Biomedical subjects

J L van Hemmen

Publications and source records attributed to J L van Hemmen.

At least 19 recordsLinked to original sources

PubMed2000

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.

Action Potentials↗

PubMed1999

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.

Algorithms↗

PubMed1999

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.

Antibodies, Anti-Idiotypic↗

PubMed1998

Extracting oscillations. Neuronal coincidence detection with noisy periodic spike input.

How does a neuron vary its mean output firing rate if the input changes from random to oscillatory coherent but noisy activity? What are the critical parameters of the neuronal dynamics and input statistics? To answer these questions, we investigate the coincidence-detection properties of an integrate-and-fire neuron. We derive an expression indicating how coincidence detection depends on neuronal parameters. Specifically, we show how coincidence detection depends on the shape of the postsynaptic response function, the number of synapses, and the input statistics, and we demonstrate that there is an optimal threshold. Our considerations can be used to predict from neuronal parameters whether and to what extent a neuron can act as a coincidence detector and thus can convert a temporal code into a rate code.

Membrane Potentials↗

PubMed1998

Analysis of a correlation-based model for the development of orientation-selective receptive fields in the visual cortex.

We analyse a model for the development of orientation-selective receptive fields of simple cells in a locally connected network of cortical neurons. The Hebbian learning rule that underlies the development is described by a linear differential equation. The structure of the emerging cortical map can be predicted by deriving the eigenfunctions corresponding to the leading eigenvalues of the associated matrix. We show that the receptive fields have the typical form of a wavelet. Mathematically, receptive fields are given by a Hermitian polynomial with Gaussian cut-off and a phase factor. Both the phase of the wavelet and the orientation are changing periodically along the surface of the cortical map as suggested by previous simulation studies and as also found in experiments. In order to get orientation-selective receptive fields, the spatial correlation function of the inputs that drive the development must have a zero crossing.

Algorithms↗

PubMed1998

Theory and implementation of infomax filters for the retina.

In the first part of this paper we discuss a technical visual sensory system, which--in analogy with the retina--includes some preprocessing of visual information. In so doing, we use an information-theoretic criterion, the infomax ansatz, to optimize the response of the sensory system. In particular, it is shown that the lattice structure of the photoreceptor array has to be taken into account. By a discrete Fourier transformation on a triangular lattice we derive the frequency response of the infomax filter within the first Brillouin zone. To illustrate the response properties, infomax filters adapted to different noise levels are applied to images with different signal-to-noise ratios. This clearly demonstrates the necessity of adaptation of the filter properties to the given noise level. Furthermore, it is shown how to efficiently implement infomax-like filters by simple networks with only nearest-neighbour interactions. A two-layered network topology proves to be very advantageous in implementing the desired high-pass or low-pass properties. The network topology allows for adaption of the network to low and high noise levels by simply adjusting the nearest-neighbour couplings. In the second part of this paper, we compare the previously described information-theoretic requirements on a visual sensory system with biological facts known from the vertebrate retina. The substantial physiological response properties of the vertebrate retina are in agreement with the main features of the infomax filter. Since available experimental data lacks information which is necessary for a more quantitative comparison, we present suggestions for future experiments. Some key anatomical features of the retina of many vertebrates compare well with our two-layered implementation of the infomax filter. The analogy, in particular, concerns the adaption mechanism. To illustrate this point, we summarize some recent experiments which demonstrate that in the retina of some species adaption is based on the release of the neuromodulator dopamine by the interplexiform cells. This causes the horizontal cells to decouple. On the basis of recently gained understanding of the outer plexiform layer of the retina some further hypotheses about the functionality of the retina become obvious and possible future experiments to verify or refute them are suggested. Finally, we discuss the infomax approach from a more general point of view. In particular, we show that redundancy is essential to obtaining noise robustness of an internal representation of the environment as it is produced by a sensory system such as the retina.

Animals↗

PubMed1997

Development of spatiotemporal receptive fields of simple cells: I. Model formulation.

