Interspike interval statistics in the Ornstein-Uhlenbeck neuronal model with signal-dependent noise

The stochastic leaky integrate-and-fire (LIF) continuous model is studied under the condition that the amplitude of noise is a function of the input signal. The coefficient of variation (CV) of interspike intervals (ISIs) is investigated for different types of dependencies between the noise and the signal. Finally, we present the CV and the ISI density resulting from the special choice of parameters of the input that gave rise to a contra-intuitive behavior of the transfer function in Lánsky and Sacerdote [Phys. Lett. A 285 (2001) 132].     

Effect of periodic stimulus on a neuronal diffusion model with signal-dependent noise

To relate the noise intensity with a periodically modulated input signal in a single neuron stochastic model we introduce a diffusion model with both time modulated drift and diffusion coefficient. Such a model is the continuous version of a Stein model with time oscillating frequencies for the Poisson processes describing the inputs impinging on the neuron. We focus here on some aspects of the resonance phenomenon for such a model. We compare the corresponding interspike interval distribution with the analogous distribution for a model sharing the same parameter values, but with constant noise intensity. Examples with two different levels for this noise intensity are discussed. The enhancement of the height of the peaks in the interspike interval distribution appearing at the modulation period, the improvement of the phase locking behavior and an enlargement of the noise ranges where a resonance like behavior arises are the main features observed in the considered cases.     

Optimum signal in a diffusion leaky integrate-and-fire neuronal model

An optimum signal in the Ornstein-Uhlenbeck neuronal model is determined on the basis of interspike interval data. Two criteria are proposed for this purpose. The first, the classical one, is based on searching for maxima of the slope of the frequency transfer function. The second one uses maximum of the Fisher information, which is, under certain conditions, the inverse variance of the best possible estimator. The Fisher information is further normalized with respect to the time required to make the observation on which the signal estimation is performed. Three variants of the model are investigated. Beside the basic one, we use the version obtained by inclusion of the refractory period. Finally, we investigate such a version of the model in which signal and the input parameter of the model are in a nonlinear relationship. The results show that despite qualitative similarity between the criteria, there is substantial quantitative difference. As a common feature, we found that in the Ornstein-Uhlenbeck model with increasing noise the optimum signal decreases and the coding range gets broader.     

Statistical approach in search for optimal signal in simple olfactory neuronal models

Several models (concentration detectors and a flux detector) for coding of odor intensity in olfactory sensory neurons are investigated. Behavior of the system is described by different stochastic processes of binding the odorant molecules to the receptors and their activation. Characteristics how well the odorant concentration can be estimated from the knowledge of response, the number of activated neurons, are studied. The approach is based on the Fisher information and analogous measures. These measures of optimality are computed and applied to locate the odorant concentration which is most suitable for coding. The results are compared with the classical deterministic approach which judges the optimal odorant concentration via steepness of the input-output function.     

Effects of random jumps on a very simple neuronal diffusion model

The effects of taking into account in a perfect integrate and fire model of neuronal activity the spatial localization of the synapses are studied by superposing to the diffusion a simple discrete jump component. Different criteria are employed to assess the role of excitatory and inhibitory discrete contributions. Comparisons are performed with respect to the case where contributions coming from synapses more distal from the trigger zone are summed up in a continuous model. A systematic study of the output frequency and of the inter spike interval coefficient of variation (CV) is performed by means of examples as the model parameters are varied.     

Different types of noise in leaky integrate-and-fire model of neuronal dynamics with discrete periodical input

Different variants of stochastic leaky integrate-and-fire model for the membrane depolarisation of neurons are investigated. The model is driven by a constant input and equidistant pulses of fixed amplitude. These two types of signal are considered under the influence of three types of noise: white noise, jitter on interpulse distance, and noise in the amplitude of pulses. The results of computational experiments demonstrate the enhancement of the signal by noise in subthreshold regime and deterioration of the signal if it is sufficiently strong to carry the information in absence of noise. Our study holds mainly to central neurons that process discrete pulses although an application in sensory system is also available.     

Effect of the number of grey levels on the detectability of a simple line signal in visual noise

The number of grey levels, G, contained in a digitized image of an external event must affect the fidelity of reproduction of that event for physical reasons. The question arises as to whether there is a separate perceptual effect of G. Three experiments are described which investigate the effect of G on the visibility of a straight-line signal in visual noise using a signal detection analysis to separate the physical and perceptual effects of G. The results show that, for the type of displays employed, and for the specific task of detection of lines in visual noise, there was no effect of G on efficiency, which suggests that G had no separate perceptual effect.     

Conductance versus current noise in a neuronal model for noisy subthreshold oscillations and related spike generation

Biological systems are notoriously noisy. Noise, therefore, also plays an important role in many models of neural impulse generation. Noise is not only introduced for more realistic simulations but also to account for cooperative effects between noisy and nonlinear dynamics. Often, this is achieved by a simple noise term in the membrane equation (current noise). However, there are ongoing discussions whether such current noise is justified or whether rather conductance noise should be introduced because it is closer to the natural origin of noise. Therefore, we have compared the effects of current and conductance noise in a neuronal model for subthreshold oscillations and action potential generation. We did not see any significant differences in the model behavior with respect to voltage traces, tuning curves of interspike intervals, interval distributions or frequency responses when the noise strength is adjusted. These findings indicate that simple current noise can give reasonable results in neuronal simulations with regard to physiological relevant noise effects.     

