Event-oriented analysis

This protocol is extracted from research article:

High-speed AFM reveals accelerated binding of agitoxin-2 to a K+ channel by induced fit

**
Sci Adv**,
Jul 3, 2019;
DOI:
10.1126/sciadv.aax0495

High-speed AFM reveals accelerated binding of agitoxin-2 to a K+ channel by induced fit

Procedure

Time series of AFM measurements, *h*(*t*), were assigned to two hypothesized states—AgTx2-bound and AgTx2-unbound—according to the AFM surface height threshold. Hence, two transitions (events) were observed: from bound to unbound and from unbound to bound. Instead of the previous analyses using autocorrelation function and dwell time (*56*, *57*), the event-oriented analysis for determining the time course of *P*_{bound}(Δ*t*) was applied to the HS-AFM measurements and the bound-unbound transitions were observed at 20 nM. First, *f*_{bound}(*h*; Δ*t*) was defined as the distribution of the height from the moment of AgTx2 binding, where Δ*t* is the time from the moment of binding; that is, Δ*t* is zero when AgTx2 binds. All binding events were collected from the measurements to evaluate *f*_{bound}(*h*; Δ*t*); that is, *f*_{bound}(*h*; Δ*t*) represents an ensemble average of trajectories of height. The number of binding events in our dataset was 6514. Then, *P*_{bound} was estimated using the following equation$${P}_{\text{bound}}(\mathrm{\Delta}t)={\displaystyle {\int}_{{h}_{\text{thre}}}^{\infty}}{f}_{\text{bound}}(h;\mathrm{\Delta}t)\mathit{dh}$$

Similarly, another time course of the binding probability *P*_{unbound}(Δ*t*) was defined, in which Δ*t* is the time from the moment of dissociation. We used this description for subsequent equations in this section and described *P*_{unbound}(Δ*t*) as “*P*_{bound}(Δ*t*) from dissociation” in the remaining text and figures. The number of dissociation events was 6511. Neither *P*_{bound}(Δ*t*) nor *P*_{unbound}(Δ*t*) were single-exponential events, as described in the text earlier, indicating the presence of more than two states in the system. To clarify this phenomenon, a persistence time in a state was introduced, *t*_{persist}, which is the time spent in the bound or unbound state without transition. Here, *P*_{bound}(Δ*t*; *t*_{persist}) was defined as follows$${P}_{\text{bound}}(\mathrm{\Delta}t;{t}_{\text{persist}})={\displaystyle {\int}_{{h}_{\text{thre}}}^{\infty}}{f}_{\text{bound}}(h;\mathrm{\Delta}t;{t}_{\text{persist}})\mathit{dh}$$

Here, Δ*t* is the time after the persistent residence in a state. Thus, *P*_{bound}(Δ*t*; *t*_{persist}) is closely related to a three-time correlation function, which is known to be a powerful tool to reveal the detailed dynamics of complicated systems, such as biomolecules (*57*–*60*). *P*_{unbound}(Δ*t*; *t*_{persist}) was defined in the same manner.

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