A model for the role of integrins in flow inducedmechanotransduction in osteocytesYilin Wang*, Laoise M. McNamara†, Mitchell B. Schaffler†, and Sheldon Weinbaum*‡

*Department of Biomedical Engineering, The City College of New York and the Graduate Center, City University of New York, New York, NY 10031;and †Leni and Peter W. May Department of Orthopedics, Mount Sinai School of Medicine, New York, NY 10029

Contributed by Sheldon Weinbaum, August 3, 2007 (sent for review May 14, 2007)

A fundamental paradox in bone mechanobiology is that tissue-level strains caused by human locomotion are too small to initi-ate intracellular signaling in osteocytes. A cellular-level strain-amplification model previously has been proposed to explain thisparadox. However, the molecular mechanism for initiating signal-ing has eluded detection because none of the molecules in thispreviously proposed model are known mediators of intracellularsignaling. In this paper, we explore a paradigm and quantitativemodel for the initiation of intracellular signaling, namely that theprocesses are attached directly at discrete locations along thecanalicular wall by �3 integrins at the apex of infrequent, previ-ously unrecognized canalicular projections. Unique rapid fixationtechniques have identified these projections and have shown themto be consistent with other studies suggesting that the adhesionmolecules are �v�3 integrins. Our theoretical model predicts thatthe tensile forces acting on the integrins are <15 pN and thusprovide stable attachment for the range of physiological loadings.The model also predicts that axial strains caused by the sliding ofactin microfilaments about the fixed integrin attachments are anorder of magnitude larger than the radial strains in the previouslyproposed strain-amplification theory and two orders of magnitudegreater than whole-tissue strains. In vitro experiments indicatedthat membrane strains of this order are large enough to openstretch-activated cation channels.

bone mechanotransduction � integrin attachments � osteocyte cellprocess � strain amplification � bone fluid flow

A fundamental paradox in bone biology is that tissue-levelstrains, which rarely exceed 0.1% in vivo (1, 2), are too small

to initiate intracellular signaling in bone cells in vitro (3, 4), wherethe necessary strains (typically 1.0%) would cause bone fracture.Osteocytes, the most abundant cells in adult bone, are widelybelieved to be the primary sensory cells for mechanical loadingbecause of their ubiquitous distribution throughout the bonetissue and their dendritic interconnections with both neighboringosteocytes and osteoblasts (5, 6), but osteocytes also require highlocal strains for mechanical stimulation. You et al. (7) developedan intuitive strain-amplification model to explain this paradoxwherein osteocyte processes are attached to the canalicular wallby transverse tethering elements in the pericellular matrix.According to this model, the drag generated by load-inducedfluid flow through the pericellular matrix would create tensileforces along the transverse elements supporting the pericellularmatrix. These resulting tensions then were transmitted by trans-membrane proteins to the central actin filament bundle in theosteocyte cell process leading to circumferential expansion ofthe cell process. The basic structural features in this model, thetransverse tethering elements, and the organization of the actinfilament bundle in the dendritic cell process were shown exper-imentally by You et al. (8). The latter study also provided keyinput data for a greatly refined three-dimensional theoreticalmodel by Han et al. (9). Although both models elegantly showedthat very small whole-tissue strains would be amplified 10-fold ormore at the cellular level because of the tensile forces in thetransverse tethering elements, the molecular mechanism for

initiating intracellular signaling was hard to identify becausenone of the likely molecules in the tethering complex [i.e.,proteoglycans, hyaluronic acid, or CD44 (8, 10–12)] are knownmediators of mechanically induced cell signaling. In this paper,we propose a paradigm for cellular-level strain amplification byintegrin-based focal attachment complexes along osteocyte cellprocesses.

