extfieldsofstudy: Chemistry Medicine

s2fieldsofstudy: Biology Chemistry

text:
Antisense Inhibition of Decorin Expression in Myoblasts Decreases Cell Responsiveness to Transforming Growth Factor b and Accelerates Skeletal Muscle Differentiation*

Decorin is a member of the family of the small leucine-rich proteoglycans. In addition to its function as an extracellular matrix organizer, it has the ability to acti-vate the epidermal growth factor receptor, and it forms complexes with various isoforms of transforming growth factor b (TGF- b ). Decorin is expressed during skeletal muscle differentiation and is up-regulated in dystrophic muscle. In this study we investigated the role of decorin in TGF- b2 dependent inhibition of myogenesis. To probe the function of decorin during myogenesis, C 2 C 12 myoblasts were stably transfected with a plasmid expressing antisense decorin mRNA. The re-sulting inhibition of decorin expression led to the expression of myogenin, a master transcription factor for muscle differentiation, under growth conditions and accelerated skeletal muscle differentiation as determined by the expression of creatine kinase. In contrast myogenin expression was inhibited by adenovirally induced decorin expression or by adding exogenous decorin. Reduced synthesis of decorin resulted in a 7-fold that the the different of wild type and antisense demonstrate that a of of avail-ability results in a decreased to TGF- findings strongly suggest a new role for decorin during muscle terminal differentiation by acti-vating TGF- b -dependent

The process of myogenic development involves an ordered sequence of molecular events, which includes commitment of muscle precursor cells, cessation of cell division, myoblast terminal differentiation, and formation of myotubes that express muscle-specific genes involved in the specialized functions of the myofiber (1). A network of muscle regulatory factors (2) governs these processes. One of the factors responsible for the induction of terminal differentiation is myogenin, a transcription factor of the basic helix-loop-helix family that activates skeletal muscle-specific products such as creatine kinase, myosin heavy chain, acetylcholine receptor, etc. (3,4). Terminal differentiation is critical as well during skeletal muscle formation as during muscle regeneration after injury (5).
The onset and progression of this process are controlled by a complex set of interactions between myoblasts and their environment. The presence of the extracellular matrix (ECM) 1 is essential for normal myogenesis (6 -9). The ability of myoblasts to differentiate is controlled in a negative manner by the extracellular concentration of specific mitogens, such as FGF-2, HGF/SF, and TGF-␤ (10 -13). In the presence of these inhibitory growth factors, myoblasts continue to proliferate and fail to fuse or to express muscle-specific gene products. Conversely, the reduction in the concentration of these growth factors below a critical level results in cell culture experiments in an irreversible arrest in the G 0 phase and in terminal differentiation.
It has been demonstrated that the activities of FGF-2, HGF/ SF, and TGF-␤ can be regulated by binding to proteoglycans (14,15). Cell surface heparan sulfate proteoglycans, in particular, have been suggested to play a role in modulating the activities of heparin-binding growth factors (16,17). They modulate terminal myogenesis probably by acting as low affinity receptors for some growth factors such as FGF-2 (18) and HGF/SF (19). We have shown that the constitutive expression of syndecan-1, a heparan sulfate proteoglycan whose expression is down-regulated during terminal skeletal muscle differ-entiation, inhibits the differentiation of myoblasts in culture (20,21). In contrast, abolishing the expression of syndecan-3, which is another heparan sulfate proteoglycan synthesized by myoblasts, results in an acceleration of skeletal muscle differentiation by a mechanism being dependent on FGF-2, too (22).
Decorin is a member of the small leucine-rich proteoglycans gene family, which consists of a core protein and a single covalently linked glycosaminoglycan chain (23). Decorin binds several types of collagen in vivo, among them being types I, II, and VI, and promotes fibril stability. By interacting with ECM molecules like fibronectin and thrombospondin it influences cell adhesion. Additionally, at least in some types of cells, decorin activates the epidermal growth factor receptor, thereby triggering a signaling cascade that leads to phosphorylation of mitogen-activated protein kinase, to the induction of p21, and to growth suppression (24,25). Great attention has been given to the observation that its core protein interacts with TGF-␤ (26 -29). There are independent binding sites of decorin core protein for TGF-␤ and type I collagen (30). Affinity measurements of the interaction between decorin and TGF-␤ indicate the presence of at least two sites with K d values of 1-20 and 20 -200 nM for the high and low affinity binding sites, respectively (31). The biological consequences of the interaction between decorin and TGF-␤ are still a matter of debate. In analogy to the curative effect of blocking antibodies against TGF-␤ on the course of the anti-Thy-1-induced glomerulonephritis (32), the beneficial effect of decorin in the same disease model has been interpreted as the consequence of the inactivation of the cytokine by the proteoglycan. The reversal of TGF-␤-mediated effects in this and other disease models by decorin gene transfer (27)(28)(29) supported this conclusion. On the other hand, the addition of decorin to osteoblasts resulted in an increased biological activity of TGF-␤ (33). Therefore, the precise mechanism whereby decorin modulates TGF-␤ activity remains to be elucidated.
In skeletal muscle decorin is found mainly in the perimysium (34). The synthesis and expression of decorin is up-regulated during skeletal muscle differentiation (35). Interestingly, the synthesis of decorin is also augmented in dystrophic mdx mouse skeletal muscle (36). In the present study we investigated the function of decorin during muscle differentiation. C 2 C 12 myoblasts were transfected with an expression plasmid containing antisense decorin cDNA. Suppression of decorin production was accompanied with accelerated terminal differentiation and with a significant decrease in the sensitivity to TGF-␤-dependent inhibition of myogenesis. It will be shown that this inhibition is mediated directly by interfering with the signaling cascade triggered upon binding of TGF-␤ to its transducing receptors. These findings demonstrate that the responsiveness of myoblasts to TGF-␤, an inhibitor of skeletal muscle differentiation, is directly modulated by decorin expression.

EXPERIMENTAL PROCEDURES
Materials-The C 2 C 12 cell line was purchased from ATCC, Manassas, VA. Trizol LS, LipofectAMINE, Dulbecco's modification of Eagle's minimal essential medium, CEE, horse serum, FCS, Opti-MEM I, Hanks' balanced salt solution, G418, and human FGF-2 were obtained from Life Technologies, Inc. Wizard plus maxipreps and prime-a-gene labeling system dual-luciferase reporter assay system, pGL3 basic vector, and pRL were from Promega, Madison, WI. F-12 medium, creatine kinase assay kit, bovine cartilage decorin, and fluorescein isothiocyanate-and tetramethylrhodamine B isothiocyanate-conjugated goat anti-rabbit IgG were from Sigma. Mexico, Mexico City, Mexico. Briefly, a modified plasmid containing adenovirus E4 promoter sequences was used to construct the 3TP promoter; a TGF-␤-responsive element from positions Ϫ636 to Ϫ740 in the human plasminogen activator inhibitor-1 promoter was synthesized and inserted upstream of the adenovirus E4 sequences; a fragment (XhoI-EcoRI) containing the 3TP promoter was isolated and cloned into XhoI-HindIII digested luciferase expression vector generating p3TP-Lux (37).
The pMyoLuc reporter construct was synthesized as described for pMyoCAT (20) with some modifications. Briefly, a 670-base pair DNA fragment corresponding to the myogenin promoter region, from ϩ55 to Ϫ615 nucleotides, was subcloned into the pGL3 basic vector, which contains the cDNA encoding the firefly luciferase enzyme.
The construction of a replication-deficient adenoviral vector containing the full-length human decorin cDNA under the control of the EF-1 promoter (38), the purification of decorin from mouse skeletal muscle (34), and the production of species-specific decorin antisera (38) have been described previously.
Cell Culture-The mouse skeletal cell line C 2 C 12 was grown and induced to differentiate as described previously (20,39). Collagen gels were prepared using collagen type I from rat tail, and the lattice was performed as described previously (38), with some modifications: cellfree collagen lattice was obtained by mixing 450 l of collagen type I (5 g/ml), 675 l of minimum medium, and 75 l of 0.1 N NaOH in hydrophobic dishes and incubated at 37°for 1 h. The formed lattice was cultured on myoblasts monolayers for different period of time.
Stable Transfection and Isolation of Clones-C 2 C 12 cells were plated at a density of 6000 cells/cm 2 in 100-mm dishes in growth medium. 24 h later the cells were transfected with the mammalian expression plasmid pCMVneo containing a 1372-bp cDNA insert containing the fulllength mouse decorin sequence, in the antisense orientation, kindly donated by Dr. Renato Iozzo, Thomas Jefferson University, Philadelphia. The complete insert and a pCMVneo plasmid were digested with EcoRI to generate the pCMVneo-decorin recombinant plasmid; positive clones were selected by ampicillin resistance, and the orientation of the insert was determined by polymerase chain reaction; the antisense orientation was confirmed by DNA sequencing. Control cells were transfected with pCMVneo containing no insert. For transfections, 40 g of plasmid DNA and 30 g of LipofectAMINE in a total volume of 600 l of Opti-MEM I were used according to the instructions of the manufacturer. After 6 h at 37°C, FCS and CEE were added to final concentrations of 10 and 0.5%, respectively, and the cells were incubated overnight. The next day the cells were rinsed twice with Hanks' balanced salt solution and cultured in normal growth medium. Medium was supplemented with G418 (400 g/ml) after 3 days. After 2-3 weeks colonies were selected using cloning rings.
RNA Isolation and Northern Blot Analysis-Total RNA was isolated from cell cultures using Trizol. RNA samples were electrophoresed in 1.2% agarose/formaldehyde gels, transferred to Nytran membranes, and hybridized with probes for creatine kinase, myogenin, MyoD, and tubulin as described previously (20,21,40). Blots were hybridized with random primed labeled probes in a hybridization buffer at 65°C. Hybridized membranes were washed twice at 65°C and exposed to Kodak x-ray film. For quantitative determination of the mRNA levels the intensity of the hybridization signals were measured by densitometric scanning (epson scanning densitometer).
Gel Filtration Chromatography and SDS-PAGE-Conditioned media from wild type and antisense decorin transfected cells, obtained after metabolic labeling during 18 h with 100 Ci/ml [ 35 S]sulfate, were fractionated on a DEAE-Sephacel column (0.5 ml of resin) pre-equilibrated in 10 mM Tris-HCl, pH 7,5, 0.2 M NaCl, 0.1% Triton X-100 and eluted with a linear NaCl gradient (0.2-1.0 M) at a flow rate of 5 ml/h. Fraction of 1.0 ml were collected, and radioactivity and conductivity were determined. Pooled fractions containing radioactive proteoglycans were then chromatographed on an analytical Sepharose CL-4B column (100 x 1 cm) equilibrated and eluted with 1% SDS, 0.1 M NaCl, 50 mM Tris-HCl buffer, pH 8.0. Samples (0.5 ml) were applied to the column together with prefractionated dextran blue (2000) and phenol red to mark void and total volumes, respectively. Columns were eluted at a flow rate of 5.0 ml/h, and effluent fractions of 0.8 ml were collected and aliquots counted for radioactivity. Selected fractions obtained from the Sepharose CL-4B column were analyzed by SDS-PAGE as described previously (41).
Decorin Immunoprecipitation and Enzymatic Degradation-Immunoprecipitation of secreted labeled decorin followed by SDS-PAGE and fluorography were carried out as described previously (42). Treatment of purified decorin with chondroitinase ABC was performed as described previously (41).
Immunofluorescence Microscopy-For immunostaining cells were grown on coverslips for 72 h. For staining of decorin the cells were rinsed with phosphate-buffered saline and fixed with 3% paraformaldehyde for 30 min at room temperature. They were then permeabilized with 0.05% Triton X-100 and incubated with the primary antibodies for 1 h at room temperature. After blocking unspecific binding sites with Blotto they were incubated for 1 h at room temperature with affinitypurified tetramethylrhodamine B isothiocyanate-labeled secondary antibodies diluted in blotto. The coverslips were viewed with a Nikon Diaphot inverted microscope equipped for epifluorescence. Immunostaining of fibronectin, biglycan, fibromodulin, lumican, and perlecan was carried out as described previously (7,39).
Analysis of Creatine Kinase Activity-Myoblasts and myoblasts induced to differentiate for the indicated days were washed twice with phosphate-buffered saline, lysed by incubation with phosphate-buffered saline containing 0.1% Triton X-100 for 10 min at 25°C, and harvested by scraping. Creatine kinase activity was determined using the creatine phosphokinase assay kit. All data points represent the means of duplicate determinations from two independent experiments.
Transient Transfection-Transfections with decorin adenoviral constructs or insert-free adenoviral preparations were performed as described previously (38). C 2 C 12 cells, which had been plated the day before (6000 cells/cm 2 in 25 cm 2 flasks), were treated with 7.5 ϫ 10 7 plaque-forming units of adenovirus containing the decorin sequence or with control virus in 1.3 ml/25 cm 2 flask of Dulbecco's modification of Eagle's minimal essential medium/F-12 containing 2% heat-inactivated FCS. After 90 min of incubation 4 ml of standard medium/25-cm 2 flask was added and incubation continued for an additional period of 23 h. Subsequently, the medium was changed for fresh medium, and the cells were grown for RNA analysis for 2 days.
For transfection with pMYOLuc and pRL, cells were plated at a density of 8000 cells/cm 2 in six-well plates for 48 h and transfected for 6 h using Opti-MEM I containing 5 g of pMyoLuc and 0.01 g of pRL DNA and 12 g of LipofectaMINE. Following transfection, 10% FCS and 0.5% CEE were added to the medium, and the cells were cultured for a further 14 h. Cells were then trypsinized and plated in 24-well plates in normal growth medium. Under these conditions, decorin or TGF-␤1 was added at the indicated concentrations. After 24 h, the cells were harvested and assayed for dual luciferase activity.
For transfection with TGF␤-inducible luciferase reporter construct (3TP-Lux), the cells were plated in growth medium 1 day before transfection at a density of 8000 cells/cm 2 in 60-mm plates. Subsequently, the cells were incubated for 6 h in Opti-MEM I containing 2 g of reporter plasmid (3TP-Lux), 2 g of ␤-galactosidase plasmid and 15 g of Lipo-fectAMINE. After transfection the cells were incubated for 14 h in Opti-MEM I containing 10% FCS and 0.5% CEE. The cells were then washed twice with Hanks' balanced salt solution and incubated for 2 days in growth medium followed by 1 day in differentiation medium or 30 h in differentiation medium containing TGF-␤1, TGF-␤2 (0 -1.0 ng/ml), or FGF-2 (0 -30 ng/ml). The cells were harvested and assayed for luciferase (37) and ␤-galactosidase activities (39), as a control of the transfection among different plates. All transfections were performed at least three times.
DNA and Protein Determination-DNA (43) and protein (44) were determined in aliquots of cell extracts as described.

