Jean ClairambaultJean Clairambault

INRIA, Bang project-team, Paris & Rocquencourt, FranceINRIA, Bang project-team, Paris & Rocquencourt, FranceLaboratoire Jacques-Louis Lions, UPMC, Paris, FranceLaboratoire Jacques-Louis Lions, UPMC, Paris, FranceINSERM U776, « Biologic rhythms and cancers», Villejuif, FranceINSERM U776, « Biologic rhythms and cancers», Villejuif, France

http://www.rocq.inria.fr/bang/JC/ http://www.rocq.inria.fr/bang/JC/ jean.clairambault@inria.frjean.clairambault@inria.fr

Healthy and cancer tissue growth, therapies and the Healthy and cancer tissue growth, therapies and the use of mathematical [cell population dynamic] models use of mathematical [cell population dynamic] models

Motivation: modelling tissue growth to represent proliferatingMotivation: modelling tissue growth to represent proliferatingcell populations as targets, wanted or unwanted, of anticancercell populations as targets, wanted or unwanted, of anticancerdrugs, to optimise their delivery at the whole body level.drugs, to optimise their delivery at the whole body level.

Main pitfalls of cancer therapeutics in the clinic:Main pitfalls of cancer therapeutics in the clinic:- unwanted toxic side effects on unwanted toxic side effects on healthy cell populationshealthy cell populations- emergence of drug-resistant clones in emergence of drug-resistant clones in cancer cell populationscancer cell populations

Designing a model of tissue growth must be undertaken afterDesigning a model of tissue growth must be undertaken afteranswering the question: answering the question: Modelling, what for? Modelling, what for? Resulting modelsResulting modelsmay be very different according to the answers to this question.may be very different according to the answers to this question.

Recalling a few facts about healthy and cancer tissue growth Recalling a few facts about healthy and cancer tissue growth

Tissues that may evolve toward malignancy Tissues that may evolve toward malignancy

……are the tissues where cells are committed to fast proliferationare the tissues where cells are committed to fast proliferation(fast renewing tissues):(fast renewing tissues):

-epithelial cells+++, i.e., cells belonging to those tissues which -epithelial cells+++, i.e., cells belonging to those tissues which cover the free surfaces of the body (i.e., cover the free surfaces of the body (i.e., epitheliaepithelia):): gut (colorectal cancer), lung, glandular coverings (breast, prostate),skin,…gut (colorectal cancer), lung, glandular coverings (breast, prostate),skin,…

-cells belonging to the different blood lineages, produced in-cells belonging to the different blood lineages, produced in the bone marrow: liquid tumours, or malignant haemopathiesthe bone marrow: liquid tumours, or malignant haemopathies

-others (rare: sarcomas, neuroblastomas, dysembryomas…) -others (rare: sarcomas, neuroblastomas, dysembryomas…)

Natural history of cancers: from genes to bedsideNatural history of cancers: from genes to bedside

• Entry in the cell cycle for quiescent (=non-proliferating) cells• Phase transitions and apoptosis for cycling cells• Ability to use anaerobic glycolysis (metabolic selective advantage for cancer cells)• Contact inhibition by surrounding cells (cell adhesion, cell density pressure)• Ability to stimulate formation of new blood vessels from the neighbourhood• Linking to the extracellular matrix (ECM) fibre network and basal membranes• Recognition (friend or foe) by the immune system

Gene mutations: an evolutionary process which may give rise to abnormal DNA Gene mutations: an evolutionary process which may give rise to abnormal DNA when a cell duplicates its genome, due to defects in tumour suppressor or DNAwhen a cell duplicates its genome, due to defects in tumour suppressor or DNAmismatch repair genes mismatch repair genes (Yashiro et al. Canc Res. 2001; Gatenby & Vincent, Canc. Res. 2003)(Yashiro et al. Canc Res. 2001; Gatenby & Vincent, Canc. Res. 2003)

Resulting genomic instability allows malignant cells to escape proliferation andResulting genomic instability allows malignant cells to escape proliferation and growth control at different levels: subcellular, cell, tissue and whole organism:growth control at different levels: subcellular, cell, tissue and whole organism:

Cancer invasion is the macroscopic result of breaches in these control mechanismsCancer invasion is the macroscopic result of breaches in these control mechanisms

Evading proliferation and growth control mechanismsEvading proliferation and growth control mechanisms

Hanahan & Weinberg, Cell 2000Hanahan & Weinberg, Cell 2000

……but just what is cell proliferation?but just what is cell proliferation?

Hanahan & Weinberg, Cell 2011Hanahan & Weinberg, Cell 2011

Cell population growth in proliferating tissuesCell population growth in proliferating tissues

One cell divides in two: a controlled process at cell and tissue levelsOne cell divides in two: a controlled process at cell and tissue levels... that is disrupted in cancer... that is disrupted in cancer

Populations of cells: Populations of cells: the right observation level to model proliferation, apoptosis, differentiationthe right observation level to model proliferation, apoptosis, differentiation

(after Lodish et al., Molecular cell biology, Nov. 2003)(after Lodish et al., Molecular cell biology, Nov. 2003)

Cyclin DCyclin D+ CDK4, + CDK4, 66

Cyclin ECyclin E+ CDK2+ CDK2

Cyclin ACyclin A+ CDK2+ CDK2

Cyclin BCyclin B+ CDK1+ CDK1

SG1

G2

M

At the origin of proliferation: the cell division cycleAt the origin of proliferation: the cell division cycle

Physiological or therapeutic control on:Physiological or therapeutic control on:- transitions between phases- transitions between phases (G(G11/S, G/S, G22/M, M/G/M, M/G11))

- death rates (apoptosis or necrosis) - death rates (apoptosis or necrosis) inside phasesinside phases- progression speed in phases (Gprogression speed in phases (G11))- exchanges with quiescent phase Gexchanges with quiescent phase G00

S:=DNA synthesis; G1,G2:=Gap1,2; M:=mitosis

(after Lodish et al., Molecular cell biology, Nov. 2003)(after Lodish et al., Molecular cell biology, Nov. 2003)

(after F. Lévi, INSERM U776)(after F. Lévi, INSERM U776)

Exchanges between proliferating (GExchanges between proliferating (G11SGSG22M) and quiescent (GM) and quiescent (G00) cell compartments) cell compartments

are controlled by mitogens and antimitogenic factors in Gare controlled by mitogens and antimitogenic factors in G11 phase phase

From Vermeulen et al. Cell Prolif. 2003From Vermeulen et al. Cell Prolif. 2003

Most cells do not proliferate physiologically, even in fast renewing tissues (e.g., gut) Most cells do not proliferate physiologically, even in fast renewing tissues (e.g., gut)

Proliferating and quiescent cellsProliferating and quiescent cells

RRRestriction pointRestriction point(in late G(in late G11 phase) phase)

before R:before R:mitogen-dependentmitogen-dependentprogression through Gprogression through G11

