A methodology based on MP theory for gene expression analysis Luca - - PowerPoint PPT Presentation

A methodology based

• n 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

A methodology based

• n MP theory for gene

expression analysis

• L. Marchetti, V. Manca

Outline Introduction MP analysis of gene expressions

Outline

1

Introduction:

introduction to Metabolic P systems

[Vincenzo Manca (2010) Metabolic P systems. Scholarpedia, 5(3):9273]

LGSS for solving the inverse dynamical problem

[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.

A methodology based

• n MP theory for gene

expression analysis

• L. Marchetti, V. Manca

Outline Introduction MP analysis of gene expressions

Outline

1

Introduction:

introduction to Metabolic P systems

[Vincenzo Manca (2010) Metabolic P systems. Scholarpedia, 5(3):9273]

LGSS for solving the inverse dynamical problem

[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.

A methodology based

• n MP theory for gene

expression analysis

• L. Marchetti, V. Manca

Outline Introduction

Metabolic P systems

MP analysis of gene expressions

An introduction to MP systems

P systems have been proposed by Gh. P˘ aun in ’98 as a discrete computational model inspired by the central role of membranes in the structure and functioning of living cells.

[G. P˘

• aun. Computing with membranes. J. Comput. System Sci., 61(1): 108–143, 2000.]

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).

A methodology based

• n MP theory for gene

expression analysis

• L. Marchetti, V. Manca

Outline Introduction

Metabolic P systems

MP analysis of gene expressions

Main components of MP systems

An MP system can be represented by means of MP grammars and MP graphs.

MP grammar

MP reactions MP fluxes r1 : ∅ → A ϕ1 = 0.1 + 3A r2 : A → B ϕ2 = 0.2C r3 : A → C ϕ3 = 0.1B r4 : B → ∅ ϕ4 = 0.6B + P r5 : C → ∅ ϕ5 = 0.4C + P A[0], B[0], C[0] = 1mol. P[0] = 0.2, P[i + 1] = P[i] + 0.2.

MP graph

A methodology based

• n MP theory for gene

expression analysis

• L. Marchetti, V. Manca

Outline Introduction

Metabolic P systems

MP analysis of gene expressions

Main components of MP systems

• SUBSTANCES -

The types of molecules taking part to reactions...

MP grammar

MP reactions MP fluxes r1 : ∅ → A ϕ1 = 0.1 + 3A r2 : A → B ϕ2 = 0.2C r3 : A → C ϕ3 = 0.1B r4 : B → ∅ ϕ4 = 0.6B + P r5 : C → ∅ ϕ5 = 0.4C + P A[0], B[0], C[0] = 1mol. P[0] = 0.2, P[i + 1] = P[i] + 0.2.

MP graph

A methodology based

• n MP theory for gene

expression analysis

• L. Marchetti, V. Manca

Outline Introduction

Metabolic P systems

MP analysis of gene expressions

Main components of MP systems

• REACTIONS -

Evolution rules for matter transformation...

MP grammar

MP reactions MP fluxes r1 : ∅ → A ϕ1 = 0.1 + 3A r2 : A → B ϕ2 = 0.2C r3 : A → C ϕ3 = 0.1B r4 : B → ∅ ϕ4 = 0.6B + P r5 : C → ∅ ϕ5 = 0.4C + P A[0], B[0], C[0] = 1mol. P[0] = 0.2, P[i + 1] = P[i] + 0.2.

MP graph

A methodology based

• n MP theory for gene

expression analysis

• L. Marchetti, V. Manca

Outline Introduction

Metabolic P systems

MP analysis of gene expressions

Main components of MP systems

• FLUXES -

Functions which give the evolution of the system...

MP grammar

MP reactions MP fluxes r1 : ∅ → A ϕ1 = 0.1 + 3A r2 : A → B ϕ2 = 0.2C r3 : A → C ϕ3 = 0.1B r4 : B → ∅ ϕ4 = 0.6B + P r5 : C → ∅ ϕ5 = 0.4C + P A[0], B[0], C[0] = 1mol. P[0] = 0.2, P[i + 1] = P[i] + 0.2.

