2016, 13(6): 1159-1168. doi: 10.3934/mbe.2016036

Modelling random antibody adsorption and immunoassay activity

1. 

School of Mathematical Sciences, Dublin Institute of Technology, Kevin Street, Dublin 8, Ireland, Ireland

2. 

Biomedical Diagnostics Institute, Dublin City University, Glasnevin, Dublin 9, Ireland

Received  December 2015 Revised  April 2016 Published  August 2016

One of the primary considerations in immunoassay design is optimizing the concentration of capture antibody in order to achieve maximal antigen binding and, subsequently, improved sensitivity and limit of detection. Many immunoassay technologies involve immobilization of the antibody to solid surfaces. Antibodies are large molecules in which the position and accessibility of the antigen-binding site depend on their orientation and packing density.
    In this paper we propose a simple mathematical model, based on the theory known as random sequential adsorption (RSA), in order to calculate how the concentration of correctly oriented antibodies (active site exposed for subsequent reactions) evolves during the deposition process. It has been suggested by experimental studies that high concentrations will decrease assay performance, due to molecule denaturation and obstruction of active binding sites. However, crowding of antibodies can also have the opposite effect by favouring upright orientations. A specific aim of our model is to predict which of these competing effects prevails under different experimental conditions and study the existence of an optimal coverage, which yields the maximum expected concentration of active particles (and hence the highest signal).
Citation: D. Mackey, E. Kelly, R. Nooney. Modelling random antibody adsorption and immunoassay activity. Mathematical Biosciences & Engineering, 2016, 13 (6) : 1159-1168. doi: 10.3934/mbe.2016036
References:
[1]

D. A. Edwards, Steric hindrance effects on surface reactions: Applications to BIAcore,, J. Math. Biol., 55 (2007), 517.  doi: 10.1007/s00285-007-0093-7.  Google Scholar

[2]

J. W. Evans, Random and cooperative sequential adsorption,, Rev. Mod. Phys., 65 (1993).  doi: 10.1103/RevModPhys.65.1281.  Google Scholar

[3]

V. Gubala, C. Crean, R. Nooney, S. Hearty, B. McDonnell, K. Heydon, R. O'Kennedy, B. D. MacCraith and D. E. Williams, Kinetics of immunoassays with particles as labels: Effect of antibody coupling using dendrimers as linkers,, Analyst, 136 (2011), 2533.  doi: 10.1039/c1an15017k.  Google Scholar

[4]

M. K. Hassan, J. Schmidt, B. Blasius and J. Kurths, Jamming coverage in competitive random sequential adsorption of a binary mixture,, Phys. Rev. E, 65 (2002).  doi: 10.1103/PhysRevE.65.045103.  Google Scholar

[5]

P. L. Krapivsky, Kinetics of random sequential parking on a line,, J. Stat. Phys., 69 (1992), 135.  doi: 10.1007/BF01053786.  Google Scholar

[6]

A. Rényi, On a one-dimensional problem concerning random space-filling (In Hungarian),, Publ. Math. Inst. Hung. Acad. Sci, 3 (1958), 109.   Google Scholar

[7]

J. C. Roach, V. Thorsson and A. F. Siegel, Parking strategies for genome sequencing,, Genome Research, 10 (2000), 1020.  doi: 10.1101/gr.10.7.1020.  Google Scholar

[8]

B. Saha. T. H. Evers and M. W. J. Prins, How antibody surface coverage on nanoparticles determines the activity and kinetics of antigen capturing for biosensing,, Anal. Chem., 86 (2014), 8158.   Google Scholar

[9]

W. Schramm and S. Paek, Antibody-antigen complex formation with immobilized immunoglobulins,, Anal. Biochem., 205 (1992), 47.  doi: 10.1016/0003-2697(92)90577-T.  Google Scholar

[10]

J. Talbot, G. Tarjus, P. R. Van Tassel and P. Viot, From car parking to protein adsorption: An overview of sequential adsorption processes,, Colloids Surf. A, 165 (2000), 287.  doi: 10.1016/S0927-7757(99)00409-4.  Google Scholar

[11]

M. L. M. Vareiro, J. Liu, W. Knoll, K. Zak, D. Williams and A. T. A. Jenkins, Surface plasmon fluorescence measurements of human chorionic gonadotrophin: role of antibody orientation in obtaining enhanced sensitivity and limit of detection,, Anal. Chem., 77 (2005), 2426.  doi: 10.1021/ac0482460.  Google Scholar

[12]

D. Wild (editor), The Immunoassay Handbook,, $3^{rd}$ edition, (2005).   Google Scholar

[13]

M. E. Wiseman and C. W. Frank, Antibody adsorption and orientation on hydrophobic surfaces,, Langmuir, 28 (2012), 1765.  doi: 10.1021/la203095p.  Google Scholar

[14]

H. Xu, J. R. Lu and D. E. Williams, Effect of surface packing density of interfacially adsorbed monoclonal antibody on the binding of hormonal antigen human chorionic gonadotrophin,, J. Phys. Chem. B, 110 (2006), 1907.  doi: 10.1021/jp0538161.  Google Scholar

