Non-isothermal bioreactors utilizing catalytic Te¯on membranes

M.S. Mohy Eldin1,a, A. De Maioa,b, S. Di Martinoa, M. Portaccioa,b, S. Stellatoa,U. Bencivengaa, S. Rossia, M. Santuccia, P. Canciglia2,a, F.S. Gaetaa, D.G. Mitaa,b,*

aInternational Institute of Genetics and Biophysics of CNR, via Guglielmo Marconi, 12, 80125 Naples, ItalybDepartment of Human Physiology and Integrated Biological Functions, Second University of Naples, via SM di Costantinopoli, 16,

80138 Naples, Italy

Received 1 December 1997; received in revised form 1 April 1998; accepted 3 April 1998

Abstract

A hydrophobic and catalytic membrane has been obtained by grafting with -radiations a Te¯on membrane in presence of

methylmethacrylate solution and by immobilizing on it, after treatment with glutaraldehyde, the b-Galactosidase enzyme.

When employed in a non-isothermal bioreactor, the membrane showed an increase in catalytic activity proportional to the

applied temperature gradients. The results have been explained in terms of distinct contributions from the process of

thermodialysis and the conformational changes induced in the dynamic structure of the enzyme by the presence of heat ¯ow.

The increase of the yield of the process has been evaluated in terms of a coef®cient � representing the percent increase of

enzyme activity when a temperature difference of 18C is applied across the membrane. The catalytic Te¯on membrane used

here gave values of 20%, which are comparable to those obtained with other membrane systems, making this kind of

membrane useful for practical applications in industrial processes. # 1998 Elsevier Science B.V. All rights reserved.

Keywords: Biocatalytic membranes; Non-isothermal bioreactors; b-Galactosidase; Grafted membranes

1. Introduction

Catalytic membranes are commonly employed in

industrial processes and in analytical apparatuses

[1±5]. All these applications are performed with bio-

reactors or instruments operating under isothermal

conditions.

It has been recently demonstrated that the ef®ciency

of enzymatic processes is increased [6±12] when the

catalytic membranes are employed in bioreactors

operating under non-isothermal conditions. The

increase is linearly proportional to the temperature

gradient applied across the catalytic membrane and

depends on the nature of the enzyme and on the

immobilization methods. Mesophilic and thermophi-

lic enzymes were employed in these studies. Analo-

gous results have been obtained with immobilized

microorganisms. In this case the temperature gradients

affected the activity of either wall or internal enzymes.

In all the non-isothermal experiments performed

until now the membrane system employed used two

Journal of Membrane Science 146 (1998) 237±248

*Corresponding author. Tel.: +39 81 2395887; fax: +39 81

2395887; e-mail: Mita@iigbna.iigb.na.cnr.it1Permanent address: Department of Polymers and Pigments,

National Research Center, Dokki, Cairo, Egypt.2Permanent address: Institute of General Physiology of the

University of Messina, Salita Sperone, 36, Messina, Italy.

0376-7388/98/$19.00 # 1998 Elsevier Science B.V. All rights reserved.

P I I S 0 3 7 6 - 7 3 8 8 ( 9 8 ) 0 0 1 1 2 - 4

membranes: one catalytic and the other a hydrophobic

Te¯on membrane. The presence of a hydrophobic

membrane is essential since it allows non-isothermal

selective mass transport when interposed between two

aqueous solutions kept at different temperatures. This

process, known as thermodialysis [13±17], occurs

only across hydrophobic membranes and the observed

selectivity is due to the differential effects on solute

and solvent particles by the radiation pressure of

thermal waves associated to the existence of thermal

gradients [18±20]. The process of thermodialysis has

been indicated as one of the causes responsible for the

increase of the activity of enzymes immobilized under

non-isothermal conditions [6±12].

The use of two membranes, however, introduces

some complications in the elaboration of a simple

theory of the observed effects and in the construction

of non-isothermal bioreactors to be employed in

industrial processes. For this reason we have tried

to prepare a single membrane, that is both catalytic

and hydrophobic. The way to obtain such a membrane

is reported and the study of its behaviour in a bio-

reactor operating under isothermal and non-isothermal

conditions is presented.

