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activation time sensitivity to hyperpolarization

(

). The S2-S3 linker is also directed toward the

S4/C-linker interface and may play a yet-unknown

role in channel gating.

Summary

The structure of rEag1 reveals a non

–

domain

swapped architecture of the S1 to S6 that is due

to a short five-residue S4-S5 linker. This repre-

sents a divergence from the domain-swapped

architecture of previous voltage-gated ion chan-

nel structures (Fig. 4) (

–

) and suggests a new

paradigm for voltage-dependent gating for the

Eag family of K

channels. On the basis of the

structure of Eag1, we propose a gating mecha-

nism in which S4 enters the cytoplasm in a

down or hyperpolarized state to interact with

and induce a rotation of the C-linker and S6

in a direction that tightens the helical bundle

to close the channel (Fig. 6B). In the up or de-

polarized state of the VS, S4 moves into the

membrane, which allows the C-linker and S6

to rotate in a direction that loosens the helical

bundle and thus relieves the high-energy bend

in S6 to open the channel (Fig. 6B).

Two important consequences result from a

gating mechanism in which the VS interacts

with the cytoplasmic domains to gate the chan-

nel. First, this allows the cytoplasmic domains

to close the channel independent of VS con-

formation. This is observed in the structure of

Eag1, as binding of CaM to the cytoplasmic

domains closes the pore, but the VS is in the

up or depolarized conformation. Second, this

provides an added level of regulation through

the interaction of intracellular domains with

the voltage-dependent gating machinery. In

Eag1, the N terminus of the PAS domain, which

confers sensitivity to hyperpolarization (

), is

poised to interact with the S4 and S4-S5 linker

in a closed conformation (Fig. 5D).

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I, Ile; K, Lys; L, Leu; M, Met; N, Asn; P, Pro; Q, Gln; R, Arg;

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ACKNOWLEDGMENTS

We thank M. Ebrahim at the Rockefeller University cryo-EM

resource center for help with data collection and J. Chen and

members of the MacKinnon laboratory for helpful discussions. This

work was supported in part by NIH grant GM43949. J.R.W. is a

Damon Runyon Fellow supported by the Damon Runyon Cancer

Research Foundation (DRG-2212-15) and R.M. is an investigator in

the Howard Hughes Medical Institute. The low-pass filtered and

amplitude-modified three-dimensional cryo-EM density maps for

rEag1 have been deposited in the EM Data Bank with accession code

EMD-8215. Atomic coordinates for rEag1 have been deposited in the

Protein Data Bank under accession code 5K7L. J.R.W. performed

functional experiments and expressed, purified, and determined

single-particle cryo-EM structure of rEag1. J.R.W. and R.M. designed

experiments, analyzed and interpreted results, and wrote the

manuscript.

SUPPLEMENTARY MATERIALS

www.sciencemag.org/content/353/6300/664/suppl/DC1

Materials and Methods

Figs. S1 to S9

References (

–

)

1 April 2016; accepted 22 June 2016

10.1126/science.aaf8070

PHYSICS

Laser spectroscopy of

muonic deuterium

Randolf Pohl,

1,2

François Nez,

Luis M. P. Fernandes,

Fernando D. Amaro,

François Biraben,

João M. R. Cardoso,

Daniel S. Covita,

Andreas Dax,

Satish Dhawan,

Marc Diepold,

Adolf Giesen,

7,8

†

Andrea L. Gouvea,

Thomas Graf,

Theodor W. Hänsch,

1,9

Paul Indelicato,

Lucile Julien,

Paul Knowles,

‡

Franz Kottmann,

Eric-Olivier Le Bigot,

Yi-Wei Liu,

José A. M. Lopes,

4,13

Livia Ludhova,

Cristina M. B. Monteiro,

Françoise Mulhauser,

10,1

|| Tobias Nebel,

Paul Rabinowitz,

Joaquim M. F. dos Santos,

Lukas A. Schaller,

Karsten Schuhmann,

11,8,15

Catherine Schwob,

David Taqqu,

João F. C. A. Veloso,

Aldo Antognini,

1,11,15

The CREMA Collaboration

The deuteron is the simplest compound nucleus, composed of one proton and one

neutron. Deuteron properties such as

theroot-mean-squarechargeradius

r

and the

polarizability serve as important benchmarks for understanding the nuclear forces and

structure. Muonic deuterium

d is the exotic atom formed by a deuteron and a negative

muon

–

. We measured three 2S-2P transitions in

d and obtain

r

12562

fm,

which is 2.7 times more accurate but 7.5

smaller than the CODATA-2010 value

r

1424

fm. The

dvalueisalso3.5

smaller than the

r

value from electronic

deuterium spectroscopy. The smaller

r

, when combined with the electronic isotope

shift, yields a

“

small

”

proton radius

r

, similar to the one from muonic hydrogen,

amplifying the proton radius puzzle.

