Mammalian cells of various types exhibit the remarkable ability to adapt to externally applied mechanical stresses and strains. Because of this adaptation, cells can maintain their endogenous mechanical tension at a preferred (homeostatic) level, which is essential for normal physiological functions of cells and tissues and provides protection against various diseases, including atherosclerosis and cancer. Conventional wisdom is that the cell possesses the ability to maintain tensional homeostasis on its own. Recent findings showed, however, that isolated cells cannot maintain tensional homeostasis. Here we studied the effect of multicellular interactions on tensional homeostasis by measuring traction forces in isolated bovine aortic endothelial cells and in confluent and nonconfluent cell clusters of different sizes. We found that, in isolated cells, the traction field exhibited a highly dynamic and erratic behavior. However, in cell clusters, dynamic fluctuations of the traction field became attenuated with increasing cluster size, at a rate that was faster in nonconfluent than confluent clusters. The driving mechanism of attenuation of traction field fluctuations was statistical averaging of the noise, and the impeding mechanism was nonuniform stress distribution in the clusters, which resulted from intercellular force transmission, known as a “global tug-of-war.” These results show that isolated cells could not maintain tensional homeostasis, which confirms previous findings, and that tensional homeostasis is a multicellular phenomenon, which is a novel finding.
- tensional homeostasis
- traction forces
- cytoskeletal tension
- multicellular clusters
- endothelial cells
the notion that organisms are able to maintain their physiological functions at a homeostatic state has been long recognized as a unifying, fundamental concept in physiology. Its origins are rooted in the recognition of the ways by which the body regulates temperature, calcium level, and blood sugar. In mechanobiology of cells and tissues, homeostasis has been linked to their ability to maintain mechanical tension (i.e., stresses or strains) at a preferred set-point value. This is known as tensional homeostasis (3), and it has been regarded as a necessity for facilitating normal physiological functions and as protection against disease progression, including atherosclerosis and cancer (7, 20, 25). Although tensional homeostasis is defined as the maintenance of a set level of tension, all physiological functions occur in the presence of fluctuations (9). Thus a quantitative description of tensional homeostasis may require both the maintenance of mechanical tension about a constant average level and the maintenance of a low level of variability about a set-point level of tension.
Conventional wisdom is that the living cell possesses means for achieving tensional homeostasis (3, 10–12, 17). Two recent studies have challenged this view, however. First, Krishnan et al. (13) observed that, in response to periodic uniaxial stretch, the traction field of isolated endothelial cells reoriented transversely to the stretch axis. However, tractions remained highly unstable, exhibiting erratic fluctuations long after their reorientation was completed, rather than attaining a stable, homeostatic value. Moreover, even in the absence of external stretch, the traction field of isolated cells exhibited unstable and erratic behavior. Since traction forces arise in response to cell-generated tension, those results suggest the absence of tensional homeostasis in isolated endothelial cells.
Second, Webster and colleagues (29) observed that, in response to mechanical deformation, isolated fibroblasts altered their cytoskeletal tension in a strain rate-dependent manner, leading to a new and stable force. Since tension did not return to its set-point level, these authors concluded that the cells exhibited tensional buffering, rather than homeostasis, which allowed cells to transition between different tensional states.
Together, these two studies (13, 29) suggest that individual cells do not have the ability to maintain tensional homeostasis on their own. Here we studied tensional homeostasis in multicellular clusters of cultured endothelial cells. Since cells in vivo often form closely packed monolayers (e.g., endothelium and epithelium), where they touch and interact with each other through cell-cell adhesions, our reasoning was that cell-cell interactions may influence their tensional homeostasis. For example, it is known that molecules of intercellular junctions control different features of vascular homeostasis (2) and regulate intercellular tension in the epithelial monolayer (1).
In this study we measured cellular traction forces in isolated endothelial cells and in multicellular clusters of different sizes and at different length scales over an extended time period. Our goal was to determine whether temporal variations of the traction field became attenuated and stabilized in multicellular clusters and whether cell-cell interactions influenced this process. We found that attenuation of traction variations was driven by increasing cluster size and, notably, that it was also influenced by cell-cell mechanical coupling.