A model for the development of spatiotemporal receptive fields of simple cells in the visual cortex is proposed. The model is based on the 1990 hypothesis of Saul and Humphrey that the convergence of four types of input onto a cortical cell, viz. non-lagged ON and OFF inputs and lagged ON and OFF inputs, underlies the spatial and temporal structure of the receptive fields. It therefore explains both orientation and direction selectivity of simple cells. The response properties of the four types of input are described by the product of linear spatial and temporal response functions. Extending the 1994 model of one of the authors (K.D. Miller), we describe the development of spatiotemporal receptive fields as a Hebbian learning process taking into account not only spatial but also temporal correlations between the different inputs. We derive the correlation functions that drive the development both for the period before and after eye-opening and demonstrate how the joint development of orientation and direction selectivity can be understood in the framework of correlation-based learning. Our investigation is split into two parts that are presented in two papers. In the first, the model for the response properties and for the development of direction-selective receptive fields is presented. In the second paper we present simulation results that are compared with experimental data, and also provide a first analysis of our model.

Animals↗

PubMed1997

Development of spatiotemporal receptive fields of simple cells: II. Simulation and analysis.

In part I of this article a correlation based model for the developmental process of spatiotemporal receptive fields has been introduced. In this model the development is described as an activity-dependent competition between four types of input from the lateral geniculate nucleus onto a cortical cell, viz. non-lagged ON and OFF and lagged ON and OFF inputs. In the present paper simulation results and a first analysis are presented for this model. We study the developmental process both before and after eye-opening and compare the results with experimental data from reverse correlation measurements. The outcome of the developmental process is determined mainly by the spatial and the temporal correlations between the different inputs. In particular, if the mean correlation between non-lagged and lagged inputs is weak, receptive fields with a widely varying degree of direction selectivity emerge. However, spatiotemporal receptive fields may show rotation of their preferred orientation as a function of response delay. Even if the mean correlation between two types of temporal input is not weak, direction-selective receptive fields may emerge because of an intracortical interaction between different cortical maps. In an environment of moving lines or gratings, direction-selective receptive fields develop only if the distribution of the directions of motion presented during development shows some anisotropy. In this case, a continuous map of preferred direction is also shown to develop.

Algorithms↗

PubMed1996

What matters in neuronal locking?

Exploiting local stability, we show what neuronal characteristics are essential to ensure that coherent oscillations are asymptotically stable in a spatially homogeneous network of spiking neurons. Under standard conditions, a necessary and, in the limit of a large number of interacting neighbors, also sufficient condition is that the postsynaptic potential is increasing in time as the neurons fire. If the postsynaptic potential is decreasing, oscillations are bound to be unstable. This is a kind of locking theorem and boils down to a subtle interplay of axonal delays, postsynaptic potentials, and refractory behavior. The theorem also allows for mixtures of excitatory and inhibitory interactions. On the basis of the locking theorem, we present a simple geometric method to verify the existence and local stability of a coherent oscillation.

Action Potentials↗

PubMed1996

A neuronal learning rule for sub-millisecond temporal coding.

A paradox that exists in auditory and electrosensory neural systems is that they encode behaviorally relevant signals in the range of a few microseconds with neurons that are at least one order of magnitude slower. The importance of temporal coding in neural information processing is not clear yet. A central question is whether neuronal firing can be more precise than the time constants of the neuronal processes involved. Here we address this problem using the auditory system of the barn owl as an example. We present a modelling study based on computer simulations of a neuron in the laminar nucleus. Three observations explain the paradox. First, spiking of an 'integrate-and-fire' neuron driven by excitatory postsynaptic potentials with a width at half-maximum height of 250 micros, has an accuracy of 25 micros if the presynaptic signals arrive coherently. Second, the necessary degree of coherence in the signal arrival times can be attained during ontogenetic development by virtue of an unsupervised hebbian learning rule. Learning selects connections with matching delays from a broad distribution of axons with random delays. Third, the learning rule also selects the correct delays from two independent groups of inputs, for example, from the left and right ear.

Animals↗

PubMed1995

Intracellular Ca2+ stores can account for the time course of LTP induction: a model of Ca2+ dynamics in dendritic spines.

