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METHODS IN CELL PHYSIOLOGY
1Department of Molecular Pharmacology and Physiology and 2Department of Physics, University of South Florida, Tampa, Florida; and 3Department of Physics, National Cheng Kung University, Tainan, Taiwan
Submitted 8 January 2008 ; accepted in final form 31 July 2008
| ABSTRACT |
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electric cell-substrate impedance sensing; cell attachment; cell adhesion; extracellular matrix; integrin
Previously, there have been two cell-electrode models used for impedance analysis of the frequency scan data obtained by ECIS. One is appropriate for cells with disklike shape, such as transformed fibroblasts, endothelial cells, and epithelial cells (3, 5, 17), and the other is used for rectangular cells with semicircular ends, such as normal fibroblasts (15). By fitting the experimental data into the model with nonlinear least-squares fitting, we have been able to estimate three morphological parameters from fibroblasts, namely, Rb,
, and Cm. Rb is the junctional resistance between cells, Cm is the transcellular membrane capacitance representing a series connection of both basolateral and apical membranes, and
is equal to 0.5W(
/h), where W is the cell width,
is the resistivity of the solution, and h is the average separation distance between the cells and the substratum (see Glossary).
Cell-cell and cell-substrate interactions are essential determinants in cell migration, embryonic development, and tissue formation. With an emerging interest to delineate the mechanisms of cell-cell and cell-substrate interactions in response to environmental stimuli using ECIS, the selection of an appropriate cell-electrode model for fitting the experimental data is critical. In this article, we have modified the previous rectangular model by accommodating the slender and rectangular shape of vascular smooth muscle cells (VSMCs) and have extended the model so that apical membrane capacitance (Ca) and basolateral membrane capacitance (Cb) can be estimated separately. Our previous rectangular model does not include the difference of current distribution through basolateral and apical membranes. In this more comprehensive model, we assume that the electrical potential inside the cell, Vi, is independent of the position inside the cell. Therefore, although the transcellular current entering through the basolateral membrane decreases, as its position moves away from the symmetrical center of the basolateral cell surface, the transcellular current exiting through the apical membrane is uniform. Since the apical cell surface of an adherent cell usually has more membrane folding than the basolateral membrane, the apical membrane capacitance should be different from that of the basolateral membrane.
We selected VSMCs from renal vasculature to test our model (4). The experimental impedance data and the data calculated by the model were consistently agreeable at various frequencies from 25 to 60 kHz. We were able to measure Rb, h, Ca, and Cb in VSMCs. To further verify this new model for impedance analysis, we tested the hypothesis that the integrin binding hexapeptide GRGDSP (Gly-Arg-Gly-Asp-Ser-Pro) induces morphological changes in VSMCs that can be detected through continuous analysis of ECIS data output. The results demonstrate that integrin binding peptide decreases junctional resistance between cells, increases the distance between the basolateral cell surface and substrate, and increases the apical membrane capacitance, indicating the occurrence of cell contractile activity. Thus we describe a comprehensive cell-electrode model that may serve as a new approach for impedance analysis of cell layers with long rectangular cell shape in general.
| Glossary |
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| MATERIALS AND METHODS |
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Impedance measurement of cell attachment.
