1. BINDING KINETICS OF FREE- AND TOTAL-PROSTATE SPECIFIC ANTIGEN USING FRACTAL ANALYSIS ATUL M. DOKE AND AJIT SADANA CHEMICAL ENGINEERING DEPARTMENT AND COMPOSITE STRUCTURES AND NANOENGINEERING RESEARCH GROUP UNIVERSITY OF MISSISSIPPI UNIVERSITY, MS 38677-1848 MAESC CHRISTIAN BROTHERS UNIVERSITY, MEMPHIS MAY 11, 2005

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

3. 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

4. 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

5. 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

6. Fractal Theory

7. 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:

8. 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 = t p1 (t < t1) (Ab.Ag) ≈ t (3- D f2,bind )/2 = t p2 (t1 <t <t2) = t c t 1/2 (t > t c )

9. 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

10. BINDING KINETICS FOR f-PSA A B C FIG:1

11. D E FIG:1

12. 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

13. 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 kk1k1 k2k2 DfDf D f1 D f2 00.00123± 0.00015 na 0.6132 ±0.0892 na 12.4 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 31.5 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 101.2 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 1000.000145± 0.00003 na 0 +0.1256 na

14. k 2 = (6.7 E-05 ± 0.4 E-05) [f-PSA] 0.0821 ± 0.0327

15. BINDING KINETICS FOR t-PSA A B C FIG:2

16. D E FIG:2

17. 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

18. 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 kk1k1 k2k2 DfDf D f1 D f2 00.00189 ±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 11.4 E-5± 0.6 E-05 na 0 +0.2862 na 39.5 E-05± 2.6 E-05 na 0 +0.1464 na 100.00089 ±0.00038 0.0184 ±0.0047 1.0 E-06 ±1 E-07 0.31441.379na 1006.8 E-05 ±5.0 E-05 0.0042 ±0.002 2.0 E-08 ±1.0E-09 na0.8317 ±0.3816 na

19. 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

20. A B C FIG:4

21. D E FIG:4

22. 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

23. 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 kk1k1 k2k2 DfDf D f1 D f2 00.09317 ±0.00574 na 1.3756 ±0.0429 na 10.08953 ±0.0726 0.02023 ±0.0047 0.384 ±0.0192 1.1952 ±0.1275 0.5649 ±0.3278 1.6749 ±0.096 20.02063 ±0.0028 0.0221 ±0.0024 0.00478 ±0.0004 0.6891 ±0.0919 0.6803 ±0.2586 0.2123 ±0.1318 100.0176 ±0.0027 0.0725 ±0.004 0.00182 ±0.0003 0.2139 ±0.1056 0.8164 ±0.0852 0 +0.0423 300.00851 ±0.0031 0.1454 ±0.018 0.00022 ±0.00004 0.0488 ±0.176 1.2403 ±0.1589 0 +0.0514

25. k 1 = (0.01744 ± 0.0033) [f-PSA] 0.6144 ± 0.0641 k 1 = (0.0883 ± 0.0377) D f 12.709 ± 0.6099

26. A B C D FIG:6

27. 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

28. 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 kk1k1 k2k2 DfDf D f1 D f2 00.3674 ±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 21.4 E-05 ±0.6 E-05 na 0 +0.2862 na 100.00089 ±0.00038 0.0184 ±0.0047 1.0 E-06 ±1 E-07 0.3144 ±0.2154 1.379 ±0.2458 na 306.8 E-05 ±5.0 E-05 0.0042 ±0.002 2.0 E-08 ±1.0E-09 na0.8317 ±0.3816 na

30. k 1 = (0.3325 ± 0.2571)[t-PSA] 0.6061 ± 0.2973 k 2 = (0.000441 ± 0.000349)[t-PSA] 2.1071 ± 0.3030 k 1 = (0.1699 ± 0.026)D f1 0.2891 ± 0.02827

31. 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.

32. 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.