rx = dX = f (X, s, I,..)

d t

Gfl

dX = PX dt

dX = PX

ii-

tWnl3n” 28

BT 421 5 7

/J =ldX- -X dt

p lihf%?lnlou~~~illwlt: (specific growth rate)

Xt

I dX = - itp dt fiun74M29-

xw X t16x7

58 BT 421

c - Lag t ime- - - fJ/

---yI---

d t

BT 421 59

td = I n 2

c1

= 0.693 tWnld 32

/-&, (h-‘1 l,, (h)

Escherichia coli 2 . 1

Saccharomyces cerevisiae 0.45

Candida utilis 0.40

Schizosaccharomyces pombe 0.17

Penicillium chrysogenum 0.20

Geotrichum la&is 0.35

Fusarium graminearum 0.28

Chlorella pyrenoidosa 0.08

0.33

1 . 5

1.7

4.0

2.5

2.0

2.5

8.5

60 BT 421

1lfl Xt = (e I”‘)”

-2muI- n = 3.32 log X,

0 980

1 0 1700

30 4000

40 6200

BT 421 61

62 BT421

FilA?lU&)lmY LCIM 1 = O.O206(ul?i)-'

48.5Y

k& 1092 = 0.0206

t Nd= 109 2

0.0206

= 1 4 . 6 UI+I

da = -k. 5, exp (p 1) d t

BT421 6 3

a0 = k, (X,, ew ( p tJ - X0)

P

a0 = k, (X,-X,,

Go

kc2

X, = X,exp(ptJ m2.m~ 33

dX = p x (1 -f (lJ%.llmAl~W))

CJt

64 BT 421

LdfliilMl.AGll6 f ( Lhlr\dfll%w) = bC,

dX = PX (1 -bC,)

dt

dX = px wpx,-d t

x, = X, w (p-1)

1 - p X, (l-exp ( p t) )

nufnd 34

BT 421 65

-dX = &, X

dt

1 dX = & dt-X

In ’ = i-b tjeath-

X*

‘a tdealh = t-g

rns = exp (d-b tdeati)

K, + S

rx = dX-

dt

= p,sx

66

K, + S

BT 421

_-_---- ---

I;?-

E ‘I6 i Ks6

l%nrua1sa1lms 6)

1 = KS 1 + 1 m.md 36- - -

CL Pnl s hll

Q = 8.5 - 3.4

r-l, 11.9

m.Yn t7.h

Teisser Equation :

Mose Equation :

p = p., (1 - e -KS)

CL = I-L s"

Centois Equation :

K, + S”

= /J, (I+ K,S4)-’