Electrode arrays, relay bank, lock-in amplifier, and software for the ECIS measurement were obtained from Applied BioPhysics (Troy, NY). Each electrode array consists of eight wells that are 1 cm in height and 0.8 cm2 in bottom area; each well contains a 250-µm-diameter gold electrode (area
5x10–4 cm2) and a much larger gold counter electrode. The large electrode and one of the small electrodes were connected via the relay bank to a phase-sensitive lock-in amplifier, and AC was applied to the sample through a 1-M
resistor. Experimental setup and circuit connection were that same as we previously described (17). For cell attachment and spreading assay, VSMCs were plated into electrode wells at a density of 105 cells/cm2, and impedance changes were measured immediately. For impedance measurements of VSMC monolayers upon addition of GRGDSP, Ham's F12 medium supplemented with 10% fetal bovine serum (FBS; 0.4 ml) was added over the electrode in each well. Cells were allowed to attach and spread for at least 24 h before impedance was measured. After 24 h in culture, the confluency and viability of the cell monolayer were confirmed by light microscopy and electrically by measuring the resistance values. Attached cells on the electrode acted as insulating particles, and the main current must therefore pass around the cells. The changes in cell dimensions manifested as changes in impedance while the cell-covered area and/or the cell-substrate separation changed. Hexapeptide GRGDSP or GRGESP (Gly-Arg-Gly-Glu-Ser-Pro) in Hanks' balanced salt solution (HBSS; Cellgro; pH 7.1
7.4) or HBSS alone was added to each cell-covered electrode well. The electrical impedance of each well was measured every 2 min. We applied a 1-V AC signal at 4 or 40 kHz to the sample through a 1-M
resistor to maintain a constant current of 1 µA through the sample. By analogy with Ohm's law for DC circuits, Z = V/I = R – j(1/
C), the equivalent resistance and capacitive reactance of the sample were calculated by dividing the measured in-phase and out-of-phase voltages by 1 µA, respectively. Typically, the magnitude of the in-phase voltage drop across the cell-free electrode was in the order of a millivolt and increased to several millivolts with a confluent VSMC layer grown on the top. The resultant voltage drop of a few millivolts had no detectable effect on the cells; hence, the measurement is believed to be noninvasive (18, 26).
Impedance measurement of cell morphology.
Frequency scan is another main method in ECIS with which we can measure the impedance of the cell-electrode system as a function of frequency ranging from 25 to 60 kHz. It took
2.5 min to measure each electrode. Generally, to obtain impedances as a function of frequency for both a cell-free electrode and the same electrode covered with confluent cells, we applied frequency scan before and after cells attached to the electrode. By comparing the experimental data of confluent cell monolayers with the calculated values obtained from the cell-electrode model, frequency scan measurements can provide morphological parameters such as Rb and h (5, 15, 17). To obtain the best-fitting values, first the model parameters Rb,
, Ca, and Cb were arbitrarily chosen to get calculated resistance and capacitive reactance using the cell-electrode model described in this article. The deviation or error between the calculated (Zcal) and measured impedance (Zexp) data was defined by |Zcal – Zexp|. Our curve-fitting criterion, know as the nonlinear least-squares fitting, was that the sum of the square of the errors was a minimum. Since both resistance and capacitive reactance at 23 different frequencies were considered equally important for data fitting, there were a total of 46 errors included in the sum. By using matrix algebra, model parameters were changed, and this process was repeated by refining the parameters until the final minimum was determined.
Model derivation. The primary objective of an ECIS model is to calculate the specific impedance of a cell-covered electrode as a function of frequency, Zc, from the measured values of a cell-free electrode, Zn, with only a few cellular morphological parameters, which are specific to different cell types and can be used as an index to examine the cell-cell and cell-substratum interaction. After the measured impedance data of the same electrode covered with cells are fitted with the calculated values of Zc, those cellular morphological parameters can then be determined. The various current paths are sketched in Fig. 1. To make the calculations tractable, six simplifying assumptions must be made: 1) the cells have a rectangular shape with length L and width W; 2) the current one-dimensionally and symmetrically passes from the central line to the edges of the cell through the space formed between the ventral surface of the cell and the substratum; 3) the current density under the cells does not change in the vertical direction; 4) the electrode potential Vc is a constant independent of position, 5) the potential in solution on the dorsal side of the cells is likewise treated as a constant Vs (for convenience, we set Vs = 0; this assignment does not affect the calculated impedance); and 6) the electrical potential inside the cell Vi, although a function of Vc, is independent of position inside the cell.
