on the kinetics and effectiveness of immobilized whole-cell batch cultures

ELSEVIER

Bioresource Technology 53 (1995) 269-275 0 1995 Elsevier Science Limited

Printed in Great Britain. All rights reserved 0960-8524195139.50 0960-8524(95)00096-S

ON THE KINETICS AND EFFECTIVENESS OF IMMOBILIZED WHOLE-CELL BATCH CULTURES

B. Prasad”

Alternate Hydro Energy Centre, University of Roorkee, Roorkee-247 667, India

&

I. M. Mishra Department of Chemical Engineering University of Roorkee, Roorkee-247 667, India

(Received 17 April 1995; revised version received 2 July 1995; accepted 7 July 1995)

Abstract A model for growth-associated fermentations is pre- sented for batch cultures of immobilized whole cells. The model encompasses exponential and steady-state growth phases and the effectiveness of the biocatalyst. Based on the model equations, experimental methods have been developed for the determination of the kinetic parameters: maximum specific growth rate (urn& Monod constant (IQ and effectiveness factor (n). These methods are illustrated by ethanol fermentations using Saccharomyces cerevisiae cells entrapped in alginate beads. The kinetic parameters obtained show consistency with those determined for free-cell systems.

Key words: Immobilized whole cells, effectiveness factor, biomass yield factor, exponential growth phase, steady-state growth phase, Gaden type I fermentations.

NOMENCLATURE

a al b bl C Cl KITI MS'

Ms’X’

MS

MsX’

defined by eqn (12) defined by eqn (18) defined by eqn (13) defined by eqn (19) defined by eqn (14) defined by eqn (20) Monod constant for growth, kg/m3 support concentration of immobilization matrix, kg/m3 concentration of immobilized cells in the immobilization matrix, kg/m” support concentration in reactor (MS’ EJE,), kg/m3 of liquid hold-up concentration of immobilized cells per unit

*Author to whom correspondence should be addressed.

P rS

s t V X X’

YC

Y X/S

Y’ x/s

Y” x/s

YPIS

liquid volume in reactor (MS’ X’E,/E~), kg/m” product (ethanol) concentration, kg/m3 rate of substrate utilization in reactor, kg/ (m”.h) substrate concentration, kg/m” time, h volume of reactor, m” free-cell concentration, kg/m3 immobilized-cell loading, per unit mass of immobilization matrix, kg/kg biomass yield factor, as defined by eqn (8) dimensionless yield of biomass based on total substrate in reactor, kg/kg yield of biomass based on total substrate in liquid space as defined by eqn (6), kg/kg yield of biomass based on total substrate in immobilization matrix as defined by eqn (7), kg/kg yield of product (ethanol) based on substrate, kg/kg

Greek letters 81 liquid hold-up in reactor, dimensionless 8, immobilization matrix (gel beads) hold-up in

reactor, dimensionless PInax maximum specific growth rate, per hour vl effectiveness factor, as defined by eqn (3)

dimensionless

Subscripts 0 initial S steady-state

INTRODUCTION

Immobilized whole-cell systems exhibit some advantages over presently accepted batch- or

269

270 B. Prasad, I. M. Mishra

continuous-fermentations using free-cells. These advantages are: operation at high dilution rates without washout; greater volumetric productivity as a result of higher cell density; tolerance to higher concentrations of substrate and products, without inhibition; relative ease of downstream processing; use of simple and less expensive reactor configura- tions. A large number of immobilization techniques are now available and the immobilization of any cell type is considered routine. Amongst others, Kolot (1981) and Karel et al. (1985) have dealt with these techniques in great detail.

The immobilization process changes the environ- mental, physiological and morphological characteristics of cells, along with the catalytic activity, The degree of retention of a particular activity normally present in free-cells will depend on the immobilization technique and reaction conditions (Karel et al., 1985). Internal mass transfer limitations affect the effectiveness of the biocatalysts. Since molecular diffusion is the only way that nutrients can reach most of the cells and products may get out from bioparticles, substrate and product concentration profiles are established in the carrier. Thus, in most cases, the effectiveness of immobilized cells will be lower than for a system where cells are freely suspended. Additionally, the cells deep inside a bioparticle may become inactive due either to dep- rivation of some essential nutrients or to accumulation of product(s) to inhibiting concentrations.

