Thermodynamic model for cell spreading

Colloids and Surfaces, 42 (1989) 215-232 Elsevier Science Publishers B .V,, Amsterdam - Printed in The Netherlands

215

Thermodynamic Model for Cell Spreading M .G . STEWART' ,s * . E. MOY', G . CHANG' •4 W . ZINGG' •4"' and A . W . NEUMANN'

4 .5

Departments of 'Mechanical Engineering, 'Physiology and'Surgery, `Institute of Biomedical Engineering, University of Toronto, Toronto, Ontario M5S IA4 (Canada) s Research Institute, Hospital for Sick Children, Toronto, Ontario M5G 1X8 (Canada)

(Received 15 November 1988 ; accepted 18 May 1989)

ABSTRACT A thermodynamic model for cell spreading, based on van der Waals interactions, was developed . The model predicts that for one and the same substrate, spreading will increase with increasing liquid surface tension if the surface tension of the substrate is lower than that of the cells ; if the surface tension of the substrate is greater than that of the cells, the opposite trend is predicted . The model also predicts that spreading will increase with increasing surface tension of the solid substrate if the surface tension of the liquid is lower than that of the cells; if the surface tension of the liquid is higher than that of the cells, the opposite trend is predicted . Experiments performed with granulocytes indicated that the predicted dependence of spreading on the liquid surface tension is observed ; however, the predicted dependence of spreading on the substrate surface tension is not observed . The experimental results suggest that van der Waals interactions play an important role in the process of cell spreading and that electrostatic interactions cannot be neglected in the analysis of such a process .

INTRODUCTION

The processes of cell adhesion to polymer substrates and of subsequent spreading are of importance in the field of medical implants, particularly in the area of endothelial seeding of polymeric cardiovascular implants . The extent of adhesion and spreading on different polymers can be used as a predictive test for biocompatibility . It has been shown by many researchers that the degree of cell adhesion [ 1-91 and of cell spreading [ 10,11 ] on polymer substrates is related to the surface tension of the substrates . This relationship between adhesion and substrate surface tension is also observed in studies performed under flow conditions [ 12-14 ] . A simple thermodynamic model for cell adhesion was developed and it was shown that the adhesion of cells to polymer substrates agreed with the model predictions [6,7 ] . This model is based on a simple free energy balance between *This work represents part of the M .A .Sc. thesis project of M .G . Stewart .

0166-6622/89/$03 .50

© 1989 Elsevier Science Publishers WV .



216

a cell in the suspended (initial) and in the adhered (final) state involving only the relevant interfacial tensions . The excellent agreement between the theoretical predictions and the experimental observations indicates that the process of non-specific cell adhesion to solid substrates was governed mainly by the interfacial tensions which are related to van der Waals interactions [ 15 ] . Also, phagocytosis of non-opsonizedparticles by granulocytes has been shown to obey a simple thermodynamic model similar to the adhesion model [ 16-18] . The process of cell spreading can be thought of as an attempt by the cell to engulf a particle that is too large . We have thus proceeded to develop a model for spreading, based on interfacial tensions, along similar lines to those of the adhesion model . From this model we hope to gain further insight as to what forces drive the process of cell spreading . Since phagocytosis of non-opsonized particles by granulocytes obeyed the thermodynamic model for engulfment, we have decided to use granulocytes to test the predictions of our simple thermodynamic model for spreading . In this paper the thermodynamic model that was developed for spreading is described and the theoretical predictions from the model are compared to results from spreading experiments performed with granulocytes . MODEL FOR CELL SPREADING

The thermodynamic model for cell spreading where only non-specific interactions are involved is analogous to the model for cell adhesion [6] . Thermodynamically, cell adhesion to a solid substrate is favoured when the change in the free energy for the process of cell attachment is negative . For a system in which the effect of electrostatic charges can be neglected, this change is, per unit surface area dF odh= Ycs - YCL - YSL

(1)

where ycs . YCL and ysL are the cell/substrate, cell/liquid and solid/liquid interfacial tensions, respectively . Theoretical predictions of cell adhesion, based on Eqn (1), therefore, require only data for the pertinent interfacial tensions . The interfacial tensions involving a solid phase can be obtained from an equation of state for interfacial tensions [19,20] . Calculations of AF" for attachment of cells from suspension to various substrates as a function of ysv indicate that cell adhesion should increase with increasing y sv if the surface tension of the suspending liquid, YLV, is lower than the surface tension of the cells, Ycv. If the surface tension of the liquid is higher than that of the cells, the opposite trend is predicted . For the special case of YLV =Ycv the extent of adhesion is independent of the substrate surface tension . Experimental observations correlate well with these theoretical predictions . These theoretical predictions are depicted in Fig. 1. where AF" is plotted as a function of ysv for various liquid surface tensions .



