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Computational Systems Biology … Biology X – Lecture 2 …

Computational Systems Biology … Biology X – Lecture 2 …. Bud Mishra Professor of Computer Science, Mathematics, & Cell Biology. Syllabus: Biology X. Evolutionary Biology Computability in Biology Reconstructibility in Biology Biology of Cancer Biology of Aging. Basic Biology

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Computational Systems Biology … Biology X – Lecture 2 …

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  1. Computational Systems Biology…Biology X – Lecture 2… Bud Mishra Professor of Computer Science, Mathematics, & Cell Biology

  2. Syllabus: Biology X • Evolutionary Biology • Computability in Biology • Reconstructibility in Biology • Biology of Cancer • Biology of Aging

  3. Basic Biology Genome Structure: Retro-Elements and their distributions Physical Properties of a genome Large Segmental Duplications Models of Segmental Duplications Genome Evolution: Point Mutations Rearrangements Evolution by Duplication RNA evolution Model Evidence for Evolution Luria-Delbruck JAckpot Polymorphisms SNPS & CNPS Haplotyping and Haplotype phasisng Genetics Linkage Analysis Association Studies Phylogeny Algorithms for Phylogenetic Trees. Evolutionary Biology

  4. Models in Biology Regulatory Networks Metabolic Networks Signaling Networks KMA Models: ODE’s describing Regulatory Networks How to create such models Questio of Reachability Hybrid Models Basic Definitions Classes of Hybrid Models Model Checking: CTL and Basic Model Checking algorithms TCTL and RTL Algorithmic problems Examples Computability in Biology

  5. Biological Networks Protein-DNA and Protein-Protein Interactions Two hybrid experiments Motifs and Scale-Free Networks Origi of strctures Network Reconstruction From Microarray Data Techniques based on Linear and non-linear regression The issue of sparsity Theory of Information Bottleneck Clustering using IB, side-information and ontology Analysis of Time-Course Data GOALIE Reconstructibility in Biology

  6. Cancer A Genomic Disease Cancer Data Analysis Genomic Data Transcriptomic Data Proteomic Data Cancer Gene Discovery Somatic Evolution n Cancer Theories of Origin of Cancer Biology of Cancer

  7. Theories of Aging: Hayflick’s model Mitochodria and Oxidative Stress Stem Cells & Niche-Clonality Genome Evolution Proteomic Explanation: E.g, Protein Degradation Key Experiments in Animals Examples: Deinococcus radiodurans Tradigrades C. Elgans Anti-Aging Immortality Biology of Aging

  8. HookeThursday 25 May 1676 Damned Doggs. Vindica me deus. • Commenting on Sir Nicholas Gimcrack character in The Virtuoso, a play by Thomas Shadwell.

  9. Hookein the Royal Society, 26 June 1689 • “I have had the misfortune either not to be understood by some who have asserted I have done nothing… • “Or to be misunderstood and misconstrued (for what ends I now enquire not) by others… • “And though many things I have first Discovered could not find acceptance yet I finde there are not wanting some who pride themselves on arrogating of them for their own… • “—But I let that passe for the present.”

  10. Hooke… • “So many are the links, upon which the true Philosophy depends, of which, if any can be loose, or weak, the whole chain is in danger of being dissolved; • “it is to begin with the Hands and Eyes, and to proceed on through the Memory, to be continued by the Reason; • “nor is it to stop there, but to come about to the Hands and Eyes again, and so, by a continuall passage round from one Faculty to another, it is to be maintained in life and strength.”

  11. Application: Modeling Apoptosis

  12. Cell Death • Cell shrink, organelles swell, chromatin condenses, DNA fragmented, cell junctions disintegrated, membrane blabbing, finally get engulfed—all within 30 minutes.

