Eur. J. Biochem. IY8, 31 -41 (1991) ? \; FEBS 1991 001429569100306V

Denaturation capacity: a new quantitative criterion for selection of organic solvents as reaction media in biocatalysis Yuri L. KHMELNITSKY ’, Vadim V. MOZHAEV’, Alla B. BELOVA’, Maria V. SERGEEVA’ and Karel MARTINEK3 A . N . Bakh Institute of Biochemistry, Moscow, USSR

’ Chemistry Department, Moscow State University, USSR Institute of Organic Chemistry and Biochemistry, Prague, Czechoslovakia (Received July 6, 1990) - EJB 90 0802

The process of reversible denaturation of several proteins (a-chymotrypsin, trypsin, laccase, chymotrypsinogen, cytochrome c and myoglobin) by a broad series of organic solvents of different nature was investigated using both our own and literature data, based on the results of kinetic and spectroscopic measurements. In all systems studied, the denaturation proceeded in a threshold manner, i. e. an abrupt change in catalytic and/or spectroscopic properties of dissolved proteins was observed after a certain threshold concentration of the organic solvent had been reached. To account for the observed features of the denaturation process, a thermodynamic model of the reversible protein denaturation by organic solvents was developed, based on the widely accepted notion that an undisturbed water shell around the protein globule is a prerequisite for the retention of the native state of the protein. The quantitative treatment led to the equation relating the threshold concentration of the organic solvent with its physicochemical characteristics, such as hydrophobicity, solvating ability and molecular geometry. This equation described well the experimental data for all proteins tested. Based on the thermodynamic model of protein denaturation, a novel quantitative parameter characterizing the denaturing strength of organic solvents, called the denaturation capacity (DC), was suggested. Different organic solvents, arranged according to their DC values, form the DC scale of organic solvents which permits theoretical prediction of the threshold concentration of any organic solvent for a given protein. The validity of the DC scale for this kind of prediction was verified for all proteins tested and a large number of organic solvents. The experimental data for a few organic solvents, such as formamide and N-methylformamide, did not comply with equations describing the denaturation model. Such solvents form the group of so-called ‘bad’ solvents; reasons for the occurrence of ‘bad’ solvents are not yet clear. The DC scale was further extended to include also highly nonpolar solvents, in order to explain the wellknown ability of enzymes to retain catalytic activity and stability in biphasic systems of the type water/waterimmiscible organic solvent. It was quantitatively demonstrated that this ability is accounted for by the simple fact that nonpolar solvents are not sufficiently soluble in water to reach the inactivation threshold concentration. Biocatalysis in non-aqueous media has received growing attention during the last decade due to its obvious potential, such as conversion of hydrophobic compounds and favorable shift of reaction equilibrium [l, 21. One of the most widely accepted approaches is based on the use of water/organic cosolvent binary mixtures containing dissolved or immobilized enzymes (for a review, see [3]). Unfortunately, the use of this approach is considerably restricted because of the difficulties emerging when one has to decide which precise organic cosolvent to choose for practical implementation of a particular biocatalytic process. In other words, one has to answer the difficult question as to which solvent will allow a predetermined water concentration in the system without significant deterioration of the enzyme’s performance, or, in other cases, what is the highest concentration of a given organic solvent that the enzyme can still endure. In order to answer these questions, a quantitative criterion for selection ~-

Correspondence to Y. L. Khmelnitsky, A. N. Bakh Institute of Biochemistry, Leninsky prospekt 33, Moscow, USSR 117071 Ahhreviations. DC, denaturation capacity; cs0, threshold concentration of an organic solvent. Enzymes. a-Chymotrypsin (EC 3.4.21.1); laccase (EC 1.10.3.2); trypsin (EC 3.4.21.4).

of water-miscible solvents is required. An attempt to formulate such a criterion was made by Martinek et al. a decade ago [4, 51. It was based on the notion that the lowest denaturing effect on proteins is exerted by solvents possessing the highest ability to maintain solvophobic interactions which play the key role in supporting the native conformation of protein molecules. As a measure of the ability of different solvents to maintain solvophobic interactions, Martinek et al. used the free energy of micellization, dG,&, of a standard surfactant in these solvents [6]. According to this criterion, the best solvents for proteins are water, glycerol and ethylene glycol, whereas other organic solvents are much stronger protein denaturants. The validity of this approach to assessing the denaturing strength of organic solvents has been verified by examples of several enzymes [4, 5, 71 and cells [8]. However, this criterion, although being generally feasible, is of only limited practical importance. The point is that in some solvents (e. g. in short-chain aliphatic alcohols) micellization does not occur, and it is therefore impossible to determine the value of AG&. As a consequence, the selection criterion based on the model micellization process can be called quantitative only with essential reservations. This criterion does not permit prediction of actual solvent concentrations that would leave

32 the enzyme intact, but only gives a semiquantitative idea of the relative denaturing efficiency of different solvents. Recently, we started a search for a new selection criterion which would be devoid of the above-mentioned limitations. In our previous publications [3, 9, 101 we have shown that logP values of water-miscible organic solvents (where P is the partition coefficient of a solvent in the water/octanol biphasic system) reveal a good correlation with their denaturing strength, viz. the higher the logP the stronger the denaturing effect. However, the logP criterion is applicable only for solvents of the same functionality, e.g. alcohols and polyols. When solvents of a different nature are included, the correlation breaks down. In other words, IogP per se cannot be regarded as a universal criterion for solvent selection, and the above-mentioned correlations reflect only a part of a more complex general picture. It was the aim of the present work to make the reflection as complete as possible, i.e. to provide a versatile quantitative criterion for solvent selection to be used for constructing biocatalytic systems in water/organic cosolvent binary mixtures. MATERIALS A N D METHODS

I

15

30

45

60

c (v01./100v0l.)