Stable Transfection of C 2 C 12 Myoblasts with Antisense
Decorin cDNA-Skeletal muscle myoblasts up-regulate decorin during differentiation (35). Because decorin binds TGFϪ␤, a strong inhibitor of skeletal muscle differentiation, we reasoned that the down-regulation of decorin expression would affect skeletal muscle differentiation by modulating TGF-␤ activity. To test this hypothesis C 2 C 12 myoblasts were stably transfected with a plasmid containing full-length decorin cDNA in the antisense orientation or with the control vector. Of the nine clones showing reduced [ 35 S]sulfate incorporation into proteoglycans, two were chosen for more detailed studies. Myoblasts were labeled with [ 35 S]sulfate followed by chromatographic analysis of the conditioned media on a Sepharose CL-4B column. Fig. 1A shows that both antisense clones, A4 and A6, synthesized significantly lower levels of sulfated proteoglycan compared with wild type cells.
The specificity of the effect on decorin synthesis is shown in Fig. 1B. SDS-PAGE followed by fluorography of three selected fractions obtained after the Sepharose CL-4B chromatography showed that in contrast to wild type cells, the antisense clones A4 and A6 did not synthesize detectable amounts of decorin. Decorin migrates like an M r 100,000ϳ110,000 protein during SDS-PAGE (34) indicated by a bracket in Fig. 1B; this material can completely be degraded by chondroitinase ABC (data not shown). On the contrary, the synthesis of cell surface proteoglycans, composed mainly of heparan sulfate-containing species, was unchanged compared with wild type cells (data not shown). Fig. 1C shows that there is no change in the synthesis of proteins by antisense clone compared with wild type cells. To further confirm the decreased synthesis of decorin in the antisense-transfected cells, antibodies against decorin were used to stain myoblast cultures. Fig. 2 shows that decorin was readily detectable in control transfected cells (35), whereas significantly lower levels were seen in the antisense clones. As a control measure, the localization of biglycan, fibromodulin, lumican, fibronectin, and perlecan was also assessed in control and transfected myoblasts and was found to indicate no changes in localization. Taken together, these results show unequivocally that stable clones with strongly reduced decorin expression were obtained by transfection with antisense decorin cDNA.
Skeletal Muscle Differentiation Is Accelerated in Antisense Decorin-transfected Myoblasts-To evaluate whether the diminished synthesis of decorin in the antisense clones had any effect on skeletal muscle differentiation, the expression of myogenin, a master regulatory gene of skeletal muscle differentiation, was determined. Total RNA was isolated from antisense clones and wild type cells and analyzed by Northern blotting, during growth and differentiation conditions. Fig. 3A shows that in contrast to wild-type cells, myogenin was expressed in both antisense clones already under growth conditions. However, MyoD, a transcription factor involved in skeletal muscle commitment, was not up-regulated by decorin suppression (Fig. 3B), and the expression of myogenin in the transfected clones was further augmented upon triggering muscle differentiation for 30 h.
To further determine the relationship between decorin repression and myogenin induction under growth conditions, the induction of decorin expression was achieved episomally by infection using adenovirus containing the full-length sequence for human decorin or by adding purified decorin to the myoblast cultures. Fig. 4A, top left panel, shows that after viral infection, antisense cells did not express myogenin when main-tained under growth conditions (compare A6i and A6), and wild type cells did not express myogenin in growth conditions (WT) or after infection with the adenovirus containing the decorin sequence (WTi), as expected. Wild type and antisense cells expressed myogenin after triggering differentiation in the above conditions (data not shown). Use of species-specific antibodies demonstrated the virus-mediated expression of decorin in antisense and wild-type cells after infection with the adenovirus containing decorin sequence (Fig. 4A, right panel). The viral infection did not affect the overall synthesis of proteins as shown in Fig. 1C. Fig. 4B shows that the application of exogenous decorin reverted myogenin expression. The effect of bovine cartilage decorin is shown in the left panel, whereas the effect of skeletal muscle-purified decorin is shown in the right panel. Treatment of purified skeletal muscle decorin with chondroitinase ABC had no effect on the reversion of myogenin expression (Fig. 4C). For both types of decorin, the IC 50 was around 50ϳ100 nM. To evaluate whether this decorin concentration was relevant to the conditions encountered by the cells, the amount of decorin in myoblast-conditioned medium was measured by Western blot assay, using skeletal muscle decorin as the standard. Conditioned medium, obtained after 24 h of culture under growth conditions, contained decorin at a concentration of ϳ70 nM (data not shown). These results strongly suggest that inhibition of decorin synthesis triggers the expression of myogenin under growth conditions and that this effect can be reversed by the endogenous production of decorin or by its exogenous application.
It is well established that skeletal muscle differentiation, including the expression of creatine kinase, is dependent on the expression of myogenin. In accordance with this fact was the  finding that the enzyme became induced more rapidly in antisense-transfected clones than in wild type cells when the cells were transferred to differentiation medium (Fig. 5). The expression of muscle-specific creatine kinase was measured in antisense-transfected clones and compared with wild type cells. As shown in Fig. 5A, creatine kinase mRNA levels were detected after 2 days of induced differentiation in antisense cells. In contrast creatine kinase mRNA was not detected until 4 days of differentiation. Creatine kinase activity was also detected earlier in the antisense-transfected cells than in wild type myoblasts (Fig. 5B). These results demonstrate that the expression of creatine kinase a skeletal muscle specific marker, controlled by the expression of myogenin, is accelerated in antisense decorin-transfected cells compared with wild type cells.

