BINDING KINETICS OF FREE- AND TOTAL-PROSTATE SPECIFIC ANTIGEN USING FRACTAL ANALYSIS

ATUL M. DOKE AND AJIT SADANACHEMICAL ENGINEERING DEPARTMENTAND COMPOSITE STRUCTURES AND

NANOENGINEERING RESEARCH GROUPUNIVERSITY OF MISSISSIPPI

UNIVERSITY, MS 38677-1848

MAESCCHRISTIAN BROTHERS UNIVERSITY, MEMPHIS

MAY 11, 2005

FRACTAL ANALYSIS USED TO MODEL THE BINDING KINETICS OF FREE- AND TOTAL-PROSTATE SPECIFIC ANTIGEN (f-PSA AND t-PSA) BY BIOSENSORS.

INTRODUCTION LANDIS ET AL. (1999) INDICATE THAT

SERUM PROSTATE-SPECIFIC ANTIGEN (PSA) IS A RELIABLE TUMOR MARKER IN THE EARLY DETECTION OF PROSTATE CANCER

PANNEK ET AL. (1998) INDICATE THE RATIO OF FREE- TO TOTAL-PSA TO BE A GOOD METRIC OF DIAGNOSIS OF PROSTATE CANCER

THE RATIO DECREASES AS THE DISEASE EMERGES

FRACTAL ANALYSIS IS USED TO RE-ANALYZE THE BINDING DATA OF DIFFERENT CONCENTRATIONS OF f-PSA AND t-PSA TO RESPECTIVE ANTIBODIES IMMOBILIZED ON A NITROCELLULOSE MEMBRANE SURFACE

THE ANALYSIS PROVIDES VALUES OF THE BINDING RATE COEFFICIENT AND THE FRACTAL DIMENSION ON THE BIOSENSOR

SURFACE

What are Fractals? SELF-SIMILAR OBJECTS THEY DON’T HAVE TO BE IDENTICAL SIMILAR SHAPE BUT DIFFERENT

HEIGHT OR WIDTH FRACTALS REPRESENT:(1) SYSTEMS HAVING COMPLEX SHAPES(2) CHARACTERIZED BY NON-INTEGER

DIMENSIONALITY

Fractal Theory

SINGLE-FRACTAL ANALYSIS

BINDING RATE COEFFICIENT HAVLIN INDICATES THAT THE DIFFUSION OF A

PARTICLE (ANALYTE [Ag]) FROM A HOMOGENEOUS SOLUTION TO A SOLID SURFACE (E.G., RECEPTOR [Ab] COATED SURFACE) ON WHICH IT REACTS TO FORM A PRODUCT IS GIVEN BY:

DUAL-FRACTAL ANALYSIS

BINDING RATE COEFFICIENT

IN THIS CASE, THE ANALYTE-RECEPTOR COMPLEX ON THE BIOSENSOR SURFACE IS

GIVEN BY: t (3- D

f1,bind) / 2 = tp1 (t < t1)

(Ab.Ag) ≈ t (3- Df2,bind

)/2= tp2 (t1 <t <t2) = tc

t1/2 (t > tc)

RESULTS FERNANDEZ-SANCHEZ ET AL. (2004)

INDICATE THE USE OF A DISPOSABLE NON-COMPETITIVE IMMUNOSENSOR TO

DETECT f-PSA AS WELL AS t-PSA STRIPS OF A NITROCELLULOSE

MEMBRANE WERE USED WITH APPROPRIATE ANTIBODIES FOR f-PSA AND t-PSA

BINDING KINETICS FOR f-PSA

A B

C

FIG:1

0

1

2

3

4

5

6

7

C/C

0

0 200 400 600 800 1000 1200 1400 Time, sec

0

2

4

6

8

10

C/C

0

0 200 400 600 800 10001200Time, sec

0

5

10

15

20

25

C/C

0

0 300 600 900 1200 1500Time, sec

D E

FIG:1

0

20

40

60

80

C/C

0

0 300 600 900 1200 1500Time, sec

0

20

40

60

80

100

120

140

C/C

0

0 500 1000 1500 2000 Time, sec

FIG 1A : BINDING OF 0 ng/mL OF FREE-PSA TO

ANTI-FREE PSA COATED IMMUNOSTRIP SINGLE-FRACTAL ANALYSIS REQUIRED FOR

BINDING FIG 1B,1C,1D & 1E : BINDING OF 1, 3, 10 AND

100 ng/mL OF FREE-PSA TO ANTI-FREE PSA COATED IMMUNOSTRIP

DUAL-FRACTAL ANALYSIS REQUIRED FOR BINDING

TABLE I: Binding Rate Coefficients and Fractal Dimension Values for Free Prostate Specific Antigen (f-PSA) in Solution to the Antibody, anti-free PSA Coated on a Nitrocellulose Membrane on an Electrochemical Transducer in a Lateral Flow Immunoassay Format. Effect of Different f-PSA Concentrations (Fernandez-Sanchez et al., 2004a)