recision spectroscopy of atomic energy

levels can be used to determine properties

of the nucleus (

). Deuterium (D), for exam-

ple, is a heavier isotope of hydrogen (H),

with a nucleus, the deuteron (d), composed

of one proton and one neutron (

). D was dis-

covered through a tiny shift in the Balmer

spectral lines of D-enriched hydrogen (

). This

shift is caused mainly by the mass difference

between the proton and the deuteron. Today, the

nuclear masses are accurately known from cyclo-

tron frequency measurements in a Penning trap

SCIENCE

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12 AUGUST 2016

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669

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(

), and the measured isotope shift of the 1S-2S

transition in H and D (

) determines the (squared)

deuteron-proton charge radius difference (

)

;

≡

−

82007

1

This is because the wave function of atomic S

states is maximal at the origin, where the nu-

cleus resides, and the wave function overlap

with the extended nuclear charge distribution

reduces the atomic binding energy. Equation 1

links measurements of transition frequencies

in H and D. These, together with elastic electron

scattering on protons (

) and deuterons (

), de-

termine the Rydberg constant

∞

and

in the

CODATA adjustment of the fundamental physical

constants (

Muonic atoms are a special class of

“

exotic

”

atoms that offer access to nuclear properties with

much higher accuracy. In a muonic atom, the nu-

cleusisorbitedbyonenegativemuon

–

,instead

of the usual electrons

–

.Themuon

’

slargermass

207

results in a muonic Bohr radius that

is smaller than the corresponding electronic Bohr

radius by the ratio of reduced masses

red

ℓ

nuc

ℓ

nuc

.Here

ℓ

is the mass of the

lepton (muon

–

or electron

−

), and

nuc

is the

mass of the nucleus. As the Bohr radius shrinks

proportionally to 1

red

, the overlap of the muon

’

wave function with the nuclear charge distribution

increases as

red

.For

red

196

,andthe

wave function overlap is

red

≈

larger

dthaninD.AmeasurementoftheLambshift

(2P-2S energy difference) in

disthereforeex-

tremely sensitive to the deuteron charge radius

Our recent measurements of the Lamb shift in

muonic hydrogen

phaveresultedinavalueof

the proton charge radius

= 0.84087(39) fm,

which is 10 times more accurate, but 4%, or 7

smaller (

) than the CODATA-2010 value (

which is the most recently published CODATA

compilation. This so-called

“

proton radius puzzle

”

has questioned the correctness of various experi-

ments or quantum electrodynamics (QED) calcu-

lations, the value of the Rydberg constant, our

understanding of the proton structure, or the

standard model of particle physics (

Here we present measurements of the three

2S-2P transitions in

d highlighted in Fig. 1, yield-

ing a precise value of

. The principle of the ex-

periment is to form

d atoms in the metastable 2S

state (

) and to measure the 2S-2P transitions by

pulsed laser spectroscopy. Comparison with theory

(

)reveals

. The muonic deuterium data pre-

sented here were acquired in the same measure-

ment period as the muonic hydrogen data in (

Independent and reliable calculations of QED

(

–

) and nuclear structure effects (

–

)in

d, which are required to interpret the experi-

ment, have recently become available and are

summarized in (

Measurement of the spectral lines of

muonic deuterium

The experiment has been described before (

In brief, a 5 × 12 mm

beam of low-energy neg-

ative muons

−

(3-keV kinetic energy, average

rate 600/s) is stopped in a 20-cm-long target

filled with 1 hPa of D

gas at 20°C. A pulsed laser

system (

) is triggered on the detection of a

single arriving muon and provides pulses with

an energy of ~0.25 mJ, tunable around a wave-

length of 6

m,andcalibratedagainstwatervapor

absorption lines known within a few megahertz

(

). A multipass mirror cavity (

)ensuresgood

laser illumination of the muon stop volume. Large-

area avalanche photo diodes (

) detect the

2-keV

x-rays from the radiative 2P

→

1S tran-

sition that follows the laser-induced 2S

→

2P exci-

tation of

d. The laser frequency is changed

every few hours, and the resonances displayed

in Fig. 2 are obtained by plotting the number of

2-keV x-rays (normalized to the number of stopped

muons) detected in time coincidence with the

laser pulse, as a function of laser frequency. On

the peak of the resonance, we recorded up to

10 laser-induced x-rays (

“

events

”

)perhourwith

all data reduction cuts (

) applied. The back-

ground level of about 2 events per hour origi-

nates mainly from misidentified muon decay

electrons. About a third of the recorded events

are without laser light, providing the expected

background level shown as horizontal bands in

Fig. 2. The resonances are fitted with a flat back-

ground plus a Lorentzian line shape model that

takes into account varying laser pulse energies

and saturation effects.