Using an acrolein-paraformaldehyde-based fixation approachfor electron microscopy,§ we observed that discrete conicalstructures protrude periodically from the bony canalicular wall,where they directly contact the cell membrane of the osteocyteprocess and, thus, resemble focal adhesion complexes (Fig. 1).Other studies pointed to �v�3 integrins as the likely adhesionmolecules for these canalicular-cell process focal attachmentsites.§

Integrins are transmembrane heterodimeric molecules com-posed of an �-subunit and a �-subunit, and they anchor the cell’scytoskeleton to the extracellular matrix molecules. More impor-tantly for understanding osteocyte mechanotransduction, inte-grin focal adhesion complexes have been implicated as majormechanical transducer sites in various other cells, initiating ahost of intracellular signaling pathways, including focal adhesionkinase and small GTPases of the Ras family (13, 14). Further-more, a growing body of evidence suggests that focal integrinattachments are functionally and even structurally integratedwith other putative membrane mechanotransducers, includingstress-activated ion channels in a range of cell types includingosteocytes (15–18).

Based on our in situ morphological studies, we herein con-struct a model to quantitatively determine the mechanicaleffects of focal attachment complexes on osteocyte cell pro-cesses. Specifically, we test the hypothesis that focal attachmentcomplexes produce locally high strains along the cell membraneof osteocyte processes. Our theoretical model provides the directprediction of the piconewton-level forces on the focal attach-ments and the radial and axial membrane strains around theseattachment complexes as a function of loading magnitude andfrequency. Axial membrane strains in the vicinity of the focalattachment sites can be an order of magnitude larger than thepreviously predicted radial strains generated by the transversetethering elements (7, 9).

Author contributions: M.B.S. and S.W. designed research; Y.W. and L.M.M. performedresearch; M.B.S. and S.W. contributed new reagents/analytic tools; Y.W., M.B.S., and S.W.analyzed data; and Y.W., M.B.S., and S.W. wrote the paper.

The authors declare no conflict of interest.

Abbreviation: IIAP, integrin intracellular anchoring protein.

‡To whom correspondence should be addressed at: Department of Biomedical Engineer-ing, City College of New York, 138th Street at Convent Avenue, New York, NY 10031.E-mail: weinbaum@ccny.cuny.edu.

§McNamara, L. M., Majeska, R. J., Weinbaum, S., Friedrich, V., Schaffler, M. B. (2006) Trans.Orthop. Res. Soc. 31:393 (abstr.).

This article contains supporting information online at www.pnas.org/cgi/content/full/0707246104/DC1.

© 2007 by The National Academy of Sciences of the USA

www.pnas.org�cgi�doi�10.1073�pnas.0707246104 PNAS � October 2, 2007 � vol. 104 � no. 40 � 15941–15946

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Experimental ResultsOur morphological studies revealed that infrequent, discretestructures resembling focal attachment complexes protrudedfrom the bony canalicular wall, completely crossing the pericel-lular space to contact the cell membrane of the osteocyteprocess. These were termed ‘‘canalicular projections’’ (Fig. 1).These projections were similar in size and shape in both longi-tudinal and transverse cross-sections, indicating a conical mor-phology, and they contained collagen fibrils, identical in size andappearance to other collagen fibrils observed in the adjacentbone matrix. Canalicular projections were randomly and asym-metrically distributed along the osteocyte process, appearing onone side of the cell process but not the other. The filament-richcytoskeleton of the cell process and the pericellular matrix in theremainder of the pericellular space around cell processes weresimilar to those reported by You et al. (8). Comparable directcontacts between the membrane of the osteocyte cell body andthe bony lacunar wall were not observed (Fig. 1).

