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Eye patches: Protein assembly ofindex-gradient squid lensesJ. Cai,1 J. P. Townsend,2 T. C. Dodson,1 P. A. Heiney,1 A. M. Sweeney1*

A parabolic relationship between lens radius and refractive index allows spherical lenses toavoid spherical aberration. We show that in squid, patchy colloidal physics resulted froman evolutionary radiation of globular S-crystallin proteins. Small-angle x-ray scatteringexperiments on lens tissue show colloidal gels of S-crystallins at all radial positions. Sparselens materials form via low-valence linkages between disordered loops protruding fromthe protein surface. The loops are polydisperse and bind via a set of hydrogen bondsbetween disordered side chains. Peripheral lens regions with low particle valence formstable, volume-spanning gels at low density, whereas central regions with higher averagevalence gel at higher densities. The proteins demonstrate an evolved set of linkers forself-assembly of nanoparticles into volumetric materials.

Maxwell showed that a “perfectmedium” ina spherical lenswould require a parabolicrelationship between radial position andrefractive index. This optical design hasevolved in parallel in both fishes and deca-

pod squid (1, 2), because in the light-limitedocean, this strategyoptimizes sensitivity andacuity(Fig. 1A) (3). Here, we describe the physical andmaterial mechanisms underlying the evolutionof this medium in squid.In amorphousbiologicalmaterials suchas lenses,

the concentration of material in aqueous cellularfluiddetermines the refractive index. The squid lensis cellular, so to a first approximation, it might bepossible to build a graded-index lens from proteinsolutions in anarray of cells inwhich each cell has ahigher concentration than the cell next to it. How-ever, dissolved proteinswould not likely result in atransparent lens. Most proteins interact attract-ively, such that aging of these solutionswould leadto aggregation and light scattering. At some con-centrations, thermal motion can also cause lightscattering (4, 5). Any aging is especially problematicbecause squid lensproteinsdonotundergo renewal:Ribosomes andnuclei are strongly light scatteringand are expelled from the developing cells (6).S-crystallins are the set of proteins that con-

stitute the refractive material in the squid lens;they are all close variants of the glutathioneS-transferase (GST) enzyme (7). This group of pro-teins has experienced episodes of strong positive(i.e., directional) evolutionary selection relativeto GST, suggesting that the many similar geneticcopies in fact serve different functional roles (8).One of themost obvious but unexplained featuresof S-crystallins is a pair of unstructured peptideloops protruding from the folded, globular sur-

face of the protein that bear little sequence sim-ilarity to other proteins (7, 8). These disorderedsequences are encoded at the center of the linearamino acid sequence and the protein folds oneither side of this central disordered region. Be-cause S-crystallins are dimeric, the rotational sym-metry of the dimer results in a neighboring pair ofloops protruding from one end. The lengths ofthese loops and the surface charges of the proteinsin the group vary (8).The thermodynamic behavior of protein mix-

tures is typically rationalizedusing thermodynamictheories for isotropicparticles (9, 10). These theories,

however, cannot account for the observed absenceof S-crystallin density fluctuations throughout thelens. We find that “patchy colloid” theory (11) canaccount for this apparent paradox of a gradient ofprotein volume fractions from 0 to 1 that escapesaging and local density fluctuation at all points inthegradient. This theory considers the interactionsof colloids, particles that are much larger thanatoms but small enough to undergo thermal col-lisions. The particles are considered “patchy” be-cause they interact throughhard-sphere repulsionplus attractive potentials that are localized to afew angularly small patches on the surface (11, 12).A surprising prediction of patchy colloid theoryis that as particles’ average valence (the averagenumber of patches per particle) approaches two,stable liquid-like materials form at arbitrarilylow densities (11, 13). Conversely, as the averagevalence of the particles increases, theminimumdensity at which the system will gel can also becontrolled (12, 13).

