Introduction to data analysis - Boston University Technologies/QCMD/Data... · Analysis Methods 1)...

Q-Sense Basic Training, April 4-5, 2006

Introduction to Data Analysis

Outline• Different types of data evaluation • Functions in QTools• Introduction to viscoelastic modeling

Analysis Methods

1) Qualitative analysis (raw data plot, D-f plot)2) Quantitative analysis (low D=Sauerbrey)3) Quantitative analysis (high D=viscoelastic

modeling)4) Curve fit functions

Qualitative Analysis

1) Raw data plot, relative comparison of responses

F_1:3�� F_2:3�� F_3:3�� F_4:3�� D_1:3�� D_2:3�� D_3:3�� D_4:3��

Time (seconds)��

F_1:

3

�

�

��

��

��

��

��

�

��

��

��

�

F_1:3�� F_2:3�� F_3:3�� F_4:3�� D_1:3�� D_2:3�� D_3:3�� D_4:3��


F_1

:3

�

�

��

��

��

��

��

�

��

��

��

�

D_1:3

��

�

��

��

��

��

�

Less mass

more mass

Viscous/floppy/elongated

Rigid,/compressed/flat

Qualitative Analysis, cont.

0

0.1

0.2

0.3

0.4

0.5

-20-15-10-50

∆D (1

0-6)

∆ f (Hz)

Low affinity

High affinity

1) D-f plot

Reveals reaction ”fingerprints”, multiple phases, time independant

Antigen coveredsensor

Binding of antibodies

-25

-20

-15

-10

-5

0

∆f (H

z)

Low affinity

High affinity

0 500 1000 1500 2000 2500

∆D

Time (s)

0.2x10-6

Low affinity

High affinity

0

0.1

0.2

0.3

0.4

0.5

-20-15-10-50

∆D (1

0-6)

∆ f (Hz)

Low affinity

High affinity

D-f plot - Monoclonal antibodies

Quantitative analysis the Sauerbrey equation

F_1:3�� F_2:3�� F_3:3�� F_4:3�� D_1:3�� D_2:3�� D_3:3�� D_4:3��


F_1

:3

�

�

��

��

��

��

��

�

��

��

��

�

D_1:3

��

�

��

��

��

��

�

F_1:3�� F_2:3�� F_3:3�� F_4:3�� D_1:3�� D_2:3�� D_3:3�� D_4:3��


F_1:

3

�

�

��

��

��

��

��

�

��

��

��

�

D_1:3

��

�

��

��

��

��

�

�D>>0, Sauerbrey will underestimate the mass

�D~0, Sauerbrey will give a correct mass estimate

The Sauerbrey relation:�m[ng*cm-2]=-17,7[cm2*ng-1*Hz-1]* �f [Hz]

Sauerbrey mass��


Sau

erbr

ey m

ass

��

��

��

��

��

��

��

��

��

��

�

The Sauerbrey relation

Overtones scaled by overtone number (n)The same constant can be used for all overtones

fn

Cm ∆−=∆ 1overtonen

sngcmC−= −− 127,17

Linear relationship between frequency and mass/surface area:

ρδ m∆=

F3/3 (Hz)F5/5 (Hz)D3 (1E-6)D5 (1E-6)

Time (min)��

F3/

3 (H

z)

�

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

D3 (1E

-6)

�

�

�

�

Film thickness

Qualitative analysis the viscoelastic model

F_1:3�� F_2:3�� F_3:3�� F_4:3�� D_1:3�� D_2:3�� D_3:3�� D_4:3��


F_1

:3�

�

��

��

��

��

��

�

��

��

��

�

D_1:3

��

�

��

��

��

��

�

�D>>0, Sauerbrey will underestimate the mass

Viscoelastic voight model

Output:�: density, (kg/m3)�: viscosity (G’’/�), (kg/ms)�: elasticity (G’), (Pa)�: thickness, (m)

Input:�f1�f3�D1�D3

Viscosity

1. Viscosity is a measure of a fluid's resistance to flow

Newton’s definition �, coefficient of viscosity, viscosity or dynamic viscosity

UnitPa·s, (which is identical to 1 N·s/m2 or 1 kg/m·s).

yu

∂∂= ητ

Time

Def

orm

atio

n

Forc

e

Shear modulus (Elasticity)

1. Elasticity 2. (Physics) The ratio of shearing stress � to shearing strain � within the

proportional limit of a material.

Unit (Pa, or N/m2)

γσ=G

Time

Def

orm

atio

n

Forc

e

Viscoelasticity

• A viscoelastic material is, as the name suggests, one which shows a combination of viscous and elastic effects.

Elastic (spring)Viscous (dashpot)

Voight element

Viscoelastic model

�f=f1(n,�f,�f,�f,�f) �D=f2(n,�f,�f,�f,�f)

Crystal

Adlayer(� f, ηf, µf)

df

Fluid(� l, ηl) n=1

n=3

n=...

Voinova et al., Physica Scripta 59 (1999) 391

G* = G' + jG'' = � + j2�fη

�: density, (kg/m3)

�: viscosity (G’’/�), (kg/ms)

�: elasticity (G’), (Pa)

�: thickness, (m)

Introduction to fitting

Model converged,

results givenUser output

QTools

Fitting routine SIMPLEXNelder, J. A., & Mead, R. 1965,Comp. J., 7, 308

Comparemeas. & fun.

Calculation ofFunction value

Generate new parameters

Initial estimate of parameters

User input

Operating range

100 101 102 103 104 105 106 107 108

Lab viscometers QCM-D

Modeled output based on a narrow frequency window

Data from lower frequency range cannot necessarily be compared with QCM-D modeled data.

