Lingchong You

Modeling T7 life cycle

BME 265-05. March 31, 2005

Individual appointments (1hr/group) next week

• Monday: 1pm-6pm

• Tuesday: 9:30am-11:30am & 1:30-5:30pm

Project report due today!

Bacteriophages: landmarks in molecular biology1939 one-step growth of viruses1946 Genetic recombination1947 Mutation & DNA repair1952 DNA found to be genetic material, restriction &

modification of DNA1955 Definition of a gene1958 Gene regulation, definition of episome1961 Discovery of mRNA, elucidation of triplet genetic

code, definition of stop codon1964 Colinearity of gene and polypeptide chain1966 Pathways of macromolecular assembly1974 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

A lytic virus; infects E. coli

Life cycle ~ 30 min at 30°C

Genome (40kbp), 55 genes, 3 classes

(Source: Novagen)

RNAse splicing sites

T7 RNAP promoters

E. coli RNAPpromoters

Phage T7 life cycle

Source: http://icb.usp.br/~mlracz/animations/kaiser/kaiser.htm

1 cycle ~ 30 min at 30 °C

T7 genome programs a dynamic infection process

Cla

ss IC

lass II

Cla

ss III

Genome

T7 RNAP expression, host interference

Gene functions

host DNA digestion, T7 DNA replication

T7 particle formation, DNA maturation and host lysis

Example: modeling transcription

]mRNA[]RNAP[]mRNA[

idmiiEi kk

dt

d

gene i

1. Compute the number of RNAPs allocated to gene i

RNAP

total[RNAP]]RNAP[

jj

ii p

p

2. Track the level of mRNA for gene i

pi

RNAP elongation ratemRNA decay rateconstant

Transcription (II)

]mRNA[]T7RNAP[]EcRNAP[]mRNA[

7 idmiiETiPEi kkk

dt

d

Density of EcRNAPallocated to the mRNA

Density of T7RNAPallocated to the mRNA

Elongation rates of EcRNAP and T7RNAP Decay rate constantof the mRNA

Translation

]protein[]ribosome][mRNA[]protein[

idpiiiEi kk

dt

d

Density of ribosomeon mRNAs

Ribosome elongation rateDecay rate constantof the protein

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)

Nurture(E. coli host)

You, Suthers & Yin (2002) J. Bact.

• 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)

Cell growth rate Feed rate

Fresh medium

Overflow

Chemostat

Start infection Measure T7 growth Extract rise rate & eclipse time

Phage grows faster in faster-growing host cells

host growth rate = 0.7 doublings/hr

1.0

1.2 1.7

minutes post infection

T7

part

icle

s /b

act

eri

um

Experiments by Suthers

Phage grows faster in faster-growing host cells

host growth rate (doublings/hour)

T7

part

icle

s/m

in

min

ute

s

rise rate eclipse time

Experiments by Suthers

simulation

simulation

simulation with one-parameter adjustment

What’s the most important host factor

contributing to T7 growth?

E. coli growth rate

T7 growth rise rate eclipse time

Bremer & Dennis, 1996Donachie & Robinson, 1987

host growth rate (hr-1)

RNAP number

RNAP elongation rate

Ribosome number

Ribosome elongation

rate

DNA content

Amino acid pool size

NTP pool size

Cell volume

correlates

determine

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)

purifying plasmid DNA(http://www.drm.ch/pages/aml.htm)

Nature’s “solution” for T7 survival(by evolution)

Engineers’solutions for(by design)

producing H2SO4(http://www.enviro-chem.com)

Probing T7 “design” in silico

purifying plasmid DNA(http://www.drm.ch/pages/aml.htm)

Nature’s “solution” for T7 survival(by evolution)

Engineers’solutions for(by design)

producing H2SO4(http://www.enviro-chem.com)

Ideal Ideal features:features:• EfficiencyEfficiency• ProductiviProductivityty• RobustnesRobustnesss

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?

HypothesisT7 has evolved to maximize its fitness in environments having limited resources

0

50

100

150

200

250

0 20 40 60

fitness = max growth rate

minutes post infection

T7

part

icle

s/ce

ll

Fitness definition

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 = 8.7e8DNA = 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

Unlimited Limited

norm

aliz

ed fi

tness

normalized promoter strengths

base case(wild type)

Unlimited

normalized fitness

nu

mber

of

mu

tan

tsT7 is robust to random perturbations in multiple parameters; the wild type is nearly optimal in

the limited environment

Limited

wt

wt

24 %5.3 %

50,000 mutants

Sliding mutations: move an element to every possible position

Toy string: 1234 1234, 2134, 2314, 2341

T7:72 variants for each element

Sliding gene 1 (T7RNAP gene): wild-type position is optimal in the limited environment

gene 1 position (kb)

Unlimited Limited

norm

aliz

ed fi

tness

1

wt

wt

In the unlimited environment: positive feedback faster growth

promoterT7RNAP

Gene 1

Negative feedback robustness

T7RNAP gp3.5+

Unlimited environment

-

Negative feedback robustness

T7RNAP gp3.5+

Limited environment

-

gp2

EcRNAP

+

+

-

Genome permutations

12341234 1243 1324 1342 1432 14232134 2143 2314 2341 2413 24313124 3142 3214 3241 3412 34214123 4132 4213 4231 4312 4321

72! = 6x10103 combinations

24 combinations

T7 is fragile to genomic perturbations; the wild type is optimal for the limited environment

Limited Unlimited

normalized fitness

num

ber

of

mu

tan

ts

5 %

100,000 mutants

82% dead 83% dead

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 wild type mutation a mutation b mutations

a & b

fitness 1 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) = - n n: # deleterious mutations

-0.1

-0.08

-0.06

-0.04

-0.02

0

0 10 20 30

number of mutations

log(

fitne

ss)

synergistic ( > 1)

multiplicative ( = 1)

antagonistic ( 0< < 1)

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)

-0.1

-0.08

-0.06

-0.04

-0.02

0

0 10 20 30

number of mutations

log(

fitne

ss)

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

In silico mutagenesis

Select mutation severity For n (# mutations) = 1 to 30

1. 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

Plot log(fitness) ~ n, and fit with power model.

Nature of genetic interactions depends on environment

poor rich

synergistic antagonistic

number of mild mutations

log

(fitn

ess

) average of 500 mutants

standard deviation

number of mutations

log

(fitn

ess

)

poor rich

increasingseverity increasing

severity

Nature of genetic interactions depends on severity of mutations

Summary: the nature of genetic interactions

Environment

Seve

rity

of

mu

tati

on

s

Weak interactionAntagonisticinteraction

Synergisticinteraction

Weak interaction

Mil

dS

eve

re

Poor 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.