ResultsLens gradient

The relationship that Maxwell described betweenradial position and refractive index is shown herefor a spherical lens that focuses an aberration-free image for a single wavelength onto the retina(Fig. 1B) (1, 14).

nðrÞ ¼ nc1þ ncne � 1

� �r2

ð1Þ

Here, n(r) is the index at the dimensionless, frac-tional radial position r,nc is the index at the centerof the lens, and ne is the index at the peripheraledge of the lens (15). In fish and squid lenses, ncapproaches the theoretical maximum for dry

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1University of Pennsylvania, Department of Physics andAstronomy, Philadelphia, PA, USA. 2University ofPennsylvania, Department of Biochemistry and Biophysics,Philadelphia, PA, USA.*Corresponding author. Email: alisonsw@physics.upenn.edu

0 0.2 0.4 0.6 0.8 1

1.35, 0.06

1.45, 0.39

1.55, 0.71

lens radius (fraction)

refr

activ

e in

dex,

vol

ume

frac

tion 1.60, 0.87

1.50, 0.55

1.40, 0.23

Fig. 1. Relationships between lens radius, refractive index, protein structure, and networkstructure. (A) In situ photograph of a decapod squid showing spherical, gradient index lenses. (B) Lensradius versus refractive index, with an overlay showing the relationship between lens radius andthe color-coding used in this work to identify discretized tissue samples (blue for r < 40%, green for40% < r < 60%, orange for radii 60% < r < 80%, and red for r > 80%).

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protein (~1.6), and ne is close to that of theseawater in which the lens is immersed (~1.34)(14, 16).We independently characterized the density gra-

dient in the squid lens and verified three premises:(i) that it is an increase in S-crystallin concentra-tion alone, not a change in average amino acidrefractive increment, that causes the observedrelationship between radius and index; (ii) thatthe shape of this relationship is consistentwith thedescription in Eq. 1; and (iii) that the lower andupper bounds of the index range are 1.33 and1.62, giving a protein packing fraction (F) of 0.04to ~1.0 (8, 15, 17). To partition the continuous den-sity gradient of the lens into an experimentallytractable number of samples, we dissected tissuefrom individual lenses into four concentric sections,with the outer edge of each subsample extendinginward from fractions of roughly 100, 80, 60, and40% of the total lens radius (Fig. 1B). We refer tothese concentric tissue samples as the 100, 80, 60,and 40% layers, and results from these samplesare color-coded with red, orange, green, and blue,respectively, in the figures.

RNA sequencing

Given the age of extant S-crystallin studies andsubsequent improvements in sequencing tech-nologies, it was important to ensure that we hadcaptured the full range of S-crystallin genetic di-versity expressed in the squid lens (17–19). There-fore, we sequenced transcriptomes ofmature lenstissue fromDoryteuthis pealeii.Our Illumina RNA

sequencing (RNA-seq) resulted in 65.8million paired-end reads for the 100% layer and 88.6 millionpaired-end reads for the 60% layer. After assem-bly, we found 53 unique S-crystallin transcripts.The predicted protein sequences are very similarto known S-crystallin sequences, with 52.0 ±15.0% amino acid identity and 60.9 ± 12.9% sim-ilarity to Lops8, an archived S-crystallin fromLoligo opalescens chosen for comparison (GenBankU19296.1) (18). In the 53 unique S-crystallins inthe transcriptome, we identified 43 unique loopsequences that varied in length from3 to 110 aminoacids (Fig. 2A).Ninety percent of the residueswithinthe set of unique loops are algorithmically pre-dicted to be disordered in solution and are likelyto encode an unstructured region of the proteinpolymer extending from the folded body of thehomodimeric protein (8, 19, 20).