(possible regression to G(possible regression to G00))

after R:after R:mitogen-independentmitogen-independentprogression through Gprogression through G11 to S to S

(no way back to G(no way back to G00))

Phase transitions, apoptosis and DNA mismatch repairPhase transitions, apoptosis and DNA mismatch repair

Repair or apoptosis

SSGG11

GG22

MM

-Sensor proteins, e.g. p53, detect defects -Sensor proteins, e.g. p53, detect defects in DNA, arrest the cycle at Gin DNA, arrest the cycle at G11/S and /S and

GG22/M phase transitions to repair /M phase transitions to repair

damaged fragments, or lead the whole damaged fragments, or lead the whole cell toward controlled death = apoptosiscell toward controlled death = apoptosis

-p53 expression is known to be down--p53 expression is known to be down-regulated in about 50% of cancersregulated in about 50% of cancers

-Physiological inputs, such as circadian -Physiological inputs, such as circadian gene PER2, control p53 expression; gene PER2, control p53 expression; circadian clock disruptions (circadian clock disruptions (shiftworkshiftwork) ) may result in low p53-induced genomic may result in low p53-induced genomic instability and higher incidence of cancerinstability and higher incidence of cancer

(F. Lévi, INSERM U776)(F. Lévi, INSERM U776)

Repair or apoptosis

p53p53

p53p53

(Fu & Lee, Nature Rev. 2003)(Fu & Lee, Nature Rev. 2003)

Invasion: local, regional and remoteInvasion: local, regional and remote1) Local invasion by tumour cells implies loss of 1) Local invasion by tumour cells implies loss of normal cell-cell and cell-ECM (extracellular matrix) normal cell-cell and cell-ECM (extracellular matrix) contact inhibition of size growth and progression in the contact inhibition of size growth and progression in the cell cycle. ECM (fibronectin) is digested by tumour-cell cycle. ECM (fibronectin) is digested by tumour-secreted matrix degrading enzymes (MDE=PA, MMP) secreted matrix degrading enzymes (MDE=PA, MMP) so that tumour cells can move out of it. Until 10so that tumour cells can move out of it. Until 1066 cells cells (1 mm (1 mm ) is the tumour in the ) is the tumour in the avascular stageavascular stage..

2) To overcome the limitations of the avascular stage, 2) To overcome the limitations of the avascular stage, local tumour growth is enhanced by tumour-secreted local tumour growth is enhanced by tumour-secreted endothelial growth factors which call for new blood endothelial growth factors which call for new blood vessel sprouts to bring nutrients and oxygen to the vessel sprouts to bring nutrients and oxygen to the insatiable tumour cells (insatiable tumour cells (angiogenesisangiogenesis, vasculogenesis), vasculogenesis)

3) Moving cancer cells can achieve3) Moving cancer cells can achieve intravasation, i.e., intravasation, i.e., migrationmigration in blood and lymph vessels (by diapedesis), in blood and lymph vessels (by diapedesis), andand extravasation, i.e. evasion from vessels, through extravasation, i.e. evasion from vessels, through vascular walls, to form new colonies in distant tissues. vascular walls, to form new colonies in distant tissues. These new colonies are metastases.These new colonies are metastases.

Proliferating rimProliferating rim

Quiescent layerQuiescent layer

Necrotic coreNecrotic core

(Images thanks to A. Anderson, M. Chaplain, J. Sherratt, and Cl. Verdier)(Images thanks to A. Anderson, M. Chaplain, J. Sherratt, and Cl. Verdier)

Mathematical modelsMathematical models

(A reference: (A reference: Optimisation of cancer drug treatments using cell population dynamics, Optimisation of cancer drug treatments using cell population dynamics, by F. Billy, JC, O. Fercoqby F. Billy, JC, O. Fercoq, , to appear soon in “to appear soon in “Mathematical Models and Methods in Mathematical Models and Methods in BiomedicineBiomedicine”, ”, A. Friedman, E. Kashdan, U. Ledzewicz, H. Schättler eds. A. Friedman, E. Kashdan, U. Ledzewicz, H. Schättler eds. Springer, Springer, NY)NY)

Mathematical models of healthy and tumour growth Mathematical models of healthy and tumour growth (a great variety of models)(a great variety of models)

• In vivo (tumours) or in vitro (cultured cell colonies) growth? In vivo (diffusion in In vivo (tumours) or in vitro (cultured cell colonies) growth? In vivo (diffusion in living organisms) or in vitro (constant concentrations) growth control by drugs?living organisms) or in vitro (constant concentrations) growth control by drugs?

• Scale of description for the phenomenon of interest: subcellular, cell, tissue or Scale of description for the phenomenon of interest: subcellular, cell, tissue or whole organism level? … may depend upon therapeutic description levelwhole organism level? … may depend upon therapeutic description level

• Is space a relevant variable? [Not necessarily!] Must the cell cycle be represented?Is space a relevant variable? [Not necessarily!] Must the cell cycle be represented?

• Are there surrounding tissue spatial limitations? Limitations by nutrient supply or Are there surrounding tissue spatial limitations? Limitations by nutrient supply or other metabolic factors? other metabolic factors?

• Is loco-regional invasion the main point? Then reaction-diffusion equations (e.g. Is loco-regional invasion the main point? Then reaction-diffusion equations (e.g. KPP-Fisher) are widely used, for instance to describe tumour propagation frontsKPP-Fisher) are widely used, for instance to describe tumour propagation fronts

• Is cell migration to be considered? Then chemotaxis [=chemically induced cell Is cell migration to be considered? Then chemotaxis [=chemically induced cell movement] models (e.g. Keller-Segel) have been usedmovement] models (e.g. Keller-Segel) have been used

Simple models of tumour growth, to begin withSimple models of tumour growth, to begin withMacroscopic, non-mechanistic models: the simplest ones:Macroscopic, non-mechanistic models: the simplest ones:exponential, logistic, Gompertzexponential, logistic, Gompertz

Exponential model: relevant for the early stages of tumour growth onlyExponential model: relevant for the early stages of tumour growth only

[Logistic and] Gompertz model: represent growth limitations (S-shaped curves with [Logistic and] Gompertz model: represent growth limitations (S-shaped curves with plateau=maximal growth, or tumour carrying capacity plateau=maximal growth, or tumour carrying capacity xxmaxmax), due to mechanical ), due to mechanical

pressure or nutrient scarcity pressure or nutrient scarcity

xx= = tumour weighttumour weightor volume, proportionalor volume, proportionalto the number of cells,to the number of cells,or tumour cell densityor tumour cell density

tt

xx

Models of tumour growth: Gompertz revisitedModels of tumour growth: Gompertz revisitedODE models a) with 2 cell compartments, proliferating and quiescent,ODE models a) with 2 cell compartments, proliferating and quiescent,or b) varying the tumour carrying capacity or b) varying the tumour carrying capacity xxmax max in the original Gompertz modelin the original Gompertz model