Fig. 1. Dependence of relative catalytic uctivity (expressed in icwns of' V,) qf dissolved enzymes on the ince cent rut ion of organic .solwnis iii waterlorganic binary mixtures. 1 , Laccase in water/acetone mixtures; 2, r-chymotrypsin in water/ethanol mixtures; 3, trypsin in water/ acetonitrile mixtures. Vertical arrows indicate corresponding threshold concentrations of organic solvents, c5"

Chemicals Proteins. Crystalline a-chymotrypsin from bovine pancreas (Sigma) contained more than 80% of active enzyme, as determined by spectrophotometric titration [l 11, and was used without additional purification. Laccase from Polyporos versicolor was obtained from Erevan Institute of Biochemistry in the form of aqueous solution containing 5 mg/ml active enzyme. Bovine pancreatic trypsin (type 111) and sperm whale myoglobin were obtained from Sigma and used as received. Substrates. N-Benzoyl-L-tyrosine p-nitroanilide and Nbenzoyl-L-arginine p-nitroanilide were the products of Sigma. Pyrocatechol (Reakhim, USSR) was purified by sublimation. Solvents. 1,2-Propanediol (BDH) and 1,3-butanediol (Ferak) were used without purification. Glycerol, ethylene glycol and aliphatic alcohols were distilled before use. Tetrahydrofuran was freshly purified by refluxing/distillation over sodium with subsequent refluxing/distillation over LiAlH4, each operation being repeated twice. All other organic solvents were purified using recommended procedures [121. Preparation ojsamples Samples for measurement were prepared by simple mixing of required amounts of components (organic cosolvent, aqueous buffer, enzyme and substrate solution) in a spectrophotometer cell. The mass of viscous cosolvents (glycerol and some diols) were determined. The pH of reaction mixtures was adjusted as described previously [9, lo]. Activity measurements Initial velocities of enzymatic reactions were measured spectrophotometrically at 25°C using a Beckman 25 spectrophotometer. For a-chymotrypsin and laccase, N-benzoyl-L-tyrosine p-nitroanilide and pyrocatechol were used as substrates, respectively (for details, see [9, 101). Catalytic activity of trypsin was measured using N-benzoyl-L-arginine p nitroanilide as a substrate at 375 nm, the wavelength of the maximal absorbance ofp-nitroaniline formed during the reaction. Concentrations of trypsin and N-benzoyl-L-tyrosine p -

nitroanilide in the reaction mixture were 0.8 pM and 0.1 10 mM, respectively, and 50 m M Tris/acetate buffer (pH 7.0) was used as a n aqueous component. Maximal velocities ( Vn,) of enzymatic reactions were determined from LineweaverBurk plots. In the case of water-immiscible organic solvents, enzymatic activities were measured as described above in corresponding aqueous buffer solutions saturated with the organic solvents. The saturation was performed by contacting' the aqueous buffer with an excess of the organic phase under constant shaking for at least one day. The aqueous phase was then carefully separated after at least 1 h standing in a separation funnel. Absorption spectra of myoglobin were recorded using a Beckman 25 spectrophotometer at 25°C. For preparation of samples, 0.1 M potassium acetate buffer (pH 5.7) was used as an aqueous component. RESULTS A N D DISCUSSION In this work, we studied catalytic properties of achymotrypsin, trypsin and laccase in various water/organic solvent homogeneous binary mixtures. We found that the addition of increasing concentrations of organic cosolvents into aqueous solutions of these enzymes eventually resulted in all cases in a profound loss of enzymatic activity. The process of enzyme inactivation was characterized by the following main features. In all systems studied the profile of enzymatic activity (expressed in terms of maximal velocity, Vm) vs. concentration of the organic cosolvent showed a very well-defined threshold behavior, in full agreement with our previous findings [9, 101. Several characteristic examples are given in Fig. 1, and the full list of threshold concentrations of different organic solvents, determined for a-chymotrypsin, trypsin and laccase, is presented in Table 1. The threshold concentration is defined as the concentration of the organic cosolvent at which half inactivation of the enzyme is observed, c50 (see Fig. 1). It has to be stressed that the threshold decrease in enzymatic activity can be observed experimentally only if the substrate has been chosen properly, as discussed in our previous paper [lo].

mol/l

From [19] and [20]

' Reference solvent.

a

1.773

-

1.293 0.899 0.982 1.205 1.383 1.152 1.245 1.313 1.465 1.486 1.307 1.480 1.536 1.419 1.511 1.692 1.663 1.724 -

-

0.9 1.1

-

1.6

-

1.0 2.3

-

5.1 4.4

-

6.7 5.0 8.7

-

5.0 2.7 1.0

1.0 15.0 10.0 6.2 2.4

10.5 9.2 7.9 6.0 6.2 5.5 4.3 4.2 3.7 3.4 3.6 2.5 2.3

b

15.6 12.1

1.724 0.665 0.982 1.291 1.560 1.199 1.386 1.137 1.364 1.549 1.376 1.537 1.706 1.651 1.559 1.635

exp.

calc.

'

-

3.7 3.4 1.6 2.1

-

4.5

-

-

-

-

-

2.0 -

-

-

0.5 -

-

-

-

1.1

-

2.1 1.3

-

2.0

1.595

1.548 1.753 1.737 1.692

-

-

-

1.642

-

'

1.463 -

-

6.0

-

7.0

-

9.8

calc.

-

1.241 1.029

-

1.061

1.6 2.6 0.7 0.8 1.1 -

-

b

3.6

-

9.4 3.8 -

-

11.0 7.2

-

6.2 6.7 6.2

-

14.1 11.6 9.5 10.2 9.1

exp.

exp.

calc.

exp.

exp.

exp.

~

Chymotrypsinogen

Laccase

z-chymotrypsin

Formamide 5.8 13.0 Ethylene glycol 10.0 Glycerol Methanol 8.0 4.9 N-Methylformamide 1,2-Propanediol 8.2 6.3 1,3-Butanediol 6.2 Ethanol 4.2 Dimethyl sulfoxide 3.4 N,N-Dimethylformamide Acetonitrile 6.1 3.6 1 -Propano1 2.6 Sulfolane 4.4 2-Propanol 1-Butanol 3.1 Acetone 1.1 2-Methyl-1 -propano1 2-Butanol Hexamethylphosphoramide 0.9 1,4-Dioxane 0.9 2-Methyl-2-propanol Tetrahydrofuran 0.6

Solvent

~~

-

3.6

-

0.7

-

-

4.6

-

4.0

-

-

-

7.2

-

12.7 10.5

-

13.9

-

exp.

1.458 -

-

-

1.754

-

1.400

-

1.451

-

0.889 1.250 -

-

0.805 0.978

-

exp.