2. Apparatus, materials and methods

2.1. The apparatus

The apparatus employed consisted of two cylind-

rical half-cells (Fig. 1), ®lled with the working solu-

tion and separated by a planar membrane. In these

Fig. 1. Schematic (not to scale) representation of the bioreactor: (A) half-cells; (B) internal working volumes; (C) external working volume;

(M) membrane; (n) supporting nets; (th)�thermocouples; (Si)�stopcocks; (T)�thermostatic magnetic stirrer; (PPi)�peristaltic pumps.

238 M.S. Mohy Eldin et al. / Journal of Membrane Science 146 (1998) 237±248

experiments both solutions are recirculated in each

half-cell by means of a peristaltic pump through

hydraulic circuits starting and ending in the common

cylinder C. Each half-cell was thermostatted at a

temperature Ti (i�1,2). When the apparatus worked

under isothermal conditions T1 was equal to T2. Ther-

mocouples, placed at 1.5 mm from each of the mem-

brane surfaces, measured the temperatures inside each

half-cell and allowed the calculation of the tempera-

ture pro®le across the catalytic membrane when the

apparatus was kept under non-isothermal conditions.

The temperatures read by the thermocouples will be

indicated by T, while the ones calculated at the mem-

brane surfaces by the symbol T*. The values related to

warm and cold sides are indicated by the subscripts w

and c, respectively. Under these assumptions �T �Tw ÿ Tc and �T� � T�w ÿ T�c , as well as Tav � �Tw�Tc�=2 and T�av � �T�w � T�c �=2. In non-isothermal

experiments T�w < Tw; T�c > Tc and �T� < �T .

2.2. The catalyst

b-Galactosidase from Aspergillus oryzae, pur-

chased from Sigma, has been used for immobilization.

b-Galactosidase hydrolyses lactose to glucose and

galactose. The kinetics parameters for this enzyme

in its free form are Km�21.4 mM and Vmax�3.2 mmol minÿ1 [21]. Enzyme activity was deter-

mined by sampling at regular time intervals the solu-

tion in the cylinder C and measuring the glucose

concentration by the GOD±Perid test. Activity was

expressed as mmol minÿ1.

The duration of each experiment was 30 min. Every

experimental point in the ®gures represents the aver-

age value of four different trials performed under the

same conditions. In all cases the experimental error

never exceeded 3%.

All reagents used were of analytical grade,

purchased from Sigma.

2.3. The catalytic membrane

The catalytic membrane was prepared in two steps.

The ®rst step concerned the grafting of the membrane

with an acrylic monomer in the presence of -radia-

tions. The second step was the enzyme immobilization

process, in absence of -radiation, using glutaralde-

hyde as cross-linking agent.

The monomer used for the grafting was methyl-

methacrylate (MMA). As solid support was used a

polytetra¯uoroethylene (PTFE) membrane of the type

TF-450, manufactured by Gelman. This membrane,

constituted of a Te¯on ®lm supported on one side by a

polypropylene net, has a thickness of 150 mm and is

endowed with anatomizing pores 0.45 mm in nominal

diameter. In these membranes the de®nition of pore is

not that of a well de®ned channel crossing all the

membrane thickness but the one of anatomizing cav-

ities connecting two liquid media separated by the

membrane through the interstitial spaces. In this frame

of reference the pore size is a measure of the minimum

diameter of the molecular species which the mem-

brane is able to retain.

To distinguish the data relative to the two different

surfaces of the membrane we will henceforward indi-

cate by subscripts p and t the polypropylene side and

the Te¯on side, respectively. In this way Ap and T�pindicate the values of the activity and temperature of

the polypropylene side, while At and T�t indicate the

corresponding values at the Te¯on side.

The irradiation source was Caesium 137 in a

gamma cell 1000 Elyte by Nordion. The average dose

rate in the core of the radiation chamber (central dose

rate) was 2.35� 104 (rad hÿ1). The irradiation time was

16 h during which the membrane was immersed in a

3% (v/v) MMA aqueous solution (25% ethanol (v/v)).

