/projects

Signal anticipation in the Fitzhugh-Nagumo neuron model

Most behaviours and perceptions are mediated by `long' chains of neurons relative to the comparison of typical reaction times, and the timescales of neuronal membrane fluctuations and signal transmission between neurons. So, unexpectedly, many studies investigate the speed of signal transmission by populations or chains of neurons.
  In this paper I investigate the group delay of the `membrane potential' of the FitzHugh-Nagumo model, a widely used model for excitable media such as neurons, near its (stable) fixed-point. I show that this group delay is negative for low frequencies (<15Hz, for typical parameter settings a=0.08, b=0.7, c=0.8), meaning that certain aspects of signals falling within this frequency band are anticipated. This means that for a chain of coupled neurons in which the first neuron is stimulated, certain aspects of stimulation signals are displayed in the membrane potential of the last neuron, before the first neuron is completely stimulated. Thus in effect the last neuron anticipates the signal being inputted in the first.

• Houben, A.M. (preprint). arXiv:2101.00500

Neuronal filters: frequency response and selectivity of IF neurons

Neurons are connected through axons and dendrites which transmit signals from one neuron to the other with finite velocities, leading to delays between the firing of one neuron and the arrival of the resultant pulses to other neurons. However, (heterogeneous) delays generally largely complicate the analysis of (neuronal) systems, which has lead to the ommission of transmission delays in the prevalent accounts of neuronal functioning.
  Focussing on a single neuron receiving several inputs, each connection is primarily apprehended by the strengths of the connection: a stronger excitatory (inhibitory) connection from one neuron to the other leads to an increased (decreased) co-occurence of their activation. Thus for an excitatory connection, increased firing of the former (pre-synaptic) neuron leads to an increased firing of the latter (post-synaptic) neuron.
  However, once you include transmission delays into the analysis of neuronal networks, the above interpretation of synaptic strenghts does not hold. A neuron receiving correlated inputs through different input 'lines' with different delays can be interpreted as a finite impulse response filter, meaning that the delay times and synaptic strenghts determine the frequencies that this neuron is sensitive to. In this project I investigate the merits, limitations and consequences of this finite impulse response view.

• Houben, A.M. (preprint). arXiv:2009.09250

Mechanisms underlying synaptic plasticity

Correlation in the activity of two neurons leads to a strengthening of the connection between them. Conversely, uncorrelated activity should lead to a decrease in synaptic strenght. Yet, how does this phenomenological description arise from the mechanisms available to neurons? This project aims to develop models connecting known and plausible biophysics of synapses with phenomenological and conceptual descriptions of synaptic plasticity, at different scales of biophysical detail. Especially, investigating predictions proposed by these models and their effects on the dynamics of spiking networks

• Houben, A.M. & Keil, M.S. (2020). J.Comput.Neurosci.

Program: neuplt

A lightweight program for the (realtime and off-line) (animated) visualisation of (neuronal) data. Started mainly because of my unstopable curiousity while running simulations, and my conviction that the `working of the brain' is best understood through the spatio-temporal dynamics of neurons.

Script: phplt

A simple script to generate GNUplot scripts to visualise the phase spaces of 1, 2 and 3D systems, and singular perturbation problems.