How Internally Coupled Ears Generate Temporal and Amplitude Cues for Sound Localization.

In internally coupled ears, displacement of one eardrum creates pressure waves that propagate through air-filled passages in the skull and cause displacement of the opposing eardrum, and conversely. By modeling the membrane, passages, and propagating pressure waves, we show that internally coupled ears generate unique amplitude and temporal cues for sound localization. The magnitudes of both these cues are directionally dependent. The tympanic fundamental frequency segregates a low-frequency regime with constant time-difference magnification from a high-frequency domain with considerable amplitude magnification.

Spike-timing-dependent plasticity for neurons with recurrent connections.

The dynamics of the learning equation, which describes the evolution of the synaptic weights, is derived in the situation where the network contains recurrent connections. The derivation is carried out for the Poisson neuron model. The spiking-rates of the recurrently connected neurons and their cross-correlations are determined self- consistently as a function of the external synaptic inputs. The solution of the learning equation is illustrated by the analysis of the particular case in which there is no external synaptic input. The general learning equation and the fixed-point structure of its solutions is discussed.

How synapses in the auditory system wax and wane: theoretical perspectives.

Spike-timing-dependent synaptic plasticity has recently provided an account of both the acuity of sound localization and the development of temporal-feature maps in the avian auditory system. The dynamics of the resulting learning equation, which describes the evolution of the synaptic weights, is governed by an unstable fixed point. We outline the derivation of the learning equation for both the Poisson neuron model and the leaky integrate-and-fire neuron with conductance synapses. The asymptotic solutions of the learning equation can be described by a spectral representation based on a biorthogonal expansion.

Mapping time.

Neuronal coding of temporal stimulus features can occur by means of delay lines. Given that neuronal activity is conducted through many parallel axons, there has to be a mechanism guaranteeing minimal temporal dispersion. We argue that plastic changes in synaptic transmission that are unspecifically propagated along presynaptic axons are a basis for the development of delay-line topologies. Furthermore, we show how two populations of afferents form a map of interaural time differences as found, for instance, in the laminar nucleus of the barn owl.

Temporal map formation in the barn owl's brain.

Barn owls provide an experimentally well-specified example of a temporal map, a neuronal representation of the outside world in the brain by means of time. Their laminar nucleus exhibits a place code of interaural time differences, a cue which is used to determine the azimuthal location of a sound stimulus, e.g., prey. We analyze a model of synaptic plasticity that explains the formation of such a representation in the young bird and show how in a large parameter regime a combination of local and nonlocal synaptic plasticity yields the temporal map as found experimentally. Our analysis includes the effect of nonlinearities as well as the influence of neuronal noise.

Intrinsic stabilization of output rates by spike-based Hebbian learning.

We study analytically a model of long-term synaptic plasticity where synaptic changes are triggered by presynaptic spikes, postsynaptic spikes, and the time differences between presynaptic and postsynaptic spikes. The changes due to correlated input and output spikes are quantified by means of a learning window. We show that plasticity can lead to an intrinsic stabilization of the mean firing rate of the postsynaptic neuron. Subtractive normalization of the synaptic weights (summed over all presynaptic inputs converging on a postsynaptic neuron) follows if, in addition, the mean input rates and the mean input correlations are identical at all synapses. If the integral over the learning window is positive, firing-rate stabilization requires a non-Hebbian component, whereas such a component is not needed if the integral of the learning window is negative. A negative integral corresponds to anti-Hebbian learning in a model with slowly varying firing rates. For spike-based learning, a strict distinction between Hebbian and anti-Hebbian rules is questionable since learning is driven by correlations on the timescale of the learning window. The correlations between presynaptic and postsynaptic firing are evaluated for a piecewise-linear Poisson model and for a noisy spiking neuron model with refractoriness. While a negative integral over the learning window leads to intrinsic rate stabilization, the positive part of the learning window picks up spatial and temporal correlations in the input.

Temporal receptive fields, spikes, and Hebbian delay selection.

The intriguing concept of a receptive field evolving through Hebbian learning, mostly during ontogeny, has been discussed extensively in the context of the visual cortex receiving spatial input from the retina. Here, we analyze an extension of this idea to the temporal domain. In doing so, we indicate how a particular spike-based learning rule can be described by means of a mean-field learning equation and present a solution for a couple of illustrative examples. We argue that the success of the learning procedure strongly depends on an interplay of, in particular, the temporal parameters of neuron (model) and learning window, and show under what conditions the noisy synaptic dynamics can be regarded as a diffusion process.