After this operation the grafted membrane was

washed with tetrahydrofurane (THF) to remove the

adherent MMA homopolymers, then dried at 508Cuntil a constant weight is obtained. A grafting degree

of 15% has been estimated. The grafting degree was

determined by the difference between membrane

masses after (GA) and before (GB) the grafting,

according to the expression x�%� � �GA ÿ GB�=GB � 100.

At this point the membrane was soaked in a 2.5%

(v/v) glutaraldehyde aqueous solution at room tem-

perature for 1 h and then washed with double distilled

water.

After drying at 408C the membrane was soaked for

16 h at 48C in an enzyme [45 mg mlÿ1] phosphate

buffer solution at pH 6.5. At the end of this operation

the membrane was washed with the same buffer

solution to remove the un-crosslinked enzymes.

The time stability of the biocatalytic membranes

was assessed by analysing every day their activity

M.S. Mohy Eldin et al. / Journal of Membrane Science 146 (1998) 237±248 239

under the same experimental conditions. After the ®rst

three days, during which the membranes lost some

activity, a stable condition was reached which

remained unchanged for over two months. Only these

stabilized membranes were used in the experiments

reported in the following. When not utilized, the

membranes were stored at 48C in 0.1 M buffer phos-

phate pH 6.5.

2.4. The temperature profile in the apparatus

To effect the right comparisons between isothermal

and non-isothermal experiments, the temperature pro-

®le in the apparatus and in the catalytic membrane

must be known. Since it is not possible to measure the

temperatures right at the faces of the membrane these

can be calculated on the basis of the continuity of heat

¯ux knowing the thermal conductivities and thick-

nesses of both ®lling solutions and membrane. It is

important, at this point, to determine the kind of ¯ow

regime within each half-cell. The two ®ns in Fig. 2(a)

function as deviators of the circulating ¯ow coming

from the peristaltic pump. To decrease the probability

and the size of eddies production, the tips of the ®ns

were rounded. From Fig. 2(a) it is possible to observe

that the duct where liquid solution ¯ows is rectangular

with dimensions a�2.2 cm and b�0.25 cm, a being

the distance between the two ®ns and b the thickness

of the half-cell. The hydraulic ¯ow in this duct is

determined by the value of the Reynolds number

Re � �hviDeq=�, where � and � are viscosity and

density of the working solutions, Deq is the equivalent

hydraulic diameter (Deq�4 S/z�0.45 cm, with

S�0.55 cm2 and z�4.9 cm) and hvi is the average

velocity of the solution ¯ow induced by the peristaltic

pumps. In the above S is the cross-section and z the

wetted perimeter of the duct, while hvi �cm sÿ1� �Q=S in our case is equal to 7.57�10ÿ2 cm sÿ1 since

Q�4.1�10ÿ2 cm3 sÿ1. In this way Re becomes <10.

This result suggests that solution ¯ow in each half-cell

Fig. 2. (a) Exploded view of a half-cell evidencing the hydraulic flow, parallel to the membrane, and constrained by two deviating fins. The

other, identical half-cell, is contiguous along the vertical (the abscissae axis in the test). The cross-sectional area drawn defines the plane

normal to fluid flow between the fin's tips. (b) Side view of the cell (sagittal section), showing position of thermocouple and membrane. Heat

flux is along the abscissae axis. (c) Temperature profile in the solutions filling the two half-cells and into the membrane thickness. While the

units on the ordinates axis are arbitrary, the ones on the abscissae axis are real, with the exception of the membrane thickness.

