a couple of approaches to modelling and analysis of biochemical networks
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A couple of approaches to modelling and analysis of biochemical networks. ”Biomodelling” seminar, October 2006. more an inspiration for a discussion than a talk. Matú š Kalaš. Contents. 1.The variety of modelling paradigms. 2.An example of systematic approach (M. Heiner & D. Gilbert). - PowerPoint PPT PresentationTRANSCRIPT
A couple of approaches to modelling and analysis of biochemical networks
”Biomodelling” seminar, October 2006
Matúš Kalaš
more an inspiration for a discussion than a talk ...
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Contents
1. The variety of modelling paradigms
2. An example of systematic approach(M. Heiner & D. Gilbert)
3. Another example(GOALIE; B. Mishra, M. Antoniotti et al.)
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Models of biochemical networks
How do various modelling paradigms differ?
entities concentrations
individuals
qualitative
continuous
discrete
AMOUNTS OF SPECIES
PRESENCE/ABSENCE, HIGH/LOW/MEDIUM, ACTIVE/INACTIVE,
HIGH-LEVEL STATES
WITH ID, WITH INTERNAL STATE
. . .
WITH SHAPE
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space
divided into homogeneous compartments
continuous
homogeneous WELL-STIRRED
discrete space points
containing non-reacting entities
Models of biochemical networks (cnt.)
”unspaced” HIGH-LEVEL STATES
AFFECTING MOVEMENT OF THE ENTITIES
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time timed
hybrid
untimed
discrete
continuous
QUANTITATIVE TIME
EVENTS, QUALITATIVE TIME
TIMED EVOLUTION + EVENTS
Models of biochemical networks (cnt.)
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progression non-deterministic
stochastic
deterministic
synchronous
asynchronous
APPROXIMATION, MORE REACTIONS IN 1 STEP
IDEAL CASE, AVERAGE CASE
MORE CASES, ”ALL” CASES, ALL CASES
INDIVIDUAL REACTIONS, CONCURRENT & COMPETITIVE
Models of biochemical networks (cnt.)
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Models of biochemical networks (cnt.)
Example models ?
entities concentrations
individuals
qualitative
continuous
discrete
space
divided into homogeneous compartments
continuous
homogeneous
discrete space points
containing non-reacting entities
time timed
hybrid
untimed
discrete
continuous
progression non-deterministic
stochastic
deterministic
synchronous
asynchronous
unspaced
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Prevalent paradigms / buzz words :
ODEs continuous concentrations
homogeneous space or compartments
continuous time
deterministic
Petri Nets qualitative, discrete or continuous concentrations
homogeneous space (or compartments)
untimed, discrete or continuous time
non-determistic, deterministic, stochastic synch. or asych.
Hybrid Automata continuous concentrations
homogeneous space or compartments
hybrid
non-determistic, deterministic, . . .
Gillespie’s Algorithm and alternatives
discrete or continuous concentrations
homogeneous space or compartments
continuous time
stochastic asynchronous or synchronous
Process Algebras and Logics
qualitative, . . .
homogeneous, compartments, . . .
untimed, timed, . . .
non-deterministic or stochastic
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Now an instant introduction to Petri Nets . . .
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An example of systematic modelling:
Step-wise modelling
David Gilbert, Monika Heiner:
From Petri Nets to Differential Equations – An Integrative Approach for Biochemical Network Analysis
ICATPN 2006, TR 2005
. . . a tutorial example of
• different useful features of different modelling paradigms
• step-wise modelling
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Step-wise modelling
REACTIONS IDENTIFICATION
QUALITATIVE MODEL
QUALITATIVE ANALYSIS
CONTINUOUS MODEL
QUANTITATIVE ANALYSIS
STRUCTURAL PROPERTIES
DYNAMIC PROPERTIES (PREDICTION/SIMULATION,
STEADY STATES...)
”debugging”
qualitative model (i.e. model structure) validated
adjusting constants
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REACTIONS IDENTIFICATION
a simple signalling system: ERK/RKIP pathway
Raf-1* + RKIP Raf-1*_RKIP
Raf-1*_RKIP + ERK-PP Raf-1*_RKIP_ERK-PP
Raf-1*_RKIP_ERK-PP Raf-1* + ERK + RKIP-P
MEK-PP + ERK MEK-PP_ERK
MEK-PP_ERK MEK-PP + ERK-PP
RKIP-P + RP RKIP-P_RP
RKIP-P_RP RP + RKIP
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QUALITATIVE MODEL
a standard place/transition Petri Net (discrete, untimed, non-deterministic)
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Static analysis of marking-independent properties
QUALITATIVE ANALYSIS – automated tool-supported checking of properties
- in the example there are 5 minimal P-invariants
(Raf-1* , Raf-1*_RKIP , Raf-1*_RKIP_ERK-PP)
(MEK-PP , MEK-PP_ERK)
(RP , RKIP-P_RP)
(ERK , ERK-PP , MEK-PP_ERK , Raf-1*_RKIP_ERK-PP)
(RKIP , Raf-1*_RKIP , Raf-1*_RKIP_ERK-PP , RKIP-P_RP , RKIP-P)
- these cover the whole net (thus, net is bounded)
- Biological meaning: P-invariants correspond to several states of a given species
• P-invariants (sets of places, over which the weighted sum of tokens is constant during operation)
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- example net is covered by T-invariants
- only 1 non-trivial minimal T-invariant: (k1; k3; k5; (k6; k8), (k9; k11))
QUALITATIVE ANALYSIS (cnt.)
