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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



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


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


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


The types of molecules taking part to reactions...



A[0], B[0], C[0] = 1mol. P[0] = 0.2, P[i + 1] = P[i] + 0.2.


MP graph - REACTIONS -



Evolution rules for matter transformation...



A[0], B[0], C[0] = 1mol. P[0] = 0.2, P[i + 1] = P[i] + 0.2.


MP graph - FLUXES -



Functions which give the evolution of the system...



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]




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.



Introduction


Metabolic P systems

u1,2,...,5 [i] = ϕ1,2,...,5 [i]




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.



Introduction


Metabolic P systems

u1,2,...,5 [i] = ϕ1,2,...,5 [i]




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]



Introduction


Metabolic P systems

u1,2,...,5 [i] = ϕ1,2,...,5 [i]


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


[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


The dynamics

The MP grammar MP reactions r1 : ∅ → A r2 : A → B r3 : A → C r4 : B → ∅ r5 : C → ∅


A[0], B[0], C[0] = 1mol. P[0] = 0.2, P[i + 1] = P[i] + 0.2.

LGSS


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


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

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.


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.


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


18631 12381 3189


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!