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On Cell Mechanics
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
Possible Application of Cell Mechanics
2
Understanding the architecture of the cytoskeleton or other cellular compartments
follow changes in the cell, including reactions to external stimuli
determine differences in cell state
with possible bio-medical or clinical implications
cell mechanics as a diagnostic tool
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
Why measuring mechanics ?
Understanding the structure and function of the actin cytoskeleton or other molecular players in mechanics
insights in mechanically interesting processes like migration or cell division
using cell mechanics as a marker of cellular function
3
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
Cell Mechanics as Diagnostic Tool
4
cancer cells
mechanical diseases of cellular compartments! nucleopathies, Alzheimer, etc.
reproducibility and reliability becomes a big issue in clinical applications
data should be comparable also for scientists
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
What is this talk about ?
5
motivation for producing reliable and reproducible quantities
some personal ideas on this topic
suggestions how to do get reproducible numbers
timeline of errors I did in the past
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
How to we get from a force curve to the Young's modulus ?
6
-800
-750
-700
-650
-600
-550
-500
defle
ctio
n [n
m]
-13-12-11-10-9z height[µm]
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
How to we get from a force curve to the Young's modulus ?
6
-800
-750
-700
-650
-600
-550
-500
defle
ctio
n [n
m]
-13-12-11-10-9z height[µm]
6050
4030
2010
0µm
6050403020100µm
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
log
of Y
oung
s's
mod
ulus
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
There are Several Issues
7
need for a mechanical model
is the model appropriate?
calibration issues: deflection, force constant
model parameters: tip shape, Poisson ratio, ...
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
Let's start with the points, often regarded as trivial: calibration of the deflection signal
8
-800
-750
-700
-650
-600
-550
-500
-450de
flect
ion
[nm
]
-8.0-7.8-7.6-7.4-7.2-7.0-6.8-6.6-6.4z height[µm]
fit a line to the linear part of a force curve
from a distance everything looks fine
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
Let's start with the points, often regarded as trivial: calibration of the deflection signal
8
fit a line to the linear part of a force curve
from a distance everything looks fine
-750
-700
-650
-600
-550
-500
defle
ctio
n [n
m]
-6.60-6.55-6.50-6.45-6.40z height[µm]
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
However, there is some variation in the slope of force curves on stiff samples
9
600
400
200
01.041.021.000.980.96
histogramm of more than 2000 force curves on the substrate
mean is 1.00
sdev is on the order of 0.02
there is a 2% error in calibration of the deflection signal
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
This looks acceptable when looking at the big picture
10
6050
4030
2010
0µm
6050403020100µm
600
400
200
01.00.80.60.40.2
Histogram of the slope of a complete force map including cell data and data on the support
Cell Petri dish
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
How well do we know the force constant?
11
The manufacturer wants to be on the safe side and gives large error margins
from. http://www.brukerafmprobes.com/Product.aspx?ProductID=3444
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
Several Ways to calibrate the force constant
12
calculate from geometry
added mass method
calibrating with a standard spring
estimate by resonance frequency (Cleveland: k ∝ f3 )
thermal noise method
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
Thermal noise is easy to use and implemented in many commercial instruments
13
2
3
4
5
678910
-12
2
3
4
5
6789
10-11
100 Hz 1 kHz 10 kHz 100 kHz 1 MHz
resonance frequency: 7.286 kHz
spring constant: 17 mN/m
Cleveland says: 12 mN/m
see for more background: http://www.physics.uwo.ca/~hutter/calibration/afmcal.html
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
Thermal noise is easy to use and implemented in many commercial instruments
14
2
3
4
5
678910
-12
2
3
4
5
6789
10-11
100 Hz 1 kHz 10 kHz 100 kHz 1 MHz
needs calibration of deflection
relies on equipartition theorem
requires low DC noise
requires DC calibration of deflection still valid at higher frequencies
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
What's the bottom line?
15
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
Why do we need models?
16
because contact area changes during indentation
because stress is transmitted in the material in a complicated way
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
Sometimes simple Shell Theory works
F = 0.8*E * d2
R*δ
kN = 0.8*E *d 2
R17
1.2
1.0
0.8
0.6
0.4
0.2
0.0
defle
ctio
n [µ
m]
1086420-2z height [µm]
Sample Slope Stiffness[mN/m]
control 0.12 1.34 control 0.15 1.81 37 µg/ml DNA 0.23 2.94 110 µg/ml DNA 0.40 6.64
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
More often the Hertz model is employed
18
homogenous material
isotropic material
no adhesion
infinite thickness
small stresses (i.e. linear regime)
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
Variants of the Hertz model for different geometries
19
Paraboloid on Flat: F = 43
E(1−ν 2 )
R *δ32
Cone on Flat: F = 2π
E(1−ν 2 )
tanα *δ 2
Pyramid on Flat:
From: Lin DC, Dimitriadis EK, Horkay F. , J Biomech Eng. 2007 Jun;129(3):430-40. "Robust strategies for automated AFM force curve analysis--I. Non-adhesive indentation of soft, inhomogeneous materials."
F = 2 E(1−ν 2 )
a*δCylinder on Flat:
F = 12
E(1−ν 2 )
tanα *δ 2
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
The Hertz model can work amazingly well,here: poly-acrylamid gels
20
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
Or not, if the model is not appropriate: fitting pyramidal data with the sphere model
21
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
How well do we know the parameters needed as input for the Hertz model?