Intra-particle mass-transfer limitations in the immobilized cell systems present an intractable problem when analyzing and designing immobilized- cell reactors. In spite of a large number of theoretical papers appearing in the literature dealing with the problem of intra-particle mass-transfer limitations (Engasser & Horvath, 1976; Goldstein, 1977; Dalili & Chart, 1987; Andrews, 1988; Atiqullah et al., 1990; Teixeira & Mota, 1990) no experimental method seems to have been evolved over the years which may be used to determine the internal mass- transfer effects (Karel et al., 1985; Prasad, 1991). Further, no experimental method is available which could be used to determine kinetic parameters and the effectiveness factor from the immobilized whole- cell reactor data.

The present paper deals with a new approach for the determination of kinetic parameters and the effectiveness factor from immobilized cell batch cultures based on the unstructured models developed for Gaden type I fermentations. Ethanol fermentation with low substrate concentration has been selected for the illustration of the method developed.

DEVELOPMENT

Using the Monod expression for inhibition-free substrate-limiting conditions as

1dX s

x dt=pm”” ~ S+K, (1)

One may relate the substrate consumption, biomass formation and product formation rates as given by Gaden (1955) and Gaden (1959):

dS 1 dX 1 dP -- =-- dt Y,, dt Yp/s dt (2)

These equations could be applied to immobilized microbial-cell systems as well, provided that the limitations of external mass transport, intra-particle diffusion and inactivation due to immobilization are incorporated to satisfy immobilized-cell systems. The effectiveness factor concept, as employed in studying heterogeneous catalysis, could be used to describe immobilized cell systems as well. This concept may also incorporate the limitations caused by nutrients and inhibitory products which are most critical in determining the rate of metabolic activity inside the immobilization matrix.

During kinetic experiments, if the fermenter is intensively mixed, the external mass transport effect could be neglected and the intra-particle diffusional limitations and inactivation due to the immobilization process could be incorporated in the effectiveness factor 11, defined as

g=actual consumption of substrate in the immobilization matrix/consumption of substrate if all the biomass retained by immobilization matrix was exposed to liquid-phase conditions (3)

The application of eqns (l)-(3) for an immobilized-cell system could then be represented as

Rate of substrate=Rate of substrate consumption in consumption liquid space

Rate of substrate consumption in immobilization matrix

or

!&lax s -_r =-Xx PITlax

s yx/s S+K, &l+T---

Y x/s

S hh’X’-

S + K,,, “’ (4)

Assuming negligible accumulation of substrate in the immobilization matrix and the rate of substrate consumption as given by eqn (4), the substrate bal- ance equation in a batch reactor may be written as

dS pL,,x S _-_ -- X- dt Ytis S+K,

S +ll !!EZMsX’ -

Y S+K, (5)

x/s

Kinetics of immobilized-cell cultures 271

where

MsX’= MS’X’ES

=concentration of immobilized cells per unit liquid volume in the reactor, kg/m”

As discussed by Wada et al. (1980) and Prasad (1991), an immobilized growing yeast-cell system is comprised of two distinct phases: exponential and steady-state. Accordingly, these two phases have been modelled separately.

Exponential growth phase Under the exponential growth phase, the biomass in the immobilization matrix proliferates and during the early stage of growth the cell leaching is negligible. However, the growth in the immobilization matrix stops at a time when the biomass proliferates to the maximum retaining capacity of the matrix. Accordingly, the present mathematical treatment pertains to the early stage of the exponential growth phase assuming no leaching from the matrix.