MATERIALS AND METHODS
Internal cytoskeletal tension is generated by the cell contractile actomyosin machinery. These forces are in part transmitted to the substrate via focal adhesions (FAs), where cellular traction forces arise in response to cell contractile tone. Using micropattern traction microscopy (22, 23), we measured traction forces in single bovine aortic endothelial cells and in cell clusters containing 2–30 cells. This approach only permits the formation of FAs on an array of micropatterned dots, and thus it can be used to measure fluctuations in traction forces of single FAs up through large cell clusters with time-lapse microscopy (21).
Bovine aortic endothelial cells were generously provided by Dr. Matthew A. Nugent (University of Massachusetts Lowell). Cells were isolated as described in detail elsewhere (8). Briefly, bacterial collagenase and gentle scraping were used to isolate cells from the intimal surface of dissected descending aortae (5–10 aortae) from 3-mo-old calves (obtained from a local slaughterhouse). These cells have been shown to take up acetylated-LDL and to express a number of endothelial cell surface markers (19). Cells were cultured in Dulbecco's modified Eagle's medium with 1 g/l glucose (Corning), supplemented with 10% bovine calf serum and 1% penicillin-streptomycin. Cells were maintained in a sterile incubator (Fisher Scientific) at 37°C and 5% CO2. Cells were grown to 90% confluence before trypsinization and used during passages 5–14. Cells were seeded onto micropatterned polyacrylamide gels immediately after passivation and allowed to adhere for 18 h before imaging. Single cells and naturally formed confluent cell clusters of different sizes were imaged and then measured to acquire traction forces.
Fibronectin isolation and fluorophore labeling.
Fibronectin was isolated from human plasma in ethylenediaminetetraacetic acid (Valley Biomedical) with 2 mM phenylmethylsulfonyl fluoride using a two-column separation technique, as previously described (26). Fibronectin was fluorescently labeled according to the manufacturer's specifications for protein labeling with Alexa Fluor dyes conjugated with succinimidyl ester. Alexa Fluor 488 (Invitrogen) was added in 70-fold excess to fibronectin and allowed to incubate at room temperature for ≥1 h. Excess dye was then removed using a PD-10 column (GE Healthcare).
An array of fluorescently labeled fibronectin dots (2-μm diameter, 6-μm center-to-center separation) was patterned onto ∼70-μm-thick polyacrylamide gels [elastic modulus (E) ≈ 7 kPa and Poisson's ratio (ν) = 0.445] using soft lithography and an indirect patterning technique, as described previously (22, 23).
A custom script written in MATLAB (Mathworks, Cambridge, MA) was used to track and analyze all images. For traction force calculations, the program determines the centroidal displacement vector (u) of each patterned dot from its assumed traction-free position on the grid pattern. Theoretically, if a tangential (in-plane) traction force (F) is applied at the center of a circular dot on an infinite half plane, the corresponding u is parallel with F, i.e., F = πEau/(2 + ν − ν2), where a is the radius of the patterned dot (14). Cell boundaries were determined by tracing the outline of the cell as seen on bright-field images. Clusters were then stained with NucBlue Live Cell Stain (Life Technologies), and a fluorescent image was taken to confirm cluster size.
Traction measurements were carried out for 2 h, at 5-min intervals.
All fluorescent, bright-field, and differential interference contrast images were taken using an Olympus IX81 microscope with a ×40 water (1.15 numerical aperture, 0.25-mm working distance) objective and a Hamamatsu Orca R2 camera controlled with Metamorph software. The microscope was outfitted with an incubation chamber to maintain samples at 37°C and 5% CO2.
Scalar metrics of the traction field.
Two scalar metrics of the traction field were used. One is the net traction moment, M(t), which is defined as the trace of the second moment tensor of the traction field (5, 6) (1) where K is the number of dot markers within a cluster, t is time, x and y are the in-plane Cartesian components of the position vector (r) of the dot center, X and Y are the Cartesian components of the traction force vector (F), and ⊗ denotes the tensor product. At 5-min intervals during the observation period, traction forces were adjusted to satisfy mechanical equilibrium (see discussion).
The significance of M(t) is that, for a plane state of stress in the cell/cluster, it is equivalent to the mean normal stress within the cell/cluster times the cell/cluster volume (6). To the extent that, during the observed time, volumetric changes of cells may be regarded as negligible, M(t) is indicative of the mean internal stress (tension) in the cluster.