Inhibition of Decorin Expression Decreases the Sensitivity of Myoblasts to TGF-␤-dependent Inhibition of Myogenin Expression-
To determine whether the accelerated expression of myogenin and other skeletal muscle markers observed in the antisense decorin-transfected cells resulted from a change in TGF-␤ signaling activity, we measured the TGF␤1-dependent inhibition of myogenin mRNA expression as a function of growth factor concentration. Wild type-and antisense-transfected myoblasts were triggered to differentiate for 30 h in the presence of different concentrations of TGF-␤1. As shown in the Fig. 6A (top left panel), exposure of wild type cells to TGF-␤1 resulted, as expected, in a significant inhibition of myogenin mRNA expression. However, the antisense-transfected cells were considerably less sensitive toward the cytokine (bottom left panel). Whereas in wild-type cells half-maximal inhibition required 0.1 ng/ml, 0.7 ng/ml was needed to achieve the same effect in the cells with suppressed decorin synthesis (Fig. 6A,  right panel). This change in responsiveness to TGFϪ␤1 was specific, since no significant difference in the inhibitory activity of FGF-2 on myogenin expression was observed in both cell types (Fig. 6B, left and right panels). To confirm this modulatory effect of decorin on myogenin expression, wild type and wild type cells infected with adenovirus containing the fulllength sequence for human decorin were triggered to differentiate for 30 h in the presence of different concentrations of Northern blot analysis for myogenin under growth conditions was performed. 10 g of total RNA isolated from myoblasts was separated by electrophoresis, blotted onto nylon membranes, and hybridized with a 32 P-labeled myogenin probe (Myo). The methylene blue-stained nylon membrane is shown in the lower part of the panel, and the ribosomal RNAs are indicated. The transcript size is indicated. Right panel, the extent of decorin synthesized by the adenovirus-infected cells described in A was evaluated by specific immunoprecipitation with antibodies against human decorin as described under "Experimental Procedures." B, A6 cells were incubated for 48 h with decorin purified from bovine cartilage (left panel) or from mouse skeletal muscle (right panel). Northern blot analysis for the effect of bovine decorin is shown in the left panel as described above. The reversion effect of skeletal muscle decorin on myogenin expression was evaluated using A6 myoblasts transiently cotransfected with pMyoLuc and pRL plasmids. The cells were incubated for 24 h in growth medium, harvested, and dual luciferase activity was determined as described under "Experimental Procedures." C, A6 cells were incubated with skeletal muscle decorin pretreated with chondroitinase ABC (Cabc) and assayed as explained in the legend of B. Decorin concentrations are as follows: D1 ϭ 0.1 M and D2 ϭ 0.5 M. The results shown are the means from two different experiments performed in duplicate.

FIG. 5. Creatine kinase expression is augmented in antisense decorin-transfected clones.
A, creatine kinase expression in wild type (WT) and antisense decorin-transfected cells (A6) was evaluated by Northern blot analysis. 10 g of total RNA, isolated from myoblasts incubated in differentiation medium for 0 h, 2, or 4 days, was separated by electrophoresis, blotted onto nylon membranes, and hybridized with a 32 P-labeled creatine kinase cDNA probe (CK). The transcript size is indicated. The ethidium bromide (EtBr)-stained gel is shown in the lower part of the panel, and the ribosomal RNAs are indicated. B, creatine kinase activity was quantitated as a function of time of differentiation as described under "Experimental Procedures." TGF-␤1. As shown in Fig. 6C, decorin-transfected cells exposed to TGF-␤1 were more susceptible to the cytokine-induced inhibition of myogenin mRNA expression than wild type cells. Whereas in decorin-infected cells half-maximal inhibition required 0.018 ng/ml, the same effect in noninfected wild type cells required 0.09 ng/ml.
Modulation of TGF-␤ Signaling by Decorin Suppression-To determine whether decorin suppression had an influence on TGF␤ signaling, a reporter construct was used where the promoter of plasminogen activation inhibitor-1 was coupled with luciferase cDNA. This reporter, p3TPLux, is activated upon binding of TGF-␤ to its transducing receptors (37). The antisense clone responded less to TGF-␤1 and TGF-␤2 when compared with wild type cells. The promoter activity was also diminished in the absence of exogeneously added TGF-␤, suggesting that the autocrine response to the cytokine was reduced (data not shown). To further examine this point, we titrated the response of the antisense clone, control transfected, and wild type cells to TGF-␤1 and TGF-␤2. Fig. 7 shows that TGF-␤1 and -␤2 increased reporter activity in all three cell lines. The antisense cells, however, showed a significant decrease in response mediated by TGF-␤ transducing receptors compared with control transfected and wild type cells (57 and 68%, respectively). Interestingly, the half-maximal effect was measured at similar cytokine concentration.
The levels of TGF-␤-RII, determined by the immunoprecipitation of metabolic labeled extract of myoblasts and the levels of betaglycan or (TGF-␤-RIII), determined by Western blot analyses, were the same in antisense-transfected and wild type cells (data not shown). These results demonstrate, therefore, that the lowered sensitivity toward TGF-␤ in the myoblasts with suppressed decorin expression was mediated by the transducing TGF-␤ receptors.

DISCUSSION
The expression of decorin is up-regulated during skeletal muscle differentiation (35). The physiological relevance of this process is not yet known. Mice with deleted decorin genes have not been reported to exhibit clinical signs of abnormal muscle development (45), although detailed studies on muscle differentiation in these mice are not available in the literature. The absence of a striking muscular phenotype in decorin-deficient mice, however, may simply be an indication of the redundancy of the small leucine-rich proteoglycans and of the possibility that other members of this family may fulfil the function of decorin in skeletal muscle during development. We have, therefore, studied muscle differentiation in a less complex model, i.e. in cultured C 2 C 12 myoblasts. Decorin expression was inhibited by stable transfection with full-length decorin antisense cDNA. As a result of abolishing decorin expression, skeletal muscle differentiation was triggered in myoblasts under growth conditions. This was evidenced by the accelerated expression of the transcription factor myogenin, a master regulator of expression of muscle-specific genes, which is silent in wild type cells under growth conditions (46,47). Expression of myogenin in the nondecorin-expressing cells was reverted by infecting the cells with an adenovirus containing the full-length sequence for endogenously produced decorin and by adding exogenous decorin from two different sources. The data obtained support the hypothesis that decorin is able to suppress myoblast differentiation. This effect could be either the consequence of a direct signaling function of the proteoglycan or an indirect one mediated by the ability of decorin to interact with ECM components and growth factors.
Recent studies indicated that, at least in some tumor cells, decorin is influencing gene expression by direct interaction with a cell membrane receptor. Clear evidence was obtained that decorin binds to the epidermal growth factor receptor with a relatively high apparent K d value of about 90 nM (25). Binding was followed by receptor phosphorylation and an induction of p21, an inhibitor of cyclin-dependent kinases (24). Another candidate molecule for signaling is the 51-kDa endocytosis receptor protein, although evidence has not yet been obtained that decorin endocytosis is accompanied by altered gene expression (48 -50). Myoblasts have been shown to respond to epidermal growth factor (51) and C 2 C 12 myoblasts endocytose decorin very efficiently. 2 In the present study, however, we have been unable to show unequivocally that decorin itself is a signaling molecule for C 2 C 12 myoblasts. When decorin, purified under nondenaturing conditions, was added to the culture medium of wild type myoblasts undergoing differentiation, no significant change in myogenin expression was detected. As mentioned above, however, decorin is able to interact with a variety of serum components like vitronectin, thrombospondin, and fibronectin, and it is not known whether these interactions have an influence on the signaling properties of decorin. The observation that decorin undergoes a secretion-recapture pathway (52) is also compatible with the idea that it is the endogenously produced and not the exogeneously added decorin that directly influences cell behavior.
The data obtained in the present investigation can best be explained by the assumption that decorin forms complexes as well with endogenously produced as with exogeneously added TGF-␤ and that these complexes allow a more efficient presentation of the cytokine to its signaling receptors than the free effector molecule. Myoblasts, being unable to synthesize relevant amounts of decorin or being deprived of the proteoglycan due to its sequestering to collagen lattices, are, therefore, less prone to the inhibitory effect of TGF-␤ on myoblast differentiation. What molecular mechanisms are involved in the activation of TGF-␤ by decorin remains to be investigated. This effect is specific to TGF-␤, because antisense-transfected cells treated with FGF-2, another strong inhibitor of myogenin (10,21,22), exhibited the same FGF-2-dependent inhibition of myogenin expression than wild type cells. These observations suggest that decorin expression can modulate the biological activity of TGF-␤ on skeletal muscle cells. However, as stated above, this activation is not a unique property of the experimental system used in this study, since osteoblasts, too, have been reported to become activated by TGF-␤-decorin complexes (33). In light of the data presented in this study, one wonders how the upregulation of decorin as an indirect, and even perhaps direct, inhibitor of muscle differentiation is controlled during muscle development. However, skeletal muscle cells possess several signaling pathways that modulate the expression of myogenin. As mentioned FGF-2 and HGF/SF are strong inhibitors of skeletal muscle differentiation via activation of specific receptors to transduce their signals.
Interestingly, proteoglycans seem to be modulators of the biological activity of several growth factors, as we observed in this paper for TGF-␤. We have shown that constitutive expression of syndecan-1, a heparan sulfate proteoglycan that is down-regulated during skeletal muscle differentiation (20), produces a 7-fold decrease in the IC 50 for FGF-2 dependent inhibition of myogenin expression (21). Inhibition of syndecan-3 expression produces a 13-fold increase in the IC 50 for FGF-2 inhibitory activity (22). The presence in the plasma membrane of syndecan-1 and -3 is critical for presentation of FGF-2 to the transducing receptors. Although decorin has been normally considered as an ECM proteoglycan, it has been shown to be associated to the plasma membrane through a specific decorin endocytosis receptor in a variety of eukaryotic cells (48 -50, 53). The ability of decorin to interact with the plasma membrane via its specific receptor raises the possibility that decorin might modulate the TGF-␤ activity in a similar fashion to that described for FGF-2 by heparan sulfate proteoglycans (16,17).
Decorin posses multiple functions besides modulation of TGF-␤ activity. Decorin has been implicated in the control of collagen fibrillogenesis (54), cell proliferation (55), and corneal transparency (56). Some of these functions resides in the core protein, whereas other are attributed to the glycosaminoglycan chain (26). Some of the binding sites for molecules, such as TGF-␤ and collagen type I, have been mapped and reside in different parts of the decorin core protein (30). The versatility of the decorin binding activity suggests that decorin may function as a modulator of fundamental biological processes during skeletal muscle differentiation, where its expression is upregulated (35). In addition decorin is an important structural constituent of the skeletal muscle ECM in normal and dystrophic mice (34,36). It remains a challenge for further work to study the relative contributions of these growth factors and ECM components for muscle development.
In summary our results support the idea that decorin plays an important role during skeletal muscle differentiation by promoting the ability of the differentiation inhibitory growth factor TGF-␤ to interact with its signaling receptors. FIG. 4. The expression of myogenin in antisense decorin clones is reverted by specific decorin re-expression and by the addition of exogenous decorin. A: left panel, myogenin expression was evaluated in wild type cells and antisense decorin-transfected cells (WT and A6) and in transfected cells infected with an adenovirus containing the full-length sequence for human decorin (WTi and A6i). Northern blot analysis for myogenin under growth conditions was performed. 10 g of total RNA isolated from myoblasts was separated by electrophoresis, blotted onto nylon membranes, and hybridized with a 32 P-labeled myogenin probe (Myo). The methylene blue-stained nylon membrane is shown in the lower part of the panel, and the ribosomal RNAs are indicated. The transcript size is indicated. Right panel, the extent of decorin synthesized by the adenovirusinfected cells described in A was evaluated by specific immunoprecipitation with antibodies against human decorin as described under "Experimental Procedures." B, A6 cells were incubated for 48 h with decorin purified from bovine cartilage (left panel) or from mouse skeletal muscle (right panel). Northern blot analysis for the effect of bovine decorin is shown in the left panel as described above. The reversion effect of skeletal muscle decorin on myogenin expression was evaluated using A6 myoblasts transiently cotransfected with pMyoLuc and pRL plasmids. The cells were incubated for 24 h in growth medium, harvested, and dual luciferase activity was determined as described under "Experimental Procedures." C, A6 cells were incubated with skeletal muscle decorin pretreated with chondroitinase ABC (Cabc) and assayed as explained in the legend of B. Decorin concentrations are as follows: D1 ϭ 0.1 M and D2 ϭ 0.5 M. The results shown are the means from two different experiments performed in duplicate.