[15]

H. Xu, X. Zhao, C. Grant, J. R. Lu, D. E. Williams and J. Penfold, Orientation of a monoclonal antibody adsorbed at the solid/solution interface: A combined study using atomic force microscopy and neutron reflectivity,, Langmuir, 22 (2006), 6313.  doi: 10.1021/la0532454.  Google Scholar

[16]

X. Zhao, F. Pan, B. Cowsill, J. R. Lu, L. Garcia-Gancedo, A. J. Flewitt, G. M. Ashley and J. Luo, Interfacial immobilization of monoclonal antibody and detection of human prostate-specific antigen,, Langmuir, 27 (2011), 7654.  doi: 10.1021/la201245q.  Google Scholar

show all references

References:
[1]

D. A. Edwards, Steric hindrance effects on surface reactions: Applications to BIAcore,, J. Math. Biol., 55 (2007), 517.  doi: 10.1007/s00285-007-0093-7.  Google Scholar

[2]

J. W. Evans, Random and cooperative sequential adsorption,, Rev. Mod. Phys., 65 (1993).  doi: 10.1103/RevModPhys.65.1281.  Google Scholar

[3]

V. Gubala, C. Crean, R. Nooney, S. Hearty, B. McDonnell, K. Heydon, R. O'Kennedy, B. D. MacCraith and D. E. Williams, Kinetics of immunoassays with particles as labels: Effect of antibody coupling using dendrimers as linkers,, Analyst, 136 (2011), 2533.  doi: 10.1039/c1an15017k.  Google Scholar

[4]

M. K. Hassan, J. Schmidt, B. Blasius and J. Kurths, Jamming coverage in competitive random sequential adsorption of a binary mixture,, Phys. Rev. E, 65 (2002).  doi: 10.1103/PhysRevE.65.045103.  Google Scholar

[5]

P. L. Krapivsky, Kinetics of random sequential parking on a line,, J. Stat. Phys., 69 (1992), 135.  doi: 10.1007/BF01053786.  Google Scholar

[6]

A. Rényi, On a one-dimensional problem concerning random space-filling (In Hungarian),, Publ. Math. Inst. Hung. Acad. Sci, 3 (1958), 109.   Google Scholar

[7]

J. C. Roach, V. Thorsson and A. F. Siegel, Parking strategies for genome sequencing,, Genome Research, 10 (2000), 1020.  doi: 10.1101/gr.10.7.1020.  Google Scholar

[8]

B. Saha. T. H. Evers and M. W. J. Prins, How antibody surface coverage on nanoparticles determines the activity and kinetics of antigen capturing for biosensing,, Anal. Chem., 86 (2014), 8158.   Google Scholar

[9]

W. Schramm and S. Paek, Antibody-antigen complex formation with immobilized immunoglobulins,, Anal. Biochem., 205 (1992), 47.  doi: 10.1016/0003-2697(92)90577-T.  Google Scholar

[10]

J. Talbot, G. Tarjus, P. R. Van Tassel and P. Viot, From car parking to protein adsorption: An overview of sequential adsorption processes,, Colloids Surf. A, 165 (2000), 287.  doi: 10.1016/S0927-7757(99)00409-4.  Google Scholar

[11]

M. L. M. Vareiro, J. Liu, W. Knoll, K. Zak, D. Williams and A. T. A. Jenkins, Surface plasmon fluorescence measurements of human chorionic gonadotrophin: role of antibody orientation in obtaining enhanced sensitivity and limit of detection,, Anal. Chem., 77 (2005), 2426.  doi: 10.1021/ac0482460.  Google Scholar

[12]

D. Wild (editor), The Immunoassay Handbook,, $3^{rd}$ edition, (2005).   Google Scholar

[13]

M. E. Wiseman and C. W. Frank, Antibody adsorption and orientation on hydrophobic surfaces,, Langmuir, 28 (2012), 1765.  doi: 10.1021/la203095p.  Google Scholar

[14]

H. Xu, J. R. Lu and D. E. Williams, Effect of surface packing density of interfacially adsorbed monoclonal antibody on the binding of hormonal antigen human chorionic gonadotrophin,, J. Phys. Chem. B, 110 (2006), 1907.  doi: 10.1021/jp0538161.  Google Scholar

[15]

H. Xu, X. Zhao, C. Grant, J. R. Lu, D. E. Williams and J. Penfold, Orientation of a monoclonal antibody adsorbed at the solid/solution interface: A combined study using atomic force microscopy and neutron reflectivity,, Langmuir, 22 (2006), 6313.  doi: 10.1021/la0532454.  Google Scholar

[16]

X. Zhao, F. Pan, B. Cowsill, J. R. Lu, L. Garcia-Gancedo, A. J. Flewitt, G. M. Ashley and J. Luo, Interfacial immobilization of monoclonal antibody and detection of human prostate-specific antigen,, Langmuir, 27 (2011), 7654.  doi: 10.1021/la201245q.  Google Scholar

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