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Jan 4, 2010. INTRODUCTION TO ELECTRICAL CONCEPTS

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  • 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  I = 1A for R = 1 k  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/ 1  G1 G2 I = I1 + I2 I1 I2 total conductance G = G1 + G2 From Ohms law I = V / R So I = V * G I total = V * (G1 + G2)
  • 6. Voltage dividers R1 R2 V E E - V * R2 /(R1 + R2) [ If V = 1 V, R1 = 9 k  and R2 = 1 k  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 R switch Switch closed
    • Voltage rises exponentially from zero to V with time constant 
    •  is time for change to 1/e  of final voltage ( e = 2.71828…)
    •  (sec) = R (  ) * C (F)
    • [what is  if R = 1 M  , C = 1  F?]
  • 9. The effect of a low-pass circuit is to pass steady or slowly changing signals while filtering out rapidly changing signals brief change in voltage longer change in voltage
  • 10. RC (resistor/capacitor circuits) 2. High-pass RC circuit V C switch E R
    • Output voltage instantly rises to match input voltage, then decays exponentially.
    • Time constant of decay
    •  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 cm 2 of membrane (R m ) R m of a lipid bilayer >10 6  cm 2 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 cm 2 of membrane : C m ) C m ~ 1  F cm -2 for cell membranes
  • 13. Input resistance of a cell Inject current (I) Record voltage (V) cell Input resistance R in = V/I R in decreases with increasing size of cell (increasing membrane area) R in 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 R m C m inside outside I Voltage changes exponentially with time constant  m
  • 15.
    •  m = R m * C m
    • So  m will be longer if R m is high
    • “ “ “ “ “ and if C m is high
    • We can directly measure R m and  m
    • so we can calculate C m =  m / R m
    • Given that C m ~ 1  F cm 2 , we can then calculate the membrane area of the cell