A tutorial review on bioprocess systems engineering

Computers them. Engng Vol. 20, No. 6/l, pp. 915-941, 1996 Copyright 0 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved

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A TUTORIAL REVIEW ON BIOPROCESS SYSTEMS ENGINEERING KAZUYUKI SHIMIZIJ Department of Biochemical Engineering and Science, Kyushu Institute of Technology, Iizuka, Fukuoka 820, Japan (Received 4 July 1995) Abstract-Brief explanation is given on the current progress in bioprocess systems engineering. Particular attention is focused on optimization and control of bioprocesses. Performance evaluation was made by comparing the noninferior sets in the vector-valued objective-function space. Applications are made to such microbial systems as biomass producing systems, metabolite producing systems, extractive fermentation systems, cell recycle systems with cross-flow filtration. As for the control system design, attention is focused on the on-line optimization and knowledge-based intelligent control such as neurofuzzy control for the efficient production of gene products.

1. INTRODUCTION

With the recent significant progress in biotechnology on microbial cultivation, recombinant DNA, hybidoma, plant cells etc., it is increasingly important to develop “Bioprocess Systems Engineering” (Shimizu, 1994b). The biotechnology industry is evolving rapidly, and it has already entered a new stage of growth. The many biotechnology-based products such as pharmaceutical and health-care products, agricultural products, and chemicals have already been commercialized and the attention is focused on the transition from laboratory to market place (Shame1 and Chow, 1987). Despite the steady progress in laboratory-scale research, however, there remain many problems associated with the scale-up of bioprocesses. Since most biochemical processes create very dilute and impure products, there is a great need to increase volumetric productivity and to increase the product concentration. As a result, the scale-up of bioprocesses requires a large investment in the development of an efficient processing technology. In this regard, significant work is needed to optimize the design and operation of bioreactors to make production more efficient and more economical. It has been believed that increased productivity can be attained through strain and media improvements. Due to the significant efforts, however, potential benefits have been recognized for the use of computers backed up with “Bioprocess Systems Engineering”. Recently, I made a brief review on bioprocess systems engineering, which covers such particular areas as “on-line sensor development”, “process

optimization”, “state and/or parameter estimation”, and “process control” to consider future perspectives for further development in this promising area (Shim& 1993). Of course, there are many other areas to be developed in the framework of “Bioprocess Systems Engineering”. Those may be “Modeling” “Process Dynamics”, “Information Processing for Gene Engineering” etc., Here, I focus on particularly important areas of optimal operation and control system design, and briefly explain recent progress based on our recent research results. 2.

OFI’IMAL

OPERATION

2.1. Biomass producing systems 2.1.1. Problem forrnulationr. Consider first the simple situation where the dynamic behavior of the bioreactor is represented by the following equations for the cell mass production:

d(VX)ldt=

-FX+p(S)VX

d(VS)ldt=F,S,-FS-p((S)VX/Y(S)

dVldt= F,,- F

(la)

(lb) (W

where X, S, V are the cell concentration, substrate concentration, and the volume, respectively. FOand Fare the feed rate and product draw-off rate respectively. SF is the feed substrate concentration. The specific growth ratep and the yield coefficient Y may typically be given as functions of S as /L(S)=/LmS/(K,+S+S’IKJ l/Y(S) = 1/y* +m//L(S) 915

@a) (2b)

*

K.

916

SHIMIZU

Consider a period$operation of the reactor in which X, Sand V are m a periodic state with period r subjectJo a periodic change in F,, and F. SF is assumed to be constant. Note that the steady-state operation or continuous operation can be regarded as the special case of the periodic operation since any constant-valued function is periodic with respect to an arbitrary value of a period. Consider the cell productivity and substrate conversion as the components of a vector-valued objective function, where those are expressed by ’FXdtlV,,,t

Ji = I

t-4 am

(W

0

0

and

F

8 (7) -

B

1 X(0)

X
x

Fig. 1. Minimal-time trajectory in the Xs-plane [s(r) CS,].

J2 = 1: FX d#

F,S,dt

(3b)

where V,,, is the maximum working volume of the reactor. Let (JT, J:) be a feasible value of the vectorvalued objective function (Jr, JJ. Then the solution (J 7, .l :) is said to be noninferior if, and only if, there exists no feasible (Jr, JZ) satisfying either Ji ZJ: and J,>J:, o;‘j,>.i: and Jz2J:. Note that the value of JI is maximized at one extreme point E,, of the noninferior set and the value of J2 is maximized at the other extreme point EI,. Assume for simplicity that the product is drawn off only at the end of each cycle for the general periodic operation. If the fraction q of the reactor content is drawn off as product, it follows that F(t)=q~V,6(t-z)

where 6 is Dirac’s delta function. shown that

(4) Then it !can be

Jl = q~X(z)lt

(Sa)

J2 = X(t)/&

(Sb)

2.1.2. Noninferior set. The noninferior set can be determined by use of the constraint method (Cohon, 1978) in which one-objective programming problem is solved repeatedly for all the feasible values of J ;. If the value of J2 is specified, the value of X(r) is fixed accordingly. If in addition the value of q is specified, the optimization problem is reduced to a minimal time problem in which the value of t is minimized for specified values of r] and X(r). The same minimal-time problem was studied by Weigand (1981) using Pontryagin’s maximum principle and the generalized Legendre-Clebsch condition. However, the more expedient condition to this problem is to invoke the optimization technique of Miele (1962), which was successfully applied by

Yamane et al. (1979) to the optimal start-up problem of chemostat culture. It follows from equation (la) that

J ~(0) where n = VX. Let I be a simple closed curve in the xS-plane and I: the region surrounded by I. Then it follows from the Green’s theorem that f, dx/&S)z = /I/‘(S)

dS d+‘(S)x

(7)

where the path of the line integral in the left hand side must be taken counter-clockwise. Any feasible trajectories connecting the points I and F mustybe contained in the region IAPB as indicated in Fig. 1, where the brances AF and IB correspond to F. = 0 while the branches IA and BF correspond to Fo= m . Let IPF and IQF be two trajectories contained in the region IAFB. If the curve IPF is located in the lower side of IQF, then it follows from equation (7) that h’F

-

4/p (S)x =

TlQF = f

IPFQI

II

w(x,S)dxds

IPFQI (8)

where w is the integrand in the RHS of equation (7). Note that the sign of o is determined by that of $(S).LetS,bethevalueofSwhen~‘(S)=Ohblds. Then it can be said that rirF>rror if IPFQI is contained in the region of 0 5 S 5 S, while rlPF< rroz if IPFQI is contained in the region S 2 S,. Thus, it is easy to determine the minimal time trajectory of interest. Yamane et nl. (1979) adopted the xp-plane in place of the xS-plane. Since, however, two values of S correspond in general to any points in the

A’tutorial review on bioprocess systems engineering

917

_ EAFB J,

JP

-

ERB ERFB

0

Jz

Jz

J 2

ERB

JZ Fig. 2. Typical possible structure of noninferior set. (a) Case of Ki+

m. (b)

Case of m = 0. (c) Case of

m>O.

former plane, the latter seems more advantageous than the former for applying Miele’s technique. If S(t) < S,,, as shown in Fig. 1, the minimal-time trajectory is IMNF, which reduces to IAF when the point A falls in the region of 05 S d S,. The brances IM, MN, and NF of the trajectory IMNF represent an instantaneous fill of the substrate, a fed-batch operation, respectively. The trajectory IAF consists of an instantaneous fill branch IA and a batch operation branch._.AF. The periodic operations corresponding to the trajectories IMNF and IAF are usually called repeated fed-batch and repeated batch operation, respectively. It can be shown (Matsubara et al., 1985) that the noninferior set for the general periodic operation consists of the branches of the repeated batch and the repeated fed-batch operation, and the latter branch disappears in the case without substrate inhibition. It can be also shown that the high productivity portion of the noninferior set is occupied by the repeated batch branch, and that the J1-extreme point is the point Ey, J,-extreme point for repeated batch operation, which agrees with the point Eg, J,-extreme point for steady-state operation. In Fig. 2, typical possible structdres of the noninferior set are illustrated. It can be seen for the substrate-inhibition kinetics that the high conversion portion of the noninferior set is occupied by the repeated fed-batch branch. It is seen in Fig. 3(a) that the value of J2 can be increased by use of the repeated batch operation at the cost of a small decrease in the value of J1 relative to the steadystate operation. The values of 7 and r increase with increase in J2 as indicated in Fig. 3(b). Once the noninferior set was determined one could choose the preferable operation mode by the trade-off between the cell productivity and the substrate conversion. It has been well known prior to this work that the cell productivity is maximized by the steady-state operation and that the repeated

batch or repeated fed-batch operation is superior to the steady-state operation if higher substrate conversion is desired. In this work, it was made clear by investigating the structure of the noninferior set that much increase in the conversion could in general be obtained at the cost of a relatively small decrease in the cell productivity, and that the repeated batch operation should be adopted in place of the repeated fed-batch operation if higher cell productivity was desired in the case of substrateinhibited growth kinetics.

