Science - USA (2022-04-08)

(Fig. 4C) encircle the EP. When the system is
initially in the state yþ

(^) ¼ðÞjicþjiv =pffiffiffi 2 ,
which is the equal to the superposition of the
cavityjicand vibrationaljiv modes, the final
state after a closed loop encircling the EP be-
comesjiy ¼ðÞjicjiv =
ffiffiffi
2
p
, which is orthog-
onal to the initial state yþ

. A second loop
around the EP brings the system back to its
initial state yþ
apart from a geometrical
phase. As seen in the Bloch sphere (Fig. 4D),
these two loops around the EP cut the Bloch
sphere directly in half and correspond to a
solid angle of 2p, which in turn implies that
the acquired geometrical phase isp(i.e., the
geometrical phase is the half of the solid angle
enclosed by the curve connecting the initial
and final states).
We have demonstrated a non-Hermitian
optical device to study EP in the collective
interaction of vibrational modes of organic
molecules with a THz field. Through use of
fully electrically tunable independent knobs,
we can steer the system through an EP that
enables electrical control on reflection topol-
ogy. Our results provide a platform for the to-
pological control of light-matter interactions
around an EP, with potential applications rang-
ing from topological optoelectronic devices to
topological control of physical and chemical
processes.

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ACKNOWLEDGMENTS

Funding:This work was funded through the European Research Council

through ERC-Consolidator grant 682723, SmartGraphene (C.K.), the

Air Force Office of Scientific Research (AFOSR) Multidisciplinary

University Research Initiative (MURI) Award on Programmable systems

with non-Hermitian quantum dynamics (Award FA9550-21-1-0202)

(S.K.O.), and the Air Force Office of Scientific Research (AFOSR) Award

FA9550-18-1-0235 (S.K.O.) A.P. acknowledges support from the

European Commission under the EU Horizon 2020 MSCA-RISE-2019

programme (project 873028 HYDROTRONICS) and from the

Leverhulme Trust under the grant RPG-2019-363.Author

contributions:M.S.E., C.K., and S.K.O. conceived the idea. M.S.E.

synthesized the graphene samples and fabricated the devices. M.S.E.

and C.K. performed the experiments. S.S. and S.K.O. performed the

simulation and developed the theory. N.K., G.B., and K.W. helped with

the measurements. A.P. and T.B.S. provided theoretical support.

M.S.E., S.K.O., S.B., and C.K. analyzed the data and wrote the

manuscript with input from all the authors. All authors discussed

the results and contributed to the scientific interpretation as

well as to the writing of the manuscript.Competing interests:

The authors declare no competing financial interests.Data and

materials availability:All data discussed in the main text

and code used in the simulations are available at Zenodo ( 30 ).

SUPPLEMENTARY MATERIALS

science.org/doi/10.1126/science.abn6528

Materials and Methods

Supplementary Text

Figs. S1 to S13

References ( 31 – 35 )

10 December 2021; accepted 10 March 2022

10.1126/science.abn6528

BIOMATERIALS

Mineralization generates megapascal contractile

stresses in collagen fibrils

Hang Ping1,2, Wolfgang Wagermaier^2 *, Nils Horbelt^2 , Ernesto Scoppola^2 , Chenghao Li^2 , Peter Werner^2 ,

Zhengyi Fu^1 *, Peter Fratzl^2 *

During bone formation, collagen fibrils mineralize with carbonated hydroxyapatite, leading to a hybrid

material with excellent properties. Other minerals are also known to nucleate within collagen in vitro. For

a series of strontium- and calcium-based minerals, we observed that their precipitation leads to a

contraction of collagen fibrils, reaching stresses as large as several megapascals. The magnitude of the

stress depends on the type and amount of mineral. Using in-operando synchrotron x-ray scattering,

we analyzed the kinetics of mineral deposition. Whereas no contraction occurs when the mineral deposits

outside fibrils only, intrafibrillar mineralization generates fibril contraction. This chemomechanical effect

occurs with collagen fully immersed in water and generates a mineral-collagen composite with tensile fibers,

reminiscent of the principle of reinforced concrete.

B

iological hybrid materials such as bone

elegantly combine hard inorganic nano-

meter-sized minerals and soft organic

matrices into hierarchical architectures

to achieve specific properties and func-

tions ( 1 , 2 ). Such complex structures, ranging

from nanoscale to macroscale, result in supe-

rior mechanical properties of biomineralized

materials compared to their artificial counter-

parts ( 3 , 4 ). Collagen is the main constituent of

extracellular tissues in our bodies, from ten-

don and bone to skin and arterial walls. In bone,

collagen is reinforced by nanometer-sized par-

ticles of carbonated hydroxyapatite ( 5 , 6 ). Col-

lagen fibrils can also be infiltrated in vitro with

hydroxyapatite ( 7 – 9 ) and with other minerals

such as calcium carbonate ( 10 ), silica ( 11 ), or

iron hydroxides ( 12 ).

Effective prestressing strategies at the nano-

scale are known to strengthen many materials

and biominerals in particular ( 13 , 14 ). As an

example, local compressive or tensile stresses

caninteractwithcracksinmineralsandde-

flect them and consequently enhance the ma-

terials’toughness ( 13 ). Prestresses in natural

collagen-based tissues contribute substantially

to their overall mechanical properties ( 15 , 16 ).

Collagen molecules in bone contract in length

when dehydrated or under osmotic stress ( 16 ),

but how this is associated with mineral depo-

sition can only be speculated. The present work

showsthatthisislikelynotaspecificinter-

action with hydroxyapatite, because similar

effects were observed for a broad range of min-

eral types.

Intrafibrillar collagen mineralization can be

achieved in vitro by applying negatively charged

macromolecules that help the penetration of

fibrils by forming mineral-protein complexes.

These disordered mineral precursors, some-

times called polymer-induced liquid precursor

( 17 ), are known to penetrate collagen fibrils

and form mineral particles that resemble

those in vivo ( 7 – 9 ). We adopted this principle

for in vitro mineralization of a collagen sub-

strate with various minerals—SrCO 3 , SrWO 4 ,

SrSO 4 , CaF 2 , and CaCO 3 —and measured the

188 8 APRIL 2022•VOL 376 ISSUE 6589 science.orgSCIENCE

(^1) State Key Laboratory of Advanced Technology for Materials
Synthesis and Processing, Wuhan University of Technology,
Luoshi Road No. 122, Wuhan 430070, China.^2 Department of
Biomaterials, Max Planck Institute of Colloids and Interfaces,
Am Mühlenberg 1, 14476 Potsdam, Germany.
*Corresponding author. Email: wolfgang.wagermaier@mpikg.
mpg.de (W.W.); [email protected] (Z.F.); peter.fratzl@mpikg.
mpg.de (P.F.)
RESEARCH | REPORTS