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fCn)–1 are respectively so-called resistance and capacitive reactance of the measured impedance of the cell-free electrode, Zn. It should be noted that the Zn value is frequency dependent, and so are Rn and Cn (22). We also assume that the specific resistance of the cell membrane, Rm, is 103
·cm2 and that the specific impedances of the apical and basal cell membranes, Za and Zb, can be calculated as a resistor and a capacitor in parallel as shown in Eqs. 21 and 22. The frequency dependence does not appear explicitly in Eq. 19, since it is included in the impedances Zn, Za, and Zb. Together, using Eq. 19 with Vi/Vc given by Eq. 17, the calculated values of Zc over the measured frequency range are based on a set of parameters, specifically Rb,
, Ca, and Cb.
Now, if we characterize the cell body as basolateral and apical membranes packed together and assume that Ca = Cb = Cm (16), the overall membrane impedance for the transcellular current to pass through is therefore
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, and Cm (15). As expected, Eq. 25 can be easily obtained by putting Vi = 0 and Zb = Zm into Eq. 19. | RESULTS |
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2 h, the resistance reached the peak and then started to fall as the cells started to develop focal adhesions, spread, and push each other to form a monolayer. By 6 h, the cells attached, spread, and reached equilibrium. Smaller changes in the cell-electrode interaction due to cell motions caused the impedance to fluctuate with time. Changes in resistance for collagen- and vitronectin-coated electrodes lagged somewhat behind those for the fibronectin-coated electrode. There was hardly any increase in resistance for the laminin-coated, BSA-coated, or uncoated electrode. These results are consistent with observations from other laboratories that smooth muscle cells prefer fibronectin, vitronectin, and type I collagen for attachment, spreading, and the formation of stable focal adhesions (10, 20, 30).
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3.1 at 6 kHz, and then decreases with increasing frequency until 2.1 at 60 kHz. The reason for the peak is that the constriction resistance masks the resistance of the cell-covered electrode at high frequency. Normalized capacitance, on the other hand, remains 1.0 from 25 Hz to 1 kHz and then decreases with increases in frequency until
0.38 at 60 kHz.
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, Ca, and Cb. Both the resistive and reactive components of the measured impedance were fitted to the model equation by nonlinear least-squares fitting at 23 different frequencies ranging from 25 Hz to 60 kHz, allowing a precise determination of the model parameters. Cell length (L) and width (W) were estimated directly by phase-contrast microscopy, and for VSMCs their values were
60 and 12 µm, respectively. With the least-squares method, the best-fitting values of Rb,
, Ca, and Cb for the data shown in Fig. 3 were 0.2
·cm2, 2.4
·cm, 2.6 µF/cm2, and 1.7 µF/cm2. The average cell-substrate separation (h) was calculated from
by using Eq. 11 with
= 60
·cm and W = 12 µm, and the result for h was 38 nm if
= 2.4
·cm. The same measured impedance was also fitted by Eq. 25 derived from the previous rectangular model (15), and the best-fitting values of Rb,
, and Cm were 0.2
·cm2, 2.5
·cm, and 2.0 µF/cm2. Along with the measured impedance data, the best-fitting curves achieved using Eqs. 19 and 25 were normalized and are shown in Fig. 4. The measured impedance curve was better simulated by the calculated impedance curve derived from Eq. 19 (filled dots) rather than by Eq. 25 (crosses). Although both model equations resulted in similar fitting values of Rb and
, the minimum value of the root mean square of the errors (defined as |Zcal – Zexp| in MATERIALS AND METHODS) was 452
using Eq. 19 and 572
using Eq. 25. In addition, the average of the percentage error defined as |(Zcal – Zexp)/Zexp| was 1.0% using Eq. 19 and 2.3% using Eq. 25. Together, these results indicate that the curve fitting between calculated and experimental data was significantly improved by using Eq. 19.