The second metric is the net traction force, T(t), which is defined as the sum of the norms (magnitudes) of all traction force vectors applied to a cluster/cell (2) where ||·|| indicates the norm.
For comparison between different cells/clusters, we normalized M(t) and T(t) of each cell/cluster with their respective initial measured values M1 ≡ M(t1) and T1 ≡ T(t1).
Definition and quantitation of tensional homeostasis.
We defined tensional homeostasis as a state where the time average of M(t)/M1 and T(t)/T1 remained close to unity and their variances remained close to zero.
From the time lapses of M(t)/M1 and T(t)/T1, we obtained for each cell/cluster the corresponding time-average values, <M/M1> and <T/T1>, i.e. (3) and the corresponding standard deviations, which we referred to as normalized standard deviations, NSDM and NSDT, respectively, i.e. (4)
According to our definition, tensional homeostasis would imply that <M/M1> and <T/T1> remain close to unity and that NSDM and NSDT remain close to zero.
Homeostasis in confluent clusters.
Traction forces were obtained from 11 single cells, 14 two-cell clusters, 7 four-cell clusters, 5 three- and five-cell clusters, 2 six-cell clusters, 3 seven-, eight-, and ten-cell clusters, and 1 thirty-cell cluster. Since the clusters were naturally formed, we could not control their size, which explains the variability in the number of clusters of different sizes. We found that, throughout the observation time, traction forces were greater near the edge of the clusters than in the cluster interior, regardless of the cluster size (Fig. 1), which is consistent with data from the literature (15, 16).
Time-lapse plots of M(t)/M1 showed that the single cells exhibited greater variability than the multicellular clusters (Fig. 2). To quantitate dispersion of M(t)/M1 around unity, we defined the absolute deviation as ADM = |<M/M1> − 1|. We found that ADM exhibited a significant negative correlation with increasing cluster size N [Spearman's correlation coefficient (ρ) = −0.273; Fig. 3A]. Significance of this trend (P = 0.0461) was calculated using a permutation test. Although the data were displayed on the semilogarithmic axes, the correlation (here and everywhere else) was obtained on the linear axes. We also calculated the range (i.e., the total range and the interquartile range), the median, and the mean of <M/M1> for each cell/cluster. Since the number of individual cells and 2-cell clusters was greater than the number of other clusters, to reduce this unevenness we grouped together 3- and 4-cell clusters, 5- and 6-cell clusters, and 7-, 8-, and 10-cell clusters. The total range of <M/M1> was greater in individual cells than in multicellular clusters (Fig. 3B). The interquartile range of <M/M1> was the same in individual cells and in two-cell clusters, and from there it decreased with increasing cluster size (Fig. 3B). Taken together, these results indicate that the dispersion of <M/M1> decreased with increasing cluster size.
We found that NSDM exhibited a negative, but nonsignificant, correlation with increasing cluster size N (ρ = −0.251, P = 0.0666; Fig. 4A). Because of the high variability of NSDM, we performed an additional statistical test. We divided cells into two groups: one that included NSDM of single cells and 2-cell clusters (n = 25) and another that included NSDM of the remaining clusters (n = 29). Using Student's t-test, we found a significantly higher mean NSDM (P = 0.023) in the first than in the second group, suggesting that the apparent decrease in NSDM with increasing cluster size was significant. We also found that, regardless of the cluster size, NSDM decreased with increasing time average of M(t) (Fig. 4B; ρ = −0.394, P = 0.0035).
On the basis of results obtained from the analysis of ADM and NSDM, we concluded that increasing the cluster size and increasing the magnitude of the average M(t) attenuated traction field variability and, thus, promoted tensional homeostasis.
Homeostasis in nonconfluent clusters.
To investigate the effect of cell-cell interactions on tensional homeostasis, we carried out an additional analysis. We created artificial, nonconfluent cell clusters from individual cells that we pooled into clusters of increasing size. From the traction measurements of 11 individual cells used in the above-described analysis, we obtained traction fields of artificial nonconfluent clusters of N = 2, 3,…,10 cells, where, for each N, we made all possible combinations of the 11 individual cells. For such traction fields, we could not use M(t) as metric, since it depends on both applied traction forces and the cluster geometry (see Eq. 1), which was not defined for the artificial clusters. Instead, we used T(t), which depends only on the traction forces (see Eq. 2). From the time lapses of T(t)/T1, we calculated NSDT according to Eq. 4. For comparison, we also calculated NSDT of the confluent clusters.
