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:
[email protected]
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 L. Marchetti, V. Manca
1
Introduction: 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]
2
MP analysis of gene expressions: 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 L. Marchetti, V. Manca
1
Introduction: 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]
2
MP analysis of gene expressions: 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 expression analysis L. Marchetti, V. Manca Outline Introduction
˘ P systems have been proposed by Gh. Paun in ’98 as a discrete computational model inspired by the central role of membranes in the structure and functioning of living cells. ˘ [G. Paun. 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 L. Marchetti, V. Manca Outline Introduction Metabolic P systems
MP analysis of gene expressions
An MP system can be represented by means of MP grammars and MP graphs.
MP grammar MP reactions r1 : ∅ → A r2 : A → B r3 : A → C r4 : B → ∅ r5 : C → ∅
MP fluxes ϕ1 = 0.1 + 3A ϕ2 = 0.2C ϕ3 = 0.1B ϕ4 = 0.6B + P ϕ5 = 0.4C + P
A[0], B[0], C[0] = 1mol. P[0] = 0.2, P[i + 1] = P[i] + 0.2.
MP graph
Main components of MP systems A methodology based on MP theory for gene expression analysis L. Marchetti, V. Manca
MP graph - SUBSTANCES -
Outline Introduction Metabolic P systems
MP analysis of gene expressions
The types of molecules taking part to reactions...
MP grammar MP reactions r1 : ∅ → A r2 : A → B r3 : A → C r4 : B → ∅ r5 : C → ∅
MP fluxes ϕ1 = 0.1 + 3A ϕ2 = 0.2C ϕ3 = 0.1B ϕ4 = 0.6B + P ϕ5 = 0.4C + P
A[0], B[0], C[0] = 1mol. 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 L. Marchetti, V. Manca
MP graph - REACTIONS -
Outline Introduction Metabolic P systems
MP analysis of gene expressions
Evolution rules for matter transformation...
MP grammar MP reactions r1 : ∅ → A r2 : A → B r3 : A → C r4 : B → ∅ r5 : C → ∅
MP fluxes ϕ1 = 0.1 + 3A ϕ2 = 0.2C ϕ3 = 0.1B ϕ4 = 0.6B + P ϕ5 = 0.4C + P
A[0], B[0], C[0] = 1mol. 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 L. Marchetti, V. Manca
MP graph - FLUXES -
Outline Introduction Metabolic P systems
MP analysis of gene expressions
Functions which give the evolution of the system...
MP grammar MP reactions r1 : ∅ → A r2 : A → B r3 : A → C r4 : B → ∅ r5 : C → ∅
MP fluxes ϕ1 = 0.1 + 3A ϕ2 = 0.2C ϕ3 = 0.1B ϕ4 = 0.6B + P ϕ5 = 0.4C + P
A[0], B[0], C[0] = 1mol. 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 L. Marchetti, V. Manca Outline
Equational Metabolic Algorithm
Introduction
EMA For each step i of computation: 1) we compute reaction units:
Metabolic P systems
u1,2,...,5 [i] = ϕ1,2,...,5 [i]
MP analysis of gene expressions
MP grammar MP reactions r1 : ∅ → A r2 : A → B r3 : A → C r4 : B → ∅ r5 : C → ∅
MP fluxes ϕ1 = 0.1 + 3A ϕ2 = 0.2C ϕ3 = 0.1B ϕ4 = 0.6B + P ϕ5 = 0.4C + P
A[0], B[0], C[0] = 1mol. P[0] = 0.2, P[i + 1] = P[i] + 0.2.
u1 [i] = 0.1 + 3A[i] u2 [i] = 0.2C[i] u3 [i] = 0.1B[i] u4 [i] = 0.6B[i] + P[i] u5 [i] = 0.4C[i] + P[i] Ex: u1 [i] gives the amount of substance which is produced and consumed by r1 at step i.
Main components of MP systems A methodology based on MP theory for gene expression analysis L. Marchetti, V. Manca Outline
Equational Metabolic Algorithm
Introduction
EMA For each step i of computation: 1) we compute reaction units:
Metabolic P systems
u1,2,...,5 [i] = ϕ1,2,...,5 [i]
MP analysis of gene expressions
MP grammar MP reactions r1 : ∅ → A r2 : A → B r3 : A → C r4 : B → ∅ r5 : C → ∅
MP fluxes ϕ1 = 0.1 + 3A ϕ2 = 0.2C ϕ3 = 0.1B ϕ4 = 0.6B + P ϕ5 = 0.4C + P
A[0], B[0], C[0] = 1mol. P[0] = 0.2, P[i + 1] = P[i] + 0.2.
2) we compute the variation of each substance ∆A,B,C [i]: ∆A [i] = u1 [i] − u2 [i] − u3 [i] ∆B [i] = u2 [i] − u4 [i] ∆C [i] = u3 [i] − u5 [i] Ex: ∆A [i] is increased of u1 [i] because r1 produces A and decreased of u2 [i] + u3 [i] because r2 , r3 consume A.
