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The Measurement of Cell Capacitance in

Multi-compartment Cells

Arif PatelArlene Pineda

Chris Khalil

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Membrane Capacitance

Cell membranes have a capacitive property.

Membrane capacitance (Cm) is related to cell surface area.

Cm plays a role in neuronal physiology.

d

AC

3

Hypothesis

The Problem: Different methods for measuring Cm produce different results.

We propose that this difference is due to the complex anatomical structure of neurons.

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Three experimental techniques for measuring Cm

Current Step Method (current clamp) Voltage Step Method (voltage clamp) Voltage Ramp Method (voltage clamp)

Three levels of modeling to compare the measurements

Experiments were performed in crab stomatogastric neurons.

Methodology

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When performed in an isopotential sphere

mmm CR

)1(10teAAV

Current Step Method

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When performed in multi compartment cells

V=R *Iin ext

Vrest

Iext

1 2/20

/1(1 ) (1 )ttV A eA eA

largest m mR C

Current Step Method

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VVtest

Iclamp

C

C

dQi

dt

Q i dt

Q C V

rcclamp iii

Voltage Step Method

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Vtest

Iclamp

iCiC

d V

d t

2iC

C

dVi C

dt

rircclamp iii

ri

Voltage Ramp Method

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Average Measured Capacitance for three methods:

Current Step (n=6): 23.68nF Voltage Step (n=8): 2.87nF Voltage Ramp (n=8):2.72nF

Why are they different?Which is correct?

Results of Experiments

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1) Dual compartment attached by a resistive cable

2) Compartmentalized cable with added membrane

3) Two cylinder with compartmentalized dendrite and cable

Soma Dendrite

Assumptions for model simplification:-Ri, Rm, Cm constant -Vr=0

Three Models

Dendrite

Soma

11mcablemdendritemsomam

cablecablemspecificmcable

dendritedendritemspecificmdendrite

somamspecificmsoma

cccc

ldCc

ldCc

dCc

Total

2

mdendritemsomam

dendritemspecificmdendrite

somamspecificmsoma

ccc

dCc

dCc

Total

2

2

mcablemdendritemsomam

cablecablemspecificmcable

dendritemspecificmdendrite

somamspecificmsoma

cccc

ldCc

dCc

dCc

Total

2

2

Soma Dendrite

Total Capacitance

Soma

Dendrite

Percent Actual Capacitance= 100Total

Measured

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IRSIRD

IAS

IAD

di

Sd

d

rdd

CR

VV

R

VV

dt

dV 1)(

IRDIAD

Current Representation

Si

dS

s

rSext

S

CR

VV

R

VVi

dt

dV 1)(

IRS IAD

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0

20

40

60

80

100

0 0.01 0.02 0.03 0.04 0.05 0.06

Dendrite Diameter (cm)

Pe

rce

nt

Ac

tua

l Ca

pa

cit

an

ce Current Step

Voltage Step

Voltage Ramp (slope = 4 V/s)

Voltage Ramp (slope = .08 V/s)

Percent Actual Capacitance vs. Dendrite Diameter

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Percent Actual Capacitance vs. Length

0

20

40

60

80

100

120

0 0.2 0.4 0.6 0.8 1 1.2

Length (cm)

Pe

rce

nt

Ac

tua

l Ca

pa

cit

an

ce

Current Step

Voltage Step

Voltage Ramp

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RmRm

Dsoma=.004 cm

l=.06 cm

Dcable=.001 cm

jj -1 j +1Soma Dendrite

D2=.004 cm

Ri Ri

Dual Compartments w/ Compartmentalized Cable

16

mm

restj

i

jj

i

jjj

CR

VV

R

VV

R

VV

dt

dV 1)( 11

Ri Ri

Rm Rm Rm

jj-1 j+1

Dual Compartments w/ Compartmentalized Cable Code

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Percent Actual Capacitance vs. Dendrite Area

0

20

40

60

80

100

0 0.0005 0.001 0.0015 0.002 0.0025 0.003

Dendrite Area (cm2)

Per

cen

t A

ctu

al C

apac

itan

ce

Current Step

Voltage Step

Voltage Ramp

Soma Dendrite

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Percent Actual Capacitance vs. Soma Area

DendriteSoma

50

60

70

80

90

100

0 0.00002 0.00004 0.00006 0.00008

Soma Area (cm2)

Per

cent

Act

ual C

apac

itanc

e

Current Step

Voltage Step

Voltage Ramp

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Percent Actual Capacitance vs. Cable Area

0

20

40

60

80

100

0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035

Cable Area (cm2)

Per

cen

t A

ctu

al C

apac

itan

ce

Current Step

Voltage Step

Voltage Ramp

DendriteSoma

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jj -1 j +1Soma

Dendrite

Dsoma=.004 cm

l=.06 cm

Dcable=.001 cm

jd-1 jd+1jd jd+1jd+1jj

Two Cylinders w/ Compartment Cable & Dendrite

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0

20

40

60

80

100

0 0.001 0.002 0.003 0.004

Dendrite Area (cm2)

Per

cen

t A

ctu

al C

apac

itan

ce

Current Step

Voltage Step

Voltage ramp

Percent Actual Capacitance vs. Dendrite Area

Soma

Dendrite

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The best method for measuring cm is the current step Voltage curve can depicts two distinct

processes Independent of morphology

Significance of Findings

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Voltage Ramp method has provided better results than Voltage Step.

Voltage Step has provided the least reliable results Not allowed to equalize in voltage clamp

Significance of Findings

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Special Thanks to..

Professor Golowasch Professor Nadim Professor Bose TA’s:

Shunbing Zhao Lakshmi Chandrasekaran