240 M.S. Mohy Eldin et al. / Journal of Membrane Science 146 (1998) 237±248

is laminar and that, accordingly, heat transport occur-

ring perpendicular to the ¯ow direction (Fig. 2(b)) is

essentially conductive, hydrodynamic advective con-

tribution being absent. This has also the consequence

of avoiding mixing of ¯uid ¯ows along the various yz-

planes along x. This liquid ¯ux occurs along essen-

tially isothermal planes in the central region of each

half-cell. This circumstance excludes the presence of

heat transport by convection along x and, accordingly,

the temperature pro®les in the liquid solutions and in

the membranes can be directly calculated by Fourier's

law. By means of computer simulation the values of

the temperatures at each point of the apparatus have

been calculated and, hence, also those at the two

surfaces of the catalytic membrane. In this way the

temperature pro®le in the bioreactor can be drawn as

in Fig. 2(c), where arbitrary units have been used for

the temperature. The temperatures on the membrane

surfaces, reported in Table 1, should be referenced for

evaluating the existence and size of the effect of non-

isothermal conditions on enzyme activity. Membrane

effective temperatures are indicated in the table by T�wand T�c without reference to the nature (Te¯on or

polypropylene) of the surface exposed to the imping-

ing heat ¯ow.

3. Results and discussion

3.1. Isothermal experiments

All the results reported here in the following were

obtained with a 0.2 M lactose solution in phosphate

buffer solution at pH 6.5.

With the aim of characterizing the catalytic mem-

brane its activity has been assessed under isothermal

conditions.

In Fig. 3(a) the isothermal glucose production is

reported as a function of time, in the temperature range

between 158C and 558C. The slopes of these plots,

which give the rates of glucose production, are

reported in Fig. 3(b) as a function of the temperature

of the bioreactor. These data, indicated by the symbol

(&), refer to experiments performed with 25 ml of

substrate solution recirculated through the half-cells

by means of two hydraulic circuits starting and ending

in the common cylinder C. For this reason these data

represent the total membrane activity. Since the mem-

brane is asymmetric, with a polypropylene supporting

net built in one side of the Te¯on mesh, the activity of

each of the two surfaces has been also separately

measured. This has been done recirculating separately

Table 1

Correspondence between the temperature values read by the thermocouples T and those calculated for the catalytic membrane surfaces T* on

the basis of the equation of heat conduction and of a non-turbulent motion of the solution in each of the two half-cells constituting the

bioreactor.

Tav (8C) �T (8C) TW (8C) TC (8C) T�av (8C) �T* (8C) T�w (8C) T�C (8C)

20 10 25 15 20 0.9 20.5 19.6

20 30 10 1.8 20.9 19.1

30 35 5 2.7 21.3 18.6

25 10 30 20 25 0.9 25.5 24.6

20 35 15 1.8 25.9 24.1

30 40 10 2.7 26.3 23.6

30 10 35 25 30 0.9 30.5 29.6

20 40 20 1.8 30.9 29.1

30 45 15 2.7 31.3 28.6

35 10 40 30 35 0.9 35.5 34.6

20 45 25 1.8 35.9 34.1

30 50 20 2.7 36.3 33.6

40 10 45 35 40 0.9 40.5 39.6

20 50 30 1.8 40.9 39.1

30 55 25 2.7 41.3 38.6

Subscripts (w) and (c) stay for warm and cold side, respectively. Apexes (*) are added to identify the values relative to the catalytic membrane.

M.S. Mohy Eldin et al. / Journal of Membrane Science 146 (1998) 237±248 241

12.5 ml of lactose solution in each half-cell through its

own hydraulic circuit starting and ending in the cor-

responding cylinder. The results of these experiments

are also reported in Fig. 3(b), where the data relative

to the polypropylene net surface are indicated by (*)

and the data relative to the Te¯on mesh side by (~). It

is possible to exclude any contribution due the diffu-

sional transport of products between the two half-cells

of the bioreactor since: (i) the membrane hydropho-

bicity ensures a separation between the two working

solutions when �C��P��T�0; (ii) the small values

of �C for the products obtained also after 30 min of

reaction (less than few mM in our case) ensure not

measurable matter transport by diffusion in that time;