To compare NSDT-N relationships of nonconfluent vs. confluent clusters, we computed the mean NSDT for each N. The mean NSDT-N relationships for nonconfluent clusters followed an inverse square root relationship: −0.048 + 0.29/N1/2 (R2 = 0.9983; Fig. 6). The mean NSDT-N relationships for the confluent clusters also exhibited a decreasing trend, but this trend was nonmonotonic. There was an intermittent increase in NSDT between N = 5 and N = 8 (Fig. 6, ○). This increase was not necessarily a result of high variability of NSDT, but it might reflect the effect of force transmission between the cells. Moreover, NSDT of nonconfluent clusters became lower than NSDT of confluent clusters with increasing N. These differences between nonconfluent and confluent clusters raised the possibility that cell-cell interactions might have a detrimental effect on attenuation of traction field fluctuations. We address this nonmonotonic shape of the NSDT-N relationships in discussion.
Traction dynamics of individual FAs.
One of the advantages of our traction microscopy system is that it simplifies measurements of traction dynamics of individual FAs. Since we did not observe tensional homeostasis in isolated cells, we did not expect it to exist at the FA length scale.
We tracked traction forces F(t) applied at individual FAs in single cells and in 10-cell clusters at 5-min intervals over 2 h. We computed the norms of individual FA traction forces, F(t) = ||F(t)||, normalized each F(t) with its corresponding initial value F1, and then computed NSDFA according to Eq. 4. We considered only FAs for which initial tractions were above the experimental noise level (i.e., F1 >0.3 nN).
Tractions tended to be more stable in the clusters than in the single cells. However, in both single cells and 10-cell clusters, FA traction forces of similar average magnitudes had similar NSDFA. Importantly, NSDFA decreased with increasing time-averaged F(t) [Fig. 7A (for single cell FAs, ρ = −0.344, P ≪ 0.001) and Fig. 7B (for 10-cell cluster FAs, ρ = −0.401, P ≪ 0.001)], which was consistent with the trend observed at the whole cluster level (Fig. 4B).
The two most significant findings of this study are as follows: 1) isolated endothelial cells did not maintain tensional homeostasis, which is consistent with previous observations (13, 29), and 2) multicellular clusters promoted homeostasis, which is a novel finding. In particular, we found that an increase in the cluster size attenuated temporal variability of the traction field and that cell-cell coupling influenced traction attenuation. This influence appeared to have an impeding effect on attenuation of traction fluctuation in confluent clusters. (See Mechanistic consideration for a mechanistic explanation of our results.)
One explanation for the attenuation of the traction field fluctuations with increasing cluster size could be the effect of statistical averaging. If cells within the clusters were independent of each other, as in the nonconfluent clusters, then, on the basis of the central limit theorem from the probability theory, the standard deviation of traction fluctuations should decrease with the inverse square root of the sample size. Indeed, we observed an inverse square root dependence of NSDT in nonconfluent clusters (Fig. 6). If, however, cells in the cluster were mechanically interdependent, as in the confluent clusters, then attenuation of traction fluctuations might be affected by the force transfer across cell-cell junctions; hence, NSDT might not follow the inverse square root dependence. Indeed, we observed in the confluent clusters that the NSDT-N relationship did not follow an inverse square root dependence and that NSDT decreased at a slower rate with increasing N, suggesting that the presence of cell-cell adhesions might impede attenuation of traction fluctuations. In other words, there might be two competing effects in the confluent clusters: one that promotes attenuation of fluctuations through statistical averaging and another that hinders attenuation through cell-cell interactions. The latter can be explained as follows.
Traction forces acting on a whole cluster are self-equilibrated, but at the level of individual cells within a cluster they are not. For equilibrium of individual cells, both cell-substrate and cell-cell traction forces need to be balanced. This balancing act has been referred to as the “global tug-of-war” (28). According to the global tug-of-war, the unbalanced portion of the cell-substrate traction force is transferred from one cell to the adjacent cell via cell-cell junctions from the cluster edge toward its center. This force transmission creates a stress buildup within the cluster (27, 28), which increases with increasing cluster size and eventually reaches a plateau (1). Because of the intrinsic variability of the intracellular stress, its buildup may also augment stress fluctuations; hence, NSD may increase.
