understanding and predicting biological complex system

Supported by

Prominent international speakers from

h"p://workshop.eisbm.eu1

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Eric Boix

Understanding and predicting biological complex system

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Modeling & Simulation

• An in-silico model is a mathematical or computational representation of a real system.

• A simulation is a virtual experiment conducted on the model.

• The CoSMo Company develops and distributes the next generation software solution dedicated to the modeling and simulation of complex systems.

• The models developed are specific to the real systems at stake and allow to run virtual experiments to facilitate and accelerate the innovation cycle, the development of new products and the implementation of new strategies.

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The CoSMo solution features: • A specific language for modeling

complex systems • Heterogeneous model coupling

and description of interactions between various levels (molecules, cells, tissues, organs, organisms) across different time scales

• Flexibility of the model architecture allows new knowledge integration with a rapid turn around

The CoSMo solution: multiscale modeling and simulation

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Biology Pharma

Key field of applications

Urban Planning

Field of Research

Smart grids, Energy supply Industrial complex systems Finance

Dedicated modeling platform Model pilot and industrialisation - Services Key partners:

Dedicated modeling platform in systems biology Co-development of models Key partners:

Large Pharmaceuticals companies in drug

discovery and Vaccin

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Complexity definition

A scientific theory which asserts that some systems display behavioral phenomena that are completely inexplicable by any conventional analysis of the systems’ constituent parts. These phenomena, commonly referred to as emergent behavior, seem to occur in many complex systems involving living organisms, such as cities or the human brain.

John L. Casti, Encyclopedia Britannica

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Complex systems

Encountered definitions : a complex system is a system composed of interacting entities applying rules and whose evolution …

displays emerging properties cannot be predicted (without simulation) is very sensitive to initial conditions is robust to many small perturbations …

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Biological question

Can we explain the flowering morphogenesis out of the known involved genes ?

What are the gene regulated mechanisms driving the differentiation of the carpel, stamen, petal and

sepal organs ?

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Modeling question

What are the dynamics of the Genetic Regulatory Network (GRN) ?

Model building :

Select relevant genes Construct the topology of the GRN network and the relative strengths of interactions among these genes (publications) Express dynamics constraints: expression patterns of differentiated tissues

Work by Mendoza-Alvarez 1998

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Modeling mapping

Select a mathematical formalism capturing all biological knowledge and enabling the expression of dynamics

Work by Mendoza et al. xi = { 0, 1 } (boolean network)

Find a possible dynamic requires numerical simulation

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CSMML : the modeling language Basic building blocks

Entity defined by :

A state : set of attributes characterizing the entity

A set of rules : methods changing the state when provided with the entity neighborhood

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CSMML : the modeling language Choosing a state

Biologist description of genes: “expressed” “mildly  expressed” “not  expressed”

• Gene A vs. gene B expressions

Question : gene entity state ? Modeling answer : 2 states genes, 3 states genes

… Modeling tool consequence : quick and agile modeling cycle is a must

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CSMML : the modeling language Interacting entities

Examples •Gene interactome •Proteome •Metabolome

Need to mediate interactions (notion of neighborhood)

• Define a graph where - Vertices represent entities - Arcs and Edges represent interactions

• ArcEntity, EdgeEntity are first class entities : interactions may attributes and rules

• Network = Entities + Graph

Neighbour 1

Neighbour 3

Neighbour 4

Neighbour 2

ENTITY

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CSMML : the modeling language Interacting entities

• Act activates gene R • Inh inhibits gene R • Act and Inh are both active: what is the status of R ?

• A possible modeling solution: weighted arcs • Interpreted data decides of relative weights

Modeling language : Arcs/Edges can be decorated with any required attributes

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CSMML : the modeling language The making of a model 1/3

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CSMML : the modeling language The making of a model 2/3

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CSMML : the modeling language The making of a model 3/3

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CSMML : the modeling language Under the hood of a model

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CSMML : the modeling language Dynamics and ordering

Modeling dynamics : rules and schedulers

Temporality defined by schedulers • Sequential orders

Rule1, Rule2, Rule3, Rule4 • Parallel orders

Rule1 || Rule2 • Mixed sequential, parallel orders

Rule1, (Rule2 || Rule3), Rule4

Example: mixed gene activation in flower gene regulatory network • (LFY || AG), LUG, (AP || UFO)… Flower regulatory network

Mendoza et al, 1998

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Studying dynamics

Configuration • Consider order on genes • Vector of states xi Trajectory • Pick  up  “some”  configuration • Iterate : apply the rules • Until reaching attractor Attractors • Fix point (static equilibrium) • Limiting cycle (oscillation)

