Science - USA (2022-01-28)

found an anticorrelation betweenkaandkd
with this measurement technique as well, with
an estimated ratio of variation inptotto varia-
tion inkoff,mof 1.97 ± 0.07 (fig. S3).
As an extension, our theoretical framework
can be used to dissect the binding path for

proteins with more complex, sequential binding

mechanisms, considering that mutations along

the binding pathway can be seen as ener-

getic barriers for binding. Accordingly, one

would first mutate a binding sequence in

several different ways, measure the resulting

macroscopic rateskaandkd, and then deter-

mine which sector of the (ka,kd)-space the

different mutations fall into (fig. S4, A and

B). Assuming that the native sequence has the

highestkavalue and that mutations introduce

a rate-limiting step, the sectors will be ordered

444 28 JANUARY 2022¥VOL 375 ISSUE 6579 science.orgSCIENCE

Fig. 2. Kinetic measurements with LacI on a
protein binding microarray.(A) Example images
taken during association (left) and dissociation
(right) of LacI-Cy3 to spots on the DNA microarray.
Orange circle,Osymoperator; red circle,O 1 operator;
green circle,O 2 operator.O 3 is not present on
the array, because initial experiments with this
operator showed no binding over background.
(B) Association and dissociation curves for theOsym,
O 1 , andO 2 operators (thick lines), and 100 examples
of their mutants (faint colors). The dissociation
curves for each operator were normalized to the
fluorescence count for the first frame of the
corresponding dissociation movie (C) Reproducibility
ofka(top) andkd(bottom) for individual operators
(cyan points) between replicates. Thekavalues
are all normalized to thekavalue ofOsymin that
replicate. Sequences associated with weak binding
(fluorescence signal at equilibrium <3% of signal for
Osym; gray points). (D) Measured association and
dissociation rates for wild-type operators (circles)
and their single and double mutants [points
are colored by operator density in that (ka,kd)
neighborhood; gray points are the same as in (C)].
The value for each operator is a mean from two
PBM replicate experiments; see fig. S1B for data
from individual replicates.

C D

Association Dissociation

B

0 1000 2000 3000

Time (s)

0

200

400

600

800

Osym

O 1

O 2

Background

Fluorescence counts

0 500 1000 1500

Time (s)

0.7

0.8

0.9

1

Osym

O 1

O 2

t = 750s

t = 1550s

t = 0s

t = 15250s

t = 2050s

t = 450s

A

Association Dissociation

0 0.2 0.4 0.6 0.8 1 1.2

kd (s-1) 10 -3

0

0.2

0.4

0.6

0.8

1

1.2

ka

/k

(a

O

sym

)

Number of operators in neighborhood

Osym

O 1

O 2

Operator library

0 0.5 1 10 -3

0

0.5

1

10 -3

kd Rep. 1 (s-1)

kd

Rep. 2 (s

-1)

ka/ka(Osym) Rep. 1

ka

/k

(Oa

sym

) Rep. 2

Negative control sequence

0 0.5 1

0

0.5

1

5

10

15

AB

O 2

kon,μ

Weak operator

Low kon,μ

Low ptot

Low ka

High kd

koff,μ

Nonspecifically

bound and

testing for recognition

Specifically

bound

kon,μ

Strong operator

High kon,μ

High ptot

High ka

Low kd

O 1

koff,μ

CD

k

(^) a
(s
-1
cell volume
)
kd (s-1)
0
2
4
6
10
-3
0 0.01 0.08
Osym
O 1
O 2
O 3
kon,max
OsymO 1 O 2 O 3
k
off,μ
(s
-1
)
10 -3
10 -2
10 -1
Reaction coordinate
0
10
Free energy (
k
Tb
)
-log(
koff,μ
)+
c
Osym
O 1
O 2
O 3
Free
Bound
Testing
state
Fig. 3. Analysis of in vivo binding kinetics.(A) Predicted effect on the association
and dissociation rates if thekon,mvalues were different butkoff,mwas identical for the
different operators. (B) Experimental single-molecule target-site association rate
constantska( 7 ) plotted against the dissociation rate constantskdfor the different
lacoperators. For the crosses,kdwas directly measured by single-molecule
imaging ( 14 ). For the dots,kdwas calculated asKD×ka, where the equilibrium
constantKDwas measured through the repression ratio of gene expression ( 12 , 13 ).
Cyan circle, measuredkon,max(see methods). Colored lines,koff,m-lines, found by
evaluating Eq. 1, for individual operators. *Due to the large error in thekdestimate
forO 3 [68% CI: (−0.08 to 0.24) s−^1 ], thekoff,m-line forO 3 is not shown. Error bars are
standard errors, obtained by propagating experimental errors. (C) Microscopic
dissociation rateskoff,mfor the different operators, estimated from the in vivo data
with Eq. 1. Error bars are 68% CI, obtained by propagating experimental errors.
(D) Energy landscapes (a putative rather than a true reaction coordinate is shown)
for the transition from free to bound states (state 1 and state 3, respectively) for
the different operators, as determined by the measuredKDandkoff,mvalues. The
activation energy on the transition path between the testing state and bound state is
not uniquely determined, but the differences in activation energies between the
different operators are. The activation energy is equal to−log(koff,m)+c, wherecis
the same constant for all operators (see supplementary text).
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