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Physics and the cell

OCTOBER 2010

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Sponsor retains sole responsibility for content

Principles and methods from the physical sciences have long been applied

to questions in biology; however, the application of such principles to the

study of cancer biology has only begun to flourish. In the latter part of the

20 th century, and especially the last decade, advanced technologies have

fueled an unprecedented period of discovery and progress in the molecu-

lar sciences that promises to revolutionize cancer medicine. In 1999, the

National Institutes of Health Director, Harold Varmus highlighted this point

in his speech at the Centennial Meeting of the American Physical Societyby

stating, Biology is rapidly becoming a science that demands more intense

mathematical and physical analysis than biologists have been accustomed

to, and such analysis will be required to understand the workings of cells.

This issue of Nature Physics Insight Physics and the Cellreviews a number

of areas in which physical scientists are tackling biological problems relating

to cells and their interaction with their surroundings.

Likewise, the National Cancer Institute (NCI) has been exploring new and

innovative scientific approaches to better understand and control cancer bycapitalizing on advances in areas such as genomics and nanotechnology, and

ensuring that state-of-the-art foundational resources are broadly available

to all cancer researchers. In 2007, NCI Director, John Niederhuber and NCI

Deputy Director, Anna Barker initiated the Physical Sciences in Oncology

Initiative with the intent of building trans-disciplinary teams of scientists

that bridged the fields of physics, mathematics, chemistry, and engineering

with the areas of cancer biology and clinical oncology to examine cancer

using approaches that have not been followed in cancer research to date.

The NCI sponsored a series of three strategic think tanks to bring together

over 300 thought leaders from across these fields to ascertain how NCI could

more effectively engage the physical sciences in cancer research. One way

the Physical Sciences in Oncology Initiative is driving cancer research is

through the embrace of principles and methods from the physical sciences

to address confounding questions in cancer. Four thematic areas emerged

from these meetings in which physical sciences approaches and principles

could profoundly influence and improve our knowledge of cancer biology

over both spatial and temporal scales (Fig. 1).

Moreover, among the extramural participants, there was a consensus to

establish trans-disciplinary teams to overcome the traditional barriers (silos)

that have existed between these two scientific communities. In September

2009, the NCI Office of Physical Sciences-Oncology (OPSO) launched the

Physical Sciences-Oncology Centers (PS-OC) program (for more informa-

tion visit: ht tp://physics.cancer.gov/) awarding 12 specialized centers that

comprise a virtual network, bringing together expertise and resources to

enable the convergence of the physical sciences with cancer biology and

clinical oncology. Each PS-OC is led by a physical scientist together with a

senior investigator from the field of cancer biology or clinical oncology and

comprises an expert team of researchers from both these disparate fields

that cover the thematic areas described. Although the PS-OC program is still

in its infancy, we highlight successful achievements by PS-OC investigators

as well as demonstrate the potential impact of converging the physical

sciences with cancer biology (see back inside cover). The NCI anticipates

this initiative to foster the development of innovative ideas and new fields of

study based on knowledge of the biological and physical laws and principles

that define both normal and tumor systems.

The NCI OPSO, houses the PS-OC program, under the leadership of Jerry

Lee and Larry Nagahara. The PS-OC program staff members including Anna

Maria Calcagno, Sean Hanlon, Nastaran Zahir Kuhn and Nicole Moore assist

in the oversight and scientific management of PS-OC projects and encourage

interdisciplinary collaborations of investigators and researchers within the

PS-OC Network. On behalf of the entire PS-OC program staff, we hope you

enjoy this issue of Nature Physics Insight Physics and the Cell.

Figure 1.PS-OCs by Theme and Length Scale.

The PS-OCs (by PI and institution) are arranged by thematic area (Y-axis) and lengthscale (X-axis). Themes from top to bottom are: De-convoluting Cancers Complexity;

Information Coding, Decoding, Transfer, and Translation in Cancer; Evolution and

Evolutionary Theory of Cancer; Physics (Physical Laws and Principles) of Cancer.

Institution abbreviations: ASU: Arizona State University; Cornell: Cornell University;

DFCI: Dana-Farber Cancer Institute; JHU: Johns Hopkins University; MIT: Massachusetts

Institute of Technology; Moftt: H. Lee Moftt Cancer Center; NU: Northwestern

University; Princeton: Princeton University; Scripps: The Scripps Research Institute;

UCB: University of California, Berkeley; USC: University of Southern California; UTH:

University of Texas Health Science Center at Houston.

Larry A. Nagahara, Ph.D. Jerry S.H. Lee, Ph.D.

Anna Maria Calcagno, R.Ph., Ph.D. Sean E. Hanlon, Ph.D. Nastaran Zahir Kuhn, Ph.D. Nicole M. Moore, Sc.D.

National Cancer Institutewww.cancer.gov

Offi ce of Physical Sciences-Oncologyphysics.cancer.gov



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nature physics | VOL 6 | OCTOBER 2010 | www.nature.co/naturephyscs 725

insight | contents

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Aquick glance at the titles othe research papers in an

interdisciplinary journal suchas Nature or Science will probably tellyou that the languages o biologists andphysicists can be ar removed. Froma physical-sciences perspective, theabstract o a biology paper can soundlike a recipe or some truly unpleasantdish. Tis hardly encourages a physicistto read any urther. Yet physicists havehistorically played an important rolein developing many o the cornerstonetheories o modern biology and, althoughthe dichotomic view o the quantitativephysicist and the descriptive biologist

is not as true as it once was, it is certainthat some o the approaches common inphysics could provide urther insight andunderstanding in the uture when appliedto biological systems.

Biophysics is ar rom a new concept,but where does physics end and biologybegin? For a manuscript editor o a researchjournal at least, this is more than merely aphilosophical question: does a particularstudy belong in a physics or a biologyjournal? Tere is no doubt that, i there isa boundary at all, it is constantly shiingand depends very much on your individual

perspective. We would certainly welcomeyour thoughts.

But the question or now is: how do wemake problems in biology more accessible

to a modern physicist? Te aim o thisNature Physics Insight is to do just this witha ew areas o research rom contemporarybiophysics. It is customary to say in theintroduction to such a collection that thetopics covered are not exhaustive. Tis is, ocourse, particularly true in this case wherethe subjects could come rom anywherewithin the massive scope o the biologicalsciences. One criterion was a ocus onways physics can be used to understand thenatural process o the cell, rather than onthe many emerging techniques or probingcells optical tweezers, imaging and

microscopy or medical nanotechnologies or, to look at it in the other direction,technologies inspired by nature, or example,DNA electronics. But even excluding allthese exciting areas o research there are stillso many possibilities. We can only provide asmall cross-section, but we hope this tasterwill inspire you to read more: you mighteven be able to contribute to the feld, andperhaps more than you frst think.

Finally, we would like to extend oursincere thanks to our sponsor, the NationalCancer Institute, or their support. O course,Nature Publishing Group takes complete

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726 nature physics | VOL 6 | OCTOBER 2010 | www.nature.com/naturephysics

perspective | insight

phy hallngd by llAna-sunana smh

cll a h buldng blok of lf. ida adonally ald o hyal oblm a now hlng o

unal h omlx my.

Despite the act that the questionWhat is lie? has traditionally beenplaced in the realms o philosophy

and theology, it is clear that the naturalsciences have an important contribution tomake. Indeed, even though some aspects othis question may remain beyond rigorousscientic proo, much understanding o the

consequences o living has been acquiredthrough the hard work o generationso scientists working at the brink o ourcollective knowledge. Among the pioneerswere the natural scientists Tomas Young,Robert Hooke, Hermann von Helmholtzand Lord Kelvin, who began to promotephysics, physiology and biology asseparate disciplines. A new era or thescience o lie, however, began in 1905when Albert Einstein gave a quantitativeexplanation or Brownian motion, puttingthe long-standing discussion on themolecular nature o matter to rest. At the

same time, he set the cornerstone or thedevelopment o statistical mechanics.Once molecules became scientic

truth, the speculative discussion turnedto the content o the genetic code

and cells. Physicists too were inspiredby the problem: Max Delbrck andKarl Zimmer, together with geneticistNikolai imoee-Ressovsky, suggestedthe molecular nature o the genetic codein 1935 (re. 1), work that marks the birtho molecular biology. Stimulated by thisadvance, Erwin Schrdinger deduced

that the gene was an aperiodic crystalcomposed o a linear array o dierentisomeric components, as presented in his1944 bookWhat is Life?2. Tis book andDelbrcks physical approach inuencedmany. Among them was James Watson,a physicist turned biologist who in 1953,together with Francis Crick (anotherphysicist), was able to solve the structureo DNA on the basis o Rosalind FranklinsX-ray data.