217 a : Yw' Ycv

b : Rv=YCv C : YLv' 'lcv

I I 70 40 50 60

80

Substrate Surtace Tension, y sv (mJ 4

Fig. 1 . Theoretical curve of free energy of adhesion . JFea'', as a function of the substrate surface tension, 7sv . For the calculations the cell surface tension was taken as k .,=65 mJ m - ' and three liquid surface tensions were considered : (a) Y LV =70 mJ m -2, (b) YLV =65 mJ m -2 , ( c) ,,= 60 mJ m 2. Obtained from Ref . [211 . Smith et al . [21 ] have demonstrated that the interpretation of results from adhesion experiments is not sensitive to the form of the equation of state ; therefore, the adhesion experiment can be used as an independent means of determining the surface tension of cells. The existence of an equation of state can be demonstrated on thermodynamic grounds [ 191 or from phase rule considerations [22 ] . It is important to realize that the existence of an equation of state implies that interfacial tensions will incorporate all the possible types of intermolecular interactions . Furthermore, it is not possible to separate the individual contributions of the various intermolecular interactions from the total interfacial tension [23,24] . Similar to the adhesion model, the change in free energy, AF`P', as the cell goes from suspension to the spread state will determine whether spreading is favoured . If dF aP' is positive spreading is not favoured and if it is negative then spreading will be favoured . Although the models for spreading and adhesion are similar, there is an important difference between the two models . The adhesion model is used to describe the trends in the extent of adhesion that . are observed as the substrate and liquid surface tensions are varied . Therefore, in the adhesion model the geometry of the cells is of no importance and the free energy of adhesion, AF adh, can be expressed on a per unit area basis . For spreading, on the other hand, the model attempts to determine the final shape of the spread cell subsequent to adhesion . This final shape will be such that dFaP' is minimized . For spreading, dFaP` is a function of the relative contributions in energy from all the interfaces (cell/substrate, cell/liquid and substrate/liquid) . Therefore, for a spreading model knowledge of the geometry of the cell in both the suspended and spread states is necessary in order to compute the final AF P' . In order to simplify the development of a thermodynamic model for cell spreading the following assumptions were made :



218

(1) The shape of the cells in suspension is spherical . (2) The shape of the cell in the spread state is that of a spherical cap . (3) The volume of the cell remains constant throughout the spreading process and is equal to the original volume of the cell in suspension . (4) The bulk thermodynamic properties of the cell do not change as it goes from the suspended to the spread state . (5) Effects of gravity are negligible . (6) The cell membrane has 'fluid'-like properties . That is, the increase in the surface area of the cell is accomplished by the unfolding of the cell membrane, similar to creating more of a fluid/fluid interface, and not by stretching the membrane, a process which would introduce surface stresses . (7) Electrostatic effects are neglected. The process of cell spreading is shown schematically in Fig . 2 . The change in AFSP` as the cell goes from suspension (initial state) to the spread state (final state) is given by :

dF 9Pr =A cs Ycs - (A

c. -A

CL) YCL -A

cs YsL

(2)

where A represents the interfacial area and y the interfacial tension . The subscripts C, S and L stand for cell, solid and liquid, respectively, and the superscripts i. and f represent the initial and final equilibrium states, respectively . From assumption (1), the cell/liquid interfacial area for a cell in suspension (initial equilibrium) is given by :

AbL =4nr ; where r, is the

(3)

A cs =nrb2 AcL =21rrh

(4)

radius of the cell in suspension . The remaining two interfacial areas, Acs and Ac ,,, for the final equilibrium state can be obtained by simple geometry with reference to Fig . 2b :

liquid

(5) liquid

~/////LIAOWN substrate

substrate

Fig . 2 . Schematic diagram of the geometry of the cell . The shape of the cell is assumed to he that of a sphere while in suspension (frame a) and it changes to that of a spherical cap in the spread state (frameb) .