If the immobilized-cell batch culture is seeded with free cell concentration X,, and immobilized cell concentration MsX& then the biomass yield coefficients based on bulk substrate concentration in the free space and in the immobilization matrix can be defined, respectively, as

x-x, Y&=-

so-s

Y$ = MsX’ -MsX;

s,-s

and the biomass yield coefficient (Yx,&) in the reactor can be expressed as

Y" y*s=F!L l-Y,

where Y, is a constant and is defined as the ratio of cell growth in the free space to the total cell growth in the reactor (Y&/Y.&. This may be called the ‘biomass yield factor’.

Equation (5) may be transformed, with the help of the above definitions and subsequent manipulation, and integrated to give

‘l&L= t so

l+ (~~-~>~y~~y~+r?y,~(1-y~)l

Xc, + qMsX:, 1 -~[&~Y&+&(1 -Yc)l

x/s m

+ (x, + YMsX:)] where S=S, at t=O.

(9)

Equation (9) provides substrate-concentration- time profiles for a batch reactor for the immobilized cell conditions to be characterized by the initial free- and immobilized-cell concentrations under an exponential growth phase. This equation reduces to the equation derived by Gates and Marlar (1968) for free-cell systems.

Steady-state growth phase The steady-state growth phase is characterized by a dynamic equilibrium existing between the growing cells in the immobilization matrix and the cells being released in the free space. The cell release from the matrix is counterbalanced by the cell growth in the matrix. Under steady-state conditions, free-cell concentration is given as

X=X, + Y,,(S,, -S) (10)

Equation (5) may then be transformed and integrated with S=S,, at t=O to yield

S fins=

Y,,(S, + K,) t-X<, + r/MsX: 0 K, Y,,

(~o-~)Yx,s

X, + qMsX,’ 1 - $+ [X0 + S, YX/s + qMsX,I] (11)

tin m

Equation (11) provides a substrate-concentration- time profile for a batch reactor where the immobilization matrix achieves the maximum cell loading beyond which further growth results in the leaching of cells into free space. Substitution of MsX,‘=O in the above equation results in the free- cell system equation given by Gates and Marlar (1968).

METHOD FOR THE DETERMINATION OF KINETIC PARAMETERS AND EFFECTIVENESS FACTOR

Exponential growth phase The biomass yield coefficient (Y,,) and biomass yield factor (YC) could be determined by direct experimental measurements of free-cell, immobilized-cell and substrate concentrations in the reactor


from eqns (6)-(8). Maximum specific growth rate (p,,,,,), Monod constant (K,,,) and the effectiveness factor (q) could be determined by using the following procedure.

Equation (9) shows a linear relationship between (l/t) In (S/So) and (l/t) ln[l +b(S,-S)], giving a slope ‘a’ and an intercept ‘c’ where a, b and c are given as

[Y~sYc+YY,,(I-Y,)l[~,+~,]+[X,+r1~~X~l a=

Krn[Y,,YC + vlYx/,(l -Yc)l

(12)

b= Yx/SYC + ulYx/s(l -Yc)

X” + qMsX:, (13)

The value of b involves ye implicitly and it cannot be determined by direct measurements. Therefore, a trial and error approach must be used to get a best- fit straight line. This will involve determination of correlation coefficients between data points for vari- ous straight lines corresponding to different values of b and selecting that value of b for which the correlation coefficient is found to be maximum; i.e. nearest to 1.0. The values of a and c can be determined from the slope and intercept of the plot directly.

Solving the three simultaneous algebraic eqns (12)-(14) one gets the values of r, Km and pmax as

Y,sY, -bX,

and

~=Msx:,-Y,,,(l-Y,)

Km= 1 +bS,

b(a-1)

(15)

(16)

c [bMsX:, - Ytis ( 1 - Yc)]

‘max= b (a - 1) [Y,M.X:, -X,,( 1 - YJ] (17)

Steady-state growth phase The value of the biomass yield coefficient (Y.& can be determined by measuring initial free cell and substrate concentrations and final free cell and substrate concentrations during the course of batch fermentation. The values of pmax, Km and q can be determined by a method analogous to that adopted for the exponential growth phase.