  13. TNF TRADD* FADD* Simplified Apoptotic Pathway FasL Fas TNF-R1 Intracellular stimuli Mitochondria Cas-8/-10 CytC Cas-9 APAF-1 Cas-3/-6/-7 *FADD: Fas associate death domain protein DNase Cell death *TRADD: TNF associate death domain protein

  14. What are Caspases? • First caspase was found in C. elegans, ced-3 gene (1993). An acronym for: • Cystein aspartate-specific protease • Activated by proteolysis; Many substrates (~40 and increasing) such as PARP (Poly (ADP-ribose) polymerase, BID (Bcl2-interacting domain) • Identified genes so far: • C. elegans (4), Drosophila (7), Human and mouse (11) • Number of caspases over phylogenetic time seems to have been increasing

  15. APAF1/casp9 holoenzyme Active holoenzyme APAF1 dATP Cytochrome c APAF1 complex Autoproteolytic process Pro-casp3 Active casp3 Procasp9 DEVD-Afc APAF1/cytc oligomer *DEVD: fluorescence protein Formation of Holoenzyme Complex *APAF1: Apoptosis activating factor1

  16. Scheme of the Analysis CytC APAF1 dATP proCas9 (pC9) APAF1/CytC/dATP DEVD-Afc Afc (fluorescence reactant) APAF1/CytC/dATP/pC9 (inactive apoptotic holoenzyme) Dissociate toAPAF1/Cytc/dATPand C9* *APAF1/CytC/dATP/C9 (active holoenzyme) C3 (activated) pC3

  17. Determine reaction parameters based on the experimental data What are the parameters

  18. Individual steps in Caspase-9 pathway k-1=2000 i0 APAF1 + dATP APAF1/dATP k2=2 k1=1000 [4nM] [5000nM] k-1=1720 APAF1/dATP + CytC i1 APAF1/dATP/CytC k2=0.5 k1=1000 [1200nM] k-1=20000 APAF1/CytC/dATP + pC9 i2 APAF1/CytC/dATP/pC9 k2=100 k1=200 [20nM]

  19. Individual steps in Caspase-9 pathway APAF1/CytC/dATP/pC9 APAF1/CytC/dATP/Caspase9 k1=3 APAF1/CytC/dATP/Caspase9 APAF1/CytC/dATP + free Caspase9 k1=0.5 k1=6 pC3 i3 free Caspase3 k-1=1080 k2=20 [15nM] k1=5000 DEVD/Afc i4 Afc k-1=50000 k2=90 [40000nM]

  20. First reaction 1. APAF1 (α): (Initial concentration (α0) = 4nM) 2. dATP (δ): (Initial concentration (δ0) = 5000nM) 3. C: Intermediate of APAF1/dATP complex (Initial concentration (C0) = 0) 4. APAF1/dATP (ω): Initial concentration (ω0)= 0 κ-1=2000 C APAF1 + dATP APAF1/dATP κ2=2 κ1=1000 [4nM] [1200nM] dα/dt = - κ1 * [α ] * [δ] κ0 + κ-1 * [C] - 2 * κ2 dδ/dt = - κ1 * [α ] * [δ] κ0 + κ-1 * [C] - 2 * κ2 dC/dt = + κ1 * [α ] * [δ] κ0 - κ-1 * [C] - 2 * κ2 dω/dt = + κ1 * [α ] * [δ] κ0 - κ-1 * [C] + 2 * κ2 Enzyme Kinetics

