Transcript IGERTPoster2009

Gabrielle J.
1
Gutierrez ,
Larry F.
2
Abbott ,
Eve
1
Marder
1Volen
Center for Complex Systems, Brandeis University
2Department of Neuroscience, Department of Physiology and Cellular Biophysics, Columbia University
Recent theoretical work on networks has shown that, due
to the nonlinear dynamics that govern its behavior, a network
does not have to be built for a specific task in order to perform
that task. With the addition of some form of “read-out”
circuitry, such as a downstream neuron or a model cell,
a given task can be achieved with the right combination of
synaptic weights for the connections from the cells in the
network to the read-out cell. However, it is unclear whether a
complex biological network can actually compute as broad a
range of functions as these models are predicting. My research
is focused on investigating whether a biological network can
act as such a dynamical computing reservoir.
Upon injecting a PD cell with sinusoidal current, many of the other cells in the network respond to the
stimulus. Due to the nonlinear interactions in the network, the output activity each cell produces is more
complex than the input. The voltage traces display two interesting features of complex network activity.
Some of the firing patterns
are phase shifted relative
to the input.
Some of the firing patterns
contain higher frequency
components.
The stomatogastric ganglion (STG) of the Jonah crab is a wonderful system for these studies.
 small, highly connected, neural network
0.1 Hz current
injection
..
 contains approximately 30 neurons, most of which are motor neurons that control the rhythmic contractions
of the stomach muscles which allow the animal to chew and filter its food
 the STG can easily be isolated from the rest of the crustacean nervous system
 the activity of most of its neurons can be recorded simultaneously
It is unclear whether a complex biological network
can actually compute as broad a range of functions as
these models are predicting. My research is focused
on finding out whether a biological network can act as
such a dynamical computing reservoir.
1.5 Hz current
injection
These data are put through Principal Components Analysis (PCA) and a set of basis functions and
a set of coefficients are calculated. A linear sum of the weighted network outputs is calculated in
order to produce the best match to a Target Function.
Target Function
Actual Output
The stomach is dissected from the crab and the Stomatogastric Nervous System (STNS) is dissected from the
stomach tissue and pinned onto a Sylgard®-coated petri dish. The STG is desheathed to allow an intracellular
electrode access to the cell bodies. Vaseline wells are made around the nerves that will be recorded
extracellularly. To obtain a recording of the activity of each cell in the network, 12-14 nerves are recorded
extracellularly and 1-2 cells are recorded intracellularly. The descending inputs from the modulatory ganglia are
blocked with local application of 10-6 M Tetrodotoxin (TTX) and Sucrose.
The Pyloric Dilator cell (PD) is injected with a sine wave of current using a current clamp protocol and a wave
function generator. The frequency of the injected current ranges from 0.01 Hz to 3 Hz and the amplitude ranges
from ± 0.1 nA to ± 5 nA.
The dynamical complexity of the
STG is quantified by performing
Principal Components Analysis (PCA).
This method picks out and ranks the
key players in transforming an input
into a target function. It also produces
basis functions that can be used to
generate a set of possible output
functions.
The dynamic range of a network’s outputs is enhanced by the neurons that display phase shifted activity
and by the neurons that have higher frequency activity. However, there is a tendency for the higher frequency
outputs to be noisier. A balance between complexity and reliability needs to be struck. This is likely to be what
differentiates a modeled neural network from a biological neural network.
This work can be extended to examine the role of
neuromodulators in expanding or contracting the set of
possible outputs. In the context of the biological functionality
of the STG, quantifying the dynamic range of this network
will provide insights into how neurons are able to switch
between two ongoing rhythms in the network.
Maass, W, Natschläger, T, Markram, H. (2002). Real-Time Computing Without Stable States: A New Framework for Neural Computation Based on Perturbations. Neural Computation 14, 2531–2560.
I’d like to thank my advisor, Eve Marder, for her support and encouragement as well as the rest of the
Marder Lab. I would also like to thank Larry Abbott who is collaborating with me on this project.
Marder, E, & Bucher, D. (2007). Understanding Circuit Dynamics Using the Stomatogastric Nervous System of Lobsters and Crabs. Annu. Rev. Physiol. 69, 291–316.
Sussillo, D, & Abbott. LF. (2009). Generating Coherent Patterns of Activity from Chaotic Neural Networks. (In publication).