219

where rb is the radius of the base of the spherical cap, r is the radius of the spherical cap and h is the height of the cap . By introducing the angle 0 (Fig . 2b), the relationships between rb, h and r are : rb =rsin 0

(6)

h=r-rcos 0

(7)

The angle 0 can vary between 0 (complete spreading) to 180° (point contact) . Substituting Eqns (3)-(7) into Eqn (2) the following expression is obtained : AFy°'=n(rsin0) 2 (Ycs -YSL)-2n[2ri-r2 (1-cos0)]YCL

(8)

From assumption (3), constancy of volume, a relation between the radius of the sphere, r, and the height of the cap, h, to the original radius of the cell r,, can be obtained:

V=3 nr ; =3 nh 2 (3r-h)

(9)

or in terms of r and 0 :

V=-nr,

=3 nr 3 (2-3cos

0+cos3 0)

(10)

In order to determine the free energy of spreading, AF sP', as a function of degree of spreading (rb or 0) all that is necessary is to give input values for r i and the various interfacial tensions . The cell surface tension, Y cv , was taken to be 69 mJ m -2 , the value obtained from adhesion experiments of granulocytes [6], and the radius, r,, to be 6 .0 pm. AF AP' was calculated for different liquid surface tensions, yi,v, and solid surface tensions, ysv . As with the adhesion model, the pertinent interfacial tensions in Eqn (8) were calculated using an equation of state for interfacial tensions [ 19,20 ] . The theoretical predictions of the spreading model are depicted in Figs 3 and 4. It should be noted that because AFB"' is a function of not only the pertinent surface tensions but also of the geometry of the cells, it is not possible to plot the theoretical predictions in the same way as for the adhesion model (Fig . 1) . In Fig. 3 AF P' is plotted as a function of the radius of the base, r b , for liquids of various surface tensions . The solid surface tension, y sv , used for the calculations was fixed at 20 mJ m -2 . From Fig . 3 it can be seen that for one and the same solid (y sv less than y cv ), spreading is not favoured for Y Lv less than y cv (AF "p positive) . For YLv greater than Ycv spreading becomes favourable (AF sP' negative) . Also, as y LV increases spreading becomes more favourable (AF'P' less positive for yLV less than y cv and more negative for y LV larger than y cv ) . SPr is independent of r b. For yLv equal to ycv , AF In Fig. 4 AF P' is plotted as a function of the radius of the base, r b, for two values of yLv : 65 and 73 mJ m -2 . The solid surface tensions used for these



220 Tlv°56m1m2

-a Yar 20 mJ rn°

/ 7

yv -60 "U m 2

" . Us W m~



2

yivsaw . -`

7

/~ 7gy-SOmJm'

,

7w- 0 m1 m'

2

~`\

2

75v' U W m'2

w -70mJm 2

Y

7gv'r m1

6 Contact Radius (µm)

m2

6 Contaci Radius (Pm)

Fig. 3. (left) Theoretical curve of free energy of spreading, AF'P' . as a function of the contact radius, r,,, for various liquid surface tensions, tv. The substrate surface tension, 7sv, was fixed at 20 mJ

M -2 .

Fig. 4 . (right) Theoretical curve of free energy of spreading, 4F'P', as a function of the contact radius, r y, for two substrate surface tensions, 7, Three liquid surface tensions, y w , were used for the computations : 65, 69 (=ycv) and 73 mJ m 2.

calculations were 20 and 50 mill m' 2 . In Fig . 4 two different trends are shown : (1) for 'Lv. less than ycv spreading becomes more favourable with an increase in ysv ; for y Lv larger than ycv spreading becomes less favourable with an increase in ysv. EXPERIMENTAL

Materials

Substrates

Cell spreading experiments were performed using the substrate materials listed in Table 1. Preparation of these substrates were performed as described previously [6] . With the exception of fluorinated ethylene propylene copolymer (FEP), all the other polymers are commercially available as thin films . For FEP, smooth films were obtained by pressing strips of the polymer between chromic acid cleaned glass slides in a Dake 44-273 heat press (Wabash, In) . Polystyrene (PS) and polyethylene terephthalate (PET) strips were sonicated in absolute ethanol for 15 min and air dried prior to use in the experiments. Sulphonated polystyrene (SPS) strips were dipped in hexane for 10 s and air dried prior to use . The surface tension of the polymer films, ysv, was calculated from contact angle data using the equation of state approach .

221 TABLE 1 Solid substrates used in the spreading experiments- Contact angles and surface tensions determined at 20'C Polymer

Source

Preparation

Contact angle Surface tension (°) (mJm 2 )

Fluorinated ethylene Commercial Plastics propylene (FEP) Toronto, Canada

Heat press

110

16.4

Polystyrene (PS)

Central Research Lab-, Dow Chemical Co .

Film

95

25 .6

Polyethylene terephthalate (PET)

Iloechst Canada Inc ., Willowdale, Canada

Film

60

47 .0

Sulphonated polystyrene (SPS)

Central Research Lab ., Dow Chemical Co .