0

0.4

0.2

J, 1-l

ERB 0.6 JS

1.0

4 1 0.6

0.6

I

J, i-1 Fig. 3. (a) Noninferior set and J, vs .I2 curves for various specified value of q. (b) The r] and 7 vs J2 curves for noninferior solutions.

K.

918 2.2. Metabolite prodhng 2.2.l.Problem

SHIMIZU

systems

@,p)=aP(S,p)+p

formulation.

In 1959, Gaden et al. classified The metabolites of the microbial processes into three types from the kinetic view point such as, TypeI_

Growth-associated products arising directly from the energy metabolism of carbohydrates supplied, Type II. Indirect products of carbohydrate metabolism, and Type III. Products apparently unrelated to carbohydrate oxidation. The periodic operation of the bioreactor producing the metabolites of Type III will be dealt with in the next section. Consider here the problem where the produced metabolite belongs to Type I or II. Typical example of the metabolites of Type I are ethanol, lactic acid etc., while those of Type II are citric acid, salicylic acid etc. Consider a well-mixed bioreactor in which some metabolites are produced by cells. The dynamic behavior may be described by d(VX)I&=

-FX+p(S,

d(VS)/dt=F&-FS-p(S,

P)VX

(94

P)VXIY

d(VP)ldt = - FP+ n(S, P)VX

(9b) (94

dVldt = F, - F

(94

where P represents the concentration of the desired metabolite. The specific growth rate may be expressed in many cases as /A(S*P)={/4,SI(KS+S+S’IKi)}.(l-P/Pm)(lO) and the specific metabolite production rate may be given by the well-known Luedeking-Piret model (Ludeking and Piret, 1959) such as

(a)

Here, fi is nonnegative, while a can be negative if /I is positive. The case where cz is negative wtiss reported for the giutamic acid cultivation by Breuibacterium sp. (Shingu and Terui, 197.11. The special case where a > 0 and /3 = 0 corresponds to the case of the metabolite production of Type I. If we can assume SF and Y to be constant, the stoichiometric relation x= Y(&-S)

(12)

holds for the entire course of cultivation if it holds at the initial time. By using this relation, the state variable X can be eliminated from equation (9). Here, we formulate the optimization problem as a three-objective programing one with respect to the productivity of the desired metabolite, Ji, its concentration, Jr, and the substrate conversion, Jr. Note that the point (JT, J:, J;) is said to be noninferior if, and there exists no feasible point (Ji, Jr, Jr) satisfying JiZJX i=1,2,3 except the point itself. In _ general, each objective function will be maximizer at different points within the noninferior set. As before, the extreme points are called /;-extreme points (i = 1,2,3) and are designated by the symbols Eli, En, and E13, respectively. 2.2.2. Noninferior set. Consider first the steadystate operation, It can be shown (Hasegawa et al., 1987) that the feasible set and the noninferior set in J,.&J,-space may indicate various patterns for the values of kinetic parameters in a complex way. Typical examples of the feasible set and the corresponding noninferior set are depicted in Fig. 4. for P,< 00. The’solid lines indicate the feasible set and the thick lines indicate the corresponding noninferior set.

(C)

J,

(11)

E:;

J,

J3 .

Fig. 4. Typical possible patterns of the feasible set and the corresponding steady-state operation (P, < m).

noninferior

set for the

919

A futorial review on bioprocess systems engineering Consider next the case thd the product is drawn off quickly only at the end of the period. The volume of the reEtor content just before the drawoff of the product should be equal to V,,, by which the productivity is maximized. Let q be the ratio of draw-off volu& to V,,,, and assume that the substrate of the volume gV,,,(O< 657) is quickly fed at the initial time. Then each objective function can be expressed as Jr = qP(r)lr

(13a)

J,=P(t)

(13b)

53 = {S, - S (t)}/S,

(13c)

8

: :

(14)

When F,-,(t)and r] are given, V(t) can be obtained as the solution to equation (9d). Thus, the threedimensional system for S, z, and V can be regarded as the two dimensional one with respect to z and S. It can be shown (Hasegawa et al., 1987) that

lb) 8 SF

0

___ ______ I /iiz (aY + p,AF)/2

(a

s SF

i0

______-

G

dzl[x(S, z)Y-~((s, I 2(0)

z)z].

i
j 0

aY + 8(1+2 l&7&)

Fig. 5. Possible types‘of locus A. (a) and (b) case of P,
z(r) r=

(aY + pm/SF)/2

0

The noninferior set can be determined by extracting the noninferior portion from the manifold in the .I, .lzJ3-space which is obtained by repeating the procedure of maximizing Jr for a feasible set of values Jz and JJ, or P(r) and S(r). The maximization of Jr reduces to that of q/r. The latter maximization can be achieved by maximizing with respect to q the solution of the minimal-time problem in which r is minimized for a specified value of 7. This minimaltime problem can be solved by Miele’s method as mentioned previously.. In application of Miele’s method to the minimaltime problem, it is convenient to introduce a new state variable z defined by z=P(S,-S)

(a)

(c)caseofP,+m.

(15)

Suppose that a simple close curve I is composed of two trajectories APB and AQB starting from the point A and ending at the point B, and that the direction of the trajectory APB is that of going around I’ counterclockwise. Let Z be the region surrounded by I. Then it follows from Green’s theorem that

The trajectory which corresponds to a periodic state must be a closed curve in the zS-plane because of the boundary condition. The directions of the state change in the zS-plane are determined by dSldt and dzldt. It can be shown (Hasegawa et al., 1987) that the sign of dSldt depending on the value of F. is positive for F,>pV, while negative for F,
=

w(z, S) dz dSl(xY-~z)2 II

z (16)

UJ(z,

S)

=

(aY -

z)p,

and pL,= aptas

We assume here that xY-pz does not identically vanish for any finite time interval.

(17)

It can be seen that dzldt>O holds in the region where z 5 aY if we consider the case where /l > 0. In the region where z > aY, the locus dzldt = 0 denoted by A exists. Typical shapes of A are indicated in Fig. 5. It can be shown that the closed trajectory is counterclockwise (respectively, clockwise) if dzldt is

K.

920

SHIMIZU

s

9

(a)

lb)

O

.i

./’

A

0

0

z

0

2

Fig. 6. The minimal-time trajectories in the Zs-plane.

positive (respectively, negative) for the portion of the branch BI.in the neighborhood of point I (see Fig. 6). In such a situation, the upper portion of the closed trajectory IABI must be lying in the region where dzldt< 0 (respectively, dz/d!> 0). In other words, the branches IA and ABI must intersect the locus A. The location of I or value of Jz and J3 for the possibility. of the closed trajectory is restricted by this condition. Points A and B should be so determined as to be optimal. Consider the’case of the counterclockwise trajectory as shown in Fig. 6(a). Suppose that the extensions of IA and IB meet at the point C. Let A’ and B’ be points lying on AC and BC, respectively. If o CO holds in the whole interior of the closed curve AA’QB’BPA, then

while if o>O holds in place of w
which means that it is beneficial to move the branch AB upward in the region where w CO as much as possible. If the whole interior of the closed curve IACBI is contained in the region w < 0, then the closed curve is the optimal trajectory. However, if curve p,=O intersects IAC and CBI at the points M and N, repectively, and if w > 0 holds in the lower side of p, = 0, the optimal trajectory is IMNI whose branch MN passes along the curve w = 0. If w is positive for the portion of BI near point I, then it is optimal to contract the closed trajectory to point I which corresponds to the steady-state operation. Evidently, this operation is located just on the locus A.

