MP Modelling of Glucose-Insulin Interactions in the Intravenous Glucose Tolerance Test

Abstract

The Intravenous Glucose Tolerance Test is an experimental procedure used to study the glucose-insulin endocrine regulatory system. An open problem is to construct a model representing simultaneously the entire regulative mechanism. In the past three decades, several models have appeared, but they have not escaped criticisms and drawbacks. In this paper, the authors apply the Metabolic P systems theory for developing new physiologically based models of the glucose-insulin system, which can be applied to the IVGTT. Ten data-sets obtained from literature were considered and an MP model was found for each, which fits the data and explains the regulations of the dynamics. Finally, each model is analysed to define a common pattern which explains, in general, the action of the glucose-insulin control system.

Recurrent Solutions to Dynamics Inverse Problems: A Validation of MP Regression

“…Conversely, the exibility of LGSS allows us to find the best regulators approximating the internal logic of the observed dynamics, without imposing a preliminary form. In papers [10- 13,21,22] where MP theory was already successful applied to biomedical problems, very good approximations are obtained even when the regulators have a form that is different from that corresponding to Taylor series. Finally, beside the wide range of applications of the MP approach to the analysis of complex phenomena, in applications section some new applications are introduced that exploit the regression capabilities of LGSS for the analysis of periodical signals.…”

“…In this paper, when we refer to MP regression, we intend the LGSS (basic) MP regression algorithm, integrating algebraic and statistical regression methods in the MP framework [7][8][9][10], that resulted completely satisfactory in all the considered cases. Dynamics inverse problems are crucial in many applicative contexts, where solving a DIP means discovering a logic relating the variables of a phenomenon, by passing from a time external manifestation to a state internal causation [11][12][13]. Here, we present an MP solution of a mathematical problem related to circular functions: which are the MP recurrent equations discovered by the MP regression from time series of sine and cosine?…”

“…MP grammars have an intrinsic versatility in describing oscillatory phenomena [13,14]. The schema of MP grammars given in Table 1, called bicatalyticus [10], has an input rule r 1 and an output rule r 3 (incrementing and decrementing the variable x and y, respectively).…”

“…The attribute MP comes from the initial application context suggesting MP grammars [1] extending Paun's P systems (multiset rewriting rules distributed in compartments) [15][16][17]. Applications in modeling biological systems were developed in the last years [3,10,13,[18][19][20][21][22].…”

Optimization Algorithms for Computational Systems Biology

“…This problem is often formulated in the form of least squares, as in models related to diabetes [10,19,20], biological pathways [21][22][23][24], and pharmacokinetics/pharmacodynamics [25,26]. Least squares problems may arise in statistical regression as well [27][28][29][30][31][32].…”