Static analysis of marking-independent properties (cnt.)
• T-invariants
- can be also read as the relative firing rates of transitions (reactions/phases in sysbio)
(this corresponds to the steady-state behaviour)
- minimal T-invariants characterise minimal self-contained subnetworks
with an enclosed biological meaning
- useful to comprehend the network if it is very complex {not in this tutorial example}
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QUALITATIVE ANALYSIS (cnt.)
Static analysis of marking-independent properties (cnt.)
• reasonable initial marking constructed with a help of identified invariants
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QUALITATIVE ANALYSIS (cnt.)
Static analysis of marking-dependent properties
• example net is boolean / 1-bounded / safe
• the net is live
Dynamic analysis of marking-dependent properties
• example net is reversible
• MODEL CHECKING of any interesting properties formulated in CTL (Computational Tree Logic)
- e.g.: ”the phosphorylation of ERK does not depend on a phosphorylated state of RKIP”
EG [ERK E (~(RKIP-P \/ RKIP-P_RP) U ERK-PP) ]
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QUALITATIVE ANALYSIS (cnt.)
VALIDATION OF THE QUALITATIVE MODEL (i.e. structure of the system)
all expected structural and general behavioural properties hold
covered by P-invariants
no minimal P-invariant without biological interpretation
covered by T-invariants
no minimal T-invariant without biological interpretation
no known biological behaviour without corresponding T-invariant
all expected logic-formulated properties hold
a break?
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- within this step, all we need is to find suitable rate constants(e.g. to fit in-vivo or in-vitro quantitative experiments)
CONTINUOUS QUANTITATIVE MODEL
Continuous Petri Net- tokens: real numbers- transitions associated with a rate- semantics: a set of ODEs (e.g. reaction-rate equation)- thus a continuous, timed (continuously) and deterministic model
- basically a set of ODEs enhanced with a graphical representation
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QUANTITATIVE ANALYSIS
• Prediction (easy)
- both qualitative and quantitative
• Steady-state properties, oscillations, sensibility, ... (hard)
(... you know better ...)
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Discussion before the next example?
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Marco Antoniotti, Naren Ramakrishnan, Bud Mishra:
GOALIE, A Common Lisp Application to Discover Kripke Models: Redescribing Biological Processes from Time-Course Data
ILC 2005
Another example: Automated modelling
Samantha Kleinberg, Marco Antoniotti, Satish Tadepalli,
Naren Ramakrishnan, Bud Mishra:
Remembrance of Experiments Past: A redescription based tool for discovery in complex systems
ICCS 2006
. . . building a model in order to understand very complex processes ...
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GOALIE approach / software system
GENOMIC MICROARRAY TIME-COURSE DATASET
SYSTEM MODEL EXPRESSED IN GENE ONTOLOGY TERMS
SYSTEM MODEL ANALYSIS BY FORMAL REASONING
GOALIE = Gene Ontology Algorithmic Logic for Invariant Extraction
MODEL OF THE SYSTEM /PROCESS
DYNAMIC QUALITATIVE PROPERTIES
=
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- qualitative, high-level, untimed and non-deterministic model with clear biological meaning
GOALIE approach / software system (cnt.)
Model: Kripke Structure
- called also ”Hidden Kripke Model” in GOALIE
- annotated by Gene Ontology terms (propositional logic)
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Controlled vocabulary: Gene Ontology
GOALIE approach / software system (cnt.)
8517 possible GO process ontology terms
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Example: yeast cell cycle
GOALIE approach / software system (cnt.)
(a small part of the whole model)
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Techniques used to automatically build a model:
- time-windowed clustering (k-means)- data-to-GO association done by GoMiner software- Fisher exact test (p-values)- empirical Bayes approach (Benjamini-Hochberg test)- information bottleneck principle (generalised Shannon-Kolmogorov’s rate-distortion theory)- connecting annotated clusters (Jaccard’s coefficient)
GOALIE approach / software system (cnt.)
Analysis:
- propositional temporal-logic reasoning (model checking of temporal invariants (CTL))
- graph rewriting rules for projection and collapsing, preserving ”bisimulation-like” relations getting higher-level clusters
- process / dataset alignment (similarity of cellular processes)
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A couple of diverse systematic approaches:
• C. Wiggins, I. Nemenman: Process Pathway Inference via Time Series Analysis, 2006
• M. Calder, S. Gilmore, J. Hillston: Automatically deriving ODEs from process algebra models of signalling pathways, CMSB 2005
• N. Chabrier-Rivier, M. Chiaverini, V. Danos, F. Fages, V. Schächter: Modeling and Querying Biomolecular Interaction Networks, TCS 2004
• A. Arkin, P. Shen, J. Ross: A Test Case of Correlation Metric Construction of a Reaction Pathway from Measurements, Science 1997
• M. Chen, R. Hofestädt: A medical bioinformatics approach for metabolic disorders: Biomedical data prediction, modeling, and systematic analysis, JBMI 2006
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”Clearly, if the truth must be found, it will need formal methods that no amount of simulation can deliver.”
DISCUSSION?
THANK YOU!
Carla Piazza & Bud Mishrain ’Stability of Hybrid Systems and Related
Questions from Systems Biology’, 2005