For the clockwise trajectory as shown in Fig. 6(b), similar discussion can be made by reversing the condition concerning the sign of w. 2.2.3. Simulation The simulation results are shown in Fig. 7(a). %ii broken line shows the upper boundary of the feasible set for the periodic operation and the corresponding noninferior set is shown by the thick line. In Fig. 7(b), the values of q, 5, and r corresponding to the noninferior set. are depicted. In consequence, the noninferior operation is the repeated batch and repeated fed-batch, respectively. Anyway, the noninferior set consists of two portions corresponding to the repeated batch operation and the repeated fed-batch operation. At the J,-extreme point E,y for the repeated batch operation, both 7 and t tend to zero andythe repeated batch operation becomes equivalent to the steady state operation. From the simulation result, it can be said that near the productivity-extreme point, the optimal operation became the repeated batch operation and at the point it became equivalent to the steady state operation. When the higher metabolite concentration andlor higher substrate conversion was desired, the optimal operation might become the repeated fed-batch operation. It was clarified that, in general, the concentration of metabolite and/or the substrate conversion could be increased at the cost of a relatively small decrease in the productivity of the desired metabolite by adopting an adequate periodic*operation. 2.3. Multiple bioreactor systems Production of L-glutamic acid is an example of Type III in Gaden’s classification, and the production of secondary metablites such as antibiotics and giberellin is a typical example of this case. In these cases, the product is rather expensive so that various

A’tutorial review on bioprocess systems engineering

921

J, (g/W

J, t-1

20

J, (g/L)

(b)

J, l-1 Fig. 7. (a) The feasible set for the steady-state operation. (b) The value of,q, 6 and r corresponding to the noninferior set.

.efforts have been focused on increasing the productivity and the product concentration. The direct application of repeated batch or fed-batch cultivation to such systems, however, may not lead to an improvement in productivity. The reason is as follows: In order to obtain a higher concentration of the product, one must wait long after the time t, , say t,, in Fig. 8. However, if a repeated batch or fedbatch operation is conducted with an inoculation of X, in Fig. 8, a longer lag phase might result since the inoculated cells are old. Thus the productivity cannot be increased. We proposed using multiple bioreactors to overcome this problem (Shimizu et al., 1985), and showed the usefulness of this idea for the efficient production of penicillin by computer simulation (Hasegawa et al., 1985) using the simple model proposed by Constantinides et al. (1970).

2.3. I. Operating procedure. The idea can be described by considering the repeated batch operation as follows (see Fig. 9): (1) Cells are inoculated into bioreactor A which is filled with nutrient, and the cultivation is started. (2) When the cell concentration X, reaches some specified value X*, or when it has been cultivated for a duration T, then a fraction 7 of the culture medium is transferred into bioreactor B. (3) Both bioreactors A and B are filled with fresh medium to the maximum working volume. Bioreactor A continues cultivation and bioreactor B starts cultivation,. (4) When the cell concentration in bioreactor B reaches X *, or it is cultivated for T, all the contents of bioreactor A are harvested.

K.

922 1

SHIMIZIJ

I

,?‘I’

Production cont.

-------

0

Cell cont.

f

Time

Fig. 8. Illustration of typical cell growth and product formation curves: x cell concentration.

(1)

(7)

??

fl

f-pt

i

. ..-..i

B A Fig. 9. Repeated fed-hatch operation using two fermentors: M, Medium; C, Cells; Pt, Product; A, B, two different fermenters.

2.3.2. Application to acetic acidfermentatiqn. The idea of using multiple bioreactors can be successfully applied to many other processes. We applied this . idea to improve the efficiency of vinegar production, and showed the usefulness of using multiple bipreactors by comparing the noninferior sets (Ito et al., 1991). In vinegar production, ethanol is supplied as the main substrate, and acetic acid is produced as the main metabolic product. It has been shown that the cell growth is little affected if the ethanol concentration in the bioreactor is kept at around S-30 g/ 1, which is not difficult to attain in practice by the conventional fed-batch mode of operation. The problem is growth inhibition due to the accumulation of acetic acid. In the conventional fedbatch operation, the productivity has been limited since the growth inhibition becomes quite significant when the acetic acid concentration increases to more than 5Ogll. It should be noted that the acetate concentration should be more than 8Og/l for the product in practice. The repeated-batch operation may be consider+ for increasing productivity. However, as has been pointed out by Park et al. (1991), the number of viable cells tends to decrease abruptly as the acetic acid concentration increases to more than about 60 g/l. This means that an improvement in the productivity can hardly’be expected if the culture broth is harvested when the acetic acid concentration reaches about 80-9Og/l and part of the culture medium is used as the inoculation for the next cultivation. It should be recalled that the acetate concentration must be:higher than about 80 g/l of the product, while the number of viable cells in the medium to be used as the inoculation should be high. These contradictory requirements can be satisfied by the repeated fed-batch operation using multiple biol reactors. Based on the batch experiemnts and the work done by Park et al. (1991), we developed the following mathematical model. dX,ldt = {p (P) -

(5) Then the fraction q of the contents of bioreactor B is transferred into bioreactor A. (6) Fresh medium is added into both bioreactors to their maximum working volume, and cultivation is continued. (7) When the cell concentration of bioreactor A reaches X *, or when cultivation time reaches T, all the contents of bioreactor B are harvested. The above procedure is repeated from step (2). By the above operation, younger cells can be used for inoculation of the repeated batch (or fed-batch) operation.

dXJdt=

K(P)xv

K(P)}X, -

dX,ldt = yX., dP/dt=x(P)(X,+X,,)

yx,,

(184 W)

(18~) (18d)

where XV, X,,,, and X, are the respective concentrations of viable, nonviable and dead cells, and P is the concentration of acetic acid. Although the specific growth rate (p) is affected by both ethanol and acetic acid concentrations, p can be considered as a function of P, since the ethanol concentration can be easily maintained at around log/l. Based on the

A tutorial review on bioprocess systems engineering

0.2s S 5 OS3 5 Q 10

20 Time(h)

30

40

O

Fig. 10. Fed-batch experimental fermentaton and simulation results (solid lines).

studies of Nanba..et al.- (1984), ,u was assumed to be the following form: j.4=pLo(l+ alP)l(bo + bSP’)

(19)

where b, a,, b,,, b3 are the constant model parameters. The specific conversion rate from viable to nonviable cells (K) and the specific acetic acid production rate (x) were assumed to be the following form: l(=cP”

(20) (21)

where c, n, no, P,,,, m are the constant model parameters. Note that the specific death rate (y) in equation (18) is also a constant model parameter. Experimental data were then fit to the mathematical model (see Fig. 10). Figure 11 shows the simulation

923

result for the conventional repeated fed-batch culture using one fermentor, in which the concentration of acetic acid obtained at the end of the batch fermentation was 80 g/l. At this point r] = 0.9 of the culture broth was removed as the product. The fraction, 1 - 7 (0.1 in this case), remaining in the fermentor was used as seed for the next batch fermentation. The productivity achieved was 1.94 g/l per hour, calculated by vPflt where t is the one batch operation time. As can be seen in the figure, if we want to obtain a higher product concentration, the number of viable cells used as seed in the next culture becomes low, which in turn prolongs the fermentation time, resulting in the decrease in the productivity. The above problem can be overcome by using multiple fermentors. Figure 12 shows the simulation result for the repeated fed-batch fermentation using two fermentors. The lower figure corresponds to fermentor A, and the upper figure corresponds to fermentor B. During the first batch operation in fermentor A, when the acetic acid concentration reached 40 g/l, r,~=O.l of the culture broth was transferred into fermentor B. Fresh medium was fed to both fermentors followed by fed-batch fermentation in fermentors A and B. When the acetic acid concentration in fermentor, B was 4Og/l, the contents in fermentor A were removed as the product, in which the concentration of acetic acid (PJ was abut 8Ogll. A fraction, 9 =O.l, of the culture broth in fermentor B was then transferred into fermentor A, and the procedure was repeated. It should be noted that the number of viable cells used as seed when the acetic acid concentration was about 40 g/l was quite high, and that the product concentration obtained from the other fermentor was quite high (abut 80 g/l). This resulted in an increase in productivity (3.55 g/l per hour in this case). The productivity was calculated as PJ2r where r is the time from inoculation to harvest. Figure 13 shows the comparison of

Time(h)

Fig. 11. Time courses of cell and acetic acid concentratons for repeated fed-batch fermentation using one firmentor: -, acetic acid concentration; -.--, non-viable cell concentration; ---, viable cell concentration.

K.