Equation (11) may be plotted as (l/t) In (S/S,) versus (l/t) In [l +bl(S, -S)] having a slope of al and an intercept cl, where al, bl and cl are given as

al= Y,s (So + Km) + (Xc, + qMsX;)

Km Ytis (18)

Y blz x/s

X, + qMsX,r (19)

and

cl= e [S,Y,, +X, + qMsX,‘] (20) xl.5 m

Solving eqns (18)-(20) one gets

Yx,s - blxo ‘= Msx:bl

K,,,= 1 +blS,

bl(al-1)

cl /&lax=..

(21)

(22)

(23)

METHODS

The following experimental programme was used to illustrate the methods for the determination of kinetic parameters and the effectiveness factor from batch cultures of immobilized yeast cells under exponential growth phase and steady-state growth phase. Ethanol fermentation by yeast cells immobilized in a calcium alginate matrix was selected as an example of Gaden type I fermentations for its sim- plicity and the mild conditions of immobilization. Batch experiments were conducted in a Biostat M fermenter of 2.0 1 working volume. However, the growth pattern experiments were conducted in 1.5 1 Erlenmeyer flasks, as discussed later. The temperature in all the experiments was maintained at 3O+O.l”C. The pH was adjusted at 5.0 *O-l with automated injection of 1 N HCl and 1 N NaOH. The agitator speed of the fermenter was kept constant at 500 rpm in all the experiments. The detailed experimental programme is given by Prasad (1991).

Cell cultivation and immobilization of cells The Saccharomyces cerevisiae NCIM 3085 strain obtained from the National Collection of Industrial Microorganisms (NICM), National Chemical Labo- ratory, Pune, India, was grown in a defined growing medium of Wada et al. (1980). The complete growing medium with 5% (w/v) glucose and 2.5 times the usual concentrations of nutrients was used. The glucose-grown cells were gravity settled and the thick slurry was used for immobilization following the method of Vorlop and Klein (1983).

Analysis Glucose was estimated using the phenol-sulphuric acid method as adopted by Dubois et al. (1956).


Absorbance measurements were made on a Shi- madzu Model UV-210A spectrophotometer. The free-cell concentration was determined by washing and filtering the centrifuged cells on 0.45 pm mille- pore filters. The membranes were dried in an oven at 105°C to a constant weight and the free-cell concentrations were expressed on a dry-weight basis. The cell loading of calcium alginate beads was determined by drying about 5-10 beads in the oven at 105°C to constant weight. The necessary corrections for molecular weight difference in sodium and calcium were made. The concentration of the yeast slurry, on a dry-weight basis, was determined before the mixing of the yeast slurry into the viscous sodium alginate solution. With a known initial mix ratio, an increase in the mass of beads and the cor- rection factor, the cell loading in the gel beads was determined and expressed as kg of dry biomass per kg of calcium alginate.

RESULTS AND DISCUSSION

Growth pattern in gel matrix In order to investigate the growth pattern of the Saccharomyces cerevisiae cells in calcium alginate gel beads, four initial cell loadings of O-051, 0.102, 0.251 and 0.363 kg/kg (kg of dry biomass per kg of calcium alginate) were employed. The rms diameter of the gel beads before incubation was 3.14 mm. The experiments were conducted in 1.5 1 Erlenmeyer flasks containing complete growing medium with 50 kg/m3 of glucose. About 600 beads of each cell loading were transferred to these flasks and incubated for 120 h at 30°C in a constant temperature rotary shaker. The cell loading was used to depict the growth pattern, as shown in Fig. 1. The release of cells from the beads was also investigated. It was found that the cell release from the beads was negligible up to an incubation period of 24-36 h, depending on the initial cell loading.