(iii) the small values of the diffusion coef®cients in

hydrophobic membranes (in our case and for solutes

of molecular mass of our substrate and products of the

order of 10ÿ7 cm2 sÿ1 or less) also ensure not measur-

able matter transport by diffusion within such a time

interval. Within the temperature range used, the total

membrane activity corresponds to the sum of the

activities of each membrane surface. The curve rela-

tive to this sum has been omitted because it practically

overlaps the curve of the total activity observed. This

means that enzyme immobilization occurs only at the

membrane surface and not within its pores. The results

in the ®gure also indicate that the number of active

enzyme molecules immobilized on the two membrane

surfaces is different, the polypropylene surface being

more active. From the data of Fig. 3(b) it is possible to

calculate the activation energy for the enzyme reac-

tion, which resulted 8.0�0.2 Kcal molÿ1. This value

is different from the result of the soluble enzyme,

9.4�0.4 Kcal molÿ1, as calculated from [21]. In both

cases the temperature ranges are comparable.

3.2. Non-isothermal experiments

In Fig. 4 the glucose production as a function of

time under non-isothermal conditions is reported for

four different experimental conditions, namely at

Tav�208C (a), at Tav�258C (b), at Tav�308C (c) and

at Tav�358C (d). In the ®gures the parameter char-

acterizing each curve is the temperature difference

measured at the position of the thermocouples. Full

lines refer to experiments performed with the poly-

Fig. 3. (a) Isothermal glucose production as a function of time. Symbols: (}) 158C; (&) 208C; (~) 258C; (*) 308C; (�) 358C; (&) 408C;

(~) 458C; (*) 508C; (^) 558C. (b) Total membrane activity as a function of temperature. Symbols: (&) total membrane activity; (*)

polypropylene side activity; (~) Teflon side activity.

242 M.S. Mohy Eldin et al. / Journal of Membrane Science 146 (1998) 237±248

propylene side facing the warm solution (i.e. when

T�p > T�t ); dotted lines refer to the reverse situation

(i.e. when T�p < T�t ). The lines through the points

indicated by the symbol (}) represent isothermal

glucose production, i.e. when T�p � T�t . Full lines

evidence a glucose production (and hence an activity)

under non-isothermal conditions higher than the one

relative to the corresponding isothermal conditions

and increasing with the applied temperature difference

�T. A different behaviour is exhibited by the plots of

dotted-lines, evidencing a phenomenon never encoun-

tered by us in previous experiments [8,11,12]. In these

investigations the inversion of the direction of the heat

¯ux across the membrane evidenced some small dif-

ferences in the size of the activity increase, but never

activity values lower than the ones of the correspond-

ing isothermal situation.

To give a possible explanation of the present beha-

viour reference must be made to Fig. 5 where, for

example, the results of Fig. 4(c) are rearranged by

plotting the membrane activities (lines `̀ a'' and `̀ b'')

as a function of the temperature difference measured

by the thermocouples. From the ®gure it is possible to

see how the activity of the catalytic membrane linearly

increases (`̀ a'' line) or decreases (`̀ b'' line) with the

applied temperature difference. Increments and decre-

ments are asymmetric with respect to the correspond-

ing isothermal condition represented by the intercept

of the two lines with the ordinate axis. Of course, the

`̀ a'' line refers to the situation T�p > T�t and `̀ b'' line to

T�p < T�t .

Possible causes responsible for the observed beha-

viour could be: (i) the different enzyme activity of the

membrane subjected to different temperatures as a

Fig. 4. Non-isothermal glucose production as a function of time; (a) Tav�208C; (b) Tav�258C; (c) Tav�308C; (d) Tav�358C. Symbols: �T�0

(}); �T�10 (&, &); �T�20 (~,~); �T�30 (*,*).Full lines refer to the case in which T�p > T�t ; dotted lines to the case in which

T�p < T�t .

M.S. Mohy Eldin et al. / Journal of Membrane Science 146 (1998) 237±248 243

consequence of the non-isothermal conditions; (ii) the

presence of substrate and products transport by ther-

modialysis across the catalytic membrane; (iii) the

presence of conformational changes induced in the

dynamic structure of the macromolecules during the

interaction with the ¯ux of thermal energy.