Theoretical ModelStructural Model. Based on the focal attachment complexesobserved in our morphological studies, we constructed a modelto determine the local mechanical environment around theseattachment sites. Fig. 2 shows a transverse cross-section of theidealized structural model in which the osteocyte process islocated at the center of the canaliculus with direct contact to alocal attachment complex and tethered to the canalicular wall bytransverse tethering elements over the rest of its circumference.A structural complex consisting of the conical canalicular pro-

jection, integrin molecule, and integrin intracellular anchoringprotein (IIAP) was introduced to represent a local attachmentcomplex. The structural model for the cytoskeleton of theosteocyte process and the transverse tethering elements in thepericellular matrix around the osteocyte process were adaptedfrom the model of Han et al. (9) and based on ultrastructuralfeatures demonstrated by You et al. (8). The particulars of thesewere as follows. The actin filament bundle at the center of thecell process is a hexagonal array of 19 parallel actin filaments(Fig. 2). Adjacent actin filaments with 12-nm spacing are cross-linked periodically by fimbrin, and the fimbrin cross-links rotate60° counterclockwise and advance 12.5 nm axially in successivecross-linking positions (see figure 1 in ref. 9). Cross-filaments,which provide the scaffold for the process membrane, as well asthe IIAP are wound in a double spiral with a 37.5-nm spacingaround the central actin filament bundle (see figure 1 in ref. 9).A proteoglycan matrix fills the pericellular space between thecell membrane of the osteocyte process and the canalicular wall;glycosaminoglycan side chains of the pericellular matrix areassumed to have a 7-nm spacing typical of the glycocalyx onendothelial cells (19). Transverse tethering elements (i.e., coreproteins of the pericellular proteoglycan matrix) are linkedphysically to cross-filaments via transmembrane molecules (e.g.,CD44) (8, 10) and also are arranged in a double-helix pattern ofcross-filaments along the axial direction of the canaliculus. Alocal conical canalicular projection takes the place of oneotherwise transverse tethering element, and the width of its baseis 75 nm as shown in Fig. 3B. Dimensional parameters of thestructural model are summarized in Table 1.

The presence of the focal attachment complex results inasymmetric loading on the osteocyte process and its cytoskele-ton. Canalicular projections here are considered to be infinitelyrigid compared with the flexible transverse tethering fibersbecause they appear structurally comparable to the adjacentbone matrix, as shown in Fig. 1, and integrins and their associatedIIAP are treated as fixed supports. Therefore, the actin filamentdirectly linked to the fixed focal attachment complex will beimmobilized by the fixed support of the focal attachment, but theother 18 actin filaments can slide axially relative to the immo-bilized actin filament. Because of this fixed attachment, all of thetransverse tethering elements carry an asymmetric load, incontrast to the axisymmetric model in ref. 9, where the axialmotion of the transverse tethering elements and actin filamentbundle are uniform. The sliding motion of actin filaments hasbeen observed previously in the bending of stereocilia about thecentral filaments at their base (20). The resulting asymmetricloading significantly complicates the mathematical modeling ofthe deflections of the central actin filament bundle and cellmembrane and necessitates our deriving a simplified computa-tional approach.

Mathematical Model for Transverse Tethering Elements. Load-induced fluid flow through the pericellular space around theosteocyte process will produce a drag force on the pericellularmatrix. This force deforms the transverse tethering elements asshown in Fig. 3 B and D. The deformed shape of the transversetethering element is described by the well known catenaryequation for the following two reasons. First, Han et al. (9)showed that the finite flexural rigidity EI of transverse tetheringelements predicted in ref. 19 has little significance for smalldeflections, and these elements can be treated as inextensible butflexible strings. Second, load-induced fluid flow in the pericel-lular space will be a nearly uniform plug flow in the cross-sectionplane because of the small glycosaminoglycan spacing; therefore,the transverse fibers are subjected to an approximately uniformhydrodynamic loading along their length. Thus, the deformedshape of an individual transverse tethering element in Fig. 3D isgiven by the catenary equation:

A BTransverse Tethering Element

Canalicular Projection

Fig. 1. Transverse cross-section (A) and longitudinal cross-section (B) of TEMmicrographs showing infrequent, discrete structures resembling focal adhe-sion complexes protruding from the bony canalicular wall, completely cross-ing the pericellular space to contact the cell membrane of the osteocyteprocess along the canaliculi. (Scale bars: A, 500 nm; B, 100 nm.)