Cytochrome c

~

Table 1 . Tl~rc~.sl~ol~l conmtifriifionsof orgirnic .rolwnt.s fbr difierent proteins Experimental cso from chymotrypsinogen and cytochrome c' are from [19] and [20]. exp., experimental; calc., calculated ~~

calc.

~~~

~~

-

2.1 4.3 5.1

-

15.2 12.6 11.7 7.9 10.3 6.7 8.2 6.1 9.1 4.3 5.3 7.0 6.3

-

exp.

-

1.476 1.391 1.326

-

1.275 -

-

1.130 1.432 1.300 1.217

-

0.637 0.434 1.027 1.196 0.944 1.199 1.185 1.345

-

exp.

Trypsin

~~~~

3.0 3.1 -

-

'

-

4.8

-

7.5 6.9 5.9 5.2 5.7

13.0 10.4 12.4 10.6 9.0 7.2

calc.

9.3" 14.3" 12.4" 7.0" 8.4" 5.3" 6.5 7.7" 5.9 2.9" 5.3 3.4" 0.9" 2.2 0.8" 1.6 2.5 2.5" 1.4

exp.

1.565 1.549 1.557 1.662

-

1.365 1.316 1.130 1.318 1.529 1.300 1.487 1.722 1.583 1.137

-

0.990 1.250 1.140

-

1.114 0.762

exp.

Myoglobin

b

6.9 6.4 5.0 5.1 4.7 4.1 4.5 3.4 3.4 3.2 1.5 1.9 2.0

h

15.3 12.1 10.7 9.6

calc.

-

w w

34 previously [9, 10, 19, 20, 241 is that the observed threshold reversible denaturation of proteins by increasing concentrations of organic cosolvents represents a general phenomenon which operates regardless of the nature of specific solvents or proteins used. In order to elucidate molecular mechanisms responsible for the above features of the denaturation of proteins in water/ cosolvent mixtures, we have developed a thermodynamic model of the process, which is described in the following section.

v

Thermodynamic model o j e n z y m e (protein) denaturation b y organic cosolvents 10

20

30

40

50

c (vol./l 00 VOI. )

Fig. 2. Dependence qf the dijference molar absorbance of myoglohin at the 409-nm Soret band on the concentration of organic solvents in water/ organic binary mixtures. 1, Water/tetrahydrofuranmixtures; 2, water/ hexamethylphosphoramidemixtures. Vertical arrows indicate corresponding threshold concentrations of organic solvents, c50

The threshold decrease in enzymatic activity was accompanied by a n abrupt change in the spectroscopic properties of dissolved enzyme. This conclusion is based on results obtained previously from parallel measurements of fluorescent properties and catalytic activity of a-chymotrypsin in various water/organic binary mixtures [9, 101. The parallelism in alteration of spectral and catalytic properties was also found for many other enzymes dissolved in binary water/organic mixtures of varying composition [13 - 181. Threshold dependences of spectroscopic properties on the concentration of various organic cosolvents were also observed for a non-enzymatic protein, myoglobin. Fig. 2 shows the dependence of the difference molar absorbance of myoglobin at the 409-nm Soret band on the concentration of several organic cosolvents in solution, and the full list of organic solvents tested with corresponding values of c50 are given in Table 1. Dependences similar to those shown in Fig. 2 were reported also for other proteins [19-231, and some of these literature data dealing with extensive series of organic solvents [19, 201 are also included into Table 1. Note that the data formyoglobin reported in the present work were obtained under exactly the same conditions as in the work by Herskovits et al. [19, 201, and therefore two sets of c5,, values for myoglobin, presented in Table 1, can be treated as a consistent single series. The abrupt change in spectroscopic properties of dissolved proteins observed at increasing concentrations of organic cosolvents has been interpreted [9, 10, 13-24] in terms of conformational transitions in protein molecules. The fact that the drop in enzymatic activity occurs a t the same concentration as the spectral perturbation implies that it is the denaturation that causes the threshold inactivation of dissolved enzymes. The discrimination between different possible mechanisms of enzyme inactivation by organic cosolvents has been discussed in detail in our previous paper [lo]. For all enzymes studied, the process of inactivation by organic solvents was fully reversible, i.e. the dilution of the enzyme solution, containing an organic cosolvent with a concentration higher than the threshold value, with water lead to complete restoration of enzymatic activity. An important conclusion which can be drawn from the results obtained in this work and from the data published

The protein molecule in aqueous solution is surrounded by a hydration shell formed by water molecules noncovalently bound to the protein surface by hydrogen bonds. According to the widely accepted notion [25, 261, this water shell, or at least some part of it, represents an integral part of the protein and is essential for its structure and function. Displacement of bound water molecules either by organic cosolvents [27,28] or by heating [27] results in a dramatic change of the whole protein structure, i.e. leads to its denaturation. In line with these ideas, we propose a thermodynamic model of protein denaturation by organic cosolvents in solution which is based on the following key assumptions. (a) Dehydration, i.e. the destruction of the hydration shell of proteins, is the primary reason for their denaturation by organic cosolvents. (b) The denaturation occurs after a certain critical amount of water in the hydration shell of the protein has been displaced by the organic cosolvent. This critical amount represents a fundamental characteristic of the protein and is the same regardless of the organic cosolvent used. In other words, the denaturation process per .ye does not depend significantly on the nature of the organic cosolvent used to displace water from the protein hydration shell, but is governed mainly by the amount of water that has been displaced. The validity of this assumption is strongly supported by recent results by Zaks and Klibanov [29] who found that the catalytic activity of solid alcohol oxidase, polyphenol oxidase and alcohol dehydrogenase, suspended in different organic solvents, was influenced only by water content of the enzyme particles and did not depend on the nature of the organic solvent used. According to the model, the process of protein denaturation in water/cosolvent mixtures is described by the following equation : K

N .a H z O

+ dS+

D . (a- h ) H 2 0 .dS

+ hH 2 0 ,

(1)

where N . a HzO is the native form of the protein with a water shell consisting of a water molecules, S is the organic solvent, D . ( a - h ) H z O - d S i s the denatured form of the protein bearing partly disturbed water shell, and K is the equilibrium constant. It has to be stressed that the model deals only with reversible protein denaturation caused by organic cosolvenih which is detected by the reversible loss of catalytic activity. I t is well known that this initial conformational perturbation in many cases is followed by a n extensive denaturation involving gross conformational changes and even aggregation and precipitation of the protein [21-23, 301. These secondary processes, observed at high concentrations of organic cosolvents, and/or during prolonged exposures of the protein to an environment rich in organic cosolvent, are not considered here. In order to single out the processes that are dependent only on the nature of the protein per se and to discriminate

