Transcript of "Jan 4, 2010. INTRODUCTION TO ELECTRICAL CONCEPTS"
1.
Cellular Neuroscience (207)
Ian Parker
Lecture # 1 - Enough (but not too
much!) electronics to call yourself
a cellular neurophysiologist
http://parkerlab.bio.uci.edu
2.
Ohm’s Law
battery
V
Current I
resistor R
V = IR
V (Volts) - 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 (how narrow the pipe is)
R = V/I so, if V = 1 volt
for R = 1 Ω I = 1A
for R = 1 k Ω I = 10^-3 A (1 mA)
3.
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??]
4.
Resistors in series and parallel
R1
R2
V
I
Total R = R1 + R2
I = V / (R1 + R2)
R1 R2
I = I1 + I2
I1 I2
1/ total R = 1/R + 1/ R2
5.
Conductance
Conductance is the reciprocal of resistance (i.e. how easily
something conducts electricity)
Conductance (G) = 1/R
Unit : Siemen (S) = 1/ 1Ω
G1 G2
I = I1 + I2
I1 I2
total conductance G = G1 + G2
From Ohms law I = V / R
So I = V * G
Itotal = V * (G1 + G2)
6.
Voltage dividers
R1
R2
V
E
E - V * R2 /(R1 + R2)
[ If V = 1 V, R1 = 9 kΩ and R2 = 1 kΩ
what is E? : what current flows through R1?]
7.
Capacitance
Capacitor - two conductors separated by an insulating gap (dielectric)
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
e.g. 2 metal plates
separated by an air gap
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
8.
RC (resistor/capacitor) circuits
1. Low-pass RC circuit
V
E
C
Rswitch
V
E
time
Switch closed
Voltage rises exponentially from
zero to V with time constant τ
τ is time for change to 1/e of
final voltage ( e = 2.71828…)
τ (sec) = R (Ω) * C (F)
[what is τ if R = 1 MΩ, C = 1 µF?]
9.
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
10.
RC (resistor/capacitor circuits)
2. High-pass RC circuit
V
C
switch
E
R
V
E
time
A
Output voltage instantly rises
to match input voltage, then
decays exponentially.
Time constant of decay
τ = RC
Effect is to block rapidly-
changing voltages (capacitor
is an insulator), but pass
rapidly changing signals
11.
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
Ω cm2
But membrane channels can greatly increase
the membrane conductance
12.
Specific membrane capacitance
membrane
extracellular fluid
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 µF cm-2
for cell membranes
13.
Input resistance of a cell
Inject current (I)
Record voltage (V)
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 ???]
14.
A neuron as an RC circuit
Inject current (I)
Record voltage (V)
cell
RmCm
inside
outside
V
E
time
I
Voltage changes exponentially
with time constant τm
15.
τm = Rm * Cm
So τm will be longer if Rm is high
“ “ “ “ “ and if Cm is high
We can directly measure Rm and τm
so we can calculate Cm = τm / Rm
Given that Cm ~ 1 µF cm2
, we can then calculate the
membrane area of the cell
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