1. Procedia Computer Science 20 (2013) 33 – 38
1877-0509 © 2013 The Authors. Published by Elsevier B.V.
Selection and peer-review under responsibility of Missouri University of Science and Technology
doi:10.1016/j.procs.2013.09.235
ScienceDirect
Complex Adaptive Systems, Publication 3
Cihan H. Dagli, Editor in Chief
Conference Organized by Missouri University of Science and Technology
2013- Baltimore, MD
Biologically Inspired Olfactory Learning Architecture
George Georgieva
, Mrinal Gosavib
, Iren Valova*b
, Natacha Gueorguievac
Abstract
Neurons communicate via electrochemical currents, thus simulation is typically accomplished through modeling the
dynamical nature of the neuron's electrical properties. In this paper we utilize Hodgkin-Huxley model and briefly compare it to
Leaky integrate-and-fire model. The Hodgkin-Huxley model is a conductance-based model where current flows across the cell
membrane due to charging of the membrane capacitance, and movement of ions across ion channels. The leaky integrate-and-fire
model is widely used example of formal spiking neuron model. In it the action potentials are generated when the membrane
potential crosses a fixed threshold value and the dynamics of the membrane potential is governed by a 'leaky current'.
Conductance-based models (HH models) for excitable cells are developed to help understand underlying mechanisms that
contribute to action potential generation, repetitive firing and oscillatory patterns. These factors contribute in modeling the
olfactory bulb's dynamic behaviors. Due to these characteristics, we have focused on the conductance-based neuronal models in
this work. The model consists of input, mitral and granule layer, connected by synapses. A series of simulations accounting for
various olfactory activities are run to explain certain effects of the dynamic behavior of the olfactory bulb (OB). These simulation
results are verified against documented evidence in published Journal papers.
: olfactory bulb, Hodgkin-Huxley, neuron models
1. Introduction
An artificial neuron consists of an input with some synaptic weight vector and a transfer function [1] inside the
neuron determining output. Many Neuron Models have been proposed by researchers, but the most popular models
are and The Hodgkin-Huxley model describes the spiking
behavior and refractory properties of real neurons and serves as a paradigm for spiking neurons based on nonlinear
conductance of ion channels. Whereas the LIF model is the simplest and the most effective model used to solve
mathematical and analytical problems.
* Corresponding author. Tel.: 5089998502; fax: 5089999144.
: ivalova@umassd.edu.
Available online at www.sciencedirect.com
© 2013 The Authors. Published by Elsevier B.V.
Selection and peer-review under responsibility of Missouri University of Science and Technology

2. 34 George Georgiev et al. / Procedia Computer Science 20 (2013) 33 – 38
In an pplications, when choosing the neuron model there is always a trade-off between the bioln ogical plausibility
and computational emm fficienff cy. For example, ifmm thf e neural network is suppuu osed to include the effect of complex
biochemical reactions in thn e cortex, the Hodgkin-Huxley model, with ionic channels should be used. On the other
hand, if the compumm tational efficiency is of greater impomm rtance than biological plausibility, the Leaky Integrate and
Fire (LIF) will most likely be adopted due to its low compumm tational cost [2].
The Hodgkin-Huxley model is one of the most
biological plausible models in computationalmm neuroscience.
inside K+
- - - - - -
+ + + + + +
outside Na-
This neuron models represents the characteristics of the
responses of real neurons, hence their parameters are
biophysically meaningful and measurable. Also, these
parameters allow us to investigate questions related to
synaptic integration, dendritic cable filtering, effects of
dendritic morphology, the interprr lay between ionic currents,
and other issues related to single cell dynamics [3]. As
seen in Fig.1, an axon has three typesyy of ion currents
- +
Fig. 1 Schematic of Hodgkin Huxley my odel
namely sodium (Na ),-
potassium (K ),++
and a leak current
that consists mainly of chloride ions (Cl-
). The semi
permeable cell membrane separates the interior of the cell from the extra cellular liquid and also stores the current.
A voltage-dependent sodium and potassium ion channels, control ttt he flow of thf ose ions through this cell membrane.
The model is basically an electrical circuit with capacitor C and three resistors for thr e ion currents. When an inpunn t
current I(t) is injected into the cell it mt ay add fuy rther charge on then capacitor, or leak through the channels in thn e
cell membrane. Because of active ion transport through the cell membrane, the ion concentrationtt insn ide the cell is
different from that in thn e extracellular liquid. The Nernst potential generated by the difference in ion concentratitt on is
represented by a battery. So, in mn athematical terms, current I(t) can be split int to two capacitive current Ic which
charges the capacitor C and current Ik which passes through the ion chn annels. Fig.2 illustrates the concept behind thee
formality of the condf uctance-based model.
Sodium channel Sodium ions enter
60
40 NaNa- channelschannels becobecomeme 3.3.
refractory. no more Na+
20 enenttersers cellcell 4.4 KK+
continuescontinues toto leaveleave
cell, causes membrane
0
-20
-40
-60
KK+KK channelschannelsn
open. K+KK begin to
leaveleave thethe cellcell
2.
NaNa- chchannelsannels
open. Na-begins
toto enterenter cellcell 1.1.
popop tentitentialal toto rereturnturnu toto
resting level
K+KK channels close
NaNa++ channelschannels openopen
5.
Fig. 2Flow of Na+
and K+
KK in an neuron

