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I am currently reading an this article by Alexandra C. Walls et. al.

I would like to ask a question about a graph that is being used in the article and I wanted to know if my analysis was correct.

Figure

I was wondering if for the Binding Response versus Time graphs of SARS-CoV-2 (panel A), and SARS-CoV-1 (panel B), can we infer that SARS-CoV-2 was more adept at binding to the human ACE2 because the y-axis has larger numbers than for SARS-CoV-1? If not, why not?

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    $\begingroup$ @EnlightenedFunky You cannot assume that a particular user downvoted you. Votes are anonymous and there is basically no obligation for a voter to explain their vote. However, I can understand that it is can be annoying as well as discouraging but it's better to ignore it for your own happiness. $\endgroup$
    – WYSIWYG
    Nov 3 '20 at 14:56
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    $\begingroup$ I've tried to clarify what your question is about this figure, and to use an informative question title that makes clear what type of question this is. Please feel free to edit if you think these changes did not capture what you were after. $\endgroup$
    – Bryan Krause
    Nov 3 '20 at 17:52
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From the linked article:

We found that hACE2 bound to SARS-CoV-2 SB and SARS-CoV SB with respective equilibrium dissociation constants of 1.2 nM (Figure 2A) and 5.0 nM (Figure 2B).

An equilibrium dissociation constant (commonly called Kd) represents the propensity of a complex to dissociate into its constituent pieces. A smaller value represents a smaller propensity to break apart, i.e. a stronger interaction.

So, yes, considering only the data presented, domain B from the SARS-CoV-2 spike protein shows a slightly higher affinity for hACE2 than the equivalent domain from SARS-CoV. Note, however, that the authors are careful with their wording, and state in multiple places that the relative affinities of the homologous domains are comparable.

The SARS-CoV-2 SB engages human ACE2 (hACE2) with comparable affinity to SARS-CoV SB from viral isolates associated with the 2002–2003 epidemic (i.e., binding with high affinity to hACE2).

What's more telling are the binding constants (kon and koff) given in Table 1:

$$\begin{array}{c|c|c|} \text{} & \text{SARS-CoV-2 S}^{B} & \text{SARS-CoV S}^{B} \\ \hline \text{K}_{D} \text{ (nM)} & 1.2 ± 0.1 & 5.0 ± 0.1 \\ \hline \text{k}_{on} \text{ (M}^{-1} \text{s}^{-1}\text{)} & 1.4 × 10^5 (2.3 ± 1.4 × 10^5) & 1.4 × 10^5 (1.7 ± 0.7 × 10^5) \\ \hline \text{k}_{off} \text{(s}^{-1}\text{)} & 1.6 × 10^{−4} (1.7 ± 0.8 × 10^{−4}) & 7.1 × 10^{−4} (8.7 ± 5.1 × 10^{−4}) \\ \hline \end{array}$$ Values reported represent the global fit to the data shown in Figures 2A and 2B and the averages obtained from five (SARS-CoV-2) or four (SARS-CoV) replicates carried out with different protein preparations are shown in parentheses.

Note that Kd is the reciprocal of the association constant, Ka, which is equal to the ratio of the binding constants.

$K_{a} = \frac{k_{on}}{k_{off}}$, $K_{d} = \frac{k_{off}}{k_{on}}$

Since the values given for kon derived from the global fit are the same for SARS-CoV-2 and SARS-CoV, the observed difference in Kd is due to the different values of koff. So, at equilibrium, SARS-CoV-2 SB and SARS-CoV SB will associate with hACE2 at the same rate, though SARS-CoV SB dissociates faster.

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  • $\begingroup$ Can you explain how the y-axis values relate to Kd? I'm not sure this answer is correct based on what you've written here (you've explained what is written in the text, but not the figure). I'm also not particularly familiar with this technique, but I'm assuming the Kds come from a parametric fit to some aspect of the curves displayed and would depend on the spacing at different concentrations rather than the Y-axis. $\endgroup$
    – Bryan Krause
    Nov 3 '20 at 23:12
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    $\begingroup$ @BryanKrause I understand and agree with your concern. The problem I've encountered in trying to better understand how binding kinetics are derived from the raw Δλ is that the software associated with biolayer interferometry appears to be proprietary. All the "guides" and literature I find give the sequence of operations in the software GUI without stating what those operations do. I'll update my answer if and when I find better resources. $\endgroup$
    – acvill
    Nov 8 '20 at 17:37

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