Contribution of intermediate filaments to cell stiffness, stiffening, and growth

Ning Wang¹ and Dimitrije Stamenovi²

¹ Physiology Program, Department of Environmental Health, Harvard School of Public Health, Boston 02115; and ² Department of Biomedical Engineering, Boston University, Boston, Massachusetts 02215

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS APPENDIX REFERENCES

It has been shown previously that intermediate filament (IF) gels in vitro exhibit stiffening at high-applied stress, and it was suggested that this stiffening property of IFs might be important for maintaining cell integrity at large deformations (Janmey PA, Evtenever V, Traub P, and Schliwa M, J Cell Biol 113: 155-160, 1991). In this study, the contribution of IFs to cell mechanical behavior was investigated by measuring cell stiffness in response to applied stress in adherent wild-type and vimentin-deficient fibroblasts using magnetic twisting cytometry. It was found that vimentin-deficient cells were less stiff and exhibited less stiffening than wild-type cells, except at the lowest applied stress (10 dyn/cm²) where the difference in the stiffness was not significant. Similar results were obtained from measurements on wild-type fibroblasts and endothelial cells after vimentin IFs were disrupted by acrylamide. If, however, cells were plated over an extended period of time (16 h), they exhibited a significantly greater stiffness before than after acrylamide, even at the lowest applied stress. A possible reason could be that the initially slack IFs became fully extended due to a high degree of cell spreading and thus contributed to the transmission of mechanical stress across the cell. Taken together, these findings were consistent with the notion that IFs play important roles in the mechanical properties of the cell during large deformation. The experimental data also showed that depleting or disrupting IFs reduced, but did not entirely abolish, cell stiffening. This residual stiffening might be attributed to the effect of geometrical realignment of cytoskeletal filaments in the direction of applied load. It was also found that vimentin-deficient cells exhibited a slower rate of proliferation and DNA synthesis than wild-type cells. This could be a direct consequence of the absence of the intracellular IFs that may be necessary for efficient mediation of mechanical signals within the cell. Taken together, results of this study suggest that IFs play important roles in the mechanical properties of cells and in cell growth.

vimentin; cytoskeleton; cellular mechanics; magnetic twisting cytometry; deoxyribonucleic acid synthesis

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS APPENDIX REFERENCES

IT HAS BEEN SHOWN previously that mechanical properties of adherent cells reside mostly in the cytoskeleton (CSK). Numerous mechanical measurements on living cells show that a selective disruption of three major CSK filament systems, actin microfilaments (MFs), microtubules (MTs), and intermediate filaments (IFs) results in a decrease of cell stiffness (13-15, 17, 23, 24). Although those studies have provided insight into the distinct roles of MFs and MTs as mechanical-supporting structures of the CSK, the role of IFs remains elusive. Although their abundance, intracellular architecture, and contribution to cell stiffness suggest an important mechanical role, IFs appear not to be critical for cell viability. We have recently shown that vimentin, a major structural protein of IFs in fibroblasts and endothelial cells, plays important roles in deformability, migration, and contractility of fibroblasts; vimentin-deficient cells are more compliant, less contractile, and less motile than wild-type cells (5).

Further information about the mechanical role of IFs in living cells are inferred from in vitro rheological measurements on vimentin and keratin gels (keratin IFs are prominent in epithelial cells). These gels exhibit highly nonlinear stress-strain behaviors, characterized by a very low initial stiffness and a relatively high stiffness at large strains (9, 12). This positive dependence of stiffness on stress or strain is known as a strain-hardening or stiffening behavior. If this in vitro stiffening behavior of IF polymers would persist in living cells, then one would predict that the contribution of IFs to cell stiffness would be minor during small deformation of the cell and would increase progressively with increasing cell deformation.

In this study, we hypothesized that in vitro stiffening behavior of IF polymers persists in living cells. We tested this hypothesis directly, using magnetic cell twisting to apply varying mechanical stress through integrin receptors to wild-type and vimentin-deficient fibroblasts and to wild-type fibroblasts and endothelial cells in which the vimentin IF network was chemically disrupted. We found that only a portion of cell-stiffening behavior could be accounted for by the rheological properties of vimentin. We also showed that vimentin-deficient fibroblasts had much slower growth rate compared with the wild-type cells. Taken together, these data indicate that compromising mechanical capabilities of the cells by depleting IFs have a significant effect on cell growth.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS APPENDIX REFERENCES

Cell culture. Primary fibroblasts were obtained from homozygous wild-type or mutant mouse embryos in which vimentin alleles were deleted as described previously (5). Cells were used between passages 6-12 for all experiments. Bovine capillary endothelial cells were cultured as described previously (24). Cells were used between passages 10-14.