924

!$HIMIZU

60 - Fermentor B = 350 P 840 -

Time(h)

Fig. 12. Time courses of cell and acetic acid concentrations for repeated fed-batch fermentation using two fermenters. The lines are the same as those in Fig. 11. the productivities for the three types of operation, namely, conventional fed-batch operation, repeated fed-batch operation using one fermentor, and repeated fed-batch fermentation using two fermentors, where P, denotes the product concentration. From the figure, it seems to be advantageous to use two fermentors and, in particular, at high product concentration. 2.3.3. Application to the eflicient production of gene product. Optimization and control are extremely important for the overproduction of gene products using gene engineering technology. The main problem is that the overproduction of gene products causes cell-growth inhibition and plasmid instability. To avoid this, inducible vectors and the separation of cell growth from the production of gene products can be employed (Iijima, 1991). In these vector systems, efficient transcription can usually be induced by adding some biochemical substances or by altering the cultivation temperature. Recent work has highlighted the importance of nutrient concentration and inducer level for foreign protein

Two fermentore

p, W) Fig. 13. Comparison of the productivities of a conventinal fed-batch operation. a repeated fed-batch operation using one fermentor and a repeated fed-batch operation using two fermentors with respect to acetic acid concentration harvested.

0

20

40

Time [h]

Fig. 14. Experimental results for conventional repeated fed-batch operation (arrows indicate IPTG addition).

production. It has been shown that a high inducer levels results in higher production of foreign protein in cells, although the cell growth rate was significantly reduced (Lee and Ramirez, 1992; Miao and Kompala, 1992). This means that the direct application of repeated fed-batch operation will not provide the performance improvement needed. In conventional repeated fed-batch operation, after fed-batch fermentation, most of the contents are removed as product and the rest is used as seed for the next cultivation. However, cell growth decreased several hours after induction, resulting in a long lag phase and the slow growth in the next cultivation as shown in Fig. 14, and no improvement in productivity. This problem can be overcome by considering multiple fermentors. Here we consider the efficient production of gene product by using Escherichia coli JM103 (thi, rpsL, endA, sbcB, A (lac-proB), [F’, proAB, lac1” A DM15, tra D36]) harboring plasmid pUR2921, which contains the /?-galactocidase structural gene. The induction of transcription was performed by adding IPTG (iso-propyl-P-D-thiogalactopyranoside).

A tutorial review on bioprocess systems engineering

925

After trial and error 0~ :/the modeling of the kinetics for the cultivatiob of genetically engineered microorganisms, the following mathematical model was developed (Fujioka and Shimizu, 1994): dXJdt=

{p(S, P, Z) -

dX,ldt =

K(P,

‘i. I)}X,

K(P,

Z)}X, - DX,

-y(P)&

dSldt=D(S,-S)-p(S,

-

DX,

Wa)

(22b)

P,Z)}XJY,,

-m(X”+X”)

WC)

dPldt = { a,~ (S, P, I) +/5,)X” - DP

Wd)

dG/dt = {az(Z)r (S, P, Z) +/32(Z)}Xv - SX, - DC (2%

where XV and X,, are the viable and nonviable cell concentrations, respectively. S is the substrate concentration, P is the concentration of metabolites inhibitory to growth such as acetic acid, and G is the concentration of the gene product, /?-galactocidase in this case. D is the dilution rate. The specific growth rate, ,u and the specific death rate, K were assumed to be p(S, P, Z) = [/.&Sl(Ks+S)](l.. K(P,

Z) = k.

PIP,)“‘(l

Fig. 15. Fed-batch experimental fermentation and simulation results (arrows indicate IFTG addition). Symbols: 0, cell concentration; 0, glucose concentration; A, concentration of /J-galactosidase. Line: -, estimated concentrations.

3o Fermentor B

-z/zmy2 (23)

exp(k,Z+ k*P)

Also, the specific decomposition cells, y was assumed to be Y(P)=YoPW

(24)

rate of nonviable

(25)

The formation of P and G were taken to obey the Ludeking-Piret type model, while the coefficients a2 and /I2 were assumed to be a function of the inducer concentration 1. /I-galactocidase formation was assumed to start 1 h after induction based on experimental observation, while product decomposition occurred due to the existence of protease produced by viable cells. Experimental data were fit to the mathematical model (see Fig. 15). _ As stated earlier, it is obvious that conventional repeated fed-batch fermentation will not yield the improved performance that is necessary. This problem can possibly be overcome by using multiple fermentors. Figure 16 shows the simulation results for the repeated fed-batch fermentation using two fermentors. The lower figure coresponds to fermentor A, and the upper figure corresponds to fermentor B. When the cell concentration of the first batch operation in fermentor A reached 6.75 g/l, fraction 7 of the culture broth was transferred into fermentor B. Fresh medium was fed to both fermentors followed by fed-batch fermentation in fermentors A and B. When the cell concentration in fermentor A reached

Time [h]

Fig. 16. The courses ofYcelland product concentrations for repeated fed-batch fermentation using two fermentors.

6.75 g/l, IPTG was added to fermentor A. When the cell concentration in fermentor B was 6.75 g/l, the contents in fermentor A were removed as the product. Fraction r] of the culture broth in fermentor B was then transferred into fermentor A, and the procedure was repeated,. Figure 16 shows the simulation results for v = 0.2. As can be seen from the figure, the product concentration decreased and one batch period decreased as the value of 7 was increased, contributing negatively and positively to the productivity, respectively. It should be noted that the cells used as seed when the cell concentration was 6.75 g/l were quite active, and that the product concentration obtained from the other fermentor was high if the appropriate value of q was chosen. This resulted in an increase in productivity compared with the fed-batch fermentation (see Fig. 17.

K.

926 30-

0

SHIMIZIJ

-100

/’ Ii’

20

Draw-offratio [%I

40

Fig. 17. The maximized productivities (Pr) and the optimal values of q with respect to product concentration (Pf) using two fermenters.

;cA+

0

20

B-

4

Time [h] Fig. 18. Experimental results for repeated fed-batch fermentation in the two fermentor systems (arrows indicate IPTG addition).

Figure 18 shows the experimental results when only one fermentor was .used to experimentally simulate the above proposed method. When the cell concentration became 6.75 g/l in fermentor A, it was necessary to transfer 7 (= 0.2) of the culture into fermentor B as seed in the proposed method. However, 1-v of the culture broth was removed, and the new culture was started after adding the appropriate fresh medium. This means that the second batch period simulated the cultivation in fermentor B. In this way, the third batch period simulated the cultivation in fermentor A again and so on, indicating that the high growth rate attained in the first batch period can be continued even after several repeated fed-batch operations. In the case of the fourth batch period, the cultivaton was continued until the cell concentration became 6.75 g/l,

where v of the culture broth was removed and fresh media added. The cultivation was then continued until the cell concentraton became 6.75 g/l, at which time when the inducer (IFTG, 0.3 mg/l) was added to produce the gene product. As can be seen from the figure, the first three batch periods retaified the exponential growth without exhibiting any decline, while the fourth batch period shows sufficient expression of /%galactosidase. In conclusion, it has been demonstrated that repeated fed-batch operation using multiple fermentors is a promising method for improving the productivity of gene products. 2.4. Extrative fermentation systems One of the major problems which prevent us from attaining high productivity in microbial processes is the end product inhibition of the microotganism involved due to the accumulation of toxic metabolites such as acetone, butanol, ethanol etc. in the bioreactor. Since the accumulation of toxic products slows down and finally stops the growth of microorganisms, the productivity attainable has Beti limited. A reasonable approach to increasing productivity may be to remove the toxic products as they are formed. One promising method of removing ‘the toxic metabolites is to make use of liquid-liquid extraction (Wang et al., 1981; Minier and Goma, 1982; Matsumura and Markle, 1984). The key to the success of this approach is to find the appropriate solvents which can effectively extract toxic products during cultivation. Significant efforts to find appropriate solvents demonstrates that this approach is becoming more and more attractive (Taya et al., 1985; Ishi et al., 1985). With the above-stated background, we have developed a general framework for the assessment of extractive cultivation and have shown a significant performance improvement, in particular for acetone-butanol extr,active fermentation using oleyl alcohol as an extractant (Honda et al., 1987). The basic equations which describe the batch extractive fermentation may be expressed as (see Fig. 19) dXldt=p(S,

P1, Pz, . . . , P,)X

(26a)

dSldt= -,u(S, P,, Pz, . . . , P.)XlY (26b) d(PiV+P:V*)/dt=p((S,

PI, Pz,. . . 1Pn)XV/Yi (i=1,2,.

