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Biomolecular Interaction Analysis Using an Optical Surface Plasmon Resonance Biosensor: The Marquardt Algorithm vs Newton Iteration Algorithm.

Hu J, Ma L, Wang S, Yang J, Chang K, Hu X, Sun X, Chen R, Jiang M, Zhu J, Zhao Y - PLoS ONE (2015)

Bottom Line: A number of experimental data may lead to complicated real-time curves that do not fit well to the kinetic model.The association and dissociation rate constants, ka, kd and the affinity parameters for the biomolecular interaction, KA, KD, were experimentally obtained 6.969×10(5) mL·g(-1)·s(-1), 0.00073 s(-1), 9.5466×10(8) mL·g(-1) and 1.0475×10(-9) g·mL(-1), respectively from the injection of the HBsAg solution with the concentration of 16 ng·mL(-1).The kinetic constants were evaluated distinctly by using the obtained data from the curve-fitting results.

View Article: PubMed Central - PubMed

Affiliation: Department of Electrical Engineering, Henan Agricultural University, Zhengzhou, China; State Key Laboratory of Wheat and Maize Crop Science, Zhengzhou, China.

ABSTRACT
Kinetic analysis of biomolecular interactions are powerfully used to quantify the binding kinetic constants for the determination of a complex formed or dissociated within a given time span. Surface plasmon resonance biosensors provide an essential approach in the analysis of the biomolecular interactions including the interaction process of antigen-antibody and receptors-ligand. The binding affinity of the antibody to the antigen (or the receptor to the ligand) reflects the biological activities of the control antibodies (or receptors) and the corresponding immune signal responses in the pathologic process. Moreover, both the association rate and dissociation rate of the receptor to ligand are the substantial parameters for the study of signal transmission between cells. A number of experimental data may lead to complicated real-time curves that do not fit well to the kinetic model. This paper presented an analysis approach of biomolecular interactions established by utilizing the Marquardt algorithm. This algorithm was intensively considered to implement in the homemade bioanalyzer to perform the nonlinear curve-fitting of the association and disassociation process of the receptor to ligand. Compared with the results from the Newton iteration algorithm, it shows that the Marquardt algorithm does not only reduce the dependence of the initial value to avoid the divergence but also can greatly reduce the iterative regression times. The association and dissociation rate constants, ka, kd and the affinity parameters for the biomolecular interaction, KA, KD, were experimentally obtained 6.969×10(5) mL·g(-1)·s(-1), 0.00073 s(-1), 9.5466×10(8) mL·g(-1) and 1.0475×10(-9) g·mL(-1), respectively from the injection of the HBsAg solution with the concentration of 16 ng·mL(-1). The kinetic constants were evaluated distinctly by using the obtained data from the curve-fitting results.

No MeSH data available.


Related in: MedlinePlus

Sensorgram showing the association and dissociation processes of biomolecular interaction between HBsAg and HbsAb.The data marked with a triangle is obtained in the average of more than three sets of measurement results in RU. This sensorgram is showing that the HBsAg was binding on the specific HBsAb (association phase) starting from the injection point a and reaches an equilibrium after approximately 251s. From the dissociation starting point b, the dissociation phase was formed sequentially. The microfludic cell of this SPR bioanalyzer was kept at a constant temperature of 37°C.
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pone.0132098.g001: Sensorgram showing the association and dissociation processes of biomolecular interaction between HBsAg and HbsAb.The data marked with a triangle is obtained in the average of more than three sets of measurement results in RU. This sensorgram is showing that the HBsAg was binding on the specific HBsAb (association phase) starting from the injection point a and reaches an equilibrium after approximately 251s. From the dissociation starting point b, the dissociation phase was formed sequentially. The microfludic cell of this SPR bioanalyzer was kept at a constant temperature of 37°C.

Mentions: The parameters and the initial values can be set manually according to the experimental data in the SPR biomolecular interaction analysis software based on the Marquardt algorithm, which was designed by our research group. Different results from various initial values can be compared each other visually so that we can select the most ideal initial values to reduce errors. From the homemade SPR analysis software, the experimental data can be imported conveniently. The x-axis of the graph represents time (s), while the y-axis of the graph represents the signal responses indicated with RU, which was computed based on the following formula RU = (1.334-RIx) ×30000, where 1.334 was the refractive index of deionized water. RIx is the refractive index of an unknown sample, which can be measured by using the SPR biosensor in real-time and 30,000 is a pre-determined factor for increasing the sensitivity of the calculated responses [22]. The initial time was set to be 250s, and the time of association phase and dissociation phase were 251s and 38s. Fig 1 is the response curve for the sequential injection of HBsAg solution, indicating the association phase and dissociation phase of HBsAg and HBsAb. The dotted lines mark the injection of the HBsAg solution with RU (response unit) values.