Film

24

66 .7

TABLE2 Surface tensions, at 20'C, of the liquid media used in the spreading experiments % DMSO in HBSS (vol/vol)

Surface tension, ,-iv (mJ m - ')

0 .0 2 .0 4 .0 6 .0 7 .5 9 .0 11 .0 15-0

72 .32 71 .02 69 .67 69 .39 68 .78 68 .10 67 .24 66 .31

Liquids

Eight solutions (volume/volume) of dimethyl sulfoxide (DMSO) in Hanks' balanced salt solution (HBSS) were used as the suspension media. The following concentrations were used : 0.0, 2.0, 4.0, 6.0, 7.5, 9.0, 11 .0 and 15.0% DMSO in HESS . The liquid combinations were chosen because they cover a wide range of surface tensions, including that of granulocytes. The surface tensions of the liquids, yLV , were measured using the modified Wilhelmy plate method [25 ] at 20°C. The surface tensions of the various liquid combinations are given in Table 2 .

222

Methods Granulocyte isolation Whole human blood was collected in 0 .5% w/v Na2EDTA . The blood was then combined with 6% dextran and 0 .9% saline and was allowed to stand for 30 min. At that time, the erythrocytes had agglutinated and precipitated out of solution . Then the supernatant was drawn off and centrifuged at 1200 rpm for 5 min at 4 0 C. The supernatant was discarded and the pellet was resuspended in HBSS . Any residual erythrocytes were lysed hypotonically . The pellet was then resuspended in HBSS and layered over Ficoll-Paque (Pharmacia, Uppsala, Sweden) in a test tube and the test tube was then centrifuged at 1200 rpm for 40 min at 4°C . Following centrifugation, the upper layers were removed leaving the granulocyte pellet at the bottom of the test tube . The pellet was then resuspended in HBSS. Spreading experiments Once the granulocytes had been isolated, they were ready for resuspension in the desired liquid medium. The granulocyte suspension was divided equally into eight aliquots which were then centrifuged at 1200 rpm for 5 min at 4'C . The supernatant was discarded and the pellet was resuspended in the appropriate liquid media . The cell counts, for each of the test tubes, were adjusted to 0 .5 . 106 granulocytes/ml. The granulocyte viability was determined using the Trypan blue exclusion test . Cell viability was always in excess of 90% . The cell suspensions were then ready to be used in spreading experiments . For these experiments, 0 .5 ml of the appropriate cell suspension was placed on the polymer surfaces and was retained in wells formed in teflon blocks separated from the substrates by Silastic gaskets . The surfaces were incubated for a period of 30 min after which time the whole assembly was placed, without exposing the adherent cells to air, in a rinsing bath containing undiluted HBSS . While in the bath, the blocks were removed but the gaskets were left in place to minimize disruption of the adherent cells . The substrates were transferred into a fresh bath, also containing undiluted HBSS, and were gently waved to remove all non-adherent cells . The substrates were then submerged into a solution of 5% formaldahyde in physiological saline for 20 min, after which time the cells were permanently fixed onto the substrates . The substrates were then rinsed in a bath containing distilled water to remove the formaldahyde . The granulocytes were stained using Wright's quick stain (Camco ) . The substrates were finally rinsed in distilled water and allowed to air dry . The dry substrates were analyzed using a microscope attached to a Bausch and Lomb Omnicon 3000 Digital Image Analysis System (DIAS) (Bausch and Lomb, Rochester, NY) . Prior to data analysis, DIAS was calibrated so that the output from it would reflect true physical dimensions . DIAS is able to deter-

223 mine the projected area, longest and shortest dimensions and the perimeter of the cells. The results obtained from DIAS for each substrate and each liquid mixture were averaged and analyzed using various statistical techniques . RESULTS AND DISCUSSION The surface tensions of the solid substrates, Ysv , calculated from contact angle data using the equation of state are given in Table 1 . The surface tensions of the liquid media, yLv, at 20°C obtained by the Wilhelmy plate method are given in Table 2 . In the adhesion experiments AF adh is an indicator of the extent of the reaction (i .e ., adhesion) ; the more negative AF aa' is, the more cells are expected to adhere to the substrate . Therefore, experimentally, counting the number of particles adhering to the substrate is the correct way of quantifying AFadh . Similarly, for the spreading model, it is assumed that there is a direct correlation between degree of spreading and AFSP' . Experimentally, the degree of spreading is determined by measuring, for example, the projected area of the spread cell . Photomicrographs of spread granulocytes, on FEP surfaces and in different liquid media, are shown in Fig. 5 . At low yLV the cells were more regularly shaped and more circular than the cells at higher Y Lv. As YLV increased the shape of the cells became less uniform and the cells tended to project pseudopodia. Four geometric parameters were measured for each granulocyte in order to determine the degree of spreading : projected area, perimeter, longest dimension and shortest dimension . The means of these results along with the associated standard errors are given in Tables 3 and 4 . For each substrate/liquid combination 90 granulocytes were analyzed . Analysis of variance (ANOVA), performed on the data presented in Tables 3 and 4, indicated that there is no significant difference between the results obtained on days 1 and 2 . ANOVA results are given in Tables 5 and 6 . ANOVA results indicate that for one and the same substrate there is a significant difference in the measured parameters for the different liquids at a confidence level of 99% [26] . All the four measured parameters provide the same information regarding the degree of spreading . Therefore, for sake of simplicity, only the projected area of the cells will be used in the discussion . In Figs 6 and 7 the mean projected areas of the granulocytes are plotted as a function of the liquid surface tension, YLv, for days 1 and 2, respectively . For all substrates there is an increase in projected area (increase in spreading) with an increase in the liquid surface tension . The means of the projected area of the cells are significantly different from one liquid mixture to the next . These results agree quite well with the theoretical predictions of the spreading model . These trends are also shown photographically in Fig . 5 .