Mechanical measurements. Ferromagnetic beads (4.5-µm diameter) were coated with a synthetic RGD (Arg-Gly-Asp)-containing peptide (Peptide 2000, Telios; 50 µg peptide/mg beads), a known ligand that binds specifically to cell integrin receptors. The beads were stored in carbonate buffer at 4°C overnight to facilitate protein absorption onto the beads (24, 25).

Wild-type or vimentin-deficient fibroblasts or normal endothelial cells were plated in a serum-free medium onto collagen I-coated wells (Removawells, Immulon II, Dynatech; 30,000 cells/well) 4 h before experiments. RGD-coated beads were added to the wells (on the average 1-2 beads/cell), and after 15 min, unbound beads were washed away with a serum-free medium. One well was placed into the magnetic cell twisting device each time, and the mechanical measurements were performed as described previously (26). Briefly, the beads were first magnetized by a strong magnetic pulse (1,000 gauss over 10 µs) in the horizontal direction. As a consequence, the beads became oriented in the horizontal plane. A twisting torque was then applied to these beads by a weak vertical magnetic field (0-25 gauss over 60 s), causing the beads to rotate in the vertical plane as compass needles. Bead rotation was transmitted directly to the CSK through a series of linking proteins, generating in that way a mechanical stress in the CSK (5, 24). The stress was defined as the ratio of the applied mechanical torque to the volume of the bead and was calibrated with a viscous standard. Bead angle of twist (angular strain) was measured by a magnetometer (25). The apparent stiffness was determined from the steady-state response as the ratio of applied stress to corresponding angle of twist. The range of applied stress was 10-80 dyn/cm².

Statistically significant differences between the mechanical properties of wild-type and vimentin-deficient cells were assessed by the Student's t-test. Differences with P < 0.05 were considered significant.

Proliferation and DNA synthesis measurements. Wild-type and vimentin-deficient confluent fibroblasts were synchronized by being placed in 0.1% serum for 48 h before being trypsinized and plated on collagen I (5 µg/ml) in the presence of 10% serum. The cell number was counted 4, 24, and 48 h after plating. To find out at what phase of cell cycle cell growth was slowed down, DNA synthesis was measured as follows. Bromodeoxyuridine (BrDU) incorporation was quantified in wild-type and vimentin-deficient cells that were synchronized, then trypsinized and plated in the presence of serum as described above. After 4 h of plating, BrDU was incubated with the cells. After 20 and 24 h of plating, the cells were fixed and stained with an antibody to BrDU. Positively stained cells were expressed as a percentage of total cells, as described previously (2).

	RESULTS AND DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS APPENDIX REFERENCES

Magnetic twisting measurements. Angle of twist vs. applied stress relationships for both wild-type and vimentin-deficient cells exhibited nonlinear dependences, with the beads undergoing a smaller rotation in the former than in the latter for a given stress (Fig. 1A). Consequently, the wild-type cells were stiffer and exhibited greater stiffening than the vimentin-deficient cells over the observed range of stress (Fig. 1B). At all but the lowest applied stress (10 dyn/cm²), the stiffness of wild-type cells was significantly greater than the stiffness of vimentin-deficient cells; at 10 dyn/cm² those stiffnesses were not significantly different (Fig. 1B). Taken together, these results suggest that the greater stiffness and stiffening in the wild-type cells than in the vimentin-deficient cells may be attributed to the rheological properties of vimentin IFs that were shown previously to exhibit a prominent stiffening behavior in vitro (9). On the other hand, it is also possible that this difference in the mechanical properties of the wild-type and vimentin-deficient cells may be primarily due to a difference in their CSK architecture. Immunofluorescent labeling of fibrillar actin revealed that in the wild-type cells, actin stress fibers and focal structures ("geodomes") are two dominant forms of polymerized actin, whereas in vimentin-deficient cells, the stress fibers are prevailing (5). To investigate whether this difference in the CSK architecture could be a primary cause of the different mechanical properties of wild-type and vimentin-deficient cells, we measured stiffness of wild-type cells before and after disrupting chemically the cell vimentin IF network.