Despite the early successes o thephysical approach, it is not entirelyevident that modern physicists can really

contribute to the question What is lie?.Neither is it evident that, beyond thedevelopment o ingenious experimentaltools, it is even a question or physics.But the observations o Schrdinger

immediately trigger the mind o aphysicist: It is by avoiding the rapiddecay into the inert state o equilibriumthat an organism appears so enigmatic,and Lie seems to be orderly and lawulbehaviour o matter, not based exclusivelyon its tendency to go over rom order todisorder, but based partly on existing order

that is kept up2

.

t dlg bologLie relies on energy consumption anddissipation. However, the conceptualramework or understanding theinteractions o subcellular and cell-like objects, with their very noisyenvironments, only started to emerge inthe past two decades, with the theory onon-equilibrium dynamics3. It was animportant realization that even i a systemis excited by an external orce in exactlythe same repeating ashion, the actual

driving orce in each cycle becomes adistribution because o uctuations. Tus,the amount o heat or work exchangedwith the bath is also characterized by adistribution. A true breakthrough came in

Active

networks

Vesiclesubstrate

adhesion

Artificial cell

Fg1| Minimal models or cellular structures. Let: Active networks composed o actin laments (green) crosslinked passively (purple) and actively

by motor bundles (brown). The motor bundles exert orces on laments in the direction o the red arrows. The elastic properties o these networks are

probed with a variety o rheological techniques. Right: Phospholipid vesicles interacting with a supported membrane. Both are decorated by unctional

molecules such as glycolipids (yellow), glycoproteins (purple) and adhesion proteins (red). I the adhesion proteins have counterparts in the opposing

membrane, adhesion domains composed o numerous bonds orm spontaneously. The contact zone between the two membranes can be observed by a

variety o techniques involving inverted microscopy. Middle: The combination o both active networks and vesicles with the addition o coupling proteins,

and active control o the whole, will lead to a more realistic model or the mechanoresponse and the rst articial cells.



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nature physics | VOL 6 | OCTOBER 2010 | www.nature.com/naturephysics 727

insight | perspective

1997 with the Jarzynsky equation, whichconnects equilibrium properties o asystem (the ree-energy dierence) and thedistribution o the non-equilibrium work4.

It is only natural that the rstconrmation o these undamentalphysical concepts came rom experiments

perormed in biophysics laboratories.A single RNA molecule was repeatedlyunolded and reolded by stretchingit in an optical trap5,6, demonstratingexperimentally both the Jarzynskyequation and the so-called Crooksuctuation theorem7. Te latter explicitlyrelates uctuations o an irreversibleprocess to those o the irreversible processin the opposite direction.

A class o generalized uctuationdissipation theorems was urthermoredeveloped that account or systemsdriven either away rom or between

non-equilibrium steady states8,9

. Tisormalism is becoming particularly useulas a tool or measuring orces in the non-equilibrium conditions typical o a cellularenvironment. In this way, torques producedby a single motor protein a molecule thatconverts chemical energy into mechanicalwork by hydrolysis o adenosinetriphosphate could be determined10.

how ll xlo Membranes, the cytoskeleton and theextracellular matrix provide the structuralintegrity o living cells. ogether, these

elements oer an eective scaoldor other smaller molecules, peptidesand proteins, to unction correctly.For example, the strong coupling obiochemical reactions to the spatialcoordination provided by membranes andthe cytoskeleton means that biologicalsignalling is subject to a plethora ophysical constraints. Indeed, manysignalling pathways involve proteindiusion and aggregation guided andregulated by these cellular structures.

One o the most striking exampleso coupling between biochemical

and biophysical pathways is in theviscoelastic behaviour o cells, whichboth determines and is determined bythe environment. In another importantadvance rom 1997, it was discovered thatthe adhesion o cells to the underlyingmatrix typically a complex polymernetwork such as collagen dependson the elastic properties o the matrix11.So matrices were associated withsmall adhesion domains (a domain is acluster o bonds between cell-membraneproteins and their receptors in the matrixor a neighbouring cell), whereas cellson sti glass substrates would develop

micrometre-sized adhesion patches andexert stronger orces12.

More recently, it was discoveredthat matrix elasticity drives humanmesenchymal stem-cell dierentiation,not only in terms o morphology butalso protein expression13. Bone-likecells develop on rigid matrices andneuron-like cells grow on so matricesthat replicate conditions in the brain.At intermediate stiness, the matrix

that imitates muscle environment ismyogenic and the polarized morphologyo muscle cells is obtained. A physicalspring model in which the mechanicalimpedance o the cell is matched to thato the matrix using a eedback loop14urther improved our understanding othese eects.

Whereas the previous exampledemonstrates the sensitivity o a single cellto the elastic properties o its environment,entire tissues can, in return, aect theenvironment. A tissue exerts contractileorces through adhesive contacts on

the extracellular matrix that modulatethe tension in the matrix itsel. By thismeans the inner homeostatic tension othe tissue is maintained. As homeostaticpressure can be associated with thebalance between the rate o cell death andthe rate o cell division and growth, theunction o the tissue may be aected bychanges in the environment. Recently, itwas proposed that homeostatic pressuremay play an important role in the earlystages o cancer development and its abilityto metastasize15.

Te implicit conclusion is that thestability and viability o the tissue is

related to the mechanical properties o theextracellular matrix. However, the relationbetween the response o a single cell andthe response o the tissue to changes inthe environment is not yet understood.Here, large-scale coordination o cellswithin the tissue is enabled by biochemicalsignalling, the role o which is, at present,equally elusive.

t boom- o

It is not within our reach to accuratelymodel the entire living cell, oreven an entire process such as themechanoresponse. Apart rom anexasperating number o degrees oreedom, the main difculty is theexistence o multiple (redundant)mechanisms that achieve the same eectthrough dierent biochemical pathways.Furthermore, the cell behaves dierentlyat dierent stages o its lie. It is thereorechallenging to distinguish betweenvarious contributions and arrive atreliable conclusions.

One successul means o circumventingthese problems is the so-called bottom-up approach, which was initiated inphysics laboratories in the 1980s and isnow a well-accepted method in all obiophysics16. Te principal idea is to buildmodels rom a limited number o basiccomponents. Once these components areexperimentally and theoretically analysedin detail, the next ingredient is addeduntil cell-like structures are created in acontrolled ashion. Tis type o approachnot only generates new bio-analogousmaterials that could potentially be usedbeyond the cellular context, but also drives

14

12

10

8

6

4

a b

4 m

h (nm)

Fg2| Specic adhesion o vesicles. , Reconstruction o the vesicle membrane height prole,

h(x, y), on adhesion, by ormation o neutravidinavidin bonds, imaged using refection intererence

contrast microscopy. b, Corresponding distribution o fuorescently labelled neutravidin in the substrate

membrane. Despite the initial uniorm distribution o mobile binders in both the vesicle and the

substrate membrane, a ring-like adhesion domain is established as a result o two coupled aggregation

processes. Figure reproduced with permission rom re. 25, 2010 EPL.



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perspective | insight

the development o experimental andtheoretical methods.

Apart rom the physical implications,the bottom-up approach is useul in

the context o understanding biologicalsystems, because it provides a detaileddescription o a systems parts and theircross-talk. For example, the comparisono cells and bottom-up models providesnew insights into the modulation othe biophysical properties o cells bybiochemical stimuli, such as hormonesand mutations. Te hope is thatbiophysical and biochemical aspects canbe consequently distinguished. As a resulto a bottom-up approach, deeper insightinto both established mechanisms and newmechanisms may arise. In summary, the

bottom-up approach enables the design obiological unctions, although activity inthis direction is still in its edgling stage.

cll o o omlx mlOne o the rst problems addressedby the bottom-up approach was thedetermination o the viscoelasticproperties o the cytoskeleton. One majoringredient o the cytoskeleton is F-actin.Tis is a semi-exible polymer that resistsbending while still exhibiting some levelo exibility. Microrheological studieso simple polymer solutions revealed

increasing stiness o the networks withstress and shear rates, which is a uniqueeature o these networks. Static anddynamic scaling laws were establishedrelating material properties such asviscoelastic impedance to topologicalproperties such as the network mesh size.Furthermore, when passive crosslinkers molecules or ions that locally connect twolaments were added to the solutions,the eective riction increased and thenetworks became even stier17.

A highlight o the bottom-up approachis certainly the creation o active actinor microtubular networks involving

molecular motors such as myosin orkinesin18 that move along the laments ina dened direction (Fig. 1a). I coupledinto bundles, they can exert orces bypulling on more than one lament at once.Te presence o motors induces non-equilibrium uctuations that have a 1/2

dependence on requency, (re. 19).Such behaviour means that the

cytoskeleton has a dual role. On the longtimescales associated with cell migration,motors can slide laments past obstaclesand each other, which leads to an increasein network uidity20. Precipitation olaments and patterned motions with asubdiusive character then ollow. On theshort timescales on which the cytoskeletonmust respond promptly to maintain thecell shape, the combination o passivecrosslinking with molecular motors isideal. Tis union causes steady-state

uctuations much stronger than thermaluctuations, and an up-to-100-oldincrease in stiening o the network inresponse to shearing19.

Whereas the cytoskeleton relates tobiophysical constraints within the cell, amembrane that encapsulates the wholecell body mediates communication o thecell with its environment. ogether, thecytoskeleton and the membrane makethe cell envelope responsible or thecell mechanoresponse. Te membranecomprises a thin uid phospholipid bilayerthat serves as a solvent or a large variety

o proteins, glycolipids and glycoproteins.Glycoproteins are so polymers thatextend rom the membrane up to 100 nminto the extracellular space. Te glycolipidsand glycoproteins orm the glycocalyx,which protects the cell rom unwantedcontacts by entropic orces. Because oits relatively low bending stiness, themembrane surace uctuates appreciably.Interestingly, harnessing these uctuationsturns out to be a convenient way ocontrolling a variety o processes occurringon the cell surace. Tis can be achievedby, or example, aecting the afnities or

binding to membrane proteins

21

.Studies o phospholipid vesicles,whose membrane may contain adhesionproteins (binders and glycolipids), haveelucidated many aspects o the adhesionprocess, particularly its early stages22.When such vesicles are placed in thevicinity o a at surace decorated withcounterbinders (mimicking another cell orthe extracellular matrix), adhesion domainsorm spontaneously owing to correlationsbetween bonds mediated by membraneelasticity and uctuations21,23 (Fig. 1b). Tisis also true or unctionalized glycolipidsthat simultaneously adhere and repel the

substrate. Te unbound, repelling glycolipidsare expelled rom the adhesion domain andthus exert a lateral osmotic pressure, whichlimits the size o the domain.