224

Fig. 5 . Photomicrographs of spread granulocytes, at 630 Xmagnification, on FEP surfaces at different liquid medium surface tensions, y cv : (a) yzv=72 .32 mJ m -2 ; ( b) y,=69.39 Mj M-2 and (c) ytv=66 .31 mJ m -2 .

225 TABLE 3 Granulocyte spreading experimental results for day 1 . All the values presented are the average ± standard error of measurements from 90 granulocytes except where indicated Substrate

Liquid medium (%DMSO)

Projected area (µm2)

FEP

0 .0 2 .0 4 .0 6 .0 7 .5 9 .0 11 .0 15 .0

236,38±3 .70 240 .01±5 .26 214 .68±5 .74 188 .56+3 .95 128 .42_3.96 107.38±2 .47 83.69+2 .17 62,34±1 .15

PS

0 .0 2 .0 4 .0 6 .0 7 .5 9 .0 11 .0 15 .0

PET

SPS

Perimeter (gm)

Length (µm)

Breadth (µm)

88.62±2 .52 94 .99±2 .90 83 .44±3 .12 72 .59±2 .46 49 .82±1 .40 44 .72±0 .95 37 .29+0 .99 34 .95±0 .58

20 .02±0.20 21 .63±0 .33 20 .35±0 .35 20 .05±0.38 14.97'0.31 13 .74+0 .21 11 .78±0 .22 10 .31+0 .12

16 .28±0.15 16 .11±0 .22 15 .15+0 .24 14 .23±0 .18 11 .91+0 .20 10 .99+0 .13 9 .70±0 .13 8 .49+0 .09

211 .68±5 .09 205 .40±5 .15 188.60±4 .97 150 .52±3 .80 122 .10+2 .36 70 .27+1 .28 53 .79+1 .06 50 .70±0.81

91 .40±2.52 100 .25+3.38 89 .86±2.91 65.93±1 .95 46.89+0.86 32.17+0.45 27.41 .+0 .31 26 .70±027

19 .17±0 .26 20 .12±0 .34 19 .16±0 .35 16 .37+0 .28 14 .29±0 .17 10 .71+0.13 9 .06+0.11 8 .74+0 .07

15 .05±0 .22 14 .99±0 .20 14 .23±0 .22 12 .91+0 .17 11 .77+0 .12 8.88±0.09 7 .87±008 7 .74±0 .07

0 .0 2 .0 4.0* 6 .0 7 .5 9 .0 11 .0 15 .0

227 .53+6 .26 218 .49±5.43 132 .02+2.72 154 .08±1 .95 123 .75+2 .22 95 .09±1 .52 89 .90+2 .39 57 .67±1 .03

102 .16+3 .34 91 .63+2 .63 52 .48+1 .03 52 .99+0 .76 48 .37+0 .94 41 .48+0 .83 43 .42±1 .32 30 .13±0 .46

20 .36+0 .33 19 .73+0 .36 14 .79+0 .18 15 .96+0 .13 14 .54±0 .15 12 .90+0 .13 12 .49±0 .23 977±0 .14

15 .92+0 .23 1.5 .83+0 .20 12 .48±0 .15 13 .34+0 .10 11 .91+0 .12 10 .42+0 .11 10 .10+0 .15 8 .19+0 .08

0 .0 2 .0 4 .0 6.0 7 .5 9 .0 11 .0 15 .0

250 .62+5 .60 207 .54+4 .63 202 .36±5 .80 163 .37+5 .62 122 .33±3 .64 70 .10+1 .64 62 .69+1 .05 62 .92±0 .89

