A simple measure of the coding efficiency of a neuronal population

We derive a simple measure for quantifying the average accuracy with which a neuronal population can represent a stimulus. This quantity, the basis set error, has three key properties: (1) it makes no assumptions about the form of the neuronal responses; (2) it depends only on their second order statistics, so although it is easy to compute, it does take noise correlations into account; (3) its magnitude has an intuitive interpretation in terms of the accuracy with which information can be extracted from the population using a simple method-"simple" meaning linear. We use the basis set error to characterize the efficacy of several types of population codes generated synthetically in a computer. In general, the basis set error typically ranks different encoding schemes in a way that is qualitatively similar to Shannon's mutual information, except when nonlinear readout methods are necessary. Because this measure is concerned with signals that can be read out easily (i.e., through linear operations), it provides a lower bound on coding accuracy relative to the computational capabilities that are accessible to a neuronal population.     

Olfactory coding: tagging and tuning odor-activated synapses for memory

A recent study in the locust olfactory system shows how neuromodulators can alter the rules of synaptic plasticity to form associative memories through the use of 'tagged' synapses.     

Temperature and neuronal circuit function: compensation, tuning and tolerance

Temperature has widespread and diverse effects on different subcellular components of neuronal circuits making it difficult to predict precisely the overall influence on output. Increases in temperature generally increase the output rate in either an exponential or a linear manner. Circuits with a slow output tend to respond exponentially with relatively high Q(10)s, whereas those with faster outputs tend to respond in a linear fashion with relatively low temperature coefficients. Different attributes of the circuit output can be compensated by virtue of opposing processes with similar temperature coefficients. At the extremes of the temperature range, differences in the temperature coefficients of circuit mechanisms cannot be compensated and the circuit fails, often with a reversible loss of ion homeostasis. Prior experience of temperature extremes activates conserved processes of phenotypic plasticity that tune neuronal circuits to be better able to withstand the effects of temperature and to recover more rapidly from failure.     

Numerical study of coding of the movement direction by a population in the motor cortex

The fundamental statistical aspects of population coding of the movement direction in the motor cortex are studied numerically. The activity of neurons in a population is simulated using pseudorandom numbers so that the directional selectivity of the neurons is similar to that observed experimentally. Accuracy of the coding, which is evaluated by the root-mean-square (rms) error, is analyzed for various population sizes, degrees of variability of neuronal activity, and degrees of nonuniformity of distribution of the preferred directions. The dependence of the rms error on the population size shows a good fit to the inverse square-root law, from which it is estimated that a single population must contain around 10 000 neurons in order to attain the accuracy that allows 1 deg rms error, for example. The coding is studied further for populations with different types of tuning function. The results support the hypothesis proposed by Georgopoulos et al. (1988) except that the tuning function must be tuned in the sense that the average value of the function for movements with components in the preferred direction is larger than for movements away from the preferred direction.     

Neural coding and contextual influences in the whisker system

A fundamental problem in neuroscience, to which Prof. Segundo has made seminal contributions, is to understand how action potentials represent events in the external world. The aim of this paper is to review the issue of neural coding in the context of the rodent whiskers, an increasingly popular model system. Key issues we consider are: the role of spike timing; mechanisms of spike timing; decoding and context-dependence. Significant insight has come from the development of rigorous, information theoretic frameworks for tackling these questions, in conjunction with suitably designed experiments. We review both the theory and experimental studies. In contrast to the classical view that neurons are noisy and unreliable, it is becoming clear that many neurons in the subcortical whisker pathway are remarkably reliable and, by virtue of spike timing with millisecond-precision, have high bandwidth for conveying sensory information. In this way, even small (~200 neuron) subcortical modules are able to support the sensory processing underlying sophisticated whisker-dependent behaviours. Future work on neural coding in cortex will need to consider new findings that responses are highly dependent on context, including behavioural and internal states. This article is part of a special issue on Neuronal Dynamics of Sensory Coding.     

Motivational dependence of centrifugal "tuning" influences on taste receptors

Bioelectrical activity was registered in the central sector of the glossopharyngeal nerve. The impulsation was processed on a specialized computer "ATAK-350" in the real-time regimen. Interval histogramms were made, based on the result of survey of 500 inter-impulse intervals. It has been established that during a 4-day food deprivation bimodal distribution of inter-impulse intervals takes place. The first maximum occurs within 10-15 ms, the second--within 190-200 ms. After the irritation of the stomach by the rubber balloon, containing 1.5-2.0 ml of water, monomolar distribution of inter-impulse intervals (with the maximum in the range of 55-60 ms) takes place. It is believed that specific motivating excitement is manifested not only in central structures, but also involves peripheral receptor structure and tunes them to accept adequate stimuli.     