We carried out a number of impedance measurements of confluent VSMC monolayers at 37°C and analyzed the data using both the previous and new rectangular models as well as the model based on disk-shaped cells (5). After the experimental data were fit individually using Eq. 19, the average values of Rb, h, Ca, and Cb were 0.32 ± 0.02
·cm2, 41 ± 0.3 nm, 2.6 ± 0.1 µF/cm2, and 1.7 ± 0.1 µF/cm2 (n = 42, Table 1). Compared with the average cell-substrate separation (h) 117 ± 6 nm, obtained by fitting the experimental data with the disk-shaped model, the values obtained from Eqs. 25 and 19 were 38 ± 3 and 41 ± 3 nm, respectively (Table 1), which were much closer to the results measured using interference reflection microscopy (11, 27). The reason for this is that application of a disk-shaped model to VSMCs overestimated the average under-the-cell path length for current and then led to an overestimation of both the cell-substrate separation and the junctional resistance between cells when applied to measured data. We also analyzed impedance data obtained from human gingival fibroblasts and WI-38 fibroblasts (n = 20, Table 1). Our results show that all Rb, h, Ca, and Cb values of these two fibroblastic cell types are quite close to those of cultured VSMCs, indicating that cultured VSMCs might have a phenotype similar to fibroblasts.
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1 µF/cm2 but can appear to be much larger if the membrane wrinkles. Morphological characterization using atomic force microscopy also showed that the surface roughness of VSMCs when treated with 1 mM GRGDSP was 74 ± 5 nm (n = 49), which was significantly higher than that of control cells, 45 ± 2 nm (n = 21). These observations suggest that Ca and membrane ruffling are correlated. The correlation between Ca and membrane ruffling can be validated when membrane ruffling is induced by biochemical agents or overexpression of the related signaling proteins such as RacGTPase.
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, Ca, and Cb for each electrode had been determined through calculation of Zc and frequency scan data fitting, these values were used as the input for the analysis of the time series data obtained from the same electrode. Whereas Ca and Cb values were kept the same to simplify the procedure of data fitting, Rb and
were used as the two variables in Eq. 19 to calculate Zc. After each impedance data point was fitted with the calculated values of Zc, including both resistive and reactive components, Rb and
values over the course of the experiment were determined. Adding different concentrations of GRGDSP to the VSMCs caused a dose-dependent drop in Rb, whereas no significant effect on h (<10 nm) was observed with the addition of GRGDSP or controls, implying a relatively constant cell-substrate contact (Fig. 8). For the 1 mM GRGDSP challenge, a similar pattern between the decreased Rb value in Fig. 8A and the decreased normalized resistance in Fig. 6 was observed. This confirms that the decrease of Rb was mainly responsible for the decrease in measured resistance in response to GRGDSP addition. Furthermore, whereas Rb reached close to zero at hour 5 (Fig. 8A), normalized resistance stayed at
60% of control (Fig. 6), indicating that there was little cell-cell contact but relatively stable cell-substrate contact.
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4.2 nF (Copen). This was the approximate capacitance value for all the electrodes at hour 0 when cells were inoculated into electrode wells. With a complete confluent layer of VSMCs in place, this was reduced to
2.2 nF (Cconfluent). The fraction of the electrode covered with cells is given approximately by (Copen – Ccells)/(Copen – Cconfluent) or by [1 – (Ccells/Copen)]/[1 – (Cconfluent/Copen)] if using the normalized capacitance values. In Fig. 9B, for example, at hour 5, the green curve, data obtained from the GRGDSP addition 3 h after cells were seeded, shows a partially confluent VSMC layer giving the normalized capacitance of 0.75. The fractional area covered by cells was calculated as (1 – 0.75)/[1 – (2.2/4.2)] = 0.53. At the 5th hour, the other three curves in Fig. 9B, black (GRGESP addition at hour 0), red (GRGDSP addition at hour 1), and blue (GRGDSP addition at hour 0), had normalized capacitance of 0.85, 0.95, and 1, respectively. Their fractional areas covered by cells were calculated as 0.32, 0.11, and 0, respectively. | DISCUSSION |
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1%). The newly improved model provides a theoretical basis to interpret measured data of ECIS with regard to the morphological characteristics and cellular parameters of VSMCs in culture. Previous studies showed that integrin binding peptide (GRGDSP) induced an increase of intracellular Ca2+ concentration in cultured renal VSMCs (4) and caused vasoconstriction in intact VSMCs of afferent arterioles (31). However, it is a challenge to measure contractility of cultured renal VSMCs because they are spread out in a thin monolayer, so we used ECIS to study the response of cultured VSMCs in terms of changes in cell-cell and cell-substrate interactions. Our results illustrate that irrespective of the ECM protein coating used on the electrode, the resistance drops drastically on addition of 0.5 mM GRGDSP peptide. A drop in resistance indicates that less area on the electrodes is covered by the cells, which can be due to contraction and rounding up of the cells. GRGDSP peptide-induced vasoconstriction in perfused afferent arterioles is dose dependent between 10–7 and 10–3 M (31). Using ECIS attachment experiments to follow the progressive cellular responses to GRGDSP, we found that the VSMCs responded fairly effectively to 0.1 mM GRGDSP and that 1 mM GRGDSP looked like a very strong dose, since many cells were lifting off the electrodes. Further investigations using frequency scan measurements and time series model analysis determined that the drop in impedance caused by the GRGDSP was primarily due to its effect on junctional resistance between cells, even though both the cell-substrate separation and the apical membrane capacitance increased slightly.