CL= PnlS

68

K,X + S

BT 421

E. co/i glucose

mannitol

lactose

Ecoli (auxotroph) trytophan

Aspergillus niger glucose

A. niger (auxotroph) arginine

Candida utilis glycerol

C. utilis O*

Saccharomyces cerevisiae

glucose

Pseudomonas sp. methanol

Pseudomonas sp. methane

Klebsiella aerogenes CO,

K. aerogenes Mg2+

K. aerogenes K+

K. aerogenes so,-*

6.8 x 1 o-

2.0

20.0

1.1 x 1o-3

5.0

0.5

4.5

0.45

25.0

0.7

0.4

0.4

0.56

0.39

2.7

BT 421 6 9

0 0.100 40.00

1 0.134 39.93

2 0.180 39.83

3 0.241 39.70

4 0.323 39.50

5 0.433 39.30

6 0.581 38.97

7 0.778 38.50

8 1.040 38.00

9 1.400 37.20

10 1.870 36.20

11 2.500 34.80

12 3.350 32.90

13 4.490 30.50

14 6.000 27.20

15 8.000 22.80

16 10.70 17.10

17 14.10 9.60

18 17.90 1.11

70 BT 421

0 0.100 - - - 40.00 0.250

1 0.134 0.040 0.298 3.356 39.93 0.025

2 0.180 0.054 0.300 3.333 39.83 0.0251

3 0.241 0.072 0.299 3.345 39.70 0.252

4 0.323 0.096 0.297 3.367 39.50 0.0253

5 0.433 0.129 0.298 3.356 39.30 0.0254

6 0.581 0.172 0.296 3.378 38.97 0.0257

7 0.778 0.230 0.296 3.378 38.50 0.026

8 1.040 0.311 0.299 3.344 38.00 0.0263

9 1.400 0.415 0.296 3.378 37.20 0.0269

1 0 1.870 0.550 0.294 3.401 36.20 0.0276

11 2.500 0.740 0.296 3.378 34.80 0.0287

1 2 3.350 0.995 0.297 3.367 32.90 0.0304

1 3 4.490 1.325 0.295 3.390 30.50 0.0328

1 4 6.000 1.755 0.293 3.413 27.20 0.0368

75 8.000 2.350 0.294 3.401 22.80 0.0438

1 6 10.70 3.050 0.285 3.509 17.10 0.0585

1 7 14.10 3.600 0.255 3.922 9.60 0.104

1 8 17.90 2.100 0.117 8.547 1.11 0.901

.4 078M7 1.p = InX,- In X,

=

5-4In (37.5)-In (5.1)

2. Y, =

=

36-16

0.1 h-'

- AX

As-(41 -1.25)

(0.625 -100)

0.4 g/g

72 BT421

3. xmax = x0 + vx/s so

= 1.25 + 0.4(150)

= 60.25 g/l

-WRTp = Ae twnvid 37

BT 421 73

‘” P = InA-E

-G-

T, ihQfidU~Ju^ T2 S:bi

/J, = A guRT1 m.J”lY?i 38

JJ2 = A gURT2 m.NllYd 39

p2 = A gBRT2

pL, A e-“RT’

(“‘5)

RT2 R T ,

= e

“(L 1)

R T2 T,

= e

74 BT 421

qfuqGuosnisrGfg

QR&@il Q6LdMQ~GLWUl~fiU QfldM@$

Psychrophiles -5 - 5 15-18 19-22

Mesophiles IO-15 30-45 35 - 45

Thermophiles 25 45-75 60 - 80

Extreme thermophiles 30 60 - 75 75 - 95

1 + (k,/[H+]) + k, [H’]

BT 421 75

n7~~~~~oJ~~~rrnsrnL~~MMUy~LlliS~~ p = p,

(noncompetitive inhibition) (1 +K,)(l +S 1- -

S Ki

nu*1~ 40

76 BT 421

& K,= K, I:vi CL= P, m.mlSi 41

K, + S + S’J Ki

(competitive inhibition) K, ( 1 + SJ Ki ) + S

2 + K,/K,

BT421 77

2 + (K,K~)‘.’ + I

(1 + $1 S ) ( 1 + P/K,)

7 8BT 421

-P/KPP = Phle

K, ( 1 + I/ KJ + S

( 1 + K, I S) (1 + I/ Ki )

X

J

dX =-

‘X

BT 421 7 9

3

L5 2

1

0 X0 2 4 B .x R

X

Lihvll.dn’l p = 14nsK, + S

X t

j

r

(Ks + S) dX = ’ dti

x, PmSX t . 3

nufmi4 47

BT421

hi4 Y,, = x-x0

- (S - S,)

nu”l6l48

0 - $1 J-4” = KS Y,, + 1)

In X + K, Yws In S, wumd 49

( - -( ‘:I-X0 + so yxJs X0 X0 + soyws s

44 0m qin Yx/s = x - x ,

- ( s - S,)

X = Y,, (S-S,) nufnsd 50

x. = 0.6 (S - IO) wumsid 51

BT 421 81

ct-to,pm = K, Yws + 1

( )

iw-md 49

X0 + so yws

(0.71)(0.6) + 1 ( In X ) +)

eiwmi 52

1 + (10) (0.6)

S

(g/1)

X t

(g/l) bd

1 0 1 0

8 2.2 0.85

6 3.4 1.33

4 4.6 1.67

2 5.6 2.16

dt

8 2 BT421

X

X

S

0 t

LO-

d in X

d t0.5 -

0 t

dX-tit

83BT421