JC NIH INRIA160407ppt

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Published on February 5, 2008

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Modelling normal and tumour tissue proliferation to optimise cancer treatment:  Modelling normal and tumour tissue proliferation to optimise cancer treatment Jean Clairambault, PhD, MD INRIA projet BANG, Rocquencourt & INSERM U 776 “Biological Rhythms and Cancers” NIH-INRIA Workshop Bethesda, April16, 2007 Outline of the talk:  Outline of the talk Age-structured physiological modelling of the cell division cycle in healthy and tumour cell populations Circadian clocks and physiological control of the cell division cycle at the cell and tissue level Mechanistic PK-PD (pharmacokinetic-pharmacodynamic) control of the cell division cycle at the cell and tissue level Macroscopic modelling of anti-cancer drug PK-PD (pharmacokinetics-pharmacodynamics) and chronotherapeutic optimisation of one-drug infusion flow Slide3:  Modelling the cell division cycle at the cell population level Slide4:  Cyclin D Cyclin E Origin of cell proliferation: the cell division cycle Physiological / therapeutic control: - on transitions between phases (G1/S, G2/M, M/G1) - on death rates inside phases (apoptosis or necrosis) on the inclusion in the cell cycle (G0 to G1 recruitment) S:=DNA synthesis; G1,G2:=Gap1,2; M:=mitosis Mitotic human HeLa cell (from LBCMCP-Toulouse) Slide5:  Modelling the cell division cycle Age-structured PDE models for cycling cell populations B. Basse et al., J Math Biol 2003 In each phase i, a linear Von Foerster-McKendrick-like equation: di , Ki->i+1 constant or periodic w. r. to time t (1≤i≤I, I+1=1) ni:=cell population density in phase i di:=death rate Ki->i+1:=transition rate (with a factor 2for i=1) Death rates di: (“loss”) and phase transition rates Ki->i+1 are targets for physiological (e.g. circadian) and therapeutic (drugs) control Clairambault, Laroche, Mischler, Perthame RR INRIA #4892, 2003 Flow cytometry Slide6:  Result: existence of a growth (Malthus) exponent  unique for all phases i, such that the are bounded and periodic if a periodic control is exerted on the di or Ki->i+1 Surfing on the exponential growth curve: example: 2 phases, periodic control on transition G2/M by 24-h-periodic CDK1-Cyclin B: CDK1 All cells in G1-S-G2 (phase 1) All cells in M (phase 2) (Here =0.147  Td = 4.7 h) All cells Michel, Mischler, Perthame, C. R. Acad. Sci. Paris 2004; J Math Pures Appl 2005 Clairambault, Michel, Perthame C. R. Acad. Sci. Paris 2006; Proceedings 5th ECMTB (Dresden 2005) Birkhäuser 2007 Slide7:  Observation: a circadian rhythm perturbation by chronic jet-lag-like light entrainment phase (advance) enhances GOS tumour proliferation in mice LD12-12 Jet-lag How can this be accounted for in the model? Major public health stake! (does shift work enhance incidence of cancer?) (The answer is yes, see e.g. Davis, S., Cancer Causes Control 2006) A question from human and animal physiopathology on growth and circadian clock disruption JL+RF Filipski et al., JNCI 2005 Here, clearly: (jet-lag) > (LD 12-12) Slide8:  Theorem (B. Perthame, 2005): If the control is exerted on the sole loss (apoptosis) terms di , then (periodic control) > (constant control) Theorem (S. Gaubert and B. Perthame, unpublished): The same result holds for control exerted on both the di and the Ki->i+1 with the definition of an arithmetico-geometric mean for the Ki->i+1 …which so far leaves open the question of accurately representing jetlag-like control of light inputs onto the circadian clocks (clearly not by suppressing it!) A theorem on periodic control: (comparison of periodic versus constant [=no] control with same mean) Clairambault, Michel, Perthame C. R. Acad. Sci. Paris 2006; Proceedings 5th ECMTB (Dresden 2005) Birkhäuser 2007 Slide9:  Exchanges between proliferative G1SG2M and quiescent G0 cell compartments are controlled by mitogens and antimitogenic factors in G1 phase (From Vermeulen et al. Cell Prolif. 