109 .98+3 .25 96 .65+2 .90 85 .22+2 .83 73 .76+2 .90 991 .07+1 .75 32 .80±056 29 .73±0 .28 29.80+0 .27

21 .81+0 .28 20 .18+0 .31 19 .46+0 .34 16.96+0.34 14.46+0.25 10 .83+0 .16 9.75±0.10 9.82+0.09

17 .11+0 .24 15 .63+0 .21 15.00±0 .24 13.70±0 .24 11 .73+0 .18 8.81±0 .10 8.60±0 .08 8.59+0 .06

*n=60

In Fig . 8 the mean projected areas of the granulocytes, for day 1, are plotted _ 2. as a function of the solid surface tension, Ysv, for y1 ,v =66 .31 and 72 .32 mJ m Results for day 2 are similar to those from day 1 . Although ANOVA indicated that the differences in the results obtained for the different substrates are sta-

226 TABLE4 Granulocyte spreading experimental results for day 2 . All the values presented are the average 1 standard error of measurements from 90 granulocytes except where indicated Substrate

Liquid medium (%DMSO)

Projected Area (µm')

Perimeter (/Am)

Length (ym)

Breadth (ym)

FEP

0 .0 2.0 4 .0 6 .0 7 .5 9 .0 11 .0 15 .0

238 .36±4. 6 20438+492 190 .91 ±4.09 192 .17±3.07 157 .18±2.65 11158±2.33 82 .64±1 .81 51 .59±1 .62

147 .82±3 .84 112 .75+3 .42 11919 `3 .45 134.14±3 .14 101 .30±2 .55 67 .65±2 .15 40 .21±1 .09 27 .24±0 .45

20 .73±0 .24 19 .74±025 19 .38±0 .27 1.9 .46±0 .26 16 .93±0 .17 13 .94±0 .16 11 .76 ± 0 .17 8 .96±0 .14

16.58±0.18 15 .02±0.17 14 .40? 017 14 .63+0.15 13 .48±0.12 11 .6610.14 9 .69±0.12 7 .71±0.11

PS

0 .0 2 .0 4 .0 6 .0 75 9 .0 11 .0 15 .0

208 .62±3 .48 193 .15±3 .09 175 .48±3 .94 141 .28±3 .21 121 .92+1,84 68.59 46.37±1 .23 44 .39±0 .78

150 .05+ 4.08 147 .45+3 .86 123 .50±3 .71 85 .40+3 .10 90 .94±224 34 .87+0.73 26.07+0 .73 26 .59±0 .63

20 .6110 .26 20.82±0 .31 18.85±0 .27 16.51±0 .25 15 .38+0 .14 10.41+0 .12 8.37±0 .12 8.34±0 .11

15 .78±0 .15 14 .7510 .17 14 .27±0 .17 12 .7610 .16 12 .23+0.12 8.96*_010 7 .34+0 .09 .22±0 .06 7

PET

() .0` 2 .0 4 .0 6.0 7 .5 9 .0 11 .0 15 .0

213 .44 193.14 ± 4 .14 147.92 ±225 130.17 ± 2 .22 154.24±3_11 98.70±2.50 76.19±1 .99 47.45±0 .83

176 .11±5 .66 155 .40±5 .43 111 .36±2 .90 91 .51±2 .05 128 .04 +3 .31 72 .08+2 .50 46 .5812 .46 25 .59±027

20.77±0 .27 1991±0 .32 16 .85± 0 .15 15 .18±0.12 17 .09±016 13.49±0 .16 11 .50+0 .20 8 .42±0 .08

16 .19±0 .19 14.89±0 .17 13 .2910 .11 12.701013 13.81+0 .16 11 .01+0 .15 9.48±0 .14 .5010 .07 7

SPS

0 .0 2 .0 4 .0 6 .0 7 .5 9 .0 11 .0 15 .0

202 .96±4 .85 189.65±4 .88 157.76±3 .49 99 .05±3 .20 145 .78+2.44 62 .51±0.80 62.84+1 .01 48.9510.42

216 .46±5 .74 193 .51 162 .33±3 .83 79 .98±4 .02 132 .83+2 .96 36 .9810 .80 38 .2011_48 26 .6010 .22

2158±0 .29 20 .96±0 .30 18 .61±0 .21 14 .14±0 .25 16 .90±0 .14 10 .10±0 .10 10 .41±0 .14 8 .61 10 .06

15.9210 .21 15.24±0 .19 14.2110 .16 11 .2410 .20 13 .3710 .13 8 .6910 .06 8.80±0_08 7.6610 .44

. n=88 .

tistically significant [26], at a 95% confidence level, there is no systematic dependence of projected area on the solid surface tension . In many cases the means of the projected areas cannot be distinguished from one substrate to another for the same liquid medium .

