Transcript Modeling T7 life cycle

BME 265-05. March 31, 2005
Modeling T7 life cycle
Lingchong You
Project report due today!
Individual appointments (1hr/group)
next week
• Monday: 1pm-6pm
• Tuesday: 9:30am-11:30am & 1:305:30pm
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.
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)
Phage T7
(Source: Novagen)
E. coli RNAP
promoters



A lytic virus; infects E. coli
Life cycle ~ 30 min at 30°C
Genome (40kbp), 55 genes, 3 classes
T7 RNAP
promoters
RNAse splicing sites
Phage T7 life cycle
1 cycle ~ 30
min at 30 °C
Source: http://icb.usp.br/~mlracz/animations/kaiser/kaiser.htm
T7 genome programs a dynamic infection process
Genome
Gene functions
Class I
T7 RNAP expression,
host interference
Class II
host DNA
digestion, T7 DNA
replication
Class III
T7 particle
formation, DNA
maturation and host
lysis
Example: modeling transcription
1. Compute the number of RNAPs allocated to gene i
RNAP
pi
gene i
pi
[RNAPi ] 
[RNAP]total
 pj
j
2. Track the level of mRNA for gene i
d [mRNAi ]
 k E [RNAPi ]  k dmi [mRNAi ]
dt
RNAP elongation rate
mRNA decay rate
constant
Transcription (II)
Elongation rates of EcRNAP and T7RNAP
Decay rate constant
of the mRNA
d [mRNAi ]
 k PE [EcRNAPi ]  kT 7 E [T 7RNAPi ]  k dmi [mRNAi ]
dt
Density of EcRNAP
allocated to the mRNA
Density of T7RNAP
allocated to the mRNA
Translation
Ribosome elongation rate
Decay rate constant
of the protein
d [proteini ]
 k E [mRNAi ][ribosomei ]  k dpi [proteini ]
dt
Density of ribosome
on mRNAs
 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
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
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?
Effects of host physiology on
T7 growth —
A nature-nurture question
Nature
(Genome)
You, Suthers & Yin (2002) J. Bact.
Nurture
(E. coli host)
• How does T7 growth depends on
the overall physiology of the host?
• What host factors contribute most
to T7 development?
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
Phage grows faster in faster-growing host cells
T7 particles /bacterium
host growth rate
= 0.7 doublings/hr
1.2
1.0
1.7
minutes post infection
Experiments by Suthers
Phage grows faster in faster-growing
host cells
simulation
eclipse time
minutes
T7 particles/min
rise rate
simulation with
one-parameter
adjustment
simulation
host growth rate (doublings/hour)
Experiments by Suthers
What’s the most
important host factor
contributing to T7
growth?
E. coli
growth rate
Bremer & Dennis, 1996
Donachie & Robinson, 1987
RNAP number
RNAP elongation rate
host growth rate (hr-1)
Ribosome number
Ribosome elongation rate
correlates
determine
DNA content
Amino acid pool size
NTP pool size
Cell volume
T7 growth
rise rate
eclipse time


T7 growth is most sensitive to
the host translation machinery
Default setting:
host growth rate =
1.5 hr-1
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)
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)
Nature’s “solution”
for T7 survival
(by evolution)
producing H2SO4
(http://www.enviro-chem.com)
Probing T7 “design” in silico
Engineers’
solutions for
(by design)
Ideal features:
• Efficiency
• Productivity
• Robustness
purifying plasmid DNA
(http://www.drm.ch/pages/aml.htm)
Nature’s “solution”
for T7 survival
(by evolution)
producing H2SO4
(http://www.enviro-chem.com)
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?
Hypothesis
T7 has evolved to maximize its
fitness in environments having
limited resources
Fitness
definition
T7 particles/cell
250
200
150
fitness = max growth rate
100
50
0
0
20
40
minutes post infection
60
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)
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
T7 is robust to single parameter perturbations; the
wild type is nearly optimal in the limited
environment
normalized fitness
Unlimited
Limited
base case
(wild type)
normalized promoter strengths
T7 is robust to random perturbations in multiple
parameters; the wild type is nearly optimal in
the limited environment
number of mutants
Unlimited
wt
Limited
wt
5.3 %
24 %
normalized fitness
50,000 mutants
Sliding mutations: move an element
to every possible position
Toy string: 1234
T7:
1234, 2134, 2314, 2341
72 variants
for each element
Sliding gene 1 (T7RNAP gene): wild-type position
is optimal in the limited environment
normalized fitness
Unlimited
Limited
wt
wt
gene 1 position (kb)
1
In the unlimited environment:
positive feedback  faster growth
T7RNAP
promoter
Gene 1
Negative feedback  robustness
T7RNAP
gp3.5
+
Unlimited
environment
Negative feedback  robustness
-
+
EcRNAP
-
T7RNAP
gp2
Limited
environment
+
+
gp3.5
Genome permutations
24 combinations
1234
1234
2134
3124
4123
1243
2143
3142
4132
1324
2314
3214
4213
1342
2341
3241
4231
1432
2413
3412
4312
1423
2431
3421
4321
72! = 6x10103 combinations
T7 is fragile to genomic perturbations; the wild type
is optimal for the limited environment
Unlimited
number of mutants
82% dead
Limited
83% dead
5%
normalized fitness
100,000 mutants
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
Quantifying genetic interactions
using in silico mutagenesis
Genetic interaction between
two deleterious mutations
genotype
fitness
wild type
1
mutation a
mutation b
mutations
a&b
0.8
0.5
?
0.4 = 0.8 × 0.5
> 0.4
< 0.4
Multiplicative
Antagonistic
Synergistic
Genetic interactions among
multiple deleterious mutations
Power model: log(fitness) = - a n b n: # deleterious mutations
log(fitness)
0
synergistic
( b > 1)
-0.02
antagonistic
( 0< b < 1)
-0.04
-0.06
multiplicative
( b = 1)
-0.08
-0.1
0
10
20
number of mutations
30
Genetic interactions are
important for diverse fields
• Robustness of biological systems
(engineering)
• Evolution of sex (population biology &
evolution)
But difficult to study experimentally…
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)
Goal: to elucidate the nature of genetic
interactions using the T7 model
log(fitness)
0
-0.02
-0.04
-0.06
-0.08
-0.1
0
10
20
number of mutations
30
In silico mutagenesis


Select mutation severity
For n (# mutations) = 1 to 30
Construct 500 T7 mutants, each carrying n
random mutations
2. Compute the fitness (for poor or rich
environments) of each mutant
3. Compute the average and the standard
deviation of log(fitness) values
1.

Plot log(fitness) ~ n, and fit with power
model.
Nature of genetic interactions
depends on environment
poor
rich
log(fitness)
average of 500 mutants
standard
deviation
synergistic
antagonistic
number of mild mutations
Nature of genetic interactions
depends on severity of mutations
log(fitness)
poor
increasing
severity
rich
increasing
severity
number of mutations
Severe
Weak interaction
Antagonistic
interaction
Synergistic
interaction
Weak interaction
Mild
Severity of mutations
Summary: the nature of genetic interactions
Poor
Environment
Rich
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.