The three resonances shown in Fig. 2 are the

transitions 2

→

and 2

→

, abbreviated as #1, #2, and

#3, respectively. Their positions and uncertainties

are

50816

T

stat

T

syst

GHz

52061

T

stat

T

syst

GHz

52154

T

stat

T

syst

GHz

The systematic uncertainties of 0.35 GHz arise

from laser frequency fluctuations (

)andZeeman

shifts from a conceivable small admixture of circular

polarizedlightandthe5Tmagneticfieldofthe

muon beam line. Line-pulling effects from off-resonant

excitation of neighboring levels are negligible (

Deuteron charge radius

For the fit of line #1, the Lorentzian width was

fixed to the natural radiative line width of

5 GHz (

), as the freely fitted value

1 GHz is 2

too small. Both fits agreed on

the line center within 0.33 GHz, and the uncer-

tainty quoted in Eq. 2 is the larger one from the

fit with fixed width. The difference

−

T

0 GHz from the fit is in good agreement

) with the theoretical value of 88.045 GHz

(

). The amplitude of line #3 is larger than zero

only with a significance of 4

, but it serves to

identify line #2 unambiguously. The alternative

—

namely, that the left peak in Fig. 2 (bottom) is in

fact line #3

—

is disfavored with 6

significance

thanks to the absence of a peak with twice the

amplitude ~90 GHz left of line #2.

Combining the three measured frequencies

and using the theoretical 2P fine structure and

3/2

hyperfine splittings (

), we determine the

2P-2S Lamb shift (LS) and 2S hyperfine splitting

(HFS) in

exp

202

8785

stat

syst

meV

5

exp

HFS

2747

stat

syst

meV

6

with total experimental uncertainties of 0

0034

and 0

0073 meV, respectively. The measured 2S

670

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SCIENCE

Max-Planck-Institut für Quantenoptik, 85748 Garching,

Germany.

Johannes Gutenberg-Universität Mainz,

QUANTUM, Institut für Physik & Exzellenzcluster PRISMA,

55099 Mainz, Germany.

Laboratoire Kastler Brossel, UPMC-

Sorbonne Universités, CNRS, Ecole Normale Supérieure

–

PSL

Research University, Collège de France, 75005 Paris, France.

LIBPhys, Department of Physics, University of Coimbra, 3004-

516 Coimbra, Portugal.

I3N, Departamento de Física,

Universidade de Aveiro, 3810-193 Aveiro, Portugal.

Physics

Department, Yale University, New Haven, CT 06520-8121, USA.

Institut für Strahlwerkzeuge, Universität Stuttgart, 70569

Stuttgart, Germany.

Dausinger + Giesen GmbH, Rotebühlstrasse

87, 70178 Stuttgart, Germany.

Ludwig-Maximilians-Universität,

Munich, Germany.

Département de Physique, Université de

Fribourg, 1700 Fribourg, Switzerland.

Institute for Particle

Physics, ETH Zurich, 8093 Zurich, Switzerland.

Physics

Department, National Tsing Hua University, Hsinchu 300, Taiwan.

Instituto Politécnico de Coimbra, ISEC, 3030

–

199, Portugal.

Department of Chemistry, Princeton University, Princeton, NJ

08544-1009, USA.

Paul Scherrer Institute, 5232 Villigen

–

PSI,

Switzerland.

*Corresponding author. Email: pohl@uni-mainz.de

†

Present

address: Deutsches Zentrum für Luft- und Raumfahrt e.V. in der

Helmholtz-Gemeinschaft, 70569 Stuttgart, Germany.

‡

Present

address: LogrusData, Vienna, Austria. §Present address:

Forschungzentrum Jülich IKP-2 and RWTH Aachen University,

Germany. ||Present address: International Atomic Energy Agency,

Vienna, Austria. ¶Present address: Honeywell Process Solutions Inc,

500 Brooksbank Avenue, North Vancouver BC V7J 3S4, Canada.

Fig. 1.

n

= 2 levels in muonic deuterium.