View larger version (14K): [in this window] [in a new window]   Fig. 1.   Angle of twist vs. stress relationships (A) and corresponding stiffness vs. stress relationships (B) for adherent wild-type and vimentin-deficient fibroblasts. Stresses ranging from 10 to 80 dyn/cm2 were applied through Arg-Gly-Asp (RGD)-coated ferromagnetic beads. Cells were plated on collagen I-coated dishes for 4 h before mechanical measurements. Means ± SE (n = 5 wells); * significantly greater values (P < 0.05).

We used acrylamide, a chemical that selectively disrupts the vimentin IF network but leaves the MF and MT networks intact (6, 16). Our rationale was that if the stiffening behavior of vimentin IFs was the key contributor to the greater stiffening of the wild-type cells (Fig. 1, A and B), then disrupting IFs in wild-type cells should cause decreases in stiffness and stiffening similar to those observed in vimentin-deficient cells.

Magnetic twisting measurements were done on wild-type fibroblasts and on bovine capillary endothelial cells, before and after acrylamide (4 × 10³ M) was added, using the same protocol as described above. In our previous experience, the dose of acrylamide of 4 × 10³ M produces maximum effects on CSK mechanics (24). Measurements were performed 1 h after acrylamide was administered to the cells to allow a complete disruption of the IF network (24). We used endothelial cells in addition to fibroblast to see if the effect of vimentin IFs on cell stiffening also existed in other cell types. It was found that cell stiffness and stiffening decreased after adding acrylamide in both fibroblasts and endothelial cells (Figs. 2 and 3). These results were consistent with those obtained from the measurements on wild-type and vimentin-deficient fibroblasts (Fig. 1B). Although we could not entirely exclude the possibility of an altered CSK architecture playing a role, our data suggest that the rheological properties of vimentin IFs contribute greatly to stiffening behavior of fibroblasts and endothelial cells.

View larger version (14K): [in this window] [in a new window]   Fig. 2.   Stiffness vs. stress relationships for wild-type fibroblasts before and after treatment with acrylamide. Stresses ranging from 10 to 40 dyn/cm2 were applied through RGD-coated ferromagnetic beads. Cells were plated on collagen I-coated dishes for 4 h before mechanical measurements. Means ± SE (n = 7 wells); * significantly greater values (P < 0.05).

View larger version (15K): [in this window] [in a new window]   Fig. 3.   Stiffness vs. stress relationships for adherent endothelial cells before and after treatment with acrylamide. Stresses ranging from 10 to 60 dyn/cm2 were applied through RGD-coated ferromagnetic beads. Cells were plated on collagen I-coated dishes for 4 h before mechanical measurements. Means ± SE (n = 5 wells); * significantly greater values (P < 0.05).

Our data also revealed that the stiffening was not totally abolished in the cell where vimentin IFs were either genetically depleted or chemically disrupted. This finding suggests that mechanisms other than the rheological properties of vimentin may also contribute to cell stiffening. We have shown previously using tensegrity models of the CSK that cell stiffening may be also attributed to the effect of realignment of CSK filaments in the direction of applied load, a phenomenon known as "kinematic stiffening" (20, 24). However, this behavior of cells could be also mimicked by other types of models (e.g., a simple model in which IFs, MFs, and MTs would be viewed as elastic springs arranged in parallel), suggesting that one need not invoke tensegrity to explain the observed features of the cell. Nevertheless, tensegrity architecture, which has been shown to incorporate some basic structural and mechanical features of the CSK of adherent cells (cf. 8), could provide a mechanistic explanation for cell stiffening by identifying the rheological properties of IFs and kinematic stiffening of the CSK as key mechanisms. An example of this particular feature of tensegrity is given in the APPENDIX. We would like to point out that kinematic stiffening is a result of temporary changes in CSK geometry for duration of applied forces. These changes are different from alterations of CSK geometry due to CSK remodeling that are more permanent in nature.