Using the above description, we explain the nonmonotonic shape of the NSDT-N relationship in the confluent clusters (Fig. 6) as follows. For small cluster sizes, the stress buildup would be minor; therefore, NSDT would decrease with increasing cluster size due to statistical averaging. As N increases, the stress buildup in the cluster and, therefore, stress fluctuation would increase, causing NSDT to increase. A further increase in the cluster size would cause the stress buildup to slow down, and the effect of statistical averaging would again become dominant, causing NSDT to decrease. In the nonconfluent clusters, however, there was no intercellular force transmission, and traction in each cell was self-equilibrated. Thus there was no stress buildup in the cluster, and traction fluctuation attenuation was entirely the result of statistical averaging. Thus NSDT decreased with the inverse square root of N.
We recently developed a mathematical model of homeostasis that could account for the experimentally observed behavior and, thus, provide more insight into the underlying mechanisms. Details of the model derivation can be found in the work of Tam et al. (27). Briefly, the model depicted cell clusters as one-dimensional, serial arrays of linearly elastic blocks (“cells”). In the case of the confluent clusters, the blocks were mechanically coupled. In the case of the nonconfluent clusters, the blocks were independent of each other (Fig. 6, inset). To each block, time-varying traction forces were applied, such that traction force balance in the cluster is maintained at every instant. Traction force fluctuations observed experimentally were mimicked using Monte-Carlo simulations. From the applied traction forces, we calculated the average stress in the cluster, and from time lapses of the stress, we obtained NSD. We found that, in the nonconfluent cluster model, NSD decreased with the inverse square root of N, as a result of statistical averaging. In the confluent model, however, an initial decrease in NSD was followed by an intermittent increase and then a decrease with increasing N (Fig. 6, inset), consistent with the experimental results (Fig. 6). This nonmonotonic NSD-N relationship obtained for the confluent cluster model is the result of the competing effects of the statistical averaging and of the global tug-of-war (27).
At the molecular level, cell-cell force transmission is associated with molecules of adherens junctions. Bazellières et al. (1) showed that, in the epithelial monolayer, adhesion proteins E-cadherins determine the rate at which intercellular tension is built up and P-cadherins determine the magnitude of tension. These findings raised the possibility that these two molecules constitute a feedback system to control intercellular tension in the monolayer (1). Although molecular pathways that mediate the interplay between E-cadherins and P-cadherins are not fully understood, their influence on tensional homeostasis has its mechanistic origin in the ability of cell-cell adhesions to transmit and control physical forces in the monolayer.
The role of cadherins in regulating cytoskeletal tension is also reflected through the “cross talk” between cell-cell and cell-matrix adhesions. Nelson et al. (18) showed that, in endothelial cells, VE-cadherin engagement regulates cytoskeletal tension, FA formation, and cell spreading via RhoA. Furthermore, an increase in Rho activities, as in cancer cells, stimulates cell contractility, which may cause disruption of cell-cell junctions and, therefore, alter tensional homeostasis (4, 20).
The observation that tensional homeostasis was hindered in confluent clusters compared with nonconfluent clusters appears counterintuitive. Cells in vivo often form continuous, confluent monolayers, and one would expect that this configuration would favor tensional homeostasis. Importantly, unlike the monolayers in culture, monolayers in vivo do not have traction-free boundaries. Consequently, the stress buildup and the associated detrimental effect on tensional homeostasis that was observed in cultured monolayers might not be present in vivo. Traction-free boundaries in monolayers in vivo may be created by injuries at the wound edge, which, in turn, may create the conditions for the tug-of-war stress buildup. Since such a stress buildup is not favorable for tensional homeostasis, it may prompt cells in the monolayer to close the wound and, thus, reestablish more favorable conditions.
Comparison with previous studies.
In their study of homeostasis of isolated fibroblasts, Webster and colleagues (29) did not observe notable temporal traction fluctuations. One reason could be that their observation time (∼6 min) was too short; our observation time was 2 h. Another reason could be that they constrained cell spreading, whereas we did not. Lastly, in the experiments of Webster et al., the cells experienced an anisotropic stiffness between the flexible tip of the atomic force microscope and the rigid substrate underneath, and it is not clear how rigidity of the substrate impacts tensional homeostasis.