Apart rom uctuations and lateralpressure, a number o other physicalmechanisms may control the ormation o

the domains. One o them is the densityand mobility o binders. Tis is possiblebecause the cost in entropy due to thebond-induced immobilization must bebalanced by the enthalpy gain associatedwith the ormation o the complex. Suchdomains are, thereore, much larger andhave a larger structural variety i bothbinding partners are mobile (cellcelladhesion) than i one is immobilized(cellmatrix adhesion)24. Even ring-like domains (Fig. 2), reminiscent othe immunological synapse, are shownto orm spontaneously owing to the

interplay o binding afnity, the diusiono the binders and the reaction rate o theormation o bonds25.

afl ll w ozo?Te coupling o the membrane (thesensory organ) and the cytoskeleton(which maintains stability) is crucial orthe survival o the cell. In terms o thebottom-up approach, this means thatactive networks need to be connedwithin vesicles and coupled to theircomposite membranes in a dynamicmanner. Such an achievement perormed

in the laboratory would result in the rstarticial cell (Fig. 1c). But construction ischallenging, rom both experimental andtheoretical points o view. Nevertheless,some preliminary work has been reported,in which sel-assembled, passive actinnetworks have been reconstituted within aphospholipid vesicle16,26,27 (Fig. 3).

Although there is a lot o ground to coverbeore we can really master these complexsystems, all the necessary ingredientsare available: physics has producedthe theoretical ramework in which tounderstand dynamic non-equilibrium

systems; a knowledge o biochemical andbiophysical pathways is emerging rom cellbiology and biochemistry; and the mainstructural components o the cell, suchas the cytoskeleton, the membrane andthe extracellular matrix, are now beingstudied in detail. A combination o theknowledge accumulated separately in eacheld will undoubtedly lead to advances, andarriving at an articial cell will become adistinct possibility.

Even i such a cell would not be ableto produce or reproduce, and remainedonly a aint shadow o the original, whichtook millions o years o evolution to

Fg3| Ring- and network-like actin assembly

within a phospholipid vesicle26. Actin is

crosslinked with -actinin and labelled with

rhodamine phalloidin. Figure courtesy o

L. Limozin.



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insight | perspective

develop, its realization would lead to greatprogress in both undamental and appliedresearch. Te articial cell is an emergingproblem, the solution o which will onlyarise rom a concerted eort o the wholenatural sciences community, with no losso identity in any discipline. Despite all

o our work so ar, the question What islie? remains. Although its transcendentalnature may render it unanswerable, beingable to build and model even a primitivecell will bring us just a little closer tounderstanding some o its many acets.Physics is, as always, most certainly up tothe challenge.

Ana-Sunana Smith is at the Institut fr

Teoretische Physik and Excellence Cluster:

Engineering of Advanced Materials, Universitt

Erlangen-Nnberg, Ngelsbachstrasse 49b, 90152

Erlangen, Germany.

e-mail: [email protected]

rfn1. imoee-Ressovsky, N. W., Zimmer, K. G. & Delbrck, M.

Nachr. Ges. Wiss. Gtt.1, 189245 (1935).

2. Schrdinge r, E. What is Life?(Cambridge Univ. Press, 1944).

3. Bustamante, C., Liphardt, J. & Ritort, F. Phys. oday

58, 4348 (2005).

4. Jarzynski, C. Phys. Rev. Lett.78, 26902693 (1997).

5. Liphardt, J., Dumont, S., Smith, S. B., inoco, I. Jr &

Bustamante, C. Science296, 18321835 (2002).

6. Collin, D. et al.Nature437, 231234 (2005).

7. Crooks, G. E. Phys. Rev. E60, 27212726 (1999).

8. Prost, J., Joanny, J-F. & Parrondo, J. M. R. Phys. Rev. Lett.

103, 090601 (2009).

9. Seiert , U. Phys. Rev. Lett.104, 138101 (2010).

10. Hayashi, K., Ueno, H., Iino, R. & Noji, H. Phys. Rev. Lett.

104, 218103 (2010).

11. Pelham, R. J. & Wang, Y-L. Proc. Natl Acad. Sci. USA

94, 1366113665 (1997).

12. Balaban, N. Q. et al.Nature Cell Biol.3, 466472 (2001).

13. Engler, A., Sen, S., Sweeney, H. L. & Discher, D. E. Cell

126, 677689 (2006).

14. Zemel, A. et al.Nature Phys.6, 468473 (2010).

15. Basan, M. et al.HFSP J.3, 265272 (2009).

16. Liu, A. P. & Fletcher, D. Nature Rev. Mol. Cell Biol.

10, 644650 (2009).

17. Gittes, F. et al.Phys. Rev. Lett.79, 32863289 (1997).

18. MacKintosh, F. C. & Schmidt, C. F. Curr. Opin. Cell Biol.

22, 2935 (2010).

19. MacKintosh, F. C. & Levin, A. J. Phys. Rev. Lett.

100, 018104 (2008).

20. Humphrey, D. et al.Nature416, 413416 (2002).

21. Reister, E. et al.Phys. Rev. Lett.101, 208103 (2008).

22. Smith, A-S. & Sackmann, E. ChemPhysChem 10, 6678 (2009).

23. Weik, . R. & Lipowsky, R. Phys. Rev. E64, 011903 (2001).

24. Smith, A-S. et al.Proc. Natl Acad. Sci. USA

105, 69066911 (2008).

25. Smith, A-S., Fenz, S. F. & Sengupta, K. Europhys. Lett.

89, 28003 (2010).

26. Limozin, L. & Sackmann, E. Phys. Rev. Lett.89, 168103 (2002).

27. Pontani, L-L. et al.Biophys. J.96, 192198 (2009).

AknowldgmnTis Perspective aims to briey introduce some o the

research topics in cell biophysics rather than present a

comprehensive overview o the literature. I acknowledge

that the mention o the work o many others would be

equally appropriate. I thank all my colleagues and students

or having the patience to discuss with me the topics that

inspired this manuscript. My particular gratitude goes to

E. Sackmann, U. Seiert, K. Sengupta and F. Reheldt.



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commentary | insight

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It has been known or a long time thatmalignant transormation and neoplasiaare associated with signicant changes

in the cellular cytoskeleton1. Stella Hurtleypointed out in her 1998 editorial orScience that changes in the cytoskeletonare key, and even diagnostic, in thepathology o some diseases, includingcancer2. Systems biology tells us thateverything is connected with everythingelse, so the central question is whetherthese cytoskeletal changes are a unctionalprerequisite or tumour progression.From a systems biology perspective,

the door handle can be accidentallymisinterpreted as the most importantpart o a cars engine because it has tobe opened rst. Cell biophysics has amore stringent viewpoint and dividesthe cell into unctional modules3. Tecytoskeleton is one o the most essentialmodules: it stabilizes and organizes thecell and provides the machinery or cellmotility and mechanotransduction4. Ithe cytoskeletal alterations in a tumourare necessary, they have to triggerbiomechanical changes that impactcellular unction.

M d, m ml Cancer, the big C word, is not just onedisease but many pathologic conditionsthat dier widely in aetiology, molecularbiology, clinical course and prognosis.Nevertheless, in all cancers malignantneoplasia uncontrolled growth (divisionbeyond the normal limits), invasion (localspread associated with destruction oadjacent tissues) and metastasis (regionaland distant spread within the body mainlythrough lymph or blood) occurs5. Tus,these diseases are experienced as oneeven though a prognosis is sometimes

substantially better than or diseasessuch as heart ailure. Recent resultsindicate that all three pathomechanismso malignancy require changes in theactive and passive biomechanics o thetumour cell and its stroma. Biomechanicalchanges can thereore be a generalprerequisite or malignancy independento the peculiar molecular maniestation inindividual cancers.

id ll olfoBiophysical methods or measuringcellular stiness, adhesion and orces,

based on scanning orce, particle-trackingand optical trapping techniques69,provide quantitative data at the single-cell level but have a limited throughputthat holds back their application inclinical trials. Undoubtedly, malignanttransormation causes cell soening orsmall deormations. Tis has been shown,rst or cell lines10,11 and then or tumourtissues (breast and oral cavity)12,13. Tedistribution o optical deormability obreast tumours shows a distinct shitowards soer cells with respect to normalmammary tissue obtained rom surgical

breast reductions (Fig. 1a). Tis shi canbe attributed to the act that the prominentbrous actin o the interphase celldisappears when the cell enters mitosis,and is replaced by a diuse distributiono actin throughout the cytoplasm14.Furthermore, cell dedierentiation maycontribute to actin downregulation15. Actinlaments act like sparsely distributedelastic rods that stabilize a tent, and cellstiness is thereore highly sensitive to areduction in these laments16,17. Tus, cellsoening is a good marker or increasedcell prolieration (Fig. 1b) and can help todetect early dysplasia13.

a

b

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.10.02

0.04

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0.14

Breasttumoursample

Breastreductionsample

0.02 0.04 0.06

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0.08 0.10 0.12 0.14

Numberofcells(103)

0

50

100

150

200250

300

350

Time (d)

1 2 3 4 5 6 7

Fg1| Cell sotening and cell prolieration.

