MODELING AND KINETICS OF PROTEIN ENZYMATIC HYDROLYSIS FROM AMARANTH FLOUR AND WHOLE GRAIN

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1 1 th International Research/Exert Conference Trends in the Develoment of Machinery and Associated Technology TMT 008, Istanbul, Turkey, 6-30 August, 008 MODELING AND KINETICS OF PROTEIN ENZYMATIC HYDROLYSIS FROM AMARANTH FLOUR AND WHOLE GRAIN Klára Kodriková, Karel Kolomazník Milan Adámek De. of Automation and Control De. of Electronics and Measurment Faculty of Alied Informatics Tomas Bata University in Zlín Czech Reublic ABSTRACT The toic of the article is oriented at modeling of amaranth rotein enzymatic hydrolysis. The urose of the hydrolysis is to enrich the solid hase with very valuable amaranth rotein which could be used not only in food industry to roduce new roducts rich in high-quality rotein, but also in harmaceutics, medicine and other branches. Regarding to diverse character of chosen materials (amaranth flour and seed) various hydrolysis course is exected, therefore a different model is built for each of the stuff. The designed mathematical models are verified by exerimental measurement. Keywords: Modeling, amaranth, enzymatic extraction 1. INTRODUCTION Amaranth, a lant falling into the grou of seudo-cereals, starts to be a goal of the research for its unique secific roerties resently. Study of this cro leads to ascertainment of remarkable content of quality rotein with high ortion of essential amino-acids and other considerable substances, like squalene and flavonoids. Amaranth roduces many thousands of tiny seeds having very valuable contents; on the other hand the leaves have also high nutritional value. High-quality vegetable oil is extracted from the amaranth seed, which is used not only in food industry. [1] Most of the so far ublished ublications deal with amaranth as a food sulement for healthy oulation or as a ossible comound in secial diets of diabetic atients or eole with rotein allergy; new amaranth roducts are conducive against civilization diseases. On the other hand, amaranth starts to be used also in different areas -medicine, harmaceutics and cosmetics. Further research is in rogress, for examle in amaranth biomass treatment. The rest of the lant after conversion of basic arts contains still high ercent of rotein, deending on growing season. Therefore amaranth biomass could be successfully used in foodstuff industry or for roduction of very ure biogas. Hardly ever are ublished aers which solve roduction of searate valuable amaranth comounds and otimalization of articular technologies from the rocess engineering oint of view. It is surrising, that most of technologies are not described quantitatively in terms of the exloitation of the transort rocess theory and the heterogenic reactions kinetics. This is imortant esecially in the rocessing of high amount of raw material that means for industry requirements. The success of amaranth roducts alication for normal utilization direct deends on ossibility of articular arts searation. The aim is to obtain roducts of high urity, abreast with rocess conditions which do not raise the rice of. However, aers dealing with searation are ublished only rarely as well as otimalization of single technology rocess using advantage of rocess engineering is seldom solved. It is known, that the searation of articular comounds is ossible by hydrolysis. The urose of our resent exeriments is to enrich the solid hase with the vegetable rotein and oosite enrich the solid hase with valuable starch. The kinetics of these reactions and modeling of concentration fields are resented in our aer. 341

2 . MATHEMATICAL MODELS OF PROTEIN ENZYMATIC EXTRACTION.1. The modeling of rotein enzymatic extraction from the amaranth flour As mentioned above, the urose of the hydrolysis is to enrich the solid hase with required comound rotein or starch. With regard to very small size of amaranth flour articles, is eventual that hydrolysis reaction is not inhibited by diffusion. On this condition we can aly the first order mechanism in the relationshi of non-reacted art of rotein for the descrition of hydrolysis kinetics. On the assumtion that the conversion (y) direct deends on irreducible starch (rotein) fraction, it is ossible to write following equation: dy k( 1 y) dτ = (1) By integration (1) we obtain k y = 1 B τ () B is equal 1 on starting condition y(0)=0. For the determination of seed constant k we use (3) ln 1 y = kτ (3) ( ) By setting out the natural logarithm of non-reacted ortion ln(1-y) to the time (τ) we acquire a straight line whose outline equals the seed constant of hydrolyzed starch (rotein)... The modeling of rotein enzymatic extraction from the amaranth grain During the enzymatic hydrolysis of amaranth flour the final heterogeneous mixture contains an aqueous solution of hydrolysed rotein and a starch mud containing fixed rotein. The searation of the heterogeneous reaction comound is ossible only by using a centrifuge, because simle filtration roceeds very slowly. By this reason we were engaged in hydrolysis exeriments of the amaranth grain on condition of its ermanent reservation. This technique enables a relative easy searation of the heterogeneous mixture by the ure filtration after finishing the reaction. For the descrition of the diffusion rotein extraction from the amaranth seed we used following model: 1 c( r, τ) c( r, τ) c( r, τ) = + 0 < r < a, τ <0 D τ r r r (4) c ( 0, τ ) = 0 c( r,0) = c r (5) (7) c c0 SD ( a, τ ) = V0 ( τ ) c( a, τ ) = εc0 ( τ) r τ (6) (8) c 0 ( 0 ) = 0 (9) The equation (4) describes the concentration field inside the amaranth grain during the extraction rocess, (5) resents the axis symmetry of the concentration field, (6) resonds the solid-state balance equality of the surface diffusion flow with the accumulation seed of the hydrolyzed rotein in the aqueous solution. (7) is a comlete mixing condition of the aqueous hase and (8), (9) are starting conditions. Through the alication of dimensionless quantities we get: c r Dτ c C =, R=, Fo=, C = c a a c Finally, we obtain dimensionless model of the diffusion extraction: C ( R, Fo) C ( R, Fo) C ( R, Fo) = + Fo R R R 0 < R <1, Fo > 0 C( 0, Fo) = 0 R (1) C( R,0) = 1 (14) C( 1, Fo) Na C0 ( Fo) = R 3ε Fo (13) C( 1, Fo) = C0 ( Fo) 0 (15) (11) (10) 34

