Lingchong You

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BME 265-05. March 31, 2005
Modeling T7 life cycle
Lingchong You
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Individual appointments (1hr/group) next week
Project report due today!

• Monday 1pm-6pm
• Tuesday 930am-1130am 130-530pm

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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.
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Applications

• Phage therapy (kills bacteria, not animal cells)
• For review http//www.evergreen.edu/phage/phaget
  herapy/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)

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Phage T7

• A lytic virus infects E. coli
• Life cycle 30 min at 30C
• Genome (40kbp), 55 genes, 3 classes

(Source Novagen)
E. coli RNAP promoters
T7 RNAP promoters
RNAse splicing sites
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Phage T7 life cycle
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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
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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
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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
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Translation
Ribosome elongation rate
Decay rate constant of the protein
Density of ribosome on mRNAs
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• 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

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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

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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?

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Effects of host physiology on T7 growth A
nature-nurture question
Nature (Genome)
Nurture (E. coli host)
You, Suthers Yin (2002) J. Bact.
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• How does T7 growth depends on the overall
  physiology of the host?
• What host factors contribute most to T7
  development?

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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
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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
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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
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Whats 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

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T7 growth is most sensitive to the host
translation machinery
Default setting host growth rate 1.5 hr-1
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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)

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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)
Natures solution for T7 survival (by evolution)
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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)
Natures solution for T7 survival (by evolution)
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Learning from Nature Whats the rationale of
T7 design?
How will T7 respond to changes in its parameters
or genomic structure? Does the environment play
a role?
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• Hypothesis
• T7 has evolved to maximize its fitness in
  environments having limited resources

Fitness definition
T7 particles/cell
minutes post infection
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Two contrasting host environments

• 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)

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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
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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
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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
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number of mutants
normalized fitness
50,000 mutants
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Sliding mutations move an element to every
possible position
Toy string 1234
1234, 2134, 2314, 2341
72 variants for each element
T7
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Sliding gene 1 (T7RNAP gene) wild-type position
is optimal in the limited environment
Unlimited
Limited
normalized fitness
wt
wt
gene 1 position (kb)
1
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In the unlimited environment positive feedback
? faster growth
T7RNAP
promoter
Gene 1
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Negative feedback ? robustness
-
T7RNAP
gp3.5

Unlimited environment
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Negative feedback ? robustness
-

T7RNAP
gp3.5
EcRNAP

-

gp2
Limited environment
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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
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T7 is fragile to genomic perturbations the wild
type is optimal for the limited environment
Limited
Unlimited
82 dead
83 dead
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number of mutants
normalized fitness
100,000 mutants
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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

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Quantifying genetic interactions using in silico
mutagenesis
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Genetic interaction between two deleterious
mutations
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Genetic interactions among multiple deleterious
mutations
Power model log(fitness) - a n b
n deleterious mutations
synergistic ( ? gt 1)
antagonistic ( 0lt ? lt 1)
multiplicative ( ? 1)
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Genetic interactions are important for diverse
fields

• Robustness of biological systems (engineering)
• Evolution of sex (population biology evolution)

But difficult to study experimentally
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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)
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Goal to elucidate the nature of genetic
interactions using the T7 model
?
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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.

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Nature of genetic interactions depends on
environment
poor
rich
average of 500 mutants
log(fitness)
standard deviation
synergistic
antagonistic
number of mild mutations
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Nature of genetic interactions depends on
severity of mutations
poor
rich
log(fitness)
increasing severity
increasing severity
number of mutations
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Summary the nature of genetic interactions
Weak interaction
Antagonistic interaction
Severe
Severity of mutations
Synergistic interaction
Weak interaction
Mild
Poor
Rich
Environment
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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.