Old SPR Paper with Derivations

Old SPR Paper with Derivations.pdf

Abstract

• best method is to estimate the $k_d$ and then attempt to estimate $k_a$

$$R_t=\{\frac{C{k}_a{R}_{max}(1-e^{-((C{k}_a+k_d)t)}}{C{k}_a+k_d}\}+R_i$$

Kinetic Analyses

• The linear method involves the following:

  • The following equation is graphed for dR/dt versus R and its slope corresponds to $k_{obs}$
  • We find $k_{obs}$ for different analyte concentrations - plot $k_{obs}$ versus C, slope would indicate $k_a$ and y-intercept would indicate $k_d$
  • But this also transforms the errors

• The integrated rate form of the rate equation is better

  • This equation is the same as the one presented in Bio-Rad BLI Overview.pdf, SPR-Pages - Data fitting methods, and in Bio-Rad BLI Overview.pdf

  • The paper suggests that

  • The equation below is corrected for a non-zero baseline measurement

  • For dissociation:

  • $R_a$ simply accounts for the change in signal from the start of the dissociation phase at t = 1 presumably, and until t_n in the dissociation phase

  • An extra term may be added to account for the non-zero signal as t → infinity

$$R_t=R_a\times e^{-k_{d}t}$$

• Use equation 10 (or 11 from the PDF) to get an estimate of $k_d$

Common Method for Kinetic Determination

• $k_d$ values can be estimated with good accuracy, while also estimating $R_a$ and $R_{t\to \inf }$
• Use the $k_d$ estimate has a constant, to constrain the estimate of $k_a$
• Tables suggest that $R_{max}$ is always estimated
• Constants include ligand concentration on sensor C, dissociation constant $k_d$ and optionally $R_i$ which was estimated with very good accuracy