Transcript Cellular Neuroscience (207) Ian Parker

Cellular Neuroscience (207)
Ian Parker
Lecture # 1 - Enough (but not too
much!) electronics to call yourself
a cellular neurophysiologist
http://parkerlab.bio.uci.edu
Ohm’s Law
Current I
battery
V
V (Volts)
resistor R
V = IR
- electrical driving force (water pressure)
[voltage, potential, potential difference, p.d. are all synonyms]
I (Amperes) - electrical current flow (gallons per minute)
R (Ohms)
- resistance
R = V/I so, if V = 1 volt
(how narrow the pipe is)
for R = 1 W
for R = 1 k W
I = 1A
I = 10^-3 A (1 mA)
Charge
Charge = amount of electricity (number of electrons : gallons of water)
= current * time
1 A * 1 sec = 1 Coulomb (C)
[How many electrons are there in a Coulomb??]
Resistors in series and parallel
I
R1
Total R = R1 + R2
R2
I = V / (R1 + R2)
V
R1
I1
I = I1 + I2
R2
I2
1/ total R = 1/R + 1/ R2
Conductance
Conductance is the reciprocal of resistance (i.e. how easily
something conducts electricity)
Conductance (G) = 1/R
Unit : Siemen (S) = 1/ 1W
total conductance G = G1 + G2
G1
I1
I = I1 + I2
G2
I2
From Ohms law I = V / R
So
I =V*G
Itotal = V * (G1 + G2)
Voltage dividers
E - V * R2 /(R1 + R2)
R1
V
R2
E
[ If V = 1 V, R1 = 9 kW and R2 = 1 kW
what is E? : what current flows through R1?]
Capacitance
Capacitor - two conductors separated by an insulating gap (dielectric)
e.g. 2 metal plates
separated by an air gap
Capacitance (C) increases as;
1. The area of the plates is increased
2. The separation between the plates is decreased
3. The dielectric constant of the insulator is increased
Capacitors store electricity, but cannot pass a steady current
Unit : Farad (F)
1 F = capacitor that will store 1 Coulomb
when connected to 1 V
Charge (q) stored on a capacitor = C * V
RC (resistor/capacitor) circuits
1. Low-pass RC circuit
switch
R
V
E
C
Voltage rises exponentially from
zero to V with time constant t
V
t is time for change to 1/e
E
of
final voltage ( e = 2.71828…)
tim e
Switch closed
t (sec) = R (W) * C (F)
[what is t if R = 1 MW, C = 1 mF?]
The effect of a low-pass circuit is to pass steady or slowly changing
signals while filtering out rapidly changing signals
B
brief change in voltage
longer change in voltage
RC (resistor/capacitor circuits)
2. High-pass RC circuit
switch
E
C
R
V
A
Output voltage instantly rises
to match input voltage, then
decays exponentially.
E
V
tim e
Time constant of decay
t = RC
Effect is to block rapidlychanging voltages (capacitor
is an insulator), but pass
rapidly changing signals
What does all this mean for a NEURON?
The cell membrane (lipid bilayer) acts as a very good insulator, but has high
capacitance.
Specific membrane resistance
1 cm
Resistance of 1 cm2 of membrane (Rm)
Rm of a lipid bilayer >106 W cm2
But membrane channels can greatly increase
the membrane conductance
Specific membrane capacitance
extracellular fluid
membrane
intracellular fluid
The insulating cell membrane (dielectric) separates two good conductors (the
fluids outside and inside the cell), thus forming a capacitor.
Because the membrane is so thin (ca. 7.5 nm), the membrane acts as a very
good capacitor.
Specific capacitance (capacitance of 1 cm2 of membrane : Cm)
Cm ~ 1 mF cm-2 for cell membranes
Input resistance of a cell
Record voltage (V)
Inject current (I)
cell
Input resistance Rin = V/I
Rin decreases with increasing size of cell (increasing membrane area)
Rin increases with increasing specific membrane resistance
[If I = 10 nA and V = 5 mV, what is Rm ???]
A neuron as an RC circuit
Record voltage (V)
Inject current (I)
I
cell
V
Cm
Rm
E
inside
tim e
outside
Voltage changes exponentially
with time constant tm
tm = Rm * Cm
So tm will be longer if Rm is high
“ “ “ “
“ and if Cm is high
We can directly measure Rm and tm
so we can calculate Cm = tm / Rm
Given that Cm ~ 1 mF cm2, we can then calculate the
membrane area of the cell