NWO-jaarthema Mathematische Biologie 2001
NWO - Special Year on Mathematical Biology

Computational Neuroscience

Friday, April 27, 2001

Netherlands Institute for Brain Research
Meibergdreef 33, 1105 AZ Amsterdam,
The Netherlands
Jaap van Pelt


The section Mathematics of the Netherlands Organization for Scientific Research (NWO) - Foundation for the Physical Sciences - organizes this year a series of seminars under the theme Mathematical Biology (NWO-jaarthema Mathematische Biologie) 2001. The series aims at exploring opportunities for joint research programs in the Mathematical and Life Sciences in the Netherlands.

The objective of the present Seminar Computational Neuroscience is to discuss recent developments in Computational Neuroscience and to bring together scientists within The Netherlands working in or interested to explore research possibilities in this multidisciplinary field of research.


Jaap van Pelt (NIBR, Amsterdam)

Arjen van Ooyen / Jaap van Pelt (NIBR, Amsterdam)
Modeling neuronal morphogenesis and network formation

Boris Lastdrager (CWI, Amsterdam)
Modeling axonal guidance


Wytse Wadman (UVA, Amsterdam)
Modeling interactions between neurons and their extracellular environment

Niels Cornelisse (KUN, Nijmegen)
Mathematical model for electrical bursting and calcium oscillations in a neuro-endocrine cell


Erik de Schutter (UIA, Antwerpen, Belgium)
Computational Neuroscience: More math is needed to understand the human brain

Bert Kappen (SNN, Nijmegen)
On the computational implications of dynamical synapses

Willem van Leeuwen (ITF, Amsterdam)
How the brain might perform motor tasks: From backpropagation and Boltzmann machines to biologically realizable machines


Maartje Raijmakers (UVA, Amsterdam)
Modeling transitions in cognitive development with bifurcations in neural networks

Pieter Roelfsema (IOI, Amsterdam)
Detection of connections among image regions by the visual brain

The seminar is sponsored by NWO. The lunch is offered by the NIBR. There is no fee for participation. In order to estimate the number of participants, we ask you to inform the local organizers Jaap van Pelt (020-5665481) or Arjen van Ooyen (020-5665483) if you plan to attend.

Netherlands Institute for Brain Research
Meibergdreef 33, 1105 AZ Amsterdam
The Netherlands
Tel: +31 20 5665500; Fax: +31 20 6961006


Modeling neuronal morphogenesis and network formation
Arjen van Ooyen, Jaap van Pelt
Neurons communicate through electrical and chemical signals, traveling along their dendritic and axonal arborisations. Neurons show an enormous variety in shapes which is believed to reflect their functional specialisation. Neurons attain their shapes as the result of a developmental process in which intracellular mechanisms and interactions with local environments are operating in concert. Many of these mechanisms are modulated by bioelectric activity. It is believed that these modulatory influences play a key role in the structural and functional tuning of the nervous system. Mathematical modeling and computational approaches are essential to obtain understanding of these dynamical processes. Examples will be discussed, concentrating on growth of dendritic arborisations, competitive phenomena during neurite outgrowth and formation of nerve connections, and implications of activity-dependent processes for neural development and network formation.

Modeling axonal guidance
Boris Lastdrager.
During the development of the nervous system neurons are connected to their targets by axons which grow from the neurons toward the targets, a process which is supposed to be governed by the secretion and detection of chemoattractants and chemorepellants. During the growth the axons are seen to form a bundle in the initial growth phase which then grows towards the target area where the axons debundle and attach to individual targets. We will discuss a simple model in which axons interact by secreting chemicals from their growth cones which are diffused through the extracellular space and sensed by other growth cones. With this simple model we can reproduce the processes of bundling, debundling and attachment which lends credibility to theories that describe axonal growth through similar simple models. In the implementation of the model we discovered a numerical pitfall that relates to the implementation of the source terms that can easily render a code useless. In our implementation we have managed to avoid this problem. It turns out that the model we consider is very sensitive to parameters, i.e., a slight change in a parameter, e.g. a diffusion constant, can prevent bundling, debundling or attachment. The parameter values for which bundling, debundling and attachment occur are however within ranges corresponding with experimental measurements.

Mathematical model for electrical bursting and Ca2+ oscillations in` neuroendocrine cell
Niels Cornelisse
Nonlinearity is essential for the computational function of the brain and occurs at various levels of the brain. At the cellular level the signaling between neurons is highly nonlinear due to the complex interactions between neurotransmitters, receptors, second messengers and ion channels that are involved. We study cellular signaling in a neuroendocrine cell of the amphibian Xenopus laevis that has a clear cellular response (hormone secretion) to neuronal input. A mathematical model has been developed to describe the specific features of the cellular signaling in these cells (electrical bursting, Ca2+ oscillations). The model is an extended Hodgkin-Huxley type model partly based on experimental data and is analysed with the use of nonlinear system analyses, phase space analyses and bifurcation theory.

On the computational implications of dynamical synapses
Bert Kappen
Recent experiments in pyramidal cells show that the amplitude of the postsynaptic membrane potential (PSP) depends on presynaptic activity. Although the details of this phenomenon depends on the type or synapse and the brain area, a common trend is that synaptic strenght decreases as a result of presynaptic activity with a characteristic time scale of about 10 msec. Recovery occurs in the order of seconds. These synaptic mechanisms can have quite profound functional consequences on the behaviour of neural networks. For instance, attractors in recurrent neural networks will become metastable states due to the changing connectivity pattern. In this presentation I will present both numerical and analytical results of this new phenomenon.

