Download EQUIVALENT CIRCUIT MODEL FOR THE CELL MEMBRANE

EQUIVALENT CIRCUIT MODEL
FOR THE CELL MEMBRANE
Reported by:
Valerie Chico
ECE 5
Nerve Membrane

The nerve membrane is a lipid bilayer that is
pierced by a variety of different types of ion
channels
Types of Ion Channels
 Passive (always open)
 Active (gates that can be opened).
Note : Each ion channel is also characterized
by its selectivity.
Three types of Passive Electrical
Characteristics
Electromotive Force
 Resistive
 Capacitive

Remember:
Active Na-K pump maintains Vm
across the cell membrane
Electromotive Force Properties
The three major ions Kþ, Naþ, and Cl are
differentially distributed across the cell
membrane at rest and across the
membrane through passive ion
channels.
This separation of charge exists across
the membrane and results in a voltage
potential Vm as described by the
Goldman Equation
Across each ion-specific channel, a concentration
gradient exists for each ion that creates an
electromotive force, a force that drives that ion
through the channel at a constant rate. The Nernst
potential for that ion is the electrical potential
difference across the channel and is easily
modeled as a battery, as is illustrated in Figure
11.11 for Kþ. The same model is applied for Naþ
and Cl with values equal to the Nernst
potentials for each.
Resistive Properties
It resists the movement of electrical charge through
the channel. This is mainly due to collisions with
the channel wall where energy is given up as heat.
The term conductance, G, measured in Siemens
(S), which is the ease with which the ions move
through the membrane, is typically used to
represent resistance. Since the conductances
(channels) are in parallel, the total conductance is
the total number of channels, N, times the
conductance for each channel, G’
G =NxG’
1
Conductance is related to membrane permeability, but they
are not interchangeable in a physiological sense.
Conductance depends on the state of membrane, varies
with ion concentration, and is proportional to the flow ions
through a membrane. Permeability describes the state of
the membrane particular ion. Consider the case in which
there are no ions on either side the membrane. No matter
how many channels are open, G ¼ 0 because there ions
available to flow across the cell membrane (due to a
potential difference). the same time, ion permeability is
constant and is determined by the state of membrane.
Capacitive Property
Capacitance occurs whenever electrical conductors are separated by an
insulating material. In the neuron, the cytoplasm and extracellular fluid
are the electrical conductors and the lipid bilayer of the membrane is the
insulating material (Fig. 11.3). Capacitance for a neuron membrane is
approximately 1 mF=cm2. Membrane capacitance implies that ions do
not move through the membrane except through ion channels. The
membrane can be modeled using the circuit in Figure 11.15 by
incorporating membrane capacitance with the electromotive and
resistive properties. A consequence of membrane capacitance is that
changes in membrane voltage are not immediate but follow an
exponential time course due to first-order time constant effects. To
appreciate the effect of capacitance, the circuit in Figure 11.15 is
reduced to Figure 11.16 by using a The´venin equivalent for the
batteries and the resistors with RTh and VTh given in Equations 11.35
and 11.36.
The time constant for the membrane
circuit model is t ¼ RTh Cm, and at 5t
response is within 1% of steady state.
The range for t is from 1 to 20ms in a
typical neuron. In addition, at steady
state, the capacitor acts as an open circuit
and VTh ¼ Vm, as it should.
Change in Membrane Potential with Distance
The larger the diameter of the
dendrite, the smaller the resistance
to the spread of current from one
section to the next
resistance is important. Most of the current flows out through the section
into which the current was injected since it has the smallest resistance
(RTh) in relation to the other sections. The next largest current flowing out
of the membrane occurs in the next section since it has the next smallest
resistance, RTh þ Ra. The change in Vm, DVm, from the injection site is
independent of Cm and depends solely on the relative values of RTh and
Ra. The resistance seen in n sections from the injection site is RTh þ n
Ra. Since current decreases with distance from the injection site, then
DVm also decreases with distance from the injection site because it
equals the current through that section times RTh. The change in
membrane potential, DVm, decreases exponentially with distance and is
given by
Na – K Pump