Organiser: Rolf Kötter (Düsseldorf, Germany)
Chair - Peter Erdi (Budapest, Hungary)
I will present several examples of predictions made by
computer simulation that were subse quently confirmed experimentally.
These examples of synaptic inte gra tion by an active dendrite demonstrate
the power of realistic model ing and its importance. The model predictions
contradicted prevalent ideas on how the cerebel lum, or neurons in general,
work and led to experiments which would not have been done otherwise.
The computer model is as biophysically realistic as was
feasible when constructed (De Schutter and Bower J. Neurophysiol. 71:
375 1994). It is a compartmental model with active membrane in soma
and dendrite, including 4588 compart ments, more than 8000 voltage-gated
channels of 10 types and about 3200 synaptic channels. This model
has predictive power because it was constructed to replicate neuronal behavior
which has no direct relevance to synaptic integration: it was tuned
to repro duce the response of Purkinje cells to current injection in vitro.
This consists of a high frequency, regular rhythm of somatic fast spikes,
interrupted by spontaneous dendritic spikes.
The in vivo firing behavior of Purkinje cells is quite
different as it consists of highly irreg ular simple spike firing only.
Occasion ally, dendritic spikes occur, but these are always synaptically
evoked by the climbing fiber input, not spontaneous. The computer
model predicted that the Purkinje cell needs to receive a continuous inhibitory
drive in addition to the excitation by parallel fibers to obtain this typical
in vivo firing. This prediction was confirmed by blocking inhibition
during in vivo intracellular recordings. More recently, we have demonstrated
that the net inhibitory drive to the Purkinje cell dendrite has to be larger
than the excitatory drive (Jaeger et al. J. Neurosci. 17: 91 1997).
Inhibition hyperpolarizes the dendrite compared to the soma, making it
act as a current sink during most of the spiking cycle. In other
words, the
cell is not an 'integrate and fire' neuron at all! D. Jaeger
has confirmed these predic tions by using the dynamic clamp method in the
cerebellar slice preparation.
Finally, I will describe the dendritic calcium responses
evoked by parallel fiber input. These simulations were confirmed
experimen tally and led to a new theory about the function of cerebellar
long-term depres sion (De Schutter TINS 18: 291 1995) which can explain
recent experimental results.
Supported by FWO (Flanders).
Dopamine- and Ca2+-sensitive signaling pathways
in striatal neurons are organized in interacting streams of considerable
complexity (Prog. Neurobiol. 1994, 44: 163). Extrapolating the global effects
of dopamine agonists from test tube assays can be misleading, whereas pharmacological
dissection of the cellular system is too crude to provide quantitative
data about individual reaction steps. The strengths of the two approaches
can be combined, however, by application of quantitative analysis and modeling
techniques to experimental data on intracellular signaling cascades.
D1 dopaminergic stimulation of striatal neurons reduces
depolarization-induced N-/P-type Ca2+ currents via a complex
intracellular signaling cascade activating protein kinase A (PKA) (Neuron
1995, 14: 385). Neither phosphorylation of channel proteins by PKA nor
PKA-dependent inhibition of protein phosphatase 1 (PP1) by phosphorylation
of DARPP32 prevent the dephosphorylation of N-/P-type Ca2+ channels.
Quantitative modeling of the signaling pathways specifies requirements
for strong equilibrium phosphorylation of channels and PKA-dependent activation
of PP1. Since the reduction of Ca2+ currents persists in the
presence of PP1 blockers, a role of protein phosphatase 2B activity in
the regulation of striatal Ca2+ currents is predicted. This
adds new modes of intracellular crosstalk between dopamine- and Ca2+-mediated
signals.
The neural circuitry behind lamprey undulatory swimming
is among the best known of vertebrate neuronal systems. Modelling of this
system was started at a point when a great deal was known about it, but
also much detail was still unknown. Developing the model over ten years
has been a process in close interaction with experiments.
Early models relied on an off-switch lateral interneuron
for burst termination at moderate to high bursting frequencies. Subsequent
examination of the model, however, suggested that this neuron was perhaps
not of primary importance for burst termination. This finding was later
verified experimentally. Early models also explained the
burst frequency reducing, spike frequency increasing, and burst prolonging
effects of 5-HT as being due to its modulatory action on the adaptation
of lamprey premotor interneurons. The significance of this finding was
not fully appreciated until recently. Current models include a dynamic
modulation of adaptation, They demonstrate a more adequate burst proportion
than previous ones and further allow for hemi-segmental bursting, which
can be observed experimentally.