Decoding cortical neuronal signals: Network models,information estimation and spatial tuning

We have studied the encoding of spatial pattern information by complex cells in the primary visual cortex of awake monkeys. Three models for the conditional probabilities of different stimuli, given the neuronal response, were fit and compared using cross-validation. For our data, a feed-forward neural network proved to be the best of these models.The information carried by a cell about a stimulus set can be calculated from the estimated conditional probabilities. We performed a spatial spectroscopy of the encoding, examining how the transmitted information varies with both the average coarseness of the stimulus set and the coarseness differences within it. We find that each neuron encodes information about many features at multiple scales. Our data do not appear to allow a characterization of these variations in terms of the detection of simple single features such as oriented bars.     

Environmental influences in the evolution of tetrapod hearing sensitivity and middle ear tuning

Vertebrates inhabit and communicate acoustically in most natural environments. We review the influence of environmental factors on the hearing sensitivity of terrestrial vertebrates, and on the anatomy and mechanics of the middle ears. Evidence suggests that both biotic and abiotic environmental factors affect the evolution of bandwidth and frequency of peak sensitivity of the hearing spectrum. Relevant abiotic factors include medium type, temperature, and noise produced by nonliving sources. Biotic factors include heterospecific, conspecific, or self-produced sounds that animals are selected to recognize, and acoustic interference by sounds that other animals generate. Within each class of tetrapods, the size of the middle ear structures correlates directly to body size and inversely to frequency of peak sensitivity. Adaptation to the underwater medium in cetaceans involved reorganization of the middle ear for novel acoustic pathways, whereas adaptation to subterranean life in several mammals resulted in hypertrophy of the middle ear ossicles to enhance their inertial mass for detection of seismic vibrations. The comparative approach has revealed a number of generalities about the effect of environmental factors on hearing performance and middle ear structure across species. The current taxonomic sampling of the major tetrapod groups is still highly unbalanced and incomplete. Future expansion of the comparative evidence should continue to reveal general patterns and novel mechanisms.     

Degeneracy in the nervous system: from neuronal excitability to neural coding

Degeneracy is ubiquitous across biological systems where structurally different elements can yield a similar outcome. Degeneracy is of particular interest in neuroscience too. On the one hand, degeneracy confers robustness to the nervous system and facilitates evolvability: Different elements provide a backup plan for the system in response to any perturbation or disturbance. On the other, a difficulty in the treatment of some neurological disorders such as chronic pain is explained in light of different elements all of which contribute to the pathological behavior of the system. Under these circumstances, targeting a specific element is ineffective because other elements can compensate for this modulation. Understanding degeneracy in the physiological context explains its beneficial role in the robustness of neural circuits. Likewise, understanding degeneracy in the pathological context opens new avenues of discovery to find more effective therapies.     

Ionic, neuronal and endocrine influences on the proopiomelanocortin system of the hypothalamus.

Increasing evidence supports a neurotransmitter or a neuromodulator action for peptides derived from proopiomelanocortin in the hypothalamus. Peptide release involves sodium, potassium and calcium ion channels and is dependent on the presence of extracellular calcium ions at the time of depolarisation of neuronal membranes. Dopaminergic and gamma-aminobutyric acid-containing neuronal systems inhibit POMC-derived peptide release from the hypothalamus through D2-dopamine and GABAA receptors, respectively. Serotoninergic mechanisms exert a biphasic effect on peptide release being directly stimulatory at low concentrations of serotonin and indirectly inhibitory at higher concentrations via interactions with the endogenous dopaminergic system. Cholinergic and glutamergic drugs stimulate peptide release through nicotinic and N-methyl-D-aspartate receptors, respectively. Finally, circulating steroids regulate the hypothalamic POMC system with testosterone stimulating POMC gene expression whilst oestradiol and glucocorticoids induce an inhibitory control.     

Seasonal influences on population spread and persistence in streams: spreading speeds

The drift paradox asks how stream-dwelling organisms can persist, without being washed out, when they are continuously subject to the unidirectional stream flow. To date, mathematical analyses of the stream paradox have investigated the interplay of growth, drift and flow needed for species persistence under the assumption that the stream environment is temporally constant. However, in reality, streams are subject to major seasonal variations in environmental factors that govern population growth and dispersal. We consider the influence of such seasonal variations on the drift paradox, using a time-periodic integrodifferential equation model. We establish upstream and downstream spreading speeds under the assumption of periodically fluctuating environments, and also show the existence of periodic traveling waves. The sign of the upstream spreading speed then determines persistence. Fluctuating environments are characterized by seasonal correlations between the flow, transfer rates, diffusion and settling rates, and we investigate the effect of such correlations on the population spread and persistence. We also show how results in this paper can formally connect to those for autonomous integrodifferential equations, through the appropriate weighted averaging methods. Finally, for a specific dispersal function, we show that the upstream spreading speed is nonnegative if and only if the critical domain size exists in this temporally fluctuating environment.     