Molecular weight characterization bygel electrophoresis

Weused sodiumdodecyl sulfate polyacrylamidegel electrophoresis (SDS-PAGE) to characterizethe protein molecular weight distribution as afunction of lens radius. At all radial positions inthe lens, more than 95% of the total protein wasfound in two broadmolecular weight classes con-sistentwith S-crystallinmonomers, onewith aver-age molecular weight ~24.5 kDa and the otherwith averagemolecular weight ~26.5 kDa (Fig. 2B).There are also two minor bands in each sample,one at 32 and another at 36 kDa, consistent withS-crystallins from our transcriptome data with

~100 residue-long loop sequences (Fig. 2B). Themolecularweight differences in SDS-PAGEare con-sistent with translations of our lens transcriptome,such that differences in S-crystallin molecularweight with lens radius are likely due to differentloop composition with lens radius.We performed a deconvolution of our SDS-

PAGE data by modeling each migration patternas a sum of Gaussian contributions from individ-ual proteins withmolecular weights encoded byfull-length sequences obtained fromRNA-seq (15).This analysis shows that although the ratio of thetwomajorpeaks centeredat 24.5 and26.5 kDa (dueto the presence of short and long loops, respectively)shifts continuously toward larger proteins as afunction of increasing radius, the underlyingmix-ture of protein sequences associatedwith this shiftis complex, not the result of a binarymixture of afew long- and short-loop sequences (Fig. 2B). Thethird peak on the gel, due to proteins with ~100amino-acid-long loops, is a minor constituent ofthe periphery, reaches a maximum of 5% totalprotein at a relative radial position of 0.36, andis also present as 5% of total protein in the core.Proteinswith very short loops are highly abundantin the core (34% of total protein) but a minor con-stituent in theperipheral layer (3%of total protein).

Small-angle x-ray scattering

We used small-angle x-ray scattering (SAXS) tounderstand the spatial structure of S-crystallinswithin the squid lens. The scattering intensity asa function of wave vector, I(q), was found to be

Cai et al., Science 357, 564–569 (2017) 11 August 2017 2 of 6

Fig. 2. Loop sequences and their estimated relative abundance asa function of lens radius. (A) Unique loop-encoding sequences asdetermined by lens RNA sequencing and the relative abundance of proteinsof different molecular weights. Parentheses show the number of aminoacids in the sequence and its molecular weight in kilodaltons. Sequence textis colored to correspond to peak decomposition in (B). (B) SDS-PAGEof lens samples taken from different radial positions of the lens and anestimated abundance of components of different loop molecular weights.

The gray curve shows both the raw SDS-PAGE staining density and thesum of the curves in the fit (the two are similar to within the width ofthe line). The colored regions show the estimated abundance of a givenmolecular weight component within a sample. Images of protein showthe predicted homology model structure of an S-crystallin in a givenmolecular weight class (isoforms with long loops in red, short loops in blue,and with 100–amino acid loops in orange; yellow indicates unstructuredregions of the proteins).

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very similar for each layer of the lens, even thoughthe packing fraction of the layers systematicallychanges fromF = 0.05 toF ≈ 1.0 (Fig. 3A). In allsamples, at small wave vector q = 4p sin(q)/l,where q is the half angle between the x-ray beamand the detector, the scattering intensity for alllayers decreases with increasing q. There werethree major features also observed in scatteringfrom all radial positions within the lens: a broad,lowpeakbetween0.01Å−1 95%of the lensmaterial. Tissuefrom intermediate radial positions resulted in asystematic gradient between these two extremes

(figs. S1 and S4A). SAXS characterization of thesupernatants from each radial position revealedstructures consistent with folded protein at highq but with a relationship of S(q)ºq−1.5 between9 × 10–3 Å−1 ≥ q ≥ 4 × 10–3 Å−1, the minimum qexperimentally accessible (figs. S2 and S3). Thisresult was independent of the salt content of thebuffer; the result was also independent of thefinal concentrationof protein in the fluid, in a rangefrom~10mg/mL (F = 1.4 × 10–2) to ~0.05mg/mL(F = 1.1 × 10–4), theminimumatwhich SAXSdatawere meaningful (fig. S4). A structural fit to theseSAXS data using the algorithmAMBIMETER pro-duced a low-ambiguity result that these solutionscontain pairwise-linked chains of S-crystallin pro-teins (21). Patchy colloid theory gives insight tothis behavior: In patchy systems, dilution will notcause a transition from glassy to isolated particles,as is the case for isotropic particles (9, 10), butinsteadwill cause a transition froman equilibriumgel to an equilibriumpercolating/cluster fluid (13).This particle assembly upon dilution meant