Avowed aim: to mimic Gompertz growth Avowed aim: to mimic Gompertz growth (a popular model among radiologists) (a popular model among radiologists)

However, a lot of cell colonies and tumours do not follow Gompertz growthHowever, a lot of cell colonies and tumours do not follow Gompertz growth(Recent refinements: Hahnfeldt et al., Canc. Res 1999; Ergun et al., Bull Math Biol 2003)(Recent refinements: Hahnfeldt et al., Canc. Res 1999; Ergun et al., Bull Math Biol 2003)

(Gyllenberg & Webb, Growth, Dev. & Aging 1989; Kozusko & Bajzer, Math BioSci 2003)(Gyllenberg & Webb, Growth, Dev. & Aging 1989; Kozusko & Bajzer, Math BioSci 2003)

Tumour burden

time

Gompertz model

Data

d9d9d8d8

d12d12

d14d14

Example: tumour growthExample: tumour growth(GOS) in a population of(GOS) in a population ofmice, laboratory datamice, laboratory data

ODE models with two exchanging cell compartments, ODE models with two exchanging cell compartments, proliferating (P) and quiescent (Q)proliferating (P) and quiescent (Q)

(Gyllenberg & Webb, Growth, Dev. & Aging 1989; Kozusko & Bajzer, Math BioSci 2003)(Gyllenberg & Webb, Growth, Dev. & Aging 1989; Kozusko & Bajzer, Math BioSci 2003)

where, for instance:where, for instance:rr0 0 representing here the rate ofrepresenting here the rate of

inactivation of proliferating cells,inactivation of proliferating cells,and and rrii the rate of recruitment fromthe rate of recruitment from

quiescence to proliferationquiescence to proliferation

Initial goal: to mimic Gompertz growthInitial goal: to mimic Gompertz growth

Cell exchanges

Models of tumour growth: stochasticModels of tumour growth: stochasticPhysical laws describing macroscopic spatial dynamics of an Physical laws describing macroscopic spatial dynamics of an avascularavascular tumour tumour

-Fractal-based phenomenological description of growth of cell colonies and tumours,-Fractal-based phenomenological description of growth of cell colonies and tumours, relying on observations and measures: roughness parameters for the 2D or 3D tumour relying on observations and measures: roughness parameters for the 2D or 3D tumour Findings: - all proliferation occurs at the outer rimFindings: - all proliferation occurs at the outer rim

- cell diffusion - cell diffusion alongalong (not from) the tumour border or surface (not from) the tumour border or surface - - linear growth of the tumour radiuslinear growth of the tumour radius after a critical time (before: exponential) after a critical time (before: exponential)

(A. Bru et al. Phys Rev Lett 1998, Biophys J 2003)(A. Bru et al. Phys Rev Lett 1998, Biophys J 2003)

-Individual-based models (IBMs):-Individual-based models (IBMs): - cell division and motion described by- cell division and motion described by a stochastic algorithm, then continuous limita stochastic algorithm, then continuous limit - permanent regime = KPP-Fisher-like- permanent regime = KPP-Fisher-like (also linear growth of the tumour radius) (also linear growth of the tumour radius) (D. Drasdo, Math Comp Modelling 2003; Phys Biol 2005(D. Drasdo, Math Comp Modelling 2003; Phys Biol 2005

H. Byrne & D. Drasdo, J. Math. Biol. 2009)H. Byrne & D. Drasdo, J. Math. Biol. 2009)

Models of tumour growth: invasionModels of tumour growth: invasionMacroscopic reaction-diffusion evolution equationsMacroscopic reaction-diffusion evolution equations

1 variable 1 variable cc = density of tumour cells): KPP-Fisher equation = density of tumour cells): KPP-Fisher equation

D(x)D(x) = diffusion (motility) in brain tissue, = diffusion (motility) in brain tissue, (reaction)=growth of tumour cells,1D (reaction)=growth of tumour cells,1D xx spatial variable and spatial variable and cc:: density of tumour density of tumour cells, used to represent brain tumour cells, used to represent brain tumour radial propagation from a centreradial propagation from a centre

(K. Swanson(K. Swanson & J. Murray, Cell Prolif 2000;& J. Murray, Cell Prolif 2000; Br J Cancer 2002; J Neurol Sci 2003)Br J Cancer 2002; J Neurol Sci 2003)

Models of tumour growth: invasion as competitionModels of tumour growth: invasion as competitionMacroscopic reaction-diffusion equations to represent invasion (recession) frontsMacroscopic reaction-diffusion equations to represent invasion (recession) fronts

2 or more variables: ex.: healthy cells 2 or more variables: ex.: healthy cells NN11, tumour cells , tumour cells NN22, excess H, excess H+ + ions ions LL

(Gatenby & Gawlinski, Canc. Res. 1996)(Gatenby & Gawlinski, Canc. Res. 1996)PredictionPrediction: interstitial cell gap between tumour: interstitial cell gap between tumourpropagation and healthy tissue recession frontspropagation and healthy tissue recession fronts

NN11NN22

LL

Models for moving tumour cells in the ECMModels for moving tumour cells in the ECMChemotaxis: chemo-attractant induced cell movementsChemotaxis: chemo-attractant induced cell movements

Keller-Segel modelKeller-Segel model

pp = density of cells = density of cellsww = density of chemical = density of chemical

(Originally designed for movements of bacteria, with (Originally designed for movements of bacteria, with ww=[cAMP])=[cAMP])(Keller & Segel, J Theoret Biol 1971)(Keller & Segel, J Theoret Biol 1971)

Anderson-Chaplain model for local invasion by tumour cells in the ECMAnderson-Chaplain model for local invasion by tumour cells in the ECM

nn = density of cells = density of cells

f f = ECM density= ECM density

mm = MDE (tumour = MDE (tumour metalloproteases)metalloproteases)

uu = MDE inhibitor = MDE inhibitor

(Anderson & Chaplain, Chap 10 in Cancer modelling and simulation, L. Preziosi Ed, Chapman & Hall 2003)(Anderson & Chaplain, Chap 10 in Cancer modelling and simulation, L. Preziosi Ed, Chapman & Hall 2003)

Models for angiogenesisModels for angiogenesisVEGF-induced endothelial cell movements towards tumourVEGF-induced endothelial cell movements towards tumour

- Biochemical enzyme kinetics- Biochemical enzyme kinetics- Chemical transport (capillary and ECM)- Chemical transport (capillary and ECM)- - “Reinforced random walks”“Reinforced random walks”- Cell movements in the ECM- Cell movements in the ECM

Models by Anderson and Chaplain, Models by Anderson and Chaplain, Levine and SleemanLevine and Sleeman(Levine & Sleeman,Chap. 6 in Cancer modelling and (Levine & Sleeman,Chap. 6 in Cancer modelling and simulation, L. Preziosi Ed, Chapman & Hall 2003)simulation, L. Preziosi Ed, Chapman & Hall 2003)