, Relative-extensibility distribution o parenchymal

cells rom a malignant human breast tumour

(dark blue) and normal breast tissue (light blue),

measured with an optical stretcher. The optical

stretcher pulls on a cell with a well-dened orce

and determines the cells extension with respect to

its diameter, dened as the optical deormability.

For small deormations, where a linear response

is observed, the tumour shows a signicantly

higher raction o soter cells than the normal cells

rom breast tissue. b, The same sotening can

be observed or a breast cancer cell line (MDA-

MB-231, red) compared with a normal breast cell

line (MCF-10, black). The increase in sot cells is

probably due to the augmented cell prolieration

shown in the lower graph. An increase in soter cells

points towards enhanced prolieration such as that

ound in early dysplastic lesions. Error bars, one

standard deviation.



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insight | commentary

tmo voAt rst sight, cell soening is contradictoryto the observation that tumours are rigidmasses a notion borne out by theact that breast tumours are oen elt aslumps. Moreover, this apparent soness otumours would hinder their invasiveness.

A cell conned by a t issue matrix can onlydivide i its stiness exceeds the opposingrigidity o its direct environment. A simpleexperiment designed by Helmlinger et al.18demonstrates to what extent tumours cangrow in a rigid environment. umourcells divide and orm small spheroidsconned in agar gels. Tese gels cannotbe dissolved by the tumour cell, nor canthey migrate through it (Fig. 2). umourgrowth ceases when the agar gel surpassesa stiness o 104 Pa, which signicantlyexceeds the mechanical strength o thereduced actin cortex. However, cytoskeletal

laments inherently strain-harden atlarger deormations, and this compensatesor the weak linear elastic strength o theactin cortex19. Intermediate lamentssuch as vimentin, the expression levelso which increase with tumour size20, areperect candidates to support the pressureagainst the normal tissue matrix generatedby dividing tumour cells. Vimentin andkeratin have been implicated in neoplasiaor a long time or example, breasttumour cells that express vimentin as wellas keratin are particularly aggressive21 but their unction or the disease

remained unclear. From a biomechanicalperspective, intermediate laments couldbe a quintessential prerequisite or tumoursto expand against a rigid t issue matrix.

MTe malignant tumours ability tometastasize regionally and distantlylimits curative therapeutic options. It iscommonly thought that not all tumour cellsparticipate in metastasis and that, amongother cellular actions, a process similarto epithelialmesenchymal transitionis required22. Epithelialmesenchymal

transition is characterized by loss o celladhesion, downregulation o epithelialcadherin expression and increased cellmobility. It is essential in embryonicdevelopment or mesoderm and neuraltube ormation. However, the ormation oa metastatic tumour could be a nucleationprocess, and micrometastasis may beginimmediately aer a malignant lesion hasormed23. Nevertheless, malignant celllines that represent dierent levels ometastatic aggression show signicantbiomechanical changes and indicate thatcytoskeletal changes oster metastasis11.Cell soening can increase individual

a b c

100 m

0 h

a

b

c

9 h 18 h

Fg2| Tumour growth. , Growth o a tumour spheroid (MCF-7 cells) in a hydrogel (1%

low-gelling-temperature agarose) with an opposing rigidity o 12 kPa. Diferent stages o the

growing spheroids are shown: 2 d old (), 11 d old (b) and 27 d old () (scale bars, 50 m). As the

agarose cannot be dissolved by the tumour cells, the assay serves as a measure o how uncontrolled

cell prolieration permits the tumour to push away the surrounding tissue matrix. The spheroids can

grow up to a rigidity o 610 kPa. The cell stifness needed to grow against such a polymer matrix

cannot be provided by the actin cortex, which is reduced during mitosis. The ability o intermediate

laments to strain-harden makes them ideal candidates to provide the mechanical support or a

tumour to grow in a resisting tissue matrix.

Fg3| Individual and collective migration o malignant versus normal cells. As reely moving

individual cells, malignant breast cells (MCF-7) move aster on average than normal breast cells

(MCF-10). , As a collective cell ront, the normal cells (MCF-10, on the let o the image) move

much aster than the malignant cells (MCF-7, on the right). Moreover, or both cell types the cells

are held back by the cell boundary and thus move as a smooth ront. b, When cell adhesiveness is

reduced by small amounts o trypsin, the cell ront becomes rougher because the MCF-10 cells are

held back less by the cell ront. , NIH 3T3 broblasts, which are cells with a pronounced ability to

contract, do not move collectively and no dened cell ront persists owing to the individual migration

paths taken by the cells.



10/38


commentary | insight

cell speed or lamellipodial motion omalignantly transormed broblasts24 andbreast cancer cell lines. Cell soeningcan also have side eects that increaseaggressiveness. Te weakened actincytoskeleton enables microtubules topenetrate through the cortical actin layer to

orm microtentacles that greatly oster themetastasis o breast tumour cells circulatingin the blood stream25. However, all cells,even endothelial cells, can migrate, andmetastatic cells are not consistently asterthan normal cells. In Fig. 3a, the ront oa normal breast cell line clearly movesaster than a malignant breast cell line.Moreover, cell motion is strongly collectivethroughout the advancing cell sheet26and the cells are not able to overcomethe cell boundary. Conceivably, it is thecapability to move individually across atumours boundary that is essential or

metastasis, a possibility that is consistentwith the dierential-adhesion hypothesisin developmental biology27. I all cells aremotile, liquid-like tissue-spreading28 andcell segregation phenomena29 arise romdierences in intercellular adhesiveness andstiness that act on a boundary betweendierent cell types, similar to surace-tension eects. Te barrier that cells eelwhen they try to leave their cell boundarycan be lowered by reducing cell adhesion,as can be seen by adding small amountso trypsin (Fig. 3b). Changes in cadherinexpression also modulate tumour cell

adhesion through nonlinear instabilities30

;but metastatic cells cannot simply reduceadhesion, because they need traction tomove. Interestingly, cells such as broblasts,with a pronounced ability to contract,also easily overcome cell boundaries andmove individually and not collectively(Fig. 3c). In breast tumour samples, smallnumbers o cells can be ound that activelycontract when an external orce tries togently stretch them (Fig. 4). Tese couldplay a key role in metastasis becausecontraction can pre-strain and thus stienthe cytoskeleton, reducing a cells ability

to orm adhesive contacts with othercells. Moreover, contractile tumour cellsmigrate signicantly better through theextracellular matrix31.

pol ll mCancer screening has become one othe most powerul tools in reducingtumour mortality, as exemplied by the

cervical Pap smear test. However, visualinspection alone does not sufce or oralcell probes as it does in Pap smears, andbiomechanical measurements may ll this

void. Preliminary clinical data indicatethat cell soening can be used to screen ororal cancer13. At our regular dental exams,cytobrushes o suspicious lesions can beanalysed or an increase in the number oso cells symptomatic o augmented cellprolieration in early dysplasia. It has beenshown or several tumour entities that themalignant neoplasm is locally connedto a permissive tissue compartment

related to embryonic development or arelatively long phase during its clinicalcourse32. As ontogenetically dierenttissue compartments have dierentsurace tension, similarities in viscoelasticproperties to the stromal cells may acilitatethe permeation o the transormed epithelialcells within a morphogenetic unit. Resectiono carcinomas o the uterine cervixperormed on the basis o this premise hasreduced mortality rom 15% to 4% (re. 32).From a medical perspective, insights into thebiomechanical changes that occur duringtumour progression may lead to novel

selective treatments by altering tumour cellsbiomechanical properties. Such drugs wouldprobably not cure by killing cancer cells,but may eectively hinder the propagationo the neoplasm. Tese possible treatmentswould cause only mild side eects and maybe an option or older and rail patients whocan no longer tolerate radical surgery andcytostatic drugs.

Anatol Fritsch, obias Kiessling,

Kenechuku David Nnetu, Franziska Wetzel,

Mareike Zink and Jose A. Ks are members o the

graduate school BuildMoNa and are in the Sof

Matter Physics Division, Institute or Experimental

Physics I, Department o Physics and Earth Science,

University o Leipzig, Linnstrasse 5, 04103 Leipzig,

Germany. Michael Hckel is in the Departmento Obstetrics and Gynecology, Medical School,

University o Leipzig, Liebigstrae 20a, 04103

Leipzig, Germany.

e-mail:[email protected]

rfs1. Weinberg, R. A. Te Biology o Cancer1st edn (Garland

Science, 2007).

2. Hurtley, S. M. Science279, 459 (1998).

3. Bausch, A. R. & Kroy, K. Nature Phys.2, 231238 (2006).

4. Vogel, V. & Sheetz, M. Natl Rev.7, 265275 (2006).

5. Friedl, P. & Wol, K. Nature Rev. Cancer3, 362374 (2003).

6. Van Vliet, K. J., Bao, G. & Suresh, S.Acta Mater.

51, 58815905 (2003).

7. Homan, B. D., Massiera, G., Van Citters, K. M. & Crocker, J. C.Proc. Natl Acad. Sci. USA103, 1025910264 (2006).

8. Puech, P. H., Poole, K., Knebel, D. & Mller, D. Ultramicroscopy

106, 637644 (2006).

9. Brunner, C., Niendor, A. & Ks, J. Sof Matter

5, 21712178 (2009).

