Introduction to Data Analysis. Q-Sense Basic Training, April 4-5, 2006

Introduction to Data Analysis Q-Sense Basic Training, April 4-5, 2006

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 Time (seconds) F_1:3 F_2:3 F_3:3 F_4:3 D_1:3 D_2:3 D_3:3 D_4:3 Less mass more mass F_1:3 Viscous/floppy/elongated Time (seconds) 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 Rigid,/compressed/flat

Qualitative Analysis, cont. 1) D-f plot 0.5 0.4 Low affinity D (10-6 ) 0.3 0.2 0.1 0 High affinity 0-5 -10 f (Hz) -15-20 Reveals reaction fingerprints, multiple phases, time independant

D-f plot - Monoclonal antibodies 0.5 0 0.4 Low affinity f (Hz) -5-10 -15-20 -25 High affinity Low affinity High affinity D (10-6 ) 0.3 0.2 0.1 0 0-5 -10 f (Hz) High affinity -15-20 D Low affinity Antigen covered sensor 0.2x10-6 Binding of antibodies 0 500 1000 1500 2000 2500 Time (s)

Quantitative analysis the Sauerbrey equation F_1:3 F_1:3 D>>0, Sauerbrey will underestimate the mass Time (seconds) F_1:3 F_2:3 F_3:3 F_4:3 D_1:3 D_2:3 D_3:3 D_4:3 D~0, Sauerbrey will give a correct mass estimate D_1:3 D_1:3 The Sauerbrey relation: m[ng*cm -2 ]=-17,7[cm 2 *ng -1 *Hz -1 ]* f [Hz] Sauerbrey mass Time (seconds) Sauerbrey mass Time (seconds) F_1:3 F_2:3 F_3:3 F_4:3 D_1:3 D_2:3 D_3:3 D_4:3

The Sauerbrey relation Linear relationship between frequency and mass/surface area: m = C 1 n f C = 17,7ngcm n overtone s 2 1 Film thickness δ = m ρ F3/3 (Hz) Time (min) F3/3 (Hz) F5/5 (Hz) D3 (1E-6) D5 (1E-6) Overtones scaled by overtone number (n) The same constant can be used for all overtones D3 (1E-6)

Qualitative analysis the viscoelastic model F_1:3 D>>0, Sauerbrey will underestimate the mass Time (seconds) 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 Input: f1 f3 D1 D3 Viscoelastic voight model Output: : density, (kg/m3) : viscosity (G /), (kg/ms) : elasticity (G ), (Pa) : thickness, (m)

Viscosity 1. Viscosity is a measure of a fluid's resistance to flow Deformation Force Newton s definition, coefficient of viscosity, viscosity or dynamic viscosity u τ = η y Time Unit Pa s, (which is identical to 1 N s/m 2 or 1 kg/m s).

Shear modulus (Elasticity) 1. Elasticity 2. (Physics) The ratio of shearing stress to shearing strain within the proportional limit of a material. Deformation Force σ G = γ Time Unit (Pa, or N/m 2 )

Viscoelasticity A viscoelastic material is, as the name suggests, one which shows a combination of viscous and elastic effects. Voight element Viscous (dashpot) Elastic (spring)

Viscoelastic model f=f 1 (n, f, f, f, f ) D=f 2 (n, f, f, f, f ) : density, (kg/m3) : viscosity (G /), (kg/ms) : elasticity (G ), (Pa) : thickness, (m) Fluid ( l, η l ) Adlayer ( f, η f, µ f ) Crystal n=... n=1 n=3 d f G* = G'+ jg ' = + j2fη Voinova et al., Physica Scripta 59 (1999) 391

Introduction to fitting Initial estimate of parameters User input Calculation of Function value QTools Compare meas. & fun. Generate new parameters Model converged, results given User output Fitting routine SIMPLEX Nelder, J. A., & Mead, R. 1965,Comp. J., 7, 308

Operating range Lab viscometers QCM-D Hz 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 Modeled output based on a narrow frequency window Data from lower frequency range cannot necessarily be compared with QCM- D modeled data.

