A methodology based on MP theory for gene expression analysis L. Marchetti, V. Manca A methodology based on MP theory for gene expression analysis Luca Marchetti Vincenzo Manca Center for Biomedical Computation (CBMC) University of Verona, Department of Computer Science web-site: http://www.cbmc.it E-mail: luca.marchetti@univr.it Twelfth International Conference on Membrane Computing (CMC12) 23-26 August 2011, Fontainebleau/Paris, France
Outline A methodology based on MP theory for gene expression analysis Introduction: 1 L. Marchetti, V. Manca introduction to Metabolic P systems Outline [Vincenzo Manca (2010) Metabolic P systems. Scholarpedia, 5(3):9273] Introduction LGSS for solving the inverse dynamical problem MP analysis of gene expressions [Vincenzo Manca, Luca Marchetti (2011) Log-Gain Stoichiometric Stepwise regression for MP systems. International Journal of Foundations of Computer Science Vol. 22, No. 1, pag 97-106] MP analysis of gene expressions: 2 introduction to gene networks [Paul Brazhnik, Alberto de la Fuente, Pedro Mendes (2002) Gene networks: how to put the function in genomics. TRENDS in Biotechnology 20, No.11] MP modelling of gene networks From microarray raw data to MP models: the analysis of HER-2 oncogene-regulated transcriptome in human SUM-225 cells.
Outline A methodology based on MP theory for gene expression analysis Introduction: 1 L. Marchetti, V. Manca introduction to Metabolic P systems Outline [Vincenzo Manca (2010) Metabolic P systems. Scholarpedia, 5(3):9273] Introduction LGSS for solving the inverse dynamical problem MP analysis of gene expressions [Vincenzo Manca, Luca Marchetti (2011) Log-Gain Stoichiometric Stepwise regression for MP systems. International Journal of Foundations of Computer Science Vol. 22, No. 1, pag 97-106] MP analysis of gene expressions: 2 introduction to gene networks [Paul Brazhnik, Alberto de la Fuente, Pedro Mendes (2002) Gene networks: how to put the function in genomics. TRENDS in Biotechnology 20, No.11] MP modelling of gene networks From microarray raw data to MP models: the analysis of HER-2 oncogene-regulated transcriptome in human SUM-225 cells.
An introduction to MP systems A methodology based on MP theory for gene P systems have been proposed by Gh. P˘ aun in ’98 as a expression analysis L. Marchetti, V. Manca discrete computational model inspired by the central role of membranes in the structure and functioning of living cells. Outline Introduction [G. P˘ aun. Computing with membranes. J. Comput. System Sci. , 61(1): 108–143, 2000.] Metabolic P systems MP analysis of gene expressions Metabolic P systems are a variant of P systems, apt to express biological processes. [Vincenzo Manca (2010) Metabolic P systems. Scholarpedia, 5(3):9273] Main features: A fixed membrane structure (many time only the skin membrane is used). A “biological” interpretation of objects as biological substances and of evolution rules as biological reactions. An evolution strategy based on a discrete, deterministic algorithm called Equational Metabolic Algorithm (EMA).
Main components of MP systems A methodology based on MP theory for gene expression analysis MP graph L. Marchetti, V. Manca An MP system can be represented by means of Outline MP grammars and MP Introduction Metabolic P systems graphs. MP analysis of gene expressions MP grammar MP reactions MP fluxes r 1 : ∅ → A ϕ 1 = 0 . 1 + 3 A r 2 : A → B ϕ 2 = 0 . 2 C r 3 : A → C ϕ 3 = 0 . 1 B r 4 : B → ∅ ϕ 4 = 0 . 6 B + P r 5 : C → ∅ ϕ 5 = 0 . 4 C + P A [ 0 ] , B [ 0 ] , C [ 0 ] = 1 mol . P [ 0 ] = 0 . 2 , P [ i + 1 ] = P [ i ] + 0 . 2.