Main components of MP systems A methodology based on MP theory for gene expression analysis L. Marchetti, V. Manca Outline
Equational Metabolic Algorithm
Introduction
EMA For each step i of computation: 1) we compute reaction units:
Metabolic P systems
u1,2,...,5 [i] = ϕ1,2,...,5 [i]
MP analysis of gene expressions
MP grammar MP reactions r1 : ∅ → A r2 : A → B r3 : A → C r4 : B → ∅ r5 : C → ∅
MP fluxes ϕ1 = 0.1 + 3A ϕ2 = 0.2C ϕ3 = 0.1B ϕ4 = 0.6B + P ϕ5 = 0.4C + P
A[0], B[0], C[0] = 1mol. P[0] = 0.2, P[i + 1] = P[i] + 0.2.
2) we compute the variation of each substance ∆A,B,C [i]: ∆A [i] = u1 [i] − u2 [i] − u3 [i] ∆B [i] = u2 [i] − u4 [i] ∆C [i] = u3 [i] − u5 [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]
Main components of MP systems A methodology based on MP theory for gene expression analysis L. Marchetti, V. Manca Outline
Equational Metabolic Algorithm
Introduction
EMA For each step i of computation: 1) we compute reaction units:
Metabolic P systems
u1,2,...,5 [i] = ϕ1,2,...,5 [i]
MP analysis of gene expressions
MP simulation
2) we compute the variation of each substance ∆A,B,C [i]: ∆A [i] = u1 [i] − u2 [i] − u3 [i] ∆B [i] = u2 [i] − u4 [i] ∆C [i] = u3 [i] − u5 [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]
The inverse dynamical problem
EMA
A methodology based on MP theory for gene expression analysis L. Marchetti, V. Manca Outline Introduction Metabolic P systems
MP analysis of gene expressions
The dynamics
The MP grammar MP reactions r1 : ∅ → A r2 : A → B r3 : A → C r4 : B → ∅ r5 : C → ∅
MP fluxes ϕ1 = 0.1 + 3A ϕ2 = 0.2C ϕ3 = 0.1B ϕ4 = 0.6B + P ϕ5 = 0.4C + P
A[0], B[0], C[0] = 1mol. P[0] = 0.2, P[i + 1] = P[i] + 0.2.
LGSS
[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]
The inverse dynamical problem A methodology based on MP theory for gene expression analysis L. Marchetti, V. Manca Outline Introduction
The dynamical problem
The inverse dynamical problem
What it is given:
What it is given:
Metabolic P systems
1 MP analysis of gene expressions
an MP grammar: stoichiometry; flux maps;
1
time-series of observations (i.e. a sampled dynamics);
2
an idea of stoichiometry.
What we want: THE DYNAMICS CALCULATION
What we want: THE MP SYSTEM WHICH REPRODUCES THE OBSERVED DYNAMICS
EMA Equational Metabolic Algorithm
LGSS Log-Gain Stoichiometric Step-wise regression
2
an initial state.
The idea behind our work. . . A methodology based on MP theory for gene expression analysis L. Marchetti, V. Manca Outline
MP systems were introduced to model metabolic processes, but, thanks to the usage of LGSS,
Introduction MP analysis of gene expressions Introduction to gene networks
they can be used in each context where we need to infer models of a system from a given set of time series.
MP modelling of gene networks From microarray raw data to MP models
In the case of gene expression analysis, MP systems should be particularly convenient since we need to manage many time series coming from microarray experiments.
A DNA microarray experiment A methodology based on MP theory for gene expression analysis
GOAL: to obtain gene-expression profile data for a target cell
L. Marchetti, V. Manca Outline Introduction MP analysis of gene expressions Introduction to gene networks MP modelling of gene networks From microarray raw data to MP models
The structure of a DNA microarray experiment: RNA is first extracted from the target cell; the RNA is then reverse-transcribed and labelled (sample preparation); the prepared RNA is hybridized to the chip; the hybridized chip is scanned and the image processed to provide corresponding gene-profiles.
A DNA microarray experiment A methodology based on MP theory for gene expression analysis
GOAL: to obtain gene-expression profile data for a target cell
L. Marchetti, V. Manca Outline Introduction MP analysis of gene expressions Introduction to gene networks MP modelling of gene networks From microarray raw data to MP models
The role of functional genomics To understand how the genes work together to comprise functioning cells and organisms.
A gene network as a projection of a global biochemical network on the gene space A methodology based on MP theory for gene expression analysis L. Marchetti, V. Manca Outline Introduction MP analysis of gene expressions Introduction to gene networks MP modelling of gene networks From microarray raw data to MP models
Corresponding gene network
A gene network as a projection of a global biochemical network on the gene space A methodology based on MP theory for gene expression analysis L. Marchetti, V. Manca Outline
Three mechanisms of gene-to-gene interactions: 1
regulation of Gene 2 by the protein product of the Gene 1;
2
regulation of the Gene 2 by the Complex 3-4 formed by the products of Gene 3 and Gene 4;
3
regulation of Gene 4 by the Metabolite 2, which in turn is produced by Protein 2.
