Biotechnological

Communication

Biosci. Biotech. Res. Comm. 9(3): 489-494 (2016)

Mathematical modeling of microbial growth and

production kinetics for -amylase production using

mustard oil cake as solid substrate

Santosh K. Mishra

a

, Shashi Kumar

b

, Ravi Kant Singh

c

* and Surendra Kumar

b

a

Department of Biotechnology, IMS Engineering College, Ghaziabad, UP, India

b

Chemical Engineering Department, Indian Institute of Technology Roorkee, Roorkee 247667, Uttarakhand,

India

c

*Department of Biotechnology, Noida Institute of Engineering & Technology, Greater Noida, UP, India

ABSTRACT

Different phases of the Gliomastix indicus growth curve and the production of -amylase using solid-state fermen-

tation process based on variation in dry weight was mathematically modeled. The result of the study reveals that

the growth of the fungal cells and the production of -amylase on a mustard oil cake as solid substrate could be

expressed by simple models incorporating the mathematical de nition of each phase and the variation in dry sub-

strate weight over the incubation time. The growth kinetics of G.indicus could be described by the mathematical

modeling parameters regarding maximum speci c growth rate and maximum biomass concentration obtained by

tting the experimental data to the logistic model. Experimental data collected from a series of batch fermentations

process were collected for 10 days (240 hrs.) and used to propose the mathematical models. Experimental observa-

tions, and predicted models made it possible to conclude that these models can be successfully employed to represent

the biomass growth and -amylase production in solid-state fermentation processes.

KEY WORDS: SOLID STATE FERMENTATION, MATHEMATICAL MODELING, BIOMASS GROWTH KINETICS, PRODUCTION KINETICS

489

ARTICLE INFORMATION:

*Corresponding Author: rksingh.iitr@hotmail.com

Received 25

th

July, 2016

Accepted after revision 5

th

Sep, 2016

BBRC Print ISSN: 0974-6455

Online ISSN: 2321-4007

Thomson Reuters ISI ESC and Crossref Indexed Journal

NAAS Journal Score 2015: 3.48 Cosmos IF : 4.006

© A Society of Science and Nature Publication, 2016. All rights

reserved.

Online Contents Available at: http//www.bbrc.in/

INTRODUCTION

Solid state fermentation process (SSF) involves the

growth of microorganisms on a moist insoluble solid

substrate in the absence or sometimes nearly absence of

free liquid (Mitchell et al 2002; Pandey 2003). The level

of water available for growth of microorganism in SSF

is low which makes it suitable for the growth and culti-

vation of fungi (Pandey 2003; Cannel and Moo Young

1980). The solid state fermentation (SSF) is used in a

number of fermentation industries for the production of

enzymes, organic acids, and other bioactive compounds.

490 MATHEMATICAL MODELING OF GROWTH AND PRODUCTION OF -AMYLASE BIOSCIENCE BIOTECHNOLOGY RESEARCH COMMUNICATIONS

Santosh, Shashi, Ravi Kant

Fermentation processes can be improved by using suit-

able methods to estimate the biomass and other main

process variables resulting in the investigation of the

associations between growth kinetics and the fermen-

tation product. In SSF precise estimate is complicated

because of the dif culty in the separation of biomass

from the fermentation media. Therefore, appropriate

data are not accessible concerning the kinetics and bio-

mass in SSF.

Substrate moisture content, temperature and, bio-

mass have been found as the critical variables that

affect growth of microorganism and enzyme production

(Khanahmadia et al.2006; Desgranges et al.1991) For

any SSF these parameters must be controlled during the

entire fermentation processes. Several approaches have

been proposed by researchers for indirect measurements

of biomass formation, such as estimating the production

of primary metabolic product (Desgranges et al.1991;

Okazaki et al.1980) amount of carbon dioxide produc-

tion (Raimbault 1998), the variation in the electrical

conductivity of the biomass and solid substrate (Carri-

azalez et al.1981) and the changes observed in the color

of the fermentation medium. Other than these methods,

a direct method of viable cell count can also be used to

estimate the amount of biomass formation.

There are consequential dif culties that have been

observed with the direct measurement of cell biomass in

SSF systems therefore a weighing method could provide

a signi cant method in kinetic studies of such processes.

Bioprocess modeling including cells and cultures can

be of signi cant importance in optimizing and control-

ling actual production process of biomass and product

(Curien et al. 2003; Grosz and Stephanopoulos 1999).

Several challenges have been observed at each stage in

the development of models of enzyme production kinet-

ics (Copella and Dhurjati 1989; Thilakavathi et al. 2007).

Earlier, a kinetic model has been developed for batch

fermentation for lactic acid production using cane-

sugar molasses by Enterococcus faecalis. Parameters of

the kinetic model have been determined and validated

based on experimental data by using genetic algorithm

(Nandsana and Kumar 2008, Gelatin et al. 2015).

The effect of temperature and substrate moisture

content on the growth and production of amylase, pro-

tease and phytase by Aspergillus niger during SSF was

investigated and a mathematical model for the kinet-

ics of growth and enzyme production were developed

earlier. A mathematical model to describe the kinetics

of enzyme production by the lamentous fungal sp.