Main components of MP systems A methodology based on MP theory for gene expression analysis MP graph L. Marchetti, V. Manca - SUBSTANCES - Outline The types of molecules Introduction Metabolic P systems taking part to reactions... MP analysis of gene expressions MP grammar MP reactions MP fluxes r 1 : ∅ → A ϕ 1 = 0 . 1 + 3 A r 2 : A → B ϕ 2 = 0 . 2 C r 3 : A → C ϕ 3 = 0 . 1 B r 4 : B → ∅ ϕ 4 = 0 . 6 B + P r 5 : C → ∅ ϕ 5 = 0 . 4 C + P A [ 0 ] , B [ 0 ] , C [ 0 ] = 1 mol . P [ 0 ] = 0 . 2 , P [ i + 1 ] = P [ i ] + 0 . 2.
Main components of MP systems A methodology based on MP theory for gene expression analysis MP graph L. Marchetti, V. Manca - REACTIONS - Outline Evolution rules for matter Introduction Metabolic P systems transformation... MP analysis of gene expressions MP grammar MP reactions MP fluxes r 1 : ∅ → A ϕ 1 = 0 . 1 + 3 A r 2 : A → B ϕ 2 = 0 . 2 C r 3 : A → C ϕ 3 = 0 . 1 B r 4 : B → ∅ ϕ 4 = 0 . 6 B + P r 5 : C → ∅ ϕ 5 = 0 . 4 C + P A [ 0 ] , B [ 0 ] , C [ 0 ] = 1 mol . P [ 0 ] = 0 . 2 , P [ i + 1 ] = P [ i ] + 0 . 2.
Main components of MP systems A methodology based on MP theory for gene expression analysis MP graph L. Marchetti, V. Manca - FLUXES - Outline Functions which give the Introduction Metabolic P systems evolution of the system... MP analysis of gene expressions MP grammar MP reactions MP fluxes r 1 : ∅ → A ϕ 1 = 0 . 1 + 3 A r 2 : A → B ϕ 2 = 0 . 2 C r 3 : A → C ϕ 3 = 0 . 1 B r 4 : B → ∅ ϕ 4 = 0 . 6 B + P r 5 : C → ∅ ϕ 5 = 0 . 4 C + P A [ 0 ] , B [ 0 ] , C [ 0 ] = 1 mol . P [ 0 ] = 0 . 2 , P [ i + 1 ] = P [ i ] + 0 . 2.
Main components of MP systems A methodology based on MP theory for gene expression analysis EMA L. Marchetti, V. Manca Equational Metabolic For each step i of computation: Algorithm Outline Introduction 1) we compute reaction units: Metabolic P systems u 1 , 2 ,..., 5 [ i ] = ϕ 1 , 2 ,..., 5 [ i ] MP analysis of gene expressions MP grammar MP reactions MP fluxes u 1 [ i ] = 0 . 1 + 3 A [ i ] r 1 : ∅ → A ϕ 1 = 0 . 1 + 3 A u 2 [ i ] = 0 . 2 C [ i ] r 2 : A → B ϕ 2 = 0 . 2 C u 3 [ i ] = 0 . 1 B [ i ] r 3 : A → C ϕ 3 = 0 . 1 B r 4 : B → ∅ u 4 [ i ] = 0 . 6 B [ i ] + P [ i ] ϕ 4 = 0 . 6 B + P r 5 : C → ∅ ϕ 5 = 0 . 4 C + P u 5 [ i ] = 0 . 4 C [ i ] + P [ i ] A [ 0 ] , B [ 0 ] , C [ 0 ] = 1 mol . Ex: u 1 [ i ] gives the amount of substance which is produced and P [ 0 ] = 0 . 2 , P [ i + 1 ] = P [ i ] + 0 . 2. consumed by r 1 at step i .