Data from proliferation and DNA synthesis measurements. Although our previous studies have shown that in the absence of vimentin, fibroblasts exhibit impaired motility and wound healing (5), it is not clear what is the effect of vimentin on cell growth. In this study, we measured cell proliferation in synchronized cells and found that it was slower in the vimentin-deficient cells than in the wild-type cells (Fig. 4). Our measurements of DNA synthesis indicated that it was much greater in the wild-type cells than in the vimentin-deficient cells; 20 h after plating, 25% of vimentin-deficient cells and 75% of wild-type cells showed BrDU incorporation, whereas 24 h after plating, 50% of vimentin-deficient and 90% of wild-type cells showed BrDU incorporation (Fig. 5). Thus in addition to what we found earlier, that vimentin-deficient cells have impaired mechanical stability, migration, and contractility (5), here we presented evidence that cell proliferation was also impaired due to a slower rate of DNA synthesis. At the present time we do not know the exact mechanism of the slower rate of DNA synthesis for vimentin-deficient cells. One possibility could be that in the absence of the IF network, the transfer of mechanical stress from the cell surface to the nucleus is impaired. This may not be an unreasonable explanation because previous studies have shown that DNA synthesis is directly correlated with the extent of cell distension (i.e., spreading) and, therefore, with the corresponding distending stress (18). The assumption is that the distending stress regulates DNA synthesis in a dose-dependent fashion. Because the ability of the cell to efficiently transfer mechanical stress depends critically on the ability of the CSK to stabilize cell shape and prevent excessive cell deformation by utilizing the stiffening mechanism, IFs, which provide a significant portion of this stiffening during large cell deformation (e.g., spreading, locomotion), are essential for normal cell function. An alternative explanation is that in the absence of IFs, the active component of CSK tension is decreased (5), which, in turn, leads to a decrease in cell stiffness and DNA synthesis. This possibility is supported by the recent finding that DNA synthesis is blocked when CSK tension is completely inhibited (7).

View larger version (14K): [in this window] [in a new window]   Fig. 4.   Synchronized wild-type and vimentin-deficient fibroblast proliferation as a function of plating time. Cells were plated on collagen I-coated dishes. Means ± SE (n = 4 wells); * significantly different values (P < 0.05).

View larger version (12K): [in this window] [in a new window]   Fig. 5.   DNA synthesis of synchronized wild-type and vimentin-deficient fibroblasts as a function of plating time. Cells were serum deprived for 48 h and plated on collagen I dishes. Positively bromodeoxyuridine-stained cells are presented as a percentage of all cells 20 and 24 h after plating. Means ± SE (n = 3 wells; 5 randomly chosen counting areas per well).

Critique. Despite similarities between data obtained from magnetic twisting measurements on wild-type and vimentin-deficient cells on one hand, and wild-type cells before and after IF disruption by acrylamide on the other hand, there are some salient differences that need to be addressed. First, at low applied stress (10 dyn/cm²) there was very little difference in stiffness between wild-type and vimentin-deficient cells (Fig. 1B). Similar observations were made in endothelial cells before and after the treatment with acrylamide (Fig. 3). On the other hand, data for wild-type fibroblasts showed that at 10 dyn/cm², the stiffness was greater, although not significantly, before than after acrylamide (Fig. 2). This, in turn, suggests that besides disrupting the vimentin IF network, acrylamide might have other effects that could cause a further reduction in cell stiffness. Because the intracellular IF, MF, and MT networks appear to be physically interconnected (21-23), disruption of the IF network may cause geometric rearrangements of the other two. It is also possible that during 1 h from the time acrylamide was added to the cells until the magnetic twisting measurements were performed, the CSK underwent a significant remodeling. Finally, acrylamide may decrease cell stiffness through decreasing the active CSK tension by inhibiting metabolic activities of the cell.