A multiscale angiogenesis model A multiscale angiogenesis model

Interacting cell populationsInteracting cell populations Proliferating cancer cell populationProliferating cancer cell population

F. Billy et al., J. Theor. Biol. 2009F. Billy et al., J. Theor. Biol. 2009

Coupling by oxygen concentration, Coupling by oxygen concentration, acting on actual commitment of cellsacting on actual commitment of cellsinto the division cycle (passing the restriction point)into the division cycle (passing the restriction point)

Aim: assessment of an antiangiogenic treatment by endostatinAim: assessment of an antiangiogenic treatment by endostatin

Modelling the cell cycle 1: single cell levelModelling the cell cycle 1: single cell levelOrdinary differential equations to describe progression in the cell cycleOrdinary differential equations to describe progression in the cell cycle

CC

XX

MM

A. Golbeter’s minimal model for the « mitotic oscillator », i.e., GA. Golbeter’s minimal model for the « mitotic oscillator », i.e., G22/M phase transition /M phase transition

CC = cyclin B, = cyclin B, MM = Cyclin-linked cyclin dependent kinase, = Cyclin-linked cyclin dependent kinase, XX = anticyclin protease = anticyclin protease

Switch-like dynamics of kinase cdk1, Switch-like dynamics of kinase cdk1, MM

Adapted to describe GAdapted to describe G22/M phase transition, /M phase transition,

which is controlled by Cyclin B-CDK1which is controlled by Cyclin B-CDK1(A. Goldebeter, Biochemical oscillations and cellular rhythms, CUP 1996)(A. Goldebeter, Biochemical oscillations and cellular rhythms, CUP 1996)

Modelling the cell cycle 2: single cell (continued)Modelling the cell cycle 2: single cell (continued)Detailed ODE models to describe progression in the cell cycle: Tyson & NovakDetailed ODE models to describe progression in the cell cycle: Tyson & Novak

Phase transitions:Phase transitions:-G-G11/S/S

-G-G22/M/M

-Metaphase/anaphase-Metaphase/anaphase

……due to steep variationsdue to steep variationsof Cyc-CDK concentrationsof Cyc-CDK concentrations(bistability with hysteresis)(bistability with hysteresis)

(Novak, Bioinformatics 1999) (Tyson, Chen, Novak, Nature Reviews 2001)

Modelling the cell cycle 2: single cell (continued)Modelling the cell cycle 2: single cell (continued)Detailed ODE models to describe progression in the cell cycle: Gérard & GoldbeterDetailed ODE models to describe progression in the cell cycle: Gérard & Goldbeter

39 variables. Growth factor, rather than cell mass39 variables. Growth factor, rather than cell mass(as in Tyson & Novak) is the driving parameter(as in Tyson & Novak) is the driving parameter

A simplified model has been proposed, with 5 variablesA simplified model has been proposed, with 5 variables

C. Gérard & A. Goldbeter, PNAS 2009; Interface Focus 2011C. Gérard & A. Goldbeter, PNAS 2009; Interface Focus 2011C. Gérard, D. Gonze & A. Goldbeter, C. Gérard, D. Gonze & A. Goldbeter, FEBS Journal 2012FEBS Journal 2012

Modelling the cell cycle 3: cell population levelModelling the cell cycle 3: cell population levelAge-structured PDE models for proliferating cell populationsAge-structured PDE models for proliferating cell populations

(after B. Basse et al., J Math Biol 2003)

In each phase In each phase i i , a Von Foerster-McKendrick-like equation:, a Von Foerster-McKendrick-like equation:

ddi i , K , K i->i+1i->i+1 constant or constant or periodic w. r. to time tperiodic w. r. to time t(1≤i≤I, I+1=1)(1≤i≤I, I+1=1)

nnii:=cell population density :=cell population density in phase iin phase iddii:=death rate:=death rate

K K i->i+1i->i+1:=transition rate:=transition rate(with a factor 2for i=1)(with a factor 2for i=1)

Flow cytometry may help quantifyFlow cytometry may help quantifyproliferating cell population repartitionproliferating cell population repartitionaccording to cell cycle phasesaccording to cell cycle phases

Death rates Death rates ddii and phase transitions and phase transitions K K i->i+1i->i+1 are targetsare targets

for physiological (e.g. circadian) and therapeutic (drugs) controlfor physiological (e.g. circadian) and therapeutic (drugs) control

Otherwise said: proof of the existence of a unique growth exponent Otherwise said: proof of the existence of a unique growth exponent ,,the same for the same for all phases all phases ii, such that the are bounded, and asymptotically , such that the are bounded, and asymptotically periodic if the control is periodic.periodic if the control is periodic.

Example (periodic control case): 2 phases, control on GExample (periodic control case): 2 phases, control on G22/M by 24 h-entrained /M by 24 h-entrained

periodic CDK1-Cyclin B (from A. Goldbeter’s minimal mitotic oscillator model)periodic CDK1-Cyclin B (from A. Goldbeter’s minimal mitotic oscillator model)

=CDK1-Cyc B Cells in G1-S-G2 (phase i=1) Cells in M (phase i=2)

Entrainment of the cell cycle by = CDK1-Cyc B at a 24 h-period

: a growth exponent governing the cell population behaviour: a growth exponent governing the cell population behaviour

time t

““Surfing on the Surfing on the exponential growth exponential growth curve”curve”

(= the same as adding(= the same as addingan artificial death term an artificial death term to theto theddii, stabilising , stabilising

the systemthe system))

““Surfing on the Surfing on the exponential growth exponential growth curve”curve”

(= the same as adding(= the same as addingan artificial death term an artificial death term to theto theddii, stabilising , stabilising

the systemthe system))

Details (1): 2-phase model, no control on transitionDetails (1): 2-phase model, no control on transition

The total population of cellsThe total population of cells

inside each phase followsinside each phase followsasymptotically an exponentialasymptotically an exponentialbehaviourbehaviour

Stationary state Stationary state distribution of cells distribution of cells inside phases inside phases according to ageaccording to age a: a: no control -> no control -> exponential decayexponential decay

Asynchronous cell growthAsynchronous cell growth

Details (2): 2 phases, periodic control Details (2): 2 phases, periodic control on Gon G22/M transition/M transition

The total population of cellsThe total population of cells

inside each phase followsinside each phase followsasymptotically an exponentialasymptotically an exponentialbehaviour behaviour tuned by a periodic tuned by a periodic functionfunction

Stationary stateStationary statedistribution of cellsdistribution of cellsinside phasesinside phasesaccording to age according to age a: a: sharp periodic sharp periodic control ->sharp rise control ->sharp rise and decay and decay

Synchronisation between cellSynchronisation between cellcycle phases at transitionscycle phases at transitions

The simplest case: 1-phase model with divisionThe simplest case: 1-phase model with division