Coming to cause (i) it must the considered that,

since the actual temperature differences across the

membrane thickness are small (�T*�2.78C when

�T�308C), from the data of Fig. 3(b) it is possible

to write:

Ap�T�w� � At�T�c � � Ap�T�c � � At�T�w� � Atot�T�av�;(1)

where T�w � T�av ��T�=2 and T�c � T�av ÿ�T�=2.

To give an example let us examine the experimental

conditions de®ned by Tav�308C, Tw�458C and

Tc�158C. From the corresponding values of T* in

Table 1 and from the data in Fig. 3(b) one has: Ap

(31.38C)�At (28.68C)�0.15�0.08�0.23. At the same

manner At(31.38C)�Ap (28.68C)�0.09�0.14�0.23.

In both cases one obtains as total activity a value

corresponding to Atot �T�av � 0:23�. The occurrence of

the identity of the Eq. (1) implies that under non-

isothermal conditions the sum of two different iso-

thermal activities on each membrane side is practi-

cally equal to the total activity of the membrane at the

corresponding average temperature, independently

from the direction in which the temperature difference

is applied.

Vice versa for obtaining the results at Tav�308C and

�T�308C, i.e. an enzyme activity equal to

0.36 mmol minÿ1, in absence of the contributions by

the process of thermodialysis and the conformational

changes in the dynamic protein structure, the experi-

ments would be performed at Tav�408C and

�T�308C. Only under these experimental conditions

one has that Ap (41.38C)�At (38.68C)�0.23�0.13�0.36�Atot �T�av � 40�C�.

At this point the two previous observations allow to

exclude cause (i) as responsible for the observed

effects.

Let us examine the rationale for the existence of the

other two causes. With reference to cause (ii) it must

be considered that during the process of thermodia-

lysis with aqueous solutions two independent and

opposite ¯uxes take place across the membrane: a

thermoosmotic volume ¯ux �JV � JH2O� and a solute

¯ux (Js,therm) produced by the thermal diffusion in the

membrane pores. To the volume ¯ux is coupled a drag

solute ¯ux given by Js;drag � VH2O � CC where VH2O is

the rate of thermoosmotic water transport across the

Fig. 5. Total membrane activity as a function of �T, the temperature difference read by thermocouples. Symbols: (}) T�p > T�t ; (&) T�p < T�t ;

(*) contribution of conformational changes; (~) contribution of thermodialysis.

244 M.S. Mohy Eldin et al. / Journal of Membrane Science 146 (1998) 237±248

membrane (cm sÿ1) and CC is solute concentration

(mol cmÿ3) in the compartment (warm in our case)

from which the water is transported.

This means that under non-isothermal conditions

the membrane is crossed by two opposite and different

solute ¯uxes. The net solute ¯ux and its versus depend

on the size of each of two ¯uxes. This from the point of

view of the thermodynamics of the irreversible pro-

cesses.

From the point of view of an enzyme immobilized

on a membrane maintained under non-isothermal

conditions the macromolecule interacts with the two

independent substrate ¯uxes produced by the tempera-

ture gradients and with the substrate diffusive ¯ux

which is the only substrate ¯ux present under iso-

thermal conditions. Since the enzyme activity is pro-

portional to the substrate concentration and is

independent from the way in which is reached, the

observed enzyme activity is increased by the process

of thermodialysis.

Coming to cause (iii) it must be remembered that

the dynamic structure of macromolecules is affected

by the exchange of energy and momentum with the

surrounding medium [22±27].

Protein ¯uctuations consist of localised oscillations

of very high-frequency and collective oscillations of

lower frequency and larger amplitude. The ®rst ones

are rather uniformly distributed throughout the macro-

molecule while the collective modes occur in special

sites [22]. The large amplitude collective oscillations

are usually correlated by a biunivocal cause-to-effect

relationship to functionally important conformational

transformations. Many studies clari®ed what happens

after a protein-quake is produced by exciting, for

instance, the heme myoglobin [23]. Vibrations propa-

gate through the whole macromolecular structure and

from it to the surrounding liquid bath. The process

proceeds with a general decrease of vibration fre-

quency and with occasional amplitude increase in

structures such as an �-helix or at hinges between

two helices, etc. More generally, strain energy

released from the enzymatic site during the catalytic

process has been shown to propagate through the

macromolecule in the form of high-frequency elastic

waves detected in myoglobin crystals [24].