10. Lekka, M., Laidler, P., Lekki, D. G. J., Stachura, Z. &

Hrynkiewicz, A. Z. Eur. Biophys. J.28, 312316 (1999).

11. Guck, J. et al.Biophys. J.88, 36893698 (2005).

12. Cross, S. E., Jin, Y-S., Rao, J. & Gimzewski, J. K. Nature Nanotech.

2, 780783 (2007).

13. Remmerbach, . W. et al.Cancer Res.69, 17281732 (2009).

14. Sanger, J. W. Proc. Natl Acad. Sci. USA72, 19131916 (1975).

15. Lautenschlger, F. et al.Proc. Natl Acad. Sci. USA

106, 1569615701 (2009).

16. MacKintosh, F. C., Ks, J. & Janmey, P. A. Phys. Rev. Lett.

75, 44254428 (1995).

17. Claessens, M. M. A. E., Tarmann, R., Kroy, K. & Bausch, A. R.

Nature Phys.2, 186189 (2006).

18. Helmlinger, G., Netti, P. A., Lichtenbeld, H. C., Melder, R. J. &

Jain, R. K. Nature Biotechnol.15, 778783 (1997).

19. Janmey, P. A., Euteneuer, U., raub, P. & Schliwa, M.J. Cell Biol.

113, 155160 (1991).

20. Chen, M. H. et al.Mod. Pathol.21, 11831191 (2008).

21. Tomas, P. A. et al.Clin. Cancer Res.5, 26982703 (1999).

22. Vernon, A. E. & LaBonne, C. Curr. Biol.

14, R719R721 (2004).

23. Basan, M., Risler, ., Joanny, J-F., Sastre-Garau, X. & Prost, J.

HFSP J.3, 265272 (2009).

24. Park, S., Cardenas, R., Ks, J. & Shih, C. K. Biophys. J.

89, 43304342 (2005).

25. Whipple, R. A. et al.Cancer Res.68, 56785688 (2008).

26. repat, X. et al.Nature Phys.5, 426430 (2009).

27. Foty, R. A. & Steinberg, M. Dev. Biol.278, 255263 (2005).28. Guevorkian, K., Colbert, M-J., Durth, M., Duour, S. &

Brochard-Wyart, F. Phys. Rev. Lett.104, 218101 (2010).

29. Duguay, D., Foty, R. A. & Steinberg, M. S. Dev. Biol.

253, 309323 (2003).

30. Basan, M., Idema, ., Lenz, M., Joanny, J-F. & Risler, . Biophys. J.

98, 27702779 (2010).

31. Mierke, C. ., Rsel, D., Fabry, B. & Brbek, J. Eur. J. Cell Biol.

87, 669676 (2008).

32. Hckel, M. et al.Lancet Oncol.10, 683692 (2009).

Laser

Cell

Laserpower(W)

0 1

Time (s)

R

elativedeformation

10.05

0.04

0.03

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0.01

0.00

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0

2 3 4 5

Fg4| Contractile cells in breast tumours.

When breast tumour cells are weakly

stretched with the optical stretcher, a small

raction o tumour cells (1 in 100) actively resists

the pulling orce and contracts. This can be seen

by the change in cell diameter (normalized by

the original diameter) in the stretching direction.

mailto:%[email protected]:%[email protected]


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INSIGHT |REVIEWARTICLESPUBLISHED ONLINE: 1 OCTOBER 2010 | DOI: 10.1038/NPHYS1797

Physical virology

W. H. Roos1*, R. Bruinsma2 and G. J. L. Wuite1*

Viruses are nanosized, genome-filled protein containers with remarkable thermodynamic and mechanical properties. Theyform by spontaneous self-assembly inside the crowded, heterogeneous cytoplasm of infected cells. Self-assembly of virusesseems to obey the principles of thermodynamically reversible self-assembly but assembled shells (capsids) strongly resistdisassembly. Following assembly, someviral shells pass through a sequence of coordinated maturation stepsthat progressivelystrengthen the capsid. Nanoindentation measurements by atomic force microscopy enable tests of the strength of individualviral capsids. They show that concepts borrowed from macroscopic materials science are surprisingly relevant to viral shells.For example, viral shells exhibit materials fatigue and the theory of thin-shell elasticity can account in part foratomic-force-microscopy-measured forcedeformation curves. Viral shells have effective Youngs moduli ranging from thatof polyethylene to that of plexiglas. Some of them can withstand internal osmotic pressures that are tens of atmospheres.Comparisons with thin-shell theory also shed light on nonlinear irreversible processes such as plastic deformation and failure.Finally, atomic force microscopy experiments can quantify the mechanical effects of genome encapsidation and capsid proteinmutations on viral shells, providing virological insight and suggesting new biotechnological applications.

The impact of viruses on our daily lives is dominated bytheir role as infectious agents of, often serious, diseases.However, viruses are now increasingly employed in more

positive roles1,2. Examples include viruses and viral shells thatare used in batteries and memory devices3,4, as nanoscaffoldsor nanoreactors for transport and catalysis5,6, and in cancertreatment7. In the context of gene therapy, they are used as vectorsfor gene delivery8, and the phage viruses that infect bacteria havebeen used as antibacterial agents9. Supporting these applicationsis the burgeoning research field of physical virology dedicated tothe study of the physical properties of viruses 10. It encompassesdomains such as viral self-assembly11,12, virus genome packagingand release mechanisms1315, andstructural andmechanistic studiesof viral particles14,16,17. The rapid growth of this field is, on the

one hand, fuelled by the development of physics-based techniquessuch as cryo-electron microscopy, X-ray crystallography, opticaltweezers and atomic force microscopy and, on the other hand, bythe increasing interest in viral particles as smart building blocksof larger-scale structures. In this brief review we shall focus on justtwo aspects of physical virology: first what physics has to tell usabout the assembly of viral shells, and second what the mechanicalproperties of assembled viral shells are: how we can experimentallyprobe mechanical properties of viral shells, how we should interpretthem andhow we canapply theinsightsthesestudies provide.

Viral self-assembly

Viruses do not carry out metabolic activity and rely entirely onhost-cell molecular machinery for reproduction. This absence of

metabolic and reproductive activity suggests that, unlike cells,the assembly of viruses could perhaps be understood on thebasis of equilibrium thermodynamics. An elegant confirmationof this idea was the discovery in 1955 by Fraenkel-Conrat andWilliams18,19 that under in vitro conditions the rod-like tobaccomosaic virus (TMV) self-assembles spontaneously and unassistedinto fully infectious viral particles from solutions containing themolecular components of this virus: the TMV capsid proteins (orsubunits) and the single-stranded (ss) RNA genome moleculesof TMV. In 1967, Bancroft, Hills and Markham20 showed that

1Natuur- en Sterrenkunde & Laser Centrum, VU University, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands, 2Department of Physics, University

of California, Los Angeles, California 90095-1537, USA. *e-mail: [email protected]; [email protected].

small sphere-like plant viruses with icosahedral symmetry alsocan be produced by in vitro self-assembly (Box 1 summarizes thegeneral classification of viruses with icosahedral viral symmetry).The connection between equilibrium thermodynamics and viralself-assembly was further strengthened by the work of Klug21,who determined the thermodynamic phase diagram of solutionsof TMV subunits in terms of acidity and salinity. Capsidproteins, or subunits, interact mainly through a combinationof electrostatic repulsion, hydrophobic attraction and specificcontacts between certain pairs of amino acids (known as Casparpairs22). Varying the acidity and salinity conditions (or theconcentration of Ca2+ ions) adjusts the relative balance betweenthese competing interactions, thereby favouring assembly ordisassembly23 of protein aggregates. For TMV subunits in ambient

conditions of aciditysalinitytemperature the most stable subunitaggregates are double-disc and double-ring protein clustersheld together by hydrophobic attractive interactions. Electrostaticrepulsion between the positively charged discs/rings preventsdisc aggregation. The addition of the oppositely charged ssRNAgenome molecules drives the self-assembly process to completionby combining the protein discs into rod-like cylinders with theRNA molecule running along the central axis, like beads ona string21. Self-assembly of most infectious sphere-like ssRNAviruses under ambient conditions requires the presence of the viralRNA genome molecules. Viral RNA molecules act in part as anon-specific electrostatic glue that links together the oppositelycharged capsid proteins24, and particular stem-loop side branchesof the RNA molecules have specific affinity for the capsid proteins.

In some cases, the encapsidated ssRNA molecules condense asdouble-stranded (ds) helical segments along a dodecahedral cageof edges of the icosahedral shell25. Self-assembly of empty capsidsin the absence of RNA may be possible as well for certain viruses,for instance under non-ambient pH or salinity levels. On theother hand, self-assembly of viral shells of most ds genomes,such as the tailed dsDNA bacteriophage viruses (that is, virusesthat prey on bacteria), does not require the presence of genomemolecules. The much larger bending rigidity of dsDNA moleculespresumably prevents them from acting as electrostatic glue.

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REVIEWARTICLES | INSIGHT NATURE PHYSICS DOI:10.1038/NPHYS1797

Box 1 | Viral shapes.