. . ,n)

(26~)

where X and S are the cell and substrate concentrations, respectively. V is the reactor volume. In equation (26c), the asterisk refers to the solvent

A iutorial review on bioprocess systems engineering

927

phase. Pi is the ith metz$?lic product among n metabolites and Yi denote the yield coefficients defined as _ Yi=AX/APi

. . ,n)

(i=1,2,.

(27)

and are assumktti be constant. The specific growth rate is assumed to be of the form

p(S, Pl,

pz,*. . PJ= I

g

fi (1 - PlPJ; ,=I

s

(28)

In the following, we assume that ri= 1 (Z=1,2,. . . , n) for simplicity without loss of practical significance (Holzberg et al., 1967; Ghose and Tyagi, 1979). The distribution (partition) coefficient, & is defined as the ratio of the concentration of the ith metabolite in the solvent phase to that in the medium (aqueous) phase such that Pf=&Pi

. . ,n)

(i=l,2,.

J1= J

=

(V+V*)z Pi(t)V+

CpXr)V*

(1+ &)Z (I

2 =

+

(3Oa)

$iE)Pi(Z)

l+&

(30b)

where E = V*/V and Pi corresponds to the metabolite concentration of interest. t is the batch operation period. Note that the following conditions hold for the repeated batch operation as part of the medium qV(O
/

*r

w

V’

-7

-60

I

w

k

-0

- 30

z k

-0

Fig. 21. Performance evaluation of the extractive repeated-batch operation for acetone-butanol fermentation.

(1 +#i&)Pi(T) =

v+v*

-1

(2%

It may be reasonalbe to evaluate the performance of extractive fermentation systems by productivity and concentration of a metabolite, butanol in the case of butanol fermentation. The objective functions .I1 and Jz for repeated batch operation are then given by Pj(Z)V+ PxZ)V*

Fig. 20. Comparison of the performances for batch fermentations: -, extractive fermentations (II = 1); --, conventional fermentation without extraction.

El

Solvent phase

PI’

Fig. 19. Schematic representation for batch extractive fermentation.

drawn off at time T, and then fresh medium of qV and solvent of V*( = EV) are added.

S(O)= (1- G!)W + I&

(314

X(O)= Cl- rr)X(r)

@lb)

Pi(O)=(l-~)Pi(Z)l(l+#i&)

(i=l,2,.

. . ,?l) (314

Figure 20 shows the simulation result for the batch operation (v = 1) for various values of f#~.It clearly shows the significant performance improvement for the extractive fermentation using oleyl alcohol (qJ=3.7). Figure 21 shows the simulation result for the repeated batch operation, where the optimization was carried out with respect to 7 and E for the specified values of J2. Here the substrate concentration was assumed to be limited to the range between 0 and 80 g/l, .because substrate inhibition occurs in practice for acetone-butanol fermentation (Taya et al., 1985). As can be seen from Fig. 21, a significant improvement is observed in comparison with the result of batch operation. On the other hand, the maximum value of Jz was below that obtained for

K.

928

SHlMlZU

the batch operation,. .,This is due to the upper limitation of the substrate concentration. Note that in such microbial processes as acetonebutanol cultivation, more than one metabolite such as acetone, butanol, ethanol etc is formed during cultivation,_ each affecting the growth of the microorganism in a complex way. We developed a solvent screening criterion based on the maximum product concentration attainable for the assessment of batch and semi-continuous multicomponent extractive fermentations (Shimizu and Matsubara, 1987). The theorem and corollary developed have proven useful in screening oleyle alcohol to be the best solvent for butanol extractive fermentation. In the extractive fermentation using oleyl alcohol as an extractant, the primary toxic metabolite, such as butanol

is selectively

As the butanol

extracted

is extracted,

bFPI4 VU)

\

F

p,(i).

v(2)

P,(l)

b

.

I

=

m-LBroth 0-L v, x, s, p,

I

I

Fig. 22. Schematic illustration of the batch extractive fermentation adding two solvents simultaneously.

from the medium.

however,

another

meta-

such as acetone becomes the next critical metabolite which slows down and finally stops the growth. With this in mind, it is quite reasonable to consider the more efficient extractive cultivation strategy using mutiple solvents each extracting a different metabolite selectively. Since the microbial process is multicomponent in nature, the theoretical development is highly complicated. We have made a detailed, yet general, mathematical formulation, where two types of solventsupplying strategies were considered. One is to add multiple solvents simultaneously and the product is removed at one time (see Fig. 22). Another is to add them one by one consecutively (see Fig. 23). This was applied to batch, fed-batch, and repeated fedbatch operation of acetone-butanol cultivation to show the power of the approach. Figures 24 and 25 show the transient of fed-batch and repeated fedbatch extractive fermentation. The optimization results show that the significant performance improvement in terms of the productivity and product concentration can be attained when two extractants such as oleyl alcohol and benzyl benzoate were used as compared with the case of using only one solvent (Shi et al., 1990).

bolite

:I +

Solvent 2

Solvent 1

r

in the medium

2.5. Cell recycle system with filtration The efficient cultivation of lactate producing microorganisms has been one of the most important subjects in the food industry, and extensive studies have been done in the past in this area. A common problem for the metabolite producing fermentations is the end-product inhibition to bacterial growth, which in turn limits the effective cell mass and metabolite production. In lactic acid fermentation, lactate and other carboxylic acids are

-7

I Product

v, x, S, P,

1 v, K s p, 1 I

t=o

t = z,

t=

I

‘L,+

Fig. 23. Schematic illustration of the hatch extractive fermentation adding two solvents consecutively.

produced, and the acids produced inhibit bacterial growth. To overcome this difficulty, a novel cell recycle system with crossflow filtration has been paid recent attention (Taniguchi et al., 1987). The success of this cultivation, however, depends on the efficient use of the fresh medium since a large amount of the medium together with metabolites needs to be drawn off through the filter. One idea is to keep the lactate concentration constant with feedback contol (Wang et al., 1988; Shi et al., 1990). Although this idea had some success, a more efficient strategy needs to be developed for the efficient use of the medium in practice. We considered the optimal draw-off strategy for the cell-recycle fermentor system making use of the Green’s theorem, and examined its usefulness by computer simulation and experiments. As for the derivation of the optimal operation of bioprocesses, extensive works have been conducted

A tuorial review on bioprocess systems engineering

10

Time

30

20

929

10

0

20

Time

(h)

30

(h)

Fig. 24. Transient acetone and butanol concentrations in the broth phase for fed-batch extractive fermentaton (a) with oleyl alcohol as an extractant and (b) with oleyl alcohol and benzyl benzoate as extractants: (-) butanol concentration; (- - -) acetone concentration.

2

2o

. .._...-....

E

0

10

20

I.

30

5

20

IO

0

Time (h)

30

Time (h)

Fig. 25. Transient acetone and butanol concentrations in the broth phase for repeated fed-batch extractive fermentation (a) with oleyl alcohol as an extractant and (b) with oleyl alcohol and benzyl benzoate as extractants: (-) butanol concentration; (- - -) acetone concentration.

in the past (Shimizu, 1993). Some researchers applied the maximum principle, while others used the Green’s theorem in deriving the optimal feeding rate of the sustrate etc. We attempted to apply the Green’s theorem in deriving the optimal draw-off rate through the filter for the cell recycle bioreactor system as shown in Fig. 26 schematically.

Fermenter

Draw-ofi stream Bleed etream

Fig. 26. Cell recycle system with cross flow filtration.

2.5.1. Model equations. Typical mathematical equations which describe the cell-recycle system with filtration may be expressed as

dXldt =/A (S, P)X dPldt=

-DP+x(S,

dSldt = D(&-

(32a) P)X

S) - u(S, P)X

Wb)

(324 where X and S tire the cell and substrate concentrations in the broth, respectively. SF is the substrate concentration of the feed, and D is the dilution rate. p, x, r~ are the specific rates associated with cell growth, lactate production, and substrate consumption, respectively. Although they may be functions of S and P as indicated in equation (32) we assume the above specific rates to be only function of P, since we can supply enough substrate so that the substate concentration in the culture broth is kept above 10 g/l which is far from the substrate-limiting situation. Then equations (32a) and (32b) can be decoupled from equation (32~).

K.

