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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

Current-Voltage (I-V) 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=(v-V2) g

Biophysics Background

Bioengineering 6460 Bioelectricity

I-V Curve Examples

I Rectifying current K-current Rectifying current + Nernst potential Vrev Vrev Na-current

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

Information

BiophysicsBackground.key

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