With the help of time-course experiments, we showed that the resistance of the electrodes during the attachment and spreading of cells did not peak in the presence of 0.5 mM GRGDSP peptide. This signifies that this peptide hinders normal formation of focal adhesion complexes by occupying integrins. On the contrary, 0.5 mM GRGESP peptide served as the control, and the peptide did not markedly affect the attachment and spreading of VSMCs. WE also noted that the effect of GRGDSP peptide in preventing cell attachment was less when added after the initial cell spreading. This peptide slightly hindered the formation of a monolayer of VSMCs when added 1 h after the inoculation of cells. However, GRGDSP peptide did not show any effect in inhibiting cell attachment when applied 3 h after the initial cell spreading. From these data, we speculate that the soluble ligand (RGD-containing peptide) binds to integrins all over the VSMCs when they are in suspension. However, once the cells have established focal adhesion, GRGDSP peptide binds more readily to the free integrins rather than replacing integrins from existing integrin-ECM complexes as shown by the lesser resistance drop in the firmly attached VSMCs. The response to GRGESP peptide at 0 h was similar to that following the addition of GRGDSP peptide after 3 h of attachment, indicating that both these ligands at the given time frame did not hinder the formation of focal adhesion, and hence the resistance of the cell-covered electrodes was higher.
The ECIS cell-electrode model, unlike other equivalent circuit models using the direct current (DC) technique, emphasizes the cell-substrate spaces and the various current paths including the current I spreading along the ±x direction in the space between ventral cell surface and the electrode surface, the current dIi passing through the basolateral membrane, and the current dIc from the electrode surface (Fig. 1B). These complex distributed currents are frequency dependent and play important roles in the measured impedance of cell-covered electrodes. For example, the ion current out of a blank electrode is perpendicular to the electrode surface. When cells cover the electrode and the cell membranes block the current, the current changes its direction to the edges of the cell through the space formed between the ventral surface of the cell and the electrode surface. Since the electric current is always from a higher potential point to a lower potential point, the electrical potential underneath the cell (V) continuously decreases from the central line (x = 0) of the ventral surface to the edges (x = ±W/2) of the cell body. Furthermore, since dIi and dIc are proportional to (V – Vi) and (Vc – V), respectively, dIi continuously decreases and dIc continuously increases as the position moves from x = 0 to x = ±W/2. At higher frequency this phenomenon is more substantial, and most dIc currents are out from the electrode area close to the cell edges, causing the measured capacitive reactance to be much larger than that of a cell-free electrode. That is why at the higher frequency the capacitance of the cell-covered electrode, which is inversely proportional to the measure capacitive reactance, is much smaller than that of the cell-free electrode (Fig. 3B). Likewise, changes of morphological parameters such as an increase of Rb or decrease of h (i.e., increase of
) cause less current coming out of the electrode. As a result, capacitive values at higher frequencies decrease, but those at low frequencies change only little (calculation data not shown) (15, 17). It is in this general manner that the impedance measurement and model analysis can return information regarding cell morphology.