2003) Most cells do not proliferate physiologically, even in fast renewing tissues (gut) Populations of proliferating and quiescent cells: a common model for healthy and tumour tissues R Restriction point (late G1 phase) Before R: mitogen-dependent progression through G1 (possible regression to G0) After the restriction point R: mitogen-independent progression through G1 to S (no way back to G0) Slide10:  Model differences between healthy and tumour tissues: recruitment from quiescence into proliferation differs Healthy tissue: homeostasis Tumour: exponential growth Bekkal Brikci, Clairambault, Ribba, Perthame submitted 2006 N=p+q: total number of cells a: age x: cyclin D Slide11:  Circadian clocks Slide12:  Peripheral oscillators Rest-activity cycle: open window on SCN central clock Central coordination TGF, EGF Prokineticin Glucocorticoids Food intake rhythm Autonomic nervous system The circadian system… Lévi, Lancet Oncol 2001 ; Mormont & Lévi, Cancer 2003 Entrainment by light (from Francis Lévi, INSERM U 776 Rythmes Biologiques et Cancers) Retina Slide13:  …is an orchestra of clocks with one neuronal conductor in the SCN and molecular circadian clocks in all peripheral cells (from Hastings, Nature Rev.Neurosci. 2003) SCN=suprachiasmatic nuclei (in the hypothalamus) Slide14:  (after Hastings, Nature Rev. Neurosci. 2003) Activation loop Inhibition loop Clock-controlled genes In each cell: a molecular circadian clock (from Francis Lévi, INSERM U 776 Rythmes Biologiques et Cancers) Circadian rhythms in the Human cell cycle:  Circadian rhythms in the Human cell cycle Example of circadian rhythms in normal (=homeostatic) Human oral mucosa for Cyclin E (control of G1/S transition) and Cyclin B (control of G2/M transition) 08 12 16 20 00 04 Sampling Time (Clock Hour) Cyclin-E positive cells/mm Sampling Time (Clock Hour) Cyclin-B1 positive cells/mm Nuclear staining for Cyclin-E and Cyclin-B1. Percentages of mean ± S.E.M. in oral mucosa samples from 6 male volunteers. Cosinor fitting, p < 0.001 and p = 0.016, respectively. (after Bjarnason et al. Am J Pathol 1999) Slide16:  A molecular connection between cell cycle and circadian clock: cdk1 (cdc2) kinase opens G2/M gate; 24 h-rhythmic Wee1 inactivates cdk1 Mitotic oscillator model by Albert Goldbeter, 1997, here with circadian entrainment by a square wave standing for Wee1 (after U. Schibler,Science, Oct. 2003) Slide17:  (from You et al. 2005, Breast Canc. Res. Treat. 2005) More connections between cell cycle and circadian clock 1) The circadian clock gene Bmal1 might be a synchroniser in each cell between G1/S and G2/M transitions 2) Protein p53, the major sensor of DNA damage, is expressed according to a 24 h rhythm (from Fu & Lee, Nature 2003) (from Bjarnason 1999) Slide18:  Circadian rhythm disruption in mice Intact+Jet-lag Electrocoagulation Intact SCN Rest-activity Body temperature Filipski JNCI 2002, Canc. Res. 2004, JNCI 2005, Canc. Causes Control 2006 Slide19:  LD12-12 Jet-lag Circadian clock disruption and cell proliferation in mice JL+RF Filipski et al., JNCI 2005 (jet-lag) > (LD 12-12) Circadian rhythm disruption in Man [= loss of synchronisation between molecular clocks?]:  Circadian rhythm disruption in Man [= loss of synchronisation between molecular clocks?] Circadian desynchronisation (loss of rythms of temperature, cortisol, rest-activity cycle) is a factor of poor prognosis in the response to cancer treatment (Mormont & Lévi, Cancer 2003) Desynchronising effects of cytokines and anticancer drugs on circadian clock: fatigue is a constant symptom in patients with cancer (Rich et al., Clin Canc Res 2005) …effects that are analogous to those of chronic  jet-lag (photic entrainment phase advance or delay) on circadian rhythms, known to enhance tumour growth (Hansen, Epidemiology 2001; Schernhammer, JNCI 2001, 2003; Davis, JNCI 2001, Canc Causes Control 2006) …hence questions: 1) is the molecular circadian clock a major synchronising factor between phase transitions? And 2) do tumours enhance their development by disrupting the SCN clock? [ …and hence resynchronisation therapies (by melatonin, cortisol) in oncology?? ] Slide21:  Simple models of the molecular circadian clock (from Leloup & Goldbeter, J Biol Rhythms 1999) Limit cycle oscillations ((Goldbeter, Nature 2002) Slide22:  Modelling the SCN as a network of coupled oscillators: diffusive coupling between neurons Vs : Vs=1.6 (1+L cos(2t/24)) target of entrainment by light; K: target of transcriptional inhibition (e.g. by cytokines); Vm(i): the carrier of variabilility of the oscillatory period. 