Differentiating neural distributions: How neural geometries can impact neural firing patterns
Max Henderson, Luis Cruz
Department of Physics, Drexel University
Introduction to neurons and neural networks
• The brain’s essential function of
thought is carried out at the most
basic level by neurons.
• Neurons are specialized cells which
convey information through electric
currents.
• When the membrane of the neuron
reaches a certain critical electric
potential, the neuron will release a
burst of current called an action
potential.
• These action potentials are used to
convey information in large
networks of neurons, called neural
networks.
Figure 1.
Example of
a neuron’s
geometric
structure.
Figure 2.
An
example
of a
neuron
firing,
called an
action
potential.
Methods
Results
• Ideas concerning synaptic loss and more detailed neural structures.
• Step 1. Create
i n i t i a l
microcolumnar
and random
networks.
Microcolumnar
networks are
constructed
using previous
methods.
Figure 5 (top).
Original crystalline
network.
Figure 6 (bottom).
The final network
with microcolumnar
geometry.
Figure 10. Results from computational
experiments of ‘aging’ brains using different
spring constant values in the x, y, and z
directions. The average RMS displacements
(shown in Figure 11C) follows theory
extremely well according to the equation:
Explaining microcolumnar structures in the brain
• The neocortex is divided up into six different layers due to the different
neural densities and characteristics in each layer.
• An interesting feature of the neocortex is that within these layers, vertical
arrangements of neurons form, called microcolumns.
• While the existence of microcolumns has observed by biologists for a long
time, very little is still known about the purpose of the structures in the brain.
• Many believe that microcolumns are simply an artifact of evolution while
others believe that the microcolumnar structure of the brain is vital for
information processing.
• The goal of this project is to better understand the effects of aging in terms of
microcolumnar loss. First, we present a method for creating both ‘young’ and
‘old’ microcolumnar networks. Secondly, we investigate the differences
between connectivity and firing dynamics of neural networks based off of
microcolumnar and random lattices.
• By measuring several parameters of the neural networks including
synchronicity and phase transitions, the goal is to explain the microcolumnar
structure of the brain using a argument for functionality.
• S t e p 2 . D e t e r m i n e
connectivity of the
neurons in the neural
network for the ‘young’
brains.
In our
experiments, we chose two
different connectivity
methods with biophysical
significance. The first is
based off a distance
dependent relation neurons
exhibit wherein neurons
are more likely to be
connected if their
intersomatic distance is
small.
The second is
based off of a novel
method which reorganizes
connectivity iteratively
based off of the number of
common neighbors shared
between neurons.
This
also has been observed in
biological systems.
Future research
r 2 = x 2 + y2 + z 2 =
kBT kBT kBT
+
+
kx
ky
kz
Figure 11. Adjusted microcolumnar strength, F,
as a function of age, shown in terms of inverse
spring constant strength as well as average RMSdisplacement. Allowing particles to undergo
Brownian motion while constrained by a
harmonic force produced a curve that shows a
decrease in microcolumnar strength as a function
of age, which matches experimental data.
Figure 15 (top). Synaptic loss
attributed to moving neurons. We
believe that another loss of
functionality could be related to the
loss of synapses torn or damaged due
to neuronal drift.
Figure 16 (right). One particular
realization of a neuronal structure
generated using a random process that
should create randomly structured
neurons within a particular class of
neurons.
References
Figure 12. Visualization of the microcolumnar system mapped onto 2D grids.
Figure 7 (top). Experimental connectivity of neurons in the
brain as a function of interneuronal distance (Perin et al 2011).
Figure 8 (bottom). Connectivity as a function of common
neighbors for the iterative reorganization of the common
neighbor connectivity algorithm (Perin et al 2013).
Papers
• 1. Luis Cruz, Sergey V. Buldyrev, Shouyong Peng, Daniel L. Roe, Brigita Urbanc, H.E.
Stanley,1, Douglas L. Rosene. “A statistically based density map method for
identification and quantification of regional differences in microcolumnarity in the
monkey brain.”
• 2. Andrew C. Felch, Richard H. Granger. “The hypergeometric connectivity
hypothesis: Divergent performance of brain circuits with different connectivity
distributions”.
• 3. Ashwin Vishwanathan, Guo-Qiang Bi, and Henry C. Zeringue. “Ring-shaped
neuronal networks: a platform to study persistent activity.”
• 4. Luis Cruz,⁎ Brigita Urbanc, Andrew Inglis, Douglas L. Rosene, and H.E. Stanley.
“Generating a model of the three-dimensional spatial distribution of neurons using
density maps.”
• 5. Perin et al. “A synaptic organizing principle for cortical neuronal groups.”
• 6. Perin et al. “Computing the size and number of neuronal clusters in local circuits.”
• Step 3. Using the connectivity matrices, we use the software program
NEURON to simulate neural networks with varying random stimulus and
analyze the network effects.
Figure 3. The different
layers of the brain.
RESEARCH POSTER PRESENTATION DESIGN © 2012
www.PosterPresentations.com
Figure 4. An example of a vertical
microcolumn in a layer of the brain.
Figure 9.
Examples of
neuronal firing
patterns, called
raster plots,
obtained by
various networks.
Additionally
shown are two
potential metrics
for measuring
network
dynamics, the
interspike interval
(ISI) and SPIKE.
Acknowledgements and contacts
Would like to thank my advisor Dr. Cruz for help guiding these endeavors and
always adding creative and practical suggestions for improving the project, as
well as the NIH grant AG021133 for making this research possible.
Figure 13. Results from connecting neurons
using distant dependent and common
neighbor connectivity. While random
geometry results in isomorphic results,
microcolumns clearly favor the axis parallel
to the columns.
Figure 14. SPIKEG-distances within
microcolumns for the various neural networks
before (BCN) and after (ACN) the common
neighbor law is applied, as a function of
stimulus for (A) microcolumnar and (B)
random lattices. While connectivity varies as
a function of geometry, the dynamics have
changed little.
Contact:
Maxwell Philip Henderson
Graduate Student
Department of Physics
Drexel University
Email: mph58@drexel.edu
Phone: 484-288-9833