35 Desolvation of hydrated native protein

Dehydration of desolvated native protein

Solvation of water molecules removed from protein

Desolvation of organic cosolvent

Binding of organic cosolvent by partially dehydrated protein

Solvation of protein-cosolvent complex

Denaturation

Fig. 3. Schematic representation o j molecular steps involved in the process of reversible protein denaturation by organic solvents. 0 Water molecule, organic cosolvent molecule, E4 surrounding solvent

them from those influenced by properties of the organic cosolvent, it is convenient to regard the denaturation process as a sum of several independent equilibria discussed below. Corresponding molecular processes are schematically depicted in Fig. 3. Desolvation of the fully hydrated protein molecule, i. e. elimination of all interactions of the protein bearing the undisturbed water shell with surrounding solvent:

Binding of the organic cosolvent by the partially dehydrated protein molecule in the desolvated state:

(2)

Conformational transition in the protein molecule resulting in the formation of a denatured form of the protein ( D ) with concomitant loss of catalytic properties:

(N.aHzO)s,~,=(N.aH~O)deso,v 7

where subscripts solv and desolv designate solvated and desolvated states, respectively. Dehydration of the protein molecule, i.e. removal of a certain critical (in the sense defined above) number (b) of water molecules from the hydration shell of the desolvated protein: ( N a HZ0)desolv '

*[ N ( a '

-

b )H Z O I d e s o l v

+ bHZodcsolv

. (3)

Note that in the framework of the present model the value of b is essentially constant for a given protein and does not depend on the nature of the organic cosolvent. Solvation of water molecules that have been removed from the protein during the previous step: bH20desolv

*

bH2Osolv

.

(4)

Desolvation of d molecules of the organic cosolvent S: dssolv

*

dsdcsolv

.

(5)

* [ N .( a-b)H

. (6) Solvation of the protein/cosolvent complex formed during the previous step:

[ N . (0- b)H2°]desolv

f dsdesoiv

2 0

'

dS1desolv

[ N ' ( ~ - ~ ) H ~ ~ ' ~ S ] ~ , S (O~ -I ~, = ) H[ N 2 0. . d S ] s 0 ~(7) v.

[ N . (a-b)HZO

'

dSls0Iv [ D (a-b)HZO. dS],oIv. (8)

Summation of Eqns (2-8) gives Eqn (1) describing the net process of the protein denaturation [in Eqn (1) subscripts solv are omitted]. The total standard free energy change during the denaturation process described by Eqn (I), expressed per mol protein, is :

+ AG; + bAG," + dAG; + AG," + AG; + AG,",

AG,",,= AG;

(9)

where AG; - AG;' are standard free energy changes corresponding to elementary steps described by Eqns (2 - 8), respectively. Considering actual values of these free energies, one can conclude from inspection of Eqn ( 3 ) that AG; represents a fundamental property of the protein and does not depend on

36 energy of solvation of the latter subgroup of bound water molecules, and AC,"'is the free energy of solvation of proteinbound molecules of the organic cosolvent. Obviously, the values of A C;"' and 468" describe thermodynamically equivalent processes which differ only in sign, and therefore

Table 2. Characteristics of organic solvents

kJ/mol Formamide -1.65 Ethylene glycol - 1.43 Glycerol - 2.50 Methanol -0.74 N-Methylformamide -1.13 1,2-Propanediol - 1.35 1,3-Butanediol - 1.02 Ethanol -0.32 Dimethyl sulfoxide -1.35 N,N-Dimethylformamide - 1.01 Acetonitrile -0.34 1-Propanol 0.34 Sulfolane -0.77 2-Propanol 0.14 I-Butanol 0.89 Acetone -0.24 2-Methyl-1 -propano1 0.83 2-Butanol 0.61 Hexamethylphosphoramide 0.28 1,4-Dioxane -0.27 2-Methyl-2-propanol 0.37 Tetrahydro furan 0.46

0.444 0.264 0.194 0.414 0.314 0.213 0.178 0.301 0.199 0.244 0.344 0.231 0.199 0.237 0.194 0.254 0.194 0.194 0.099 0.240 0.190 0.241

237 236 238 232 226 226 22 1 213 188 183 192 21 2 184 203 210 177 205 197 171 151 184 156

0.0 18.7 20.2 30.5 32.4 38.8 49.1 54.4 60.3 63.3 64.3 69.2 69.3 70.2 77.2 78.2 19.2 80.4 90.1 92.1 92.2 100.0

the nature of the organic cosolvent. The same is true also for AC; [cf. Eqn (8)], as follows from the second underlying assumption of the model (see above). Thus, we have: (10) The value of AC; represents the free energy of solvation of the naked (dehydrated) patches on the protein surface by the organic cosolvent [see Eqn (6)]. The binding of cosolvent molecules to the protein is realized in this case mainly by means of hydrogen bonds and electrostatic interactions with polar and charged groups on the protein surface (van der Waals forces can be neglected because they are much weaker than hydrogen bonds and electrostatic interactions [31]). The ability of different solvents to solvate polar fragments is described by the Dimroth-Reichardt parameter, E7(30) [32, 331 which is directly related to the free energy of the solvation process [34], so that we can write: AC;, A C ;

AG,"

= constant.

L Y ~ET(30)

+

(1 2 ) where cil and c ( ~are numerical coefficients. The values of ET(30) for many different solvents are available from literature [35, 361; those relevant for the present study are given in Table 2. Four remaining steps of the denaturation process, described by Eqns (2), (4), ( 5 ) and (7), deal with solvation/desolvation of water and organic cosolvent molecules either existing in the free state [Eqns (4) and (5)] o r bound to the protein surface [Eqns (2) and (7)]. For the subsequent discussion it is convenient to subdivide the values of ACf and AC; into the following sums: 1

~ ( 2 ,

+ ( a - b)AG;'" , ACZ = dAC&' + h ) ACZ",

AC;' = bAC;"

(12)

(13) where AG;' and AG,"' are free energies of desolvation of bound water molecules that eventually will leave the protein surface and that will remain bound to it, respectively, AGZ" is the free (0-