Biomolecular Interaction Analysis Using an Optical Surface Plasmon Resonance Biosensor: The Marquardt Algorithm vs Newton Iteration Algorithm.

Hu J, Ma L, Wang S, Yang J, Chang K, Hu X, Sun X, Chen R, Jiang M, Zhu J, Zhao Y - PLoS ONE (2015)

Sensorgram showing the association and dissociation processes of biomolecular interaction between HBsAg and HbsAb.The data marked with a triangle is obtained in the average of more than three sets of measurement results in RU. This sensorgram is showing that the HBsAg was binding on the specific HBsAb (association phase) starting from the injection point a and reaches an equilibrium after approximately 251s. From the dissociation starting point b, the dissociation phase was formed sequentially. The microfludic cell of this SPR bioanalyzer was kept at a constant temperature of 37°C.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4493042&req=5

pone.0132098.g001: Sensorgram showing the association and dissociation processes of biomolecular interaction between HBsAg and HbsAb.The data marked with a triangle is obtained in the average of more than three sets of measurement results in RU. This sensorgram is showing that the HBsAg was binding on the specific HBsAb (association phase) starting from the injection point a and reaches an equilibrium after approximately 251s. From the dissociation starting point b, the dissociation phase was formed sequentially. The microfludic cell of this SPR bioanalyzer was kept at a constant temperature of 37°C.
Mentions: The parameters and the initial values can be set manually according to the experimental data in the SPR biomolecular interaction analysis software based on the Marquardt algorithm, which was designed by our research group. Different results from various initial values can be compared each other visually so that we can select the most ideal initial values to reduce errors. From the homemade SPR analysis software, the experimental data can be imported conveniently. The x-axis of the graph represents time (s), while the y-axis of the graph represents the signal responses indicated with RU, which was computed based on the following formula RU = (1.334-RIx) ×30000, where 1.334 was the refractive index of deionized water. RIx is the refractive index of an unknown sample, which can be measured by using the SPR biosensor in real-time and 30,000 is a pre-determined factor for increasing the sensitivity of the calculated responses [22]. The initial time was set to be 250s, and the time of association phase and dissociation phase were 251s and 38s. Fig 1 is the response curve for the sequential injection of HBsAg solution, indicating the association phase and dissociation phase of HBsAg and HBsAb. The dotted lines mark the injection of the HBsAg solution with RU (response unit) values.

Bottom Line: A number of experimental data may lead to complicated real-time curves that do not fit well to the kinetic model.The association and dissociation rate constants, ka, kd and the affinity parameters for the biomolecular interaction, KA, KD, were experimentally obtained 6.969×10(5) mL·g(-1)·s(-1), 0.00073 s(-1), 9.5466×10(8) mL·g(-1) and 1.0475×10(-9) g·mL(-1), respectively from the injection of the HBsAg solution with the concentration of 16 ng·mL(-1).The kinetic constants were evaluated distinctly by using the obtained data from the curve-fitting results.

View Article: PubMed Central - PubMed

Affiliation: Department of Electrical Engineering, Henan Agricultural University, Zhengzhou, China; State Key Laboratory of Wheat and Maize Crop Science, Zhengzhou, China.

ABSTRACT
Kinetic analysis of biomolecular interactions are powerfully used to quantify the binding kinetic constants for the determination of a complex formed or dissociated within a given time span. Surface plasmon resonance biosensors provide an essential approach in the analysis of the biomolecular interactions including the interaction process of antigen-antibody and receptors-ligand. The binding affinity of the antibody to the antigen (or the receptor to the ligand) reflects the biological activities of the control antibodies (or receptors) and the corresponding immune signal responses in the pathologic process. Moreover, both the association rate and dissociation rate of the receptor to ligand are the substantial parameters for the study of signal transmission between cells. A number of experimental data may lead to complicated real-time curves that do not fit well to the kinetic model. This paper presented an analysis approach of biomolecular interactions established by utilizing the Marquardt algorithm. This algorithm was intensively considered to implement in the homemade bioanalyzer to perform the nonlinear curve-fitting of the association and disassociation process of the receptor to ligand. Compared with the results from the Newton iteration algorithm, it shows that the Marquardt algorithm does not only reduce the dependence of the initial value to avoid the divergence but also can greatly reduce the iterative regression times. The association and dissociation rate constants, ka, kd and the affinity parameters for the biomolecular interaction, KA, KD, were experimentally obtained 6.969×10(5) mL·g(-1)·s(-1), 0.00073 s(-1), 9.5466×10(8) mL·g(-1) and 1.0475×10(-9) g·mL(-1), respectively from the injection of the HBsAg solution with the concentration of 16 ng·mL(-1). The kinetic constants were evaluated distinctly by using the obtained data from the curve-fitting results.

No MeSH data available.


Related in: MedlinePlus