Main components of MP systems A methodology based on MP theory for gene expression analysis EMA L. Marchetti, V. Manca Equational Metabolic For each step i of computation: Algorithm Outline Introduction 1) we compute reaction units: Metabolic P systems u 1 , 2 ,..., 5 [ i ] = ϕ 1 , 2 ,..., 5 [ i ] MP analysis of gene expressions 2) we compute the variation of MP grammar each substance ∆ A , B , C [ i ] : MP reactions MP fluxes ∆ A [ i ] = u 1 [ i ] − u 2 [ i ] − u 3 [ i ] r 1 : ∅ → A ϕ 1 = 0 . 1 + 3 A ∆ B [ i ] = u 2 [ i ] − u 4 [ i ] r 2 : A → B ϕ 2 = 0 . 2 C r 3 : A → C ϕ 3 = 0 . 1 B ∆ C [ i ] = u 3 [ i ] − u 5 [ i ] r 4 : B → ∅ ϕ 4 = 0 . 6 B + P r 5 : C → ∅ ϕ 5 = 0 . 4 C + P Ex: ∆ A [ i ] is increased of u 1 [ i ] A [ 0 ] , B [ 0 ] , C [ 0 ] = 1 mol . because r 1 produces A and decreased of u 2 [ i ] + u 3 [ i ] because P [ 0 ] = 0 . 2 , P [ i + 1 ] = P [ i ] + 0 . 2. r 2 , r 3 consume A .
Main components of MP systems A methodology based on MP theory for gene expression analysis EMA L. Marchetti, V. Manca Equational Metabolic For each step i of computation: Algorithm Outline Introduction 1) we compute reaction units: Metabolic P systems u 1 , 2 ,..., 5 [ i ] = ϕ 1 , 2 ,..., 5 [ i ] MP analysis of gene expressions 2) we compute the variation of MP grammar each substance ∆ A , B , C [ i ] : MP reactions MP fluxes ∆ A [ i ] = u 1 [ i ] − u 2 [ i ] − u 3 [ i ] r 1 : ∅ → A ϕ 1 = 0 . 1 + 3 A ∆ B [ i ] = u 2 [ i ] − u 4 [ i ] r 2 : A → B ϕ 2 = 0 . 2 C r 3 : A → C ϕ 3 = 0 . 1 B ∆ C [ i ] = u 3 [ i ] − u 5 [ i ] r 4 : B → ∅ ϕ 4 = 0 . 6 B + P 3) we compute the next state: r 5 : C → ∅ ϕ 5 = 0 . 4 C + P A [ i + 1 ] = A [ i ] + ∆ A [ i ] A [ 0 ] , B [ 0 ] , C [ 0 ] = 1 mol . B [ i + 1 ] = B [ i ] + ∆ B [ i ] P [ 0 ] = 0 . 2 , P [ i + 1 ] = P [ i ] + 0 . 2. C [ i + 1 ] = C [ i ] + ∆ C [ i ]
Main components of MP systems A methodology based on MP theory for gene expression analysis EMA L. Marchetti, V. Manca Equational Metabolic For each step i of computation: Algorithm Outline Introduction 1) we compute reaction units: Metabolic P systems u 1 , 2 ,..., 5 [ i ] = ϕ 1 , 2 ,..., 5 [ i ] MP analysis of gene expressions 2) we compute the variation of MP simulation each substance ∆ A , B , C [ i ] : ∆ A [ i ] = u 1 [ i ] − u 2 [ i ] − u 3 [ i ] ∆ B [ i ] = u 2 [ i ] − u 4 [ i ] ∆ C [ i ] = u 3 [ i ] − u 5 [ i ] 3) we compute the next state: A [ i + 1 ] = A [ i ] + ∆ A [ i ] B [ i + 1 ] = B [ i ] + ∆ B [ i ] C [ i + 1 ] = C [ i ] + ∆ C [ i ]
Some beautiful oscillation patterns which can be achieved with simple MP grammars... A methodology based on MP theory for gene expression analysis L. Marchetti, V. Manca Outline Introduction Metabolic P systems MP analysis of gene expressions [Vincenzo Manca, Luca Marchetti (2010) Metabolic approximation of real periodical functions. The Journal of Logic and Algebraic Programming 79 (2010), pag.363-373]
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