  21. Simpathica: Simulation for the Biological Pathway • http://www.bioinformatics.nyu.edu/Projects/Simpathica/

  22. Simpathica generates differential equations from scipy import * from scipy.integrate import * from Numeric import * class ___simpathica: def jack1027dATP1(self, X, t): xdot = [] xdot.append( + -1*(+600000000*X[1]**(+1)*X[0]**(+1)) + +1*(+.006*X[13]**(+1)) ) xdot.append( + -1*(+600000000*X[1]**(+1)*X[0]**(+1)) + +1*(+.006*X[13]**(+1)) ) xdot.append( + +1*(+2*X[13]**(+1)) + -1*(+1000*X[3]**(+1)*X[2]**(+1)) + +1*(+1720*X[14]**(+1)) ) xdot.append( + -1*(+1000*X[3]**(+1)*X[2]**(+1)) + +1*(+1720*X[14]**(+1)) ) xdot.append( + +1*(+.5*X[7]**(1)) + +1*(+0.5*X[14]**(+1)) + -1*(+200*X[5]**(+1)*X[4]**(+1)) + +1*(+20000*X[15]**(+1)) ) xdot.append( + -1*(+200*X[5]**(+1)*X[4]**(+1)) + +1*(+20000*X[15]**(+1)) ) xdot.append( + -1*(+3*X[6]**(1)) + +1*(+100*X[15]**(+1)) ) xdot.append( + +1*(+3*X[6]**(1)) + -1*(+.5*X[7]**(1)) + -1*(+6*X[8]**(+1)*X[7]**(+1)) + +1*(+1080*X[16]**(+1)) + +1*(+20*X[16]**(+1)) ) xdot.append( + -1*(+6*X[8]**(+1)*X[7]**(+1)) + +1*(+1080*X[16]**(+1)) ) xdot.append( + +1*(+20*X[16]**(+1)) + -1*(+5000*X[11]**(+1)*X[9]**(+1)) + +1*(+50000*X[17]**(+1)) + +1*(+90*X[17]**(+1)) ) xdot.append( + +1*(+.5*X[7]**(1)) ) xdot.append( + -1*(+5000*X[11]**(+1)*X[9]**(+1)) + +1*(+50000*X[17]**(+1)) ) xdot.append( + +1*(+90*X[17]**(+1)) ) xdot.append( + +1*(+600000000*X[1]**(+1)*X[0]**(+1)) + -1*(+.006*X[13]**(+1)) + -1*(+2*X[13]**(+1)) ) xdot.append( + +1*(+1000*X[3]**(+1)*X[2]**(+1)) + -1*(+1720*X[14]**(+1)) + -1*(+0.5*X[14]**(+1)) ) xdot.append( + +1*(+200*X[5]**(+1)*X[4]**(+1)) + -1*(+20000*X[15]**(+1)) + -1*(+100*X[15]**(+1)) ) xdot.append( + +1*(+6*X[8]**(+1)*X[7]**(+1)) + -1*(+1080*X[16]**(+1)) + -1*(+20*X[16]**(+1)) ) xdot.append( + +1*(+5000*X[11]**(+1)*X[9]**(+1)) + -1*(+50000*X[17]**(+1)) + -1*(+90*X[17]**(+1)) ) return xdot initial = [ 4,1200,0,5E+6,0,20,0,0,15,0,0,40000,0,0,0,0,0,0] compoundsNames = ["APAF1", "cytc", "APAF1/cytc", "dATP", "APAF1/cytc/dATP", "pC9", "APAF1/cytc/dATP/pC9", "APAF1/cytc/dATP/casp9", + "pC3", "free Casp3", "free Casp9", "DEVD-Afc", "Afc", "i0", "i1", "i2", "i3", "i4"] functionName = "___simpathica().jack1027dATP1"

  23. Binding order? Active casp3 Non-Linear? Inhibition Pro-casp3 Questions that can be answered by Simpathica APAF1 Cytochrome c dATP APAF1/cytc oligomer Pro-casp9 casp9 APAF1/casp9 holoenzyme Active holoenzyme DEVD-Afc X factors? Afc fluorescent

  24. Model Checking: Recombinant System Use purified recombinant components Easy to determine rate changes (synthesis or degradation)

  25. E1A cells RNAi(APAF-1) mix Extract with little APAF1 Extract with APAF1 100% 80% 70% 60% 40% 20% 0% Measure the caspase 3 activity of the mixed cell extract Model Checking: In Vitro Assay • Mix RNAi(APAF-1) treated and untreated E1A cell extract.

  26. Simpathica recapitulates the holoenzyme formation process 25 APAF1 APAF1/dATP APAF1/cytc/dATP 20 pC9 APAF1/cytc/dATP/pC9 APAF1/cytc/dATP/casp9 pC3 15 free Casp3 free Casp9 Afc_rate Concentration (nM) 10 5 0 -5 0 5 10 15 20 25 30 35 Time (min) Rodriguez and Lazebnik (1999) Simulation in Simpathica

  27. APAF1 cytc APAF1 dATP APAF1/cytc dATP APAF1/dATP cytc APAF1/cytc/dATP APAF1/cytc/dATP Which molecule initiates caspase-9 pathway? Model (I) Model(II) APAF1 Cytochrome c APAF1 dATP dATP Cytochrome c APAF1 oligomer APAF1 oligomer

