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1

A Formal Language Model of DNA Polymerase Enzymatic Activity

Enaganti S. K., Kari L., Kopecki S.

Fundamenta Informaticae

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2015

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Vol. 138, nr 1/2

179--192

EN

We propose and investigate a formal language operation inspired by the naturally occurring phenomenon of DNA primer extension by a DNA-template-directed DNA Polymerase enzyme. Given two DNA strings u and v, where the shorter string v (called primer) is Watson-Crick complementary and can thus bind to a substring of the longer string u (called template) the result of the primer extension is a DNA string that is complementary to a suffix of the template which starts at the binding position of the primer. The operation of DNA primer extension can be abstracted as a binary operation on two formal languages: a template language L1 and a primer language L2. We call this language operation L1-directed extension of L2 and study the closure properties of various language classes, including the classes in the Chomsky hierarchy, under directed extension. Furthermore, we answer the question under what conditions can a given language of target strings be generated from a given template language when the primer language is unknown. We use the canonic inverse of directed extension in order to obtain the optimal solution (the minimal primer language) to this question.

2

Optimal control of a fractional-order enzyme kinetic model

Al-Basir F., Elaiw A. M., Kesh D., Roy P. K.

Control and Cybernetics

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2015

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Vol. 44, no. 4

443--461

EN

Enzymes play a signiﬁcant role in controlling the characteristics of various chemical and biochemical reactions. They act as catalysts that increase the rate of reaction without undergoing any change in quantity. Enzymatic reactions occur through the active sites, which combine with the substrates to form intermediate complexes, subsequently leading to products. An enzyme having two active sites can show cooperative phenomena. Against this background, an enzyme-kinetic mathematical model is formulated using fractional order derivatives. Optimal control mechanism has been incorporated into the fractional-order model system to maximize the product output. Euler-Lagrange optimality conditions are derived for the FOCP (fractional order control problem) using maximum principle. Numerical iterative schemes have been developed to solve the fractional order optimal control problem through Matlab.

3

Mathematical modeling to optimize the product in enzyme kinetics

Nandi S., Ghosh M. K., Bhattacharya R., Roy P. K.

Control and Cybernetics

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2013

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Vol. 42, no. 2

431--442

EN

Optimization of product in enzyme kinetics is successful by the showers of mathematical analysis with control measures. Enzymes are an important functional aspects of all biochemical processes, as they catalyze numerous reaction taking place within living organisms. With this view, optimization and quantification of product is stressed upon and in such a context, optimal control approaches have been applied in our study. In this article, we have formulated a mathematical model of enzymatic system Dynamics with control measures with a view to optimize the product as well as process conditions. Here, Pontryagin Minimum Principle is used for determination of optimal control with the help of Hamiltonian. We discuss the relevant numerical solutions for the concentration of substrate, enzyme, complex and product with respect to a specified time interval by varying control factors.