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Application of mathematical optimization methods in microbiology

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Abstract

Mathematical methods of experiment design have so far found little use in the optimization of microbiological processes. The conventional optimization procedure is still the transformation of functional relationship ofn variables into n unidimensional optimizations; furthermore, the Bos-Wilson gradient method is often used. This paper presents a review of methods used in other fields, and their application in microbiological practice. The methods are classified according to whether they require, besides the simple determination of the objective function (direct search methods), also the finding of its first (gradient methods) or second derivative (Newton-Raphson method). A modified Rosenbrock’s method of direot optimum search and the gradient Box-Wilson method were used in parallel for the optimization of yeast growth on methanol. Their comparison showed that Bosenbrock’s method is more suitable for multiparameter systems.

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References

  • Adler Yu. P., Markova E. V., Granovskii Yu. V.: The design of experiments to find optimal conditions. Mir Publs., Moscow. 1975.

    Google Scholar 

  • Auden J., Grüner J., Nüesh J., Knüsel F.: Some statistical methods in nutrient medium optimalisation.Pathol. Microbiol. 30, 858 (1967).

    CAS  Google Scholar 

  • Balitskaya P. M., Kazarinova L. A., Balitskii V. A., Muzychenko L. A.: Application of mathematical experiment design methods in the selection of an optimal medium for the synthesis of inosine by the cultureof Bacillus subtilis Gen-265. (In Russian)Prikl. Biokhim. Mikrobiol. 9, 694 (1973).

    CAS  Google Scholar 

  • Biryukov V. V.: Practical instructions for the use of mathematical methods of experiment design in the search for optimum conditions in multifactorial processes. (In Russian) Zinatne, Riga, 1969.

    Google Scholar 

  • Bogorov V. G., Maksimov V. N., Fedorov V. D.: Selection of optimum medium composition for photosynthesizing serobacteria with the aid of mathematical statistical methods. (In Russian)Dokl. Akad. Nauk SSSR 165, 686 (1965).

    Google Scholar 

  • Box G. E. P., Wilson K. B.: On the experimental attainment of optimum conditions.J. Roy Stat. Soc. B 13, 1 (1951).

    Google Scholar 

  • Dean W. K., Heald K. J., Deming S. N.: Simplex optimization of reaction yields.Science 189, 805 (1975).

    Article  PubMed  CAS  Google Scholar 

  • Deming S. N., Morgan S. L.: Simplex optimization of variables in analytical chemistry.Analyt. Chem. 45, 278 A (1973).

    Google Scholar 

  • Dumenil G., Cremieux A., Phan-Tan-Luu R., Combet M.: Bioconversion from DL-homoserine to L-threonine. I. Application of factorial design.Europ. J. Appl. Microbiol. 1, 213 (1975a).

    Article  CAS  Google Scholar 

  • Dumenil G., Cremteux A., Phan-Tan-Luu R., Aune J. P.: Bioconversion from DL-homoserine to L-threonine. II. Application of the simplex method of optimization.Europ. J. Appl. Microbiol. 1, 221 (1975b).

    Article  CAS  Google Scholar 

  • Fedobov V. D., Maksimov V. N., Bogorov V. G.: Experimental development of nutritive media for micro-organisms.Biometrika 55, 43 (1968).

    Google Scholar 

  • Grachev Yu. P., Tubol’tsev A. K., Lushchik T. A.: Optimization of cultivation conditions forBacillus mesentericus strain 11-11 with the use of a mathematical process model in the form of power function. (In Russian)Mikrobiologiya 39, 945 (1970).

    CAS  Google Scholar 

  • Himmelblau D. M.: Process analysis by statistical methods. Wiley, New York, 1970.

    Google Scholar 

  • Hoffmann V., Hoffmann H.: Einführung in die Optimierung mit Anwendingskeispielen aus Chemie Ingeneur-Wesen. Verlag Chemie, Weinheim, 1971.

    Google Scholar 

  • Hooke R., Jeeves T. A.: Direct rearch solution on numerical and statistical problems.J. Assoc. Comput. Mach. 8, 212 (1961).