Fig. 2. Transverse cross-section of the idealized structural model for a cellprocess in a canaliculus attached to a focal attachment complex and tetheredby the pericellular matrix.

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wLTx

� sinh� wdTx� , [1]

where d is the radial distance between the canalicular wall andthe cell process membrane, Tx is the constant radial componentof the tension on the transverse tethering element, and w is theuniform hydrodynamic drag force per unit length of transversetethering element. Because the canalicular projections are in-frequent and located at discrete locations along the canaliculi,the majority of the pericellular space in the canaliculi can beassumed to be of the same geometry as the model in ref. 9.Therefore, the pressure gradient along the cell process and thedrag force FD on the transverse tethering elements per unitlength of cell process will be nearly the same as in ref. 9. w isevaluated by dividing the total drag force on an axial periodicunit of length Lf � 37.5 nm in Fig. 3B by the total length of the12 transverse tethering elements associated with the periodicunit and is given by

w �FDLf

12L. [2]

Here L is the length of each individual transverse tetheringelement, FD is the drag force on the transverse tetheringelements per unit length of cell process and is evaluated by thesame expression as equation 8 in appendix A of ref. 9. The modelfor the fluid flow through the pericellular matrix is based on thetheoretical model in ref. 21.

Mathematical Model for Osteocyte Cell Processes. Two mathemat-ical idealizations are introduced to simplify the analysis butretain the essential physics of the deformation for the centralactin filaments shown in Fig. 2. First, the central actin filament

bundle with its fimbrin cross-links in the core of the osteocyteprocess is replaced by a homogenous cylindrical elastic structurethat has the same size and overall radial elastic modulus as theoriginal cross-linked structure. Han et al. (9) show that cornerand central actin filaments in the outer ring of the actin filamentbundle shown in Fig. 2 undergo different radial displacements�m1 and �m2, respectively, but that �m1 is �91% of �m2, and,therefore, the difference is small enough to use an average value.Second, the eleven transverse tethering elements and the focalattachment shown in Fig. 2 are mathematically assumed to act inthe same cross-sectional plane when dealing with the overallradial force balance as shown in Fig. 3A. As in ref. 9, it isreasonable to assume that the deformations of these cross-filaments and IIAP are substantially smaller than the bendingdeformation of the actin filaments, which are loaded transverseto their axes. Thus, the cross-filaments and IIAP are assumed notto deform in the radial direction.

With these idealizations, one can reduce the complex struc-tural geometry in Fig. 2 and its loading to a much simpler planarloading configuration in which the osteocyte process is asym-metrically located and loaded with a fixed focal attachment siteat point I at the apex of the canalicular projection, as sketchedin Fig. 3 A and B. Thus, the deformation induced by the tension,Ti, is given by

�i � fTi �i � 0,1,2, . . . , 6�, [3]

where

f �Lf

3

340EIa

is the radial elastic modulus of the of the homogeneous cylin-drical core [derived in supporting information (SI) Appendix A],T0 is the tension associated with the focal attachment, T1–T6 arethe tensions on the transverse tethering elements, and the local�i are the deflections of the homogenous cylindrical core inducedby the Ti. Here, Lf is the length of one periodic unit shown in Fig.3B, and EIa is the bending rigidity of a single actin filament in theactin filament bundle of the osteocyte process.

The deformations �i (i � 1, 2, . . . , 6) of the transversetethering elements are derived in SI Appendix B. These defor-mations are related to the radial distances, di (i � 1, 2, . . . , 6),between the canalicular wall and the deformed cell processmembrane associated with individual transverse tetheringelements:

d1 � L � �1 ��32

�0; d2 � L � �2 � �0/2; d3 � L � �3;

[4A–C]

d4 � L � �4 � �0/2; d5 � L � �5 ��32

�0; d6 � L � �6 � �0,

[4D–F]

where L is the length of the transverse tethering element.Because the tensions T0–T6 are assumed to act in the same

plane, the overall force balance for T0–T6 sketched in Fig. 3A canbe expressed as

T0 � �3T1 � T2 � T4 � �3T5 � T6. [5]

Eqs. 4A–F and 5 provide seven equations for the seven unknownT0–T6, which are related to the displacements �0–�6 through Eqs.1 and 3.