The order

of the 2P

3/2

sublevels is changed by the nuclear

quadrupole moment (

). The three measured

transitions are indicated.

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HFS is in excellent agreement with the theoret-

ical value,

theo

HFS

2791

meV (

The Lamb shift in

d is extraordinarily sen-

sitive (

) to the root mean square (RMS) deu-

teron charge radius

theo

228

7766

meV

TPE

7

−

1103

meV

where

TPE

theo

Þ¼

7096

200

meV

8

is the deuteron polarizability contribution (

)from

two-photon exchange (TPE), recently calculated

with good accuracy (

–

). The charge radius

effectinEq.7contributesasmuchas14%tothe

2P-2S Lamb shift, which explains the excellent

sensitivity of our measurement to

.Weobtain

from equating Eqs. 5 and 7, and using Eq. 8,

which yields

Þ¼

12562

exp

theo

9

where the theory uncertainty is almost ex-

clusively from

TPE

(Eq. 8). This radius is in

disagreement with the CODATA value (

which is the best estimate of the deuteron ra-

dius obtained from precision spectroscopy of H

and D and electron scattering on protons and

deuterons,

CODATA

Þ¼

1424

10

(seeFig.3).Wearehencefacedwiththefactthat

precision determinations of the Lamb shift in

both

p and

d, from a total of five measured

resonances, each show a

≥

discrepancy to the

predictions based on fundamental physical con-

stants from the self-consistent CODATA world

average (

), carefully checked QED calculations

(

), and physics within the standard model.

The CODATA deuteron radius

is tightly

linked to the CODATA proton radius

,byvirtue

ofEq.1.However,asdetailedin(

), we have

deduced a deuteron charge radius considering

spectroscopy data in regular deuterium alone

—

i.e.,

without relying on the value of the proton radius.

This yields a value of

Dspectroscopy

Þ¼

1415

11

in excellent agreement with the CODATA value,

but 3

larger than the value obtained here

from muonic deuterium (see Fig. 3, blue point,

“

spectroscopy

”

This distinct 3

discrepancy between the

atomic physics determinations of

from D and

d is almost as severe as the 4

atomic physics

discrepancy between the

values from H spec-

troscopy [see (

), table XXXVIII, adjustment 8]

and

) (see Fig. 4). These two discrepancies

are independent, as explained in (

The difference between the deuteron radii from

the spectroscopy of electronic and muonic deute-

rium is only 0.017 fm, or 0.8%. Thus, even though the

deuteron charge radius

−

dscatt

Þ¼

130

fm, extracted from elastic electron-deuteron scatter-

ing (

), is accurate to 0.5%, it is unfortunately not

accurate enough to distinguish between the values

from

dandCODATA.

Proton and deuteron radius puzzle

Many attempts to explain the proton radius dis-

crepancy exist (

). Our muonic deuterium

result provides fresh insight, as the so-called

“

proton radius puzzle

”

is in fact not limited to

the proton; there is a distinct deuteron radius

puzzle. Using

(CODATA) in Eq. 7 yields a Lamb

shift that is

Þ¼

438

meV smaller than

the measured value, Eq. 5, and hence resonance

frequencies that are

∼

104 GHz smaller than ob-

served (Fig. 2). The

is even somewhat larger

than the proton radius discrepancy

Þ¼

329

meV between the LS we observed in

p and the one calculated with the CODATA value

(

The ratio of discrepancies in

dand

Þ¼

is in agreement with the ratio of

the wave-function overlap from the reduced mass

ratio,

red

17. Such a scaling

is expected for several beyond

–

standard model

(BSM) physics scenarios (

–

), where

a new force between muons and protons is

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671

Fig. 2. Three measured resonances in muonic deuterium.

The resonances are labeled #1 (

), and #2

and #3 (

). The signal (

axis) is

“

normalized number of events

”

as described in (

). Predicted resonance

positions are shown based on Eqs. 7 and 8: The CODATA-2010 deuteron radius (pink, Eq. 10) would

correspond to ~104 GHz lower resonance positions, which is a difference of 7.5

.The

“

expected

”

deuteron

radius Eq. 13, (

“

p + iso,

”

brown) obtained by combining the proton radius from muonic hydrogen (

)

and the electronic isotope shift (

“

iso

”

), Eq. 1, is consistent with the observed resonance positions

within ~2.6

.The top and bottom panel

’

s data were recorded in 1 week and 2 days, respectively. As an

example, the three highest points around the peak of resonance #1 contain a total of 260 events,

recorded in 21 hours.

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