    Google Scholar 

  • Iegorov N. S., Baranova I. P., Kozlova Yu. I.: Optimization of the composition of nutrient medium forStreptococcus lactis, the producer of the antibiotic nisine. (In Russian)Mikrobiologiya 40, 993 (1971).

    Google Scholar 

  • Krayushkina E. A., Zhebebitsov N. A., Zvyagintsev V. I.: Optimization of the composition of nutrient medium for the cultivation of the mould fungusMucor pusillus 917. (In Russian)Biokhim. Mikrobiol. 9, 883 (1973).

    CAS  Google Scholar 

  • Kubíček M., Hxaváček V.: Numerical Methods and Optimization in Chemical Engineering. (In Czech) SNTL, Prague, 1972.

    Google Scholar 

  • Lewis J. C., Ijichi K.: Multiple factor experimentation with reference to biosynthetic yield of aterrimin.Appl. Microbiol. 5, 124 (1957).

    PubMed  CAS  Google Scholar 

  • Loginova L. G., Iegobova L. A., Tsaplina I. A., Maksimov V. N.: Optimization of synthetic medium composition by the steep ascent method serving for the activation of neutral protease synthesis by the thermophilic bacteriumBacillus brevis 224. (In Russian)Mikrobiol. Promyshl. 1970 (4), 11 (1970a).

    Google Scholar 

  • Loginova L. G., Iegobova L. A., Tsaplina I. A., Maksimov V. N.: Activation of growth and protease synthesis in the thermophilic bacteriumBacillus brevis. (In Russian)Mikrobiologiya 39, 588 (1970b).

    CAS  Google Scholar 

  • McDaniel L. E., Bailey E. G., Ethiraj S., Andrews H. P.: Factorial and central composite experiments with computer analysis for optimizing fermentation processes. Bacteriol. Proc. 1970, 70th Ann. Meet., Boston, Mass. 26 April-1 May, 1970. Abstract A 42, p. 7.

  • Maksimov V. N., Fedorov V. D.: Application of mathematical methods of experiment design in the search for optimum conditions in microorganisms cultivation. (In Russian) MGU, Moscow, 1969.

    Google Scholar 

  • Maksimov V. N.: Search for optimum medium composition for the cultivation of green serobacteria (Ghl. thiosulphatophilum). (In Russian)Mikrobiologiya 40, 258 (1971).

    CAS  Google Scholar 

  • Maksimova E. P., Ustinnikov B. A., Maksimov V. N., Fedorov V. D.: Determination of optimum conditions for the cultivation ofBac. diastaticus with the use of the steep ascent method. (In Russian)Prikl. Biokhim. Mikrobiol. 3, 373 (1968).

    Google Scholar 

  • Morgan S. L., Deming S. N.: Simplex optimization of analytical chemical methods.Analyt. Ghent. 46, 1170 (1974).

    Article  CAS  Google Scholar 

  • Murgov I. D., Zaitseva Z. M.: Optimization of the composition of nutrient medium for L-lysine biosynthesis byBrevibacterium flavum 178 by the method of mathematical experiment design. (In Russian)Prikl. Biokhim. Mikrobiol. 9, 845 (1973).

    CAS  Google Scholar 

  • Nalimov V. V., Chernova N. A.: Statistical Methods of Extreme-search Experiment Design. (In Russian) Nauka, Moscow, 1965.

    Google Scholar 

  • Nalimov V. V.: Theorie des Experiments. VEB Deutsehe Landwirtschaftverlag, Berlin, 1975.

    Google Scholar 

  • Nelder J. A., Mead R.: A simplex method for function minimisation,Comput. J. 7, 308 (1965).

    Google Scholar 

  • Palagina N. A., Rozmanova N. V., Vitrinskaya A. M., Khrycheva A. I.: Optimization of cultivation conditions for baker’s yeast. (In Russian)Prikl. Biokhim. Mikrobiol. 11, 500 (1975).