  28. 70 60 50 40 30 20 10 0 0 20 40 60 80 100 120 -10 Model (I): CytC first Model (II): dATP first 350 140 300 120 250 100 200 80 Afc Rate Afc Rate 150 60 100 40 50 20 0 0 0 20 40 60 80 100 120 0 20 40 60 80 100 120 cytc cytc Recombinant System Can Validate a Model DEVD-Afc rate@3min(fc/min) Lazebnik lab (CSHL) [cytc], uM, 3min

  29. Facilitates APAF-1multimerization •  model (I) (2) Activate holoenzyme  model (II) Are There Duals Roles for Cytochrome c? • Determine from experimental data: • Cytochrome c is needed for APAF-1 multimerization • Cytochrome c stays in the holoenzyme complex after multimerization • Cytochrome c may have another role

  30. 25 APAF1 APAF1/dATP pC9 APAF1/dATP/pC9 20 APAF1/dATP/casp9 pC3 free Casp3 free Casp9 Afc_rate 15 10 5 0 0 2 4 6 8 10 12 Results: Cytochrome c may NOT have a dual role Standard model Dual role of CytC 20 APAF1 APAF1/dATP APAF1/cytc/dATP pC9 APAF1/cytc/dATP/pC9 15 APAF1/cytc/dATP/casp9 pC3 free Casp3 free Casp9 Afc_rate Early 10 5 0 0 2 4 6 8 10 12 Concentration (nM) teq = 18 teq = 14 25 25 APAF1 APAF1 APAF1/dATP APAF1/dATP APAF1/cytc/dATP pC9 20 pC9 20 APAF1/dATP/pC9 APAF1/cytc/dATP/pC9 APAF1/dATP/casp9 APAF1/cytc/dATP/casp9 pC3 pC3 free Casp3 15 15 free Casp3 free Casp9 free Casp9 Afc_rate Afc_rate Late 10 10 5 5 0 0 -5 -5 0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35 Time (min)

  31. APAF-1 unit binding: Binding rate (γ) Next APAF-1 unit binding: next binding rates (γ2 = γ1) or (γ2 >> γ1) Is there cooperative binding during the formation of APAF-1 complex? γ γ γ Multiple APAF-1 units promote the binding of the next APAF-1 unit.

  32. Modeling the formation of APAF-1 oligomer APAF-1 complex unit γ1 Model (I) γ2 = γ1 Model (II) γ2 >> γ1

  33. Model (I): γ2 = γ1 Model (II): γ2 >> γ1 800 70 700 60 600 50 500 40 Afc Rate 400 Afc Rate 30 300 20 200 10 100 0 0 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 [APAF1] [APAF1] APAF-1 titration in recombinant system 95 75 55 DEVD-Afc rate@37Cx5min(fc/min) 35 15 Lazebnik lab (CSHL) -5 0 10 20 30 40 50 60 70 [APAF1], nM, 0.2mMdATP

  34. 2nd Procasp9 binding: APAF1/ casp9 interaction + Casp9/casp9 interaction (δ2 = δ1) or (δ2 >> δ1) 1st Procasp9 binding: Only APAF1/casp9 interaction (δ1) Is there cooperative binding during the holoenzyme formation? Recruitment of 1st Procasp9 promotes the binding of the 2nd Procasp9.

  35. Modeling the formation of holoenzyme Pro-casp9 Multimeric APAF-1 complex δ1 Pro-casp9 Model (II) δ2 >> δ1 Model (I) δ2 = δ1

  36. 50 45 40 Model (I) δ2 = δ1 Model (II) δ2 >> δ1 35 30 Afc Rate 25 20 15 γ2 = γ1 10 5 0 0 10 20 30 40 50 60 70 APAF1 γ2 >> γ1 Cooperative behavior of holoenzyme is due to the binding of APAF-1 complex

  37. Active casp3 Active casp3 Active casp3 Pro-casp3 Pro-casp3 Pro-casp3 Free Caspase-9 Activity Caspase-9 is much more active in holoenzyme, and free caspase-9 have little activity (Rodriguez et al., Genes & Dev., 1999). Is it valid? Model (I) Model (II) APAF1/cytc oligomer APAF1/cytc oligomer Pro-casp9 Pro-casp9 casp9 casp9 APAF1/casp9 holoenzyme APAF1/casp9 holoenzyme Active holoenzyme Active holoenzyme