Integrins mediate a neuronal survival signal for oligodendrocytes.

Target-dependent survival of newly differentiated cells is an important part of neural development. In the case of myelin-forming oligodendrocytes, it matches the number of oligodendrocytes to the available axons [1]. In addition to growth factors, an axonal signal regulates this survival: when axons are transected, oligodendrocytes die and, conversely, when the number of axons is increased by genetic manipulation, oligodendrocyte numbers increase [2] [3]. Newly formed oligodendrocytes that fail to contact axons undergo apoptosis, and co-culture experiments that model axon-glial interactions in vitro reveal a neuronal survival effect not present in neuron-conditioned medium [4] [5], suggesting that the signal is non-diffusible and present on the surface of axons. The nature of these neuronal signals is unknown, as are the mechanisms by which they interact with growth-factor-mediated survival signals. As integrins can regulate survival in other cell types [6] [7] [8], we determined whether integrins are involved in the neuronal survival effect. We found that the laminin receptor alpha6beta1 integrin, which is expressed on oligodendrocytes, enhances the sensitivity of oligodendrocytes to the survival effect of growth factors. On the basis of this interaction between integrin and growth-factor-mediated signalling, we propose a simple model by which signals from axons and other cell types might interact to regulate oligodendrocyte cell numbers.     

On a simple epidemic model with a heterogeneous infective population

This paper is concerned with a generalization of the simple epidemic model in which the infective population is partitioned intom classes, each of specific infectiousness. Attention is restricted, however, to the case where all the meeting rates between two individuals are equal to each other. Both deterministic and stochastic versions are examined. In either case the development in time of the epidemic process is investigated by exploiting a connection with the standard simple epidemic model. Finally, it is shown that the technique used also applies to a similar model for the spread of information.     

A RIP tide in neuronal signal transduction

The generation of nuclear signaling proteins by regulated intramembrane proteolysis (RIP) is a new paradigm of signal transduction. Mammalian proteins that are processed by RIP include SREBP-1, Notch-1, amyloid precursor protein (APP), and ErbB-4. Intramembranous gamma-secretase cleavage of APP plays a central role in Alzheimer's disease by generating the amyloid beta protein. An intriguing possibility is that the cognate C-terminal fragment generated by gamma-secretase cleavage could also play a role through the regulation of nuclear signaling events. Thus, RIP may contribute to both brain development and degeneration and may provide unexpected diversity to the signaling repertoire of a cell.     

Spike correlations in a songbird agree with a simple markov population model

The relationships between neural activity at the single-cell and the population levels are of central importance for understanding neural codes. In many sensory systems, collective behaviors in large cell groups can be described by pairwise spike correlations. Here, we test whether in a highly specialized premotor system of songbirds, pairwise spike correlations themselves can be seen as a simple corollary of an underlying random process. We test hypotheses on connectivity and network dynamics in the motor pathway of zebra finches using a high-level population model that is independent of detailed single-neuron properties. We assume that neural population activity evolves along a finite set of states during singing, and that during sleep population activity randomly switches back and forth between song states and a single resting state. Individual spike trains are generated by associating with each of the population states a particular firing mode, such as bursting or tonic firing. With an overall modification of one or two simple control parameters, the Markov model is able to reproduce observed firing statistics and spike correlations in different neuron types and behavioral states. Our results suggest that song- and sleep-related firing patterns are identical on short time scales and result from random sampling of a unique underlying theme. The efficiency of our population model may apply also to other neural systems in which population hypotheses can be tested on recordings from small neuron groups.     

Neuromimetic model of a neuronal filter

Experimental work in cats has shown that a series of afferent impulses from muscle receptors activated during contractions of an ankle extensor elicit declining inhibitory potentials in homonymous and synergic motoneurones. Inhibitory potentials were ascribed to the action of Ib afferents from Golgi tendon organs that are specific contraction-sensitive mechano-receptors. The decline of inhibition was, at least partly, due to presynaptic inhibition acting as a filter of tendon organ information in the spinal cord. In the present work, a computer model of the simplest spinal pathways from Ib fibres to motoneurones was designed. In order to make the model as realistic as possible, the most pertinent of the known functional properties of the neuronal elements were incorporated. Functions simulating primary afferent depolarizations of Ib terminals, i.e. the electrophysiological correlate of presynaptic inhibition, were introduced in the network. Simulations showed that declining inhibitory potentials were computed in the output stage of the network that represented the motoneurone-like element. These results support the assumption that the filtering out of Ib inputs is to a great extent due to presynaptic inhibition. The model behaved as expected, suggesting that predictions of the behaviour of neural components in the biological network should be possible upon introduction in the model of other, more complex, spinal pathways from Ib fibres to motoneurones.     

Optimum flux-detection in the absence of a priori knowledge about the signal

Detection systems based on photon counting have to discriminate between two types of fluctuations in the photon count: those resulting from statistical fluctuations (=noise) and those caused by changes in the radiance set by the source (=signal). In contrast with earlier studies on ways of discriminating noise from signal changes, no specific assumptions are made about the source. An optimal discrimination-method has been developed for a detector that has no prior information about the mean of the Poisson distribution that describes its input signal. Because the detector has no prior information at its disposal it has to assume an a priori probability for the mean in a unique and objective way and it has to estimate the actual mean using Bayes rule of inference. This new discrimination-method is discussed in the context of signal processing in the visual system, but is generally applicable in all systems where photon-noise is important.