Considering the values of AG,"' and AC,"',we assume that in the first approximation the free energy of solvation of a solvent molecule in the free state is about twice as high as the free energy of solvation of the same molecule bound to the protein surface, because in the latter situation roughly one half of the bound molecule is shielded from the contact with surrounding solution by the protein surface. Using this approximation, we obtain AG,"'= -SAG:, (15 ) Combination of Eqns (9) and (11 - 16) gives

where n = d/b

This ratio indicates how many molecules of water can be displaced from the protein surface by one molecule of the organic cosolvent. In the first approximation, the value of n can be assessed from comparison of geometric molecular characteristics of water and organic cosolvent, following the idea that the bigger the cosolvent molecule, the more water molecules it will displace from the protein surface. One of geometric characteristics that can be used to make such a comparison is the surface area of a n isolated solvent molecule. This value can be calculated using the approach suggested by Bondi [37], according to which the surface area of any organic molecule can be found by simple summation of surface areas of basic atomic groups (- CH2-, -OH, - NH2,etc.) present in the molecule. We used this approach to calculate molecular surface areas of organic solvents listed in Table 1. The water molecule was regarded as a sphere with a radius of 0.14 nm [38]. The values of n were calculated as the ratio of molecular surface area of water (A,) to that of corresponding organic cosolvent (Aorg): n = Aw/Aorg, (19 ) and are given in Table 2. In order to check the validity of this approach, we calculated molecular surface areas of different amino acids and compared them with corresponding accessible surface areas available from literature [39, 401. The results are presented in Fig. 4, which shows that there is a satisfactory correlation between calculated and literature values. This means that the calculated molecular surface area is a reasonable quantitative estimate for assessing relative sizes of simple molecules and can be used for the determination of n according to Eqn (29). Under such a definition of n, the sum in brackets standing in the right of Eqn ( 3 7) represents the difference between the free energy of solvation of water and the free energy of solvation of the number of molecules of the organic cosolvent possessing the same total molecular surface area as the number of water molecules taken. The direct evaluation of this difference, which can be designated AAG,",is a difficult task, because there is no simple way to determine solvation free energies of water and organic cosolvent in their mixtures of varying

31

1

1 0.2

1

, 0.6

,

1 1.0

,

,

,

1.4

1 1.8

,

,

,

2.2

A,,, (nm2)

Fig. 4. Correlation herween molecular surface areas ($different amino and acids calculated according to the method of Bondi /37J (ABondi) corresponding accessible surface areas taken f r o m literature [ 3 9 , 4 0 ] (Aliti

compositions. Therefore, we turned to the analysis of the solvation behavior of model compounds in water/organic binary mixtures. We analyzed the literature data [41] on the solubility behavior of several hydrocarbons (hexane, heptane, benzene, toluene and xylene) in wateriethanol binary mixtures and calculated AAG," for different pairs of hydrocarbons using the following expression for the solvation free energy [42]: AG,'; = - R T l n X , , (20) where A', is the solubility of the hydrocarbon in a given binary mixture, expressed in mole fractions, R is the gas constant, and Tis the absolute temperature. For a pair of hydrocarbons 1 and 2 we can write [cf. the term in brackets in Eqn (17)]:

,

20

I

,

60

/

100

Cethano,(vol./l OOVOI.)

Fig. 5. Dependence of AAG: f o r different pairs of hydrocarbons dissolved in waterlethanol mixtures of various compositions. (a) Hcxane/ heptane, 30°C; (b) toluene/benzene, 30°C; (c) toluene/xylene, 25 C. Calculated molecular surface areas are 1.60 nm2 for hexane, 1.83 nm2 for hepatane, 1.37 nm2 for xylene, 1.I8 nm2 for toluene, and 1.OO nm2 for benzene. Temperatures are 30°C and 25°C for the first and second pairs, respectively. See text for detailed explanations

where a3 and a4 are numerical coefficients, and where A l and A 2 are molecular surface areas of hydrocarbons 1 and 2 , respectively, calculated as described above from incremental surface areas of constituting atomic groups. Dependences of AAG;" on the composition of binary wateriethanol mixtures calculated using Eqn (21) for several pairs of hydrocarbons are shown in Fig. 5. It is seen that AAG," is fairly constant over a wide range of compositions of the binary mixtures. On these grounds we can conclude that the sum in brackets in Eqn (17) is approximately the same in water/ organic mixtures and in pure water. This conclusion has two important implications. First, the value of AG,O in Eqn (17) becomes a constant, because it now represents the free energy of hydration of water [cf. Eqn (4)] which, of course, depends neither on the nature of the organic cosolvent, nor on that of the protein. Second, the value of AG," now corresponds to the process of dehydration of the organic cosolvent [cf. Eqn (5)], e.g. to the transfer of the cosolvent from water to vacuum. The free energy of the latter process is known [43] to correlate linearly with the free energy of the transfer from water to octanol, AG;',,, so that we can write

+

AG,O = LX~AG,",,~ ( 4 ,

(22)

AG,",,=

-

2.3RT lOgP,

(23)

where P is the partition coefficient of the cosolvent in water/ octanol biphasic system, which is defined [44] as the ratio of equilibrium concentrations of the cosolvent in octanol and water phases of the biphasic system:

The latter relation indicates that higher P values correspond to more hydrophobic organic solvents. The P values for different solvents are well documented [441; those relevant for the present study are given in Table 2. By combining Eqns (22) and (23) with Eqn (17), one easily obtains AGE, = BA

+ Bin + BiE.,(30) + Bin logP.

(25)

where coefficients Bi include all constant parameters defined in the preceding discussion and remain unchanged for a given protein at constant temperature regardless of the nature of

38 Table 3. Coefjcients of Eqn (28) for diflerent proteins Abbreviations: FA, formamide; MFA, N-methylformamide;DMFA, N,N-dimethylformamide;Me2S0,dimethyl sulfoxide; MeOH, methanol Protein

‘Bad’ solvents

Bo

B1

B~ x i 0 3

B3

R squared

a-Chymotrypsin Laccase Trypsin Myoglobulin Cytochrome c Chymotrypsinogen

FA, MFA FA, MFA, MeOH MFA, Me2S0 FA, MFA, DMFA

2.58 2.02 1.80 1.99 1.79 1.42

0.65 1.16 1.20 1.16 I .08 1.21

- 5.2

-0.21 -0.31 0.20 -0.27 0.30 0.52

0.91 0.90 0.83 0.94 0.93 0.91

2-butanol -

the organic cosolvent used as a denaturant. O n the other hand, AG:;, can be expressed according to Eqn (1) as follows: AGE, = -2.3RTlogK [ D . ( a - b ) H 2 0 .dS][H2OIb = -2.3RT [ N .aH2O][SId

(26)

(‘50

(27)

