Fig 1.
Flow chart summarizing the inference processes in our proposed Bayesian approach.
Fig 2.
Screen Shot of the implemented software.
The implemented software has the interface to allow the user to define the initial values of the parameters (A) and specify the input files (B) as well as controlling the behavior of the Gibbs sampler inference. It also has the interface to show the summary statistics (C) and trace plots of estimations (D).
Fig 3.
(A), the SPR response data were simulated according to Eqs (12), (13) and (14) with no measurement error. In simulations Rmax was 31.5 RU, A0 was 30nM, ka values varied between 1x105 and 3x108/M/s, kd values were adjusted so that KD was constant 1nM and kM was 3.15x107 RU/M/s. The mass transport limiting coefficients (MTLC) of these responses varied between 0.1 (little/no mass transport effect) and 300 (high/full mass transport effect). (B), same as in A, but measurement error with a constant standard deviation of 1.5 RUs was added to the simulated data. The level of noise was chosen based on empirical data obtained from the Bio-Rad Proteon XPR36 biosensor in our lab through a variety of antibody-antigen interactions (1~3 RUs in our experiments).
Fig 4.
The trace plots for evaluation of the simulated SPR response data.
The SPR response data were simulated as in Fig 2 with Rmax 31.5RU, ka 3x106/M/s, kd 3x10-3/s, kM 3.15x107RU/M/s, A0 30nM and σ2 1.5. The data were analyzed as described in the text. The trace plots are shown for six parameters in the analysis of the data set with ka * Rmax/kM = 3.0. The returned parameters are summarized in Table 1.
Table 1.
Parameter values estimated by the proposed Bayesian method using the simulated SPR response Data.
Fig 5.
The kinetic analysis of the emzyme CAII and its small molecule inhibitor 4-CBS in the SensiQ Pioneer biosensor.
CAII was immobilized by the amine coupling chemistry at a level of about 3000RU, and then 50μM 4-CBS was injected at a flow rate of 50μl/min at 25˚C. The generated sensorgram data were exported and analyzed by the proposed Bayesian approach. The diffusion coefficient and mass transport coefficient were first derived, and then the kinetic parameters as well as the active concentration were determined. The fitted values of the responses were overlaid with the original sensorgram (the red dashed line) on the top figure, and the residuals were showed on the bottom.
Table 2.
Parameter values estimated by the proposed Bayesian approach using the experimental SPR response data.
Fig 6.
The kinetic analysis of BMP10 with hEndECD-hFC in BiaCore 3000 and hCGRPα with 4901 IgG in Proteon XPR36 by the proposed Bayesian approach.
Two sets of data were extracted from literature. (A), the interaction between BMP10 and immobilized hEngECD-hFc was measured in a Biacore 3000 system [32]. (B), the analyte human CGRPα and immobilized 4901 IgG were studied in a Proteon XPR36 biosensor [33]. The values of mass transport coefficient kM were derived according to Eqs (9) and (10) for both cases. The two datasets were then analyzed by the proposed approach to estimate the active concentration of analyte A0, rate constants ka and kd, and the dissociation constant KD. The returned parameters were listed in Table 2. The raw sensorgrams (solid lines) and fitted curves (dashed lines) were overlaid.