in the Organization of
a Biological Network
Yong-Yeol Ahn*, Beom Jun Kim, Hawoong Jeong
KAIST, Republic of Korea
Putting a “Neural Network Model”
on a “Neural Network”
The ability to recognize patterns must be
crucial for surviving and mating
• Hopfield model on C. elegans neural
network. (Beom Jun Kim, 2004)
Neurons can have two states. At each time step, each
neuron’s state is determined by other neurons which have
links to it. -> The state vector falls into some attractors.
Ex) (+1) x 2 + (-1) x (-3) + …
• By the Hebb’s rule, the Hopfield network
can learn several patterns.
• After learning process, we try with the
testing pattern which has some error in it.
• Does this testing pattern end up to the
learned pattern? How much is the overlap?
• If we assume that the measure is good, Possible
other constraint is ‘wiring cost’.
• Energy consumption acts a crucial role in the
operation of the brain. (A brain consumes more
energy than heart, about 20% of all energy spent)
• Ganglia order in C. elegans is the global minima.
The C. elegans neuronal map
• Head neurons are
placed in the virtual
cylinder which wraps
• Body neurons are
placed just below the
cuticle layer (because
of the body cavity)
Is C. elegans neural network
optimized by wiring cost?
Two variational methods
and degrees of all
Optimized Network vs.
The C. elegans
network is far from
If we neglect the
It approaches toward
the optimal network.
Cumulative Distribution of
distance(cost) between two neurons
• Three length
• Body spanning
Links (like spinal
Is Clustering Coefficient
Playing an Important Role?
• We equilibrate the
network by rewiring
• C. elegans has much
bigger c.c. than this
• We constructu the C. elegans neural network with
• The distribution of distances between neurons in C.
elegans neural network follows piecewise exponential
• Although the neural network is not optimal, it is far from
• The performance measure (Hopfield model) does not play
a crucial role in the organization of C. elegans neural