Goldbeters mitotic oscillator entirely V. Manca, L. Marchetti - PowerPoint PPT Presentation

Goldbeter’s mitotic oscillator entirely modeled by MP systems Goldbeter’s mitotic oscillator entirely V. Manca, L. Marchetti modeled by MP systems Vincenzo Manca Luca Marchetti Center for Biomedical Computation (CBMC) University of Verona, Department of Computer Science web-site: http://www.cbmc.it E-mail: luca.marchetti@univr.it Eleventh International Conference on Membrane Computing (CMC11) 24-27 August 2010, Jena, Germany

Outline Goldbeter’s mitotic oscillator entirely Introduction: 1 modeled by MP systems introduction to Metabolic P systems V. Manca, L. Marchetti (i.e. the mathematical framework used for this work. . . ) Outline [Vincenzo Manca (2010) Metabolic P systems. Scholarpedia, 5(3):9273] Introduction presentation of the Log-Gain Stoichiometric Step-wise Research results regression (LGSS) Conclusions and future (i.e. the regression algorithm used to create models work descripted here. . . ) [Vincenzo Manca, Luca Marchetti (2010) Log-Gain Stoichiometric Stepwise regression for MP systems. International Journal of Foundations of Computer Science, to appear] Presentation of research results: 2 introduction to mitotic oscillations (i.e. the biological phenomenon under examination. . . ) [A. Goldbeter (1991) A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase. PNAS 88(20), 91079111] classification of mitotic MP models (i.e. the topic of our paper!!!)

Outline Goldbeter’s mitotic oscillator entirely Introduction: 1 modeled by MP systems introduction to Metabolic P systems V. Manca, L. Marchetti (i.e. the mathematical framework used for this work. . . ) Outline [Vincenzo Manca (2010) Metabolic P systems. Scholarpedia, 5(3):9273] Introduction presentation of the Log-Gain Stoichiometric Step-wise Research results regression (LGSS) Conclusions and future (i.e. the regression algorithm used to create models work descripted here. . . ) [Vincenzo Manca, Luca Marchetti (2010) Log-Gain Stoichiometric Stepwise regression for MP systems. International Journal of Foundations of Computer Science, to appear] Presentation of research results: 2 introduction to mitotic oscillations (i.e. the biological phenomenon under examination. . . ) [A. Goldbeter (1991) A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase. PNAS 88(20), 91079111] classification of mitotic MP models (i.e. the topic of our paper!!!)

An introduction to MP systems Goldbeter’s mitotic oscillator entirely P systems have been proposed by Gh. P˘ aun in ’98 as a modeled by MP systems discrete computational model inspired by the central role of V. Manca, L. Marchetti membranes in the structure and functioning of living cells. Outline [G. P˘ aun. Computing with membranes. J. Comput. System Sci. , 61(1): 108–143, 2000.] Introduction Metabolic P systems LGSS Research results Metabolic P systems are a variant of P systems, apt to Conclusions and future express biological processes. work [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 Goldbeter’s mitotic oscillator entirely modeled by MP MP graph systems An MP system can be V. Manca, L. Marchetti represented by means of Outline MP grammars and MP Introduction graphs. Metabolic P systems LGSS Research results MP grammar Conclusions and future work 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 Goldbeter’s mitotic oscillator entirely modeled by MP MP graph systems - SUBSTANCES - V. Manca, L. Marchetti Outline The types of molecules Introduction taking part to reactions... Metabolic P systems LGSS Research results MP grammar Conclusions and future work 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 Goldbeter’s mitotic oscillator entirely modeled by MP MP graph systems - REACTIONS - V. Manca, L. Marchetti Outline Evolution rules for matter Introduction transformation... Metabolic P systems LGSS Research results MP grammar Conclusions and future work 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 Goldbeter’s mitotic oscillator entirely modeled by MP MP graph systems - FLUXES - V. Manca, L. Marchetti Outline Functions which give the Introduction evolution of the system... Metabolic P systems LGSS Research results MP grammar Conclusions and future work 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 Goldbeter’s mitotic oscillator entirely modeled by MP EMA systems Equational Metabolic V. Manca, L. Marchetti For each step i of computation: Algorithm Outline 1) we compute reaction units: Introduction Metabolic P systems u 1 , 2 ,..., 5 [ i ] = ϕ 1 , 2 ,..., 5 [ i ] LGSS Research results MP grammar Conclusions and future work 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 Goldbeter’s mitotic oscillator entirely modeled by MP EMA systems Equational Metabolic V. Manca, L. Marchetti For each step i of computation: Algorithm Outline 1) we compute reaction units: Introduction Metabolic P systems u 1 , 2 ,..., 5 [ i ] = ϕ 1 , 2 ,..., 5 [ i ] LGSS Research results 2) we compute the variation of MP grammar Conclusions and future each substance ∆ A , B , C [ i ] : work 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 Goldbeter’s mitotic oscillator entirely modeled by MP EMA systems Equational Metabolic V. Manca, L. Marchetti For each step i of computation: Algorithm Outline 1) we compute reaction units: Introduction Metabolic P systems u 1 , 2 ,..., 5 [ i ] = ϕ 1 , 2 ,..., 5 [ i ] LGSS Research results 2) we compute the variation of MP grammar Conclusions and future each substance ∆ A , B , C [ i ] : work 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 Goldbeter’s mitotic oscillator entirely modeled by MP EMA systems Equational Metabolic V. Manca, L. Marchetti More “algebrically”, the vector of Algorithm substance variation Outline Introduction ∆[ i ] = (∆ A [ i ]; ∆ B [ i ]; ∆ C [ i ]) Metabolic P systems LGSS is given by the following matrix Research results product:   MP grammar u 1 [ i ] Conclusions and future   1 − 1 − 1 0 0 u 2 [ i ] work     MP reactions MP fluxes 0 1 0 − 1 0 × u 3 [ i ]     r 1 : ∅ → A ϕ 1 = 0 . 1 + 3 A 0 − 1  u 4 [ i ]  0 0 1 r 2 : A → B ϕ 2 = 0 . 2 C u 5 [ i ] � �� � A r 3 : A → C ϕ 3 = 0 . 1 B � �� � U [ i ] r 4 : B → ∅ ϕ 4 = 0 . 6 B + P � �� � r 5 : C → ∅ ϕ 5 = 0 . 4 C + P ∆[ i ] = A × U [ i ] A [ 0 ] , B [ 0 ] , C [ 0 ] = 1 mol . Z [ i + 1 ] = Z [ i ] + ∆[ i ] P [ 0 ] = 0 . 2 , P [ i + 1 ] = P [ i ] + 0 . 2. where Z [ i ] = ( A [ i ]; B [ i ]; C [ i ]) .