extfieldsofstudy: Biology Medicine

text:
BAG-1 is a Novel Cytoplasmic Binding Partner of the Membrane Form of Heparin-binding EGF-like Growth Factor: A Unique Role for proHB-EGF in Cell Survival Regulation

Several cell functions related to growth and survival regulation have been attributed specifically to the membrane form of heparin-binding EGF-like growth factor (proHB-EGF), rather than to the diffusible, processed HB-EGF isoform. These findings suggest the existence of a functional binding partner specifically for the membrane form of the growth factor. In this study we have identified the prosurvival cochaperone, BAG-1, as a protein that interacts with the cytoplasmic tail domain of proHB-EGF. Interaction between BAG-1 and the 24-amino acid proHB-EGF cytoplasmic tail was initially identified in a yeast two-hybrid screen and was confirmed in mammalian cells. The proHB-EGF tail bound BAG-1 in an hsp70-independent manner and within a 97 amino acid segment that includes the ubiquitin homology domain in BAG-1 but does not include the hsp70 binding site. Effects of BAG-1 and proHB-EGF co-expression were demonstrated in cell adhesion and cell survival assays and in quantitative assays of regulated secretion of soluble HB-EGF. Because the BAG-1 binding site is not present on the mature, diffusible form of the growth factor, these findings suggest a new mechanism by which proHB-EGF, in isolation from the diffusible form, can mediate cell signaling events. In addition, because effects of BAG-1 on regulated secretion of soluble HB-EGF were also identified, this interaction has the potential to alter the signaling capabilities of both the membrane-anchored and the diffusible forms of the growth factor. In this study we report that the cytoplasmic tail of proHB-EGF interacts with BAG-1, a multifunctional protein first identified as a binding partner of the anti-apoptotic protein Bcl-2 (11). BAG-1 associates with several signaling molecules and is capable of suppressing apoptosis. Our findings suggest a novel mechanism through which proHB-EGF might mediate physiological processes related to growth, adhesion and cell survival. MC2-proHB-EGF-AP cells were either treated or untreated by 0.4 mM etoposide for 24 h and cells were fixed with incubation with 2% paraformaldehyde for 1 h at room temperature. Cell permeabilization was performed with 0.1% Triton-X-100 in PBS for 3 min on ice. Cells were washed with PBS, blocked for 30 min with PBS/0.1% BSA/0.075% glycine (blocking buffer) and incubated with anti-AP monoclonal Ab (8B6, Sigma) (1:250) and rabbit polyclonal anti-BAG-1 antibody (1:1000) (N20, Santa Cruz) diluted in blocking buffer for 1 h at room temperature. After washing with blocking buffer, cells were incubated with Texas-red-conjugated donkey anti-mouse IgG and fluorescein (FITC)-conjugated donkey anti-rabbit IgG (Jackson ImmunoResearch, Inc. West Grove, PA) for 45 min. Slides were washed extensively with blocking buffer prior to mounting and were viewed using a BioRad 1024 Laser Scanning Confocal Imaging System. Up to forty serial optical sections (approximately 0.5 m m section thickness) were collected on informative cells. Individual channels of double labeled cells were collected as two separate series and merged in Confocal Assistant (written by Todd Breljie).

Cell culture and transfection. LNCaP and PC-3 cells were grown in RPMI-1640/10% FBS. CHO-K1 cells were cultured in F12K/10%FBS. NRK52E and COS7 cells were grown in DMEM/10% FBS. MC2 cells were cultured in T medium as described (13). All cells were maintained in a humidified atmosphere of 95% air/5% CO 2 at 37 o C.
MTT and DNA fragmentation assays were performed as described HB-EGF secretion assay. Secretion of HB-EGF was measured by determining levels of alkaline phosphatase (AP) in the medium using cells expressing proHB-EGF-AP fusion proteins as described previously (13). Briefly, 40,000 cells/well were seeded in 24-well plates and 24 h later, cells were stimulated by etoposide at the different concentrations under serum free conditions. Medium was collected 24 h later and AP activity was measured spectrophotometrically.
Statistical Analysis. Data were compared using a paired Student t-test. P values less than 0.05 were considered significant.

Results
The HB-EGF tail domain interacts with the prosurvival protein, BAG-

1
The 24-residue cytoplasmic tail of proHB-EGF exhibits a high degree of inter-species sequence conservation (95% amino acid identity between mouse and human), suggesting an important functional role for this region of the protein. In a previous study, proHB-EGF was shown to protect NRK52E renal epithelial cells from apoptosis induced by H 2 O 2 or etoposide treatment (9).
Soluble HB-EGF was not able to replicate this cytoprotective effect. In order to determine if the proHB-EGF tail is involved in this process, NRK52E cells were transfected with intact proHB-EGF or proHB-EGF tail-deleted expression constructs. Cells expressing the two forms of the protein were then challenged with etoposide or H 2 O 2 . NRK52E cells expressing the proHB-EGF construct exhibited less apoptosis than vector-only control cells ( Fig. 1), consistent with findings reported by Takemura et al. (9). In contrast, cells expressing the taildeleted construct exhibited a similar level of apoptosis to the vector-only cells, suggesting a role for the tail domain in cytoprotection from apoptosis inducers.
These observations led us to search for proteins that interact with the proHB-EGF cytoplasmic domain. We screened a yeast two-hybrid expression library, constructed from a human prostate (LNCaP) xenograft tumor growing in a mouse host, with the proHB-EGF tail domain (a.a. 185-208), using a LexAbased system. Approximately 10 6 independent clones were screened. From the 6 strongest potential interactors identified in the screen, two clones, pJG45-B11 and pJG45-E68 ( Fig. 2A), each contained the entire open reading frame of the short form of the mouse protein, BAG-1 (219 amino acids, expected MW 24.5 kDa) (11). These two clones are identical but were derived from two independent yeast transformations. In follow-up experiments, BAG-1 and the HB-EGF tail also interacted in the yeast two-hybrid system when the cDNAs were switched into the opposite (prey<-->bait) plasmid vectors.
To confirm the association between BAG-1 and HB-EGF, a GST fusion protein containing the HB-EGF cytoplasmic tail (GST-HB-EGF  ) was constructed and used in pull-down assays. COS7 cells were transiently transfected with expression plasmids encoding mouse BAG-1. Lysates from these cells or from LNCaP cells (to test for binding with the native/endogenous, human form of BAG-1) were incubated with purified GST-HB-EGF  . A complex was formed between GST-HB-EGF (185-208) and BAG-1 but not between BAG-1 and GST alone (Fig. 2B). The converse experiment was also performed with a GST-BAG-1 fusion protein, using lysates from cells expressing AP-tagged proHB-EGF. In these experiments, a complex was formed between proHB-EGF and GST-BAG-1, but not between proHB-EGF and GST, or between GST-BAG-1 and proHB-EGF in which the tail domain was deleted (Fig. 2C). Complex formation between BAG-1 and the proHB-EGF tail was also demonstrated by Far-Western blot, in which the HB-EGF tail was immobilized and the interaction occurred on blotting membranes instead of in solution (Fig. 2D).
The 219 amino acid form of BAG-1 identified in the screen contains a ubiquitin homology domain (residues 37-73) and a central region (residues 90-172) that binds to Bcl-2 (11). Its carboxyl-terminal domain is required for direct interaction with the ATPase domain of hsp70 heat shock protein (16). We generated a GST-BAG-1(∆C) construct (residues 1-97), containing the ubiquitin homology region, and GST-BAG-1 (∆N) (residues 100-219), which carries binding sites for most of the known BAG-1 interactors. Complex formation with proHB-EGF was observed with GST-BAG-1 and GST-BAG-1(∆C), but not with 1(∆N) and hsp70 (Fig. 2E), demonstrating the capability of GST-BAG-1(∆N) to bind to a known BAG-1 binding protein despite its failure to bind to proHB-EGF.
This result also indicates that the BAG-1 interaction with proHB-EGF is not mediated by hsp70 and it rules out the possibility that aberrant folding of GST-BAG-1(∆N) is the reason for the absence of binding to HB-EGF. In a reciprocal experiment, GST-HB-EGF  was also able to form a complex with endogenous BAG-1 (MW 33-35 kDa) and endogenous hsp70 from human (LNCaP) cells (Fig. 2F).
We also investigated the dynamics of the BAG-1/HB-EGF tail interaction in cells induced to undergo apoptosis. LNCaP cells were treated with wortmannin, a PI3-kinase inhibitor that rapidly induces apoptosis in this cell line (15), and lysates were used in pull-down experiments. Interestingly, complex formation between the HB-EGF tail and endogenous BAG-1 diminished in a time-dependent manner following wortmannin treatment (Fig. 2G). Similar results were obtained when wortmannin-insensitive PC-3 cells were induced to undergo apoptosis by treatment with staurosporine, a protein kinase inhibitor (data not shown). These results suggest that the BAG-1/proHB-EGF interaction is not favored when cells undergo programmed cell death.
Taken together, these experiments 1) demonstrated a direct interaction between BAG-1 and the proHB-EGF cytoplasmic domain, 2) localized the HB-EGF interacting domain to within residues 1-97 of BAG-1 and 3) also revealed that BAG-1 can form a ternary complex with both proHB-EGF and hsp70 through interactions with these proteins at distinct binding sites.