Because the free ends of the transverse tethering elements aredisplaced both radially and axially (i.e., in directions perpendic-

Fig. 3. Deformation diagrams for the idealized mathematical model. (A)Transverse cross-section of the idealized homogeneous elastic cylinder andthe idealized plane for all of the transverse tethering elements and focalattachment. (B) Longitudinal cross-section of the deformed transverse teth-ering elements and sliding actin filaments. (C) Top view of the undeformedand deformed cell process membrane around the focal attachment site (not toscale). (D) Force balance on a deformed transverse tethering element. Thedashed lines indicate the deformed structural elements.

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ular and parallel to the central line of the cell process), both theresulting radial and axial strain components on cell processes willbe evaluated as a function of tissue loading. The radial strain �rin the plane through the focal attachment is defined as the ratioof the summation of deformations �0 and �6 to the undeformeddiameter of the cell process membrane 2a in Fig. 3A, and isgiven by

�r � ��0 � �6�/2a. [6]

The axial strain �a in the vicinity of focal attachment site isdefined as the relative change of the nonradial component of thedeformation of In (i.e., the deformation of the cell membrane ofosteocyte process generated by the deformed transverse tether-ing element adjacent to the focal attachment) to its undeformedlength as shown in Fig. 3C and given by

�a � �In�nr � Innr� � Innr . [7]

Here In�nr is the nonradial component of In�, the deformed stateof In, and Innr is the nonradial component of In.

Parameter Values. The values of the parameters used in the model,which are grouped as parameters for the hydrodynamic model,parameters for the canaliculus and cell process, and parametersfor the central actin filament bundle, are shown in Table 1.

Theoretical ResultsThe radial strain �r given by Eq. 6 and the axial strain �a givenby Eq. 7 are shown in Fig. 4 A and B, respectively, as a functionof loading frequency using tissue-loading amplitude as a param-eter. For comparison, radial strain in the cell process membranefor axisymmetric loading from ref. 9 for a tissue loading of 10MPa is shown in Fig. 4A, open arrow. Radial strains predictedby the current model are �70% of those in Han et al. (9).Strikingly, �a is approximately one order of magnitude largerthan �r for the same tissue loading. �a is predicted to be �6% ata physiological loading of 20 MPa at 1 Hz and can exceed 1% forlow-amplitude, high-frequency tissue loadings, e.g., small tissue

strains of 5 �� (0.1 MPa) at 30 Hz produce an axial strain aroundthe focal attachment site of 1.5%.

In Fig. 5, we show the tensile force on the focal attachment,T0, as a function of loading frequency up to 40 Hz withtissue-loading amplitude as a parameter. T0 exhibits a monotonicincrease as loading frequency increases for a given tissue-loadingamplitude. One observes that T0 is �10 pN at a physiologicalloading of 1,000 �� at 1 Hz.

The dashed lines in Figs. 4 and 5 show the power-lawrelationship between tissue-level strain amplitude and loadingfrequency derived from the whole-bone strain measurement byFritton et al. (2).

Table 1. Values of the parameters used in the model

Parameter Value

Osteonal hydrodynamic model (21, 45)B, dimensionless relative compressibility

of bone matrix to water0.53

c, pore fluid pressure diffusion constantof the Biot theory, mm2/s

0.13

ro, radius of the osteon, �m 100r1, radius of the osteonal lumen, �m 27

Canaliculus and cell process (7, 8, 19)b, radius of the canaliculus, nm 130a, radius of the osteocyte process, nm 52c, radius of the homogenous elastic

cylinder, nm25

�, the spacing neighboring twoglycosaminoglycan chains, nm

7

Kp, Darcy’s permeability of matrixbetween cell process and canalicularwall, nm2

10.3

�, fluid viscosity, dyne*�s/cm2 10�2

Central actin bundle (7, 46)Lf, length of periodic fimbrin cross-over

along actin filament, nm37.5

Ela, bending rigidity of actin filaments,pN�nm

21.5 104

*1 dyne � 10 �N.

