Biophysical Background
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Biophysics Background Bioengineering 6460 Bioelectricity Biophysical Background Bioengineering 6460 Bioelectricity Biophysics Background 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
Transcript of Biophysical Background
Biophysics Background Bioengineering 6460 Bioelectricity
Biophysical Background
Bioengineering 6460 BioelectricityBiophysics Background
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
V
Bioengineering 6460 BioelectricityBiophysics Background
Conductors & Resistors
• Conductors– Electrons free to move– Current flow in response to
electric field– In static state, no net charge
(E=0) • Resistors
– Electrons less free to move– Create potential differences– Depend on material properties
--
-------
---
- -E!0
E = 0
∆V = 0
Bioengineering 6460 BioelectricityBiophysics Background
Capacitance
+Q-Q
V
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-+
+
+
- +• Dielectric– Charges not free to move, just shift– E!0 inside, opposes applied E– Result is reduce v and increased C
Does anything change when the plates move?
Q = CV
+++
--- +Q-Q
V
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+
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- +?
Yes, V increases while Q and E are the same so C decreases.
Bioengineering 6460 BioelectricityBiophysics Background
Membrane Equivalent Circuit
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Cm
Em
Rm
Lipid Bilayer
Channel
Charged Polar Head
Bioengineering 6460 BioelectricityBiophysics Background
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 x0
jx v(x)v(0)
L
I =1R
V = GV
Bioengineering 6460 BioelectricityBiophysics Background
Current-Voltage (I-V) Curves
v
i
V
?? A
Bioengineering 6460 BioelectricityBiophysics Background
Equivalent circuits 1
v
i
g
g
2g3g
Bioengineering 6460 BioelectricityBiophysics Background
Equivalent circuits 2
v
i
g
V1 V1
g
V2 V2
I1=(v+V1) g
v
I2=(v-V2) g
Driving force
Bioengineering 6460 BioelectricityBiophysics Background
I-V Curve Examples
V
I
K-current
Na-current
Rectifying current + Nernst potential
Rectifying current
Vrev Vrev
Positive Nernst potential
Bioengineering 6460 BioelectricityBiophysics Background
Circuit Analysis
• Conservation of charge: currents sum at nodes• Conservation of energy: sum of voltages = 0
i1i2 i3
i1 + i2 + i3 = 0
v1
v2
v3
v4
v4 = v1+ v2+ v3
Bioengineering 6460 BioelectricityBiophysics Background
Voltage Divider
R1
R2
vB
v2
i=vB/(R1+R2)
i=v2/R2
v2=vB R2/(R1+R2)
Examples of voltage dividers in EP measurements?
Bioengineering 6460 BioelectricityBiophysics Background
Electrical Profile of a Cell
Inside OutsideOutside
v
E
+ -
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