930

P

SHIMIZIJ

where

:I’./;

o(P,X)=--=-

w

PW (37)

ap FIX

Where (‘) means the derivative with respect to P, namely p’(P) = d(p (P))IdP. Note that w <.O ‘since p is the decreasing function with respect to P, which means that r,,,< qOF. Thus the minimal time trajectory is obtained as the horizontal broken line in Fig. 27, where the corresponding operation is that D=m.

The result obtained so far may be of some help, but it is not of practical interest since large amount of medium is drawn off without efficient use. A constraint on the total amount of medium to be used may be expressed as follows: Fig. 27. Minimal time trajectories. rD(t)dr=C 25.2.

I

Analysis of the optimal operation problem

without constraint. The problem

can now be stated

as follows: Problem 1. Given the initial state, find the optimal strategy for D(t) which attains the specified value of X(r) in the minimal time, where T is the cultivation time. ‘.The solution to Problem 1 can be obtained by making use of the Green’s theorem (Miele, 1962) as follows: It follows from equation (32a) that

where C is some specified constant. 2.5.3. Analysis of the optimal operation problem under constraint. As stated above, Pl needs tra b modified from the practical application point of view such as Problem 2. Consider Problem 1 under the constraint of (38). To solve this problem reexpress the constraint (38) using equation (32b) as

x(r) r=

9 (F, X) dX I z(O)

(38)

0

‘v(P,X)dt=C+ln{P(r)/P(O)}=C*

(33)

I

(39)

0

where

where #(F, X) = l/p (P)X

‘I (P, X) = x(P)X/P

W)

(39) can be reexpressed

using equation

(34)

Let F be a simple closed curve in the PX-plane and Z the region surrounded by F. Then it follows from the Green’s theorem that

Equation (32a) as

x(r)

q*(P, X) dX= c*

(41)

x(0) ?dPdX xap

(35)

where the path of the line integral in the left side of equation (35) must be taken counterclockwise. Let Z and F be the initial and final states, respectively, in the PX-plane as shown in Fig. 27. Let IPF and IQF be the trajectories connecting I and Fin the PX-plane. Then if the curve IPF is located in the lower side of IQF, it follows from equations (33) and (35) that %PF -

TIOF =

where rl*

TIPF -

w (P, X) dXdP IPFOI

TIQF =

@*U’s f

where

dX

w*(P, X) dXdP IPFOI

(36)

W

IPMI

=

IPFOI

=

(42)

Then the optimal operation problem under the constraint (41) can be solved by introducing the Lagrange multiplier 1. In a similar manner as before, we have

9(PIW~ f

(PI X) = JmWP u-7)

(43)

A tutorial review on bioprocess systems engineering 15

yip ,a;' aq* W*=_-_~ap ap

and

(Mb)

The set satisfying ‘{_~_w*(P, X) = 0

(45)

represents a family of curve, and more specifically one curve for each value oft. The particular value of rl associated with our problem is to be determined by the prescribed boundary conditions and the value of C. Note that whenever equation (45) is satisfied for a finite interval of time, the following equation must also be satisfied: do*(P, X)ldt=

0

0

(46)

Although various forms for x may be considered, the Ludeking-Piret type model is by far important from the practical application point of view, namely, 3r=aj.4+B

(47)

If we consider equation (47) for x, equations (45) and (46) reduce to the following respective equations /l’= -nxq.llP(P+~/9x)

(4%

..

and

5

lime@] Fig. 28. Optimal operations for varous values of 1.

dP/dt = f = - AXp (q +/3P/d)I{ZP/d + P’/l” + nx(2q.J

+ pP/d”)}

(49)

Then the draw-off strategy can also be obtained from equations (32b) and (49) as

20 OptimalOpenlion

15

(50)

10

data were fitted to equation (32) where p was assumed to be of the following form:

5

D(t)=(-~+JcX)/P 2.5.4.

Simulation. The batch experimental

p(P)=p,exp(-aP+b)

(51)

Figure 28 shows the simulation result which represents a family of curves of the dilution rate and the lactate concentration, more specifically, one curve for each value of 1. Figure 29 shows the comparison of the performances obtained by the simulation for the optimal operation and the case of keeping the lactate concentration constant. Suppose that 60 1 of the medium was allowed to use. Then as can be seen from Fig. 29, the productivity of 13 [OD,,,/h] could be attained by the optimal operation, while around 8.5 was attained by keeping the lactate concentration constant. Thus Fig. 29 indicates the advantage of the optimal operation in particular at high cell density cultivation as compared with the case of keeping the lactate concentration constant. The experimental verification was also made, and the superiority of the proposed method was shown (Shimizu, 1994a).

.

I \ constantP. Id 0

20

40

60

80

100

Total medium used[dm3 ] Fig. 29. Comparison between the performance of optimal operation and the case of constant lactate concentration. 3. CONTROL SYSTEM DESIGN

The ability to control fermentation processes at their optimal states accurately and automatically is now of considerable interest to many fermentation industries since it can enable them to reduce their production costs and increase the yield while at the same time maintaining the quality of metabolic products. It should be noted, however, that the control system design of bioreactors is not straightforward due to (1) significant model uncertainty, (2) time-varying and nonlinear nature, (3) lack of reliable on-line sensors, and

K.

932

SHIMIZIJ

(4) slow response.

,,’.i” To cope with the first problem, the control system must be -robust for model uncertainties with the ability of disturbance rejection. For the second problem, the adaptive type of control strategy may be considered. As for the third problem, the effective on-line sensors are limited for use in many cases so that some sort of observer and/or parameter estimator needs to be designed from the available measurement variables. As for the fourth problem, the predictive type of control strategy may be considered. Many control strategies have been proposed so far and applied in practice to overcome the above problems, and many others are still in progress (Shimizu, 1993). 3.1. On-line optimizing control The above characteristics must be carefully considered for the on-line optimizing control of continuous lactic acid fermentation. The objective of on-line optimizing control of bioreactors is to keep tracking the optimal state in accordance with enzymatic deactivation and environmental changes. Although._several techniques have been developed in the field of chemical engineering, the direct application of the steady-state optimization turns out to be very slow in reaching the optimum point. Here we considered the method of on-line optimization with dynamic model identification (Bamberger and Iserman, 1987). Several applications to bioprocesses show some success (Rolf and Lim, 1984, 1985). It is particularly useful and convenient to consider the control problem in the framework of hierarchical structure (Garcia and Morari, 1981). Here, the control task is divided into two, one of which is to search for the optimal operating point and pass the set point to the lower layer in the hierarchical control structure. The other task is then to make the process output follow the set point as soon as possible in the lower-layer. To cope with the disturbances and model uncertainties, the closedloop optimizing control structure (Garcia and Moarari, 1984) was used. 3.1.1. Hierarchical control structure. The performance index for a continuous bioreactor system may be expressed as J=J(r,

u,p)

index J must be optimized by changing the inputs u, and the relationships of the nonlinear process y= g(u,p) are not known accurately, some sort of search algorithm must be incorporated. Furthermore, the optimization must take into account the process dynamics since the direct-Lapplication of a steady-state optimization turns out to be very slow in reaching the optimum point. Let the local dynamics of a process be expressed by the following model: A(z-‘)y(k)=B(z-‘)u(k-l)+E

(53)

where z-l denotes the backward-shift operator and E is the process bias. The sampling instant is denoted by k(f), 192,. . .). A is a diagonal polynomial matrix with elements: . . . . + ajf)z-” >

,Jii(z-‘) = I + ak)z-l+

. . ,m

i=l,Z,.

(54)

and B is a polynomial matrix with elements: Bik(z-l) =bji’+ b$)z-‘+

i=l,2

,...,

m:

. . . + b$‘Z-’

k=1,2

,...,

m

(55)

Here, we assume the time-delay associated with the input to be negligible. The inclusion of the timedelay will give us the similar result parallel to the following discussion, Let the data vector and parameter vector for the ith output be denoted by $i and Bi, respectively, and let them be defined as #T(k)=[-yi(k-1)~

n. m,

-yi(k-2),

-YiW-n),

udk-

11,. . . , ...,

ri,(k-r-l),u,(k-l), t&-r-l),.

. . ,u,(k-l),.

u,(k-r-l),

l]

i=l,2,.