0

5

10

15

0 10 20 30 40Frequency (Hz)

)%( niart

S laixA

1 MPa, 50 με

5 MPa, 250 με

20 MPa, 1000 με

10 MPa, 500 με

0.1 MPa, 5 με

B

0.0

0.5

1.0

1.5

0 10 20 30 40Frequency (Hz)

)%( niart

S laidaR

A20 MPa, 1000 με

10 MPa, 500 με

1 MPa, 50 με

5 MPa, 250 με

Fig. 4. Membrane strains in the vicinity of focal attachment complex. (A) Theradial strain �r (open arrow points to the radial strain on the cell process mem-brane for an axisymmetric loading for a tissue loading of 10 MPa, from ref. 9). (B)The axial strain �a as a function of loading frequency with tissue-loading ampli-tude as a parameter. The dashed lines in both A and B show the physiologicalloadings of bone tissue based on the power-law relationship between strainamplitudes and loading frequencies observed by Fritton et al. (2).

0

10

20

30

40

0 10 20 30 40Frequency (Hz)

)Np( noisne

T

20 MPa, 1000 με

1 MPa, 50 με

5 MPa, 250 με

10 MPa, 500 με

Fig. 5. The tension on the focal attachment T0 as a function of loadingfrequency with tissue-loading amplitude as a parameter. [The dashed lineshows the physiological loadings of bone tissue based on the power-lawrelationship between strain amplitudes and loading frequencies observed byFritton et al. (2).]

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DiscussionThe current studies reveal that osteocyte processes contactdiscrete structures resembling focal adhesion complexes thatprotrude from the bony canalicular wall. Similar structures werenot observed at osteocyte cell bodies. Immunohistochemistrystudies point to �v�3 integrins as the likely adhesion moleculesfor these canalicular-cell process focal attachment sites.§ Mostsignificantly, our mathematical model for the mechanical envi-ronment around these focal attachment complexes predicts thatthese attachment complexes will dramatically and focally amplifycellular strains at these sites.

In our model, canalicular projections are considered to berigid as they appear as extensions from the adjacent bone matrix.Thus, the adhesion molecules on their apex behave as fixed-pointsupports, whereas the transverse tethering elements are flexibleand their attachment sites move with the actin cytoskeleton inthe osteocyte process. This structural asymmetry can give rise toasymmetry in the local mechanical effects on the cell membraneand cytoskeleton of the osteocyte process. In the axisymmetricmodels of You et al. (7) and Han et al. (9), the central actinbundle moves axially as a solid body because of the uniform axialdisplacement of the mobile ends of the transverse tetheringelements. In both axisymmetric models and the present model,the cross-filaments and the IIAP are treated as relatively rigid.Their change in length is small compared with the axial dis-placement of the transverse tethering elements and also thedeformation of the individual actin filaments in the actin fila-ment bundle because the latter are loaded transverse to theiraxes. Second, it was well established from the studies in ref. 20on stereocilia that fimbrin cross-linked actin filaments can sliderelative to one another. Therefore, in our model the individualactin filament directly linked to the more rigid integrin attach-ment complex would be relatively immobilized, whereas theother filaments within the central actin bundle could experiencesignificant axial displacements relative to this fixed filament. Ourmodel quantitatively predicts that local axial strains in thevicinity of the integrin attachment sites can be two orders ofmagnitude larger than the global tissue-level strains and an orderof magnitude larger than the radial strains previously predicted(7, 9). Parametric analysis, in SI Appendix C, found that only theprojection height and resulting asymmetry of the process withinthe canalicular cross-section would have a significant effect onlocal force/strain. Strain amplifications on the order of 10-fold orgreater always were present at projection attachments when theirheights were (b � a)/2, but the tensile force at the integrinattachment would be significantly increased as its height wasdecreased and the axial strain was reduced because of theshortening of the neighboring tethering filaments. A halving ofprojection height led to approximately a tripling of the tensileforce and a 4-fold reduction in the axial strain.