Viral particles come in many shapes, of which sphere-like androd-like particles are the most common, but spherocylinders,cones and other shell shapes are seen as well. About half of allviral families share icosahedral symmetry, even when the viralgenomes share little homology92. Examples include the plantvirus CCMV, the animal virus HBV and bacteriophage viruses

discussed in this review. Caspar and Klug (CK) developed aclassification system for icosahedralviruses, illustrated in Fig. B1,based on the T number defined as T=m2 + n2 +mn. Here,m and n indicate the number of steps along the crystallographicdirections of a hexagonallattice connecting twoadjacent verticeson the icosahedron93,94. A CK icosahedral shell consists of 12pentamers located at equidistant sites on the icosahedral verticeswith a further 10(T 1) hexamers with T= 1, 3,4, 7,... located in between the pentamers. Following earlier workby Crick and Watson95, CK argued that this type of icosahedralshell minimizes the geometrically unavoidable elastic strains ofidentical proteins placed on a closed shell (quasi-equivalence).

A

Aa2

a

b c

a1

Figure B1 | Caspar and Klug construction of icosahedral viral shells.

a, Template consisting of equilateral triangles of which an

icosahedron can be folded. The lattice vector A=ma1+na2 of ahexagonal lattice with basis vectors a1 and a2 forms an index for the

triangles. b, An example for m= 3 and n= 1. c, Result of folding atemplate with this lattice vector into an icosahedron. It has a

T=m2+n2+mn= 13 structure with 10(T 1)= 120 hexamers in total.Reproduced with permission from ref. 48, 2005 APS.

In these cases, the genome is usually inserted, after capsid assemblyhas been completed, by the action of a rotary molecular motorimbedded in the capsid15.

Assembly studies by the group of Zlotnick of the assembly oftwo icosahedral viruses cowpea chlorotic mottle virus (CCMV;ref. 26) and hepatitis B virus (HBV; ref. 27) were an importantmilestone for the application of equilibriumthermodynamics. Theymeasured the concentrations of subunit clusters of different sizesas a function of the total protein concentration and encountered adouble-peaked population composed of, respectively, small clusters(for example, dimers or pentamers) and fully formed capsids. Thesurprise was that the ratio of the concentrations of free subunitsand fully formed capsids seemed to obey quantitatively the lawof mass action (LMA). The LMA would demand that for a viral

shell composed of N subunits the concentration of assembledcapsids should be proportional to N, with the concentration offree subunits, which must be distinguished from the total proteinconcentration T. An important consequence of the LMA is the factthat, as a function ofT, the fractionf(T) of proteins incorporatedinto capsids rises sharply at a quasi-critical concentration crit with

f(T) 1crit/T for T > crit. As, according to the LMA, thevalue ofcrit

exp(G0/N) is determined by the standard Gibbs

free energy G0 of the assembly reaction, that is, the assembly freeenergyof thecapsid, importantthermodynamic information can beobtained by measuring crit. This form for f(T) fits very well theequilibrium self-assembly curves of, for example, micelles (criticalmicelle concentration)28. It describes quite well the self-assemblyof CCMV and HBV with a crit typically in the M range. Underbiological conditions, inside infected cells, the concentration ofcapsid proteins produced by transcription would thus have toexceed crit before viral self-assembly could start. Fitted values forG0 were in the reasonable range of about 10 kBTper subunit, so intotal about 103 kBTfor small viral shells. The measured dependenceof the fitted G0 on pH and salinity was also consistent withsimple models for the interactions between subunits23. The LMAis a direct consequence of the minimization of the Gibbs free

energy: it requires that capsid proteins in solution have the samechemical potential as the proteins incorporated in a shell. However,when the total concentration of capsid proteins is reduced backdown below crit after the assembly has reached completion, thencapsids should disassemble spontaneously according to the LMA.In actuality this either does not happen at all, or happens only aftera very long period of time, or after quite substantial changes in pH,salinity or other solution conditions29. This excess thermodynamicstability of assembled viral shells when compared with conventionalequilibrium self-assembly is, from a biological viewpoint, of coursea prime survival feature, as viral shells need to remain intact inhostile environments that contain no free capsid proteins at all,such as the host bloodstream, stomach or tissue. This means thatviral self-assembly really should not be viewed as an equilibrium

process. Analytical and numerical studies30

of simple models ofcapsid assembly kinetics31 indicate that provided most assemblysteps are reversible, with one or a few assembly steps irreversible, anLMA-type double-peaked distribution obeying f(T)1crit/Twill still develop under certain conditions. However, the G0extracted from this crit in general is considerably smaller than theactual standard free energy of the capsid, and reflects the assemblyfree energy of reversible intermediate structures.

Kinetic studies of viral self-assembly would be necessaryto probethis limited form of irreversibilitybut, unlikethe case of therod-likeTMV, it has turned out to be very challenging to identify exper-imentally the assembly intermediates of spherical viruses. Kineticstudies of viral assembly by electron microscopy carried out in the1980s on brome mosaic virus (BMV) assembly reported partially

formed shells

32

. In 1993, the group of Prevelige studied the kineticsof scaffold-based assembly of the phage P22 using light scattering33.Capsid assembly was shown to be preceded by a lag time after initi-ation followed by a more rapid sigmoidal growth curve, indicatingthat the capsid-assembly rate is determined by nucleation. A criticalprotein concentration is required below which assembly does nottake place. The initial formation rate depended on the proteinconcentration to the fifth power, which suggests that in this casepentamers are thecritical nuclei. RNA genome molecules have beenshown to catalyse the assembly process by assisting the formationof the critical nucleus of BMV (ref. 34). Subsequent capsid growthseems to be sequential, resembling a polymerization reaction.Studies of theassemblykinetics of a numberof viruses have reportedsimilar scenarios, with lag times in the secondsminutes range35.Particularly detailed was a multi-angle light-scattering study by

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NATURE PHYSICS DOI:10.1038/NPHYS1797 INSIGHT | REVIEWARTICLES

Casini et al.36 of the assembly kinetics of human papilloma virus;they again found that the rate-limiting step of the assembly processwas theformation of protein oligomers.

Numerical simulations of viral assembly kinetics could com-plement assembly-kinetics experiments. However, simulations onthe relevant timescale of seconds to minutes that account forthe internal degrees of freedom of capsid proteins interactingthrough realistic potentials are, for currently available computa-

tional resources, not practical. Instead, rigid geometrical modelsof the capsid proteins (or capsomeres) and other coarse-grainedrepresentations are used, with the model proteins/capsomeres in-teracting through some model pair potential3742. In the simplestcase, capsid proteins or capsomeres could even be representedas point particles. A Newtonian-dynamics study by Hagan andChandler41 of such a model reported that the choice of this pairpotential sensitively determined whether kinetic traps preventedproper assembly of small shells. Hicks and Henley42 used an elasticmodel, with the proteins now represented as deformable triangles,and found that the probability for successful assembly of largershells rapidly decreased when the elastic rigidity was increased.An example of an assembly error could be a five-fold-symmetriccapsomere inserted at a location that is not appropriate for an

icosahedral shell (see Box 1). More recently, molecular dynamics(MD) simulations of viral assembly have been carried out where thecapsomeres/proteins were represented by more realistic geometricalshapes. MD simulations by Nguyen, Reddy and Brooks43 were ableto reproduce the self-assembly of smaller T= 1 and T= 3 shells.They found though that proper assembly was accompanied bythe production of significant numbers of non-icosahedral aber-rant particles associated with assembly errors and kinetic traps,in particular when temperature and protein concentrations werenot optimally chosen. Next, Rapaport44 included explicit solventmolecules and succeeded in assembling T= 1 particles with a highlevel of fidelity and sigmoidal assembly kinetics. The high levels ofassembly fidelity in this case seemed to be characterized by highlevels of assembly reversibility. Recall that high levels of assembly

reversibility were also required for the observed quasi-LMA. Alocal-rule scheme has been proposed45, engineered to prevent theassembly-error problem by assuming that viral proteins can adoptT different internal configurations coding for proper assembly ofan icosahedral shell with index T(seeBox 1). Sofar,no evidence hasbeen found for local-rule-based codingconfigurations.

If only the minimum-free-energy state of a shell is required thenviral shell assembly also can be studied by Monte Carlo simulations.A two-disc Monte Carlo simulation by Zandi et al., representingpentamers and hexamers placed on a spherical support scaffold,found that the Caspar and Klug (CK) T-number icosahedralsymmetry is indeed the minimum-free-energy structure providedthat the size ratio of the discs is fixed appropriately46. Chen,Zhang and Glotzer47 investigated cluster formation of attractive

cone-shaped particles without support scaffold using Monte Carlosimulation. By varying the cone angle they found that the conesassembled into a sequence of convex shells characterized by magicnumbers that included the icosahedral shells. Non-icosahedralshell structures, like those of human immunodeficiency virus(conical) and of phage 29 (prolate/spherocylinder), can beobtained as minimum-energy structures for certain parameterranges in elastic-shell models48. Design principles of prolate phageswere reviewed by Moody49 in 1999. Monte Carlo simulationsof the packing of hard spheres on a prolate, spheroidal surfaceidentified the minimal requirements to form shells resemblingthose of a few selected viruses50, and Monte Carlo simulations ofcapsomerecapsomere interactions in prolate shells yielded optimalstructures for particles with icosahedral end caps connected bycylinders of hexamers51. Finally, the capsids of many animal viruses,

such as human immunodeficiency virus (HIV), HBV and herpessimplex virus,are surrounded by a lipid bilayer envelope,and Zhangand Nguyen studied the effect of this lipid bilayer on the nucleationof the cone-shaped HIV shells52.

