3' Neuron models

1
A large scale biologically realistic model of the
neostriatum Ric Wood, Mark Humphries, Kevin
Gurney
Contact ric.wood_at_sheffield.ac.uk m.d.humphries_at_s
heffield.ac.uk
3. Neuron models
1. Morphology
2. Model of connectivity

• The volume data for each cell was used to
  calculate the probability of an apposition.
• 30 MS dendrograms, and 30 FS dendrograms were
  generated.
• The mean volume of space occupied by the
  dendrites, as a function of distance from the
  soma, was calculated.
• To obtain a continuous function of the dendritic
  volume a truncated power law was fitted to the
  data,
• where Pv is the proportion of space occupied by
  the dendrites, d is the distance from the soma
  and a, ß, ? are the free parameters.
• The total space was divided up into 1µm3 voxels,
  and Pv used to calculate the probability of an
  apposition occurring between two processes,
  P(Idi), for each voxel i, where
• where P(Ddi) and P(Adi) are the probabilities
  for the dendrites and axons individually.
• with the expected number of appositions given by
• Connection probabilities were calculated for the
  MS collaterals, the FS collaterals, the FS to MS
  collaterals, and for the gap junctions between
  the FS neurons.
• The probability functions were used to generate a
  network of MS and FS neurons in a 1000 X 1000 X
  250 µm space, which included 22800 neurons.

• The MS and FS neurons are modelled using the
  Izhikevich formula. Parameters for the models are
  based on those published in Izhikevich (in
  press).
• This class of model was chosen for its
  computational efficiency and ability to replicate
  membrane properties.
• The gap junctions between the FS neurons were
  modelled with a time constant, t, a weight, g,
  and a notional voltage, V, and the voltages of
  the two FS neurons, V1 and V2, where
• The currents for each cell are then defined as
  I1g(V-V1) and I2g(V-V2) respectively.
• A pair of simulated FS neurons, connected with
  the gap junction model, was used to fit data from
  cortical FS neurons, to obtain values for t and
  g. Sinusoidal currents of different amplitudes
  are injected into one cell, and the coupling
  ratio and phase lag between the two cells
  recorded.

• Introduction
• The basal ganglia is a group of subcortical
  nuclei thought to play a central role in action
  selection (Redgrave et al., 1999). The
  neostriatum forms the major input nucleus of the
  basal ganglia, and accounts for approximately 95
  of the total neuron population of these
  structures in the rat. Within the neostriatum
  over 95 of the neurons are medium spiny (MS)
  projection cells. The remaining neuron population
  comprises several species of interneuron,
  including the fast spiking (FS) interneuron. Both
  the MS and FS neurons receive direct cortical
  inputs. The FS neurons are interconnected via
  local GABAergic collaterals, and by a network of
  gap junctions. They provide feed forward
  inhibition to the MS neurons. The MS neurons are
  also interconnected via a network of lateral
  collaterals.
• Given the prominent position of the striatum
  within the basal ganglia it seems reasonable to
  assume that it plays a major computational role
  in the function of these nuclei. So far,
  unravelling the functional organisation of the
  striatum has proved difficult. There are many
  similarities between the neural circuits of the
  striatum and cortex, with both structures showing
  a similar range of GABAergic interneurons.
  However, unlike the cortex, which has a clear
  laminar structure, the striatum forms a
  homogenous structure making it hard to unravel
  the organization of the micro circuitry.
• In order to investigate the functional properties
  of the striatum, and its individual components,
  we are currently building a biologically
  realistic model of the nucleus. It includes
  detailed connectivity maps, based on both
  anatomical data and the morphology of the neuron
  species. This poster outlines the methods used to
  construct the model, and gives some initial
  simulation results
• Biologically realistic connectivity
• Accurate neuroscientific data on the densities of
  connections between neural populations is often
  incomplete or entirely absent from the
  literature, while many published values are
  estimates, based on back of an envelope
  calculations. This presents a problem for the
  modeller when building networks of neurons. One
  recently developed method is to estimate the
  number of appositions between cells by
  reconstructing the morphology of several axonal
  and dendritic fields, placing the reconstructions
  in the same volume, and then counting the number
  of appositions while moving the relative
  positions of the two fields. However, detailed
  morphological reconstructions are not usually
  publicly available, and can be very time
  consuming to perform. We have developed an
  alternative approach where the number of
  appositions is estimated by calculating the
  volume of space the axons and dendrites occupy as
  they extend away from the soma. The probability
  of an apposition can then be calculated as a
  function of the distance between the two cells,
  and of the volume of space occupied by the
  intersecting axonal and dendritic fields.
• Network simulation results
• Individual neuron behaviour resembles
  electrophysiological data recorded from MS and FS
  neurons in vivo.
• MS neurons showed a low level of activity, with
  most cells silent.
• FS neurons are considerably more active, with
  most cells showing continuous or periodic
  bursting behaviour.
• Stimulating small groups of MS neurons allows
  them to fire more rapidly, with the surrounding
  neurons showing little or no activity.
• In contrast, stimulating groups of FS neurons
  appeared to have little effect, with some failing
  to show significant increases in firing while
  surrounding cells continued to fire at high
  frequencies.