This large local increase in strain amplification has importantimplications for both the high-amplitude, low-frequency loadingcharacteristic of locomotion and the low-amplitude, high-frequency loading characteristic of forced vibrations and mus-cular contractions required for the maintenance of posture (2,22). The threshold value of cellular strains needed for excitingosteocytes in culture appears close to 0.5% (3, 4). In the case ofhigh-amplitude loading, the classic experiment of Rubin andLanyon (23) shows that bone mass will be maintained at aloading of 20 MPa (1,000 ��) at 1 Hz applied only 100 cycles aday. Our results in Fig. 4A show that the radial strains are juston the borderline of satisfying the requirement of cellularsignaling for cultured bone cells, 0.5% for this loading (20 MPaat 1 Hz). In marked contrast, axial strains are 6%, far in excessof this threshold. Our model also predicts that axial strains couldreach 1.5% for very-low-amplitude, high-frequency vibrations of�5 �� (0.1 �Pa) at 30 Hz, for which bone maintenance also is

observed (22). Such large axial strains fall into the range thatinitiates intracellular signaling in bone cells (3). Therefore, thehigh focal axial strain concentrations could provide a potentialmechanism for osteocyte excitation.

For the integrin attachment complexes along osteocyte pro-cesses to serve a mechanosensory function, the tensile force T0on the focal attachment must lie below a maximum value theirwould lead to detachment of the adhesive molecules from theirsubstrate. Our model predicts that T0 rarely exceeds 10 pN overthe entire physiological loading range estimated from the power-law relationship observed by Fritton et al. (2) as shown in Fig. 5.In contrast, experimental measurements revealed rupturestrength for single �3 integrin–ligand pairs on the order of50–100 pN at a loading rate of 10,000 pN/s (24, 25). Physiologicalloading rates are much lower. The dashed power-law curves inFigs. 4 and 5 correspond to a loading rate that varies from �40to 300 pN/s over the entire physiological loading range. Althoughloading rate has been shown to have a significant effect onintegrin–ligand bond strength, with this strength decreasing asloading rate decreases (26, 27), this decrease in strength typicallyis a factor of 2 and not a factor of 5 or more (27). Therefore, focalattachments should be stable over the entire physiologicalloading range even if they are composed of only a single integrinmolecule.

Many studies have demonstrated that mechanically sensitiveion channels exist in bone cells (28–30). Cyclical strain has beenshown to modulate the activity of certain channels—chronicallystrained osteoblasts had significantly larger increases in whole-cell conductance when subjected to additional mechanical strainthan unstrained controls (31). In addition to direct activation ofintracellular signaling cascades, influx of a charged species suchas calcium also can alter membrane potential and activatevoltage-sensitive channels that are not directly mechanosensitivebut are modulated by a related mechanosensitive element. Forexample, the L-type voltage-gated calcium channel has beenimplicated in mechanosensitivity in vivo in bone (32). Gadolin-ium, which blocks a number of stretch/shear-sensitive cationchannels, was shown to block load-related increases in prosta-glandin synthesis and nitric oxide release in mechanically loadedlimb bone cultures (33). Furthermore, osteoblast response tomechanical loading was even more sensitive to nifedipine, whichblocks calcium channels. Similar results have been reported forosteocyte-like cells (34). Recent studies (35, 36) implicate theP2X7 purinergic receptor in osteoblast and osteocyte mechano-sensitivity, and data from other systems suggest that P2X7-basedmechanical signaling may work through a mechanically sensitivechannel in the pannexin family (37). However, it still remains tobe determined how these channels are regulated by upstreamload-induced mechanical signals.