4 0

where W s 0is the critical concentration of water in the system at which half denaturation of the protein occurs, and n = d/b is defined by Eqn (18). Combination of Eqns (25) and (27) gives log

w 50 ~

= Bo

+ B l n + B2ET(30)+ B,n

logP,

does exist. Reasons for the occurrence of ‘bad’ solvents are not yet clear; one possible explanation is that the interaction between such solvents and protein molecules involves some specific aspects not allowed for by the present model. Denaturation capacity of organic solvents

Under conditions corresponding to the half inactivation of the protein, i.e. when [S] = ~ 5 (see 0 Fig. 1) and hence [D . (ab ) H 2 0 . d S ] = [ N . a H 2 0 ] ,Eqn (26) becomes AG& = - 2 . 3 R T l o W,”O g T = -2.3RTblog-, W50

-2.4 - 2.4 - 2.4 - 2.4 -0.01

(28)

4 0

where coefficients Bi = - Bli2.3RTb are constant for a given protein at constant temperature. In order to check the validity of the model for describing protein denaturation by organic solvents, we performed the regression analysis of the experimental data from Table 1 according to Eqn (28) using the Statgrafics computer program. The results of the computer analysis are given in Table 3. The quality of the correlation described by Eqn (28), as judged by the value of the adjusted coefficient of determination, R squared [45] (Table 3), was good for all proteins tested. This means that the above model provides a reasonably adequate description of protein denaturation by organic solvents. One following point concerning the results of the computer correlation analysis deserves a special comment. It turned out that in most cases a good correlation could be achieved only if certain solvents had been excluded from the analysis. The data in Table 3 refer to the sets of solvents for which the best correlation for each protein was obtained after trying numerous different solvent combinations (data not shown). ‘Bad’ solvents, that do not comply with Eqn (28) and are therefore excluded from correlation, are indicated in Table 3 for each protein. Comparison of ‘bad’ solvent sets corresponding to different proteins shows that these sets invariably include a fixed subgroup containing formamide and N-methylformamide (provided, of course, that these solvents were tested at all). We realize, of course, that the number of proteins included in the analysis is too limited for any decisive conclusions to be made, and therefore a more thorough treatment based on a broader series of proteins may bring about some changes into the subgroup of ‘bad’ solvents. However, even at the present stage there is little doubt that such a subgroup

Close inspection of the data in Table 1 shows that if one arranges the solvents in the order of increasing log (Wso/ ego), the sequence of solvents will be similar for different proteins. This implies that the value of log ( W,ojc;o) may be regarded as a universal measure of denaturing ability of organic solvents, or, in other words, it is possible to construct a scale of denaturing strength of organic solvents based on log ( Wso/c;o).As a basis for such a scale we chose the data set for a-chymotrypsin, because it includes the largest number of organic solvents (Table 1) and provides a good correlation as described by Eqn (28) (Table 3). For construction of the scale, we employed the values of log (W50/cto)calculated from Eqn (28) using coefficients Bi for a-chymotrypsin (Table 3), rather than experimental ones, because in the former case we saw better chances to eliminate random deviations due to experimental errors and/or possible minor unaccounted specific interactions of organic solvents with the particular protein, a-chymotrypsin. The scale was produced simply by ascribing arbitrary values of 0 and 100 to the lowest (corresponding to formamide) and the highest (corresponding to tetrahydrofuran) calculated values of log ( W50/c!j’o), respectively, and the values for all intermediate solvents were then calculated from the simple proportion. In order to designate the new parameter introduced in this way, we propose the term denaturation capacity, or DC. Thus

THF, calc

FA, calc

where subscripts FA, T H F and x refer to formamide, tetrahydrofuran and an intermediate solvent, respectively. The values of D C calculated for different solvents as described above are given in Table 2. Taken together, these values form the D C scale of organic solvents, which provides a quantitative means of assessing the relative ability of different organic solvents to exert denaturing effect on proteins : the higher the D C of the solvent, the stronger its denaturing ability. It is worthwhile to note that ethylene glycol, glycerol and methanol are among the solvents possessing the lowest values of DC. This observation is in full agreement with generally accepted empirical knowledge that these solvents, being relatively mild protein denaturants, represent the most favorable substitutes

39 of water as a solvent for proteins, for example, in cryoenzymological studies. Formamide, which has the lowest value of DC, is an exception in the sense that this solvent, being a member of the subgroup of ‘bad’ solvents, in fact possesses significantly higher denaturation strength than predicted by the DC scale (cf. the data in Tables 1 and 2). The DC parameter can be used as a quantitative criterion for selection of organic solvents to be employed as components of the reaction medium for enzyme-catalyzed reactions. To put it differently, the DC scale enables one to predict the value of ~ 5 for 0 a given organic solvent taken in combination with any enzyme (protein). To make such a prediction for a particular protein, one first has to measure experimentally ~ 5 values 0 for any two solvents with known DC values in order to adjust the arbitrary DC scale to the protein under study. The value of log (W50jc;o) for any other organic solvent is then easily calculated from simple proportion as follows:

where subscripts 1, 2 and x refer to the pair of reference solvents and the solvent to be tested, respectively. The value of ( ~ 5 0 can ) ~ then be extracted from [log ( W50/c;o)]x using, for example, the calibration curve drawn in coordinates ( ~ 5 0 vs. ) ~ [log(Wso/c;o)lx. In this calculation procedure, the important question is how to choose reference solvents. In order to make a proper choice, it is useful to follow several simple recommendations. First, the difference between DC values of reference solvents should be as high as possible. Second, it is quite obvious that solvents from the ‘bad’ subgroup (such as formamide and Nmethylformamide) should not be used as references. Here, the difficulty is that the limits of this subgroup remain rather uncertain, and a solvent proved to be good for one protein may turn out to be bad for another (see Table 3). This uncertainty will probably be eliminated in further studies; for the time being we recommend the use as references of those solvents that were found to fit well the correlation described by Eqn (28) for all proteins tested, such as ethylene glycol, glycerol, ethanol, l-propanol, 2-propanol, 1,4-dioxane, tetrahydrofuran, hexamethylphosphoramide, acetonitrile, 1,2propanediol and acetone. We used the above approach to calculate cso values for different organic solvents and proteins. Results are presented in Table 1 where experimentally determined ~ 5 values 0 are also given. It is seen that for all proteins tested predicted and experimental values are in general agreement with each other. Exceptions, as a rule, are represented by ‘bad’ solvents defined above (Table 3 ) and perhaps also by isomeric butyl alcohols which show significant deviations of calculated values from experimental ones more frequently than other alcohols. For this reason predictions made for butyl alcohols should be treated with caution. Furthermore, we made sure that calculated values of ~ 5 are 0 only slightly affected by the choice of reference solvents, provided that they are selected from the subgroup of ‘good’ solvents defined above. As an example, Fig. 6 shows the correlation between ~ 5 values 0 for different organic solvents calculated for myoglobin using ethyleneglycol and acetone or 1,2-propanediol and tetrahydrofuran as pairs of reference solvents. Thus, we conclude that the DC

1

/

h

7

-

0 17

60-

0

> -

50-

0

.? 4 0 -

i zr

6 0“

30-

20- *3 *2

10

20

30

40

cs0 (EG-AC)

50

60

70

80

90

(VO1./1OOVOl.)