Multiple influences of a heparin-binding growth factor on neuronal development

Heparin-binding growth factor-2 (HBGF-2; also known as basic fibroblast growth factor) is mitogenic for most anchorage-dependent cells. It is shown here that HBGF-2 stimulates cell-substratum adhesion and neurite extension in the sympathetic nerve cell line PC12. When HBGF-2 is adsorbed to artificial extracellular matrices consisting of heparin or chondroitin sulfate, it causes the formation of cellular aggregates or circles of cells, respectively. HBGF-2 is also a nerve cell survival molecule, for it potentiates the survival of primary cultures of embryonic chick ciliary ganglion cells but not of embryonic neural retina cells. Finally, a series of synthetic peptides from the HBGF-2 sequence is described that selectively alter the biological effects of HBGF-2. The amphiphilic nature of one of these peptides is discussed with respect to its ability to stimulate cell adhesion.     

Oscillations, resonances and noise: basis of flexible neuronal pattern generation

Modulation of neuronal impulse pattern is examined by means of a simplified Hodgkin-Huxley type computer model which refers to experimental recordings of cold receptor discharges. This model essentially consists of two potentially oscillating subsystems: a spike generator and a subthreshold oscillator. With addition of noise the model successfully mimics the major types of experimentally recorded impulse patterns and thereby elucidate different resonance behaviors. (1) There is a range of rhythmic spiking or bursting where the spike generator is strongly coupled to the subthreshold oscillator. (2) There is a pacemaker activity of more complex interactions where the spike generator has overtaken part of the control. (3) There is a situation where the two subsystems are decoupled and only resonate with the help of noise.     

Estimating environmental effects on population dynamics: consequences of observation error

Within the paradigm of population dynamics a central task is to identify environmental factors affecting population change and to estimate the strength of these effects. We here investigate the impact of observation errors in measurements of population densities on estimates of environmental effects. Adding observation errors may change the autocorrelation of a population time series with potential consequences for estimates of effects of autocorrelated environmental covariates. Using Monte Carlo simulations, we compare the performance of maximum likelihood estimates from three stochastic versions of the Gompertz model (log–linear first order autoregressive model), assuming 1) process error only, 2) observation error only, and 3) both process and observation error (the linear state–space model on log‐scale). We also simulated population dynamics using the Ricker model, and evaluated the corresponding maximum likelihood estimates for process error models. When there is observation error in the data and the considered environmental variable is strongly autocorrelated, its estimated effect is likely to be biased when using process error models. The environmental effect is overestimated when the sign of the autocorrelations of the intrinsic dynamics and the environment are the same and underestimated when the signs differ. With non‐autocorrelated environmental covariates, process error models produce fairly exact point estimates as well as reliable confidence intervals for environmental effects. In all scenarios, observation error models produce unbiased estimates with reasonable precision, but confidence intervals derived from the likelihood profiles are far too optimistic if there is process error present. The safest approach is to use state–space models in presence of observation error. These are factors worthwhile to consider when interpreting earlier empirical results on population time series, and in future studies, we recommend choosing carefully the modelling approach with respect to intrinsic population dynamics and covariate autocorrelation.     

New roles for the gamma rhythm: population tuning and preprocessing for the Beta rhythm

Gamma (30–80 Hz) and beta (12–30 Hz) oscillations such as those displayed by in vitro hippocampal (CA1) slice preparations and by in vivo neocortical EEGs often occur successively, with a spontaneous transition between them. In the gamma rhythm, pyramidal cells fire together with the interneurons, while in the beta rhythm, pyramidal cells fire on a subset of cycles of the interneurons. It is shown that gamma and beta rhythms have different properties with respect to creation of cell assemblies. In the presence of heterogeneous inputs to the pyramidal cells, the gamma rhythm creates an assembly of firing pyramidal cells from cells whose drive exceeds a threshold. During the gamma to beta transition, a slow outward potassium current is activated, and as a result the cell assembly vanishes. The slow currents make each of the pyramidal cells fire with a beta rhythm, but the field potential of the network still displays a gamma rhythm. Hebbian changes of connections among the pyramidal cells give rise to a beta rhythm, and the cell assemblies are recovered with a temporal separation between cells firing in different cycles. We present experimental evidence showing that such a separation can occur in hippocampal slices.     

Neural coding of categories: information efficiency and optimal population codes

This paper deals with the analytical study of coding a discrete set of categories by a large assembly of neurons. We consider population coding schemes, which can also be seen as instances of exemplar models proposed in the literature to account for phenomena in the psychophysics of categorization. We quantify the coding efficiency by the mutual information between the set of categories and the neural code, and we characterize the properties of the most efficient codes, considering different regimes corresponding essentially to different signal-to-noise ratio. One main outcome is to find that, in a high signal-to-noise ratio limit, the Fisher information at the population level should be the greatest between categories, which is achieved by having many cells with the stimulus-discriminating parts (steepest slope) of their tuning curves placed in the transition regions between categories in stimulus space. We show that these properties are in good agreement with both psychophysical data and with the neurophysiology of the inferotemporal cortex in the monkey, a cortex area known to be specifically involved in classification tasks.