Lingchong You

1. BME 265-05. March 31, 2005 Modeling T7 life cycle Lingchong You

2. Individual appointments (1hr/group) next week Project report due today! • Monday: 1pm-6pm • Tuesday: 9:30am-11:30am & 1:30-5:30pm

4. Bacteriophages: landmarks in molecular biology 1939 one-step growth of viruses 1946 Genetic recombination 1947 Mutation & DNA repair 1952 DNA found to be genetic material, restriction & modification of DNA 1955 Definition of a gene 1958 Gene regulation, definition of episome 1961 Discovery of mRNA, elucidation of triplet genetic code, definition of stop codon 1964 Colinearity of gene and polypeptide chain 1966 Pathways of macromolecular assembly 1974 Vectors for recombination DNA technology Source: Principles of Virology. Flint et al, 2000.

5. Applications • Phage therapy (kills bacteria, not animal cells) For review: http://www.evergreen.edu/phage/phagetherapy/phagetherapy.htm & http://www.phagetherapy.com/ptcompanies.html • Phage display (high-throughput selection of proteins with desired function • Expression systems based phage elements • E.g. T7 RNA polymerase (very high efficiency)

6. Phage T7 • A lytic virus; infects E. coli • Life cycle ~ 30 min at 30°C • Genome (40kbp), 55 genes, 3 classes (Source: Novagen) E. coli RNAP promoters T7 RNAP promoters RNAse splicing sites

7. 1 cycle ~ 30 min at 30 °C Source: http://icb.usp.br/~mlracz/animations/kaiser/kaiser.htm Phage T7 life cycle

8. Class I Class II Class III T7 genome programs a dynamic infection process Genome Gene functions T7 RNAP expression, host interference host DNA digestion, T7 DNA replication T7 particle formation, DNA maturation and host lysis

9. Example: modeling transcription 1. Compute the number of RNAPs allocated to gene i RNAP pi gene i 2. Track the level of mRNA for gene i mRNA decay rate constant RNAP elongation rate

10. Transcription (II) Elongation rates of EcRNAP and T7RNAP Decay rate constant of the mRNA Density of EcRNAP allocated to the mRNA Density of T7RNAP allocated to the mRNA

11. Translation Ribosome elongation rate Decay rate constant of the protein Density of ribosome on mRNAs

12. 92 coupled ordinary differential equations and 3 algebraic equations. • 50 parameters from literature • host cell treated as a bag of resources. Endy et al, Biotech. Bioeng. 1997 Endy et al, PNAS, 2000 You et al, J. Bact., 2002

14. Simulated versus measured T7 growth(host growth rate = 1.5 doublings per hour) • Experimental • Grow E. coli in a rich medium at 30C • Use chloroform to break open cells • Determine intracellular progeny over time

15. Applications of the T7 model – a “digital virus” • Effects of host physiology on T7 growth (You et al, 2002 J. Bact.) • Quantifying genetic interactions (You & Yin, 2002, Genetics) • Design features of T7 genome (Endy et al. 2000. PNAS, You & Yin. 2001, Pac. Symp. Biocomput.) • Methods to infer gene functions from expression data (You & Yin, 2000, Metabolic Eng.) • Generating data sets for evaluating reverse engineering algorithms?

16. Effects of host physiology on T7 growth —A nature-nurture question Nurture (E. coli host) Nature (Genome) You, Suthers & Yin (2002) J. Bact.

17. How does T7 growth depends on the overall physiology of the host? • What host factors contribute most to T7 development?

18. Measuring the dependence of T7 growth on E. coli growth rate (experimental) Chemostat Fresh medium • Start infection • Measure T7 growth • Extract rise rate & eclipse time Overflow Cell growth rate  Feed rate

19. Phage grows faster in faster-growing host cells host growth rate = 0.7 doublings/hr 1.0 T7 particles /bacterium 1.7 1.2 minutes post infection Experiments by Suthers

20. Phage grows faster in faster-growing host cells rise rate eclipse time simulation with one-parameter adjustment simulation T7 particles/min minutes simulation host growth rate (doublings/hour) Experiments by Suthers

21. What’s the most important host factor contributing to T7 growth? Bremer & Dennis, 1996 Donachie & Robinson, 1987 E. coli growth rate RNAP number RNAP elongation rate Ribosome number Ribosome elongation rate DNA content Amino acid pool size NTP pool size Cell volume host growth rate (hr-1) determine correlates T7 growth • rise rate • eclipse time

22. T7 growth is most sensitive to the host translation machinery Default setting: host growth rate = 1.5 hr-1

23. Summary: effects of host physiology • Phage grow faster in faster growing host cells (experiment & simulation) • Phage growth depends most strongly on the translation machinery (simulation)

24. Probing T7 “design” in silico(You & Yin, manuscript in preparation) Engineers’ solutions for (by design) purifying plasmid DNA (http://www.drm.ch/pages/aml.htm) producing H2SO4 (http://www.enviro-chem.com) Nature’s “solution” for T7 survival (by evolution)

25. Probing T7 “design” in silico • Ideal features: • Efficiency • Productivity • Robustness Engineers’ solutions for (by design) purifying plasmid DNA (http://www.drm.ch/pages/aml.htm) producing H2SO4 (http://www.enviro-chem.com) Nature’s “solution” for T7 survival (by evolution)

26. Learning from Nature: What’s the rationale of T7 design? How will T7 respond to changes in its parameters or genomic structure? Does the environment play a role?