227 TABLE ,5 ANOVA results for the effect of liquid medium on projected area Substrate

Source

df

Mean square

F value

FEP

Liquid Error

7 712

451617 .73 1324 .26

341 .03

PS

Liquid Error

7 712

410370 .88 1131 .73

362 .60

PET

Liquid Error

6 623

385103 .75 1110 .73

346.71

SPS

Liquid Error

7 712

493416 .16 1528 .42

322 .83

FEP

Liquid Error

7 712

383948 .26 922 .02

416.42

PS

Liquid Error

7 712

389860 .17 621 .83

626 .96

PET

Liquid Error

7 712

289940 .91 791 .84

366 .16

SPS

Liquid Error

7 712

332660 .43 871 .97

381 .50

Day 1

Day 2

Comparing the model predictions with experimental observations it can be seen that there is only partial agreement between the model and experimental results. Cell spreading dependence on liquid surface tension, yLV , is observed but the predicted dependence of spreading on substrate surface tension, y sv , is not observed. The use of DIAS with an upright microscope to quantify the degree of spreading might introduce some difficulties in the analysis of the data . When the projected area of the cell is measured, using DIAS, it is not possible to ascertain whether this projected area corresponds exactly with the cell/substrate interfacial area . The two areas will be the same only if the angle 0 is less than 90° (Fig. 9) . For 0 greater than 90° the projected area will correspond to the cross-sectional area of the cell at its equator . Therefore, for one measured projected area two possible situations can occur and, with the present experimental set-up, it is not possible to determine which one is operative . This difficulty in discriminating between the two situations means that it would be

228 TABLE 6 ANOVA for the effect of substrate on projected area Liquid (% DMSO)

Source

df

Mean square

Substrate Substrate Error Substrate Error Substrate Error Substrate Error Substrate Error Substrate Error Substrate Error

3 356 3 356 3 326 3 356 3 356 3 356 3 356 3 356

23940 .67 2478 .85 22573 .87 2363 .46 90095 .65 2324.24 26511 .67 1472 .22 776 .72 887.58 31188.78 286.80 26233.06 284.21 2873 .38 86 .30

Substrate Error Substrate Error Substrate Error Substrate Error Substrate Error Substrate Error Substrate Error Substrate Error

3 356 3 356 3 356 3 356 3 356 3 356 3 356 3 356

21915 .18 1722 .36 3704 .58 1500 .02 32668 .29 1115 .08 134863 .87 786 .04 22997 .68 585 .14 50068 .19 327 .03 23160 .42 219.62 812 .18 92 .25

F value

Day 1

0 .0

Error

2 .0 4 .0 6 .0 7 .5 9.0 11 .0 15 .0

9 .66 9.55 38 .76 18 .01 0 .88 108 .75 92 .30 33 .29

Day 2

0 .0 2 .0 4.0 6 .0 7 .5 9 .0 11 .0 15 .0

12 .30 2.47 29.30 171 .57 39.30 153 .10 105 .46 8.80

impossible to detect any expected dependence of spreading on either liquid or substrate surface tensions . However, it is quite clear from Figs 5 and 6 that a strong dependence of spreading on liquid surface tension, as expected, was observed. Thus, it can be concluded that the use of DIAS to quantify degree of spreading is justified . A possible solution to the question of whether the angle 0 is greater or less than 90° may he to determine the projected area of the cell



229 300e

Ps

•

PS PET scs

a

•

e

0 1 Q 0

v

a

t

066

70

68

Liquid Surace Tension . YLV ("

72 V2)

Fig, 6. Projected area of cells as measured by DIAS versus liquid surface tension, )1v, for experiments performed on day 1 . Error bars representing standard errors fall within the symbols. Moa

• s

•

PEP PS PET SPS

a S

I

0 66

68

72

70

74

Liquid Surface Tension, YLV (nu m' 2)

Fig . 7 . Projected area of cells as measured by DIAS versus liquid surface tension, yLv, for experiments performed on day 2. Error bars representing standard errors fall within the symbols . no a

yLV .72.32rWff2

a

a a

TLV -

esm

m..1

0 10

20

30 Substrate Surface

40

, ysvin Tension

60

70

r^'2)

Fig. 8 . Projected area of cells as measured by DIAS versus solid surface tension, ysv, for experiments performed on day 1 . Error bars representing standard errors fall within the symbols .