• A dendrogram model was constructed, using an
  algorithm published in Burke et al (1992).
• The parameters of the model were fitted, using a
  genetic algorithm, to branch order, dendritic
  radius, number of terminals, and terminal
  diameter data. This was repeated for both the MS
  and FS neurons. Dendritic lengths were adjusted
  for wiggle.
• To accurately estimate the volume of the MS
  dendrites, additional volume was added to account
  for the dendritic spines. The amount of volume
  added was calculated using a spine density
  function, which was a piece-wise linear fit to
  spine density data published in Wilson et al
  (1983), and by assuming a mean spine volume of
  0.12 µm3.

• Only very limited data was available for the
  axons of the MS and FS neurons. Consequently,
  they were each modelled as a single tree, with a
  diameter of 0.5µm over the initial 250µm, and
  then branching into 4 collaterals with diameters
  of 0.25µm.
• The MS neuron model accurately predicted
  dendritic taper data kindly supplied by Charles
  Wilson.

4. Network simulation results

• The response of the MS and FS neurons closely
  resembles the responses of real MS and FS
  neurons.
• Most MS neurons remained quite for the entire
  duration of the simulation, and the active MS
  neurons fired at low frequencies of up to 10Hz.
• Most FS neurons fired periodic bursts of action
  potentials at much higher frequencies.
• The network of fast spiking neurons showed signs
  of synchronised bursts of activity. This was
  reflected in the MS network in slightly lower
  firing frequencies over the duration of the
  synchronised FS activity.

• The model was driven with simulated cortical
  input, using a post synaptic current model
  published in Destexhe et al (2001)

Membrane potential of a MS neuron from the
simulation
Burke, R. E. Marks, W. B. Ulfhake, B. (1992) A
parsimonious description of motoneuron dendritic
morphology using computer simulation. J
Neurosci,, 12, 2403-2416 Destexhe, A. Rudolph,
M. Fellous, J. M. Sejnowski, T. J. (2001)
Fluctuating synaptic conductances recreate in
vivo-like activity in neocortical neurons.
Neuroscience, 107, 13-24 Wilson, C. J. Groves,
P. M. Kitai, S. T. Linder, J. C. (1983)
Three-dimensional structure of dendritic spines
in the rat neostriatum. J Neurosci, 3,
383-388 Izhikevich (in press) Dynamic systems
in neuroscience. Galarreta, M. Hestrin, S.
(2001) Electrical synapses between
GABA-releasing interneurons. Nat Rev Neurosci.
2, 425-433

• Four groups of neurons, each containing 101 MS
  neurons and 3 FS neurons, were given twice as
  much input.
• The groups of MS neurons showed a clear increase
  in activity, with firing rates rising up to 30Hz,
  while surrounding neurons outside of the groups
  showing little or no activation.
• The additional input appear to have had little
  effect on the groups of FS neurons, with no
  change in the firing rates, and some groups
  showing less activity than the surrounding cells.

Membrane potential of a FS neuron from the
simulation