Fig. 6. Correlation between threshold concentrations of d$ferent organic solvents calculated for rnyoglobin using ethylene glycol and acetone [cso ( E G - A C ) ] or 1,2-propanediol and tetrahydrofuran [cso ( P D - T H F ) ] as pairs of reference solvents. 1, tetrahydrofuran; 2 , 1,4-dioxane; 3, 2-methyl-2-propano1, 4, acetone; 5 , 2-butanol/hexamethylphosphoramide; 6, acetonitrile; 7, I-butanol; 8, 2-propanol ; 9, l-propanol; 10, sulfolane; 11, ethanol; 12, N,N-dimethylformamide; 13, dimethyl sulfoxide; 14, methanol; 15, N-methylformamide; 16, 1,2-propanediol; 17, formamide; 18, ethylene glycol

scale can be successfully used in practice to obtain reasonable quantitative estimates of limiting concentrations of different organic cosolvents at which proteins (enzymes) still retain their native (e. g. catalytically active) state. It is to be stressed that there is no straightforward correlation between DC and ~ 5 0 In . other words, higher values of DC do not automatically imply lower values of cs0, despite the fact that the overall trend along the DC scale as a whole does show the decrease in ~ 5 with 0 increasing DC. As one can see from the data in Tables 1 and 2, in certain parts of the scale the situation may be reverse. The reason for such a behavior is that log (W50/~;0), which is proportional to DC, depends not only on ~ 5 0 but , also on n, and the latter value differs significantly for different solvents (see Table 2). The case of organic solvents not miscible with water

The DC scale given in Table 2 can be extended to include any additional organic solvent provided that logP, ET and n values for this solvent are available. Then log (W50jc;o) and corresponding DC value can be easily calculated using Eqn (28) with coefficients Bi for a-chymotrypsin (Table 3 ) and Eqn (29). The DC values found in this way may be useful for assessing the denaturing strength of organic solvents in cases when the direct measurement of c50 is hardly possible, e. g. because of low solubility of the organic solvent. We used this approach to estimate ~ 5 for 0 several nonpolar organic solvents frequently employed for construction of biphasic systems of the type water/water-immiscible organic solvent. The results of calculations for six different proteins are given in Table 4 which also contains solubilities of organic solvents in water taken from the literature [41] (reference solvents used in these calculations were the same as in Table 1). Inspection of the data in Table 4 shows that in all cases calculated c50 values are higher than solubilities of corresponding solvents in water, or at least are comparable with them. This

40 Table 4. Calculated threshold concentrations (mole 1- ’) of nonpolar organic solvents f o r d8erent proteins. CT, a-chymotrypsin; LC,laccase; TR,trypsin; MG, myoglobin; CTG,chymotrypsinogen; CC,cytochrome c; S, solubility in water Solvent

log P

&(30)

n

DC

kJ/mol Hexane Chloroform Benzene Diisopropyl ether Ethyl acetate Toluene

3.51 1.71 2.15 2.03 0.83 2.80

129 164 144 142 159 142

s

x 102

c50

x 102

CT

LC

TR

MG

CTG

CC

1 16 3.3 2 19 1.5

3 75 22 32 132 12

7.0 120 39 60 220 24

1 50 15 20 110 6

0.1 8 2.2 2 20 0.7

0.5 37 10 9 87 3

mol/l 0.154 0.246 0.247 0.144 0.191 0.199

144.4 116.7 133.9 121.7 102.9 137.9

means that despite a very high denaturing strength of nonpolar solvents, as judged from their high D C values (Table 4), only in rare cases proteins can be denatured by such solvents in solution due to the simple fact that the latter are not enough soluble in water to reach the inactivation threshold. We confirmed this conclusion experimentally by measuring catalytic activities (expressed in terms of the maximal velocity, Vm) of a-chymotrypsin, trypsin and laccase in aqueous solutions saturated with organic solvents indicated in Table 4. In each of 18 reaction systems (each of the three enzymes was tested in combination with each of the six organic solvents from Table 4) the observed catalytic activity was identical to that observed in purely aqueous solution (data not shown). This result explains a very well known and widely used property of enzymes to retain the catalytic activity and stability in biphasic systems composed of water and a nonpolar organic solvent. Concluding this section, we would like to stress that when the above approach is to be used for practical assessment of enzyme stability in biphasic systems, one should keep in mind that enzymes in such systems can be inactivated also because of highly specific interactions with the organic solvent and/or as a result of the adsorption at the interface [46-491; these types of the inactivation mechanism are not taken into account by the present model. Concluding remarks

The most important result of the present work is the thermodynamic model of protein denaturation by organic solvents in solution, which explains the molecular mechanism of the denaturation process and establishes a quantitative relation between physicochemical properties of organic solvents and their denaturing strength. As a useful practical outcome, this relationship enables one to construct the D C (denaturation capacity) scale of organic solvents permitting to predict quantitatively limiting concentrations of various organic solvents at which dissolved proteins still retain their native properties. It is possible that future studies, involving a larger number of proteins of different nature (e. g. proteins with quarternary structure), may introduce some refinements into the D C scale concerning, for example, actual values of the D C parameter for different solvents or the problem of so-called ‘bad’ solvents not complying with the denaturation model and the D C scale. However, our results show that even in its present form, the D C scale can be successfully used in practical work for optimization of enzyme-catalyzed processes proceeding in reaction systems containing organic solvents.

0.16 9.1 1.1 2.5 9.9 0.51

The authors are grateful to Professor A. V. Lcvashov for helpful discussions.