Trichoderma harzianum was developed using sugarcane

bagasse as solid substrate for the production of cel-

lulase, beta glucosidase and xylanase. In all the stud-

ies, it has been found that temperature and substrate

moisture content of the media play a signi cant role for

the growth of microorganism and enzyme production

(Saithi et al. 2016).

In recent years, SSF has gained renewed interest

from researchers for the production of enzymes which

have industrial important in view of its economic and

engineering advantages. In this work we are propos-

ing a mathematical model can be used as an aid for

improving the design and control of SSF processes. The

major objective of this study was to identify and develop

model for the growth, stationary, and death phases of the

growth curve and -amylase production kinetics dur-

ing SSF processes using a comparatively simple weigh-

ing method by using G. indicus as a fungal strain. The

knowledge gained from our research work may contrib-

ute to the understanding and control of SSF processes

for large scale enzyme production using fungal strain.

MATERIAL AND METHODS

Inoculum preparation: The microorganism Gliomastix

indicus (MTCC 3869) was procured from the Institute of

Microbial Technology (IMTECH) Chandigarh India. G.

indicus comprises the properties of lamentous fungi

and rapidly grows on all common mycological media

such as malt extract, potato dextrose agar etc. This fun-

gal strain was maintained on the potato dextrose agar

(PDA) medium which contains; potatoes 200g/l, dex-

trose 20g/l and Agar 15g/l. The pH of the medium was

adjusted to 6 by using 1N NaOH. The organism was

maintained by the serial transfer on the PDA medium

after every fortnight and incubated at 30°C.

Inoculum was prepared by transferring 5ml suspen-

sion culture, into 250ml conical ask containing 95ml

of sterile inoculum medium. The composition of the

inoculum medium was (g/l): Glucose (20g/l), NH

4

NO

3

(3g/l), MgSO

4

.7H

2

O (0.5g/l), KCl (0.5g/l), K2HPO

4

(1g/l),

FeSO

4

.7H

2

O (0.01g/l), with a pH of solution 6.0. The

asks were incubated on a rotary shaker at 200rpm at

28°C for 48 hrs (Nagalaxmi et al. 2008; Kammoun et al

2008).

Cultivation of Fungal Strain: G.indicus was cultivated

in SSF using mustard oil cake as solid substrate and

moistened with distilled water (1:1.2). After autoclaving

at 121˚C for 20 min, the culture medium was inoculated

with 15% (v/v) of the above applied inocula and mixed

thoroughly to ensure uniform distribution. The inocu-

lated MOC was distributed in Petri dishes (8 cm in diam-

eter) as follows: 1.0 cm average thickness of the culture

medium, 10 g initial weight of inoculated medium per

dish, 80% initial moisture content, and incubated at

30˚C for 0-240 hr. Dish samples were removed from the

incubator at regular intervals for the determination of

the number of viable cells, the total dry weight of the

fermented substrate, and the production of -amylase.

BIOSCIENCE BIOTECHNOLOGY RESEARCH COMMUNICATIONS MATHEMATICAL MODELING OF GROWTH AND PRODUCTION OF -AMYLASE 491

Santosh, Shashi, Ravi Kant

Analytical methods: Viable cell count: The viable

bacterial count was determined by suspending the fer-

mented substrate in peptone-phosphate buffer at a 1:10

ratio and shaking the suspension for 15 min, followed

by serial dilution and plating onto plate count agar. The

number of viable colonies in the fermented substrate

after 96 h incubation at 30°C is reported as cfu/g.

Total dry weight: The total dry solid weight per dish

was evaluated by drying at 80 ± 3°C to constant weight.

Then the nal dry weight was calculated and presented

as the variation in the dry matter of the fermented wheat

bran during the test as Wt.

-amylase activity: Crude enzyme was extracted by

mixing a known quantity of fermented substrate with

distilled water in a 1:10 ratio on a rotary shaker (180

rpm) for 1 h. The slurry was squeezed through wet

cheesecloth. Then the ltrate was centrifuged (10,000 ×

g, 10 min, 4 °C), and the clear supernatant was used as

the source of the crude enzyme. The activity of -amylase

was determined by the Bernfeld procedure using soluble

starch (Qualigens) as a substrate (Bernfeld 1955). The

reaction mixture was incubated for 15 min at 35˚C. One

unit (U) of -amylase is de ned as the amount of enzyme

that releases 1 mol of reducing sugar as maltose per

minute under the assay conditions and is expressed as

U/g of dry fermented substrate.

Mathematical Model:The total weight of medium

under SSF using MOC as solid substrate can be written

as:

Total Wt (W) = Wt of Solid substrate(S)

+Wt of Biomass(B)+ Wt of Product(P) …(1)

The value of all the three parameters will change as the

fermentation process progress. Hence above equation

can be represented in differential form with respect to

time. Therefore:

…(2)

The substrate consumption rate by biomass will be dif-

ferent in different growth stages. Hence rate of substrate

consumption with respect to time under different stages

can be represented as:

…(3)

The substrate consumption rate under different growth

phase can be de ned by either biomass growth equation

and biomass yield coef cient or by using enzyme pro-

duction equation and coef cient of yield (Amrane and

Pregent 1994; Venkatesh et al 1993; Yeah et al. 1991)

As suggested by Hashemi et.al, the equation for the

estimation of total biomass weight with respect to total

medium weight can be represented as:

…(4)

Furthermore, the equation for the estimation of total

weight of product can also be represented as:

…(5)

The above equations indicate that the amount of

biomass and product concentration in the fermentation

media can be estimated with the help of total value of W

(Hashemi et al 2011).