An inverse process has been also proposed [25±27]

by which thermal excitations derived from the bath as

small amplitude stochastic oscillations, might proceed

through the protein, channelled in some way to the

enzymatic site, anharmonically combining to generate

large amplitude oscillations. These would cause the

functionally important conformational transforma-

tions triggering catalysis.

Since thermal energy in the condensed phases has

been demonstrated to be constituted by hyperfre-

quency elastic waves capable of exchanging energy

and momentum when impinging on an obstacle [18±

20] we suppose that the changes in the dynamic

structure occur when the heat ¯ux interacts with an

enzyme molecule. The change in the dynamic con-

formation of the enzymes persists as long as the non-

isothermal conditions exist. Any change in either the

static or dynamic enzyme conformation, may there-

fore in¯uence enzyme activity.

With the aim of quantifying the contribution of

these two last cases and calling x and y the contribu-

tions due to the conformational changes and to non-

isothermal mass transport, respectively, the experi-

mental data of Fig. 5, lines a and b, can be expressed

by the equations system:

x� y � c0; ÿx� y � c00; (2)

where c0 and c00 represent, at each value of the tem-

perature difference, the differences between the activ-

ities found under non-isothermal conditions and the

activity found under comparable isothermal condi-

tions, given by the value of the intercept with the

ordinate axis. This last value gives the contribution of

the isothermal diffusion. c0 is referred to the case in

which T�p > T�t , and c00 to the reverse situation. The

variable x has opposite sign in the two equations since

the conformational changes of the protein may depend

on the direction in which heat ¯ows across the cata-

lytic membrane. The variable y, instead, has always

the same sign since substrate and product ¯uxes

induced by the process of thermodialysis across the

catalytic membrane are independent from the direc-

tion of the temperature gradient and the physical

interaction between the enzyme and the substrate does

not be dependent from the direction in which the

substrate hits the catalytic site.

The solution of the system of equations gives the

points through which the plots indicated with `̀ c'' (for

the conformational change contribution) and by `̀ d''

(for thermodialysis contribution) have been drawn in

Fig. 5. Comparison between the plots `̀ c'' and `̀ d''

M.S. Mohy Eldin et al. / Journal of Membrane Science 146 (1998) 237±248 245

shows that, with the catalytic membrane used in this

research, the contribution of the conformational

changes is, in absolute value, higher than that due

to thermodialysis. When T�p > T�t the two effects act in

a synergetic way, while when T�p < T�t the two effects

act in an antagonistic way so that in this case the

negative contribution of the conformational changes

prevails. Results similar to the ones reported in Fig. 5

have been obtained also in the cases illustrated in

Fig. 4, (a,b and d).

We are aware that this is a hypothetical explanation,

not resting on direct experimental evidence, but at

present this is the only hypothesis that we can advance.

The circumstance that this behaviour was not observed

before [8,11,12] is due to the fact that in previous

experiments higher non-isothermal mass ¯uxes were

present. The untreated Te¯on membranes previously

used were more hydrophobic than the treated ones to

bind the enzymes and therefore gave higher rates of

mass transport by thermodialysis. The untreated

Te¯on membranes, indeed, give, under the same

experimental conditions, non-isothermal mass ¯uxes

about three times greater than the ones observed with

the same membranes treated with MMA.

In any case, independent of any actual knowledge of

the physical causes affecting the activity of the

enzymes immobilized on membranes subjected to

temperature gradients, it is possible to conclude that

the Te¯on/MMA membranes exhibit increased

enzyme activity when T�p > T�t , so opening the pos-

sibility for successful employment of these new cat-

alytic membranes in non-isothermal bioreactors.