3. 35George Georgiev et al. / Procedia Computer Science 20 (2013) 33 – 38
The idea behind developing the Leaky Integrate and Fire model is to replace the rich dynamics of Hodgkin-
Huxley type models by an essentially one-dimensional fire-and-reset process [4]. LIF model is very popular due to
the ease with which it can be analyzed and simulated. Conductance-based models, on the other hand, are the most
common formulation used in neuronal models and can incorporate as many different ion channel types as are known
for the particular cell being modeled. In its simplest version, it represents a neuron by a single isopotential electrical
compartment, neglects ion movements between subcellular compartments, and represents only ion movements
between the inside and outside of the cell. Conductance-based models for excitable cells are developed to help
understand underlying mechanisms that contribute to action potential generation, repetitive firing
and oscillatory patterns [5, 6, 7].
2. Network Architecture
Fig.3 shows the general architecture of the spiking neuron network for modeling the dynamics of the mitral and
granule cells. The architecture resembles the oscillatory models in its two layered structure [8]. The network consists
of three main layers each represented by three neurons connected by synapses: the glomerulus layer, mitral layer and
the granule layer. The connections between input layer and mitral layer are excitatory. The synaptic connections
have weights, where the connections to neighboring cells are weaker. The weight of synapses between m1 and g1
are 0.5 and -0.5, respectively, and between m1 and g2 and between m1 and g3 are 0.2 and -0.2.The main difference
between the biological parameters and the model is concerning the membrane capacity m and membrane resistance
m of the cells. We used the values provided by the CSIM software, i.e., m=0.03 and m =1.0. The model allows
setting values for noise and injected current for a neuron.
The dynamics of the OB depends on the structure of the connections between the layers and values of the
parameters in network. The reciprocal inhibition effects in the OB is achieved by circuit connection of mitral and
granule cells in model and weighting the synapses of granule-mitral connection negative. By changing the weight
one can impact the strength of this inhibition effect. Reducing the weights of mitral-granule and/or granule-mitral
synaptic connections will weaken the inhibitory effect, whereas raising the weight will give stronger inhibitory
effect. The change of the delay of the synapse results in an early or later inhibition of a mitral cell. The inhibition of
mitral cells by granule cells leads to reduction of firing rate of the membrane potential of mitral cells. Sidewise
connections of mitral cells through granule cells in the model allow for lateral inhibition of mitral cells.
Neuron +
Synapse
n1 n2 n3
+ + +
m1 m2 m3
g1 g2 g3
Fig.3 Architecture of the utilized spiking neuron model

