuli with an acuity equal to that of vertebrates; however, the underlying neural mechanisms and coding schemes are only partially understood. In this study, we analyze the response characteristics of the peripheral auditory system of grasshoppers with special emphasis on the representation of species-specific communication signals. We use both natural calling songs and artificial random stimuli designed to focus on two low-order statistical properties of the songs: their typical time scales and the distribution of their modulation amplitudes. Based on stimulus reconstruction techniques and quantified within an information-theoretic framework, our data show that artificial stimuli with typical time scales of >40 msec can be read from single spike trains with high accuracy. Faster stimulus variations can be reconstructed only for behaviorally relevant amplitude distributions. The highest rates of information transmission (180 bits/sec) and the highest coding efficiencies (40%) are obtained for stimuli that capture both the time scales and amplitude distributions of natural songs. Use of multiple spike trains significantly improves the reconstruction of stimuli that vary on time scales <40 msec or feature amplitude distributions as occur when several grasshopper songs overlap. Signal-to-noise ratios obtained from the reconstructions of natural songs do not exceed those obtained from artificial stimuli with the same low-order statistical properties. We conclude that auditory receptor neurons are optimized to extract both the time scales and the amplitude distribution of natural songs. They are not optimized, however, to extract higher-order statistical properties of the song-specific rhythmic patterns.

Neural codes: firing rates and beyond.

Computational neuroscience has contributed significantly to our understanding of higher brain function by combining experimental neurobiology, psychophysics, modeling, and mathematical analysis. This article reviews recent advances in a key area: neural coding and information processing. It is shown that synapses are capable of supporting computations based on highly structured temporal codes. Such codes could provide a substrate for unambiguous representations of complex stimuli and be used to solve difficult cognitive tasks, such as the binding problem. Unsupervised learning rules could generate the circuitry required for precise temporal codes. Together, these results indicate that neural systems perform a rich repertoire of computations based on action potential timing.

Viral dynamics in vivo: limitations on estimates of intracellular delay and virus decay.

Anti-viral drug treatment of human immunodeficiency virus type I (HIV-1) and hepatitis B virus (HBV) infections causes rapid reduction in plasma virus load. Viral decline occurs in several phases and provides information on important kinetic constants of virus replication in vivo and pharmacodynamical properties. We develop a mathematical model that takes into account the intracellular phase of the viral life-cycle, defined as the time between infection of a cell and production of new virus particles. We derive analytic solutions for the dynamics following treatment with reverse transcriptase inhibitors, protease inhibitors, or a combination of both. For HIV-1, our results show that the phase of rapid decay in plasma virus (days 2-7) allows precise estimates for the turnover rate of productively infected cells. The initial quasi-stationary phase (days 0-1) and the transition phase (days 1-2) are explained by the combined effects of pharmacological and intracellular delays, the clearance of free virus particles, and the decay of infected cells. Reliable estimates of the first three quantities are not possible from data on virus load only; such estimates require additional measurements. In contrast with HIV-1, for HBV our model predicts that frequent early sampling of plasma virus will lead to reliable estimates of the free virus half-life and the pharmacological properties of the administered drug. On the other hand, for HBV the half-life of infected cells cannot be estimated from plasma virus decay.

Rapid local synchronization of action potentials: toward computation with coupled integrate-and-fire neurons.

The collective behavior of interconnected spiking nerve cells is investigated. It is shown that a variety of model systems exhibit the same short-time behavior and rapidly converge to (approximately) periodic firing patterns with locally synchronized action potentials. The dynamics of one model can be described by a downhill motion on an abstract energy landscape. Since an energy landscape makes it possible to understand and program computation done by an attractor network, the results will extend our understanding of collective computation from models based on a firing-rate description to biologically more realistic systems with integrate-and-fire neurons.

Collective phenomena in spatially extended evolutionary games.

A class of spatially extended evolutionary games with simple local rules is introduced. The emergent properties are studied through two complementary approaches. One is based on a heuristic local analysis, the other on exact global techniques. The local analysis provides criteria to group the games into classes with distinct behavior. The results facilitate numerical simulations and reveal that even simple games allow for complex spatio-temporal phenomena. The global analysis demonstrates that certain games perform an uphill march in a fitness landscape determined by the payoff parameters and the topology of the underlying lattice structure. For generic game parameters, the landscape is rugged owing to competing interactions and generates dynamical phenomena well known from frustrated systems: trapping in local maxima for noiseless dynamics and very long relaxation times for stochastic dynamics. Although the model is a mere caricature of evolutionary processes, some of its emergent properties are reminiscent of those observed in nature. It is argued that similar dynamical phenomena will be present in more elaborate approaches.