1. A model of Ca2+ dynamics in spines of CA1 hippocampal neurons is presented. In contrast to traditional models, which concentrate on the effects of Ca2+ influx, diffusion, buffering, and extrusion, we also consider the additional effect of intracellular Ca2+ stores. 2. It is shown that traditional models without Ca2+ stores cannot account for the time course of long-term potentiation (LTP) induction as found in recent experiments. Experimental data suggest that the intracellular Ca2+ concentration should be elevated for up to 2 s, whereas the Ca2+ concentration in standard models of Ca2+ dynamics decays much faster. 3. When intracellular Ca2+ stores are taken into account, a much slower decay is found. In particular, a model simulation with a stimulation paradigm consisting of two bursts of four impulses at 100 Hz each and variable interburst intervals can reproduce experimental results found for primed or theta-burst stimulation. 4. In our model, Ca2+ release from the store has a nonlinear, bell-shaped dependence on the intracellular Ca2+ concentration, similar to the one found for inositoltrisphosphate and ryanodine receptors. These receptors are known to control calcium release from intracellular stores. 5. Our model suggests an important role of intracellular calcium stores in the induction of LTP. The stores serve as a long-term calcium source that can sustain an intracellular Ca2+ concentration above the resting level for 1-2 s.

Animals↗

PubMed1995

Spontaneous excitations in the visual cortex: stripes, spirals, rings, and collective bursts.

As a simple model of the cortical sheet, we study a locally connected net of spiking neurons. Refractoriness, noise, axonal delays, and the time course of excitatory and inhibitory postsynaptic potentials are taken into account explicitly. In addition to a low-activity state and depending on the synaptic efficacy, four different scenarios evolve spontaneously, viz., stripes, spirals, rings, and collective bursts. Our results can be related to experimental observations of drug-induced epilepsy and hallucinations.

Action Potentials↗

PubMed1994

A biologically motivated and analytically soluble model of collective oscillations in the cortex. II. Application to binding and pattern segmentation.

Feature linking and pattern separation are shown to be performed as simultaneous processes by a highly connected auto-associative network of spiking neurons (spike response model). In principle, many (e.g., with nine) patterns can be separated, but with a biological set of parameters the number is limited to four. The patterns have been learned by an asymmetric hebbian rule that can handle a low activity which may vary from pattern to pattern (in a range between 4% and 7%). Spikes are generated by a threshold process and--with some delay--transmitted to postsynaptic neurons. There they evoke an excitatory or inhibitory postsynaptic potential (EPSP or IPSP). Spike emission is followed by an absolute refractory period (1 ms) and activates an inhibitory delay loop that prevents continuous firing. Three different network topologies are discussed, i.e., a structureless fully connected system, a network composed of two 'hemispheres', and finally a hierarchical network with four subsystems that represent different 'functions' and interact via feedforward and feedback connections. Functional feedback turns out to be essential for context-sensitive binding. The coherence between the two hemispheres is dependent on the interhemispheric delays. If these are on average too large, the two hemispheres oscillate coherently by themselves but phase-shifted by half a period with respect to each other.

Animals↗

PubMed1993

Memory to antigenic challenge of the immune system: synergy of idiotypic interactions and memory B cells.

Memory to antigenic challenge of the immune system is described as a synergy of two components: cycles of interacting B cells in a dynamic equilibrium which store an internal image of an antigen, and long-lived memory B cells which stabilize the cycle that generates them. Small cycles are most relevant to the immune system's memory. The network is globally stable and supports Jerne's idea that suppression is important. Our model allows for exponential increase of antigens during the initial stage of infection. It has a number of stable fixed points, viz the virgin state, the healthy immunized state, and a state of chronic infection, the last occurring if the antigen is virulent enough. Numerical simulations show a difference between primary and secondary response and exhibit both predator-prey and intracycle oscillations. In the case of a chronic infection, the simulations suggest a specific stimulation therapy triggered by repeatedly injecting the antigens, thus making the infection acute. An optimal therapy is indicated.

Antigens↗

PubMed1993

A biologically motivated and analytically soluble model of collective oscillations in the cortex. I. Theory of weak locking.

A model of an associative network of spiking neurons with stationary states, globally locked oscillations, and weakly locked oscillatory states is presented and analyzed. The network is close to biology in the following sense. First, the neurons spike and our model includes an absolute refractory period after each spike. Second, we consider a distribution of axonal delay times. Finally, we describe synaptic signal transmission by excitatory and inhibitory potentials (EPSP and IPSP) with a realistic shape, that is, through a response kernel. During retrieval of a pattern, all active neurons exhibit periodic spike bursts which may or may not be synchronized ('locked') into a coherent oscillation. We derive an analytical condition of locking and calculate the period of collective activity during oscillatory retrieval. In a stationary retrieval state, the overlap assumes a constant value proportional to the mean firing rate of the neurons. It is argued that in a biological network an intermediate scenario of 'weak locking' is most likely.