With the aim of better quantifying the observed

effect we replot, after appropriate interpolations, the

results of Fig. 4 accounting for the effective tempera-

ture on the warm surface of the catalytic membrane

and the actual temperature difference across it. These

results are reported as total membrane activity in

function of �T* in Fig. 6 for the case in which

T�p > T�t . The case in which T�p < T�t has been dis-

regarded since it is not interesting for practical appli-

cations. The ®gure shows how the membrane activity

increases linearly with the applied �T*. This beha-

viour gives useful indications for the exploitation of

non-isothermal bioreactors in industrial processes.

The linear plots of the ®gure lead to the following

equation

A�T�pw��T� 6�0 � A�T�pw��T��0�1� ��T��; (3)

where A�T�pw��T� 6�0 and A�T�pw��T��0 are the activities

of the membrane when the temperature of the poly-

propylene membrane side is T�w and the experimental

Fig. 6. Total membrane activity as a function of �T*, the actual difference across the catalytic membrane. Curve parameter is the temperature

of the warm side of the membrane. Symbols: (})T�pw � 20�C; (&) T�pw � 25�C; (~) T�pw � 30�C; (*) T�pw � 35�C.

246 M.S. Mohy Eldin et al. / Journal of Membrane Science 146 (1998) 237±248

conditions are non-isothermal or isothermal, respec-

tively. In this expression the coef®cient � represents

the percent activity increase when a temperature

difference of 18C occurs across the catalytic mem-

brane. The � values relative to the experiments

reported in Fig. 6 are listed in Table 2.

A close inspection of the � values reported in the

table shows that these values, obtained with a single

membrane ± at the same time catalytic and hydro-

phobic ± are comparable with the ones obtained in

previous experimentations [8] using a double mem-

brane system, which is not very useful for industrial

applications.

4. Conclusions

The primary goal of this research was that of

obtaining a membrane endowed with both the pre-

requisites of having a catalytic activity and of being

hydrophobic and therefore able to sustain thermodia-

lysis. The experimental results proved that this goal

has been reached.

The Te¯on/MMA membrane, loaded with b-Galac-

tosidase, placed in a non-isothermal bioreactor ®lled

with a substrate solution, exhibited a behaviour and

led to results comparable with the ones previously

obtained with a catalytic hydrophilic membrane

coupled with a hydrophobic untreated Te¯on mem-

brane [6±12]. The catalytic activity of the membrane

used in this research increases with the temperature

and with the intensity of the applied temperature

gradient. In particular the � values obtained with

the grafted membrane are equivalent to the ones

previously found. The actual values are such to encou-

rage the employment of catalytic membranes of the

kind used in this research in non-isothermal bioreac-

tors operating in biotechnological processes.

The possibility of obtaining membranes hydropho-

bic and at same time catalytic, whose activity

increases in presence of temperature gradients, makes

design and construction of new non-isothermal bior-

eactors easier, as for instance capillary reactors, able

to work in thermodialysis with high yields of the

process. The double recirculation system represents,

moreover, an improved way to apply the technology of

the non-isothermal bioreactors in industrial processes,

since in this way it is possible to obtain enzymatic

impoverishment of the unwanted substrate and enrich-

ment of wanted products without altering the compo-

sition of the other components of the treated solution.

The circumstance that the � values decrease with

increasing temperatures of the warm side of the

membrane makes advantageous use of this technol-

ogy, since under the same temperature gradients the

yield of the process is higher at lower temperatures.

This is an important point for economical evaluation

of the use of non-isothermal bioreactors. In any case

such a bioreactor will become economically compe-

titive when the costs for maintaining the temperature

gradients are reduced by using low-enthalpy heat

sources, such as hot ¯uids resulting from industrial

processes.

Acknowledgements

This work was partially supported by the CNR

(CT96.00065.PF.01, CT.95.02352 and Target Project

`̀ Biotechnology'') as well as by the MURST (40%

and 60% funds). We are also grateful to the UNIDO/

ICGEB which supported with a fellowship the activity

of Mohy Eldin at IIGB of CNR in Naples.

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The percent increase of catalytic activity (�) listed as a function of

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Membrane system T�pw � (% increase)

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