(Here, (Here, vv(a)(a)=1, =1, a* a* is the cell cycle duration, and is the cell cycle duration, and is the timeis the time

during which the 1-during which the 1-periodic controlperiodic control is actually exerted on cell division)is actually exerted on cell division)

Then it can be shown that the eigenvalue problem:Then it can be shown that the eigenvalue problem:

has a unique positive 1has a unique positive 1-periodic-periodic eigenvector eigenvector NN, with a positive eigenvalue , with a positive eigenvalue

Experimental measurements to identify transition kernels Experimental measurements to identify transition kernels KKi_i+1i_i+1

(and simultaneously experimental evaluation of the first eigenvalue (and simultaneously experimental evaluation of the first eigenvalue ))In the simplest model with In the simplest model with dd=0 =0 (one phase, no cell death) and assuming (one phase, no cell death) and assuming K=K(x)K=K(x)(instead of indicator functions , experimentally more realistic transitions):(instead of indicator functions , experimentally more realistic transitions):

Interpreted as: if Interpreted as: if is the age in phase at division, or transition: is the age in phase at division, or transition:

With probability density (experimentally identifiable):With probability density (experimentally identifiable):

withwith

Whence (by integration Whence (by integration along characteristic lines):along characteristic lines):

i.e.,i.e.,

Experimental identification of basic model parametersExperimental identification of basic model parameterswith with FUCCI reporters FUCCI reporters on a 2-phase model G1 / S-G2-Mon a 2-phase model G1 / S-G2-M

FUCCI=Fluorescent Ubiquitination-based Cell Cycle IndicatorFUCCI=Fluorescent Ubiquitination-based Cell Cycle Indicator

FUCCI: a movie (Sakaue-Sawano 2008) on HeLa cellsFUCCI: a movie (Sakaue-Sawano 2008) on HeLa cells

Another FUCCI movie (C. Feillet, IBDC Nice), NIH3T3 cellsAnother FUCCI movie (C. Feillet, IBDC Nice), NIH3T3 cells

FUCCI reportersFUCCI reporters

Measuring time intervals: G1 and total division cycle durationsMeasuring time intervals: G1 and total division cycle durations

Data from G. van der Horst’s lab, Erasmus University, Rotterdam, processed by Frédérique Billy at INRIA(NIH3T3 cells) (Billy et al., Math. Comp. Simul. 2012) (Billy et al., Math. Comp. Simul. 2012)

Phase transitions w.r.t. age Phase transitions w.r.t. age xxGamma p.d.f.s Gamma p.d.f.s f(x) f(x) fitted from data on 55 NIH 3T3 cellsfitted from data on 55 NIH 3T3 cells

(Billy et al., Math. Comp. Simul. 2012) (Billy et al., Math. Comp. Simul. 2012)

Phase transitions w.r.t. age Phase transitions w.r.t. age xxTransition rates Transition rates K(x)K(x) from p.d.f.s from p.d.f.s f(x)f(x) on NIH 3T3 cellson NIH 3T3 cells

and resulting population evolution on one complete cycleand resulting population evolution on one complete cycle

G1G1

SG2MSG2M

KK11 (G1 to S) (G1 to S) KK22 (M to G1) (M to G1)

(Billy et al., Math. Comp. Simul. 2012) (Billy et al., Math. Comp. Simul. 2012)

One cell divides in two: a physiologically controlled process at cell and tissue levelsOne cell divides in two: a physiologically controlled process at cell and tissue levelsin all healthy and fast renewing tissues (gut, bone marrow) that is in all healthy and fast renewing tissues (gut, bone marrow) that is disrupted in cancer:disrupted in cancer:

Is cell cycle phase synchronisation a mark of health in Is cell cycle phase synchronisation a mark of health in tissues? tissues?

(from Lodish et al., Molecular cell biology, Nov. 2003)(from Lodish et al., Molecular cell biology, Nov. 2003)

A possible application to the investigation ofA possible application to the investigation ofsynchronisation between cell cycle phases synchronisation between cell cycle phases

A working hypothesis that could explain differences in A working hypothesis that could explain differences in responses to drug treatments between healthy and cancer tissuesresponses to drug treatments between healthy and cancer tissues

Healthy tissues, i.e., cell populations, would be well synchronisedHealthy tissues, i.e., cell populations, would be well synchronisedw. r. to proliferation rhythms and w. r. to circadian clocks, whereas…w. r. to proliferation rhythms and w. r. to circadian clocks, whereas…

...tumour cell populations would be desynchronised w. r. to both, and ...tumour cell populations would be desynchronised w. r. to both, and suchsuchproliferation desynchronisation would be a consequence of an escapeproliferation desynchronisation would be a consequence of an escapeby tumour cells from central circadian clock control messages, just asby tumour cells from central circadian clock control messages, just asthey evade most physiological controls, cf. e.g., Hanahan & Weinberg:they evade most physiological controls, cf. e.g., Hanahan & Weinberg:

Question: Question: is cell cycle phaseis cell cycle phasedesynchronisation desynchronisation another hallmark of another hallmark of cancer cancer in cell in cell populationpopulations? s?

A mathematical result: A mathematical result: increases with desynchronisation increases with desynchronisation (expected, and shown in Th. Ouillon’s internship report, INRIA 2010)(expected, and shown in Th. Ouillon’s internship report, INRIA 2010)

where desynchronisation is defined as a measure of phase overlapping at transitionwhere desynchronisation is defined as a measure of phase overlapping at transition

i.e.,for a given family (i.e.,for a given family (ffii) ) of p.d.f.s with second moment of p.d.f.s with second moment ii, , is increasing with each is increasing with each ii

(also shown in Billy et al., Math. Comp. Simul., 2012)(also shown in Billy et al., Math. Comp. Simul., 2012)

Computing the growth exponent, fitting data to p.d.f.s:Computing the growth exponent, fitting data to p.d.f.s:Gamma p.d.f.s were best fits and yielded simple computations:Gamma p.d.f.s were best fits and yielded simple computations:

2-phase Lotka’s equation simply reads:2-phase Lotka’s equation simply reads:

... which yields here ... which yields here = 0.039 = 0.039 hh-1-1

Now, what if we add periodic (e.g., circadian) control??Now, what if we add periodic (e.g., circadian) control??i.e., what if we put i.e., what if we put K(x,t) = K(x,t) = (x).(x).(t)(t)with with = FUCCI-identified and = FUCCI-identified and = a cosine? = a cosine?[cosine: in the absence of a better identified clock thus far] [cosine: in the absence of a better identified clock thus far]

(and yields mean doubling time (and yields mean doubling time TTd d =17.77 h, and mean cell cycle time =17.77 h, and mean cell cycle time TTc c ==17.95 h) 17.95 h)

Phases: asynchronous cell growth Global: sheer exponential cell growth

[Agreement betweenmodel and data onthe first division]