Modeling neuronal assemblies: theory and implementation.

Models that describe qualitatively and quantitatively the activity of entire groups of spiking neurons are becoming increasingly important for biologically realistic large-scale network simulations. At the systems and areas modeling level, it is necessary to switch the basic descriptional level from single spiking neurons to neuronal assemblies. In this article, we present and review work that allows a macroscopic description of the assembly activity. We show that such macroscopic models can be used to reproduce in a quantitatively exact manner the joint activity of groups of spike-response or integrate-and-fire neurons. We also show that integral as well as differential equation models of neuronal assemblies can be understood within a single framework, which allows a comparison with the commonly used assembly-averaged graded-response type of models. The presented framework thus enables the large-scale neural network modeler to implement networks using computational units beyond the single spiking neuron without losing much biological accuracy. This article explains the theoretical background as well as the capabilities and the implementation details of the assembly approach.

Th1 or Th2: how an appropriate T helper response can be made.

Two types of T helper (Th) cells have been defined on the basis of their cytokine secretion patterns. The decision of a naive T cell to differentiate into Th1 or Th2 is crucial, since to a first approximation it determines whether a cell-mediated or humoral immune response is triggered against a particular pathogen, which profoundly influences disease outcome. Here we show that the internal behaviour of the T helper system, which emerges from regulatory mechanisms 'built into' the T helper system, itself can usually select the appropriate T helper response. This phenomenon arises from an initial Th1 bias together with the induction of Th1-->Th2 switches when Th1 effectors do not lead to efficient antigen clearance. The occurrence of these shifts is based on the antigen dose dependence of T helper differentiation, which is a consequence of asymmetries in cross-suppression. Critical for this feature is the rate with which Th2 cells undergo antigen-induced cell death.

Formation of temporal-feature maps by axonal propagation of synaptic learning.

Computational maps are of central importance to a neuronal representation of the outside world. In a map, neighboring neurons respond to similar sensory features. A well studied example is the computational map of interaural time differences (ITDs), which is essential to sound localization in a variety of species and allows resolution of ITDs of the order of 10 micros. Nevertheless, it is unclear how such an orderly representation of temporal features arises. We address this problem by modeling the ontogenetic development of an ITD map in the laminar nucleus of the barn owl. We show how the owl's ITD map can emerge from a combined action of homosynaptic spike-based Hebbian learning and its propagation along the presynaptic axon. In spike-based Hebbian learning, synaptic strengths are modified according to the timing of pre- and postsynaptic action potentials. In unspecific axonal learning, a synapse's modification gives rise to a factor that propagates along the presynaptic axon and affects the properties of synapses at neighboring neurons. Our results indicate that both Hebbian learning and its presynaptic propagation are necessary for map formation in the laminar nucleus, but the latter can be orders of magnitude weaker than the former. We argue that the algorithm is important for the formation of computational maps, when, in particular, time plays a key role.

Does corticothalamic feedback control cortical velocity tuning?

The thalamus is the major gate to the cortex, and its contribution to cortical receptive field properties is well established. Cortical feedback to the thalamus is, in turn, the anatomically dominant input to relay cells, yet its influence on thalamic processing has been difficult to interpret. For an understanding of complex sensory processing, detailed concepts of the corticothalamic interplay need to be established. To study corticogeniculate processing in a model, we draw on various physiological and anatomical data concerning the intrinsic dynamics of geniculate relay neurons, the cortical influence on relay modes, lagged and nonlagged neurons, and the structure of visual cortical receptive fields. In extensive computer simulations, we elaborate the novel hypothesis that the visual cortex controls via feedback the temporal response properties of geniculate relay cells in a way that alters the tuning of cortical cells for speed.

Combined Hebbian development of geniculocortical and lateral connectivity in a model of primary visual cortex.

We present a network model of visual map development in layer 4 of primary visual cortex. Our model comprises excitatory and inhibitory spiking neurons. The input to the network consists of correlated spike trains to mimick the activity of neurons in the lateral geniculate nucleus (LGN). An activity-driven Hebbian learning mechanism governs the development of both the network's lateral connectivity and feedforward projections from LGN to cortex. Plasticity of inhibitory synapses has been included into the model so as to control overall cortical activity. Even without feedforward input, Hebbian modification of the excitatory lateral connections can lead to the development of an intracortical orientation map. We have found that such an intracortical map can guide the development of feedforward connections from LGN to cortical simple cells so that the structure of the final feedforward orientation map is predetermined by the intracortical map. In a scenario in which left- and right-eye geniculocortical inputs develop sequentially one after the other, the resulting maps are therefore very similar, provided the intracortical connectivity remains unaltered. This may explain the outcome of so-called reverse lid-suture experiments, where animals are reared so that both eyes never receive input at the same time, but the orientation maps measured separately for the two eyes are nevertheless nearly identical.