Hz

Quartz crystal

Lipid film

Lipase solution

~100 nm

A practical modeling example

Lipase (E.C. 3.1.1.3)Molecular Weight ~30kDaConcentration 1 �g/ml

Lipoprime (lipase)

Formula: C��H��O�

Molecular Weight: 885.43 Da CAS Registry Number: 122-32-7

Triolein (triacylglycerol)

Snabe and Petersen, Aalborg UniversityChemistry and Physics of Lipids 125(2003), 69-82

Enzymatic degradation of lipid films

•Raw data indicates multiphase process•Viscoelastic modeling gives additional information


F1 (Hz) - 5MHz F3/3 (Hz) -15MHz F5/5 (Hz) - 25MHz

Time (min)��

Freq

uenc

y, (H

z)

��

��

��

��

�

�

D1 (1E-6) D3 (1E-6) D5 (1E-6)

Time (min)��

Dis

sipa

tion

(1e-

6)

��

�

��

��

�

��

��

��

0

1

2

3

4

5

6

0 1 2Time (min)

Vis

c (k

g m

-1 s

-1) o

r E

last

icity

(105

Pa)

0

20

40

60

80

100

120

Film

Thi

ckne

ss (n

m)

Quartz Crystal

Lipid film

A

A

A) Adsorption of lipase

Quartz crystal

Lipid film

B

B

B) Cluster formation

Quartz Crystal

Lipid film

C

C

C) Mass ejection

Quartz Crystal

Lipid film

D

D

D) Lipid layer removal

Enzymatic degradation of lipids

0

1

2

3

4

5

6

0 5 10 15 20

Time (min)

Vis

c (k

g m

-1 s

-1) o

r E

last

icity

(105

Pa)

0

20

40

60

80

100

120

Film

Thi

ckne

ss (n

m)

A

D

BC

0

1

2

3

4

5

6

0 5 10 15 20

Time (min)

Vis

c (k

g m

-1 s

-1) o

r E

last

icity

(105

Pa)

0

20

40

60

80

100

120

Film

Thi

ckne

ss (n

m)

A

D

BC


Thought process

Are there high values in my

data?

SauerbreyD/f plot

Raw data plot

D/f plotRaw data plot

Are the resultswithin the model

assumptions

Viscoelastic modelD/f plot

Raw data plot

Homogenous adlayerNewtonian fluid

0>∆D D∆If Sauerbreywill under estimate the

thickness

Raw data, Qsoft data file

Yes

No

Yes

No

Comments Evaluation methods

Curve fitting functions

Fitting of of f and D data to1) Predefined adsorption models2) User defined equations

Method: Determination of kinetic constants with QCM-D

1) Response parameter;- frequency- Dissipation- Modeled thickness

)1()( )( tkCkeq

offoneRtR +−−=

)1()( )( 1 tCkeq eRtR −−=

2) Perform adsorption at different C

3) Equation system for k� with C and R�

��

tkeq

offeRtR −=)(

4) Determine k��from dissociation phase

F3/3 (Hz)D3 (1E-6)

Testdata kinetic2wfi t: 2003-09-30 15:33:00

Time (min)��

F3/

3 (H

z)

�

��

��

�

��

�

��

�

��

��

��

��

��

��

��

D3 (1E

-6)

�

�

�

B+S BSkon

koff

[ ][ ][ ] off

ona k

kSB

BSK ==

5) Calculate k�� from k��k�

6) Calculate K�

Swelling of celluloseCellulose coated crystal, (100nm)

EtOH H2OSwelling

Susanna Fält, Mitthögskolan, Sundsvall, Sweden

•High charge, more swelling

•Swelling kinetics

-2000

-1500

-1000

-500

0

500

-5 0 5 10 15 20 25 30 35 40 45 50

Time (hrs)

F(15

) Hz

20 ueq/g409 ueq/g

-1600

-1400

-1200

-1000

-800

-600

-400

-200

0

200

0 10 20 30 40

Time (min)

F (1

5) H

z

20 ueq/g409 ueq/g

Swelling of Cellulose

OffseteAtF

AeytFkt

bt

+−=

+=−

−

)1()(

)()*

/0

Determination of the decay constant

F(t)= frequency

t= time

Y0=A+Offset= F at t=very large

Offset= F at t=0

b=1/k, decay constant (swelling parameter)

CFit C

Time (s)��

F2

(Hz)

[3 *

Hz]

�

��

��

��

��

��

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��

��

��

� ��

� �

��

��

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��

��

��

b ~2000

Summary

1) Qualitative, Raw data, D-f

2) Quantitative Sauerbrey

3) Quantitative Viscoelastic

4) Curve fit

F3/3 (Hz)D3 (1E-6)

Time (min)��

F3/

3 (H

z)

�

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

D3 (1E

-6)

�

�

�

D3 (1E-6)

F3/3 (Hz)��

D3

(1E

-6)

�

�

�

F3/3 (Hz)F5/5 (Hz)fir f3fit f5D3 (1E-6)D5 (1E-6)fit d3fit d5

Time (min)��

F3/

3 (H

z)

�

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

D3 (1E

-6)

�

�

�

Sauerbrey mass��


Sau

erbr

ey m

ass

��

��

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��

��

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��

��

�

CFit C

Time (s)��

F2

(Hz)

[3 *

Hz]

�

��

��

��

��

��

��

��

��

��

��

��

��

��

� ��

� �

��

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Thank you for your attention!

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