.., . . ,m

@= [a!;), af), . . , , al:), bf) 1. . . , bj:‘, b$“, . . . , bk’, . . . , b:,

. . . , bit 51,

i=l,2,...,m

Then, the recursive least squares parameter estimation is given by

(52)

where y, u, and p are the output, input, and parameter vectors of appropriate dimensions, respectively. As the performance index, the yield of product per gram of substrate, the product concentration, the rate of product formation, etc., may be considered for a microbial process. Since performance

x [Y

w - m - lMi(~)l

(56)

Pi(k+ l)={llrti(k)} Pi(k)$i(k)#T(k)P,(k) '

[

p'(k)-l,(k)ll*(k)

+#:(k)Pi(k)$i(k)

1

(57)

933

A tutorial review on bioprocess systems engineering where fii is the ideqtified, p&Aeter vector and Pi(k) is the error covariance matrix. Note that the higher order Hammers&in models may also be used for equation (53). Let gik(z-l) .ve the (ik)th element of the inputoutput transfer fu&tion matrix of the process. Then ga(z-‘) =Bik(z-‘)IAii(z-‘) The steady state gain is obtained

(58)

by setting z = 1 in

equation (58) such that gti(I)=Bik(I)IAii(I)

(59)

Now, if the gradient search algorithm is employed for the on-line optimization, the input u(k) are updated as follows: u(k+l)=u(k)+cU(k)V,JI,

U)lk’MY,

model Identifier ri

Fig. 30. Block diagram for the on-line optimizing control.

(60)

where 6 is the fixed step size and S(k) is a positive definite matrix. V,JI,, is the gradient of the objective function at u(k), and is obtained from: EJ(Y,

Dynrmlc

u)lauTIL

Lw contraII--er

+ ~J(Y, 4WT14Wdu?, (61) where (dylduT)k can be evaluated from equation (59). ‘.3.1.2. Application to lactic acid fermentation. Lactic acid fermentation has been one of the most important microbial processes in food industry, and there is a strong interest in industry to obtain the lactic acid continuously with the maximum production rate. Let the performance index be expressed as a polynomial of a single output variable such as J(k)=a.y”(k)+a,_ly”-‘(k)+...+a,y(k)+~ (62)

where k is the sampling instant. It was assumed that J(k) is computed from the measured input and output variables. ai (i = 0, 1, . . . , n) are identified on-line using the recursive least squares method. In the lower layer, multivariable self-tuning controllers were designed. We applied the on-line optimizing control strategy to the cell recycle system with cross-flow filtration (Shi et al., 1989, 1990). The block diagram of the control system is shown in Fig. 30. The input variables were the draw-off rate through the filter and the bleed stream flow rate. The output variables were the lactate and cell concentrations. Noting that lactate is the only organic acid to be produced in homofermentative lactic acid bacteria, an on-line estimation of lactate concentration could be made by counting the amount of alkaline solution supplied to neutralize the culture broth. For the on-line measurement of cell concentration, the laser turbidimeter was used (see Fig. 31). The experiments were

Fig. 31. Schematic illustration of the control system for lactic acid fermentation. conducted so as to maximize the productivity of lactate while keeping the lactate concentration at 3Og/l. Figure 32 shows the experimental result, where QP, vP, ,u denote the productivity of lactate, the specific lactate production rate, and the specific growth rate, respectively. The productivity of about 22 g/l/h could be attained by this experiment. Now, in many bioprocesses, a large amount of energy is required for the purification in the downstream processes. We, therefore, considered the optimizing control of the total system which includes some down-stream processes since the lactate concentration in the filter fermentation is not so high, and some culture medium was drawn-off without efficient use. Several types of down stream processes were considered. One is the extraction process using alamin 336. The overall control system is shown in Fig. 33, where two computers were used. One is to control the fermentor and the other is to control the down-stream process. Two computers were communicated with RS232C cable. 3.2. Knowledge-based control Although it is fairly difficult to describe exactly the behavior of microorganisms by means of mathematical expression in many cases, it may be possible to make use of the information obtainable from

K.

934

SHIMIZU

1150

4c

0

2

0

P g

Oo

Ml 0

% A

2

000

100 g 8

2c 50

0

Time (h) Fig. 32. Optimizing control for the continuous fermentation was set at 30 g/l.

of o-lactate where lactate concentration

Fig. 33. Schematic illustration for computer control of lactic acid fermentation: (1) fermenter; (2) laser turbidimeter; (3) pH-mater; (4) medium; (5) hollow-fiber module; (6) mixer; (7) settler; (8) solvent; (9) NaOH solution; (10) computer; (11) HCI solution. operators’

intuitions

and experiences

for the control

of bioreactors. The expert system characterizes the process dynamics by symbolic and logic description

to check data consistency,

equipment failure, and contamination for the efficient operation (Endo et al., 1989; Asama et al., 1991)

A tutorial review on bioprocess systems engineering 935 . It seems, therefore, to be quite natural to consider On the other hand, ft&)r”sets theory has been hybrid types of control strategies which retain both paid recent attention, and has been applied to variadvantages of fuzzy control and the neural ous bioprocesses&ch as glutamic acid fermentation networks. Several schemes have recently been pro(Nakamura et al., 1985)) antibiotic fermentation (Fu posed, and those may be classified as shown in Fig,.. et al., 1988; C&n et al., 1988), SCP production 34 (Hayashi and Umano, 1993). (Konstantinov and Yoshida, 1989) coenzyme Qio 3.3.2. Neuro-fuzzy control of bioreactor systems. production (Yamada et al., 1991), and sake brewing In baker’s yeast cultivation, certain relationships (Oishi et al., 1991; Matsuura et al., 1991). Since the exist between the glucose concentration in the ferprocess state significantly changes as time proceeds mentor and the changing patterns in the DO (disin the batch or fed-batch type of operation, the solved oxygen) and ethanol concentrations; an membership functions should be changed in accordexcess amount of glucose causes the Crabtree effect ance with the process state (Konstantinov and and the ethanol concentration tends to increase, Yoshida, 1989; Kishimoto et al., 1991). We prowhile if glucose is not present in the fermentor the posed a neuro-fuzzy control strategy where the accumulated ethanol is consumed as a substrate and membership functions were changed in accordance the ethanol concentration tends to decrease. with the changing patterns of the state variables where the patterns were recognized on-line by Moreover, if the substrate is consumed and no substrate is present in the fermentor, the cell growth neural networks (Shi and Shimizu, 1992). stops and the DO concentration abruptly increases Recently, Konstantinov and Yoshida (1992) because of the mass balance for oxygen. In this reviewed the knowledge-based control strategies situation, if glucose is supplied the DO concentraand summarized their functions as follows: tion returns to its original level. When the cell (1) input data validation, concentration becomes high, the supplied glucose is (2) identification of the state of the cell culture, consumed quickly, and the repetition of the (3) detection and diagnostics of instrumentation sequence makes the DO concentration tend to oscilfault, late. (4) supervision of conventional control, Now the idea is to make use of these relationships (5) communication with the user, for indirect but efficient monitoring of the glucose (6) plantwide supervision and scheduling. concentration in the fermentor. Here we considered adjusting the membership functions of fuzzy control It should be noted that the control system must on-line with the aid of neural networks, where the eventually be extended to the related upstream or role of neural networks is to recognize the patterns downstream processes. Konstantinov and Yoshida (1989) proposed a of the changes in DO and ethanol concentrations (see Fig. 35 for the block diagram of the control methodology for the control of bioprocesses based system). on the expert identification of the physiological state As for the pattern recognition, we employed the of the cell population. The physiological state was 3-layered neural netowrk as shown in Fig. 36. Figure defined quantitatively by a set of specially selected variables that form the physiological state space of 37(a) shows the experimental result where wild strain of E. coli B was cultivated with DO-stat. the culture. Upon transfer from one to another Figure 37(b) shows the corresponding change in DO state. It often exhibits variable structure behavior, concentration. Figure 38 shows another experiment and therefore different control strategy must be using the same strain. After training of the experiapplied. mental data of Fig. 37(b), we studied how the neural network can recognize the specific oscillating pat3.3. Neuro-fuzzy control tern. Figure 39 shows the output of the neural 3.3.1. Classification of neuro-fuzzy control strate- network. Although the identification may not be good enough, the identifying ability can be signifigies. The advantages of the fuzzy control approach cantly improved by learning two experimental data are that mathematical models are not required, and (see Fig. 40). that qualitative information, even vague knowledge, One of the eventual goals of gene engineering is can be treated by linguistic rules. However, it has to maximize the production of useful metabolites. long been said that it is a cumbersome procedure For the overproduction of gene products, the optiand it takes too much time to decide the IF-THEN mization and control become more and more type of linguistic rules and membership functions. important. The main problem is that the overproOn the other hand, attention has recently been duction of gene products causes the inhibition of cell focused on the learning ability of neural networks.

