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Cellular Neuroscience (207)
Ian Parker
Lecture # 1 - Enough (but not too
much!) electronics to call yourself
a cellular ne...
Ohm’s Law
battery
V
Current I
resistor R
V = IR
V (Volts) - electrical driving force (water pressure)
[voltage, potential,...
Charge
Charge = amount of electricity (number of electrons : gallons of water)
= current * time
1 A * 1 sec = 1 Coulomb (C...
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 + ...
Conductance
Conductance is the reciprocal of resistance (i.e. how easily
something conducts electricity)
Conductance (G) =...
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 thr...
Capacitance
Capacitor - two conductors separated by an insulating gap (dielectric)
Capacitance (C) increases as;
1. The ar...
RC (resistor/capacitor) circuits
1. Low-pass RC circuit
V
E
C
Rswitch
V
E
time
Switch closed
Voltage rises exponentially f...
The effect of a low-pass circuit is to pass steady or slowly changing
signals while filtering out rapidly changing signals...
RC (resistor/capacitor circuits)
2. High-pass RC circuit
V
C
switch
E
R
V
E
time
A
Output voltage instantly rises
to match...
What does all this mean for a NEURON?
The cell membrane (lipid bilayer) acts as a very good insulator, but has high
capaci...
Specific membrane capacitance
membrane
extracellular fluid
intracellular fluid
The insulating cell membrane (dielectric) s...
Input resistance of a cell
Inject current (I)
Record voltage (V)
cell
Input resistance Rin = V/I
Rin decreases with increa...
A neuron as an RC circuit
Inject current (I)
Record voltage (V)
cell
RmCm
inside
outside
V
E
time
I
Voltage changes expone...
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 ca...
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Jan 4, 2010. INTRODUCTION TO ELECTRICAL CONCEPTS

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Transcript of "Jan 4, 2010. INTRODUCTION TO ELECTRICAL CONCEPTS"

  1. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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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