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Simple trajectories demo

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Studying dynamics

Structure of dynamic space

Fixed point attractor Limit cycle attractor

Basin of attraction Trajectory

Configuration space and basins of attraction

Basins of attraction

Attractors

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000100000000

SEPALS

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CoSMo platform

Protocols : sets of related simulations (with a objective) Protocol usages :

study the structure of dynamic space • Search the attractors • Compute associated basins of attraction size

Model parameter sweep Sensitivity analysis, structural/dynamical robustness Model reconstruction …

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Studying dynamics Basins of attraction

Attractors

0x0xxxxx00xx 0x0xxxxx010x 0x0xxxxx0111 0x1xxxxxx0xx 0x1xxxxxx10x 0x1xxxxxx111

000100000000 SEPALS Simulation protocol result :

• If you take THIS scheduler (EMF1 || TFL1), (LFI || API || CAL), (LUG || UFO || BFU), (AG || AP3 || PI),

SUP • Only attractors : six fix points

Answer to the biological question : proposed GRN can explain flower morphogenesis (when not : back to modeling cycle)

0x0xxxxx0110 0x0xxxxxx110 000100010110

PETALS

0x0xxxxx10xx 0x0xxxxx110x 0x0xxxxx1111

000000001000 CARPELS

0x0xxxxx1110 000000011110 STAMENS

1xxxxxxxx0xx 1xxxxxxxx10x 1xxxxxxxx111

110000000000 NOT OBSERVED

0x0xxxxx1110 110000010110 NOT OBSERVED

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Biological question What are the mechanisms explaining carpel

invagination (plant), blastula gastrulation (animals) ?

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Integrative model with geometry

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CSMML : the modeling language Grouping things

Modeling : Compound Entities Compound entities • Contain sub-entities • Graph on sub-entities • Scheduler on sub-entities

- Cross-scale synchronization • Also an entity

- Set of states, rules.

Example: cell (proposition) • Components:

- Gene regulatory network - Scheduler on the network

• Attribute: - Geometry

GEOMETRY GRAPH of GENES

CELL

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CSMML : the modeling language Compounding induces hierarchies

Morphogenesis 2 levels

Mendoza 1 level

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Demos 1. Active flows (edges) 2. Fully integrated model 3. Ascidians (on going)

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Multi-scale model

Difference between : • Intra-nuclear : Tbet / Gata3 • Cell-cell : IL4<->IL4R

Modeling beyond simple delay : ambient diffusion

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Diffusion space

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Probes : observing the system

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Intestinal cancer integrative model

Gene expression

Mechanical adhesion

GRN

Cell Cycle

Cell Signaling

Geometry • Cell growth • Migration • Division • Apoptosis

Model: van Leeuwen, Byrne, Jensen, 2009, University of Notthingham UK

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Intestinal Microbiota

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“  Biological”  question

Epidemiology : how does host treatment, host susceptibility and host exposure impact on the spreading of a disease?

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Networks within networks

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Dynamical networks (structures)

Platform : model rules • dynamic entities • dynamic networks • dynamic scheduler

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Demo Epidemiology (two views)

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• City: random graph, average degree of 10 • Computational time: generation and simulation (100 steps) • City graph: fully connected graph • Dynamic case: at each iteration city graphs are regenerated

Epidemiology stress test

1 city 10 cities 50 cities

N=1000 E=10000 static 8.45’’ 86’ 425s’’

N=1000 E=10000 dynamic 11’ 108’ 538’

Epidemiology stress test

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Complex system phenomena with • Explicit networks: structure • Multi-scale: hierarchies • Geometry based symmetry breaking • Many dynamical feedback mechanisms • Multiple time scale

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CoSMo relevance

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The CoSMo solution: multiscale M&S

CoSMo delivers a comprehensive simulation platform to master and predict biological systems The CoSMo solution allows heterogeneous model coupling and description of interactions between various levels (molecules, cells, tissues, organs, organisms) in a changing environment across different time scales CoSMo has developed a specific language for modeling complex systems: csmML

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Close collaboration between modelers and biologists

Feasibility study

Model building

In silico simulation

Needs analysis and assessment of existing data, models and knowledge

Looking backward to describe the system and its behaviour

Looking forward: What if…  ?

A 3-step methodology

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[1] Entity: heterogeneous building blocks [2] Graphs:  representation  of  “neighbors” [3] Scheduler: dynamics sequence/parallel trees [4] Compound: nodes of descriptive hierarchy

Complex Systems Model = [1 + 2 + 3 + 4]

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Complex systems model

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Complex system phenomena with • Explicit networks: structure • Multi-scale: hierarchies • Geometry based symmetry breaking • Many dynamical feedback mechanisms • Multiple time scale

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CoSMo relevance

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Contact us : Eric Boix, CSO eric.boix@cosmo-platform.org Thierry de Lumley, Development Director - Biology tdelumley@thecosmocompany.com