After the initial assembly of a virus, the capsid proteins areoften modified, a process known as maturation. For example, thecapsids of many tailed dsDNA bacteriophages undergo a wholesequence of conformational changes and chemical reactions that

tend to strengthen the shell, which is necessary in part because ofthelargeinternal pressure of phages, which is discussedlateron. Theshell-maturation steps, which have been shown to be cooperative incertain cases, resemble structural phase transitions in crystals. Theapplication of GinzburgLandau theory to describe the maturationsteps indicates that near a step we could expect to encounter thesame soft modes as characterize structural transitions53. An ex-ceptional case is the bacteriophage HK97, where, after an elaboratesequence of steps, the shell ends up being armoured by a cross-linked mesh of amino-acid chains that has the topology of medievalchain-mail54. Tama and Brooks55,56 carried out all-atom numericalstudies of some of the maturation steps of HK97 and found that theconformational changes of the shell do indeed tend to follow thetrajectory of soft modes of the shell, associated with rotation of the

pentamers and hexamers. Widom et al. used the continuum elastic-ity theory of thin shells to show that, even in the absence of internalprotein conformational degrees of freedom driving the maturation,icosahedral shells should still exhibit soft modes near the buck-ling transition between spherical and icosahedral shapes57. Finally,Yang et al.58 showed that the same theory could account for thelow-frequency modes of theshells of simpleviruses suchas BMV.

Mechanical virology

After a virus or an empty viral shell has assembled, we can inquirehow resilient it is in terms of its response to external force and otherperturbations. Capsids need to meet conflicting demands: theyshould be sufficiently stable to protect their genome in the extra-cellular environment, but sufficiently unstable that they can release

their genome molecules into host cells. Various bulk and single-particle assays have been developed to measure the mechanicalproperties of viruses, the budding field of mechanical virology.Osmotic-shock experiments were used to study the stability ofbacteriophage viruses under pressure against rupture14,59 and themechanical properties of crystals and films composed of viruseswere analysed by Brillouin light scattering60,61. A disadvantage ofthese multiparticle techniques is that (1) they represent an averageover large numbers of viruses and (2) they represent a rotationalaverage, so any directionality of the mechanical properties withrespect to the shell orientation is lost. The mechanics of singleparticles and their directionality can however be probed withthe atomic force microscopy (AFM-) based nanoindentationtechniques summarized in Box 2.

The relation between the applied force and the resulting changein shell diameter is called the forcedeformation curve (FDC; seeBox 2). Depending on whether or not the capsid returns to itsoriginal state after the probe force is removed (unloading), we callthis a reversible, respectively irreversible, deformation. The forcemeasured by a nanoindentation probe results, at a fundamentallevel, from the fact that the probe forces the viral shell away froma state of minimum free energy. To interpret measured FDCs,including irreversibility effects, we can compare them with thedeformation free energy obtained from the continuum elasticitytheory of thin elastic shells (thin-shell theory or TST) that wehave already mentioned. TST is used extensively by engineersto predict the effects of external forces on thin-walled, hollowmacroscopic structures, such as aeroplanes or oil tanks. In thesimplest application of TST we model a viral shell as a thin spherical



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Box 2 | AFM nanoindentation.

The mechanical properties of various biological entities havebeen characterized by AFM-based nanoindentation96, includingcells97,98, microtubules99,100, peptide nanotubes101 and viruses67,79.Figure B2 shows a schematic diagram of a nanoindentationexperiment on a virus. Theexperimentscan be carried outin airaswell as in liquid. The minimal radius of curvature of commercialAFM tips is 220 nm, a value that is, respectively, a little lowerthan or comparable to the size of small viruses. Before the startof a nanoindentation experiment, the viral particle needs to beimaged102,103 to check whether it has the correct shape and size(Fig. B3a). Viral imaging under liquid conditions in combinationwith mechanical probing has been carried out in tapping-mode104

and jumping-mode105 AFM, two relatively non-invasive imagingmodes, which is of importance for theimaging of fragile biologicalstructures such as icosahedral viruses. The more rigid, rod-likeviruses have been imaged in contact-mode AFMwithout inducingvisible damage69. Imaging is followed by indentation of the virus,during which a forcedistance curve (FZC) is recorded. This

FZC involves the bending of two springs in series, the cantileverand the viral particle. For this reason, a calibration FZC of thecantilever deflection on the solid substrate next to the virus mustbe recorded. From these two FZCs the FDC of the virus can bedetermined, showing the force as a function of the indentationof the virus (Fig. B2b,d). The schematic FDC of Fig. B2d showsan initially linear deformation regime with positive slope, forforces up to 1.7 nN, that is fully reversible. The slope of alinear, reversible indentation curve yields the particles springconstant and Youngs modulus, as discussed in the text. Thisis followed by a deformation regime with negative slope, whichis usually irreversible. This drop in force can indicate bucklingof the shell or fracture of the shell (failure). Figure B3 showsa viral particle before and after a nanoindentation experiment.A hole produced by shell failure is clearly visible. Note thatindividual capsomeres are discernible. By comparing the imagebefore and after indentation, the capsomeres that were removedby the indentation can be identified.

Quadrant photodiodeLaser

Cantilever

Sample

Piezo scanner z

x

y

Force(nN)

Approach

20 10 0 10 20 30 40

Indentation (nm)

10 0 10 20 30 40

Indentation (nm)

Deformation

Reversible

indentation

regimeCapsid failure

a

b

c

d2.5

2.0

1.5

1.0

0.5

0

Force(nN)

20

2.5

2.0

1.5

1.0

0.5

0

Figure B2 | Schematic diagram of AFM nanoindentation. a,b, The piezo is extending in a, but the AFM tip has not yet touched the virus surface and

therefore the exerted force is zero (b). c,d, The AFM tip is indenting the virus and the cantilever bends ( c); the change in signal on the quadrant

photodiode is a measure for the exerted force, plotted in d as a function of the indentation.

12 3

47 8 9 10

11 12 13 1415 15

16 17 18 19

20 21 2223 24

25

5 6

12 3

4

11 12 131416 17 18 192021 22

23 2425

5 6

60 nm 60 nm

ab

cd

e

Height(nm)

0 100 200 300

Lateral distance (nm)

Before

After

7 8 9 10

indentation

indentation

120100

80

60

40

20

0

Figure B3 | AFM images of a single viral particle before and after nanoindentation. a,b, Three-dimensional rendered AFM topography images of a

liquid-immersed HSV1 particle before (a) and after (b) indentation. The structural subunits (capsomeres) can be recognized on the viral shell. c, The

height profile, taken along the white arrows in a and b, shows the capsomeres on top of the particle before indentation and the hole left after

indentation. The indented profile most probably represents the tip shape and because of the finite width of the AFM tip it was not possible to image

inside the broken capsid. d,e, Numbering of the capsomeres before and after indentation reveals the removal of seven (denoted in red) central

capsomeres as a result of shell failure. Reproduced with permission from ref. 65, 2009 NAS, USA.

736 NATURE PHYSICS | VOL 6 | OCTOBER 2010 | www.nature.com/naturephysics


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NATURE PHYSICS DOI:10.1038/NPHYS1797 INSIGHT | REVIEWARTICLES

shell of uniform thickness and radius R. If the viral shell enclosesgenome molecules, then an internal osmotic pressure must beincluded, which can be as large as 50 atm (refs 62,63). Let (r) betheindentationprofile of theshell generated, forexample, by a forceprobe. Specifically, (r) is defined as theradial inward displacementof the surface of the sphere expressed in terms of a two-dimensionalcoordinate systemthat covers theshell. In thelimit of small (r), theTST deformation free energyF is a simplefunctional of (r)inthe

form of an integral over the shell surface:

F=

dS

1

2 ( )2+ 1

2( )2+ 1

2Y

2

R

2(1)

The first term of equation (1) describes the bending-energy cost ofthe indentation note that is the shell curvature wherethe bending modulus has units of energy. The second termrepresents the work by the probe against the genome osmoticpressure with = R/2 an effective surface tension. Thethird term measures the stretching of the layer induced by theforce with the two-dimensional Young modulus Y of the layer.A dimensionless number = YR2/ the Fpplvon Krmnnumber and a characteristic length scale lB

=

/Y the

buckling radius can be constructed from the stretching andbending moduli, which will play an important role. For example,equation (1) is valid only if 2 l2B. The FDC must be obtainedfrom the thermodynamic condition that the functional derivativeF/ (r) of the deformation free energy with respect to (r) isequal to the radial force per unit areaf(r) exerted by the probe. Thedifferential equation F/ (r)=f(r) can be solved analyticallyfor the case of a point force f(r) = F(r). The force creates adimple with a radius of order

RlB and the resulting FDC is

linear. In other words, for weak applied forces, the shell behaveslike a harmonic spring. For zero osmotic pressure, for example, (0)/R= F/8

Y, in which case the effective spring constant is

k = 8

Y/R. Alternatively, we can also apply three-dimensionalelasticity theory to compute the elastic response of an elastic shell

with a finite thickness h. Werecover the TST resultin the limit hRwith a spring constant

k E3Dh2/R (2)

where E3D is the three-dimensional Young modulus. For largerindentation forces equations (1) and (2) should not be used. Thecalculation of the FDC of TST in the nonlinear regime requires thesolution of a pair of somewhat challenging nonlinear differentialequations, known as the Fpplvon Krmn (FvK) equations (theyresemble Einsteinsequations of general relativity). Instead of tryingto solve the FvK equations analytically or numerically, it is morepractical to numerically minimize the elastic energy directly usingfinite-element modelling (FEM). The inset of Fig. 1b shows the

fully nonlinear FDC of a shell indented by a hemispherical tip ascomputed by FEM. The initial state was a uniform sphere. The FDCis plotted as a dimensionless relation between (0)/R and F/

Y.