230 Top

A d

Am a

NVANimm 0<90 0 d-2'b

Side

9>90, d-2r

Fig. 9 . Schematic view of two possible geometries assumed by a spread cell which have the same measured projected area .

from both above and below the substrate . These measurements, however, would only be possible if the substrates were transparent. The lack of experimental evidence for the dependence of spreading on the substrate surface tension, ysv, might indicate that physico-chemical interactions are not the only mechanisms for the process of cell spreading . In the theoretical model developed it was assumed that the process of spreading could be determined solely from the change in free energy of the system as the cell went from the suspended to the spread state . In reality the cell, being alive, may also be actively doing work to increase the cell/substrate contact area, work which may be more significant than the change in free energy calculated by the theoretical model. Indeed, it is well known that when a granulocyte phagocytosizes a particle, the cytoskeleton undergoes a local restructuring by the assembly of actin into microfilaments and the formation of large microtubules from tubulin [27] . This process of cytoskeleton restructing requires energy input which comes from cellular stores . While this process may account for the lack of dependence of spreading on ysv , the same effect should also be operative for the yLv dependence of spreading . It seems therefore unlikely that the lack of ysv dependence can be attributed to such biological processes . The use of DMSO to vary the surface tension of the liquid media might also explain the lack of dependence of spreading on the substrate surface tension . DMSO can cause the cell membrane to become more permeable such that cellular material may leak out of the cell into the liquid medium. This cellular material could coat the polymer substraters so that the surface tension of the coated substrates would become essentially the same for all the different substrates. Hence, should coating of the substrates occur, no dependence of spreading on the bare substrate surface tension would be expected . Although this explanation might seem plausible, it is not corroborated by results from adhesion experiments [6,71 . In the adhesion experiments the results obtained followed the pattern predicted by the adhesion model, indicating that if any leakage of cellular material into the system occurred, it did not affect either the liquid or substrate surface tensions . Had any of the cellular contents leaked

231

into solution, the expectation is that any released materials would migrate to the highest energy interface, that is, the liquid-vapour interface . However, liquid media surface tension measurements, performed before and after adhesion experiments with neutrophils, do not show any significant differences indicating that protein adsorption to the liquid-vapour interface does not occur [6 ] . For the development of the spreading model it was assumed that electrostatic interactions were negligible when compared to van der Waals interactions . While this assumption was shown to be valid for the case of spreading . ANOVA results indicate that the differences in the results obtained for the different substrates, in the same liquid medium, are significant . The non-systematic, but significant, dependence of spreading on the substrates may be the result of varying electrostatic properties of the different substrates . It may be speculated that the process of adhesion involves, initially, the selective extension of protrusions on the cells towards uncharged sites on the substrate . Once the protrusions attach on the substrate, adhesion of the cell onto that substrate is considered to have occurred . That is, the cell is considered to be permanently attached to the surface and cannot easily be removed even by strong mechanical force. In the adhesion process, therefore, the electrostatic interactions would not be important and could be neglected . The process of spreading, however, would require the cell to increase the cell/substrate contact area which necessarily implies indiscriminate spreading over charged and uncharged sites of the substrate. If such a scenario is probable, it is not surprising that only the dependence of spreading on the liquid surface tension is observed . For one and the same substrate, when the liquid surface tension is varied, the cell/liquid and substrate/liquid interfacial tensions change resulting only in a change of dF'P' . When the liquid medium is kept constant and the substrates are changed, in addition to the change in dF SP', there is a change in the electrostatic properties of the substrate . These changes in the electrostatic properties of the substrate are not accounted for in the spreading model and the predicted spreading dependence on ysv should, therefore, not be observed experimentally. ANOVA results, therefore, seem to support the notion that electrostatic interactions cannot be neglected in the process of spreading . The experimental evidence for the dependence of cell spreading on y LV indicates that van der Waals interactions play an important role in the process of cell spreading. From the theoretical curves of AF `P' as a function of rb (Fig . 3) it was shown that spreading became more favourable as yLV increased, i.e., as AF 'P' decreased. The apparent independence of spreading on the substrate surface tension, ysv, could be caused by electrostatic interactions which are not considered in the spreading model . CONCLUSIONS

A thermodynamic model for cell spreading, based on van der Waals interactions, was developed . There was partial agreement between model predic-

232

tions and experimental observations. From the observed dependence of spreading on the liquid surface tension it can be concluded that physicochemical interactions play an important role in the process of spreading . The observed non-systematic dependence of spreading on the substrate surface tension seems to indicate that electrostatic interactions cannot be neglected in the modelling of cell spreading.

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