Current research focus on experimental studies of neuromodulator
circuitry and action, on more detailed models, and on the improved performance
of a neuro-mechanical model of lamprey swimming.
Theories of cortical computations have focussed largely
on the possibilities offered by computing with single neurons. In this
domain, a number of hypotheses have been proposed that give local synaptic
interactions specific roles in generating an algebra or logic for computations
in the neocortex. Experimental work, however, has provided little support
for such schemes. Instead, it is increasingly evident that the computations
performed by cortical circuits may depend not only on the biophysical properties
of neurons, but on the physical relationships in 3-D of the neurons that
form the circuits. It is clear that such relationships generate the well-known
'columnar' systems as well as the clear functional differences in response
properties of neurons in the different cortical layers. This 'architecture'
provides a basic framework for the cortical computations.
Structural and functional studies agree that characteristically
cortical functions, e.g. the identification of motion or orientation of
objects involve computations that are achieved with high accuracy through
the collective action of hundreds of neurons connected in recurrent microcircuits.
Surprisingly, some important principles of this recurrent architecture
can be captured in simple electronic models. More detailed models exploiting
the advantages offered by recurrent architectures can perform the computations
for a variety of functions, including extraction of features such as motion,
orientation, depth, as well as coordinate transforms and 'gain control'.
In these the 2-D or 3-D pattern of local recurrent connections plays a
significant role.
Recurrent circuit models explain how the computations
remain so remarkably robust in the face of various sources of noise, including
variability in the anatomical connections themselves, large variance in
the synaptic responses and trial-to-trial output of single neurons, changes
in ambient lighting, and weak or degraded input signals. Such investigations
also point to the advantages of detailed anatomical studies down even to
the sub-synaptic level as well as the importance of biologically-based
high level theories for extracting basic principles of operation of the
neocortical circuits.
We present a new theoretical approach
for the understanding of ionic selectivity
among monovalent alkali cations. The approach
is based on well known techniques of
statistical mechanics, such as the Langevin
equations and Kramer Theory of reaction rates.
We provide a theoretical equation relating
the permeability ratio P_B/P_A among
two ions A and B to simple
physical properties of the channel, such
as its radius and other molecular properties. The
equation has the form P_B/ P_A = (tau_B/ tau_A) / (Z_B/Z_A) where
tau_B/tau_A depends on the diffusion coefficient of the two ions, the recrossing
rates, ... and Z_A (Z_B) is the partition function of ion A (B) at the
highest barrier of the Gibbs energy profile in the channel. Both contributions
tau_B / tau_A and Z_B / Z_A are computed explicitly taking into account
the thermodynamics of ion hydration, ion-charged (or polar) group interactions
and channel geometry. Usually, tau_B/tau_A is of the order of 1,
so P_B/P_A depends primarily on Z_B/Z_A.
By computing the partition function in different
cases it is possible to evaluate the contribution of
geometrical factors and electrostatic interactions.
We show that the selectivity found in usual
K+, gramicidin, Na+, cyclic nucleotide gated and
endplate channels can be simply explained as
originating from geometrical properties of the inner
core of the channel and hydration
thermodynamics. In this view charged and polar
groups do not constitute the selectivity
filter but act as catalyst for ion
permeation.
One approach in computational neuroscience is analytic:
modelling. It begins with real experimental data and uses computational
methods as means of data analysis. One of my interests has been in applying
this approach to neuroanatomical data, to try to find out what these data
mean in terms of the organisation of the brain. Computational analysis
is necessary because anatomical data are numerous and complex, and informal
speculation about them reaches only unreliable conclusions.
There are three types of data available for analysis at
the systems level: a small amount of quantitative data on relative labelling
densities; a modest amount of data on laminar projection patterns, which
have been used to inform ideas about cortical hierarchy; and a large amount
of qualitative data about which brain structures are connected.
Mathematical modelling of the quantitative data shows that all
cortical systems are constrained to be hierarchies. Evolutionary optimisation
analysis of laminar data shows both that the primate visual system is surprisingly
strictly hierarchical, and that it is nonetheless not possible to specify
a single hierarchy from this analysis. Analysis of area-to-area connection
patterns by seriation, optimal set analysis, clustering methods, and non-metric
multidimensional scaling has provided a large number of conclusions, which
we have used to predict successfully the location of specific cell populations,
and to account for the paradoxical effects of some combinations of brain
lesions.