  38. 120 100 90 100 80 70 80 60 60 Afc Rate 50 Afc Rate 40 40 30 20 20 10 0 0 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 APAF1 APAF1 Caspase-3 Activity may not depend on Free Caspase-9 Model (I): Only holoenzyme activates Casp3 Model (II): Free casp9 also activates casp3

  39. Active casp3 Pro-casp3 Caspase-9 inhibition XIAP is thought to bind apoptosome via caspase9 and inhibit its activity. Does it exert a significant inhibition at that point? APAF1/cytc oligomer Pro-casp9 casp9 XIAP* APAF1/casp9 holoenzyme Active holoenzyme Inactive holoenzyme *XIAP: human inhibitor of apoptosis

  40. Simulate Caspase-9 inhibition

  41. XIAP Simulation with Simpathica k-1 = 50 APAF1/CytC/dATP/casp9 + XIAP APAF1/CytC/dATP/casp9/XIAP k1 = 0.5 [50nM] No XIAP With XIAP Concentration (nM) Time (min)

  42. Summary • Simpathica recapitulates • Formation of Caspase9/APAF1 holoenzyme. • dATP binds to APAF-1 and initiates the caspase-9 pathway. • Cytochrome c is not necessary to activate holoenzyme. • Non-linear interaction is due to cooperative binding of APAF-1 complex unit. • Free caspase-9 is not necessary to activate caspase-3.

  43. Recombinant system In vitro system 300 95 250 75 200 DEVD-Afc rate@37Cx5min(fc/min) 55 150 DEVD-Afc rate@37Cx10min 100 35 50 15 0 -5 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 -50 [rAPAF1], nM, 0.2mMdATP [rAPAF1], nM, 0.2mM dATP Lazebnik lab (CSHL) CONUNDRUM • Different outcomes from two experimental systems Find possible regulators with simulation model

  44. Other Examples • C. elegans (Gonad) • Yeast and Mammalian Cell Cycle • Wnt Signaling • Host-pathogen Interactions • RAS pathways…

  45. Some Biology

  46. Introduction to Biology • Genome: • Hereditary information of an organism is encoded in its DNA and enclosed in a cell (unless it is a virus). All the information contained in the DNA of a single organism is its genome. • DNA molecule • can be thought of as a very long sequence of nucleotides or bases: • S= {A, T, C, G}

  47. Complementarity • DNA is a double-stranded polymer • should be thought of as a pair of sequences over S. • A relation of complementarity • A , T, C , G • If there is an A (resp., T, C, G) on one sequence at a particular position then the other sequence must have a T (resp., A, G, C) at the same position. • The sequence length • Is measured in terms of base pairs (bp): Human (H. sapiens) DNA is 3.3 £ 109 bp, about 6 ft of DNA polymer completely stretched out!

  48. Genome Size • The genomes vary widely in size: • Few thousand base pairs for viruses to 2 » 3 £ 1011bp for certain amphibian and flowering plants. • Coliphage MS2 (a virus) has the smallest genome: only 3.5 £ 103bp. • Mycoplasmas (a unicellular organism) has the smallest cellular genome: 5 £ 105bp. • C. elegans (nematode worm, a primitive multicellular organism) has a genome of size » 108bp.

  49. DNA ) Structure and Components • Double helix • The usual configuration of DNA is in terms of a double helix consisting of two chains or strands coiling around each other with two alternating grooves of slightly different spacing. • The “backbone” in each strand is made of alternating sugar molecules (Deoxyribose residues: C5 O4 H10) and phosphate ((P O4)-3) molecules. • Each of the four bases, an almost planar nitrogenic organic compound, is connected to the sugar molecule. • The bases are: Adenine ) A; Thymine ) T; Cytosine ) C; Guanine ) G

  50. Genome in Detail The Human Genome at Four Levels of Detail. Apart from reproductive cells (gametes) and mature red blood cells, every cell in the human body contains 23 pairs of chromosomes, each a packet of compressed and entwined DNA (1, 2).

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