The growth pattern of cells was comprised of three distinct phases. In the first phase, exponential growth of cells in the gel occurred and the cell

2.5 r 5 2.0

h A - 1.5 ,” 4

Initial cell loading

m s 1.0 0 0.051 kg/kg A 0.102 kg/kg

=: 3 l 0.251 0.5 kg/kg A 0.363 kg/kg

“0 12 24 36 48 60 72 84 96 108 120

Time (II)

Fig. 1. Growth pattern of immobilized Saccharomyces Fig. 2. Substrate concentration/time profile employed in cerevisiue in the gel matrix. the illustration for exponential growth phase.

release from the gel was negligible. In the second phase, cell release from the immobilization matrix started. Subsequently, in the third phase, the growth of cells in the gel was balanced by the release of cells into the free space. Thus, a steady-state cell loading in the gel matrix was established and the lost cells in the gel were replaced by the cells growing on the nutrients. The final concentration of the immobilized cells in the gel, thus achieved, was the maximum irrespective of the initial cell loading at the time of formation of the beads. Similar growth phases of immobilized yeast cells in kappa-carragee- nan have been reported by Wada et al. (1980). The effect of initial cell loading on the final steady-state concentration of the immobilized cells has also been discussed by Nakasaki et al. (1989), who have shown that the final concentration of immobilized cells is independent of the initial cell concentration.

ILLUSTRATION OF THE METHOD FOR THE DETERMINATION OF KINETIC PARAMETERS AND EFFECTIVENESS FACTORS

Exponential-growth phase The exponential-growth phase experiments were conducted for low initial cell loadings so that the release of cells from the gel matrix was negligible. Five experiments were conducted with approxi- mately the same initial glucose, free-cell and immobilized-cell concentrations. The substrate concentration/time course for such a typical run is shown in Fig. 2 which was employed in the determination of kinetic parameters and the effectiveness factor. The operating parameters for this typical run are given in Table 1.

The values of biomass yield coefficients, Y& in the liquid space, Yzs in the gel matrix and Y,, in the reactor were determined from eqns (6)-(g) by measuring free-cell, immobilized-cell and the substrate concentrations. Subsequently, Y, was determined from eqn (8) using the experimentally known values of Y,, and Yzs. These parameters are given in Table 2.

3.2 4.8

Time (h)


Table 1. Operating parameters for the illustration of the exponential growth phase

Initial substrate (glucose) concentration, S, (kg/m”) 39.21 Initial cell loading, XA (kg/kg) 0.267 Initial immobilized cell concentration in the gel beads, Ms’Xd (kg/m3) 6.331 Liquid hold-up, E, (non-dimensional) 0.5481 Gel matrix hold-up, E, (non-dimensional) 0.4519 Immobilized cell concentration per unit liquid volume, 5.22

MsXL ( kg/m3) Root mean square diameter of gel beads (mm) 3.14 Initial free cell concentration, X0 (kg/m3) 0.316

Table 2. Biomass yield coefficients and biomass yield factor of the exponential growth phase

Biomass yield coefficient in liquid space, Y$, (kg/kg)

0.0113

Biomass yield coefficient in gel matrix, Y$ (kg/kg)

0.0774

Biomass yield coefficient in reactor, Yti, (kg@)

0.0887

Biomass yield factor, Y, (non-dimensional)

0.128

The value of b was determined using the regression analysis. For the data of this illustration, the correlation coefficient was found to be maximum (0.987) for a value of b = 0.0175. Subsequently, a plot was prepared between ( - l/t) In (S/S,) and (l/t) In [l +b(S,-S)] (Fig. 3).

The slope a and intercept c from this plot were found to be 34.521 and 2.989, respectively. The values of q, K, and pL,,, as determined from eqns (15)-(17) are given below:

~j=O.412; K, = 2.872 kgfm3; pL,,,=0.183/h.