that it was not possible to measure a form factorin the usual manner. Therefore, we calculated aform factor of isolated S-crystallin dimers usingatomic positions taken fromS-crystallin homologymodels (15). The predicted form factors of allS-crystallin homodimers are similar: They are

flat at small values of q < 0.05 Å−1, then decreaseto aminimumnear q=0.17 Å−1, with aminor peakat q ≈ 0.21 Å−1 (Fig. 3A).

Structure factor

The structure factor, S(q), is a reciprocal-spacerepresentation of the interactions betweendefinedparticles in a sample, foundby dividing the overallscattering of a sample by the form factor. TheFourier transform of the structure factor then be-comes the pair-distribution function of the par-ticles defined by the form factor. We calculatedthe structure factor of the lens tissue using thetotal SAXS scattering intensity and the averageof the calculated form factors from individualS-crystallin dimers. This structure factor was alsofound to share a few prominent features for allradial positions of the lens: a strong peak in thestructure factor at q=0.15Å−1, a trough at 0.03Å−1<q < 0.1 Å−1, and at q < 0.01 Å−1 a relation D(log I)/D(log q) of about –2.3 (Fig. 3B).The most prominent peak in the structure fac-

tors at q ≈ 0.15 Å−1 corresponds to the real-spacesize of the S-crystallin dimer. This suggests thatthe structure factor of all regions of the lens isdominated by pairwise dimer-dimer interactions.This peak shifts toward higher q toward the centerof the lens,meaning that the real-space pairwise

Cai et al., Science 357, 564–569 (2017) 11 August 2017 3 of 6

Fig. 3. SAXS, DAMMIF structures, and modeled networks of particles. is the average protein coordination number. (A) X-ray scatteringintensity as a function of q, I(q). Measurements from different radial portionsof the lens are indicated by color. Gray traces show the calculated formfactor of isolated S-crystallin dimers. (B) Structure factors of differentconcentric regions of the lens, calculated using I(q) and the calculated formfactor shown in (A). (Inset) Peak position associated with particle pairwiseinteractions in numerical simulation [top, data from (22)] and experimentallymeasured in this study (bottom). The peak associated with pairwiseinteractionsmoves toward higher q as increases whenF is held constant.

(C) Structure factors of simulated branching networks of particles withcoordinate numbers predicted to exist in the squid lens. (D) RepresentativeDAMMIF predictions of lens material structure, calculated using the SAXSdata in (A), as a function of lens radius. Scale bar applies to all panels of (D).Individual S-crystallins are colored according to radial position, and predictedlinks between S-crystallins are colored yellow. (E) Representative structuresfromnetwork simulations,whose structure factors are shown in (C). Scale barapplies to all panels of (E). About 10,000 particles were included in thecalculation of structure factor; a few hundred particles from each simulationare shown here in a box of the same volume for each simulation.