proHB-EGF and BAG-1 functionally cooperate in vivo
To explore the possibility of a functional interaction between proHB-EGF and BAG-1, CHO cell populations were engineered sequentially to stably express either BAG-1, proHB-EGF, or both proteins. BAG-1+proHB-EGF-expressing cells exhibited a more epithelial-like cellular morphology, in comparison to cells expressing either BAG-1 or proHB-EGF alone or control vectors, or the parent cell, all of which exhibited a more fibroblastic appearance (Fig. 3). These data suggest that coexpression of both proteins confers functional properties on transfected cells that are not seen when each protein is expressed separately.
A similar requirement for proHB-EGF and BAG-1 co-expression to change a cellular phenotype was observed in other assays. BAG-1+proHB-EGF-expressing cells exhibited quantitatively reduced cell adhesion, as measured by sensitivity to trypsin/EDTA treatment, in comparison to cells expressing either BAG-1 or proHB-EGF or control plasmids (Fig. 4A). The presence of BAG-1 with proHB-EGF in CHO cell transformants also affected the sensitivity of these cells to certain apoptotic stimuli. BAG-1+proHB-EGF cells demonstrated increased resistance to apoptosis induced by etoposide, a topoisomerase inhibitor, in comparison to cells expressing either BAG-1 or proHB-EGF alone (Fig.4B). This resistance to apoptosis induction appeared to be confined to specific survival pathways, however, because BAG-1+proHB-EGF cells did not show synergistic protective effects when apoptosis was induced by staurosporine (data not shown).
We also compared secretion of soluble HB-EGF in response to apoptotic stimuli in proHB-EGF-and proHB-EGF(∆tail)-expressing MC2 cells transfected with BAG-1 and vector only. Etoposide treatment induced rapid secretion of soluble HB-EGF in cells expressing transfected BAG-1 but not in cells transfected with an empty vector (Fig. 5A). In contrast, in cells expressing a tail-deleted form of proHB-EGF, transfection with BAG-1 did not alter the secretion response to etoposide. EGFR levels in proHB-EGF and proHB-EGF(∆tail) expressing cells were equivalent (Fig. 5B), indicating that differential capture of the soluble HB-EGF ligand by the EGFR cannot account for the observed differences in the secretion response. Similar results were observed in the CHO cell background (data not shown). These data suggest that the proHB-EGF tail is involved in regulated processing of the cell-associated form of the growth factor to the soluble form and that BAG-1 is capable of modulating this process in a manner that is dependent on the presence of the tail domain.
Immunofluorescence confocal microscopy indicated that proHB-EGF and BAG-1 co-localized within cytoplasm vesicles and at the plasma membrane, consistent with the possibility that BAG-1 can affect trafficking and maturation of soluble HB-EGF (Fig. 6). BAG-1 and proHB-EGF colocalized sites diminished in frequency when cells were treated with etoposide.

Discussion
The results of this study demonstrate that the membrane form of HB-EGF interacts with the anti-apoptotic protein, BAG-1, and that this interaction is likely to have functional significance. The BAG-1/HB-EGF tail interaction was demonstrated in a number of independent assays, including yeast two-hybrid, GST-pull-down, and Far-Western blot methods. Evidence for colocalization of BAG-1 and proHB-EGF was also obtained with immunofluorescence confocal microscopy. In addition, cooperative effects of BAG-1 and proHB-EGF expression were observed in assays of cell adhesion, apoptosis, and growth factor secretion. Consistent with these findings, we found that deletion of the proHB- Importantly, our results suggest a novel mechanism whereby the membrane-anchored form of HB-EGF might alter cell function independently of the soluble form of the molecule. BAG-1 was originally identified as a Bcl-2binding protein but is now known to interact with and regulate a number of signaling proteins. Because the proHB-EGF tail and membrane-anchoring domains are removed from the mature growth factor by proteolytic cleavage, these results provide the first unambiguous mechanism whereby the HB-EGF pro-form could mediate processes distinct from those conferred by processed HB-EGF.
Several previous studies have identified bioactivities solely attributable to proHB-EGF, although the reason for the distinction between the precursor and secreted forms is not clear because both proteins presumably function principally by activating identical high-affinity receptor tyrosine kinases.
However, BAG-1 is the first protein to be identified that interacts with the proHB-EGF cytoplasmic domain in an ectodomain-independent manner. Because CHO cells express low or negligible EGFR levels (18) -2 (11,26). From these and other data, a critical role for BAG-1 in cell signaling related to cell survival mechanisms, but also to other processes, can be inferred despite uncertainty as to its precise mechanism of action.
The heat shock protein, hsp70, has been reported to be a favored BAG-1 interactor. In this case, BAG-1 appears to function as a regulator of protein folding and/or trafficking by acting as a competitive antagonist of the cochaperone, Hip (27). Although a number of proteins are thought to associate with BAG-1 because of its ability to bind hsp70 (16), we demonstrate in this study that proHB-EGF binds to a C-terminal deletion mutant of BAG-1 which does not bind hsp70 and that the HB-EGF interaction site on BAG-1 is distinct from the hsp70 interaction site. Furthermore, the HB-EGF tail-BAG-1 interaction occurs in yeast and yeast hsp70 is not a BAG-1 binding partner (16). Taken together, these data indicate that proHB-EGF and BAG-1 interact directly and in an hsp70-independent manner. This finding suggests that interaction of BAG-1 with proHB-EGF, and possibly with other regulatory proteins, may be functionally distinct from its role as a cochaperone in mechanisms of protein folding and/or stabilization.


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Structure and Interactions of Lipid Bilayers(cid:2)

The cell is the fundamental unit in biology. Each cell is spatially defined by its cytoplasmic membrane. The structural basis for each membrane is lipid in bilayer form. Following this reductionist point of view, it is therefore not surprising that lipid bilayers have been much studied using a great variety of techniques.

Introduction
The cell is the fundamental unit in biology. E a c h cell is spatially de ned by its cytoplasmic membrane. The structural basis for each m e m brane is lipid in bilayer form. Following this reductionist point of view, it is therefore not surprising that lipid bilayers have b e e n m uch studied using a great variety o f techniques.
What is surprising is the large uncertainty for simple structural quantities that has been generated by the di erent studies. Let us consider the most studied of all bilayers, the one composed of the lipid DPPC in the fully hydrated, biologically relevant phase (L = uid(F)=liquid-crystalline) at T = 5 0 o C. V arious di raction and NMR studies have g i v en values for the interfacial area A per DPPC lipid that range from 56 A 2 to 72 A 2 1,2]. A most distinguished neutron di raction study suggested A = 5 8 A 2 3] while a m uch used x-ray method obtained A = 7 1 A 2 4]. The real uncertainty i n these numbers is even larger than the nominal 24% obtained by dividing one result by the other because A for DPPC in the low temperature gel (G) phase is A G D PPC = 4 8 A 2 1,5,6]. Therefore, the e ect of uidizing the DPPC bilayer (i.e., making it biologically relevant) should be de ned to be A F ;A G . Using the above di erences for the uid phase area of DPPC yields an enormous uncertainty i n A F D PPC ; A G D PPC -from 8 A 2 to 24 A 2 . E v en though one does expect to achieve as good precision in biophysics as in the physical sciences, this 100% level of uncertainty is ridiculous! Uncertainty i n A is directly related to uncertainty in the bilayer thickness. A common de nition of bilayer thickness is D B = 2 V L =A, where V L is the volume of a lipid molecule in the bilayer V L has been measured accurately (0:2%) by a n umber of groups 7]. The thickness of lipid bilayers (vide infra for discussion of various de nitions of thickness) is an important structural quantity for discussing the incorporation of intrinsic membrane proteins.
Molecular dynamics simulations give m uch i n s i g h t i n to lipid bilayer structure at a level of detail not available experimentally, but uncertainty i n A negatively impacts such s i m ulations. Some simulations are done with lipids and water in a simulation box of xed size, in which c a s e A is xed in the simulation. Results obtained from such s i m ulations performed at the wrong A will be misleading and could even lead the unwary simulator to vary interaction parameters in order to t other data, such as the NMR order parameters. Many simulations are now done with constant lateral pressure 8{10]. It is then in principle possible for the simulation to nd the correct value of A, but the computer time necessary to equilibrate can be large if the starting A is far from the equilibrated value. Furthermore, even if the simulation can be equilibrated, experimental uncertainty i n A reduces the ability t o t e s t t h e interaction parameters used in the simulation.
This chapter will review some of the e orts to obtain structural results for L phase lipid bilayers with an emphasis on recent w ork from our lab. To obtain some of these structural results we found that it was necessary to deal with the e ects of uctuations. This in turn led us to the issue of interactions between bilayers, which is the second topic that will be discussed in this chapter. Underlying both these e orts is the central role of uctuations.
Fluctuations are important in biology. The fact that the biologically relevant uid phase of lipid bilayers is the one with the largest uctuations supports this paradigm. Bilayers with greater uidity can seal leaks and tears more readily. Local uctuations in the lipid molecules a ect passive permeability of solutes through the membrane and can facilitate the function of intrinsic membrane proteins by transiently reducing activation energy barriers 11]. In addition to uctuations at the molecular length scale, there are also longer length scale uctuations that can be adaptive for cell shape changes. Longer wavelength uctuations give rise to an additional force between membranes, and these are the uctuations that degrade di raction data necessary to obtain structure. This chapter will focus upon these longer length scale uctuations. We will nish this general introduction with Fig. 1 which s h o ws one key piece of structural information from our lab 12,13], the volume per lipid V L . The temperature dependence in Fig. 1 indicates the various thermodynamic phases of DPPC. This chapter will focus on the most biologically relevant phase, identi ed in di raction studies as the L phase. There will be some use made of results for the gel phase, which w e believe is the best characterized of all the phases 5]. The chapter of Katsaras and Raghunathan 14] complements this chapter by focussing on the lower temperature phases, especially the subgel and the ripple phases.