REFERENCES 1. Tramper, J., Van der Plas, H. C. & Linko, P., eds (1985) Biocatalysis in organic synthesis, Elsevier, Amsterdam. 2. Laane, C.,Tramper, J. & Lilly, M. D., eds (1987) Biocatalysis in organic media, Elsevier, Amsterdam. 3. Khmelnitsky, Yu. L., Levashov, A. V., Klyachko, N. L. & Martinek, K. (1988) Enzyme Microb. Technol. 10, 710-724. 4. Klibanov, A. M., Semenov, A. N., Samokhin, G . P. & Martinek, K. (1978) Bioorg. Khimiya 4, 82-87. 5. Martinek, K. & Semenov, A. N. (1981) J . Appl. Biochem. 3,93126. 6. Ray, A. (1971) Nature231, 313-315. 7. Martinek, K., Klibanov, A. M. & Berezin, I. V. (1977) J . SolidPhase Biochem. 2, 343 - 385. 8. Freeman, A. & Lilly, M. D. (1987) A@. Microb. Biotechnol. 25, 495 - 501. 9. Rodionova, M. V., Belova, A. B., Mozhaev, V. V. & Berezin, I. V. (1988) Biotekhnologiya 4 , 69 -72. 10. Mozhaev, V. V., Khmelnitsky, Yu. L.,Sergeeva, M. V., Belova, A. B., Klyachko, N. L., Levashov, A. V. & Martinek, K. (1989) Eur. J . Biochem. 184, 597-602. 11. Schonbaum, G. R., Zerner, B. & Bender, M. L. (1961) J . Biol. Chem. 236,2930-2935. 12. Perrin, D. D., Armagero, W. L. F. & Perrin, D. R. (1980) Purification of laboratory chemicals, Pergamon Press, Oxford. 13. Elodi, P. (1961) Actu Physiol. Acad. Sci. Hung. 20, 311 -323. 14. Bettelheim, F. A. & Senatore, P. (1964) J . Chim. Phys. Phys. Chim. Biol. 61, 105-110. 15. Villanueva, G. B., Batt, C. W. & Brunner W. (1974) J . Chem. SOC.Chem. Commun. 766- 767. 16. Adams, P. A., Baldwin, B. A., Collier, G . S. & Pratt, J. M. (1979) Biochem. J . 179, 273 - 280. 17. Duran, N., Baeza, J., Brunet, E. J., Gonzalez, G. A., Sotornayor, P. C. & Faljoni-Alario, A. (1981) Biochem. Biophys. Res. Commun. 103, 131 - 138. 18. Kise, H., Shirato, H. & Noritomi, H. (1987) Bull. Chem. Soc. Japan 60, 3613-3618. 19. Herskovits, T. T. & Jaillet, H. (1969) Science 163, 282-285. 20. Herskovits, T. T.,Gadegbeku, B. & Jaillet, H. (1970) J . Biol. Chem. 245, 2588 - 2598. 21. Singer, S. J. (1962) Adv. Protein Chem. 17, 1-68. 22. Tanford, C.(1 968) Adv. Protein Chem. 23, 122 - 282. 23. Timasheff, S. N. (1970) Acc. Chem. Res. 3, 62-68. 24. Ebina, S., Suzuki, M., Naitoh, I., Yamauchi, K. & Nagai, Y. (1982) Int. J . Biol. Macromol. 4, 406 - 41 2. 25. Kuntz, I. D. & Kauzmann, W. (1974) Adv. Protein Chem. 28, 239 - 345.

41 26. Rupley, J . A,, Gratton, E. & Careri, G. (1983) Trends Biochem. Sci. 8, 18-22. 27. Gekko, K. & Timasheff, S. N. (1981) Biochemistry 20, 46674676. 28. Gekko, K. & Morikawa, T. (1981) J . Biochem. (Tokyo) YO, 3950. 29. Zaks, A. & Klibanov, A. M. (1988) J . Biol. Chem. (Tokyo) 263, 8017 - 8021. 30. Butler, L. G. (1979) Enzyme Microb. Technol. I , 253-259. 31. Schulz, G. E. & Schirmer, R. D. (1979) Principles of protein structure, Springer-Verlag, Berlin. 32. Reichardt, C. (1979) Solvent exfects in organic chemistry, Verlag Chemie. Weinheim. 33. Kamlet, M . J., Abboud, J. L. & Taft, R. W. (1981) Prog. Phys. Org. Chenz. 13, 485-630. 34. Reichardt, C . (1979) Angew. Chem. Int. Ed. Engl. 18, 98- 130. 35. Carlson, R., Lundstedt, T. & Albano, C. (1985) Acta Chem. Scand. B39, 79 - 91. 36. Stolarova, M., Buchtova, M. & Bekarek, V. (1984) Acta Univ. Palacki. Olomuc. Fac. Rerum Nat. Bid. 79, 77-88. 37. Bondi, A. (1964) J . Phys. Chem. 68, 411-451.

38. Ooi, T., Oobatake, M., Nemethy, G. & Scheraga, H. A. (1987) Proc. Nut1 Acad. Sci. USA 84, 3086 - 3090. 39. Chothia, C. (1976) J . Mol. Biol. 105, 1-14, 40. Richards, F. M. (1977) Annu. Rev. Biophys. Bioeng. 6, 151 -176. 41. Kogan, V. B., Fridman, V. M. & Kafarov, V. V., eds (1963) Solubility handbook, vol2, Academy of Sciences of the USSR, Moscow. 42. Tanford, C. (1980) The hydrophobic effect: formation ofmicelles and biological membranes, Wiley, New York. 43. Rose, G. D., Gierasch, L. M. & Smith, G. A. (1985) Adv. Protein Chem. 37, 1 - 109. 44. Leo, A,, Hansch, C. & Elkins, D. (1971) Chem. Rev. 71, 525616. 45. Afifi, A. A. & Azen, S. P. (1979) Statistical analysis. A computer oriented approach, Academic Press, New York. 46. Ghosh, S. & Bull, H. B. (1962) Arch. Biochem. Biophys. 9Y, 121 125. 47. Cecil, R. & Louis, C. F. (1970) Biochem. J . 117, 139-145. 48. Philips. M. C. (1977) Chem. Ind. (Lond.) 1, 170-176. 49. Graham, D. E. & Philips, M . C. (1979) J . Colloid Inte~jac,cSci. 70,427-439.