27. Hypothesis T7 has evolved to maximize its fitness in environments having limited resources Fitness definition T7 particles/cell minutes post infection

28. Unlimited RNAP =  Ribosome =  NTP =  Amino acid =  DNA =  Limited (Cell growth rate = 1.0 hr-1) RNAP = 503 Ribosome = 10800 NTP = 5.5e7 Amino acid = 8.7e8 DNA = 1.8 (genome equivalents) Two contrasting host environments

29. Probing T7 design by perturbing… • Parameters • Single parameter perturbations • Random perturbations on multiple parameters • Genomic structure • Sliding mutations • Permuted genomes Expectation: Wild-type T7 is optimal for the limited environment but sub-optimal for the unlimited environment

30. T7 is robust to single parameter perturbations; the wild type is nearly optimal in the limited environment Unlimited Limited base case (wild type) normalized fitness normalized promoter strengths

31. T7 is robust to random perturbations in multiple parameters; the wild type is nearly optimal in the limited environment Limited Unlimited wt wt 5.3 % 24 % number of mutants normalized fitness 50,000 mutants

32. Sliding mutations: move an element to every possible position Toy string: 1234 1234, 2134, 2314, 2341 72 variants for each element T7:

33. Slidinggene 1 (T7RNAP gene): wild-type position is optimal in the limited environment Unlimited Limited normalized fitness wt wt gene 1 position (kb) 1

34. In the unlimited environment: positive feedback  faster growth T7RNAP promoter Gene 1

35. Negative feedback  robustness - T7RNAP gp3.5 + Unlimited environment

36. Negative feedback  robustness - + EcRNAP T7RNAP gp3.5 + - + gp2 Limited environment

37. Genome permutations 24 combinations • 1243 1324 1342 1432 1423 • 2134 2143 2314 2341 2413 2431 • 3124 3142 3214 3241 3412 3421 • 4123 4132 4213 4231 4312 4321 1234 72! = 6x10103 combinations

38. T7 is fragile to genomic perturbations; the wild type is optimal for the limited environment Unlimited Limited 82% dead 83% dead 5 % number of mutants normalized fitness 100,000 mutants

39. Features of T7 design • Optimality • The wild-type T7 is nearly optimal for the limited environment • Optimality especially distinct in the genome structure • Robustness and Fragility • Robust to perturbations in parameters, but very fragile to its genomic structure • Negative feedback loops  robustness

40. Quantifying genetic interactions using in silico mutagenesis

41. Genetic interaction between two deleterious mutations

42. Genetic interactions among multiple deleterious mutations Power model: log(fitness) = - a n b n: # deleterious mutations synergistic (  > 1) antagonistic ( 0<  < 1) multiplicative (  = 1)

43. Genetic interactions are important for diverse fields • Robustness of biological systems (engineering) • Evolution of sex (population biology & evolution) But difficult to study experimentally…

44. Difficulties in characterizing genetic interactions experimentally • Obtaining mutants with many deleterious mutations systematically. • Estimating the number of mutations • Accurately quantifying fitness and mutational effects Example: experimental test of synergistic interactions in E. coli: 225 mutants, three data points (too few). (Elena & Lenski, Nature, 1997)

45. Goal: to elucidate the nature of genetic interactions using the T7 model ?

46. In silico mutagenesis • Select mutation severity • For n (# mutations) = 1 to 30 • Construct 500 T7 mutants, each carrying n random mutations • Compute the fitness(for poor or rich environments) of each mutant • Compute the average and the standard deviation of log(fitness) values • Plot log(fitness) ~ n, and fit with power model.

47. Nature of genetic interactions depends on environment poor rich average of 500 mutants log(fitness) standard deviation synergistic antagonistic number of mild mutations

48. Nature of genetic interactions depends on severity of mutations poor rich log(fitness) increasing severity increasing severity number of mutations

49. Summary: the nature of genetic interactions Weak interaction Antagonistic interaction Severe Severity of mutations Synergistic interaction Weak interaction Mild Poor Rich Environment

50. Take-home messages • Existing data & mechanisms at the molecular level can be integrated to create computer models • Such models can serve as “digital organisms”, and facilitate the study of fundamental and applied biological questions.