A practical modeling example Lipoprime (lipase) Lipase solution Lipase (E.C. 3.1.1.3) Molecular Weight ~30kDa Concentration 1 g/ml Lipid film ~100 nm Triolein (triacylglycerol) Quartz crystal Formula: C H O Molecular Weight: 885.43 Da CAS Registry Number: 122-32-7 Snabe and Petersen, Aalborg University Chemistry and Physics of Lipids 125(2003), 69-82

Enzymatic degradation of lipid films Frequency, (Hz) Dissipation (1e-6) Time (min) F1 (Hz) - 5MHz F3/3 (Hz) -15MHz F5/5 (Hz) - 25MHz Time (min) D1 (1E-6) D3 (1E-6) D5 (1E-6) Raw data indicates multiphase process Viscoelastic modeling gives additional information Snabe and Petersen, Aalborg University Chemistry and Physics of Lipids 125(2003), 69-82

Enzymatic degradation of lipids Visc (kg m -1 s -1 ) or Elasticity (10 5 Pa) 6 5 4 3 2 B C A Visc (kg m -1 s -1 ) or Elasticity (10 5 Pa) 6 5 4 3 2 1 0 D 0 Time (min) 1 2 1 20 A) Adsorption of lipase B) Cluster formation 0 0 C) Mass ejection 0 5 Lipid 10 film 15 20 D) Lipid layer removal BC DA Time (min) A B C Quartz crystal Crystal D 120 100 80 60 40 20 0 Film Thickness (nm) 120 100 80 60 40 Film Thickness (nm) Snabe and Petersen, Aalborg University Chemistry and Physics of Lipids 125(2003), 69-82

Thought process Comments Raw data, Qsoft data file Evaluation methods If D > 0 Sauerbrey will under estimate the thickness Are there high values in my data? D No Sauerbrey D/f plot Raw data plot Yes Homogenous adlayer Newtonian fluid Are the results within the model assumptions No D/f plot Raw data plot Yes Viscoelastic model D/f plot Raw data plot

Curve fitting functions Fitting of of f and D data to 1) Predefined adsorption models 2) User defined equations

Method: Determination of kinetic constants with QCM-D 1) Response parameter; - frequency - Dissipation - Modeled thickness 4) Determine k from dissociation phase R( t) = R eq e k off t 2) Perform adsorption at different C R( t) = R eq (1 e ( k C+ k ) t on off ) F3/3 (Hz) D3 (1E-6) F3/3 (Hz) D3 (1E-6) [ BS] kon [ B][ S] koff K = = a k on B+S BS k off R( t) = R eq (1 e ( k 1 C ) t ) Time (min) Testdata kinetic2wfit: 2003-09-30 15:33:00 5) Calculate k from k k 3) Equation system for k with C and R 6) Calculate K

Swelling of cellulose Cellulose coated crystal, (100nm) 500 0 F (15) Hz 200 0-200 -400-600 -800 20 ueq/g 409 ueq/g High charge, more swelling F(15) Hz -500-1000 -1000-1200 -1400-1600 0 10 20 30 40 Time (min) 20 ueq/g 409 ueq/g Swelling kinetics -1500-2000 -5 0 5 10 15 20 25 30 35 40 45 50 Time (hrs) EtOH Swelling H 2 O Susanna Fält, Mitthögskolan, Sundsvall, Sweden

Swelling of Cellulose Determination of the decay constant F( t) = F( t) = y 0 + Ae A(1 e t / b t* k ) ) + Offset F(t)= frequency t= time Y0=A+Offset= F at t=very large F2 (Hz) [3 * Hz] C Fit C Offset= F at t=0 b=1/k, decay constant (swelling parameter) Time (s) b ~2000

Time (s) Sauerbrey mass C Fit C Summary 1) Qualitative, Raw data, D-f F3/3 (Hz) Time (min) D3 (1E-6) F3/3 (Hz) D3 (1E-6) D3 (1E-6) F3/3 (Hz) D3 (1E-6) 2) Quantitative Sauerbrey Sauerbrey mass Time (seconds) 3) Quantitative Viscoelastic F3/3 (Hz) Time (min) D3 (1E-6) F3/3 (Hz) F5/5 (Hz) fir f3 fit f5 D3 (1E-6) D5 (1E-6) fit d3 fit d5 4) Curve fit F2 (Hz) [3 * Hz] Thank you for your attention!