22
Poisson ratio! generally assumed to be 0.5
tip opening angle or radius! specs: ! ! 17,5˚ ±2.5˚, 25˚ ±2.5˚
! measured:! 19˚, 29˚
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
How well do we know the parameters needed as input for the Hertz model?
22
Poisson ratio! generally assumed to be 0.5
tip opening angle or radius! specs: ! ! 17,5˚ ±2.5˚, 25˚ ±2.5˚
! measured:! 19˚, 29˚
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
Summary of Errors
23
calibration of deflection!! ! ! ! 2%
calibration of force constant of cantilever! ! 5 %
tip shape (pyramidal tips)! ! ! ! 15 %
negligible: calibration of piezo/distance sensor!! -
total error in slope:! ! ! ! ! 20 %
could translate in an error in E-modulus:! ! 50 %
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
The largest uncertainty is in the tip shape
24
characterize tip shape very accurately
possibly use beads, which are better defined
make only relative measurements
referred to a reference sample
or compare cells before/after drug treatment
or compare different cells, like healthy versus diseased
Possible work arounds
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
What is wrong/missing in Hertz models?
25
cells are not homogenous and isotropic
cells are not infinitely thick
AFM measurements may lead to high strains, so any material will act non-linear
cells are visco-elastic
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
Cancer versus normal cells - AFM data
Normal Cells
S784
Cancerous Cells
S277
26
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
Cancer versus normal cells - AFM data
Normal Cells
S784
Cancerous Cells
S277
100
80
60
40
20
0
-20
defl
ecti
on [
nm
]
-11.0-10.5-10.0-9.5-9.0-8.5-8.0
z height [µm]
Force Data
100
80
60
40
20
0
-20
defl
ecti
on [
nm
]
-12.0-11.5-11.0-10.5-10.0-9.5-9.0
z height [µm]
Force Data
26
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
Cancer versus normal cells - AFM data
Normal Cells
S784
Cancerous Cells
S277
100
80
60
40
20
0
-20
defl
ecti
on [
nm
]
-11.0-10.5-10.0-9.5-9.0-8.5-8.0
z height [µm]
Elastic Modulus Retract: 5100 PaApproach: 3700 Pa
Force Data Hertz Fit to Force Data
100
80
60
40
20
0
-20
defl
ecti
on [
nm
]
-12.0-11.5-11.0-10.5-10.0-9.5-9.0
z height [µm]
Elastic Modulus Retract: 1600 PaApproach: 670 P
Force Data Hertz Fit to Force Data
26
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
Viscoelasticty is often neglected
27
-500
-400
-300
-200
-100
LVD
T (n
m)
1.00.80.60.40.20.0Time (s)
200
100
0
-100
-200
Def
lect
ion
(nm
)
1.00.80.60.40.20.0Time(s)
150
100
50
0
Def
lect
ion
(nm
)
-4.0-3.5-3.0-2.5-2.0-1.5-1.0-0.5LVDT (µm)
Approach Retract
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
New Model to include bottom effect
28
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
Pyramidal Tips overestimate Young's moduli
29
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
Testsample Poly-Acrylamide Gels
30
very homogenous
stable over time
E-modulus depends critically on concentration of cross linkers
preparation is hard to reproduce exactly
10
8
6
4
2
0
1.00.80.60.40.20.0
10
8
6
4
2
0
0.3880.3860.3840.3820.3800.3780.3760.374
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
Testsample Poly-Acrylamide Gels
31
14
12
10
8
6
4
2
0
31.030.530.029.529.028.528.0x10
3
10
8
6
4
2
0
0.3880.3860.3840.3820.3800.3780.3760.374
Slope:! ! ! 0.38 +/- 0.002 (0.5%)Young's Modulus:! 29.5kPa +/- 0.5 kHz (2%)
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
Does it work between labs ?
32
45
40
35
30
25
20
Youn
g M
odul
us [k
Pa]
Gel06 Gel07
Pos1 Pos2 Pos3 Pos4 Pos1 Pos2 Pos3 Pos4Barcelona Barcelona
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
Variability in different positions
33
40
30
20
10
0
36343230282624x10
3
Position 1 0.5 Hz Position 2 0.5 Hz Position 2 1 Hz Position 2 2 Hz Position 2 3 Hz
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
However, real data show some miracles
34
180
160
140
120
100
80
60
40
20
Youn
gs's
Mod
ulus
[kP
a]
321
MLCT old α=40˚ k = 17.7 pN/m Glasbead R=5µm k= 27.5 pN/m MLCT new α=19˚ k = 15.8 pN/m
Same gel
different tips
very different E-Moduli
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
However there are many issues to be addressed
35
experimental details! same tips, similar forces
calibration sample! which sample ?! does the recipe allow to make the sample everywhere ?! or do we need a supplier ?
data analysis issues! which part of the data is analyzed ?! how is the contact point determined ?! how is the deflection signal calibrated ?! how is the force constant calibrated ?! how are tip shape parameters defined ?
COST AFM4BioMedNano
BIOPHYSICSINSTITUTE
Manfred Radmacher
Acknowledgements
36
Barcelona! Daniel Navajas! Tomas Luque!Bremen! Jens Schäpe
Cracow! Malgorzata Lekka
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