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distance decreases from the periphery to the coreof the lens. Measurements on samples from dif-ferent lens radii also shared aminimum in struc-ture factor at q ≅ 0.05 Å−1 that increased withdecreasing lens radius. This relationship is sim-ilar to previous numerical work, which found thatthis peak in S(q), indicating pairwise interactions,shifted to the right with increasing numbers ofcontacts betweenproteins (coordination numberor ) (Fig. 3B, inset) (22).The broad feature in structure factor between

0.01 Å−1 < q < 0.03 Å−1 could be due to a few, pos-sibly interacting, phenomena. First, there could belocal swelling of the gel due toweak vanderWaals,electrostatic, hydrophobic interactions, orwatermi-gration within the lens (23). This feature could alsoindicate complex,multiparticlenodeswithin thepro-tein network, consistentwith those observed in sim-ulations (22). Samples fromall regions in the lensalsohadsimilar structure factors in the region0.006Å−1<q < 0.01 Å−1, where the signal exhibited a slope ofslightly more than –2 in a log-log plot, consistentwith expectations for a percolating network (24).

Dilution and characterization of networkcoordination number

Weobserved that when tissue fromdifferent radialpositions was diluted to a volume fraction of 0.01and then centrifuged, twomaterials formed: a pro-

tein fluid and a pellet (fig. S1). As described above,the sparse phase is a percolating protein fluid (figs.S2 to S4). Both the relative amount of protein inand thedensity of the pellet increasedwithdecreas-ing lens radius (Fig. 4A). In samples taken from theperiphery of the lens, the pellet was a soft, volume-spanning translucent gel, whereas the core of thelens formed a white powder (fig. S1). Because allS-crystallins are extremely hydrophilic (meangrandaverageof hydropathy indexper sequenceof –5.61±0.07), this variation in pellet formation is due todifferent protein-protein interactions at differentradial positions of the lens, not differences inprotein-water interactions (25). Except for the ex-treme peripheral edge of the lens, the pellet thatformedwas always less dense than the lens tissuethat went into the sample, even after accountingforpore space of volume fraction0.35 in thepowderpellets. This result suggests that a phase or statetransition of S-crystallins occurs upon dilution ofthe native tissue (Fig. 4, A to C, and fig. S1).This phase or state transition upon dilution al-

lowed us to explore the intrinsic average coordi-nationnumber,, of the particles as a functionof lens radius (11). Given the high sequence poly-dispersity present at every radial position in thelens (Fig. 2), a polydisperse set of effective protein-protein bond temperatures must also be present.If this set of effective bond temperatures spans the

spinodal line for the system, the phase diagrampredicts that upon dilution the proteins will sep-arate into a sparse phase containing the “high-temperature” (low bond energy) particles locatedabove the spinodal line and a dense material con-taining the “low-temperature” (high bond energy)particles (Fig. 4B) (11). The low-temperature par-ticles, when relocated to the unstable region of thephase space under the spinodal line, must thenreequilibrate to a density dictated by the averagevalence of this subset of the original total proteinmixture (Fig. 4, B and C). This phenomenon al-lowed us to estimate for the pelletmaterial,given its density. We used the measured particledensity in each material, the inferred of thepellet, and the fact that in the sparse phase, theparticles are in chains with = 2 to calculate as a function of radial position. We foundthat in the periphery of the lens was slightlygreater than two and increased toward the coreof the lens to a maximum near six (Fig. 4A).

Monte Carlo analysis

Weused the algorithmDAMMIF, aMonte Carloapproach, to predict a coarse-grain real-space struc-ture given SAXSdata (26). For the outermost layerof the lens, this result shows a network of 3- to5-nm-diameter spheres that are connected by pairsof “arms”protruding fromthebodyof an individual

Cai et al., Science 357, 564–569 (2017) 11 August 2017 4 of 6

Fig. 4. Experimental data mapped to patchy colloid theory. (A) Volumefraction (F) of the intact lens, of the dense material after dilution,percent total protein in the dense state, and calculated resultingfrom this experiment, as a function of lens radius. Each symbol representsone measurement, and three lenses were sampled for each curve.(B) Schematic showing how a polydisperse set of effective bondtemperatures in a patchy colloidal system, when diluted, will phase-separate. Vertical line indicates the likely range of effective bondtemperatures (T) in a given mixture in the lens, and the filled red and blueshapes indicate a possible set of “high” and “low” effective temperaturebonds in the system. Arrows indicate how high-temperature particles inthe system will reequilibrate into a percolating fluid, while low-temperatureparticles are in an unstable part of the diagram and reequilibrate into adense material. (C) Experimental data for the lens system plotted in thecontext of patchy colloid theory. Likely bond temperatures for the systemare shown in the height of the colored squares, whereas the densityspanned by each experimentally characterized layer is shown in the width.Spinodal lines from theory (11) are shown in shades of gray. Circlesunder the x axis indicate the densities of the dense materials producedupon dilution; the radius from which samples were taken is shown inside.