Free PSA

concentration

ng/mL

k k1 k2 Df Df1 Df2

0 0.00123±

0.00015

na na 0.6132

±0.0892

na na

1 2.4 E-06±

0.7 E-06 2.5 E-06±

1.0 E-06

6.9 E-05±

0.2 E-05

0

+0.191

0

+0.3622

0

+0.239

3 1.5 E-05±

0.5 E-05

7.1 E-06±

0.3 E-06

5.9 E-05±

0.3 E-05

0

+0.1936

0

+0.3304

0

+0.1594

10 1.2 E-06±

0.3 E-06

5.5 E-07±

1.5 E-07

5.7 E-05±

0.1 E-05

0

+0.1486

0

+0.1946

0

+0.1147

100 0.000145±0.00003

na na 0

+0.1256

na na

k2 = (6.7 E-05 ± 0.4 E-05) [f-PSA] 0.0821 ± 0.0327

5.4E-05

5.6E-05

5.8E-05

6E-05

6.2E-05

6.4E-05

6.6E-05

6.8E-05

7E-05 B

indin

g r

ate

coeffic

ient, k

2

0 2 4 6 8 10 f-PSA concentration, ng/mL

BINDING KINETICS FOR t-PSA

A B

C

FIG:2

0

0.5

1

1.5

2

2.5

3

C/C

0

0 200 400 600 800 10001200Time, sec

0

1

2

3

4

5

6

7

C/C

0

0 200 400 600 800 1000 1200 Time / s

0

2

4

6

8

10

12

14

C/C

0

0 500 1000 1500 2000 Time, sec

D E

FIG:2

0

5

10

15

20

25

30

35

C/C

0

0 500 1000 1500 2000 Time / s

0

20

40

60

80

100

C/C

0

0 500 1000 1500 2000 Time / s

FIG 3A: BINDING OF 0 ng/mL OF TOTAL-PSA TO ANTI-TOTAL PSA COATED IMMUNOSTRIP DUAL-FRACTAL ANALYSIS REQUIRED FOR BINDING FIG 3B & 3C : BINDING OF 1 AND 3 ng/mL OF TOTAL-PSA TO ANTI-TOTAL PSA COATED

IMMUNOSTRIP SINGLE-FRACTAL ANALYSIS REQUIRED FOR BINDING

FIG 3D & 3E : BINDING OF 10 AND 100 ng/mL OF TOTAL-PSA TO ANTI-TOTAL PSA COATED

IMMUNOSTRIP DUAL-FRACTAL ANALYSIS REQUIRED FOR BINDING

TABLE II: Binding Rate Coefficients and Fractal Dimension Values for Total Prostate Specific Antigen (t-PSA) in Solution to the Antibody, anti-total PSA Coated on a Nitrocellulose Membrane on an Electrochemical Transducer in a Lateral Flow Immunoassay Format. Effect of Different t-PSA Concentrations (Fernandez-Sanchez et al., 2004a)

Total PSA

concentration

ng/mL

k k1 k2 Df Df1 Df2

0 0.00189

±0.00079

0.0314

±0.0023

2.3 E-07

±1.5 E-07

1.1018

±0.2634

2.1284

±0.0847

0

+0.2978

1 1.4 E-5±

0.6 E-05

na na 0

+0.2862

na na

3 9.5 E-05±

2.6 E-05

na na 0

+0.1464

na na

10 0.00089

±0.00038

0.0184

±0.0047

1.0 E-06

±1 E-07

0.3144 1.379 na

100 6.8 E-05

±5.0 E-05

0.0042

±0.002

2.0 E-08

±1.0E-09

na 0.8317

±0.3816

na

RESULTS FERNANDEZ-SANCHEZ ET AL. (2004)

DEVELOPED A SANDWICH TYPE IMMUNOASSAY TO DETECT f-PSA AND t-PSA

THIS IMMUNOSENSOR USED AN IMPEDANCE MEASUREMENT OF A DEGRADATION PROCESS OCCURING ON A pH-SENSITIVE POLYMER COATED ELECTRODE

IMMUNOSTRIPS CONTAINED NITROCELLULOSE MEMBRANES WITH ANTI-f-PSA OR ANTI-t-PSA ANTIBODIES

A B

C

FIG:4

0

5

10

15

20

C/C

o

0 100 200 300 400 500 600 700 Time (s)

0

5

10

15

20

25

30

35

C/C

o

0 100 200 300 400 500 600 700 Time (s)

0

10

20

30

40

50

C/C

o

0 100 200 300 400 500 600 700 Time (s)

D E

FIG:4

0

50

100

150

200

C/C

o

0 100 200 300 400 500 600 700 Time (s)

0

50

100

150

200

250

300

350

C/C

o

0 200 400 600 800 1000 Time (s)

FIG 4A: BINDING OF 0 ng/mL OF FREE-PSA TO ANTI-FREE PSA COATED IMMUNOSTRIP

SINGLE-FRACTAL ANALYSIS REQUIRED FOR BINDING

FIG 4B, 4C, 4D & 4E : BINDING OF 1, 2,10

AND 30 ng/mL OF FREE- PSA TO ANTI-FREE PSA

COATED IMMUNOSTRIP DUAL-FRACTAL ANALYSIS REQUIRED FOR

BINDING

TABLE III: Binding Rate Coefficients and Fractal Dimension Values for Free Prostate Specific Antigen (f-PSA) in Solution to the antibody, anti-free PSA coated on a Nitrocellulose Membrane on an Electrochemical Transducer in a Lateral Flow Immunoassay Format. Effect of Different f-PSA Concentrations (Fernandez-Sanchez et al., 2004a)