Levels of Description of Structure
It is important to appreciate that it makes no sense to contemplate an atomic level structure at the sub{ A level for lipid bilayers. This is not because of poor di raction technique or sample preparation. Lipid bilayers have biologically vital uctuations. This means that atoms are not inherently localized. The proper description for the positions of atoms in the lipid molecule is that of broad statistical distribution functions. Fig. 2a shows simulations for distribution functions for several of the component groups of the lipid molecule along the direction of the bilayer normal 15]. The widths in this direction are of order 5 A. I n c o n trast, in the`in-plane' direction the distribution functions for the L phase are just constants because the lipid molecules are in a twodimensional uid phase. (Of course, one can still consider pair correlation functions, which are important for di use wide angle scattering, but this is a little explored area.) In contrast, for the lower temperature phases there is interesting and valuable in-plane structure 14,5].
Fluctuations in biologically relevant fully hydrated uid phase bilayers mean that x-ray di raction data can only yield electron density pro les like the one shown in Fig. 2b. The peaks in such electron density pro les are associated with the electron dense phosphate group and the lower electron density in the center is associated with the hydrocarbon region and especially with the low electron density of terminal methyl groups of the fatty acids. Therefore, electron density pro les con rm the usual picture of bilayer structure and they give another measure of the bilayer thickness, namely, the head{ head thickness, D HH . H o wever, electron density pro les do not yield the z coordinate of molecular groups along the bilayer normal. Such information has been obtained using neutron di raction, either with selective deuteration of various component groups (DPPC at 98% RH 3]), or combined with x-ray di raction (DOPC at 67% RH 16]).
The transverse description of the bilayer as a set of distribution functions along the z axis is valuable, but it does not include other important information, such a s A in the lateral direction, or volumes. Therefore, a complementary description of bilayer structure, shown in Fig. 2c Fig. 2c divides the volume V L of the lipid into two regions. The tail region is essentially a hydrophobic hydrocarbon chain region by de nition, it includes only the methylenes and terminal methyls on the fatty a c i d c hains. The head region is essentially a hydrophilic region, which includes the remainder of the lipid molecule (carbonyls, glycerol, phosphate and choline). An average structure is depicted by d r a wing two sharp boundaries, one between chains and heads and one between heads and water, as shown on the left side of Fig. 2c. In view of the uctuations shown in Fig. 2a, such sharp boundaries with all the chains on one side and the heads on the other are clearly arti cial, but it is still a valid representation in the sense that the sharp lines can be justi ed as Gibbs dividing surfaces 17]. Nevertheless, in the case of the interface between the headgroups and the water, it is useful to consider a re nement to the simple description on the left side of Fig. 2c. This re nement, shown on the right side of Fig. 2c, explicitly mixes the heads and water in the polar, interfacial region. This gives better correspondence with the distribution function description in Fig. 2a in particular, it gives a better representation of the steric thickness, de ned to be D 0 B .

Problem with the Gravimetric Method
A popular method for obtaining structural information 4,6] is most easily explained from the description shown on the left side of Fig. 2c. The total volume V L of one lipid molecule and its associated n w water molecules is AD=2, where D is the repeat distance that is easily and accurately measured by di raction on stacks of lipid bilayers. (Using synchrotron x-rays and a high resolution setup, we h a ve measured D with accuracy of 0:01 A, though reproducibility with nominally identical samples is usually not so good.) Therefore, AD = 2 ( V L + n w V w ) (1) where V L is the measured lipid volume 12], V W is the volume of water and n w is the number of water molecules/per lipid. The gravimetric method simply weighs the amount o f w ater and the amount of lipid to obtain n w . Then, A is obtained as a function of n w from Eq. 1. The procedure is then to vary n w and measure D. In principle, as n w increases towards full hydration, D increases until an excess water phase forms at the fully hydrated value of n w . Increasing n w further just adds to the excess water phase and D should remain constant.
While the concept of the gravimetric method is simple and elegant, it has been criticized and a number of studies have obtained di erent r e s u l t s 1,18{21]. So let us elucidate the aw. The gravimetric method assumes that all the water added to the system goes between the lipid bilayers that are neatly stacked in regular one-dimensional arrays. In fact, gravimetric experiments are performed on lipid dispersions consisting of multilamellar vesicles (MLVs). Such samples have m a n y defect regions. For example, it is customary to visualize MLVs as consisting of spheres of about 10 m diameter composed of stacks of nearly a thousand bilayers. As is well known, packing of spheres leaves defect volumes between the spheres that amount to about 26% of the total volume (for a nice schematic see Fig. 3 in 21]). Such defect volumes, which m ust be lled with water, escape detection by di raction, which focusses on the more ordered structure. Therefore, the value of n w that should be used in Eq. 1 should be smaller than the gravimetric value of n w because the total weighed water includes defect water that is invisible to di raction.
This artifact suggests that the gravimetric method will tend to overestimate A. Direct veri cation of this tendency for the gravimetric method to overestimate n w and A was given for the gel phase of DPPC, for which i nplane chain-packing and tilt angle were measured directly from wide angle di raction. This gave A G DPPC = 4 8 A 2 and n w = 12 1,5]. The results of the most recent g r a vimetric studies 4,22] gave n w in the range 17:5 ; 19 which would require A G D PPC to be in the range 52 ; 54 A 2 1]. The only exception we k n o w to this tendency of the gravimetric method to overestimate is for EPC where 23] obtained A F EPC = 6 4 A 2 using the gravimetric method which is smaller than our best value of A F EPC = 6 9 :4 A 2 24].
The gravimetric method also indicated that A increases strongly as the limit of full hydration is approached 6,21]. Indeed, A should increase in this limit. Recall that less than full hydration is equivalent to exerting osmotic pressure P on the water. The major e ect of osmotic pressure is to decrease the water space D w and thereby t h e D space. However, osmotic pressure also decreases A because this too extracts water from stacks of bilayers. The appropriate formula to describe this second e ect is 25] where A 0 is the fully hydrated area when P = 0 and K A is the phenomenological area modulus. However, while A should increase as full hydration is approached, Rand and Parsegian 25] realized that the changes in A obtained from the unadulterated gravimetric method became much too large near full hydration for the measured values of K A 26]. They then used gravimetric values of A obtained under osmotic pressure at 10 atmospheres and they used Eq. 2 to extrapolate to fully hydrated P = 0. This reduced the estimate of A F D PPC from 71 A 2 obtained from the unadulterated gravimetric method to 68:1 A 2 25]. However, this is still larger than the value obtained by a n alternative method that we n o w proceed to discuss.

Electron Density Pro le Method
The electron density pro le (z) for symmetric bilayers with a lamellar repeat spacing D is where for the di erent orders h > 0, h is the phase factor which can only assume va l u e s o f + 1 o r ;1. F h is the bilayer form factor which is routinely obtained from the intensity I h = F 2 h =C h under the di raction peak. C h is the Lorentz polarization correction factor for low angle scattering C h is nearly proportional to h 2 for unoriented MLV samples and to h for oriented samples. The zeroth order form factor F(0) is given by 2 7 ] AF (0) = 2(n L ; W V L ) = 2 ( L ; W )V L (4) where A is the area per lipid, n L is the number of electrons in the lipid molecule, V L is the lipid molecular volume and L n L =V L is the average electron density of the lipid molecule. The form factors F h involve a n u nknown scale factor, so only the absolute ratio r h = jF h =F 1 j of form factors are measured directly and this means that only relative electron density proles are routinely reported. Obtaining absolute electron density pro les will be discussed in Sec. 2.7.
The most reliable quantitative information that can be obtained from the electron density pro le is the headgroup spacing D HH , de ned to be the distance between the two peaks in the electron density pro le. In practice, four orders (h max = 4) su ce to give a reasonably accurate estimate of D HH . Recently, w e h a ve found that, even with four orders, the measured D HH should be corrected due to the limited number of Fourier terms 24,28,29]. This realization came by examining reasonable model electron density proles. The model we prefer 30], and that adequately represents the results of several simulations 31], employs a Gaussian function for the headgroup region and a Gaussian function for the terminal methyls on the chains as well as a constant for the methylene region. When we F ourier analyze this hybrid model and compare D HH obtained from the 4th order Fourier reconstruction with the model D HH , w e nd that there is a small error that systematically varies with D HH =D 5]. In our current use of this method (Yufeng Liu, unpublished), the parameters used to construct the hybrid model are obtained from the experimental form factors and so the hybrid model used for corrections to D HH is tuned to the particular lipid being studied.
McIntosh and Simon 32] introduced a method to use D HH to obtain A for the L phase. The idea is to compare the more poorly determined L phase with the much better determined gel phase and to use di erences to extrapolate from the gel phase structure to the L structure. Then, the L phase area A F is obtained in terms of the di erence in bilayer thickness D HH = D F HH ; D G HH , the measured lipid volume V F L and gel phase values for the hydrocarbon thickness D G C and headgroup volume V G H , This method was rst applied to DLPE 32] which w as a favorable rst choice for two reasons. The chains in DLPE are perpendicular to the bilayer in the gel phase, so gel phase quantities are easier to obtain than for PCs where the chains are tilted. However, we h a ve been able to obtain a structural determination of gel phase DPPC in the sense of Fig. 2c 1,5]. The second reason DLPE was more favorable than the PCs is that there were four orders of di raction for fully hydrated L phase DLPE, but not for DPPC, and we now turn to this major hurdle.

Why are there so few orders of di raction?
The immediate shortcoming of the electron density pro le approach i s t h a t fully hydrated samples of many lipids, such as unoriented DPPC dispersions in the L phase, have o n l y t wo robust orders of di raction. Electron density pro les using two orders of di raction are not quantitative, even for D HH . The generic explanation for so few orders is that uctuations and disorder reduce higher order intensities. However, to make sense of di raction data, it is necessary to understand that there are two quite di erent pieces to this explanation.
Most of the analyses of electron density and neutron scattering length pro les implicitly make the assumption that stacks of bilayers are one dimensional crystals with regular D spacing. Disorder and local molecular uctuations within each bilayer give rise to the broad distribution functions in Fig. 2a. Broad electron distribution functions, in turn, require that higher order terms in the Fourier expansion be small, so the higher order peak intensities are small. This point, which has been made forcefully by Wiener and White 33], is, however, only the rst part of the explanation for the absence of higher order peaks.
The second reason for the absence of higher order peaks is that stacks of lipid bilayers are not one dimensional crystals, but smectic liquid crystals. Smectic liquid crystals have large scale (long wavelength) uctuations that destroy crystalline long range order and replace it with quasi-long-range-order (QLRO) in which pair correlation functions diverge logarithmically instead of remaining bounded as in crystals. Because long range order is destroyed, Debye-Waller theory of scattering from crystals with uctuations is not appropriate (see appendix to 31]). Instead, QLRO c hanges the scattering peak shape from an intrinsic delta function by removing intensity from the central scattering peak and spreading it into tails of di use scattering centered on the original peaks. The magnitude of this shifting of intensity increases with increasing di raction order. For high enough order, the scattering peaks are completely converted to di use scattering even if the Fourier component for the local lipid bilayer is large. In-plane x-distance (Å) The preceding distinction between short range and long range uctuations can be summarized as follows. Short range uctuations are intrinsic to the single lipid bilayer. These are the uctuations that one sees in MD simulations. They correspond to disorder within a unit cell in a crystalline stack of repeat units. In contrast, long range uctuations are uctuations in the relative positions of the unit cells which m a y be thought of as the centers of the bilayer. These longer range uctuations do not change the distribution functions of molecular components relative to the bilayer center, so they do not a ect the structure of the single lipid bilayer.
Both kinds of uctuations reduce the intensity of the higher orders. The rst kind of uctuations are local and their reduction in higher orders faithfully re ects the true bilayer structure. In contrast, the reduction in intensity due to the second kind of uctuations at large length scale is an artifact that should be removed in order to obtain bilayer structure. This removal requires taking data with high instrumental resolution and then analyzing it using liquid crystal theory.
A v ery appropriate name for this method is \liquid crystallography". This name, however, should not be confused with the same name that has been used by Wiener and White 16] in a series of papers that introduced a di erent major innovation, namely, t h e j o i n t re nement method for combined x-ray and neutron di raction data. Wiener and White properly emphasized that the rst kind of molecular uctuations within each unit cell are intrinsic to liquid crystals. However, this rst kind of short range disorder is also present in highly disordered solids and no particular properties of liquid crystals appear in the Wiener and White analysis. It is the second kind of long range uctuations that requires an analysis speci cally tailored to liquid crystals and that we suggest should be called \liquid crystallography".