RESULT AND DISCUSSION

Change in dry weight of medium during the fermenta-

tion process was calculated by substracting the weight

recorded each day for continuously ten days from the

initial weight i.e. W

0

=10.3 gm as shown in gure-1.

Growth phase was observed during the time period

of 0-96 hr, stationary phase was found to be between

96-144 hr and subsequently decline phase was observed

between 144-240 hr onwards. Now the values of growth

phase and decline phase time frames were used to get

the following equations respectively:

…(6)

…(7)

For the above Eqs. (6) and (7) coef cients of determinant

(R

2

) were found to be 0.842 and 0.979. Along with it,

the residual sums of squares (rss) for both the equations

were 0.302 and 0.133 respectively. These values indi-

cates that the Eqs. correlate the experimental data with

a very approximation.

We can differentiate the Eqs. (6) and (7) with respect

to time in order to get the relation for time dependent

total medium weight degradation.

…(8)

…(9)

492 MATHEMATICAL MODELING OF GROWTH AND PRODUCTION OF -AMYLASE BIOSCIENCE BIOTECHNOLOGY RESEARCH COMMUNICATIONS

Santosh, Shashi, Ravi Kant

FIGURE 1. Change in dry weight of medium observed during

fermentation

Eqs. (4) and (8) represent the equation for time depend-

ent medium weight variation during biomass growth

phase. Similarly, Eqs. (4) and (9) represent the equation

for time dependent medium weight variation during bio-

mass death phase. If the values of and are known,

Eqs. (4) and (8) can be used for the calculation of bio-

mass dry weight (B) during growth phase. Similarly, Eqs.

(4) and (9) can also be used for the calculation of B dur-

ing death phase.

The and values depend upon the selection of

medium, choice of microorganism and the environmental

conditions of fermentation process and it can be experi-

mentally determined. For representation, the trend of

growth curve based on the derived mathematical equa-

tion, / value was assumed to be 0.01. Initial biomass

dry weight (B

0

)was experimentally determined and found

to be 0.0042 g. Hence, Eqs. (8) and (4) will give:

…(10)

Therefore, the nal Eq. for biomass growth in growth

phase will be:

…(11)

As per the earlier assumptions t=96-144 were considered

as stationary phase. Hence, B

144

= B

96

= 0.0052 g. Eqs. (9)

and (4) will give:

…(12)

Therefore, the nal Eq. for biomass growth in death

phase will be:

…(13)

Using equation (11) and (13) and considering the time

period of growth, stationary and death phase, the calcu-

lated values were plotted as shown in gure-2.

As shown in the gure, the calculated values on the

basis of medium dry weight variation are in good cor-

relation with the experimental values.

The mathematical model for -amylase production

kinetics in SSF is very convenient to represent the com-

plex problem of such process. Here we are introducing

a model for the prediction of -amylase production

kinetics on solid substrate using fungal strain G. indi-

cus during fermentation process. Eq. (5) correlates the

total product (P) with respect to fermentation time (t)

using weight variation data of medium. The total prod-

uct i.e. -amylase was assayed for the entire period of

fermentation process at regular time intervals. Follow-

ing Eqs. (14), (15) and (16) were derived to represent the

-amylase production during growth phase, stationary

phase and death phase respectively:

…(14)

BIOSCIENCE BIOTECHNOLOGY RESEARCH COMMUNICATIONS MATHEMATICAL MODELING OF GROWTH AND PRODUCTION OF -AMYLASE 493

Santosh, Shashi, Ravi Kant

…(15)

…(16)

Form the above Eqs. (14), (15) and (16), the coef cients of

determination (R2) were calculated as 0.99, 0.97 and 0.98

respectively. Figure-3 represents the correlation between

experimental and predicted data calculated from the

product kinetic mathematical model given above.

CONCLUSION

Because of the complexity of SSF systems, estimation of

the biomass and product formation during the incuba-

tion time could give highly valuable information leading

to a more comprehensive understanding of such compli-

cated systems. We investigated a feasible approach for

modeling the different phases of the fungal growth curve

and production of -amylase as product by G. indicus

in a SSF process based on variation in dry weight. The

result showed that fungal growth and the production of

-amylase on a MOC as solid substrate could successfully

be modeled based on variations in solid substrate weight

and can be used for large scale industrial production.

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FIGURE 2. Change in dry weight of biomass with time variation

FIGURE 3. Predicted and experimental -amylase activity

Santosh, Shashi, Ravi Kant

494 MATHEMATICAL MODELING OF GROWTH AND PRODUCTION OF -AMYLASE BIOSCIENCE BIOTECHNOLOGY RESEARCH COMMUNICATIONS

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