MP graph

A methodology based

• n MP theory for gene

expression analysis

• L. Marchetti, V. Manca

Outline Introduction

Metabolic P systems

MP analysis of gene expressions

Main components of MP systems

Equational Metabolic Algorithm

MP grammar

MP reactions MP fluxes r1 : ∅ → A ϕ1 = 0.1 + 3A r2 : A → B ϕ2 = 0.2C r3 : A → C ϕ3 = 0.1B r4 : B → ∅ ϕ4 = 0.6B + P r5 : C → ∅ ϕ5 = 0.4C + P A[0], B[0], C[0] = 1mol. P[0] = 0.2, P[i + 1] = P[i] + 0.2.

EMA

For each step i of computation: 1) we compute reaction units: u1,2,...,5[i] = ϕ1,2,...,5[i] 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.

A methodology based

• n MP theory for gene

expression analysis

• L. Marchetti, V. Manca

Outline Introduction

Metabolic P systems

MP analysis of gene expressions

Main components of MP systems

Equational Metabolic Algorithm

MP grammar

MP reactions MP fluxes r1 : ∅ → A ϕ1 = 0.1 + 3A r2 : A → B ϕ2 = 0.2C r3 : A → C ϕ3 = 0.1B r4 : B → ∅ ϕ4 = 0.6B + P r5 : C → ∅ ϕ5 = 0.4C + P A[0], B[0], C[0] = 1mol. P[0] = 0.2, P[i + 1] = P[i] + 0.2.

EMA

For each step i of computation: 1) we compute reaction units: u1,2,...,5[i] = ϕ1,2,...,5[i] 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.

A methodology based

• n MP theory for gene

expression analysis

• L. Marchetti, V. Manca

Outline Introduction

Metabolic P systems

MP analysis of gene expressions

Main components of MP systems

Equational Metabolic Algorithm

MP grammar

MP reactions MP fluxes r1 : ∅ → A ϕ1 = 0.1 + 3A r2 : A → B ϕ2 = 0.2C r3 : A → C ϕ3 = 0.1B r4 : B → ∅ ϕ4 = 0.6B + P r5 : C → ∅ ϕ5 = 0.4C + P A[0], B[0], C[0] = 1mol. P[0] = 0.2, P[i + 1] = P[i] + 0.2.

EMA

For each step i of computation: 1) we compute reaction units: u1,2,...,5[i] = ϕ1,2,...,5[i] 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]

A methodology based

• n MP theory for gene

expression analysis

• L. Marchetti, V. Manca

Outline Introduction

Metabolic P systems

MP analysis of gene expressions

Main components of MP systems

Equational Metabolic Algorithm

MP simulation EMA

For each step i of computation: 1) we compute reaction units: u1,2,...,5[i] = ϕ1,2,...,5[i] 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]

A methodology based

• n MP theory for gene

expression analysis

• L. Marchetti, V. Manca

Outline Introduction

Metabolic P systems

MP analysis of gene expressions

Some beautiful oscillation patterns which can be achieved with simple MP grammars...

[Vincenzo Manca, Luca Marchetti (2010) Metabolic approximation of real periodical functions. The Journal of Logic and Algebraic Programming 79 (2010), pag.363-373]

A methodology based

• n MP theory for gene

expression analysis

• L. Marchetti, V. Manca

Outline Introduction

Metabolic P systems

MP analysis of gene expressions

The inverse dynamical problem

EMA

The MP grammar

MP reactions MP fluxes r1 : ∅ → A ϕ1 = 0.1 + 3A r2 : A → B ϕ2 = 0.2C r3 : A → C ϕ3 = 0.1B r4 : B → ∅ ϕ4 = 0.6B + P r5 : C → ∅ ϕ5 = 0.4C + P A[0], B[0], C[0] = 1mol. P[0] = 0.2, P[i + 1] = P[i] + 0.2.