Liquid Crystallography
The beginning of liquid crystallography w as a remarkably succinct three page paper by Caill e 35] and communicated to the French Academy of Sciences by Guinier. That paper predicted power law tails for smectic liquid crystals (including stacks of bilayers) and it related the powers (exponents) to bulk phenomenological material properties, the bending modulus K c and the bulk compression modulus B the latter represents the interactions between adjacent bilayers in a stack. These predictions of the theory were later veri ed by highly precise experiments on general smectics 36] and later on lipid bilayers 37].
Readers of Guinier's ne book on di raction 38] will recall that, before Caill e's paper, Guinier had discussed the important distinction between disorder of the rst and second kind, where disorder of the second kind destroys crystalline long range order. Applied to a one-dimensional stack of bilayers, Guinier's theory is the same as the paracrystalline theory of Hosemann 39]. The Caill e theory also treats uctuations of the second kind, but it is considerably di erent from the earlier theories 38,39]. The earlier theories assumed that any disorder in the unit cell dimension propagated uniformly in the in-plane direction. This is clearly arti cial because bilayers can also undulate so the local water spacing can vary with in-plane coordinates (x,y). Another major distinction between the theories is that Caill e's is based on a realistic Hamiltonian model rather than the purely stochastic approach o f paracrystalline theory. H o wever, the Caill e theory is considerably more difcult to apply, and paracrystalline theory has been used in biophysics, so it was necessary to test whether Caill e theory really represents a signi cant improvement. Our group has documented the de nite superiority of Caill e theory for L phase DPPC bilayers 40]. On the other hand, for low temperature phases with smaller undulation uctuations, we h a ve found that the scattering peaks are broader and appear not to follow the Caill e form, but perhaps are dominated by frozen-in defects.
There are two main e ects of liquid crystallography. The rst is that the proportion of di use scattering to total scattering increases with order h.
Indeed, for high enough h the scattering is entirely di use and no central peak can be seen. The second is that the proportion of the scattering that is di use increases for all orders as the lipids become more fully hydrated.
Before the e ect of uctuations was understood, it was well known that more orders of di raction could be obtained by drying lipid bilayer stacks. For example, Wiener and White 16] obtained h=8 orders of di raction for DOPC at 67% relative h umidity. H o wever, drying the sample raises the spectre that the bilayer parameters one wishes to measure are changed. Indeed, they found A F67 DOPC = 5 9 :4 A 2 for DOPC 16] whereas we n d A F100 DOPC = 7 2 :2 A 2 for fully hydrated DOPC at 100%RH 29]. As mentioned in Sec. 2.2, the unadulterated gravimetric method generally gives quite large increases in A near full hydration. The method of electron density pro les would seem to agree that there were large structural changes if one interprets the data from a purely crystallographic viewpoint. The higher orders of di raction disappear and even the second order of di raction for DPPC systematically falls o the continuous transform obtained at 98% RH as the humidity is increased to full hydration 31]. However, liquid crystallography predicts these very same e ects, at least qualitatively.
To v erify that liquid crystallography predictions are quantitative requires considerably more e ort. The rst e ort, skillfully carried out by R. Zhang in our lab, was to improve the Caill e theory to give quantitative predictions, not just for the power laws, but also for the amplitudes of the scattering 41]. The ensuing modi ed Caill e theory enables us to predict the shapes of the scattering peaks for all orders using only a few parameters, primarily the average domain size L, which a ects the width of the central peak, and the Caill e 1 parameter 35], 1 is proportional to the mean square uctuations 2 in the water space and 1 governs the size of the scattering tails as well as the power law decay.
The second e ort was to obtain the peak shapes experimentally. W e use a silicon analyser crystal with instrumental resolution q = 0 :0001 A ;1 40]. However, with such high resolution, most scattered x-rays do not get to the detector, so a synchrotron source is helpful and we use the CHESS facility a t Cornell. We are able to measure su ciently far into the power law tails (before signal/noise becomes too small) so that we can obtain the 1 parameter. It might be noted that the classic way of obtaining power law exponents such as 1 is to use log{log plots 36,37]. This is di cult because the number of decades in q over which straight line behavior on a log{log plot can be seen is rather small. The small q range in the central peak is limited by t h e crossover to a regime dominated by the sample domain/correlation size L and the large q range is limited by signal/noise and is further degraded by continuous changes in the form factor F(q). In contrast, our method relies, not only on the power law behavior, but also on the larger amplitudes in the tails when 1 is larger. Once we h a ve obtained the parameters in the model, we can extrapolate the di use scattering that is in the tails of the structure factor S(q). Even though this extrapolated di use scattering intensity i s s o small that it can't be separated from background, the total amount o f i t i s large because it extends all the way b e t ween scattering peaks. Fig. 4 indicates the amount o f i n tegrated intensity that is recovered using this extrapolation. When this missing intensity is added, the result is that liquid crystallography does indeed predict the e ects in the preceding paragraph quantitatively, and the use of it enables more accurate form factors F h to be obtained that are true to the bilayer structure. Our former student, Horia Petrache, has made available a program to perform liquid crystallography data analysis. (Send e-mail to nagle@andrew.cmu.edu to obtain access.)

Structural Results
The method we h a ve been using to obtain structural results rst obtains uctuation corrected form factors for unoriented samples using liquid crystallography. Electron density pro les are drawn for those samples that have four orders of di raction. Such samples are typically under osmotic stress of 20-60 atmospheres, corresponding to relative h umidities of 95 ; 98%. To exert osmotic pressure we use the now classic method of Rand and Parsegian 25] with the polymer PVP or dextran. There is never a problem of choosing the correct phases for F h either plots of F(q) a t m a n y osmotic pressures or tting hybrid electron density models to the intensities always give u n a mbiguous phases, which are often (; ; +;). For PC lipids, we use Eq. 5 to obtain A as a function of osmotic pressure P . The reference phase that we have used in Eq. 5 is the gel phase of DPPC, for which headgroup volume V G H and hydrocarbon thickness D G C are accurately known from gel phase studies 1,5]. The volume V F L in the L phase is accurately ( 0:2%) measured 12]. The value of D HH used in Eq. 5 is obtained from the electron density pro les. Inspired by Eq. 2, we plot the ensuing values of A against AD w P, where the slope is ;1=K A and the intercept is the full hydration value A o .
To d o t h i s w e also need the Luzzati water thickness D w , w h i c h is obtained from the partitioning indicated in Eq. 1, namely, AD w = n w V w , w h e r e n w is now obtained directly from Eq. 1 and the value of A. (Note that Eq. 1 is valid, even if the gravimetric method of using it is not.) Fig. 5  In the case of DMPC, K A for giant unilamellar vesicles is 145 dyn/cm 26]. One concern is that this kind of measurement o f K A is in the expansion mode whereas our use of K A is in the compression mode. This issue was recently addressed using NMR as a function of osmotic pressure with nearly the same result K A = 141 dyn/cm 21]. This K A was combined with a g r a vimetric x-ray determination of A limited to osmotic pressures greater than 20 atmospheres (98%RH) to obtain A o = 5 9 :5 A 2 21]. In comparison, our unconstrained result K A = 108 dyn/cm is again somewhat smaller than the measured values, but this makes little di erence in our value of A o . C o nstraining the slope K A gives excellent agreement of our A o = 5 9 :4 A 2 with 21].
In for a non-in nite K A . If they had, our best A would probably increase to about 64 A 2 from our quoted value A = 6 2 :9 1:3 A 2 31].

Absolute Electron Density P r o l e s
Obtaining absolute electron density pro les requires information in addition to low angle scattering. Wide angle x-ray studies of the gel phase and volumetric studies as a function of temperature give the electron density of the lipid molecule V L and some of its component groups, especially the methylenes V CH2 and the terminal methyls V CH3 in the chains 7,12]. This kind of information is better used with the hybrid electron density model 30] than with the Fourier representation. Also, the hybrid model has the additional advantage over the Fourier representation in that data for many samples, including di erent osmotic pressures and D spacings if there is little change in structure, can be used simultaneously to obtain the best t.
If one ts any model to measured relative form factors, the model must contain an unknown scale factor K. O n e w ay to constrain K in the hybrid model is to require that the model have the correct value for the electron density in the methylene plateau. Another way is to require that the methyl trough be the correct size to account for the known de cit of electron density in the terminal chain methyls. Yet another way to constrain K is to require that the model has the value of F(0) that is obtained from V L and A using Eq. 4. (This latter way cannot work when F(0) is e ectively zero, which i s the case for many L phases, but even then F(0) still acts as a constraint o n the overall hybrid model parameters.) Although any one of these constraints should su ce in principle, in practice, when only one or two are applied, the others are then not satis ed. It is therefore best to use all three constraints simultaneously 31]. This is not surprising or disturbing because the low a n g l e di raction information is con ned to small q, corresponding to h = 4 , s o l o w angle x-ray information should be supplemented as much as possible by other information.
The preceding, somewhat strenuous, method of constructing electron density pro les has only been applied to the DPPC L phase 31]. It has also been applied to the L 0 phase, but with data only at full hydration 30]. Derivation of absolute electron density pro les for other PC lipids is based on a simple argument. Since the headgroups are the same, the integrated electron density under the headgroup peak in excess of the level due to water on one side, and hydrocarbon on the other, should scale inversely with the area A, and the prefactor can be determined from V H and the number of electrons in the headgroup 24].
It might also be noted that one could contemplate scaling the electron density pro les from simulations. However, di erent s i m ulations give rather di erent scaling factors (see Fig. 7 in 31]), so a more immediate use of absolute electron density pro les is to test simulations.

