Parameter estimation of nonlinear models in biochemistry: a comparative study on optimization methods

Yıldırım, Necmettin; Akçay, Fatih; Okur, Hüseyin; Yildirim, Derya

doi:10.1016/s0096-3003(02)00190-x

Cited by 22 publications

(9 citation statements)

References 2 publications

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“…Even though Levenberg-Marquardt is complicated than Gauss Newton algorithm, Levenberg-Marquardt works in most cases because Levenberg-Marquardt combines the steepest descent and Gauss Newton algorithm. 21 It is important to note that in a linearized form of Michaelis-Menten equation; almost four different possible linear equations have been proposed. It is somewhat easy to analyze and minimize the change in error statistics by comparing results obtained from different linearized form of Michaelis-Menten equation by using various chemometric tools and numerical error analysis respectively.…”

Section: Introductionmentioning

confidence: 99%

Non-Linearization of Modified Michaelis-Menten Kinetics

Nesakumar¹,

Sethuraman²,

Krishnan³

et al. 2014

j comput theor nanosci

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In view of the difficulties in finding the precise value of Michaelis-Menten constant (K M ) and maximum net current (I max ) of a biosensor from linear plots, we framed two modified non-linear equations employing Michaelis-Menten equation. In this work, data of lactate detecting sensor were used to exemplify practicability and accuracy of the modified Michaelis-Menten equation. Standard and modified Michaelis-Menten model was normalized using Levenberg-Marquardt algorithm. The validity of the two modified Michaelis-Menten models was statistically analyzed using numerical error analysis, unpaired student t-Test and Akaike's Information Criterion (AIC) method, and the results were satisfactory. This method is quite easy and has assured convergence with no initial guess for K M and I max .

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Section: Introductionmentioning

confidence: 99%

Non-Linearization of Modified Michaelis-Menten Kinetics

Nesakumar¹,

Sethuraman²,

Krishnan³

et al. 2014

j comput theor nanosci

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“…Classical Michaelis-Menten kinetics [10] is one the most working approximation of many models in different fields of biochemistry, microbiology and biotechnology, for example, in pharmacological models [11], chemostat models [12], or batchkinetics models [13][14][15]. A number of research publications discuss the Michaelis-Menten control approach applied to the enzyme network [16][17][18][19][20][21]. Recently, Michaelis-Menten kinetics has been used to describe the changing rates of cellular activity during bone resorption [22].…”

Section: Accepted M Manuscriptmentioning

confidence: 99%

Allosteric control model of bone remodelling containing periodical modes

Moroz¹,

Wimpenny²

2007

Biophysical Chemistry

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To help to understand the modelling process that occurs when a scaffold is implanted it is vital to understand the rather complex bone remodelling process prevalent in native bone.We have formulated a mathematical model that predicts osteoactivity both in scaffolds, as well as in bone in vivo and could set a basis for the more detailed allosteric models. The model is extended towards a bio-cybernetic vision of basic multicellular unit (BMU) action, when some of the regulation loops have been modified to reflect the allosteric control mechanisms, developed by Michaels-Menten, Hill, Koshland-Nemethy-Filmer, Monod-Wyman-Changeux.By implementation of this approach a four-dimensional system was obtained that shows steady cyclic behaviour using a wide range of constants with clear biological meaning. We have observed that a local steady-state appears as a limiting cycle in multidimensional phase space and this is discussed in this paper. Physiological interpretation of this limiting four-dimension cycle possibly related to a conservative-like value has been proposed. Analysis and simulation of the model has shown an analogy between this conservative value, as a kind of substrateenergy regenerative potential of the bone remodelling system with a molecular nature, and to the classical physical value -energy. This dynamic recovery potential is directed against both mechanical and biomechanical damage to the bone. Furthermore, the current model has credibility when compared to the normal bone remodelling process. In the framework of widely recognised Hill mechanisms of allosteric regulation the cyclic attractor, described formerly for a pure cellular model, prevails for different forms of feedback control. This result indicates the viability of the proposed existence of a conservative value (analogous to energy) that characterises the recovery potential of the bone remodelling cycle. Linear stability analysis has been performed in order to determine the robustness of the basic state, however, additional work is required to study a wider range of constants.

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“…The solutions of such models cannot be expressed by elementary functions, in most cases where system contains unknown parameters which are usually estimated by experimental data obtained from well-defined standard conditions. This type of problem is usually called parameter estimation in the literature and is often solved by deterministic optimization methods [2], [3], [4]. Unfortunately, the solution to the problem using these methods is usually around the local minima if there are more than one minimum available.…”

Section: Introductionmentioning

confidence: 99%

Parameter estimation of a tumor growth model using the real-valued genetic algorithm

Agrawal

2014

Global Journal of Mathematical Analysis

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This paper presents the use of real-valued Genetic Algorithm (GA) to evolve set of unknown parameters and initial conditions for tumor growth model using data extracted from El-Gohary [1]. The main focus of this work is to reach beyond the possibilities of traditional optimization methods in obtaining the far situated global optimum solutions with the help of arithmetic crossover and uniform mutation operators. Experimental results show the effectiveness of our approach by comparing the results obtained against the one mentioned in El-Gohary [1].

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Parameter estimation of nonlinear models in biochemistry: a comparative study on optimization methods

Cited by 22 publications

References 2 publications

Non-Linearization of Modified Michaelis-Menten Kinetics

Non-Linearization of Modified Michaelis-Menten Kinetics

Allosteric control model of bone remodelling containing periodical modes

Parameter estimation of a tumor growth model using the real-valued genetic algorithm

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