Cytokine-modulated regulation of helper T cell populations.

Helper T (Th) cells are a crucial component of the adaptive immune system and are of fundamental importance in orchestrating the appropriate response to pathogenic challenge. They fall into two broad categories defined by the cytokines each produces. Th1 cells produce interferon- gamma and are required for effective immunity to intracellular bacteria, viruses and protozoa whereas Th2 produce IL-4 and are required for optimal antibody production to T-dependent antigens. A great deal of experimental data on the regulation of Th1 and Th2 differentiation have been obtained but many essential features of this complex system are still not understood. Here we present a mathematical model of Th1/Th2 differentiation and cross regulation. We model Fas-mediated activation-induced cell death (AICD) as this process has been identified as an important mechanism for limiting clonal expansion and resolving T cell responses. We conclude that Th2 susceptibility to AICD is important for stabilizing the two polarized arms of the T helper response, and that cell-cell killing, not suicide, is the dominant mechanism for Fas-mediated death of Th1 effectors. We find that the combination of the anti-proliferative effect of the cytokine TGF- beta and the inhibiting influence of IL-10 on T cell activation are crucial controls for Th2 populations. We see that the strengths of the activation signals for each T helper cell subset, which are dependent on the antigen dose, co-stimulatory signals and the cytokine environment, critically determine the dominant helper subset. Switches from Th1- to Th2-dominance may be important in chronic infection and we show that this phenomenon can arise from differential AICD susceptibility of T helper subsets, and asymmetries in the nature of the cross-suppressive cytokine interactions. Our model suggests that in some senses a predominantly type 2 reaction may well be the "default" pathway for an antigen-specific immune response, due to these asymmetries.

Unifying framework for neuronal assembly dynamics.

Starting from single, spiking neurons, we derive a system of coupled differential equations for a description of the dynamics of pools of extensively many equivalent neurons. Contrary to previous work, the derivation is exact and takes into account microscopic properties of single neurons, such as axonal delays and refractory behavior. Simulations show a good quantitative agreement with microscopically modeled pools of spiking neurons. The agreement holds both in the quasistationary and nonstationary dynamical regimes, including fast transients and oscillations. The model is compared with other pool models based on differential equations. It turns out that models of the graded-response category can be understood as a first-order approximation of our pool dynamics. Furthermore, the present formalism gives rise to a system of equations that can be reduced straightforwardly so as to gain a description of the pool dynamics to any desired order of approximation. Finally, we present a stability criterion that is suitable for handling pools of neurons. Due to its exact derivation from single-neuron dynamics, the present model opens simulation possibilities for studies that rely upon biologically realistic large-scale networks composed of assemblies of spiking neurons.

Theory of arachnid prey localization.

Sand scorpions and many other arachnids locate their prey through highly sensitive slit sensilla at the tips (tarsi) of their eight legs. This sensor array responds to vibrations with stimulus-locked action potentials encoding the target direction. We present a neuronal model to account for stimulus angle determination using a population of second-order neurons, each receiving excitatory input from one tarsus and inhibition from a triad opposite to it. The input opens a time window whose width determines a neuron's firing probability. Stochastic optimization is realized through tuning the balance between excitation and inhibition. The agreement with experiments on the sand scorpion is excellent.

Time window control: a model for cerebellar function based on synchronization, reverberation, and time slicing.

