Frequency selectivity emerging from spike-timing-dependent plasticity.

Periodic neuronal activity has been observed in various areas of the brain, from lower sensory to higher cortical levels. Specific frequency components contained in this periodic activity can be identified by a neuronal circuit that behaves as a bandpass filter with given preferred frequency, or best modulation frequency (BMF). For BMFs typically ranging from 10 to 200 Hz, a plausible and minimal configuration consists of a single neuron with adjusted excitatory and inhibitory synaptic connections. The emergence, however, of such a neuronal circuitry is still unclear. In this letter, we demonstrate how spike-timing-dependent plasticity (STDP) can give rise to frequency-dependent learning, thus leading to an input selectivity that enables frequency identification. We use an in-depth mathematical analysis of the learning dynamics in a population of plastic inhibitory connections. These provide inhomogeneous postsynaptic responses that depend on their dendritic location. We find that synaptic delays play a crucial role in organizing the weight specialization induced by STDP. Under suitable conditions on the synaptic delays and postsynaptic potentials (PSPs), the BMF of a neuron after learning can match the training frequency. In particular, proximal (distal) synapses with shorter (longer) dendritic delay and somatically measured PSP time constants respond better to higher (lower) frequencies. As a result, the neuron will respond maximally to any stimulating frequency (in a given range) with which it has been trained in an unsupervised manner. The model predicts that synapses responding to a given BMF form clusters on dendritic branches.

Optimality in mono- and multisensory map formation.

In the struggle for survival in a complex and dynamic environment, nature has developed a multitude of sophisticated sensory systems. In order to exploit the information provided by these sensory systems, higher vertebrates reconstruct the spatio-temporal environment from each of the sensory systems they have at their disposal. That is, for each modality the animal computes a neuronal representation of the outside world, a monosensory neuronal map. Here we present a universal framework that allows to calculate the specific layout of the involved neuronal network by means of a general mathematical principle, viz., stochastic optimality. In order to illustrate the use of this theoretical framework, we provide a step-by-step tutorial of how to apply our model. In so doing, we present a spatial and a temporal example of optimal stimulus reconstruction which underline the advantages of our approach. That is, given a known physical signal transmission and rudimental knowledge of the detection process, our approach allows to estimate the possible performance and to predict neuronal properties of biological sensory systems. Finally, information from different sensory modalities has to be integrated so as to gain a unified perception of reality for further processing, e.g., for distinct motor commands. We briefly discuss concepts of multimodal interaction and how a multimodal space can evolve by alignment of monosensory maps.

Neuronal identification of signal periodicity by balanced inhibition.

Many animals, including men, use periodicity information, e.g., amplitude modulations of acoustic stimuli, as a vital cue to auditory object formation. The underlying neuronal mechanisms, however, still remain a matter of debate. Here, we mathematically analyze a model for periodicity identification that relies on the interplay of excitation and delayed inhibition. Our analytical results show how the maximal response of such a system varies systematically with the time constants of excitation and inhibition. The model reliably identifies signal periodicity in the range from about ten to several hundred Hertz. Importantly, the model relies on biologically plausible parameters only. It works best for excitatory and inhibitory neuronal couplings of equal strength, the so-called 'balanced inhibition'. We show how balanced inhibition can serve to identify low-frequency signal periodicity and how variation of a single parameter, the inhibitory time constant, can tune the system to different frequencies.

Modeling the cochlear nucleus: a site for monaural echo suppression?

Echo suppression plays an important role in identifying and localizing auditory objects. One can distinguish between binaural and monaural echo suppression, although the former is the one commonly referred to. Based on biological findings we introduce and analyze a mathematical model for a neural implementation of monaural echo suppression in the cochlear nucleus. The model's behavior has been verified by analytical calculations as well as by numerical simulations for several types of input signal. It shows that in the perception of a pair of clicks the leading click suppresses the lagging one and that suppression is maximal for an interclick interval of 2-3 ms. Similarly, ongoing stimuli will be affected by the suppression mechanism primarily a couple of milliseconds after onset, resulting in a reduced perception of a sound shortly after its start. Both effects match experimental data.

Neuronal identification of acoustic signal periodicity.

Acoustic signals transmit information by temporal characteristics and envelope periodicity as well as by their frequency content. Many animals can extract the frequency content of a signal by means of specialized organs such as the cochlea but for the detection and identification of higher-order periodicity, e.g., amplitude modulations, this type of organ is useless. In addition, many animals do not have a cochlea but still depend on a reliable identification of different frequencies in the vast variety of acoustic signals they perceive in their natural environment. Hence, neural mechanisms to decode periodicity information must exist. We present a detailed mathematical analysis of a recurrent and a feedforward model of neuronal periodicity extraction and discuss basic constraints for neuronal circuitry performing such a task in a biological system. Both the recurrent and the feedforward model perform well using neuronal parameters typical for the auditory system. Performance is limited mainly by the temporal precision of the connections between the neurons.