Animals↗

PubMed1993

Memory in idiotypic networks due to competition between proliferation and differentiation.

A model employing separate dose-dependent response functions for proliferation and differentiation of idiotypically interacting B cell clones is presented. For each clone the population dynamics of proliferating B cells, non-proliferating B cells and free antibodies are considered. An effective response function, which contains the total impact of proliferation and differentiation at the fixed points, is defined in order to enable an exact analysis. The analysis of the memory states is restricted in this paper to a two-species system. The conditions for the existence of locally stable steady states with expanded B cell and antibody populations are established for various combinations of different field-response functions (e.g. linear, saturation, log-bell functions). The stable fixed points are interpreted as memory states in terms of immunity and tolerance. It is proven that a combination of linear response functions for both proliferation and differentiation does not give rise to stable fixed points. However, due to competition between proliferation and differentiation saturation response functions are sufficient to obtain two memory states, provided proliferation precedes differentiation and also saturates earlier. The use of log-bell-shaped response functions for both proliferation and differentiation gives rise to a "mexican-hat" effective response function and allows for multiple (four to six) memory states. Both a primary response and a much more pronounced secondary response are observed. The stability of the memory states is studied as a function of the parameters of the model. The attractors lose their stability when the mean residence time of antibodies in the system is much longer than the B cells' lifetime. Neither the stability results nor the dynamics are qualitatively changed by the existence of non-proliferating B cells: memory states can exist and be stable without non-proliferating B cells. Nevertheless, the activation of non-proliferating B cells and the competition between proliferation and differentiation enlarge the parameter regime for which stable attractors are found. In addition, it is shown that a separate activation step from virgin to active B cells renders the virgin state stable for any choice of biologically reasonable parameters.

Animals↗

PubMed1993

Why spikes? Hebbian learning and retrieval of time-resolved excitation patterns.

Hebbian learning allows a network of spiking neurons to store and retrieve spatio-temporal patterns with a time resolution of 1 ms, despite the long postsynaptic and dendritic integration times. To show this, we introduce and analyze a model of spiking neurons, the spike response model, with a realistic distribution of axonal delays and with realistic postsynaptic potentials. Learning is performed by a local Hebbian rule which is based on the synchronism of presynaptic neurotransmitter release and some short-acting postsynaptic process. The time window of this synchronism determines the temporal resolution of pattern retrieval, which can be initiated by applying a short external stimulus pattern. Furthermore, a rate quantization is found in dependence upon the threshold value of the neurons, i.e., in a given time a pattern runs n times as often as learned, when n is a positive integer (n > or = 0). We show that all information about the spike pattern is lost if only mean firing rates (temporal average) or ensemble activities (spatial average) are considered. An average over several retrieval runs in order to generate a post-stimulus time histogram may also deteriorate the signal. The full information on a pattern is contained in the spike raster of a single run. Our results stress the importance, and advantage, of coding by spatio-temporal spike patterns instead of firing rates and average ensemble activity. The implications regarding modelling and experimental data analysis are discussed.

Animals↗

PubMed1992

Universality in neural networks: the importance of the 'mean firing rate'.

We present a general analysis of highly connected recurrent neural networks which are able to learn and retrieve a finite number of static patterns. The arguments are based on spike trains and their interval distribution and require no specific model of a neuron. In particular, they apply to formal two-state neurons as well as to more refined models like the integrate-and-fire neuron or the Hodgkin-Huxley equations. We show that the mean firing rate defined as the inverse of the mean interval length is the only relevant parameter (apart from the synaptic weights) that determines the existence of retrieval solutions with a large overlap with one of the learnt patterns. The statistics of the spiking noise (Gaussian, Poisson or other) and hence the shape of the interval distribution does not matter. Thus our unifying approach explains why, and when, all the different associative networks which treat static patterns yield basically the same results, i.e., belong to the same universality class.

Mathematics↗