We present a new hypothesis of cerebellar function that is based on synchronization, delayed reverberation, and time windows for triggering spikes. Our model suggests that granule cells admit mossy fiber activity to the parallel fibers only if the Golgi cells are firing synchronously and if the mossy-fiber spikes arrive within short and well-defined time windows. The concept of time window control organizes neuronal activity in discrete 'time slices' that can be used to discern meaningful information from background noise. In particular, Purkinje cell activity can trigger rebound spikes in deep cerebellar nuclei cells, which project via brain stem nuclei and mossy fibers back to the cerebellar cortex. Using a detailed model of deep cerebellar nuclei cells, we demonstrate that the delayed firing of rebound spikes is a robust mechanism so as to ensure that the reverberated activity re-arrives in the mossy fibers just during the granule-cell time window. Large network simulations reveal that synaptic plasticity (LTD and LTP) at the parallel fiber/Purkinje cell synapses that relies on the timing of the parallel fiber and climbing fiber activities allows the system to learn, store, and recall spatiotemporal patterns of spike activity. Climbing fiber spikes function both as teacher and as synchronization signals. The temporal characteristics of the climbing fiber activity are due to intrinsic oscillatory properties of inferior olivary neurons and to reverberating projections between deep cerebellar nuclei, the mesodiencephalic junction, and the inferior olive. Thus, the reverberating loops of the mossy fiber system and climbing fiber system may interact directly with the time windows provided by the circuitry of the cerebellar cortex so as to generate the appropriate spatio-temporal firing patterns in the deep cerebellar nuclei neurons that control premotor systems. In future studies the model will be extended in that high frequency simple spike activities will be included and that their relevance for motor control will be addressed.

Spatiotemporal adaptation through corticothalamic loops: a hypothesis.

The thalamus is the major gate to the cortex and its control over cortical responses is well established. Cortical feedback to the thalamus is, in turn, the anatomically dominant input to relay cells, yet its influence on thalamic processing has been difficult to interpret. For an understanding of complex sensory processing, detailed concepts of the corticothalamic interplay need yet to be established. Drawing on various physiological and anatomical data, we elaborate the novel hypothesis that the visual cortex controls the spatiotemporal structure of cortical receptive fields via feedback to the lateral geniculate nucleus. Furthermore, we present and analyze a model of corticogeniculate loops that implements this control, and exhibit its ability of object segmentation by statistical motion analysis in the visual field.

Modeling synaptic plasticity in conjuction with the timing of pre- and postsynaptic action potentials.

We present a spiking neuron model that allows for an analytic calculation of the correlations between pre- and postsynaptic spikes. The neuron model is a generalization of the integrate-and-fire model and equipped with a probabilistic spike-triggering mechanism. We show that under certain biologically plausible conditions, pre- and postsynaptic spike trains can be described simultaneously as an inhomogeneous Poisson process. Inspired by experimental findings, we develop a model for synaptic long-term plasticity that relies on the relative timing of pre- and post-synaptic action potentials. Being given an input statistics, we compute the stationary synaptic weights that result from the temporal correlations between the pre- and postsynaptic spikes. By means of both analytic calculations and computer simulations, we show that such a mechanism of synaptic plasticity is able to strengthen those input synapses that convey precisely timed spikes at the expense of synapses that deliver spikes with a broad temporal distribution. This may be of vital importance for any kind of information processing based on spiking neurons and temporal coding.

Short-term synaptic plasticity and network behavior.

We develop a minimal time-continuous model for use-dependent synaptic short-term plasticity that can account for both short-term depression and short-term facilitation. It is analyzed in the context of the spike response neuron model. Explicit expressions are derived for the synaptic strength as a function of previous spike arrival times. These results are then used to investigate the behavior of large networks of highly interconnected neurons in the presence of short-term synaptic plasticity. We extend previous results so as to elucidate the existence and stability of limit cycles with coherently firing neurons. After the onset of an external stimulus, we have found complex transient network behavior that manifests itself as a sequence of different modes of coherent firing until a stable limit cycle is reached.

Adaptive control: a strategy to treat autoimmunity.

Anti-idiotype of (natural) autoantibodies participate in the regulation of autoantibodies, their idiotypes. Focusing on an idiotype/anti-idiotype pair embedded in an environment such as the central immune system, we start with the experimental fact that the level of anti-idiotypes is low in autoimmune patients but high in healthy individuals, and present a quantitative model. This is then used to develop an adaptive control strategy that induces a transition back to the tolerant, healthy, state and thus offers a vista of treating autoimmune diseases caused by the failure of idiotypic control of autoreactive B cells. The idea is to introduce an antigen or anti-idiotype that binds to the autoantibodies with high affinity, and to determine whether or not a fixed dose is to be injected depending on the autoantibody titer exceeding or not exceeding a threshold. Quantitative criteria are provided. The procedure is the more adaptive in that monitoring the autoantibody titer need only happen every x-th day where x can greatly exceed one. Adaptive control turns out to be robust. The arguments presented here also give a quantitative explanation of why the antigen-autoantibody interaction has to be specific so as to induce a backward transition and why an IVIg treatment therefore does not lead to a permanent improvement.