dynamic processes in cells (a systems approach to biology)

Transcription

1 dynamic processes in cells (a systems approach to biology) jeremy gunawardena department of systems biology harvard medical school lecture 9 6 october 2015

2 blood work hematopoietic stem cell myeloid = from the bone marrow granulocytes monocytes platelet red blood cell basophil eosinophil B-cell T-cell mast cell neutrophil C/EBP macrophage PU.1 Laszlo et al, Cell 126:

3 neutrophil/macrophage differentiation eperiment phosphoglycerate kinase promoter PU.1 transcription factor tamoifen (OHT)-inducible estrogen receptor puromycin resistance PU-/- myeloid progenitor cells were transformed and clones selected which epressed PUER at low (PUER lo ) and high (PUER hi ) levels individual PUER hi cells ehibit a mied lineage of macrophage and neutrophil markers 1 day after OHT treatment single-cell multiple RT-PCR transcriptional priming how does mied lineage transcriptional priming arise?

4 neutrophil/macrophage differentiation theory nonlinear dynamical system BISTABILITY cross-antagonism neutrophil macrophage C/EBP PU.1 PU.1 C/EBP primary determinants can remain high despite lineage resolution Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering, Westview Press, 2001

5 quantitative to qualitative dynamics k 1 constant production k 2 first order degradation from a quantitative analytical solution to a qualitative geometric perspective PARAMETER SPACE k 2 STATE SPACE 0 0 k 1

6 nonlinear qualitative dynamics STATE SPACES PARAMETER SPACE 0 k k 1

7 state space landscapes and parameter geography STATE SPACES PARAMETER SPACE single stable state single stable state two stable and one unstable state stable limit cycle

8 state space landscapes and cellular identity Conrad Waddington Sui Huang Rudolf Jaenisch tri-stability dynamics on a potential surface Slack, Conrad Hal Waddington: the last renaissance biologist?, Nature Rev Genetics 3: Huang, Reprogramming cell fates: reconciling rarity with robustness, Bioessays, 31: ; Hana, Saha, Jaenisch, Pluripotency and cellular reprogramming: facts, hypotheses and unresolved issues, Cell 143:

9 dynamics in the state space steady states positive feedback by a gene on itself a potential way to create bistability a nonlinear dynamical system 1 2 b the first thing to calculate are the steady states because they are the skeleton around which the dynamics takes place

10 method of nullclines for 2D systems the 1 nullcline is the locus of points satisfying the 2 nullcline is the locus of points satisfying weakness of positive feedback STATE SPACES synthesis rates degradation rates stability of steady states depends on the eigenvalues of the Jacobian (lecture 4)

11 a stability theorem for genetic auto-regulation assume general transcription & translation functions, linear degradation and arbitrary (positive or negative) feedback 1 2

12 nullcline geometry determines stability 1 nullcline, in the 1 st quadrant, crosses above 2 nullcline, in the 1 st or 4 th quadrants STABLE nullcline, in the 1 st quadrant, crosses below 2 nullcline, in the 1 st quadrant UNSTABLE 2 1 see the nullcline theorem handout for details

13 positive auto-regulation of a single gene one stable steady state ( off ) one stable ( on ) and one unstable ( off ) steady state how do we make bistability with the off state and the on state both stable?

14 bistability requires sharpness positive feedback has to be combined with a sharp, sigmoidal ( S-shaped ) nullcline to create a threshold often referred to as cooperativity the model of Laszlo et al uses Hill-like functions activating repressing n A = 1 n R = Hill function Hill coefficient Hill-like functions are widely used in GRN models but the Hill function is not a legitimate GRF its denominator is not a valid partition function

15 the problem with Hill functions Archibald Vivian Hill oygen binding-curve of hemoglobin h A V Hill, The combinations of haemoglobin with oygen and with carbon monoide, Biochem J 7: The Hill equation remains what Hill intended it to be: an empirical descriptor Engel, A hundred years of the Hill equation, Biochem J /BJ Despite its appealing simplicity, the Hill equation is not a physically realistic reaction scheme, raising the question of whether it should be abandoned in favor of realistic schemes; at the very least, its limitations should be more widely recognized Weiss, The Hill equation revisited: uses and misuses, FASEB J 11:

16 aside a new interpretation for Hill functions recall slide 19 from lecture 8 TF binding at 3 sites with all-or-nothing epression the Hill line Hill functions define a Hopfield barrier at thermodynamic equilibrium Estrada, Wong, DePace, Gunawardena, Higher-order cooperativity and energy dissipation can sharpen switching of eukaryotic genes, submitted, 2015

17 testing bistability by hysteresis bistable systems ehibit history dependence to changes in parameters the switch between low and high (on/off) takes place at different values of the control parameter, depending on the starting state and the direction of change change parameter slowly ( adiabatically ) decreasing 2 steady state 2 high/low low/high 1 parameter

18 in practice Pomerening, Sontag & James Ferrell Building a cell cycle oscillator: hysteresis and bistability in the activation of CDC2, Nature Cell Biol 5: Sha, Moore, Chen, Lassaletta, Yi, Tyson & Sible, Hysteresis drives cell-cycle transitions in Xenopus laevis egg etracts, PNAS 100: Ozbudak, Thatai, Lim, Shraiman & van Oudenaarden, Multistability in the lactose utilization network of Escherichia coli, Nature 427: Isaacs, Hasty, Cantor & Collins, Prediction and measurement of an autoregulatory genetic module, PNAS 100:

19 bifurcations occur at the jumps local near a steady state; co-dimension one involving one parameter only the real part of an eigenvalue of the Jacobian goes through 0 1. a single real eigenvalue becomes 0 eigenvalues of the Jacobian in the comple plane symmetric under conjugation there are three normal forms for this

20 normal forms in the vicinity of the bifurcation, and in the vicinity of the steady state, the dynamics is given approimately by one of the following forms saddle-node k < 0 k = 0 k > 0 mutual annihilation transcritical stability echange pitchfork (supercritical) spawning

21 the Hopf bifurcation 2. a pair of comple conjugate eigenvalues reaches the imaginary ais eigenvalues of the Jacobian in the comple plane Selkov model (*) limit cycle (*) Strogatz, Nonlinear Dynamics and Chaos: with Applications to Physics, Biology, Chemistry and Engineering, Westview Press 2001

22 pluripotency in embryonic stem (ES) cells pre-implantation mouse blastocyst ES cells, GFP epression from Nanog locus serum + LIF, 2i ES cells Oct4 So2 Nanog weak linkage by variation/selection (lecture 6) Kalmar, Lim, Hayward, Munoz-Descalzo, Nichols, Garcia-Ojalvo, Martinez-Arias, Regulated fluctuations in Nanog epression mediate cell fate decisions in embryonic stem cells, PLoS Biol 7:e