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sphere (Fig. 1C). Most of the ~5-nm spheres show arotational symmetry consistent with dimers oftwo structurally similar monomers. The distancebridged by these arms is typically ~40 Å, and thearms leave individual ~5-nm spheres at anglesranging from60° to 120°with respect to eachother.The average nearest-neighbor distance betweenthe centers of two bridged proteinswas 75Å in the100% layer and 60 Å in the 80% layer. These pre-dictions are consistent with sequencing data andhomologymodels that S-crystallins have extendedloops protruding from the two pairs of helicesforming the core of the folded structure (Figs. 2B,3D, and 5), with the loops linking the bodies of theproteins into a network of spherical particles.Because DAMMIF is a Monte Carlo technique,

each calculation generates a likely but not uniquestructural fragment, given a single SAXS measure-ment. However, the volume-spanning material inthe lens ismuch larger than the ~100-nm real-spacespanaccessedby SAXS. Therefore,we generated anensemble of 100DAMMIFoutputs for each layer ofthe lens and treated theseas ensemblesof fragmentsof the larger protein network forming the lens.

This approach generated an independent es-timate of as a function of lens radius andshowed how emerges from S-crystallin sec-ondary and tertiary structure. In the ensemblesfrom the 100 and 80% layers, we observed 5-nmproteins connected by thin bridges that vary inlength from 50 to 400 Å to a minimum of oneand amaximumof four other dimers (Fig. 3D). Inthe 100% layer, the majority of particles have twocontacts, with the pair of unstructured loops froman S-crystallin dimer forming contacts with loopsfrom other dimers. A few particles have a thirdcontact resulting from loop-body interactionwithanother dimer. The 80% layer had a greater propor-tion ofM = 3 nodes in the network than the 100%layer. In the 80% layer, a second form of M = 3interactions appears: loops of length ~100 aminoacids bifurcate to form a Y-shaped structure. ThisY-shaped structure results in two points of con-tact within a single loop, each capable of contact-ing the end(s) of another loop (Fig. 3D).These structural ensembles showed =

2.19 for the 100% layer and = 2.45 for the80% layer, and a permutation test showed the dis-

tribution of M to be different between the twoensembles. The dilution experiment found=2.01 to 2.22 for the 100% layer and = 2.22 to3.11 for the 80% layer (Fig. 4A), so two indepen-dent estimates of agree.At samples from lens radii of 60 and 40%, the

predicted structures were dense, with contacts be-tween particle surfaces occupying much of thesurface area. The 60% layer prediction showed5-nm-thick ramifying lamellae, consistent with in-terconnected sheets of S-crystallin dimers (Fig. 3D).In the 40% layer prediction, protein completelyfilled the volume, consistent with a solid containinglittle or no bulk water (Fig. 3D). The dilution anal-ysis described above found that = 3.1 to 3.9for the 60% layer and = 3.9 to 5.8 for the40% layer (Fig. 4A), qualitatively consistent withthese structural predictions.