The dynamics

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]

A methodology based

• n MP theory for gene

expression analysis

• L. Marchetti, V. Manca

Outline Introduction

Metabolic P systems

MP analysis of gene expressions

The inverse dynamical problem

The dynamical problem

What it is given:

1

an MP grammar: stoichiometry; flux maps;

2

an initial state. What we want: THE DYNAMICS CALCULATION

EMA Equational Metabolic Algorithm

The inverse dynamical problem

What it is given:

1

time-series of observations (i.e. a sampled dynamics);

2

an idea of stoichiometry. What we want: THE MP SYSTEM WHICH REPRODUCES THE OBSERVED DYNAMICS

LGSS Log-Gain Stoichiometric Step-wise regression

A methodology based

• n 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 idea behind our work. . .

MP systems were introduced to model metabolic processes, but, thanks to the usage of LGSS, they can be used in each context where we need to infer models of a system from a given set of time series. 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 methodology based

• n 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

A DNA microarray experiment

GOAL: to obtain gene-expression profile data for a target cell

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 methodology based

• n 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

A DNA microarray experiment

GOAL: to obtain gene-expression profile data for a target cell

The role of functional genomics

To understand how the genes work together to comprise functioning cells and organisms.

A methodology based

• n 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

A gene network as a projection of a global biochemical network on the gene space

Corresponding gene network

A methodology based

• n 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

A gene network as a projection of a global biochemical network on the gene space

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.

Corresponding gene network

A methodology based

• n 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 grammars vs Gene networks

We found a standard way for translating an MP grammar involving gene expressions into a corresponding gene network. MP grammar MP graph Gene network Simple promotion r : ∅ → G2 ϕ : k1 · G1 Simple inhibition r : G2 → ∅ ϕ : k1 · G1 Simple prom./inhib. r : G2 → G3 ϕ : k1 · G1

A methodology based

• n 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 grammars vs Gene networks

We found a standard way for translating an MP grammar involving gene expressions into a corresponding gene network. MP grammar MP graph Gene network Combined promotion r : ∅ → G3 ϕ : k1 · G1 + k2 · G2 Combined inhibition r : G3 → ∅ ϕ : k1 · G1 + k2 · G2

• Comb. prom./inhib.

r : G3 → G4 ϕ : k1 · G1 + k2 · G2

A methodology based

• n 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 grammars vs Gene networks

MP grammar r1 : G1 → ∅ ϕ1 = k1 · G1 r2 : ∅ → G2 ϕ2 = k2 · G3 + k3 · G4 r3 : G2 → ∅ ϕ3 = k4 · G2 r4 : G2 → G3 ϕ4 = k5 · G1 r5 : G3 → ∅ ϕ5 = k6 · G3 r6 : ∅ → G4 ϕ6 = k7 · G2 r7 : G4 → ∅ ϕ7 = k8 · G4

A methodology based

• n 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

From microarray raw data to MP models (I)

Genomics and gene expression experiments are sometimes derived as “fishing expeditions” 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. 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.

A methodology based

• n 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

From microarray raw data to MP models (II)

Genomics and gene expression experiments are sometimes derived as “fishing expeditions” 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. 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!

A methodology based

• n 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

From microarray raw data to MP models (III)

The number of the raw time series which need to be processed for a generic experiment on human cells is usually

• f the order of tens of thousands.

BUT 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

A methodology based

• n 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 (I)

A methodology based

• n 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)

Number Description 24256 Number of time series in RAW data (each time series has 16 points) 18631 Number of different genes analysed 12381 Number of time series with reliable measures 3189 Number of genes which exhibit a time-dependent expression level change 1175 Number of genes after the filtering procedure 40 Number of sub-clusters which group genes with similar log2 expression profile 8 Number of clusters which give the different behaviours occurring in HER-2 gene regulation 1 Final MP grammar which gives the rules and the regulation of the phenomenon

A methodology based

• n 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!

Thank you!