4. 36 George Georgiev et al. / Procedia Computer Science 20 (2013) 33 – 38
3. Experiments and Discussion
Experiment 1 shows how mitral cells react to an incoming spike train (Fig.4). There is no reciprocal and lateral
inhibition influencing the mitral cells. The saturation of the cells is also ignored. The input for all the three mitral
cells is same and so is the output of these cells. This is achieved by having no connection between granule and
mitral layers. Thus, we are just representing results of m1. The first row in Figure 7 displays input train of spikes to
m1. In row two we have changes of the membrane potential of a mitral cell. The incoming spikes trigger outgoing
spikes by brining the membrane potential over threshold. The last action of spike train shows conductance. Several
biological papers support the same results of conductance [9]. The effect of membrane potential depends on
concentration of sodium (Na+
) and potassium (K+
). The incoming spike increases the Na+
ions hence the membrane
potential increases and crosses the threshold value causes depolarization. Whereas the K+
ions bring the membrane
potential down towards resting potential, this is called hyper polarization. As a result of this we can see the rise and
fall of membrane potential of m1 in row two. However sodium conduction occurs faster than potassium due to
which there is a prolonged decrease in the membrane potential. The membrane potential of granule cell g1 in row
four shows no change as there is no connection between m1 and g1.
Fig.4 Experiment 1 – no reciprocal and lateral connections
In experiment 2, we only utilize connections between the mitral and granule cells, i.e. reciprocal inhibition. The
input spike excites the mitral cell producing output spike. This depolarization activates the excitatory synapse of
granule cell. As a reaction, the ESPS activates the inhibitory synapse back onto mitral cell, which causes
hyperpolarizing IPSP in mitral cells. The hyperpolarization is caused by opening and closing of K+
channels. Due to
this more K+
leaves the cell than necessary to repolarise the membrane. This, with the input spike, depolarizes the
mitral cell again generating input to granule cell. Although the voltage activated channels are closed, the potassium
leaks through other open channels to retune the cell to the resting voltage. Along with this one can also see the
changes of the membrane potential of g1 and output spike train of g1 in row four. As proved in biological paper [10,
11], a result of reciprocal or recurrent inhibition is a decrease in firing rate of the output spikes in m1. This is
demonstrated in Fig.5.
Experiment 3 is performed to emphasize more on the effects produced in experiment 2. Here we have used
higher weights for inhibitory(-0.02) connection between mitral and granule layer. This change generates stronger
inhibitory effects in mitral cells and a decrease in the spike rate of output as compared to the first two experiments
as shown in Fig.6 [3].
The next experiment 4 utilizes the fully connected architecture of Fig.3. As seen in Fig.7, the input spike causes
ESPS in m1 which generates action potentials in granule cells, which is followed by conduction. Hence we can see
an output spike and the change of membrane potential in g1. Since the mitral cell have reciprocal and lateral
inhibition connections with granule cells, m1 receives input from g1, g2 and g3. Thus, the membrane potential of
m1 exhibits a prolonged IPSP followed by hyperpolarization. The influence of m2 and m3 through granule cells
generates an inhibitory response in m1, which suppresses the excitability of m1 until the effect has worn off [8, 12].
That results in slow output spikes from m1. After the membrane potential of m1 goes into negative values, it rises
back to positive values and finally comes back to 0. This corresponds to the biological description of functionality of
sodium-potassium pump that acts to re-establish the original ion concentration by pumping Na+
out and brining K+
in [13].

5. 37George Georgiev et al. / Procedia Computer Science 20 (2013) 33 – 38
Fig.5 Experiment 2 with reciprocal inhibition
Fig. 6 Experiment 3 with emh phasizedmm inhibitory connection
4. Conclusion
In thn is paper we evaluated HH and LIF models in varin ous aspects like the basic structure of thf ese models and
their ar pplication advantages. Then we discussed the differff ences between these models based on thn eir performance
and cost, which has helped us in choosin ng Conduction based HH model for our OB simulations.
The paper also proves that the spiking neuron networks are very strong and powerful tools and are capable of
modeling dynamics of thef OB. We were able to model three main dyn namics of OB which are verified with
biological experimental results and papers:
1. No reciprocal and lateral inhibition - With non reciprocal and later synaptic connection between min tral and
granule layer the membrane potential of granule cells is not changed. However the inputn spike causes ESPS in

6. 38 George Georgiev et al. / Procedia Computer Science 20 (2013) 33 – 38
mitral cells generating an output spike train. It is then followed by hyperpolarization. The membrane potential of mitral cells
shows rise and fall due to sodium-potassium conduction.
Fig.7 Experiment 4 results, (reciprocal and lateral inhibition)
2. Reciprocal inhibition - The circular connection of mitral and granule cells in model and weighting the synapses of the
granule –mitral connection negatively, enables the simulation of reciprocal inhibitory effects in OB. By changing the weights
one can impact the strength of this inhibitory effect.
3. Reciprocal and lateral inhibition -As with reciprocal and lateral inhibition connection of synapses results in earlier or later
inhibition with various strengths. This also reflects that mitral-granule connections vary in their distance between cells and a
greater distance has weaker impact than a close distance. While the lateral connections of mitral cells causes suppression
in cell excitability leading into slow firing rate of mitral cells.
In a further development of model one could integrate mitral cell saturation by STDPSynapses [14] of CSIM.
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