Our observation that NSDFA of individual FAs diminished with increasing magnitude of the traction force seemed to be in contrast with the observations of Plotnikov et al. (24), who found lower traction forces in FAs with stable traction forces than in FAs with “fluctuating” tractions. This apparent discrepancy might be due to the fact that we normalized traction forces with their initial values, whereas Plotnikov and colleagues did not. The normalization with forces of smaller magnitudes accentuates their variability with respect to their initial values, whereas the normalization with forces of greater magnitudes abates their variability with respect to their initial values.
Another possible explanation is that the apparent discrepancy between our results and the results of Plotnikov et al. (24) reflects the difference between their traction microscopy techniques and those used in the present study. In our traction microscopy technique, the size of FAs was constrained by the size and the circular shape of the micropatterned adhesion dots (2-μm diameter) (22, 23). In the traction microscopy technique used by Plotnikov et al., the size of FAs was not constrained; thus their FAs were larger and elongated. They showed that the elongated shape of FAs allowed an asymmetric distribution (i.e., away from the FA center) and high dynamics of traction forces within the FA. If, however, the traction forces were applied at the FA center, they were much less dynamic. In our technique, traction forces of greatest magnitude were near the edges of cells/clusters (Fig. 1), where the FAs had an approximately circular shape, as shown previously (21). Because of the circular shape of the FAs, those forces were probably applied near the FA center and, therefore, according to Plotnikov et al., should be less dynamic and more stable.
Limitations of the approach.
Experimental noise was present in a variety of steps in our measurements. For example, imperfections in the pattern of fluorescent fibronectin dots resulted from microcontact printing and pattern transfer. Also, all tractions were not evenly distributed across the entire circular dot. Consequently, measured traction forces did not satisfy mechanical equilibrium, and they had to be adjusted by a least-squares procedure to obtain traction forces closest to the measurements that satisfied equilibrium, which we described previously (6). This procedure influenced our estimates of M and T. Nevertheless, this noise was assumed to apply evenly to cells and clusters; hence, trends should not be affected when large numbers of individual cells and clusters were included.
Because different cells/clusters exhibited different levels of contractility, our data exhibited a high degree of variability of the traction field for a given cell/cluster size. We tried to reduce this variability by normalizing M(t) and T(t) of each cell/cluster with their respective initial measured value. While the normalized data showed reduced variability, some of the correlations of NSDs and ADs vs. N still showed a weak significance.
Finally, we did not consider the influence of substrate rigidity on tensional homeostasis. It has been shown previously that substrate rigidity has significant impact on the homeostasis-related cell mechanosensing behaviors (4, 20). While we do recognize the importance of substrate rigidity, the focus of the current study was on the effect of the cluster size and mechanical coupling between cells on tensional homeostasis.
Results of our study showed that tensional homeostasis is a multicellular phenomenon and that attenuation of temporal variability of intracellular tension is driven by increasing cluster size via statistical averaging of the noise. This process, however, might be impeded in confluent clusters due to the stress buildup that results from intercellular force transmission known as a global tug-of-war.
Taken together, these findings suggest that tensional homeostasis does not exist across multiple length scales, as suggested previously (10–12, 25), but that it may require a higher level of organization than that of a single cell. To obtain a comprehensive description of tensional homeostasis, future studies should consider the effects of cross-signaling between cell-cell and cell-matrix adhesions, of rigidity sensing, and of matrix composition.
This study was supported by National Science Foundation Grants CEBET-115467 (M. L. Smith) and CMMI-1362922 (D. Stamenović) and by the Boston University Training Program in Quantitative Biology and Physiology.
No conflicts of interest, financial or otherwise, are declared by the authors.
E.P.C., M.L.S., and D.S. developed the concept and designed the research; E.P.C. and A.J.Z. performed the experiments; E.P.C., A.J.Z., S.N.T., and D.S. analyzed the data; E.P.C., S.N.T., M.L.S., and D.S. interpreted the results of the experiments; E.P.C., A.J.Z., and D.S. prepared the figures; E.P.C., A.J.Z., M.L.S., and D.S. edited and revised the manuscript; E.P.C., A.J.Z., M.L.S., and D.S. approved the final version of the manuscript; D.S. drafted the manuscript.
We thank Drs. Béla Suki and Harikrishnan Parameswaran (Boston University) for helpful discussion.
Present address of E. P. Canović: Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139.
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