1. Systems/Computational Biology (I) Introduction Kevin Burrage and Andre Leier Advanced Computational Modelling Centre The University of Queensland leier@acmc.uq.edu.au kb@maths.uq.edu.au Introduction to Systems Biology

3. The cell

4. Wish to understand different types of dynamical processes and transports within a cell through experimentation (Single Particle Tracking, microarrays etc), mathematical models and simulations. Three D EM image of a insulin mammalian secreting cell (Marsh)

5. I. Cell Membranes and Lipid Rafts Magnify a cell a million times Water molecule: full stop; Protein: ping pong ball; Ribosome: soccer ball; Mitochondion: person; Nucleus: car; Cell membrane: <1 cm thick! Singer and Nicholson, 1972: “protein icebergs floating in a sea of lipids”

6. II. Segmental oscillating gene expression Chick embryo

7. III. Tubulation Untreated cells have little tubulation Massive tubulation event following EGF treatment

8. Modelling and Simulation

9. In silico humans-spatial & temporal scales 1 mperson 1 mmelectrical length scale of cardiac tissue 1  mcardiac sarcomere spacing 1 nmpore diameter in a membrane protein Range = 10 9 Requires a hierarchy of inter-related models pathway models ODEs stochastic models PDEs (continuum models) gene reg. networks 10 9 s (70 yrs) human lifetime 10 6 s (10 days) protein turnover 10 3 s (1 hour) digest food 1 sheart beat 1 msion channel HH gating 1  sBrownian motion Range = 10 15

10. Michaelis – Menten Reaction The stoichiometric vectors are and the Law of Mass Action gives

11. An example: a system with three species of molecules and four reactions If the current state is (x1,x2,x3)=(100,100,100), After reaction 2, (x1,x2,x3)=(98, 101,100) 4, (x1,x2,x3)=(98, 100,101) The four state transfer vectors are

12. (CalBioChem) MAP kinase pathways in the cell: components, regulation, translocation and crosstalk between different signalling pathways

13. MAP kinase pathway activated by EGF receptor (230 reactions and 94 species) (Black: plasma membrane and cytosol, Green: internalized subsystem) (Schoeberl, et al., Nature Biotech., 2002)

14. Basics of Molecular Cell Biology - A Review

15. All Living Things Are Made of Cells Cells have a variety of different shapes, sizes and functions, grow and divide (reproduce themselves), convert energy / digest, sense and respond to their environment, are able to swim and to cooperate to form complex organisms, … HOW DOES THIS WORK?

16. All Living Things Are Made of Cells (cont.) Alberts et al., Molecular Biology of the Cell, 4th Edition (2002).

17. The Cell – A Chemical Factory Basic constituents inside cells are sugars (monosaccharides) fatty acids nucleotides amino acids plus some ions, water (~70%), other organic molecules. These are linked into macromolecules All cells are governed by the same chemical machinery. Alberts et al., Molecular Biology of the Cell, 4th Edition (2002).

18. Genetic Regulation and cascading reactions

19. Elements of Genetic Regulatory Networks Transcription factors bind to DNA sequences in regulatory regions of genes. Binding regulates the rate at which transcripts (polymerase) of the gene are initiated. Protein is made off mature mRNA transcripts by translation (ribososomes). Central Dogma: DNA RNA Protein transcriptiontranslation Feedback: DNA RNA Protein

20. DNA and its Building Blocks Genetic information is encoded in the nucleotide sequence. Prokaryotes: DNA in the cytoplasm; Eukaryotes: DNA in the nucleus (packaged into chromosomes). Genome: all cell DNA. Alberts et al., Molecular Biology of the Cell, 4th Edition (2002).

21. Gene Control Region Promoter: DNA sequence to which RNAP binds to begin transcription. Transcription factor (TF): protein required to initiate or regulate transcription. Alberts et al., Molecular Biology of the Cell, 4th Edition (2002).

22. From DNA to Proteins: Transcription and Translation (cont.) Differences in eukaryotic and prokaryotic cells: Alberts et al., Molecular Biology of the Cell, 4th Edition (2002).

23. From DNA to Proteins: Transcription and Translation (cont.) A ribosome translates mRNA (using tRNA). Transcription initiation by RNA polymerase (RNAP) II in an eukaryotic cell. Alberts et al., Molecular Biology of the Cell, 4th Edition (2002).

