Factors that impact the systematic error of k_a and k_d

Old Notes:

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

$$R_t=\{\frac{C{k}_a{R}_{max}(1-e^{-((C{k}_a+k_d)t)}}{C{k}_a+k_d}\}+R_i$$ $$R_t=R_a\times e^{-k_{d}t}+R_{t\to \inf }$$

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Potentially:

Currently immeasurable effects on estimation

• Mass Transfer: If diffusion to the interaction surface is slower than the rate of binding to the ligand, the diffusion rate becomes a bottle neck
  • Two methods for determination of k_t and k_m which affect response
  • Mass transport lowers the estimated k_a value
  • Solving this includes reducing the surface density of ligand (ensures more local ligand is available for continual binding), or in SPR, increasing analyte injection flow rate (improves convection)
  • Source
• High ligand density on sensor: rebinding of analyte to ligand on sensor may cause an underestimated k_d value

The systematic error of $k_a$ is numerically based upon:

• systematic error of analyte concentration, C
• systematic error of estimated $k_d$, $k_{d-det}$

ChatGPT suggests multiple factors ​

Concerns:

• Based on previous literature review $R_{max}$ is commonly fitted via nonlinear regression (see Old SPR Paper with Derivations.pdf), so does that omit both ligand loading and baseline drift (both of which are associated to $△R$)?
  • Answer: $R_{max}$ is generally fitted in most BLI/SPR analysis programs, because it requires high analyte concentrations and longer injection times.
  • In certain cases for SPR, the $R_{max}$ has a theoretical value based upon the density of ligand on the sensor and molecular weights - in such cases, $R_{max}^{theoretical}$ is a fixed value = ERRORS WILL PROPAGATE IN THIS CASE because factors such as baseline draft or improper ligand loading will cause systematic errors in the responses produced.

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The systematic error of $k_d$ is numerically based upon:

• There are no variables which are being substituted in the equation, $R_a$ and $k_d$ are both fitted for, via nonlinear regression

Chatgpt suggests the following non-numerical factors: