MP Modelling for Systems Biology: Two Case Studies

Marchetti, Luca; Manca, Vincenzo; Pagliarini, Roberto; Bollig‐Fischer, Aliccia

doi:10.1007/978-3-319-03191-0_7

Cited by 6 publications

(9 citation statements)

References 56 publications

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“…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.…”

Section: Discussionmentioning

confidence: 99%

“…It is interesting to see that, thanks to the fact that this time the considered sampling step is bigger, the coefficient estimates computed by LGSS consider more terms of Taylor series. In particular, coefficients of grammar (22) correspond to a Taylor series of (Table 3), the maximum degree that is possible to considerate with a precision of 15 decimal digits.…”

Section: An Mp Grammar For Sine and Cosinementioning

confidence: 99%

“…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].…”

Section: Introductionmentioning

confidence: 99%

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

M¹

2014

J Appl Computat Math

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The paper is focused on a new perspective in solving dynamics inverse problems, by considering recurrent equations based on Metabolic P (MP) grammars. MP grammars are a particular type of multiset rewriting grammars, introduced in 2004 for modeling metabolic systems, which express dynamics in terms of finite difference equations. Regression algorithms, based on MP grammars, were introduced since 2008 for algorithmically solving dynamics inverse problems in the context of biological phenomena. This paper shows that, when MP regression is applied to time series of circular functions (where time is replaced by rotation angle), the dynamics that is found turns out to coincide with recurrent equations derivable from classical analytical definitions of these functions. This validates the MP regression as a general methodology to discover deep logics underlying observed dynamics. At the end of the paper some applications are also discussed, which exploit the regression capabilities of the MP framework for the analysis of periodical signals and for the implementation of sequential circuits providing periodical oscillators. When an initial state X [0] is given to an MP grammar G, then, starting from it, we pass from any state to its following state by applying all the rules of the grammar, that is, by summing the decrements and increments acting on each variable, according to all the rules where it occurs. It is easy to show that the corresponding dynamics is expressed with recurrent equations, which are synthetically represented in matricial form [10]. Recurrent Solutions to DynamicsWhen variables are equipped with measurement units (related to their interpretation), and a time duration is associated to each step, the MP grammar is more properly called an MP system.

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Section: Discussionmentioning

confidence: 99%

Section: An Mp Grammar For Sine and Cosinementioning

confidence: 99%

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

M¹

2014

J Appl Computat Math

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“…In such systems, regulators play a role that is analogous to that played by derivatives in ODE systems. Despite these analogies, MP systems proved to be advantageous in many modeling situations which ranged from the theoretical field of real function approximation [15] to the modeling of complicated biological dynamics relevant in Systems Biology [22], [21], [19], [15], [14], [20].…”

Section: Mp Chaotic Systemsmentioning

confidence: 99%

“…3). Successful modeling results comprise metabolic dynamics, gene expression networks, and population dynamics [22], [21], [19], [15], [14], [20], [13].…”

Section: Introduction To Mp Systemsmentioning

confidence: 99%

On the inference of deterministic chaos: Evolutionary algorithm and metabolic P system approaches

Marchetti

Manca

Zelinka

2014

2014 IEEE Congress on Evolutionary Computation (CEC)

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This paper shows the possibility of using Metabolic P systems (MP systems) for chaotic system identificationreconstruction and it compares presented results with previous ones obtained by evolutionary algorithms. An important potentiality of MP theory is given by its powerful computational chaos generation that can be also used as an internal module of evolutionary algorithms by increasing their ability in specific cases of their application. Reported numerical experiments are discussed at the end.

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