24. Regulation Of Gene Expression Alberts et al., Molecular Biology of the Cell, 4th Edition (2002). Controlled by environmental signals (ligands bind to receptors)

25. Biology and Noise

26. Biological Evidence of noise “ Stochasticity is evident in all biological processes … the proliferation of both noise and noise reduction systems is a hallmark of organismal evolution” – Federoff et al.(2002). “Transcription in higher eukaryotes occurs with a relatively low frequency in biologic time and is regulated in a probabilistic manner” – Hume (2000). “Gene regulation is a noisy business” – Mcadams et al. (1999).

27. Stochastic mechanisms Physiological activity and cell differentiation within a mammalian cell is controlled by more than 10,000 protein coding genes. Many genes are expressed at low level copy numbers, which gene profiling methods cannot reliably detect. “Initiation of gene transcription is a discrete process in which individual protein-coding genes in an off state can be stochastically switched on, resulting in sporadic pulses of mRNA production” – Sano 2001.

28. Internal Noise: stochastic fluctuations in number of proteins. Discrete interacting processes. CTRW describes position x(t) Waiting time and jump y sampled from Sampled from Gaussian Sampled from Exponential Leads to Bownian motion and diffusive limit is Diffusion Eqn. External Noise: fluctuations in environment/control parameters. Continuous Wiener processes. Phenotypic noise : leading to qualitative differences in a cell phenotype (example: lysis-lysogen pathway). Stablizable noise: leading to fluctuations in protein concentrations (robustness properties of biological systems).

29. Brownian Motion Brown – 1827, Scottish Botanist Einstein – 1905, Einstein relation Mesh example PDE, Diffusion PDF CLT {X j } iid, X is N dist i-1 i i+1 D = Diffusion Constant N(0,2Dt),

30. Observation: In a stochastic simulation there is no one right answer. We may compute a single simulation for insight; compute many ensembles and compute statistics; solve a Fokker-Planck Eqn for the pdf.

31. Modelling Regimes Discrete and stochastic – Small numbers of molecules. Exact description via Stochastic Simulation Algorithm (SSA) - Gillespie. Large computational time. Continuous and stochastic - A bridge connecting discrete and continuous models. Described by SDEs – The Chemical Langevin Equation. Continuous and deterministic – Law of Mass Action. The Reaction Rate equations. Described by ordinary differential equations. Not valid if molecular populations of some critical reactant species are small.

32. Noise in genetic regulatory networks The Central Dogma |____________regulation___________| For example, biological reactions in gene network (X: transcriptional factor, D: binding site) 1.Binding reaction 2.Transcription 3.Translation 4.Degradation

34. A regulatory model 10 reactions, 6 unknowns. m (monomer protein) D (dimer transcription factor) RNA (mRNA produced by transcription) DNA (free of dimers) DNA1 (bound by D at binding site R1) DNA2 (bound at sites R1 and R2). X = (m, D, RNA, DNA, DNA1, DNA2). t_end = 600; X_initial=[2 6 0 2 0 0]';

36. Transcription to mRNA when D occupies R1; mRNA translated into proteins (both can decay); protein dimerises to transcription factor, D; binding of D at R1 activates transcription of m; binding of D at R2 excludes RNA polymerase from binding and transcription repressed.

38. The Hes1 gene

39. Hes1 oscillates in cultured mouse cells Hirata et al., Science 298, 840–843 (2002). Half–lives: mRNA: ~24 min protein: ~22 min … but a non-delayed (ODE) model cannot oscillate… Hirata et al. predicted extra components in the feedback loop. hes1Hes1 mRNA Hes1 protein –

40. Eukaryotic transcription and time delays There is an irreducible delay of ~15–20 min from initiation of a transcript to appearance of functional mRNA in the cytoplasm The delay can be much longer (>16 hrs for human dystrophin) Delay equations should be used to model transcription

41. Delay estimates RNA polymerase moves along DNA at 20 nucleotides/sec; Genome size; 8 minutes for introns to be spliced out; 4 minutes after splicing before mRNA in cytosol; mRNA translated by ribosomes at 6 nucleotides/sec.

42. Monk model for the Hes1 feedback loop  = 18.5 min The transcriptional delay has now been observed directly for Hes7 Bessho et al. Genes & Dev. 17, 1451 (2003). x hes1Hes1 mRNA Hes1 protein y  g is a hill function with n  4 – co-operativity

43. Thank you