!!

Hayssam Soueidan

U.Bordeaux, France!!LaBRI & INRIA project “MAGNOME”

!! Why do we care about modeling?

!! ! Understanding how systems give rise to emerging

behaviour!! Types of models:!! Stoichiometric flux models!! Metabolic kinetic models!! Analysis:!! Metabolic analysis global qualitative!! Kinetic anaylsis local quantitative!! ! Klipp et al., 2007:!! Modeling: PowerPoint and Excel!! Analysis: MatLab!! Why hierarchical modular modeling ?

!! How we do it in BioRica modeling andsimulation tool!! Yeast rejuvenation study

!! ESF Grand Challenges, NSF Funding Objectives

Hierarchical modeling!! Integrating genome-scale and fine-grained
phenomena!!

!! 1. Multiple time-scales!! Transforming metabolites: fast!! Synthesizing an enzyme: slow!! ODE stiff systems (Brenan et al., 1996) fast-scaled reactions

are stable, but slow reactions determine the system's
trajectory

2. Deterministic vs stochastic!! Excess of metabolites!! Lack of metabolites

!! Webster's dictionary: “a system is a complex unity

formed of many often diverse parts subject to acommon plan, serving a common purpose”!! an electronic circuit!! nuclear power plant!! an S. cerevisiae cell!! Systems are comprised of specific components(sub-systems) that interact!! some components’ activities occur concurrently(independently)!! some components’ activities are linked in some way!! system’s behaviour mainly defined by interactions ofcomponents!! ! two main specificities: hierarchy and composition

!! “System” approaches in industrial

engineering (since late 1980’s)!! AltaRica modeling language(1999)!! Modeling platform!! textual and graphical modelinginterface!! simulation and verification tools!! trace analysis!! Models are compositional andhierarchical!! behavioral hierarchy!! architectural hierarchy!! ! Well-suited to modelingchallenges

specification

modelanalysis

!! Languageandsemantics!! Simulation!! Tracedatabase!! Analysis!! Casestudy

!! Based on AltaRica!! Industrial-strength!! Designed forengineers!! Simple declarative andhierarchical language!! Formal semantics!! Description of bothmodels and propertiesof models!! (e.g. Teddy onthology)

!! Compositional(Connections,synchronization)!! Generality: Highexpressivity, captures
most existing models!! Mathematically sound andoperational!! Why do we care ?

Coherent composition
with almost any!! calculation (ex: MatLab)

1.!Language andsemantics!
2.!Simulation!
3.!Trace
database!
4.!Analysis!
5.!Case study!

!! Automatic translation of!!
!!
!!
!!

models into C++ code
Simulator architecture
open for customizationand extension
EfficientParameterized
Subject to profiling anddebugging tools (GDB,Shark etc.)

Simulation in BioRica1.!Language andsemantics!
2.!Simulation!
3.!Trace
database!
4.!Analysis!
5.!Case study!

!! Saves simulation resultsfor varying parameters!! Comparative studies!! Simulation time control(replay, pause, reverse,fast forward)!! Randomized decisions
can be replayed for
different outcomes1.!Language andsemantics!
2.!Simulation!
3.!Trace
database!
4.!Analysis!
5.!Case study!

!! Extraction of high level

qualitative properties!! Statistical synthesis!! Features extraction byuser defined scripts
connecting to thedatabase!! Python!! Mathematica!! Tulip!! MySQL

1.!Language andsemantics!
2.!Simulation!
3.!Trace
database!
4.!Analysis!
5.!Case study!

!! Joint work with M. Cvijovic and E.

Klipp (MPI)!! Extension of a single-cell model
to a structured population!! Hierarchical simulation withdynamic creation!! Automatized large scale
exploration of parameter sets(>100 000 simulations)“virgin” cell

Generation(cell cycle)

Ageing1stdaughter1

nthdaughterndead cell(lysis)

Lifespan = n (20-40)

!! In every daughter cell, the lifespan “clock” is reset tozero!! Each division produces a cell that can divide many
more times!! “Old” cells are very rare in a large exponentiallygrowing population (1/2a+1)

Occasionally, daughters of old mothers are born prematurely
aged!
!!
Their lifespan equals the mother’s remaining lifespan•!