K.

936

SHIMIZU

(4

UN

Input

Input

outpul

output

Different control object (I) lntergratlon

type

Input

oulput

(c) Input

OUlPUl giEEFor1 (II) Correctlon

Input

type

output

(4 Input

oulput

Fuzzy-neuro

If A then S

(f) Input

output

Structure llke fuzzy rule

(9) Input

(h)

OlHput

Fig. 34. Classificaton of neuro-fuzzy control strategies.

Set Points

/ ,A AF Fuzzy Controller +

+

F+AF

??

Woreactor

Neural Network 1 Regulation of Membership

Fig. 35. Block diagram of neuro-fuzzy control.

e

DO.ETOR ; *

A tutorial review on bioprocess systems engineering

937

0 Optical density at 620nm A Qlucose concentration ?? Acetic acid concentration

Time (h) Hidden layer

Input layer

Output layer

Fig. 36. Configuration of neural network.

B

(b)

‘+-+

I

7

‘+-j

Oocillatlon

it_*i

Oaoillation

Omdlatlon

Optlcal density at 620nm concentration ?? Acetlc acid concentration

??

A Giucose

01

0

5

10

15

Time (h) Fig. 38. 2nd experimental result of E. coli cultivation. 1)

I

I

Time (h)

(b) &

P g

e-

0

4

10

5

15

Time (h)

8 g

Fig. 39. Output of the neural network trained by the 1st cultivation data. The value 1 corresponds to the specific oscillating pattern.

2

-1

0

4

0

12

16

Time (h) Fig. 37. 1st experimental result of E. coli cultivation.

growth

and instability

of plasmids.

To avoid this,

one can use inducible vectors and separate cell growth from the production of gene products. In

these

vector

systems,

efficient

transcription

can

K.

938

SHIMIZU

where Ai and Bk represent linguistic labels.. ei, ck, are the parameters which define the OAi, &?, membership functions, and those values are determined by training. In level 2, application of fuzzy rules and the logic i. operation are made such as x =

1 10

5’

15

Time (h) Fig. 40. Output of the neural network trained by the 1st and 2nd cultivation data. The value 1 corresponds to the specific oscillating pattern.

Level 4

Level 2

Level

’ oBk

.w

where OAi and Oak mean the outputs from level 1 and “ . ” means AND operation. Levels 3 and 4 are the conventional neural network, where the weights Wikare determined by training. Figure 42 shows the schematic illustration of the. experimental configuration. Figure 43 shows how the membership functions are changed before and after training, where ApH and Ap (specific growth rate) were used as the input variables to FNN. In the experiment, E. coli JM103 harboring pUR2921 plasmid was used. The plasmid contains the structure gene of /Igalactosidase and the induction of the transcription was made by adding IPTG (isopropyl-fi-DBi thiogalactopyranoside). Figure 44 shows the experimental result where different membership functions were employed before and after induction. The high productivity of gene product could be attained by this control method. 3.4. Controlled

1

oAi

cultivation

of

gene-engineered

microorganisms

IXVClO c

c

Fig. 41. The architecture of the FNN.

usually

be induced by adding some biochemical such as isopropyl B-Dthiogalactopyranoside (IPGT) etc or by shifting the culture temperature. For the overproduction of gene products, it is of critical importance to control the culture environment, in particular, it is of primal importance to control the substrate concentration in the broth. We therefore, considered a new type of fuzzy neural network (FNN) as shown in Fig. 41 (Ye etal., 1994). In level 0 of Fig. 41, the scaling is made for the input variables. In level 1, membership functions are adjusted where the following type of membership functions were used: substances

[ - Ue- ei)l~,Jl fL&>= [ - {Cc - mJB,1*1 f&r) =

(634 WI

Recent progress in gene engineering will permit the overproduction of industrially important enzymes, hormones, drugs, at an industrial scale. In the overproduction of gene products by gene engineering, the enhancement of plasmid copy number, stabilty of plasmid, and high efficiency of transcription are important, and many plasmid vector systems such as expression vectors and high copy number plasmids have been developed. However, the overproduction of gene products causes the depressed cell growth and the instability of plasmids. Runaway-replication plasmids render cell growth independent of gene product formation, and the amplification of plasmid DNA is inducible by raising the culture temperature. The copy number of these plasmids is restricted to about 20 copies per cell below 30” C, but the plasmid replicates as much as 2000 copies per cell at temperatures higher than 35 “C. The increased plasmid copy number yields overproduction of gene products due to gene dosage effect. The problem is how to change the culture temperature during fed-batch cultivations (Mizutani et al., 1987).

A tutorial review on bioprocess systems engineering

-4 Glucose

939

AID

Air 02 14 %

Fermentor

~................................__._.._______..._.............

LJ

\

oDIA ..... . .. ..

:.......................................................................

Fig. 42. Schematic illustration of the control system for the fed-batch cultivation of recombinant E. coli. ..

High

expression

vectors

are useful whenever

with

cell growth

strong

promoters

can be segregated

from overproduction of gene product. Several researchers used some E. coli cells harboring a

NS

NM

PM PL

recombinant moter.

plasmid

Biosynthesis

ZE

Fuzzy subsets of ApH

1acZ fused

to trp pro-

is stimulated

8

NS

NM

ZE

PM

PL

Fuzzy subsets of Ap

PM PL

by

tryptophan deficiency and repressed by tryptophan. In the fed-batch cultivation, when tryptophan is

Fuzzy subsets of ApH

NM

with

of gene’product

ZE

NS NM

Fuzzy subsets of Ap

Fig. 43. Membership functions before (a) and after (b) training.

PM

PL

940

K.

SHIMIZU

20.000 15.000 10,000 5000

0

4

s

12

16

20

24

Time [h] Fig. 44. Controlled cultivation of gene-engineered

absent, the trp promoter is switched on from the start of the cultivation. Therefore, the efficient switching strategy for the trp promoter from off to on by altering the tryptophan concentration is critical for the production of gene product (Mizutani et al., 1988). To increase the transcription efficiency, baker’s yeast carrying SUC and PGK promoters is promising. In this case, on-off regulation of gene expression from SUC promoter can be attained by controlling the glucose concentration in the fermentor (Lin et al., 1989). The efficient control of culture environment is, therefore, quite important in particular for the high density cultivation of gene-engineered microorganisms, animal cells etc.

4. DISCUSSIONS

AND FUTURE PERSECTIVES

With the recent significant developments in biotechnology, it is increasingly important to control bioreactor systems (Omstead, 1990; Leigh, 1987), and a variety of control strategies have been applied to many bioprocesses. The current problem which needs to be solved may be the on-line optimizing control for batch or fed-batch type of cultivation since such modes of operations are extensively employed in industry. There may be several approaches to attain optimizing control for such modes of operations. One way is to consider the hierarchical control structure where the task of the upper layer is to recognize or learn the dynamics of the whole stage of cultivation based on the past cultivations, and to find the optimal trajectory. This may be made using the artificial neural networks. The main task of the lower layer is to track the optimal trajectory determined in the upper layer, but the problem is not so simple since the current process state may not be the same as that corresponding to the optimal trajectory. Then the

microorganisms.

optimal trajectory must be modified taking into account the current state condition. One idea to cope with this problem is to employ the predictive of control strategy. It should be noted that the important thing in considering the control problem is not simply to apply sophisticated control theory but to consider* with deep understanding of the dynamics of the physiological state changes. It is, therefore, quite important to investigate how the physiological state changes in relation to genetic changes and environmental change, and the so called “metabolic engineering” seems to be quite promising (Bailey, 1991; Stephanopoulos and Vallino, 1991). During the past several years, some of the chemical engineering departments and applied chemistry departments have changed their department names to bioengineering-related names, and many new bioengineer$g-related departments have recently been established in Japan. It is estimated that nearly 3000 students will graduate from bioengineering departments by the end of this century in Japan. This seems to be quite a big move. On the other hand, the Japanese govemment recognizes the importance of computer science in accordance with the significant recent progress in computer machines. Noting the current growing information society, the Japanese government estimates that information engineers will be in short supply in the early 21st century, and is making significant efforts in computer science education. Based on the above two developments in Japan, it is not difficult to understand that the research on “Bioprocess Systems Engineering” is becoming more and more important. REFERENCES

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