F. Billy

Steep synchronisation within the cell cycle Stepwise cell population growth

F. Billy

Soft synchronisation within the cell cycle Stepwise cell population growth

F. Billy

F. Billy

Other cell population dynamic models relying on the cell cycle Other cell population dynamic models relying on the cell cycle

A model of tissue growth with proliferation/quiescenceA model of tissue growth with proliferation/quiescenceAn age[An age[aa]-and-cyclin[]-and-cyclin[xx]-structured PDE model with proliferating and quiescent cells]-structured PDE model with proliferating and quiescent cells(exchanges between (exchanges between (p)(p) and and (q)(q), healthy and tumour tissue cases: G, healthy and tumour tissue cases: G00 to G to G1 1 recruitment differs)recruitment differs)

Healthy tissue Healthy tissue recruitment: recruitment: homeostasishomeostasis

Tumour recruitment:Tumour recruitment:exponential (possiblyexponential (possiblypolynomial) growthpolynomial) growth

F. Bekkal Brikci, F. Bekkal Brikci, JC, B. Ribba, JC, B. Ribba, B. PerthameB. PerthameJMB 2008; MCM JMB 2008; MCM 20082008

M. Doumic-M. Doumic-Jauffret, MMNP Jauffret, MMNP 20082008

p: proliferating p: proliferating cellscells

q: quiescent cellsq: quiescent cells

N: all cells (p+q)N: all cells (p+q)

00for smallfor small00for large Nfor large N

00for allfor all

P-Q again: Simple PDE models, age-structured withP-Q again: Simple PDE models, age-structured withexchanges between proliferation and quiescenceexchanges between proliferation and quiescence

pp=density of proliferating cells; =density of proliferating cells; qq=density of quiescent cells; =density of quiescent cells; =death terms;=death terms;KK=term describing cells leaving proliferation to quiescence, due to mitosis;=term describing cells leaving proliferation to quiescence, due to mitosis;=term describing “reintroduction” (or recruitment) from quiescence to proliferation=term describing “reintroduction” (or recruitment) from quiescence to proliferation

DelayDelay differential differential models with two cell compartments,models with two cell compartments, proliferating (P)/quiescent (Q): proliferating (P)/quiescent (Q): Haematopoiesis models Haematopoiesis models

(obtained from the previous model with additional hypotheses and integration in age x along characteristics)(obtained from the previous model with additional hypotheses and integration in age x along characteristics)

(from Mackey, Blood 1978)(from Mackey, Blood 1978)

Properties of this model: depending on the parameters, one can have positiveProperties of this model: depending on the parameters, one can have positivestability, extinction, explosion, or sustained oscillations of both populationsstability, extinction, explosion, or sustained oscillations of both populations

(Hayes stability criteria, see Hayes, J London Math Soc 1950)(Hayes stability criteria, see Hayes, J London Math Soc 1950)

Oscillatory behaviour is observed in Oscillatory behaviour is observed in periodic periodic Chronic Myelogenous LeukaemiaChronic Myelogenous Leukaemia((CMLCML) where oscillations with limited amplitude are compatible with survival, ) where oscillations with limited amplitude are compatible with survival, whereas explosion (blast crisis, alias acutisation) leads to whereas explosion (blast crisis, alias acutisation) leads to AMLAML and death and death (Mackey and Bélair in Montréal; Adimy, Bernard, Crauste, Pujo-Menjouet, Volpert in Lyon)(Mackey and Bélair in Montréal; Adimy, Bernard, Crauste, Pujo-Menjouet, Volpert in Lyon)

(delay (delay cell division cycle cell division cycle time)time)

Modelling haematopoiesisModelling haematopoiesisforfor Acute Myelogenous LeukaemiaAcute Myelogenous Leukaemia (AML) (AML)……aiming at aiming at non-cell-killing therapeuticsnon-cell-killing therapeuticsby inducing by inducing re-differentiation of cells usingre-differentiation of cells usingmolecules (e.g. ATRA)molecules (e.g. ATRA) enhancing differentiationenhancing differentiationrates represented by Krates represented by Kii terms terms

where where rrii and and ppii represent resting and proliferating represent resting and proliferating

cells, respectively, with reintroduction term cells, respectively, with reintroduction term ii==ii(x(xii) )

positive decaying to zero, positive decaying to zero,

with population argument:with population argument:

and boundary conditions:and boundary conditions:

From Adimy, Crauste, ElAbdllaoui J Biol Syst 2008 (see also: Özbay, Bonnet, Benjelloun, JC MMNP 2012)From Adimy, Crauste, ElAbdllaoui J Biol Syst 2008 (see also: Özbay, Bonnet, Benjelloun, JC MMNP 2012)

Modelling leukaemic haematopoiesis: Modelling leukaemic haematopoiesis: (Mackey/Adimy) proliferation advantage?(Mackey/Adimy) proliferation advantage?

Stem cells CD34+/CD38-Stem cells CD34+/CD38-

Committed cells CD34+/CD38+Committed cells CD34+/CD38+

TK (flt3-ITD) mutationTK (flt3-ITD) mutation

Blood/ bone marrow samplingBlood/ bone marrow samplingin AML patientsin AML patientsCell sorting (magnetic beads)Cell sorting (magnetic beads)

FACS for cell cycle phases FACS for cell cycle phases Self-renewalSelf-renewalMeasuring apoptosis and cellMeasuring apoptosis and celldivision in each populationdivision in each population Model adaptation (in charge: A. Ballesta, Hosp. St Antoine)Model adaptation (in charge: A. Ballesta, Hosp. St Antoine)

Optimisation of cancer therapy by cytotoxic drugs Optimisation of cancer therapy by cytotoxic drugs

• Optimal control strategies to overcome the development of drug resistant cell populations, using different drugs (Kimmel & Swierniak, 2006)(Kimmel & Swierniak, 2006)

• Pulsed chemotherapies aiming at synchronising drug injections with cell cycle events to enhance the effect of drugs on tumours: e.g. optimal control of IL21 injection times and doses ui (t-ti) using variational methods (Z. Agur, IMBM, Israel)(Z. Agur, IMBM, Israel)

• Chronotherapy = continuous infusion time regimens taking advantage of optimal circadian anti-tumour efficacy and healthy tissue tolerability for each particular drug: has been in use for the last 15 years, with particular

achievements for colorectal cancer (F. Lévi, INSERM U776, M.-C. Mormont & F. Lévi, Cancer 2003)(F. Lévi, INSERM U776, M.-C. Mormont & F. Lévi, Cancer 2003)

Examples of (still theoretical) applications to therapeutics:Examples of (still theoretical) applications to therapeutics:Controlling unwanted toxic side effects on healthy tissuesControlling unwanted toxic side effects on healthy tissues

PK-PD simplified model for cancer chronotherapyPK-PD simplified model for cancer chronotherapy(here with only toxicity constraints; target=death rate)(here with only toxicity constraints; target=death rate)

Healthy cells (jejunal mucosa)Healthy cells (jejunal mucosa) Tumour cells (Glasgow osteosarcoma)Tumour cells (Glasgow osteosarcoma)

f(C,t)=F.C/(C50+C).{1+cos 2(t-S)/T} g(D,t)=H.D/(D50

+D).{1+cos 2(t-T)/T}

(PK)(PK)

(« chrono-PD »)(« chrono-PD »)

(homeostasis=damped harmonic oscillator)(homeostasis=damped harmonic oscillator) (tumour growth=Gompertz model)(tumour growth=Gompertz model)

(JC et al. Pathol-Biol 2003; Basdevant, JC, Lévi M2AN 2005; JC ADDR 2007)(JC et al. Pathol-Biol 2003; Basdevant, JC, Lévi M2AN 2005; JC ADDR 2007)

Aim: balancing IV delivered drug anti-tumour efficacy by healthy tissue toxicity Aim: balancing IV delivered drug anti-tumour efficacy by healthy tissue toxicity

(pop.(pop.dyn.)dyn.)