•!The asymmetry has broken down - accompanied by loss of size
asymmetry (“symmetric buds”)•!The daughters of symmetric buds have normal lifespan" Symmetric buds have inherited a “senescence factor”…

Equations:dP
k1=! k 2 P int ! k 4 Pdam
dt ks + P int + PdamdP intk1=! k 2 P int ! k 3 P int
dt
ks + P int + Pdam
dPdam
= k 3 P int ! k 4 Pdam
dtTrigger:
P int > Pdiv
Events:for daughters:Pdam) + Pdam # daughter # ( 1 ! re )
P int
Pdam
P int " P int # daughter # ( 1 + re #)P int
Pdam " Pdam # daughter # ( 1 ! re )P " P int # daughter # ( 1 + re #Legend :P - total protein
Pint - intact proteins
Pdam - damaged proteins
Pdiv - treshold for division
k1 - limits the system in terms not to have continues expansion in volume
k2 - represents degradation rate of intact proteinsk3 - represents damage rate
k4 - represents degradation rate of damaged proteinsre - retention coefficientdaughters - daughter size (25 or 50)
mothers - mother size (50 or 75)

for mothers:
Pdam 1 ! mother#) + Pdam # ( mother + ( 1 ! mother ) # re )P intmotherPdam 1 ! motherP int " P int # mother # ( 1 ! re ##)P intmotherPdam " Pdam # ( mother + ( 1 ! mother ) # re )P " P int # mother # ( 1 ! re #Pedigree analysis

Discrete events: division (Pint > 1500) and clonal senescence (!Pint < 0)alive: immortality, senescence
update: state vars of the mother, statistics; create daughter, add to D and P

!! Mathematica andBioRica!! Maximization ofrejuvenation forthe whole
population!! Three layer
approachSingle Cell!
Population!
Model Properties!

Calibrate and validate the hierarchical model: 625 simulations•! Complete simuations to depth 4•! Symmetric and asymmetric, k1, k2 and k4 fixed, k3 step 0.1" [0.1,2.3]

Simulation to depth 30•! Select simulations: #daughters 20-24•! For each cell: in a cell cycle Pdam initial fand final, generation time,
date of birth (arb. time units), fitness (#div in 1st time unit)! 230 cells in parallel, 232 diff. equations

Parameter exploration•! Identify sets of parameters that exibit emerging
behaviour•! Ex: #daughters, high rejuvenation value

Pedigree analysis

Pedigree analysis

d1

motherd2

d3

Rejuvenation- Symmetry with retention -M: 6.780

D1
Fitness: 6.69

D1:1
Fitness: 6.67

Eglimez et al, 1989

D19
Fitness: 5.609

D20

D1:17
Fitness: 5.98

D19:1
Fitness: 6.51

D19:17
Fitness: 5.60

Rejuvenation- Asymmetry without retention -M: 6.947

D25

D1
Fitness: 6.677

D1:1
Fitness: 6.582
Nyström et al, work in progess

D24
Fitness: 4.882

D1:23
Fitness: 4.978
D24:1
Fitness: 6.047

D24:18Fitness: 5.017

Rejuvenation- Symmetry without retention -M: 4.563

D1
Fitness: 4.267

D1:1
Fitness: 3.962

D11
Fitness: 2.827

D20

D1:18
Fitness: 0
D11:1
Fitness: 2.765

D11:7
Fitness: 0

Exploring lineage viabilityrek3

fitness

PeopleOriginal model MPI, Berlin
Marija Cvijovic, Edda Klipp, Thomas Nyström
Experimental work CMB, Goteborg
Marija Cvijovic, Thomas Nyström
Hierarchical model Bordeaux
Macha Nikolski, David Sherman, Grégoire Sutre

Summary•!Younger siblings born "prematurely old" (Kennedy et. al, 1994)•!Daugterns born early have low damage, and their daughters havenormal fitness•!Both asymmetry and retention increase fitness in second generation•!Control: symmetry, no retention•!Exponential increase in generation time for symmetry and retention(Egilmez et al., 1989)•!Linear increase in generation time for asymmetry and no retention(T. Nystrom, work in progress on #Sir2 mutant)•!Fitness and viability sensitive to k3