It Is Always Been a Challenge to Characterize the Antibiotic Fermentation Process in Complex

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1 A process model for rifamycin B has been described in detail recently (Bapat et al.,

2006a). The model is based on cybernetic principles and assumes that in complex

medium the organism has access to up to three substrate combination: (i)

Combination I: uptake of AA [Equation (A.1a), (A.1b) for stoichiometry and

growth rate on this substrate], (ii) Combination II: simultaneous uptake of AA (S1)

and glucose (S2) [ Equation (A.2a), (A.2b)] and (iii) Combination III:

simultaneous uptake of glucose (S2) and AMS (S3) [Equation (A.3a), (A.3b)]. It is

assumed that the free AA is released by hydrolysis of proteins and peptides (S 4)

[Equation (A.4a), (A.4b)]. Equation (A.1a), (A.1b) – (A.4a), (A.4b) represents the

four main growth reactions with each equation consisting of the stoichiometry

followed by the kinetic model form. The uptake of substrate combination ‘i’ is

dependent on the level of the corresponding key enzyme (XEi), which may be

inducible. Thus, the organism invests resources to synthesize XEi based on the

growth achievable on the corresponding substrate combination. Although a unique

growth rate exists corresponding to each substrate combination, the overall

specific growth rate, μ, and specific production rate, qp, are the weighted sums of

the specific growth and production rates on the individual substrate combination.

The weights αi are estimated using the optimality criteria [Equation (A.8)] in

which the organism allows the uptake of all the substrate combinations as long as

the specific growth rate obtained by summing the rates on different substrate

combination is less than its intrinsic growth capacity denoted by μmax. The

complete model comprises of component mass balances represented by ordinary

differential equation (ODE’s) [Equation (A.9) – (A.16)] along with the optimality

2 criteria stated in Equation (A.8). The simulation exercise to predict growth,

product formation and substrate utilization was carried out by integrating the set

of simultaneous differential equations as an initial value problem. The model

parameters and bounds or nominal values of the process variables are listed in

Table I and II, respectively.

The key features of the model include:

. The nitrogen catabolite repression of rifamycin B formations [Equation (A.21),

(A.22)].

. The sequential utilization of substrates in a complex multi-substrate media

[Equation (A.8)].

. The model captures the fact that rifamycin B formation does not occur when AA

are taken up as sole source of carbon and nitrogen.

. The model considers inhibition of AA utilizing enzyme (XE1) by glucose (S2)

due to carbon catabolite repression [Equation (A.15)].

. The enzymes (XEi) are inducible and are assumed to undergo degradation via first

order kinetics [Equation (A.15) and (A.16)].

For greater details about the model, the interested reader may refer to (Bapat et al.,

2006a). The model equations are summarized below.

Amino acid uptake:

Equation “a” is used to represent stoichiometry and Equation b is used to represent the kinetic form.

3 X  Y1,3CO 2 - Y1,1 S1  Y1,4O2  Y1,5 H 2O 0 (A.1a)

max  X  * μ  α μ  E1  r (A.2b) 1 1 1  X  1  E1 ,Re f 

Simultaneous uptake of AA and glucose:

X  Y2,3CO 2 - Y2,1 S1  Y2,2 S2  Y2,4O2  Y2,5H 2O 0 (A.2a)

max  X  * μ  α μ  E 2  r (A.2b) 2 2 2  X  2  E 2 ,Re f 

Simultaneous uptake of AMS and glucose:

X  Y3,3CO 2 - Y3,3 S3  Y3,2 S2  Y3,4O2  Y3,5H 2O 0 (A.3a)

max  X  * μ  α μ  E3  r (A.3b) 3 3 3  X  3  E3 ,Re f 

Conversion of insoluble nitrogen to AA:

S1  S4 0 (A.4a)

 X E  r   4  r* k X (A.4b) diss.  X  4 4  E4 , Re f 

Rifamycin B production:

P  Y5,3CO 2 - Y5,1 S1  Y5,2 S2  Y5,4O2  Y5,5 H 2O 0 (A.5a)

max  X  qp  α qp  E 2  r* (A.5b) 2 2 2  X  2,P  E 2 ,Re f 

P  Y6,3CO 2 - Y6,3 S3  Y6,2 S2  Y6,4O 2  Y6,5H 2O 0 (A.6a)

4 max  X  qp  α qp  E 3  r* (A.6b) 3 3 3  X  3,P  E3 ,Re f 

Enzyme synthesis:

X  X 0 Ei (A.7a) r  K r* Ei Ei i ; For i = 1, 2, 3 (A.7b)

Optimality criteria:

max(μ),

,0  αi  1, (A.8) s.t. and μ  μmax

3 Where μ  αiμi i1

Mass Balance Equations

Biomass: dX   .X ; (A.9) dt

Amino acids: d( S ) 骣 S 1 =F C -轾 ym a + y m + y q a X + k E 琪 4 (A.10) S1 FS 2 臌( 1,1 1) 1( 2,1 2 5,1 P ,2) 2 4 ( prot ) dt桫 kS 4+ S 4

Glucose: dS  2  F C  y   y q   y   y q  X (A.11) dt S 2 FS 2 2,2 2 5,2 P,2 2 3,2 3 6,2 P,3 3

Ammonium Sulfate: dS  3  F C  y   y q  X (A.12) dt S 3 FS 3 3,3 3 6,3 P,3 3

5 Insoluble nitrogen: dS   S  4  F C  y   y   y q  X  k E  4  (A.13) S 4 FS 4 1,1 1 2,1 2 5,1 P,2 4 prot   dt  kS 4  S4  dP 3  qP .X ; Where q P  αi q P i (A.14) dt i1

Enzymes:

X E d 1 X X E E 1,Ref max S1   1 (A.15) = (μ  k )  μ  k  dt i deg,i S 2  deg,i  X S  Ks  S  1 E 2 1,1 1 1,Ref KI1,1

X E d i X X E E i,Ref max *   i (i = 2, 3) (A.16) = (μ  k ) r  μ  k  dt i deg,i i  deg,i  X E i, Ref

* Where, ri indicate the effect of substrate limitation on growth and product formation and are given by,

Growth on amino acids,

* S1 r1  2 S1 (A.17) Ks1,1  S1  K I1,1

Growth on substrate combination, 2 (Fig. 3)

* S1 S2 r2  2 2 S1 S2 (A.18) Ks 2,1  S1  Ks 2,2  S2  K I 2,1 K I 2,2

Production on substrate combination, 3 (Fig. 3)

6 * S3 S2 r3  2 2 S3 S2 (A.19) Ks3,3  S3  Ks3,2  S2  K I3,3 K I 3,2

* S4 r4  (A.20) ks 4,1  S4

Production on substrate combination, 2

* S1 S2 r2,P  2 2 S1 S2 (A.21) Kp5,1  S1  Kp  S  K 5,2 2 PI 5,1 K PI 5,2

Production on substrate combination, 3

* S3 S2 r3,P  2 2 S3 S2 (A.22) Kp6,1  S3  Kp  S  K 6,2 2 PI 6,1 K PI 6,2

Some of the terms and parameters used in the equations have been explained below for clarity:-

αk : Control parameter that determines the metabolic flux through

branch k CFsi : Concentration of substrate combination i in the respective feed

stream Fsi Fsi : Feed flow rate of substrate combination i -1 Kdeg,i : Degradation constant for the enzyme Ei, h

Ksi, j and Kpi, j : Substrate half saturation constant for substrate j in the model for

reaction i, g L-1 -1 qp2 : Specific product formation rate on amino acid and glucose, h -1 qp3 : Specific product formation rate on AMS and glucose, h ri : Reaction rate for substrate combination i

7 max -1 1 : Specific growth rate on S1, h max -1 2 : Specific growth rate on S2 and S1, h max -1 3 : Specific growth rate on S2 and S3, h XEi : Concentration of the enzyme responsible for uptake of substrate

combination i. -1 Y i, j : Stoichiometric coefficient of substrate j in reaction i, g g .