Optimal control, step 1: deriving an objective Optimal control, step 1: deriving an objective function from the tumoral cell population modelfunction from the tumoral cell population model

Eradication strategy: minimise Eradication strategy: minimise GGBB(i(i), where:), where:

Stabilisation strategy: minimise Stabilisation strategy: minimise GGBB(i(i), where:), where:

or else:or else:

characteristic characteristic function of the function of the allowed infusion allowed infusion periods)periods)

(t(t11 < t < tf f being some fixed observation timebeing some fixed observation time

after tafter t00,beginning of infusion interval),beginning of infusion interval)

Optimal control, step 2: deriving a constraint Optimal control, step 2: deriving a constraint function from the enterocyte population modelfunction from the enterocyte population model

Minimal toxicity constraint, for 0<Minimal toxicity constraint, for 0<AA<1<1 (e.g. (e.g. AA =50%): =50%):

±other possible constraints:±other possible constraints:

Optimal control problem: defining a lagrangian:Optimal control problem: defining a lagrangian:

then:then:

If GIf GBB and F and FA A were convex, then a necessary and sufficient condition would be:were convex, then a necessary and sufficient condition would be:

……i.e. the minimum would be obtained at a saddle point of the lagrangian, i.e. the minimum would be obtained at a saddle point of the lagrangian, reachable by a Uzawa-like algorithmreachable by a Uzawa-like algorithm

Optimised control: results of a tumour stabilisation strategy Optimised control: results of a tumour stabilisation strategy using this simple one-drug PK-PD modelusing this simple one-drug PK-PD model

Objective: Objective: minimising the maximumminimising the maximum of the tumour cell populationof the tumour cell population

Constraint : Constraint : preserving the jejunal mucosa preserving the jejunal mucosa according to the patient’s state of healthaccording to the patient’s state of health

(Basdevant, JC, Lévi M2AN 2005; JC ADDR 2007; Lévi, Okyar, Dulong, JC Annu Rev Pharm Toxicol 2010)(Basdevant, JC, Lévi M2AN 2005; JC ADDR 2007; Lévi, Okyar, Dulong, JC Annu Rev Pharm Toxicol 2010)

Result : optimal infusion flow i(t) Result : optimal infusion flow i(t) adaptable to the patient’s state of health adaptable to the patient’s state of health

(according to a tunable parameter(according to a tunable parameter AA: : here preserving here preserving AA=50% of enterocytes=50% of enterocytes))

Theoretical chronotherapeutic optimisationTheoretical chronotherapeutic optimisationof a 1st eigenvalue (cancer growth) under the constraintof a 1st eigenvalue (cancer growth) under the constraint

of preserving another 1st eigenvalue (healthy tissue growth)of preserving another 1st eigenvalue (healthy tissue growth)

Another way to take into account a toxicity constraint (with Frédérique Billy and Olivier Fercoq):Another way to take into account a toxicity constraint (with Frédérique Billy and Olivier Fercoq):

Circadian + pharmacological control on transitionsCircadian + pharmacological control on transitionsK(x,t) = K(x,t) = (x).(x).(t).[1-g(t)]: (t).[1-g(t)]: FUCCI-identified, FUCCI-identified, clock, g drug effect to be optimised clock, g drug effect to be optimised

green and red: green and red: gating at transitions gating at transitions

blue: blue: (1-g)(1-g)..therapy g blocks therapy g blocks

Evolution of the two populations of cancer and healthy cellsEvolution of the two populations of cancer and healthy cells

Circadian control,Circadian control,no drug infusionno drug infusion

Circadian control,Circadian control,added drug infusionadded drug infusion

(F. Billy et al. 2012)(F. Billy et al. 2012)

CancerCancer

CancerCancer

HealthyHealthy

HealthyHealthy

Numerical solution to the optimal infusion problemNumerical solution to the optimal infusion problemand effect on eigenvalues, healthy and cancer and effect on eigenvalues, healthy and cancer

Infusion scheme Infusion scheme g(t)g(t)

Target eigenvalues:Target eigenvalues:Cancer (blue)Cancer (blue)Healthy (green)Healthy (green)

In favour of this approach:In favour of this approach:- characterises long-term - characterises long-term trends with one number,trends with one number,- easily accessible- easily accessible target for controltarget for control- fits to physiologically- fits to physiologically structured growth modelsstructured growth models

Its drawbacks:Its drawbacks:- deals with asymptotics,deals with asymptotics,not with transientsnot with transients- assumes a linear modelassumes a linear model for proliferationfor proliferation- assumes periodic control- assumes periodic control by drugs (but the periodby drugs (but the period can be infinitely long)can be infinitely long)

...within the “DarEvCan” French research consortium...within the “DarEvCan” French research consortium

Darwinian Evolution and CancerDarwinian Evolution and Cancerhttp://www.darevcan.univ-montp2.fr/http://www.darevcan.univ-montp2.fr/

Now tackling the problem of drug resistanceNow tackling the problem of drug resistance

Carlo MaleyCarlo Maley Robert Gatenby, MDRobert Gatenby, MD**

First international First international Evolution and cancer conferenceEvolution and cancer conference SF, June 3-5, 2011, next one in SF, June 3-5, 2011, next one in 20132013

A soaring theme on the international scene:A soaring theme on the international scene:

* RG advocates ‘adaptive therapy’, cf. Gatenby Nature 2009, Gatenby et al. Cancer Research 2009 * RG advocates ‘adaptive therapy’, cf. Gatenby Nature 2009, Gatenby et al. Cancer Research 2009

Gatenby’s new paradigm: rational management of cancer burden by ‘adaptive therapy’Gatenby’s new paradigm: rational management of cancer burden by ‘adaptive therapy’

See also review on evolution and cancer by Aktipis et al. PLoS One, Nov. 2011 See also review on evolution and cancer by Aktipis et al. PLoS One, Nov. 2011

Tackling this other issue in cancer pharmacotherapeutics:Tackling this other issue in cancer pharmacotherapeutics:Emergence of drug resistance in cancer cell populations Emergence of drug resistance in cancer cell populations

Instead of controlling drug resistance at the individual cell level (ABC transporters),Instead of controlling drug resistance at the individual cell level (ABC transporters),representation of the possible emergence of resistant cell clones due to mutationrepresentation of the possible emergence of resistant cell clones due to mutationoccurring at mitoses or adaptation to the environment in a occurring at mitoses or adaptation to the environment in a cell Darwinism perspective.cell Darwinism perspective.