We explained impaired DNA synthesis in the vimentin-deficient cells relative to the wild-type cells by the absence of IFs in the former to mediate efficient transfer of mechanical stress from the cell surface to the nucleus. On the other hand, it has been shown previously that the IFs of living cells appear slack (cf. 1, 8). This would imply that IFs do not affect transfer of mechanical stress across the CSK unless the cell is highly spread and the IFs are fully extended. To explore this possibility, we performed the mechanical measurements in endothelial cells that were plated over an extended period of time (16 h). The measurements were done before and after acrylamide was added. We found that the cells exhibited a significantly greater stiffness before than after acrylamide even at the lowest applied stress of 10 dyn/cm² (Fig. 6). This result is consistent with the possibility that in highly spread cells, IFs are fully extended and thus participate in stress transmission across the CSK even at very low-applied stress. Because our DNA synthesis measurements were done 20 and 24 h after plating, there was sufficient time for the cells to fully spread and for IFs of the wild-type cells to be fully extended during both measurements. This is consistent with the fact that the DNA synthesis in wild-type cells increased by only 20% between 20 and 24 h after plating (Fig. 5), suggesting that IFs were involved in the stress transfer.

View larger version (14K): [in this window] [in a new window]   Fig. 6.   Stiffness vs. stress relationships for adherent endothelial cells before and after treatment with acrylamide. Stresses ranging from 10 to 60 dyn/cm2 were applied through RGD-coated ferromagnetic beads. Cells were plated on collagen I-coated dishes for 16 h before mechanical measurements. Means ± SE (n = 5 wells); * significantly greater values (P < 0.05).

	CONCLUSIONS

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An important question about the mechanical behavior of adherent cells is what is the mechanism of the observed stiffening response. Janmey et al. (9) and Ma et al. (12) have demonstrated that IF gels exhibit stiffening in vitro. Results of our study suggested that this mechanical behavior of IF polymers could also persist in the complex CSK network of living cells and could account for the part of the cell-stiffening behavior. This was the first direct evidence for the mechanical role of IFs in living cells exposed to varying applied stress. Our study also demonstrated that in the absence of vimentin, cells exhibited slower rates of proliferation and DNA synthesis. We speculated that these effects were a direct consequence of the absence of the intracellular IF network that might be necessary to efficiently mediate the transfer of mechanical signals from the cell surface to the nucleus.

	APPENDIX

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS APPENDIX REFERENCES

We used a six-strut tensegrity model as a representative of cellular tensegrity. This particular model was very useful in our previous studies, in which we analyzed the microstructural basis of various aspects of cell mechanical behavior (3, 4, 19, 20). In this study, we added the contribution of IFs to the model.

The model is composed of three types of elements: 1) tension-bearing peripheral cables that play the role of MFs, 2) compression-bearing struts that play the role of MTs, and 3) tension-bearing radial cables that play the role of IFs (Fig. 7). This arrangement is consistent with the intracellular distribution of the CSK filamentous structures; MFs are concentrated in the peripheral cortical region, whereas MTs and IFs occupy a more central region, extending from the nucleus to the cell surface (cf. 1).

View larger version (40K): [in this window] [in a new window]   Fig. 7.   Six-strut tensegrity model. Microtubule struts: AA, BB, CC; microfilament cables AB, AC, BC; intermediate filament (radial) cables OA, OB, OC. Stretching force T/2 (thick arrows) is applied at the strut endpoints A in the x direction.

The model was stretched uniaxially by pulling apart a pair of parallel struts (Fig. 7), and its stiffness was calculated using methods of engineering mechanics as described below. To mimic the behavior of the IF-deficient and IF-disrupted cells, the stiffness was calculated for the case where the IF elements were not included in the model. All relevant equations are given below.

From the geometry of the six-strut tensegrity model (Fig. 7) it follows that


where l_AB, l_AC, and l_BC are lengths of cables AB, AC, and BC; L_AA, L_BB, and L_CC are lengths of struts AA, BB, and CC; r_OA, r_OB, and r_OC are lengths of radial cables OA, OB, and OC; and s_x, s_y, and s_z are distances between the pairs of parallel struts along x, y, and z axes, respectively. At the reference state (before stretching force T was applied), L_AA = L_BB = L_CC  L₀, s_x = s_y = s_z  s₀ = L₀/2, l_AB = l_AC = l_BC  l₀ =  L₀, r_OA = r_OB = r_OC  r₀ =  L₀/4. For simplicity, it was assumed that L₀ was of unit length (L₀ = 1).

Equilibrium equations, obtained by considering force balance at nodes A, B, and C, are the following


where T is external stretching force, F_AB, F_AC, and F_BC are forces in cables AB, AC, and BC, and N_OA, N_OB, and N_OC are forces in radial cables OA, OB, and OC, respectively.