Introduction MP analysis of gene expressions Introduction to gene networks MP modelling of gene networks From microarray raw data to MP models
Corresponding gene network
MP grammars vs Gene networks A methodology based on MP theory for gene expression analysis L. Marchetti, V. Manca Outline
We found a standard way for translating an MP grammar involving gene expressions into a corresponding gene network. MP grammar
Introduction MP analysis of gene expressions Introduction to gene networks MP modelling of gene networks
Simple promotion r : ∅ → G2 ϕ : k1 · G1
From microarray raw data to MP models
Simple inhibition r : G2 → ∅ ϕ : k1 · G1
Simple prom./inhib. r : G2 → G3 ϕ : k1 · G1
MP graph
Gene network
MP grammars vs Gene networks A methodology based on MP theory for gene expression analysis L. Marchetti, V. Manca Outline
We found a standard way for translating an MP grammar involving gene expressions into a corresponding gene network. MP grammar
Introduction MP analysis of gene expressions Introduction to gene networks MP modelling of gene networks
Combined promotion r : ∅ → G3 ϕ : k1 · G1 + k2 · G2
From microarray raw data to MP models
Combined inhibition r : G3 → ∅ ϕ : k1 · G1 + k2 · G2
Comb. prom./inhib. r : G3 → G4 ϕ : k1 · G1 + k2 · G2
MP graph
Gene network
MP grammars vs Gene networks A methodology based on MP theory for gene expression analysis L. Marchetti, V. Manca Outline Introduction MP analysis of gene expressions Introduction to gene networks MP modelling of gene networks From microarray raw data to MP models
MP grammar r1 : G1 → ∅ r2 : ∅ → G2 r3 : G2 → ∅ r4 : G2 → G3 r5 : G3 → ∅ r6 : ∅ → G4 r7 : G4 → ∅
ϕ1 ϕ2 ϕ3 ϕ4 ϕ5 ϕ6 ϕ7
= k1 · G1 = k2 · G3 + k3 · G4 = k4 · G2 = k5 · G1 = k6 · G3 = k7 · G2 = k8 · G4
From microarray raw data to MP models (I) A methodology based on MP theory for gene expression analysis L. Marchetti, V. Manca
Genomics and gene expression experiments are sometimes derived as “fishing expeditions”
Outline Introduction MP analysis of gene expressions Introduction to gene networks
the goal is the individuation of new genes involved in a pathway, potential drug targets or expression markers that can be used in a predictive or diagnostic fashion.
MP modelling of gene networks From microarray raw data to MP models
The idea: 1
consider some target cells and treat them with some specific inhibitors or some targeted up-regulators;
2
get the time series of gene expression profiles for the entire genome by means of suitable microarray experiments;
3
use the time series to infer a model which explains the gene regulations which act during the experiment.
From microarray raw data to MP models (II) A methodology based on MP theory for gene expression analysis L. Marchetti, V. Manca
Genomics and gene expression experiments are sometimes derived as “fishing expeditions”
Outline Introduction MP analysis of gene expressions Introduction to gene networks
the goal is the individuation of new genes involved in a pathway, potential drug targets or expression markers that can be used in a predictive or diagnostic fashion.
MP modelling of gene networks From microarray raw data to MP models
In our case we should develop an MP model with a number of substances equal to the number of genes in the entire genomes This means MP models with more then 18000 substances!
From microarray raw data to MP models (III) A methodology based on MP theory for gene expression analysis L. Marchetti, V. Manca Outline Introduction MP analysis of gene expressions
The number of the raw time series which need to be processed for a generic experiment on human cells is usually of the order of tens of thousands. BUT
Introduction to gene networks MP modelling of gene networks From microarray raw data to MP models
Generally only a small part of them exhibit an expression profile which can be related to the phenomenon under examination.
Before defining the MP model, raw data will be preprocessed following a methodology which comprises normalization, filtering and clustering
The analysis of HER-2 oncogene-regulated transcriptome in human SUM-225 cells (I) A methodology based on MP theory for gene expression analysis L. Marchetti, V. Manca Outline Introduction MP analysis of gene expressions Introduction to gene networks 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 (II) A methodology based on MP theory for gene expression analysis L. Marchetti, V. Manca Outline
Number 24256
Introduction MP analysis of gene expressions Introduction to gene networks MP modelling of gene networks
18631 12381 3189
From microarray raw data to MP models
1175 40 8 1
Description Number of time series in RAW data (each time series has 16 points) Number of different genes analysed Number of time series with reliable measures Number of genes which exhibit a time-dependent expression level change Number of genes after the filtering procedure Number of sub-clusters which group genes with similar log2 expression profile Number of clusters which give the different behaviours occurring in HER-2 gene regulation Final MP grammar which gives the rules and the regulation of the phenomenon
Thank you! A methodology based on MP theory for gene expression analysis L. Marchetti, V. Manca Outline Introduction MP analysis of gene expressions Introduction to gene networks MP modelling of gene networks From microarray raw data to MP models
Thank you!