How the brain might perform motor tasks: From backpropagation and Boltzmann machines to biologically realizable machines
Willem van Leeuwen
As is well-known, backpropagation and Boltzmann machines yield ways to adapt the weights (synapses) of a neural net in such a way that desired input-output relations (for instance motor tasks) can be realized by the net. However, since the existing algorithms, like `backpropagation' and `Boltzmann machines' require an outside observer and outside computer, these algorithms do not help us to understand the way in which the actual brain might work. Recently, the neuroscientists D.R. Chialvo and P. Bak of the Divison of Neural Systems in Copenhagen suggested a hormone controlled way to adapt the synapses. This control mechanism might be realized by an actual brain to adapt itself in such a way that it can perform the desired input-output relations. By combining the suggestion of Chialvo and Bak at the one hand and the recipe called Hebbian learning at the other hand, the theoretical physicists Reinier Bosman and Bastian Wemmenhove of the Institute of Theoretical Physics in Amsterdam could make the Danish idea not only more realistic biologically, but also more effective.

Modeling transitions in cognitive development with bifurcations in neural networks
Maartje Raijmakers
In the field of cognitive science, artificial neural network simulation usually is carried out with configurations that are, from a developmental-biological point of view, in a mature state. That is, the contours of neural field organization are given and simulation usually pertains to the adaptation of interconnections within and between the given fields. Recently, constructive neural networks of development model maturation by the addition of structure during and in addition to learning (e.g., Elman, 1993; Quartz, 1994). In these cases, more inspired by computation theory than by biology, resources, such as hidden units are added to the network as a function of learning. Our future objective is to model the maturation process of a cognitively applied neural network by ordinary differential equations that describe the evolution of real valued parameters as a function of activation. As will be shown, in the plane of these parameters local bifurcations of activation dynamics occur. That is, parameter changes trigger qualitative changes in network dynamics and, as a consequence, qualitative changes in the cognitive network behavior as well. The latter induction of qualitative new cognitive behavior without adding resources is a consistent interpretation of epigenetic theories of cognitive development, like Piaget's stage theory (Molenaar, 1986; Raijmakers, 1997).

Detection of connections among image regions by the visual brain
Pieter R. Roelfsema
Connectedness is one of the most important grouping criteria that allow the visual system to segregate objects from each other and from the background. Algorithms for the detection of connectedness will be reviewed from a neurophysiological and psychophysiological point of view. It will be suggested that connectedness detection by a feedforward network is physiologically implausible. Instead, I present evidence that visual cortical neurons label connected image regions serially, by exhibiting an enhanced firing rate. Psychophysical results imply that connectedness detection requires visual attention.

Addresses of Speakers:

Niels Cornelisse
Dept. Medical & Biophysics, Dept. Cellular Animal Physiology,
Nijmegen Institute for Neurosciences
University of Nijmegen, Geert Grooteplein 21,
PO Box 9101, 6500 HB Nijmegen, The Netherlands
Tel: +31-24-3614235; Fax: +31-24-3541435
Email: cornelis@sci.kun.nl

Bert Kappen
SNN, University of Nijmegen
Tel: +31-24-3614241; Fax: +31-24-3541435
Email: bert@mbfys.kun.nl

Boris Lastdrager
Kruislaan 413, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands
Phone: +31-20-5924077; Fax: +31-20-5924199
Email: Boris.Lastdrager@cwi.nl

Willem van Leeuwen
Institute for Theoretical Physics, University of Amsterdam
Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands
Tel: +31 20 525 5773 (5747); Fax: +31 20 525 5788
E-mail: leeuwen@science.uva.nl

Arjen van Ooyen
Netherlands Institute for Brain Research
Meibergdreef 33, 1105 AZ Amsterdam, The Netherlands
Tel: +31-20-5665483; Fax: +31-20-6961006
Email: a.van.ooyen@nih.knaw.nl

Jaap van Pelt
Netherlands Institute for Brain Research
Meibergdreef 33, 1105 AZ Amsterdam, The Netherlands
Tel: +31-20-5665481; Fax: +31-20-6961006
Email: j.van.pelt@nih.knaw.nl

Maartje Raijmakers
Department of Psychology, University of Amsterdam
Roeterstraat 15, 1018 WB Amsterdam, The Netherlands
Tel. +31-20-5256826; Fax. +31-20-6390279
Email: op_raijmakers@macmail.psy.uva.nl

Pieter Roelfsema
IOI, Afdeling Visuele Systeem Analyse, Academisch Medisch Centrum
Meibergdreef 15, 1105 AZ Amsterdam
Tel. +31-20-5665603
Email: p.roelfsema@ioi.knaw.nl

Erik de Schutter
Theoretical Neurobiology, Born Bunge Stichting, Universitaire Instelling Antwerpen UIA
Universiteitsplein 1, B2610 Antwerpen, Belgium
Email: erik@bbf.uia.ac.be

Wytse Wadman
Institute for Neurobiology, University of Amsterdam
Kruislaan 320, 1098 SM Amsterdam, The Netherlands
Tel: +31-20-5257641; Fax: +31-20-5257709
Email: wadman@bio.uva.nl