Network-of-spheres simulations

As an aid to visualization,we simulated branchingchains of particles, generating nonequilibriumstructures with qualitative similarity to those inour SAXS data, and calculated the resulting struc-ture factors (15). We added spheres at arbitraryangles to a growing chain of spheres, with the ad-dition of two spheres causing a bifurcation in thechain (Fig. 3E). We chose bifurcation frequenciesso that average particle valences were similar tothose in the lens. For all simulated , therewas a peak at q = 0.15 Å−1 corresponding to theparticle-particle nearest-neighbor distance, a mini-mum in structure factor between0.03 < q

studymeasured theGibbs free energy of hydrogenbonding between hydrated strandlike peptides toaverage2.6 kcal/H-bond/mol (27). For links consist-ing of 3 to 8H-bonds at 10°C,T=0.08 to 0.03. Thisestimate of T applies to the 100 and 80% radiusregionof the lens,where linkages betweenproteinsare primarily between disordered loops.At radial positions less than 60%, proteins form

ramifying lamellae and then a proteinaceous ma-terial with no bulk water. These structures areconsistent with patchy systems in which patcheshave become so large and/or numerous that theirinteractions approach those of isotropic, sphericalparticles (Figs. 3D and 4D). Here, the energies ofprotein-protein binding are likely similar to thoseinvolved in protein docking, in the range of 10 to20 kcal/bond/mol, so the lower bound for T forthese interactions is ~0.01 (28).

Discussion

Our data show that at all radial positions andevery possible density, structure in the intact squidlens are dominated by attractive interactions be-tween S-crystallin dimers, a result that is incon-sistent with isotropic potentials, because thesesystems will undergo liquid-liquid phase separa-tion and opacification at some point (29).From a materials perspective, this lens could

in principle be built from a single mixture of par-ticles with M slightly greater than two, since anysystem to the right of the spinodal line for =2.1 in the patchy colloid phase diagrammay forma volumetric material with low density variation.However, our data show that changesmono-tonically with lens radius, from aminimum neartwo in the periphery to a maximum near six atthe core of the lens.There is a biological rationale for the lens evolv-

ing an array of rather than simply using onemixture with ≈ 2.1 at many different den-sities. New lens cells must be filled gradually withprotein through the process ofmRNAs and aminoacids diffusing to large ribosomes, with full-lengthproteins then diffusing away from the ribosome.In any cell whose proteome-determined al-lowed for gelation at a density lower than theappropriate endpoint for a given radial position,protein synthesis would be arrested prematurely.Patchy colloidal physics allows for a cellularmech-anism by which lens cells gel near the opticallyappropriate endpoint density for a given radialposition. The cellular transcriptomes systematicallytitrate S-crystallin isoforms as changes as afunction of lens radius.We hypothesize that a cellthen passively ceases protein synthesis at the ap-propriate density, because upon gelation, proteinsynthesis would simply stop due to inability oflarge polymers (mRNAs and newly transcribedprotein) to diffuse through the material.Given that, in principle, one protein sequence

could encode one valence in the lens, requiringa minimum of six S-crystallin sequences, therewere a large number of unique S-crystallin se-quences encoded by the genome, and the loopsencoded by these sequences that form the link-ages between proteins also had high chemical

polydispersity. We speculate that this high degreeof polydispersity in loop sequence and subsequentlinker interaction dynamics may both avoid kinetictraps during nucleation and reduce the entropiccost of forming a volume-spanning network (30).This set of linker sequences generated by evolu-tion may then help inform experimental attemptsto exploit the self-assembly principles revealed bypatchy particle theories.We observed that the difference between the

original density of the lens and the density of thepellet formed from loweffective temperature bondsincreased from near zero at the periphery to afactor of two at the core (Fig. 4, A to C). At the coreof the lens, the pellet after a dilution-inducedphase/state transition had a packing fraction near0.5, indicating for the system near six, orsquare-lattice-like packing, whereas the intact lenscore has little or no bulk water and a packingfraction approaching 1.0 (consistent withM= 12).We speculate that in the squid embryo, these orig-inal,most-central cells in the lens structure initiallygel near the lower square-lattice packing fractionof0.5, consistentwith constituentproteinsof≈6. Then, as new cells are added to the organ pe-riphery during lens growth, thenewermaterialwillbe both more compliant due to a lower coordina-tion number and have a higher charge densitydue to the increasingly positive surface charge ofthe proteins in the peripheral layers (8). Both ofthese factors will tend to cause water to migrateoutward from the lens core as the structure grows,systematically increasing the density of centralregions of the lens with the animal’s age and sizeand potentially resulting in a near-dry lens corein the mature organ.Our data also describe a gradual “inside-out”