Recent experiments indicate that integrin attachments canplay a central role in modulation of stretch-activated and othercation channels (15, 16) in addition to their well characterizedrole in FAK- and MAPK-based signaling events (13, 14). Boththe �5�1 and �v�3 integrins have been shown to regulate L-typecalcium channels in brain and vascular smooth muscle excitabil-ity (38), and these also are associated with focal adhesion typecomplexes (39). In particular, �v�3 integrins have been shown toregulate mechanosensitive cation channels in osteocyte cultures(18). Furthermore, evidence suggests that integrins colocalizewith ion channels forming a mechanoreceptor complex (17).

Based on the lines of evidence above, we speculate that thelarge axial strains in the vicinity of the integrin-based focalattachments play a direct role in osteocyte excitation by regu-lating mechanosensitive or even voltage-sensitive channels iffocal attachments colocalize with these channels and permiteither the passage of ions, as in the case of tip link attachmentson stereocilia (40), or the passage of the nucleotides ATP and/orprostaglandin E2 (PGE2). Observations from several recent

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experiments are particularly germane to this speculation.Charras et al. (41) found that the cellular-level strains needed toopen half of the mechanosensitive channels in bone cells wasquite large, larger than the strain that bone tissue can withstandwithout fracture and on the same order as the strains at focalattachment sites predicted by our model. Reilly et al. (42) foundthat enzymatic removal of the pericellular glycocalyx fromMLO-Y4 cells with hyaluronidase eliminated their PGE2 re-sponse to fluid shear stress, but calcium signaling was not alteredby removing the pericellular glycocalyx, suggesting an additionalcomponent for mechanotransduction: namely, focal adhesioncomplexes attaching osteocyte processes to the bone matrixsubstrate. Indeed, Miyauchi et al. (18) recently reported that theactivity of volume-sensitive calcium channels in osteocytes wasgreatly potentiated by osteopontin, a ligand for the �v�3 integrinsexpressed by these cells, and stretch activation of calciumsignaling in these osteocytes could be suppressed by disruptingthe �3 binding with echistatin.

In summary, our theoretical model shows that integrin-basedattachment complexes along osteocyte cell processes woulddramatically and focally amplify small tissue-level strains. Giventhe increasing evidence that integrins play a central role in cationchannel regulation, it seems reasonable to speculate that highfocal strain concentrations at these attachment sites play a directrole in osteocyte mechanotransduction.

Experimental MethodsTo optimize preservation of osteocyte cell membranes andsurrounding bone matrix architecture and proteins for trans-mission electron microscopy, rapid penetrating acrolein-paraformaldehyde-based fixatives were used. Acrolein is a highlyreactive low-molecular-weight aldehyde that penetrates tissuemuch more rapidly than either paraformaldehyde or glutaral-dehyde and thus dramatically enhances fixation (43, 44). Thisfixation approach initially was developed and reported to besuperior to all other approaches by McNamara et al.§ A briefdescription of that approach is as follows. Under InstitutionalAnimal Care and Use Committee (IACUC) approval, anesthe-tized adult C57BL/6J mice (4–5 months old) were perfused viaaortic cannulation with the fixative. Tibiae and femora wereexcised, immersion-fixed, decalcified in 10% EDTA, and thenpostfixed in 1% OsO4. Samples were embedded in Epon. Ul-trathin sections then were cut by using a diamond knife, mountedon Formvar grids, and stained with uranyl acetate–lead citratesolution in 50% ethanol. Sections were viewed with a Philips 300transmission electron microscope. Images of osteocytes wereacquired at 80,000 to 100,000 magnifications.

We thank Dr. Robert J. Majeska (Mount Sinai School of Medicine) forhelpful discussion and Damien Laudier (Mount Sinai School of Medi-cine) for technical assistance. This study was supported by NationalInstitutes of Health Grants AR48699 and AR41210.

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