Kinetic analysis of unwinding time courses was carried out by applying DYNAFIT
(BioKin Ltd., WA) 30, which is a conventional global fitting program that is analogous to
the KINSIM and FITSIM programs that have been successfully used to analyze
unwinding kinetics in the past 20.
As a first step in the kinetic analysis, timecourses of RNS unwinding were analyzed
in the manner previously described by Ali and Lohman18, by which a simple model of N
sequential rate-limiting steps is used to account for the observed lags in the unwinding of
duplexes of various lengths (Scheme 1). In this scheme, S and P represent the double-
stranded substrate and single-stranded product, respectively, and Pn represents a partially
unwound intermediate that is formed after n steps. Each rate-limiting event (for each
step, n) is described by the same kinetic rate constant, k .
k k k k k
S P1 P2 … Pn P, (1 n N) Scheme 1
To identify the number of rate-limiting steps for duplexes of increasing lengths,
each timecourse was successively fit using Scheme 1, where the total number of steps, N,
was increased from 1 to 8, and the unwinding rate constant, k, was allowed to float. The
sums of the squared residuals for each fit were then plotted versus number of steps, N.
For each duplex length, the best value of N was determined as the one that corresponded
with the absolute minimum in the sum of squared residuals. Representative raw data from
this model discrimination analysis is provided for base pairs 18 to 25 and 38 to 45
(Supplementary Figure 2). These data indicate that the number of rate limiting steps
increases in a stepwise manner as duplexes become longer and that the observed
transitions in N are extremely local; i.e. the boundaries between different kinetic steps are
well-defined. For example, the boundary between the first and second steps (N changes
from 1 to 2) is located between base pairs 21 and 22, and the boundary between kinetic
steps #2 and #3 can be placed between base pairs 41 and 42 (Supplementary Figure 2).
The kinetic step size, defined as the number of base pairs unwound per kinetic step, can
therefore be estimated from the distance between the two boundaries, which is
approximately 20 base pairs. The overall kinetic rate constant, k, per step is 0.8 s-1.
Characterization of kinetic behavior between step boundaries:
Although the timecourses within a 20-base pair step are quite similar, the kinetic
traces are not perfectly superimposable: there is a small, progressive increase in the time
required for unwinding nucleotides later in a step, as the duplex length increases
(Supplementary Figure 4). In contrast to the abrupt and major change in unwinding
kinetics at step boundaries (manifest as a large shift in the amount of timecourse lag),
there is also a regular, continuous decrease in unwinding rate during progression through
each 20 base pair step. From the change in the time required for unwinding the duplex
within a step (Supplementary Figure 4), one can compute the translocation rate constant
between major step boundaries. This capability underscores a distinctive strength of the
RNS method: kinetic behavior can be evaluated at each nucleotide in the duplex and
subtle deviations can be monitored.
To assess the intra-step kinetic behavior in a quantitative manner, we refined the
model shown on Scheme 1 by introducing an additional kinetic phase. Each major step
shown on Scheme 1 was divided into two kinetic events: (a). A slow local event that
occurs at step boundaries with rate constant kp. (b). This is followed by a fast
translocation event that occurs with rate constant ktrans (Scheme 2).
Pn Tn Pn+1 Scheme 2
The major kinetic event (described by kp) takes place at a single base pair, so it is
considered schematically as a pause (Pn) that precedes formation of a translocation-
competent state (Tn). Unwinding proceeds rapidly (with rate constant ktrans) from Tn to
the next boundary state, or pause, Pn+1 (Scheme 2). Values of kp and ktrans were calculated
by performing global fitting of timecourses within a given kinetic step to Scheme 2 (such
as the data in Supplementary Figure 4). The value of kp was allowed to float but was
assumed to be the same for all duplex lengths in the step. The time required for
unwinding base pairs within a given step () was allowed to float freely. Values of ktrans
were then obtained from a simple plot of vs. duplex length, in base pairs (Fig. 3, inset)
using Equation 1, which links the rapid sequential unwinding of base pairs within a
kinetic step with the characteristic unwinding time for duplex of a given length:
= m/ktrans Equation 1
where m is the number of sequential unwinding steps (e.g., base pairs)
Like the related NPH-II protein, NS3 unwinding is preceded by a slow initiation
event during which the helicase does not appear to move (Scheme 3).
S T0 P1, Scheme 3
This event was observed to occur with a rate constant, kinit of 0.4 sec-1, which was
determined from global fitting of timecourses for duplex lengths 14-19. Additional
kinetic features of the first step were not extracted because only the terminal portion of
the first step could be evaluated (unwinding could be effectively monitored only for
duplexes longer than 12 base pairs).
The overall kinetic mechanism of unwinding by NS3 is represented by Scheme 4,
where rate constants kI, kII, … kN correspond to the major rate limiting steps analogous to
those described by Scheme 1.
kinit ktrans kp ktrans kp ktrans kp ktrans
S T0 P1 T1 P2 … Pn-1 Tn-1 Pn Tn P Scheme 4
kI kII kN-1 kN