Note that the deformation of the sphere does not deviate muchfrom the linear harmonic spring for deformation ratios (0)/R upto 0.6. Then, for slightly larger values of (0)/R, a discontinuousdrop takes place in the FDC. This is due to the fact that forlarger deformations the elastic energies of two different shapes ofthe deformed shell cross each other. In the engineering literature,singularities in the FDC of this type are known as bucklingtransitions. They are identified with the well-known catastrophicfailures of hollowstructures subjectto external loads,that is,failureswithout anyvisible precursor warning in theFDC.

Comparison with the FDC of Box 2 suggests a relation betweenthe buckling instabilities of TST and the irreversible nonlinearities

of the FDCs of viral shells. However, mathematically, the bucklingdiscontinuities of TST are quite similar to first-order phasetransitions and, like first-order phase transitions, they could benucleated by local structural defects. This indicates that the elasticresponse of the non-uniform icosahedral shells might differ fromthat of uniform spherical shells, which must be discussed before wecan compare with experiment. The FDC of icosahedral shells wasobtained by starting from a perfect icosahedron as the initial trial

state. Thesharp folds linking the12 vertices of a perfect icosahedronare not compatible with the bending-energy term in equation (1).However, as long as the FvK parameter = YR2/ exceeds athreshold value of theorder of 102, the minimum-free-energy shapestill remains icosahedrally facetted. For FvK numbers less thanthis threshold, however, the shell adopts a nearly spherical shape 64

(confusingly, this also is known as a buckling transition, but weshall not use this terminology). The FvK number of a viral shell canbe estimated by comparing computed shapes of undeformed shellswith those measured, for example, by cryo-transmission electronmicroscopy. Figure 1b itself shows the FDCs of icosahedral shellsfor various values deformed by a spherical tip of the same sizeas the shell. For lower values of , the FDC remains quite closeto the harmonic spring prediction. For larger values of , the

relation is increasingly nonlinear, and then develops the bucklingdiscontinuity. The size of the discontinuity increases with increasing and the critical value of the indentation for the bucklingdiscontinuity decreases. Figure 1a shows the shape of a shell with= 1,200 immediately after the buckling discontinuity. The stresscontours are indicated. One of the 12 conical five-fold-symmetrysites of theicosahedralshellhas buckledand inverted.In thebuckledstate, the shell is detached from the tip at the centre, which isnot the case in the small-force regime. The five-fold-symmetrysites thus indeed seem to act as structural defects that triggerbuckling. The discontinuity of the FDC of a spherical shell withthe same elastic moduli takes place at a much larger indentation(see the inset of Fig. 1b).

How do the predictions of TST compare with the AFM

nanoindentation experiments? For small applied forces, themeasured FDCis indeed linearin many cases. Comparing thethree-dimensional Young moduli (equation (2)) of various particlesshows that sphere-like viruses that package their genome intopreformed capsids, such as phage 29, phage , HSV1 (herpessimplex virus type 1) and MVM (minute virus of mice) have aYoung modulus that is at least double that of sphere-like virusesthat self-assemble around their genome such as CCMV and HBV(Table 1). The FvK numbers in Table 1 were, incidentally, notobtained by comparing with measured shell shapes but, instead,were estimated assuming the TST relation

= 12(12)

R

h

2(3)

with Poissons ratio. An interesting application is the use of TSTto explain measured differences in spring constants of nuclearand viral HSV1 capsids65,66. The latter are stiffer than the formerbecause they possess an extra protein layer, the inner tegument.Using equation (2), and assuming that the E3D values for the capsidand inner tegument are similar, it follows that this extra proteinlayer should have a thickness of0.8 nm (ref. 65), a prediction thatis verifiable by electron microscopy.

For smaller viral particles, when the shell thickness h is notnegligible compared with the radius R, TST is no longer expectedto apply. The simplest extension is to use FEM to compute theFDC of a homogeneous elastic shell with a finite thickness. Theelastic energy of a solid elastic sphere that is indented scales as 5/2, which is known as a Hertzian response. The FDC of athick-walled shell is expected to show, as a function of h, scaling



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00 0.2 0.4 0.6 0.8 1.0

0.5

1.0

1.5

2.0

2.5

3.0

0

0.5

1.0

1.5

F(

Y)1/2

F

(

Y)1/2

2.0

2.5 IcosahedralSpherical

3.0

0 0.2 0.4 0.6

/R

0.8

= 100

1.0

/R

= 400

= 100

= 1,200

= 900

= 1,200

a b

Figure 1 | FEM analysis of shell deformation. a, Shapes of icosahedral shells with = 100 and = 1,200. Undeformed shells (left) and shells that aredeformed to 35% of their radius (right) are shown. The deformed shells are shown in a cutaway view and the = 1,200 shell has buckled, leading to theinversion of a five-fold apex. The strain energy due to stretching and bending is indicated by colour coding. b, FDC of icosahedral shells with isotropic

elastic properties. The force Fand the shell deformation are expressed in dimensionless units. The graph shows that the FvK parameter determines

whether a shell buckles. The inset compares FDCs on spherical and icosahedral shells for =900. Reproduced with permission from ref. 77, 2006 APS.

Table 1 | Geometrical and mechanical properties of viral shells/tubes.

Radius*

(nm)

Thickness*

(nm)

Genome

(encapsidation)Youngs modulus (GPa) FvK number Tnumber

29 prohead 23.2 (ref. 70) 1.6 dsDNA (P) 1.8 (ref. 67)/4.5 (ref. 70) 2,100 Prolate

29.5 (ref. 76) 1.8 dsDNA (P) 1.0 (ref. 76) 2,700 T= 7HSV1 49.5 (ref. 65) 4 dsDNA (P) 1.0 (ref. 65) 1,500 T= 16MVM 11.5 (ref. 68) 2 ssDNA (P) 1.25 (ref. 68) 350 T= 1CCMV 11.8 (ref. 70) 2.8 ssRNA (S) 0.14 (ref. 71)/0.28 (ref. 70)/0.22 (ref. 72) 180 T= 3HBV T3 11.9 (ref. 74) 2.4 ssRNA/DNA (S) 0.37 (ref. 74) / 0.26 (ref. 73) 250 T= 3HBV T4 13.6 (ref. 74) 2.1 ssRNA/DNA (S) 0.36 (ref. 74) / 0.26 (ref. 73) 400 T=4TMV 5.5 (ref. 69) 7 ssRNA (S) 0.9 /1.0 (ref. 69) Cylindrical Cylindrical

*Averagedshell radii (average of averaged outer andinner radius)and thicknesses areused. Phage 29has a prolateshell, buthasbeenapproximatedas a sphere.Theshellradiusand thicknessof HSV1

and HBV are taken without the respective protrusions and spikes on the capsid surface.

ss: single stranded, ds: double stranded. HBV self-assembles around an ssRNA genome, which is then retrotranscribed into DNA that is partially ss and partially ds. Encapsidation mode: P, packaging of

genome into preformed capsids; S, self-assembly of capsid around genome.

The FvK number is calculated from equation (3), with =0.4 (ref. 70); rounded values are printed.

crossoverfrom theTST resultfor largerapplied forcesto a nonlinearHertzian-type FDC for smaller applied forces. FEM studies ofthe indentation of elastic shells by point forces67,68, as well as byrealistically shaped models for the AFM tip6971, were carried out. Itwas indeed observed that Hertzian nonlinearities occur at the onsetof deformation of thick-shelled particles69,71. The next step is to useinformation on the heterogeneous geometry of the viral particles

available from X-ray diffraction and cryo-electron microscopystudies, while still maintaining a uniform elastic modulus. Suchan approach was followed by Klug and co-workers to investigateCCMV and HBV (refs 72,73). By comparison with the measuredFDC, a Young modulus of 0.22 GPa was found for CCMV, whichhappens to lie between the estimates obtained by the previous twomethods70,71. A comparable Young modulus, namely 0.26 GPa, wasdetermined for HBV (ref. 73), which is a little lower than thatobtained by using a TST approximation74. Determining the Youngmodulus thus depends to some extent on the model that is usedto analyse the FDC, as indicated in Table 1. Another examplewas a detailed FEM study of MVM that predicted stabilizinginteractions between the encapsulated DNA and specific sitesat the capsid interior (Fig. 2), which was later experimentallyconfirmed75. Furthermore, the orientation-dependent indentation

behaviour of HBV was determined by comparing experimentswith detailed FEM simulations73. Table 1 summarizes mechanicaland geometrical parameters of various viruses including the CKtriangulation number T.

Reversible versus irreversible deformation

We now turn to thequestionof howthe irreversibledeformations of

capsids canbe described. TheFDCscomputed from elasticity theoryare of course always reversible, though they may show hysteresisnear buckling instabilities, but could a buckling instability seen inTST (or FEM) act as an indicator of fracture or some other formof irreversibility? This is actually the case for the failure of hollowmacroscopic structures. First, recall that the critical deformationfor the buckling instability is controlled by the FvK number.Buckling occurs at lower deformations for higher FvK numbers.Table 1 summarizes the approximate FvK numbers of a numberof viruses. HSV1 capsids have an FvK number of 1,500 and theempty capsids break at a relative deformation of 36% of theradius65. Prohead 29 and the empty phage have FvK numbersbetwe

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