Also in the Article

Event-oriented analysis

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 Pboundt) was applied to the HS-AFM measurements and the bound-unbound transitions were observed at 20 nM. First, fbound(h; Δt) was defined as the distribution of the height from the moment of AgTx2 binding, where Δt is the time from the moment of binding; that is, Δt is zero when AgTx2 binds. All binding events were collected from the measurements to evaluate fbound(h; Δt); that is, fbound(h; Δt) represents an ensemble average of trajectories of height. The number of binding events in our dataset was 6514. Then, Pbound was estimated using the following equation$Pbound(Δt)=∫hthre∞fbound(h;Δt)dh$

Similarly, another time course of the binding probability Punboundt) was defined, in which Δt is the time from the moment of dissociation. We used this description for subsequent equations in this section and described Punboundt) as “Pboundt) from dissociation” in the remaining text and figures. The number of dissociation events was 6511. Neither Pboundt) nor Punboundt) 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, tpersist, which is the time spent in the bound or unbound state without transition. Here, Pboundt; tpersist) was defined as follows$Pbound(Δt;tpersist)=∫hthre∞fbound(h;Δt;tpersist)dh$

Here, Δt is the time after the persistent residence in a state. Thus, Pboundt; tpersist) 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 (5760). Punboundt; tpersist) was defined in the same manner.

Q&A