Assumption: cancer cell populations, under the pressure of a drug-enrichedAssumption: cancer cell populations, under the pressure of a drug-enrichedenvironment, may develop (costly) mutations or adaptations yielding resistant cellenvironment, may develop (costly) mutations or adaptations yielding resistant cellclones, less fit in a drug-free environment, but better survivors in a hostile environment.clones, less fit in a drug-free environment, but better survivors in a hostile environment.

A therapeutic objective, under these circumstances, may be not to eradicate allA therapeutic objective, under these circumstances, may be not to eradicate allcancer cells (in fact only all drug-sensitive cells), but instead to let some of themcancer cells (in fact only all drug-sensitive cells), but instead to let some of themlive so as to limit the growth of an emergent resistant cell clone (‘adaptive therapy’).live so as to limit the growth of an emergent resistant cell clone (‘adaptive therapy’).

Mathematical modelling: design of cell population models structured according to aMathematical modelling: design of cell population models structured according to aphenotypic trait (representing drug resistance, cell division cycle not considered here)phenotypic trait (representing drug resistance, cell division cycle not considered here)

First point of view: ‘mutations only’, one cytotoxic drugFirst point of view: ‘mutations only’, one cytotoxic druga) Healthy cellsa) Healthy cells

First point of view: ‘mutations only’, one cytotoxic drugFirst point of view: ‘mutations only’, one cytotoxic drugb) Cancer cells b) Cancer cells

Point of view ‘mutations only’: monomorphism in the healthy cell population

Point of view ‘mutations only’: monomorphism also in the cancer cell population

Simulations by Alexander Lorz Simulations by Alexander Lorz (JC, T. Lorenzi, A. Lorz, B. Perthame, in revision)(JC, T. Lorenzi, A. Lorz, B. Perthame, in revision)

2nd point of view : two different drugs, cytotoxic and cytostatic, two resistance traits x and y,‘no mutations, exchanges with the environment instead’

Monomorphism in the healthy cell population

No mutations: non-resistant (‘healthy’) cells: starting from a common medium phenotype (cytotoxic res.=.5, cytostatic res.= .5), evolution towards the non-resistant (0,0) phenotype

Model, simulations and figures by Tommaso Lorenzi Model, simulations and figures by Tommaso Lorenzi

Dimorphism in the cancer cell population

No mutations: Resistant (‘cancer’) cells: starting from the same common medium phenotype

(.5,.5), evolution towards 2 different resistant phenotypes: (1,0) and (0,1)

Model, simulations and figures by Tommaso Lorenzi Model, simulations and figures by Tommaso Lorenzi

What more now? Need for multiscale models!!What more now? Need for multiscale models!!

Drugs act at the molecular and Drugs act at the molecular and cell levelcell level, produce measurable effects, produce measurable effectsat the at the cell population levelcell population level, and are delivered at the , and are delivered at the whole body levelwhole body level

(JC, Personalized Medicine, 2011)(JC, Personalized Medicine, 2011)

Modelling challenge: integratingModelling challenge: integratingthese levels in whole body modelsthese levels in whole body modelsto optimise drug control on tissue to optimise drug control on tissue proliferation, healthy and cancer,proliferation, healthy and cancer,in a in a systems biology systems biology perspective:perspective:

- intracellular signalling networks,intracellular signalling networks, actual drug targetsactual drug targets- cell populations: proliferation, cell populations: proliferation, apoptosis, differentiationapoptosis, differentiation- whole body ensemble of tissueswhole body ensemble of tissues as interacting cell populations as interacting cell populations under drug controlunder drug control

CollaboratorsCollaborators

Bang & LJLL: Bang & LJLL: Annabelle Ballesta,Annabelle Ballesta, Fadia Bekkal Brikci, Frédérique Billy, Luna Dimitrio, Fadia Bekkal Brikci, Frédérique Billy, Luna Dimitrio, Marie Doumic, Pierre Gabriel, Herbert Gayrard, Erwan Hingant, Thomas Lepoutre, Marie Doumic, Pierre Gabriel, Herbert Gayrard, Erwan Hingant, Thomas Lepoutre, Tommaso Lorenzi, Alexander Lorz, Thomas Ouillon, Benoît Perthame, Emilio Seijo SolisTommaso Lorenzi, Alexander Lorz, Thomas Ouillon, Benoît Perthame, Emilio Seijo Solis

Other INRIA teams: Other INRIA teams: Catherine Bonnet (Catherine Bonnet (DiscoDisco), Stéphane Gaubert, Olivier Fercoq ), Stéphane Gaubert, Olivier Fercoq (Maxplus),(Maxplus), Jean-Charles Gilbert Jean-Charles Gilbert (Estime), (Estime), Mostafa Adimy, Samuel Bernard, Fabien Mostafa Adimy, Samuel Bernard, Fabien Crauste, Stéphane Génieys, Laurent Pujo-Menjouet, Vitaly Volpert (Crauste, Stéphane Génieys, Laurent Pujo-Menjouet, Vitaly Volpert (DraculaDracula))

INSERM U776 “Biological Rhythms and Cancers” (INSERM U776 “Biological Rhythms and Cancers” (Francis LéviFrancis Lévi, Paul-Brousse hospital, , Paul-Brousse hospital, Villejuif): Solid tumours of Mice and Men, chronotherapeutics of colorectal cancerVillejuif): Solid tumours of Mice and Men, chronotherapeutics of colorectal cancer

UMRs UPMC- INSERM U872 Team 18 “Resistance and survival of tumour cells” UMRs UPMC- INSERM U872 Team 18 “Resistance and survival of tumour cells” ((J.-P. Marie, J.-P. Marie, Cordeliers Research Centre and St Antoine Hospital, Paris): LeukaemiasCordeliers Research Centre and St Antoine Hospital, Paris): Leukaemias Université Paris-Nord (Université Paris-Nord (Claude Basdevant)Claude Basdevant):: Optimal control theory and algorithmsOptimal control theory and algorithms

FP7FP7 ERASysBio C5Sys: ERASysBio C5Sys: http://www.erasysbio.net/index.php?index=272ANR Bimod (Lyon, Paris, Bordeaux)ANR Bimod (Lyon, Paris, Bordeaux)GDR DarEvCan (Montpellier, Paris, Lyon,...): GDR DarEvCan (Montpellier, Paris, Lyon,...): http://www.darevcan.univ-montp2.fr/http://www.darevcan.univ-montp2.fr/