mechanism for evolving a gradient index lensfrom a single protein fold. In this view, an initialprotein closely related to enzymatic GST duplicatedfor lens expression and formed a high-densitycolloidal gel through near-isotropic interactions.Selection pressure for a gradient index then re-sulted in proteins with less-isotropic interactionsand the resulting lamellar structures observedin extant lenses, consistent with patchy colloi-dal systems of intermediate average valence (31).Further selection on S-crystallins resulted in anunstructured loop encoded in anovel exon thatwasable to undergo flexible, nonspecific hydrogen-bonding interactions with other similar loops.These loops, coupled to the increase in positivecharge on the folded, spherical surfaces of the pro-tein, represent an evolutionary innovation of aprotein particle able to enforce a coordinate num-ber ofM = 2. With this loop-binding innovation,squid lenses were then able to exploit the entirephysics of the patchy colloid phase diagram, andthe thermodynamically stablematerials with lowdensity fluctuation that result from this physics.It is also possible that this patchy colloidal per-spective could provide insights into still poorlyunderstood aspects of vertebrate lens biology. Inparticular, the polydisperse nature of alpha crys-tallins in the low-density regions of the vertebratelens have been a puzzle; even in solution, they ap-

pear to interact via “tentacles” inways that are hardto specifically characterize (32). It is possible thatthey are also acting as low-valence patchy colloidalgels in vivo, as is the case for squid S-crystallins.

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ACKNOWLEDGMENTS

We are grateful to R. Kamien and E. Eiser for useful discussions andto D. Fox for assistance with data visualization. S. Johnsen’s commentsimproved the manuscript. We are also grateful to an anonymousreviewer whose thoughtful questions improved the work. Financialsupport was provided by the National Science Foundation MaterialsResearch Science and Engineering Center DMR11-20901 to P.A.H.;by the Packard Foundation Fellowship for Science and Engineering,Sloan Foundation, NSF-1351935, Kaufman Foundation, and Universityof Pennsylvania to A.M.S.; and by the Department of Defense’s NationalDefense Science and Engineering Graduate fellowship program toT.C.D. SAXS data are archived at Small Angle Scattering Biological DataBank under accession numbers SASDCQ5 to U5, and RNA-seq dataare archived at GenBank under SRR5528268–9.

SUPPLEMENTARY MATERIALS

www.sciencemag.org/content/357/6351/564/suppl/DC1Materials and MethodsFigs. S1 to S4References (33–42)

23 October 2016; resubmitted 6 February 2017Accepted 7 July 201710.1126/science.aal2674

Cai et al., Science 357, 564–569 (2017) 11 August 2017 6 of 6

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Eye patches: Protein assembly of index-gradient squid lensesJ. Cai, J. P. Townsend, T. C. Dodson, P. A. Heiney and A. M. Sweeney

DOI: 10.1126/science.aal2674 (6351), 564-569.357Science

, this issue p. 564; see also p. 546Scienceprinciples of patchy colloid theory to construct a self-assembling, complex optical device.particles to counter spherical aberration (see the Perspective by Madl). Thus, the evolutionary process has used thelenses of squid eyes have an internal structure containing a set of globular proteins that form a gradient of colloidal

show that theet al.problem can be overcome if the refractive index of the lens is varied according to the curvature. Cai When light rays pass through a curved lens, greater refraction at the edges can distort the resulting image. This

Squid lenses beat spherical aberration

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REFERENCES

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