The MF cables l_AB, l_AC, and l_BC were assumed to be linearly elastic (Hookean) of stiffness k and of resting length l_r, based on the observed behavior of isolated actin filaments (11) and actin gels (9) and that they support only tensile forces. Thus the force in those cables is given as
For simplicity, it was assumed that k was of unit stiffness (k = 1).

The radial IF cables r_OA, r_OB, and r_OC were assumed to be nonlinear (quadratic) elastic, and thus exhibited stiffening, based on similar behavior of vimentin gels (9) and that they support only tensile forces. Thus the force in those cables is given as
where k₁ and k₂ are constants and r_r is the resting length. To mimic the in vitro stress-strain behavior of vimentin gels (9), it was assumed that k₁ = 0.1 and that k₂ = 1.0.

The MT struts were assumed to be rigid, and thus transmit forces but do not directly contribute to the model deformability. Our previous modeling studies showed that this assumption of rigid struts was reasonable for obtaining good qualitative simulations of cell mechanical behavior (4, 20).

It was also assumed that the MF cables were initially tensed (i.e., l_r  l₀) and that the IF cables were initially slack (i.e., r_r  r₀). The former assumption was based on the evidence that the actin CSK is initially tensed ("prestressed") even before external forces are applied to the cell (cf. 15), whereas the latter assumption was based on the slack appearance of IFs in living cells (cf. 1, 8).

The above equations were simultaneously solved for s_x, s_y, and s_z for a given T (ranging from 0 to 2 units of force), l_r  0.90l₀, and r_r  1.05r₀ using a numerical procedure (TK Solver Plus software). In the case where the IF elements were not present in the model, the above equations were solved by setting N_OA = N_OB = N_OC  0 (cf. 20). The applied stress was computed as 8T/5L₀², and the corresponding strain as (s_x  s₀)/s₀ (19). The stiffness was defined as the ratio of stress to strain.

Model predictions. The model predicted several features that were consistent with the data obtained from magnetic cell twisting (Fig. 1B and Figs. 2 and 3). First, at a given stress, the stiffness was greater in the case where the IF elements (i.e., radial cables in Fig. 7) were present than when they were absent from the model (Fig. 8). This difference was minor at low stress, and it increased progressively with increasing stress. Second, the stiffening was greater when the IF elements were present in the model than when they were not (Fig. 8). The above differences were primarily due to the nonlinear (stiffening) properties of the IF elements. Third, the model exhibited stiffening even when the IF elements were absent. This was entirely due to the effect of kinematic stiffening (Fig. 8). Because the absence of IF elements from the model produced changes in its mechanical properties that were similar to the changes caused by the absence or disruption of vimentin IFs in living cells, we concluded that the mechanisms that determined the model stiffening behavior might also be present in the cell, i.e., that the cell stiffening was partly due to the rheological properties of IFs and partly due to the kinematic stiffening of the CSK.

View larger version (10K): [in this window] [in a new window]   Fig. 8.   Stiffness vs. stress relationships predicted by the model for the cases where the intermediate filament (IF) cables are present and when they are not present in the model; stiffness and stress are given in units force per length square. Note that in the presence of IF elements, the model exhibits greater stiffening and greater stiffness than when the IF elements are not present. This behavior is consistent with the observations in living cells (Fig. 1B and Figs. 2 and 3).

	ACKNOWLEDGEMENTS

We thank Dr. Victor Koteliansky for providing wild-type and vimentin-deficient fibroblasts and Jianxin Chen and In Lim for technical assistance.

	FOOTNOTES

This work was supported by National Heart, Lung, and Blood Institute Grant HL-33009.

Address for reprint requests and other correspondence: N. Wang, Physiology Program, Dept. of Environmental Health, Harvard School of Public Health, 665 Huntington Ave., Boston, MA 02115 (E-mail: nwang{at}hsph.harvard.edu) or D. Stamenovi, Dept. of Biomedical Engineering, Boston Univ., 44 Cummington St., Boston, MA 02215 (E-mail: dimitrij{at}engc.bu.edu).

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. §1734 solely to indicate this fact.

Received 29 November 1999; accepted in final form 28 January 2000.

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