Free PSA

concentration

ng/mL

k k1 k2 Df Df1 Df2

0 0.09317

±0.00574

na na 1.3756

±0.0429

na na

1 0.08953

±0.0726

0.02023

±0.0047

0.384

±0.0192

1.1952

±0.1275

0.5649

±0.3278

1.6749

±0.096

2 0.02063

±0.0028

0.0221

±0.0024

0.00478

±0.0004

0.6891

±0.0919

0.6803

±0.2586

0.2123

±0.1318

10 0.0176

±0.0027

0.0725

±0.004

0.00182

±0.0003

0.2139

±0.1056

0.8164

±0.0852

0

+0.0423

30 0.00851

±0.0031

0.1454

±0.018

0.00022

±0.00004

0.0488

±0.176

1.2403

±0.1589

0

+0.0514

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Bin

din

g r

ate

coeffic

ient, k

1

0 5 10 15 20 25 30 f-PSA concentration (ng/ml)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

k1

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 Df1

k1 = (0.01744 ± 0.0033) [f-PSA] 0.6144 ± 0.0641

k1 = (0.0883 ± 0.0377) Df 12.709 ± 0.6099

A B

C D

FIG:6

0

5

10

15

20

25

30

35

C/C

o

0 50 100 150 200 250 300 Time (s)

0

20

40

60

80

100

120

C/C

o

0 100 200 300 400 500 Time (s)

0

100

200

300

400

C/C

o

0 200 400 600 800 Time (s)

0

200

400

600

800

1000

1200

C/C

o

0 200 400 600 800 1000 Time (s)

FIG 6A, 6B, 6C AND 6D : BINDING OF 0, 2, 10 AND

30 ng/mL OF TOTAL-PSA TO ANTI-TOTAL PSA COATED IMMUNOSTRIP

DUAL-FRACTAL ANALYSIS REQUIRED FOR BINDING

TABLE IV: Binding Rate Coefficients and Fractal Dimension Values for Total Prostate Specific Antigen (t-PSA) in Solution to the Antibody, anti-total PSA Coated on a Nitrocellulose Membrane on an Electrochemical Transducer in a Lateral Flow Immunoassay Format. Effect of Different t-PSA Concentrations (Fernandez-Sanchez et al., 2004a)

Total PSA

concentration

ng/mL

k k1 k2 Df Df1 Df2

0 0.3674

±0.0533

0.1997

±0.0239

2.3 E-07

±1.5 E-07

1.1018

±0.2634

2.1284

±0.0847

0

+0.2978

2 1.4 E-05

±0.6 E-05

na na 0

+0.2862

na na

10 0.00089

±0.00038

0.0184

±0.0047

1.0 E-06

±1 E-07

0.3144 ±0.2154

1.379 ±0.2458

na

30 6.8 E-05

±5.0 E-05

0.0042

±0.002

2.0 E-08

±1.0E-09

na 0.8317

±0.3816

na

0

0.05

0.1

0.15

0.2

0.25

k1

0 5 10 15 20 25 30 Concentration (ng/ml)

0

0.2

0.4

0.6

0.8

k2

0 5 10 15 20 25 30 Concentration (ng/ml)

0

0.05

0.1

0.15

0.2

k1

0 0.2 0.4 0.6 0.8 1 1.2 Df1

k1 = (0.3325 ± 0.2571)[t-PSA]0.6061 ± 0.2973

k2 = (0.000441 ± 0.000349)[t-PSA]2.1071 ± 0.3030

k1 = (0.1699 ± 0.026)Df10.2891 ± 0.02827

CONCLUSIONS A FRACTAL ANALYSIS IS APPLIED TO BINDING KINETICS OF f-PSA AND t-PSA IN SOLUTION TO THE BIOSENSOR SURFACE.

THE VALUES OF THE BINDING RATE COEFFICIENT, k LINKED WITH THE DEGREE OF HETEROGENEITY EXISTING ON THE BIOSENSOR SURFACE PROVIDES A COMPLETE PICTURE OF THE REACTION KINETICS ON THE BIOSENSOR CHIP SURFACE.

THE DUAL-FRACTAL ANALYSIS IS USED ONLY WHEN THE SINGLE-FRACTAL ANALYSIS DID NOT PROVIDE AN ADEQUATE FIT.

IT IS SUGGESTED THAT THE ROUGHNESS ON

THE BIOSENSOR SURFACE LEADS TO TURBULENCE WHICH ENHANCES MIXING AND DECREASES DIFFUSIONAL LIMITATIONS (MARTIN ET AL., 1991). THIS LEADS TO AN INCREASE IN THE BINDING RATE COEFFICIENT ON THE BIOSENSOR CHIP SURFACE.