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Biophysical Background
Biophysics Background
Bioengineering 6460 Bioelectricity
The Basics
· Materials
Conductor, capacitors
· Ohm's Law and Circuits
Ohms law, IV curves, dynamic circuit analysis
· Fields
Electric field, potential field
· Sources, Sinks, and Vector Calculus
Current monopoles, dipoles Volume conductor fields Div, grad, curl and all that
Biophysics Background
Bioengineering 6460 Bioelectricity
Conductors & Resistors
· Conductors
Electrons free to move Current flow in response to electric field In static state, no net charge (E=0)
 V
E=0 V = 0
· Resistors
Electrons less free to move Create potential differences Depend on material properties

E!0
Biophysics Background
Bioengineering 6460 Bioelectricity
Capacitance
· Dielectric Charges not free to move, just shift
E!0 inside, opposes applied E
+ + +Q + +
Q V

Result is reduce v and increased C
Does anything change when the plates move? Q = CV Yes, V increases while Q and E are the same so C decreases.
 + Q + +
+

+ +Q +
V
?
+
Biophysics Background
Bioengineering 6460 Bioelectricity
Membrane Equivalent Circuit
Channel
Lipid Bilayer
Charged Polar Head
Rm Cm +
Biophysics Background
" Em
Bioengineering 6460 Bioelectricity
Current and Ohm's Law
· Without potential difference there is no current! · Without conductance, there is no current. · Ohm's law:
linear relationship between current and voltage not universal, especially not in living systems
1 I = V = GV R
v(0) 0 L jx v(x) x
Biophysics Background
Bioengineering 6460 Bioelectricity
CurrentVoltage (IV) Curves
i ?? A
V
v
Biophysics Background
Bioengineering 6460 Bioelectricity
Equivalent circuits 1
3g 2g g g v
i
Biophysics Background
Bioengineering 6460 Bioelectricity
Equivalent circuits 2
i
V1 g
V2 g
V1
V2 v
v
Driving force
I1=(v+V1) g
I2=(vV2) g
Biophysics Background
Bioengineering 6460 Bioelectricity
IV Curve Examples
I Rectifying current Kcurrent Rectifying current + Nernst potential Vrev Vrev Nacurrent
Positive Nernst potential V
Biophysics Background
Bioengineering 6460 Bioelectricity
Circuit Analysis
· Conservation of charge: currents sum at nodes · Conservation of energy: sum of voltages = 0
v1 i1 i2 i3
v4 v4 = v1+ v2+ v3 v3
Biophysics Background
v2
i1 + i2 + i3 = 0
Bioengineering 6460 Bioelectricity
Voltage Divider
i=vB/(R1+R2) i=v2/R2
R1
vB R2 v2
v2=vB R2/(R1+R2)
Examples of voltage dividers in EP measurements?
Biophysics Background
Bioengineering 6460 Bioelectricity
Electrical Profile of a Cell
v
E
+ Outside + + + +
Biophysics Background
Inside 
+ + Outside + + +
Bioengineering 6460 Bioelectricity
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