Science - USA (2022-01-28)

according to the position of the mutations along
the reaction pathway. Thus, rate-limiting steps
closer to the bound state will result in fewer
rebinding events, leading to an increase inkd
forthesamevalueofka. In the case of LacI
(Figs. 2 and 3), the mutations fall on one line
corresponding to one common rate-limiting step.
In the supplementary materials, we apply this
method to high-throughput association and dis-
sociation data available for dCas9 binding to off-
target, mismatched mutants ( 16 )(fig.S4andS5).
As expected, mutations related to the same step
in the reaction pathway fall into sectors of the
(ka,kd)-space, and the order of the sectors corre-
sponds to the previously known reaction path.
In conclusion, the efficiency of target-site
recognition is not only crucial for determining
protein-DNA association rates, but also plays
an equally important role in determining how
long proteins remain bound to their targets. In
the case of thelacrepressor, we have shown
that the efficiency of target-site recognition
(ptot)—and not how long the protein remains
in the bound state—is the main determinant
for binding strength observed for different
sequences. This behavior may represent an
evolutionary adaptation to facilitate fast search
by minimizing the risk of the protein being
retained on sequences that resemble bona

fide operators. We note that the measure-

ments and models for LacI in this work all

consider the noninduced, allolactose analog-

free repressor, which is the conformation of

LacI that is capable of binding to DNA with

sequence specificity and high affinity ( 17 , 18 ).

Addition of an inducer pushes the system into

a new steady state where thekd/ka-ratio is

very high. Moreover, earlier work ( 19 ) indi-

cates that the induced repressor spends some

amount of time in a nonspecific testing state

before binding the inducer. What this implies

on the microscopic level—i.e., if the inducer

exerts its effect mainly through a change in

kon,morkoff,m—is not clear from the current

study. However, considering that dissociation

is very fast at high concentrations of inducer

( 14 ), changes inkoff,mare expected.

The coupling between association and dis-

sociation rates proposed in this work holds for

all bimolecular association-dissociation pro-

cesses adhering to detailed balance, where a

step of rapid testing for molecular recogni-

tion precedes the strong binding of a target.

Indeed, the anticorrelated relationship between

association and dissociation has been observed

previously for numerous other systems when

perturbing the sequence or salt conditions

( 16 , 20 – 22 ). We therefore believe that our

theoretical result is very likely to be generally

applicable to a wide range of kinetic systems

in addition to the ones investigated here, in-

cluding processes that do not involve protein-

DNA interactions.

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ACKNOWLEDGMENTS

We thank O. Berg, M. Ehrenberg, H. Danielson, J. Wiktor, M. Lüking,

D. Fange, I. Barkefors, and D. Jones for discussions.Funding:This

research was supported by the Knut and Alice Wallenberg Foundation

(2016.0077 and 2019.0439 to J.E.; 2019.0306 to S.D.), the Swedish

Research Council (2016-06213 to J.E.; 2020-06459 to E.M.), the

European Research Council (Starting Grant, 714068 to S.D.; Advanced

Grant, 885360 to J.E.), the eSSENCE e-science initiative and the

Swedish National Infrastructure for Computing (SNIC) at UPPMAX.

Author contributions:J.E. and E.M. conceived the study; E.M.

derived models and equations; S.D., E.M., and M.G. designed the

single-molecule experiments; M.G. performed the single-molecule

experiments; E.M. analyzed the single-molecule data; J.Y., E.M.,

and J.E. designed the PBM experiments; J.Y. performed the PBM

experiments; J.Y. and S.Z. analyzed the PBM experiments; E.M. and

EA designed, EA performed, and E.M. analyzed the SPR experiments;

E.M., J.E., and S.D. interpreted the results and wrote the paper, with

input from all authors.Competing interests:The authors declare

no competing interests.Data and materials availability:All raw data

and analysis codes are available at the SciLifeLab Repository ( 23 ).

SUPPLEMENTARY MATERIALS

science.org/doi/10.1126/science.abg7427

Materials and Methods

Supplementary Text

Figs. S1 to S5

Table S1

References ( 24 – 38 )

MDAR Reproducibility Checklist

25 January 2021; resubmitted 13 September 2021

Accepted 21 December 2021

10.1126/science.abg7427

SCIENCEscience.org 28 JANUARY 2022•VOL 375 ISSUE 6579 445

A

Low kd

lengthsliding

High [NaCl]

Low ptot

Low ka

High kd

Low [NaCl]

High ptot

High ka

C

D

Colocalized

PEG

Cy3

ka

LacI

kd

Cy5

B

kd (s-1) 10 -3

01234

0

0.1

0.2

ka

(s

-1

nM

-1

)

0 5 10 15

Time (s)

0

0.5

Association

0 25 50

Time (s)

0.8

0.9

1

Dissocation

(^050) Cumulative signal (AU)
Time (s)
0
5
10
Fluorescence counts (AU)
104
0
0.2
0.4
0.6
Cumulative signal (AU)
Association
0 50 100 150
Time (s)
0
5
10
Fluorescence counts (AU)
104
0.7
0.8
0.9
1
1.1
Cumulative signal (AU)
Dissociation
Fig. 4. Effect of changing the salt concentration.(A) Single-molecule colocalization measurements
detect association and dissociation for LacI binding to its operators (top) and the predicted effect on
association and dissociation rates of changing the salt concentration (bottom). (B) Example single-molecule
traces showing binding to and unbinding from theO 1 operator at 100 mM NaCl (colored lines), and the
normalized association and dissociation curves (black lines) obtained after summing 649 and 777 traces
for the association and dissociation experiment, respectively. AU, arbitrary units. (C) Normalized association
and dissociation curves forO 1 binding at 1 mM (dashed dotted lines), 100 mM (solid lines), and 200 mM NaCl
(dashed lines). (D) Measuredkaandkdvalues forO 1 binding at different salt concentrations, and a fit
to Eq. 1 (red line). The salt concentrations used for the different experiments are in the range of 1 to
250 mM supplemented NaCl (fig. S2, A to D).
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