Steady-state growth phase The steady-state growth phase experiments were conducted after ensuring that the calcium alginate gel beads retained Saccharomyces cerevisiae cells to their maximum loading capacity. The following procedure was adopted for this. Calcium alginate beads of desired rms diameter were transferred aseptically to the 2.0 1 Biostat M fermenter containing complete growing medium of 50 kg/m3 glucose concentration. In order to ensure that the cell loading in the immobilization matrix remained constant during the operation, this reactor was run in continuous mode after 24 h of batch operation. Continuous mode was selected so that the medium did not run out of nutrients due to consumption during the growth phase. A medium flow rate of 24 ml/h was maintained. After about 100 h of continuous operation at this flow rate it was found that a steady-state growth phase had existed. This was also ensured by measuring the effluent free-cell concentrations and the cell concentrations in the alginate beads and these were

b = 0.0175 0.44 a = 34.5210

c = 2.9890

mlvp R = 0.9870 0.38

E -

-

0.12 I I I I

0.065 0.069 0.073 0.077 0.081 0.085

f In [ltb (So-S)]

Fig. 3. Plot of [-(l/t) In (S/S,)] against [(l/t> In [l +b(S, -S)]] for exponential growth phase.

found to be invariant with time after about 40-50 h of continuous operation.

As in the case of the exponential growth phase, five experiments were conducted under steady-state growth phase. The substrate (glucose) concentration/ time course as obtained from run 3 is shown in Fig. 4 and has been employed in this illustration. The operating parameters for this experiment are given in Table 3.

From the measurements of free-cell concentration and substrate concentration Ytis was determined as 0.0881 kg/kg.

The value of bl was determined by the regression analysis and was found to be O*OlOl, for which the correlation coefficient was found to be maximum as 0.974.

From the plot of ( - l/t) In (S/S,) against (l/t) In [l+bl(S,-S)] for bl=O.OlOl as shown in Fig. 5, the slope (al) and the intercept (cl) were found to be 49.426 and 8.778, respectively. Using eqns (21)-(23), the values of effectiveness factor (q), the Monod constant (Km) and the maximum specific growth rate (pLmax) were determined as

q =0.257; K, =2*970 kglm3; ,u”,,=O.l84/h.

For the purpose of comparison K,,, and prnax were also evaluated under free-cell conditions from the batch reactor at the same initial glucose and free- cell concentrations as those of Gates and Marlar


n” 100.0

E ‘M 2.3

E

.-.\

2 10.0 = .I. E \.

z 8 0 \ :: 1.0 . =

9 E z

s v) 0.1 I I I I I

0 0.5 1.0 1.5 2.0 2.5

Time (h)

Fig. 4. Substrate concentration/time profile employed in the illustration for steady-state growth phase.

1.60 -

bl = 0.0101 1.36 - al = 49.4260

cl = 8.7780

~lvp R = 0.9740

1.12 -

-7~ 0.88 -

I

0.64 -

0.40 I

0.140 0.148 0.156 0.164 0.172 0.180

+ In [ltbl (So-S)]

Fig. 5. Plot of (-l/t) In (S/S,) against (l/t) In [l + bl (S, -S)] for steady-state growth phase.

Table 3. Operating parameters for illustration of the steady-state growth phase

Initial (substrate) glucose concentration, S, (kg/m”) 38.75 Steady-state immobilized cell loading, X,’ (kg/kg) 2.11 Steady-state immobilized cell concentration in gel beads, 50.13

MS ‘Xl ( kg/m3) Liquid hold-up, &I (non-dimensional) Gel matrix hold-up, E, (non-dimensional) Immobilized cell concentration per unit liquid volume,

Msx,’ (kg/m3)

0.6288 0.3712

29-59

Root mean square diameter of beads (mm) Initial free-cell concentration, X0 (kg/m3)

3.17 1.017

(1968). The kinetic parameters pL,, and Km were found to be 0*214/h and 2.567 kg/m3, respectively. This shows that pm_ is higher under free-cell conditions, whereas Km is higher for the immobilized cell system.

CONCLUSIONS

An experimental methodology has been devised for the determination of the kinetic parameters and the effectiveness factor from batch cultures of immobilized whole cells under exponential as well as steady-state growth phases. The experimental ver- ification of the reaction-coupled diffusion mechanism is possible using this new approach.

REFERENCES

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Dalili, M. & Chau, P. C. (1987). Intraparticle diffusion effects in immobilized cell particles. Appl. Microbial. Biotechnol., 26, 500-6.

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on the kinetics and effectiveness of immobilized whole-cell batch cultures

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