3 variables for the ith neuron that communicates with all other (j≠i) neurons of the SCN through cytosolic PER protein, with coupling constant Ke: electric? gap junctions? VIP / VPAC2 signalling? (from Aton & Herzog, Neuron 2005) (after Leloup, Gonze, Goldbeter, J Biol Rhythms 1999) Slide23:  Disrupted clock model: averaged peripheral oscillator 1) without entrainment by light; 2) with; 3) without 1) Desynchro D/D (T: varying around 21h30) 3) Desynchro D/D (T: varying around 21h30) 2) Synchro L/D (entrainment at T=24h) Clairambault, Proc. IEEE-EMBC New York 2006, IEEE-EMB Mag 2007 Resulting Per (or Bmal1) to control Wee1, hence CDK1=  Slide24:  Mechanistic PK-PD (molecular pharmacokinetics-pharmacodynamics) Slide25:  Pharmacokinetics of IV delivered anticancer drugs: -binding to plasma proteins, hepatic enzymatic detoxification -distribution from plasma to peripheral tissues -intracellular shielding (e.g. glutathione detoxification) and actual targets -catabolism (biliary conjugation, renal elimination) Pharmacodynamics at the tissue level: 1) actions on cell cycle determinants: -DNA, histones, enzymes (e.g. topoisomerase, thymidylate synthase) -cyclins and cyclin dependent kinases -growth factor receptors (EGFRs) 2) other actions: on invasion (ECM degradation), angiogenesis 3) possible limitations due to the occurrence of drug resistances Slide26:  Molecular PK of oxaliplatin: plasma compartment Mass of active oxaliplatin Instantaneous infused dose (flow) Rate of transfer from plasma to peripheral tissue (cellular uptake) Constant clearance Binding rate of oxaliplatin to plasma proteins Mass of plasma proteins (albumin or other hepatic proteins) Hepatic synthesis activity of plasma proteins L tunes the period of the cycle of plasma proteins L tunes the amplitude of the cycle of plasma proteins  tunes the robustness of GSH oscillations, from harmonic to relaxation-like Plasma protein synthesis shows circadian rhythm Slide27:  Molecular PK of oxaliplatin: tissue concentration Tissue concentration in free oxaliplatin (C=[DACHPt]) GST-mediated binding of reduced glutathione (G) to oxaliplatin (C), i.e., cell shielding by GSH Degradation of free DNA (F) by oxaliplatin (C) W = volume of tissue in which the mass P of free oxaliplatin is infused “Competition” between free DNA [=F] and reduced glutathione GSH [=G] to bind oxaliplatin [=C] in proliferating cells Slide28:  Molecular PD of oxaliplatin activity in tissue Mass of free DNA DNA Mismatch Repair (MMR) function (1 < 2 : activation and inactivation thresholds; gR: stiffness) Mass of reduced glutathione in target cell compartment Activity of -Glu-cysteinyl ligase (GCS) Action of oxaliplatin on free DNA (F) Glutathione synthesis ( detoxification) in cells shows circadian rhythm G tunes the period of the cycle of GSH synthesis by GCS Oxaliplatin cell concentration G tunes the amplitude of the cycle of GSH synthesis by GCS = -Glu-cysteinyl ligase  tunes the robustness of GSH oscillations, from harmonic to relaxation-like 1-F/F0 =DNA damage Slide29:  Action of oxaliplatin on DNA and repair function genetic polymorphism in tumour cells: drug resistance …the same with stronger MMR function (ERCC2=XPD-determined): F (free DNA) F (free DNA) G (glutathione) S (GCS activity) (Diminished VGST binding to GSH / cellular uptake , changed infusion peak time, lead to comparable results) Slide30:  Connecting DNA damage with cell cycle arrest and apoptosis: inhibition by p53 of phase transitions  . NB: 1) p53 expression is circadian clock-controlled; 2) p53 is mutated (down-regulated) in 50% of cancers Per Per Bmal1 Existing models by Ciliberto, Geva-Zatorsky, Chickarmane of DNA damage-ATM-p53-MDM2 dynamics (ODEs) Further with molecular PK-PD to optimise treatment:  Further with molecular PK-PD to optimise treatment Representation of the action of several drugs simultaneously to optimise pharmacotherapeutic synergies that are actually used in clinical oncology Taking into account specificities of individuals w. r. to enzymatic profiles (genetic polymorphism of detoxification enzymes) to design ‘patient-tailored therapeutics’ Representation of acquired drug resistance as a stochastic process describing the evolution of genes involved in resistance: DNA MMR, synthesis of detoxification molecules, tolerance to damaged DNA, drug cellular uptake, drug cellular efflux Refined representation of circadian clock, cellular detoxification mechanisms and cell cycle interactions to design optimised chronotherapies, using the circadian system as an open window on cell cycle timing to optimise dynamic drug delivery Taking advantage of differences between healthy and tumour cell populations: p53, drug processing enzymatic mechanisms, loss of synchronisation between cells by circadian clocks in tumour tissues Slide32:  PK-PD modelling for one-drug chronotherapeutic optimisation Slide33:  Cancer chronotherapy: clinical results Lévi et al. JNCI 1994; Lancet 1997; Lancet Onc 2001 INSERM U 776 Rythmes Biologiques et Cancers Slide34:  Centralised programmation Any modulation of delivery rate 4 reservoirs (100-2000 mL) 2 independent channels Rates from 1 to 3000 mL/h Multichannel pump for chronotherapy Over 2000 cancer patients registered in clinical Phase I, II or III trials Chronotherapy technology in the clinic INSERM U 776 Rythmes Biologiques et Cancers Images from the Chronotherapy Unit, Paul-Brousse Hospital, Villejuif, France Slide35:  Implemented chronotherapy technology Multichannel programmable ambulatory injector for intravenous drug infusion (pompe Mélodie, Aguettant, Lyon, France) Can such time schedules be improved? INSERM U 776 Rythmes Biologiques et Cancers Slide36:  PK-PD macroscopic modelling for one-drug cancer chronotherapy, with identification on a murine tumour Healthy cells (jejunum villi enterocytes) 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) (« chrono-PD ») (homeostasis=damped harmonic oscillator) (tumour growth=Gompertz model) Clairambault Pathol-Biol 2003; M2AN 2005; submitted ADDR 2006 Goal: balancing IV-delivered drug anti-tumour efficacy and healthy tissue toxicity Slide37:  Simulation: dynamics of variables Drug infusion Drug concentration in plasma Cell flow from crypts Mature healthy cells (villi) Drug concentration in tumour Tumour cells Slide38:  Optimal control of drug infusion flow i(t): tumour stabilisation using this simplified PK-PD model Objective: minimising the maximum of the tumour cell population Constraint : preserving the jejunal mucosa according to the patient’s state of health (A) Result : optimal drug infusion flow adaptable to the patient’s state of health (according to a parameter A: here preserving at least A=50% of enterocytes) Basdevant, Clairambault, Lévi M2AN 2005 Slide39:  Other challenges for cancer therapeutic optimisation Overcoming drug resistances -Developing strategies to minimise the occurrences of gene mutations (e.g. fewer doses of more different drugs to diminish dose-dependent mutation pressure) -Reversing drug insensitivity by adding other drugs (e.g. imatinib reverses resistance to SN-38 by drug efflux mediated by ABCG2 protein: modelling ABCG2 inhibition?) Blocking the recruitment from quiescence to proliferation e.g. by anti-EGFRs or other tyrosine kinase inhibitors: in association with cytotoxics Fighting neoangiogenesis in association with cytotoxics e.g. by antagonists of VEGFRs (bevacizumab) associated with 5-FU Fighting invasion by cancer cells that use anti-ECM enzymes Stimulating the immune system (Vaccination?) Collaborations and networks:  Collaborations and networks INSERM: U 776 “Biological Rhythms and Cancers” (F. Lévi, Villejuif) Clock gene expression and design of optimised cancer chronotherapeutic regimens INRIA: ARC ModLMC “Modelling Chronic Myelogenous Leukemia” (M. Adimy, Bordeaux) INRIA network dedicated to CML modelling and optimisation of treatment by imatinib European projects: 1) M3CSTGT “Mathematical Methods, Modelling and Computer Simulation of Tumour Growth and Therapy” (N. Bellomo, Torino) Academic exchanges of students, conferences and workshops 2) Biosim Network of Excellence “Biosimulation, a new tool in drug development” (E. Mosekilde, Lyngby) WP13: chronotherapeutics of cancer with 5FU, Oxaliplatin, and CDK inhibitors 3) Tempo Specific Targeted Research Project “Temporal genomics for tailored chronotherapeutics” (F. Lévi, Villejuif) Defining chronotoxicity profiles for Camptothecins and CDK inhibitors

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