3 C 0 ( 0 ) = 0 (16) The analytical solution of the equations (10) to (1) was ublished for the temerature field of sherical body []. By the modification of the ublished solution for concentration field in the amaranth grain we acquire: c ε Na C = = c Na R Na ε q Na q + 9 sin ε Rq sin q Na Na ε ε ( ) ( ) 4 n n n n + ε 3ε n= 1 4 q 9 1 n + + qn Foqn e Foq n c0 1 6Na e C0 = = c Na+ ε ε n= 1 Na Na 3q q 9 1 n + + tg ( q) = (19) ε ε Na 3 + q Dτ ε Fo = a (18) where qn are the equation roots. The rotein concentration fields in the seed of sherical shae are shown in the following ictures Fig.1 to Fig.. Axis x reresents the radius of a seed (R), axis y shows the concentration (c) of the enzyme solvent and finally, axis z resents non-dimensional time Fo. The differences between varied dimensionless consumtion of the enzyme solution are visualized in interactive modeling environment Matlab. In the first icture, you can see the concentration field inside the amaranth grain by the elected dimensionless solvent consumtion 1. In the second case in figure is well seen, how the concentration field changes with high-introduced consumtion of enzyme Na equals to 10. (17) Figure 1. Concentration field for the dimensionless Figure. Concentration field for the dimensionless solvent consumtion Na = 1 dimensionless solvent consumtion Na = EXPERIMENTAL SET-UP 3.1. Protein enzymatic hydrolysis of the amaranth technical flour The exeriments were focused on the hydrolyze effectivity of amaranth flour rotein with usage of several readily available enzymes in the market. Protein liquefaction of the technical flour runs under slight reaction conditions (temerature, neutral H) which were roosed: rate flour/water = 1/0 seed of reaction mixture warming C. min -1 enzyme doze: 0,1% to the total flour solids in laboratory conditions 5 mg of enzyme.5 g -1 of the total flour residue 343

4 Tab.1 Comosition of the amaranth technical flour The exeriments roceed in variable hydrolyze Parameter Value (%) times (minimum 1 hour, maximum 5 hours) and variable temeratures (30 C to 50 C). Into the boiling flask was 5 g of the flour weighted out, after that 100ml of distilled water was added and Total residue 86,91 the mixture was stirred in the water bath and simultaneously warmed u. After achieving of Ash in the total solids 3,57 the secified temerature 500µl of enzyme solution was tacked with a iette. Enzyme Nitrogen (TKN),8 hydrolysis was running for required time and by rated temeratures. After it the reaction alloy was Proteins (N x 5,70) in total 16,07 centrifuged with 6000 rm. Liquid and solid hase were analyzed for the total residue content solids and finally screened using TKN method. Liid in total residue 9,81 Examles of the exeriments results are resented in the table 1. and showed in the grahs Starch in total solids 67,79 above. Out of the exeriments results it is evident, that the highest efficiency by the enzyme liquefaction of the amaranth technical flour enzyme Alcalase roved. By the five hours hydrolysis and 50 C got almost 37% of rotein liquid. 40 3, ,5 % řeměny bílkovin % řeměny bílkovin 1, , Alcalase Polarzyme Eserase Everlase Savinase 19,5 Alcalase Polarzyme Eserase Everlase Savinase Fig. 4, 5: Percentage of rotein conversion using several enzymes by the 1h hydrolysis and 30 C temerature, res. 5 h hydrolysis and 50 C temerature 4. CONCLUSION In this aer, the modeling of amaranth raw material (flour and seed) is solved using Matlab comuter environment. Amaranth flour articles have very small size so that the enzyme hydrolysis is not broken by diffusion; hence the mathematical model is simler. On the other hand, amaranth seed has a diffusion bar resenting by its skin. The grains mathematical model was built in sherical coordinates. The models were verified by exerimental measurements, which acknowledged the advantages of the whole grain hydrolysis. Fulfilling the condition of seed ermanent reservation after rotein extraction we considerably simlify the rocess of mixture searation which leads to an economical rofit when industry used. 5. ACKNOWLEDGEMENTS The work has been suorted by the grant VZ MSM the Ministry of Education of the Czech Reublic. This suort is very gratefully. 6. REFERENCES 344

5 [1] PAREDES-LOPEZ, O., Amaranth biology, chemistry and technology, Library of Congress Cataloging in Publication Data, 1994, [] CARLSLAW, H.S. and JAEGER, J.C., Conduction of heat in solids, Oxford at the Clarendon Press,