    PubMed  CAS  Google Scholar 

  • Pilát P.: Study of growth kinetics ofCandida boidinii 11 Bh on methanol. (In Czech) Ph.D. thesis, Prague, 1975.

  • Pisarenko T. N., Yarovenko V. L., Dobrolinskaya G. M.: Effect of medium salt composition on glucoamylase biosynthesis by the fungusAspergillus awamori 224-21 as determined by the random equilibrium method. (In Russian)Mikrobiol. Promyshl. 1970(3), 9 (1971).

    Google Scholar 

  • Powell M. J. D.: An iterative method for finding stationary values of a function of several variables.Comput. J. 5, 147 (1962).

    Google Scholar 

  • Powell M. J. D.: An efficient method for finding the minimum of a function of several variables without calculating derivatives.Comput. J. 5, 155 (1964).

    Article  Google Scholar 

  • Rosenbrock H. H., Storey C.: Computational techniques for chemical engineers. Pergamon Press, Oxford, 1970.

    Google Scholar 

  • Schröder K. D.: Optimierung der Kulturbedingungen für der Hefe-StammCandida guillermondii H 17 beim Abbau von Kohlenwasserstoffen. Ph. D. thesis, Greiflswald, 1972.

  • Schröder K. D., Weide H.: Optimization of growth conditions for yeasts.Biotechnol. Bioeng. Symp. No.4 (Pt II), 713 (1974).

  • Tsaplina I. V., Maksimov V. N., Vorovyeva G. I.:Mikrobiol. Promyshl. 12, 19 (1973).

    Google Scholar 

  • Undén G. Å., Hedén C.-G.: An approach to on-line continuous culture optimization. In: Proo. 1st Europ. Conf. on Computer process control in fermentation. Sept. 3.–5., 1973, Dijon, INRA, Dijon. Session 2, 1973.

  • Ustinnikov B. A., Tuseva V. M., Maksimov V. N., Moskvicheva E. P.: Optimization of cultivation medium and conditions for ASP Batatal 61 by the method of mathematical design. (In Russian)Prikl. Biokhim. Mikrobiol. 9, 32 (1973).

    PubMed  CAS  Google Scholar 

  • Veksler M. A., Zavadu V. A., Markova E. V., Khefets S. E.: Optimierung der Processe zur Drogengewinnung mit Hilfe mathematisch-statischer Methoden III. Optimierung des Process der Nicodingewinnung.Chim. Pharmacol. 4, 31 (1970).

    CAS  Google Scholar 

  • Voino L. I., Grachev Yu. P., Sivacheva T. A.: Determination of optimum cultivation conditions forAspergillus oryzae with the use of mathematical methods of experiment design. (In Russian)Mikrobiologiya 39, 827 (1970).

    CAS  Google Scholar 

  • Volfová O., Pilát P.: Studies on methanol-oxidizing yeast I. Isolation and growth studies.Folia Microbiol. 19, 249 (1974).

    Article  Google Scholar 

  • Votruba J., Pilát P., Prokop A.: Optimization of nutrient medium for culturing microorganisms bymeans of modified Rosenbrock’s method.Biotechnol. Bioeng. 17, 1833 (1975).

    Article  PubMed  CAS  Google Scholar 

  • Zeltin’ R. P.: Selection of optimum medium for the biosynthesis of cellulolytic enzymes byAspergillus terreus 17 P by the steep ascent method. (In Russian)Mikrobiologiya 39, 832 (1970).

    CAS  Google Scholar 

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Authors and Affiliations

  1. Department of Technical Microbiology, Institute of Microbiology, Czechoslovak Academy of Sciences, 142 20, Prague 4

    P. Pilát, J. Voteuba, P. Doberský & A. Prokop

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  1. P. Pilát
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  2. J. Voteuba
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  3. P. Doberský
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  4. A. Prokop
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Pilát, P., Voteuba, J., Doberský, P. et al. Application of mathematical optimization methods in microbiology. Folia Microbiol 21, 391–405 (1976). https://doi.org/10.1007/BF02876966

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