To our knowledge, this is the first application of ECIS to characterize morphological properties of smooth muscle cell layers that display a slender and rectangular shape as most normal fibroblasts do. Although the interpretation may seem complex, it is a straightforward numerical calculation with the developed cell-electrode model. The key advantages of using Eq. 19 (new model) rather than Eq. 25 (previous model) for the impedance analysis of VSMC layers are providing additional information of capacitive properties of apical and basolateral membranes and improving the accuracy of fitting between the model prediction and the measured impedance data, particular in the high-frequency range. In general, the value for Cb in Eq. 19 giving the best fit to experimental data will be somewhat smaller than the value used for Cm in Eq. 25, whereas Ca will be larger than Cm (Table 1). This is because using Eq. 25 at the high frequency range underestimates the transmembrane impedance Zm and then causes an overestimation of the transcellular current, leading to an underestimation of the spreading current under the cell and the cell-substrate separation (Table 1). The new cell-electrode model characterizes the impedance with four cellular parameters as variables. Theoretically, if a problem has n unknowns, its solution requires n equations. An impedance data point, like a complex number, contains a real part (resistance) and an imaginary part (reactance) data, and it can be used to solve two parameters using Eq. 19. If the frequency of the measurement is changed, the impedance characteristics of the cell-covered electrode (Zc) will change as well. Frequency scan in ECIS measures the impedance of the cell-electrode system at multiple frequencies ranging from 25 Hz to 60 kHz, which allows good quality of the data fitting by least-squares evaluation.
Different cell types display different profiles of impedances as a function of frequency. As shown in Fig. 4A, for VSMCs the largest change of the measured resistance curve between cell-free and cell-covered electrodes appears at 6 kHz. This frequency is quite different from that for epithelial cells such as Madin-Darby canine kidney cells, for which the largest change is at 700 Hz (17). However, it is quite similar to fibroblastic cells such as WI-38 VA13 and HGF cells, where the largest changes are at about 4 and 6 kHz, respectively (5, 15). The frequency shift in the largest change of the measured resistance curve basically results from the changes in both
and Ca. Therefore, in the cell attachment measurement of VSMCs, we usually set the AC signal at 4 kHz (or sometimes at 40 kHz) to obtain the substantial responses of resistance (or capacitive reactance) variations to cellular activities. It is worth noting that, regarding h changes in response to 1 mM GRGDSP challenge (Fig. 8B), an unexpected decrease of h (i.e., increase of
) was observed over the last 1.5 h. A possible explanation is that during that period VSMCs contracted and rounded up, leading to the decrease of both Rb and h. However, according to the frequency scan data shown in Table 2, the Ca value of VSMCs 5 h after exposure to 1 mM GRGDSP peptide increased to 3.7 µF/cm2 compared with that of the control, 2.6 µF/cm2. Model calculation for understanding how different parameters affect the calculated impedance demonstrated a similar peak shift of normalized resistance curve resulting from increasing
or Ca. Because the attachment measurement is carried out at a single frequency, the change of Ca, unlike that of Rb and
, was not included as a variable in the fitting process of time series data. As a result, in response to 1 mM GRGDSP challenge, the impedance changes of VSMCs due to the increase of Ca might be calculated as if they were contributed from the increase of
. A continuous and speedy frequency scan measurement that allows us to calculate and fit time series impedance data with more parameters is being developed in our laboratory.
In summary, a theoretical cell-electrode model for impedance analysis of cells with slender and rectangular shape was developed and validated. Impedance analysis of VSMCs upon challenge with integrin binding hexapeptide GRGDSP was used to test the sensitivity of the model. The model was able to detect changes in the junctional resistance, the average distance between the ventral cell surface and substratum, and capacitance values of apical and basolateral cell membranes. The model provides a theoretical basis to interpret measured data of ECIS regarding to the morphological characteristics and cellular parameters of cells in culture. Because of the simplicity of the system, impedance analysis of cells layers measured by ECIS will find more applications in biological research.
| GRANTS |
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| ACKNOWLEDGMENTS |
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| FOOTNOTES |
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The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
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