Interactions between Bilayers
From the preceding section, it is clear that long range uctuations of the second kind are really a nuisance for obtaining average structure of lipid bilayers in the highly uctuating, fully hydrated, biologically relevant L phase. From a structural point of view these uctuations have n o i n trinsic value. We n o w turn to a topic where these uctuations do have i n trinsic importance that is directly addressed by liquid crystallography.

Hard versus Soft Con nement Regimes
As was originally shown by Helfrich 43], long range uctuations are the cause of an e ective i n teraction between lipid bilayers that is called the uctuation interaction. The conceptual basis for this interaction is that two bilayers close to one another cannot uctuate as much a s t wo bilayers far from each other. Mutual suppression of independent uctuations leads to a decrease in entropy and an increase in free energy as the average water separation distance a is decreased, so this interaction is repulsive and entropic. It is an entropic energy (-TS) that is absent at absolute zero temperature, rather than a bare energetic interaction (E).
Helfrich showed that, when the only bare energetic interaction between bilayers is steric (excluded volume interaction), the form of the e ective u ctuation free energy is 43] f U = 0 :42 (k B T) 2 K c a 2 : This result has been con rmed experimentally in systems where the bare interaction V B (a) can be closely approximated as zero over most of the relevant range in water spacing a 44]. This regime is called the hard con nement regime because the bare potential can be thought of as con nement of each bilayer between hard walls formed by neighboring bilayers. Of course, the neighboring bilayers can also move, so the hard wall potential also uctuates, but this does not change the form of the uctuation interaction. Everything about the hard con nement regime is quite well established, except for the magnitude of the prefactor 45].
In general there are additional bare interactions besides the obvious steric interaction. If these interactions have ranges that are comparable to the average water spacing a, then the approximation of the bare interaction V B (a) by a hard box-like potential is obviously de cient. It is then appropriate to consider a soft con nement regime 46,47].
One important b a r e i n teraction is the strong repulsive h ydration force which, even though not so well understood, has been well documented experimentally 25,42] to have the form V hyd (z) = P h e ;z= (8) with parameters (decay length) and prefactor P h . Another important b a r e interaction is the van der Waals attractive i n teraction, V vdW (z) = ; H 12 1 z 2 ; 2 (z + D B ) 2 + 1 (z + 2 D B ) 2 (9) where D B is the bilayer thickness and H is the Hamaker parameter. This is the interaction assumed to be responsible for limiting the swelling in bilayers composed of lipids with no net charge. We will de ne a o to be the limiting water space for fully hydrated bilayers with osmotic pressure P = 0. Because a o is only 10 ; 30 A, a graph of bare potential V B (z) v ersus z on this length scale shows considerable variation, especially as z approaches 0. For charged lipids in low salt, one should also consider an electrostatic interaction, but this is absent for the neutral lipids. An additional very short range repulsion has been measured and attributed to protrusions 48]. We do not include it since it only plays a role for lipids under high osmotic pressure and small water space a. I t d o e s p l a y the formal role of suppressing the singularity i n the van der Waals potential at z = 0 .
It has been proposed for the soft con nement regime that the uctuation interaction free energy in Eq. (7) should be modi ed 47,46] and a formula involving an exponential with decay length fl f U2 = ( k B T= 16)(P h =K c ) 1=2 exp(;a= fl ) (10) has been o ered 26,47]. This exponential functional form is quite di erent from the power law form in Eq. 7 established for the hard con nement regime. Furthermore, the decay length fl was predicted to be twice the decay length 2 of the hydration force.
For lipid bilayers the now traditional way 2 5 ] t o i n vestigate interbilayer forces experimentally is to measure the average water space a as osmotic pressure P is varied such data are usually plotted as logP(a) as in Fig.  6. The data from many groups clearly show an exponential increase for P greater than 10 atmospheres and this is the experimental basis for the force that is named the hydration force. However, there are at least three energies involved with four parameters ( , P h , H and K c ). There are also uncertainties in how one de nes and obtains water space a (gravimetric D W versus steric D 0 W -see Fig. 2c) and bilayer thickness (D B vs D 0 B ) 7]. While it has been encouraging that ts to the P(a) data make sense with reasonable values for the parameters 49], there are too few data to provide ts that uniquely separate P(a) i n to its constituent forces. As noted by P arsegian and Rand 17], \... dissection of the measured pressure P into its physically distinct components is a problem almost as di cult as the theoretical explanation of these components themselves". In particular, the functional form of the uctuation pressure is an important assumption in carrying out such ts. Since the derivation of the soft con nement f o r m ula for uctuation pressure was non{trivial (involving some close self{consistency arguments that are di cult to improve upon and di cult to validate by analytic theory), it therefore seemed appropriate to test Eq. 10.

Experimental Window on the Fluctuation Force
We realized that our experimental study of the uctuation correction for structural studies also provided an experimental window on uctuational forces that could help reduce the ambiguity inherent in only using P (a) data this was a major part of Horia Petrache's research in our group. The most direct connection is that the uctuational free energy F fl is related to the Caill e 1 parameter 50] by Since the bending modulus K c is a property of the single, isolated bilayer, the functional form of F fl (a) can be obtained from 1 and D. A plot of 1= 1 D 2 therefore shows the functional form of F fl . Data for EPC are shown in Fig. 7. Data for DPPC, DMPC, EPC 50] and DOPC 29] are all inconsistent with the hard con nement functional form in Eq. 7, proving that a theory of soft con nement is necessary. The data are consistent with the prediction of the soft con nement theory that the uctuation free energy has an exponential decay with a. H o wever, the e ective decay length of the uctuation free energy, w h i c h is de ned to be fl , is consistently larger than the theoretical prediction fl = 2 as indicated in Fig. 7 for EPC. For the four lipids that we h a ve studied, the ratio fl = is in the range 2:5 ; 3.

Simulations
We undertook simulations to address several questions regarding interactions. The rst one, from the preceding subsection, concerns our experimental result that fl = is consistently greater than 2. This result could have b e e n d u e t o several reasons, including: (i) the soft con nement theory (Eq. 10) may n o t b e correct, (ii) the bare interactions may be incorrectly described or (iii) there may be experimental discrepancies. By doing a simulation with the same form of the interactions as in Eq. 8 and Eq. 9, we b ypassed (ii) and (iii) and tested (i) directly. The result of the simulation is that fl = is about 2. 4 34].
Although this is a bit smaller than the experimental ratio, it clearly agrees with the experimental conclusion that the ratio is larger than the value of 2 given by Eq. 10.
The simulations were at the nano-scale in which the bilayer was treated as an elastic continuum with a bending modulus K c and the interactions between bilayers consisted of the phenomenological van der Waals and hydration forces. This is the appropriate length scale for the long wavelength uctuation forces. In particular, atomic level molecular dynamics simulations are not able to probe this longer length scale because the system size and number of atoms becomes prohibitively large to equilibrate in reasonable computer times. Since motional dynamics are unclear at the nano-scale, the appropriate kind of simulation is Monte Carlo rather than molecular dynamics. Monte Carlo also has the advantage that sampling phase space can be done more e ciently than following equations of dynamical motion. Nikolai Gouliaev in our lab implemented a particularly e cient algorithm that employed changes in the Fourier coe cients of the bilayer positions so that rather large, multiple moves in real space could be made while changing the bending energy by small amounts. This method, which w e c a l l F ourier Monte Carlo, decreases the equilibration time by a factor of at least 30 when compared to the usual method of moving one local point on the bilayer at each step 51]. This allowed Gouliaev to extrapolate thermodynamic properties to stacks consisting of many larger bilayers by using sequences consisting of as many a s M = 3 2 b i l a yers in a stack, N 2 = 1 0 2 4 F ourier modes (equivalent to lattice sites) and lateral extents L up to 2800 A 34,51]. Fig. 3 shows a snapshot of a slice through a simulation of M=8 bilayers.
The thermodynamic quantities of greatest interest are the osmotic pressure P (a) and the root mean square uctuation (a) i n w ater spacing, both as a function of mean interbilayer spacing a. is simply related to the measured Caill e 1 parameter 50] by 2 = 1 D 2 = 2 : (12) The simulation results compare favorably with the analytic theory 47] for small a and when there are no van der Waals interactions, but the discrepancy grows as a approaches full hydration when P = 0 34,51]. These discrepancies are too large to ignore when trying to t data.
The simulations also allowed us to address another issue 34]. Our experimental analysis that determines the Caill e 1 parameter is based on liquid crystal theory which assumes that the interaction between bilayers is harmonic. However, the phenomenological potential consisting of the sum of van der Waals and hydration interactions is not harmonic. Furthermore, the analytic theory approximates the true potential self-consistently with a harmonic potential. Since the analytic theory shows discrepancies with the results of the simulations, the obvious question was whether the uctuational data analysis is also awed. However, the di raction line shapes depend upon the functional form of the pair correlation functions. The simulations show t h a t the functional form for the true potentials agrees well with that obtained from harmonic theory, thereby v alidating the data analysis. The problem with the analytic theory is that the self-consistency relation gives a di erent v alue for the harmonic modulus than the one that best describes the results of the simulations 34].

Determination of Interaction Parameters
An important goal now is to determine the values of the interaction parameters. The basic experimental approach 50] determined the decay length fl of the uctuation force and its magnitude up to a factor of the bending modulus K c . G i v en a value of K c , ts to the bare pressure P bare (a) = P (a) ; P fl gave w ell determined values for H Hamaker , and P h . H o wever, ts with different v alues of K c over the range spanned by literature values gave equally good ts, essentially because variations in H compensated for variations in K c whereas values of (about 2 A) a n d P h were robustly determined 50].
The basic experimental approach of the preceding paragraph used the uctuation data 1 (a) only to eliminate the e ective modulus B for interbilayer interactions and this throws away information about the absolute size of the uctuations. Simulations, however, give both P(a) and 1 (a). Requiring both to agree with the data is a stronger constraint o n t h e i n teraction parameters. Detailed ts of simulations and data have not yet been carried out for all the lipids our group has worked on. However, for DMPC at 30 o C the following parameter set ts both P (a) a n d 1 (a) fairly well 52]: H = 7 :13 10 ;14 erg, K c = 0 :5 10 ;12 erg, = 1 :91 A and P h = 1 :32 10 9 erg/cm 2 and it is clear that larger values of K c provide inferior ts. This value of K c agrees well with 53] and is smaller than the value given by 5 4 ] . T h e v alue of H is somewhat larger than preferred by 55]. However, more lipid systems should be studied before drawing de nitive conclusions for these parameter values.