Eletroni Model of glutamate reeptors
Tiger Wutu Lin
June 12, 2010
Abstrat
It has long been known that the spiking dynamis of a neuron an be
mimiked by some simple iruit elements (Hodgkin and Huxley, 1990). In
this projet we propose a harging-disharging neuron whose dynami an
be ontrolled by two inputs. One input is used to resemble the glutamate
release and the other works as a
M g 2+ like hannel bloker. In general
the iruit is analogous to the NMDA reeptors.
1 Introdution
Neuron models, whih is still under intensive study, an be dated bak to the
seminar work of Hodgkin and Huxley in 1952 (Hodgkin and Huxley, 1952a,b,).
They shown that the spike ativity of a neuron an be modeled by a iruit that
only have very basi eletroni elements. Remarkably, eah iruit element,
suh as the resistor, the apaitor and the voltage soure has a biophysial
ounterpart in the biologial neurons. With the fast development of the silion
industry in the past few deades, eletroni pioneers, suh as Carver Mead,
draw their attention to building eletroni iruits that an simulate ertain
neural funtions (Mead, 1989) . Experimental studies (Shi et al., 1999) have
shown that NMDA reeptors signiantly ontribute to the synapti plastiity
and people (Morris et al., 1990) speulate that it is important for memory and
learning. Thus, an eletroni iruit that ould resemble NMDA reeptors an
be potentially useful in ahieving ertain brain funtions. In this projet, we
propose a simple design for NMDA reeptors that is modulated by an input
that represents glutamate release and a voltage threshold that represents the
voltage-gated M g 2+ bloker.
1
2 Methods
Fig.1
NMDA iruit design.
Synapti iruit designs have been proposed in the past (Mead, 1989) . In this
projet, our design is based on the harge-disharge synapti design that was
proposed by Rashe and Douglas (1999) . Shown in gure 1, our iruit ould
be separated into three parts by its funtions. In the membrane segment, a
apaitor C1 ats as the ell membrane. Instead of having a negative voltage
potential as in neurons, here, our membrane holds a positive potential beause
this is easier to implement at the iruit level by onneting to a voltage soure
at V2. The two transistor M1 and M2 at as a urrent mirror to repliate the
urrent through the membrane. Although this urrent mirror is not neessary
in the ontext of this projet, we expet it to be useful in future large sale
designs. This repliated urrent an be used as a referene for glutamate release
at the presynapse when neurons are onneted together.
In the M g 2+ segment, we used a dierential pair as the voltage gate. The
urrent ow through the ommon soure of M4 and M5 depends on the gate
voltage of M4 and M5. We note here that the gate voltage of M5 is the membrane
voltage. If this voltage is higher than the gate voltage of M4, i.e. the threshold
voltage, the drain-soure resistane ( rds ) of M5 will be negligible and we an
think of M5 as a short iruit. On the other hand, if the membrane voltage is
lower than the threshold voltage, the resistane between the drain and soure
of M5 will be very large and M5 ould be approximated as an open iruit.
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Lastly, for the glutamate segment, we used a periodi square funtion to
represent the glutamate release from the presynapse. Sine the square wave
is onneted to the gate of transistor M3, a high voltage whih represents high
glutamate onentration, will redue the drain-soure resistane ( rds ) of M3. In
other words, in the presene of glutamate, M3 is approximately a short iruit.
So, there are mainly two stages for the iruit. If the membrane voltage is above
the threshold voltage, then sine both M5 and M3 ould be regarded as short
iruits, the membrane will disharge. This ould be onsidered as the open
state of the NMDA hannel. At ertain point of the disharge, the membrane
voltage will drop down to a value that is lower than the threshold. Then M5
will beome an open iruit as if the NMDA hannel is losed. Also, if there
is no glutamate signal, M3 has high resistane. Then the membrane an not
disharge.
3 Results
To validate our iruit design, we simulated the dynamis of the iruit in software with dierent threshold voltages.
NMDA Simulation
1.99
1.8V
1.9V
2.0V
2.1V
1.98
V (V)
1.97
1.96
1.95
1.94
1.93
Fig.2
0
0.005
0.01
0.015
0.02
0.025
Time (sec)
0.03
0.035
0.04
Simulated spike trains with dierent threshold voltages.
3
0.045
0.05
As shown in gure 2, due to the harging and disharging mehanisms mentioned
in the method setion, the iruit an generate spike trains. Also in this gure,
we show that the spike amplitude depends on the threshold voltage.
After putting suh iruit into reality, we see similar spike patterns as the
simulation results in gure 2. In order to have a more quantitative view about
the resemblane of our iruit to the biology NMDA reeptors, we studied how
the spike hanges with respet to two inputs. One is the hange of the spikes
due to the amount of glutamate release. The other is the variane of the spikes
with respet to the threshold voltage. We argue that these two properties are
harateristi for NMDA reeptors and are ritial for desribing the dynamis
of the NMDA reeptors. Also real physiology experiments have been done on
similar tasks and an be used as a referene to evaluate our design (Jahr and
Stevens, 1990a; Popesu et al., 2004) .
Glutamate Release vs. Spike Amplitude
0.1
Spike Amplitude (V)
0.08
0.06
0.04
0.02
0
0
Fig.3
1
2
3
4
Glutamate Release (V)
5
6
Spike amplitude as a funtion of the glutamate release level.
As shown in gure 3, the spike amplitude has a nonlinear relationship to the
onentration of the glutamate release and this nonlinear pattern is onurred
by experimental results (Popesu et al., 2004). Tiny amount of glutamate an
not trigger any hannel open. On the other hand, if the glutamate is above
ertain level, all the hannel will be open and the urve is saturated.
4
Threshold Voltage vs. Spike Amplitude
0.1
Spike Amplitude (V)
0.08
0.06
0.04
0.02
0
−0.5
Fig.4
0
0.5
1
1.5
2
Threshold Voltage (V)
2.5
3
Spike amplitude as a funtion of the threshold voltage.
Shown in gure 4, we also investigated the eet of the threshold voltage to the
spike amplitude. The nonlinear pattern and rational we propose here has also
been raised before in experimental and theoretial studies (Jahr and Stevens,
1990a,b) . A very low or zero threshold voltage is analogous to a M g 2+ free
extraellular medium and this will ause the hannel to be open all the time.
Shown in the plot, this is onrmed by no spikes in our iruit system sine
the membrane is disharged all the time. With the M g 2+ level inreasing, the
NMDA hannel will have a higher hane of been bloked by it and less disharge
for the membrane. This is shown in the graph as an rising spike amplitude with
respet to the inreasing M g 2+ level. Eventually, we are expeting to see the
spike amplitude be stable at ertain value when the M g 2+ level is high enough,
beause at this time, the NMDA hannel should be almost bloked by the M g 2+
ions. But on the urve we see a small drop down of the voltage and this puzzle
is still under study.
4 Disussion
To onlude, our projet was initially motivated by the idea that biophysial
models of neurons ould be repliated on eletroni iruit board. In this projet,
we nished design of a NMDA reeptor that is regulated by its threshold voltage
and glutamate release level. As was briey mentioned in this report, the urrent
mirror gives our iruit the ability to be onneted as a network. We envision
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this to be a valuable design and future works an put this iruit in parallel to
ahieve ertain network funtions suh as Hebbian learning.
Referenes
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