Transcript Integration Architecture

Stochastic simulation algorithms
ESE680: Systems Biology
Relevant talks/seminars this week!
• Prof. Mustafa Khammash (UCSB)
 “Noise
in Gene Regulatory Networks: Biological
Role and Mathematical Analysis ”
 Friday
23 Mar, 12-1pm, Berger Auditorium
• Dr. Daniel Gillespie (Dan Gillespie
Consultant)
 “Stochastic
 Friday
Chemical Kinetics”
23 Mar, 2-3pm, Berger Auditorium
Chemical reactions are random events
B
B
A
A
A+B
AB
A+B
AB
3
Poisson process

Poisson process is used to model the occurrences of
random events.
event
event
event
time

Interarrival times are independent random variables,
with exponential distribution.

Memoryless property.
4
Stochastic reaction kinetics

Quantities are measured as #molecules
instead of concentration.
 Reaction rates are seen as rates of Poisson
processes.
k

A + B  AB
Rate of Poisson process
5
Stochastic reaction kinetics
A
AB
time
reaction
reaction
reaction
time
6
Multiple reactions

Multiple reactions are seen as concurrent
Poisson processes.
k1
A + B  AB
k2
Rate 1

Rate 2
Gillespie simulation algorithm: determine
which reaction happens first.
7
Multiple reactions
A
AB
time
reaction 1
reaction 2
reaction 1
time
8
t – leaping scheme
A
AB
r1
r2
D
r2
r1
D
time
r2
r1
r1
D
D
time
9
Erlang distribution

0.4
0.35
0.3
Erlang distribution
0.25
0.2
0.15
0.1
0.05
0
0
2
4
6
8
10
n
12
14
16
18
20
10
Erlang  Gaussian

0.08
Erlang distribution
0.07
Normal distribution
0.06
0.05
0.04
0.03
0.02
0.01
0
0
5
10
15
20
25
30
35
40
45
50
11
Stochastic simulation with Gaussian rv
12
Stochastic simulation with Gaussian rv
Ito stochastic
integral
13
Chemical Langevin equation
White noise driving
the original system
14
Stochastic fluctuations triggered
persistence in bacteria
ESE680: Systems Biology
Bacterial persistence
•
•
Discovered as soon as antibiotics were used (Bigger, 1944)
A fraction of an isogenic population survives antibiotic treatment
significantly better than the rest
•
If cultured, the surviving
fraction gives rise to a
population identical to the
original one
Bimodal kill curves
Persisters are a very small
fraction of the initial
population (10-5-10-6)
•
•
(from Balaban et al, Science, 2003)
Persistence as an evolutionary
advantage
•
•
•
•
Persisters are an alternative phenotype
Similar to dormancy or stasis
Since they do not grow, they are less vulnerable
Presence of multiple phenotypes has an evolutionary
advantage in survival in varying environments
• Transitions between phenotypes are of stochastic nature –

Random events, triggered by noise
• What is the underlying molecular mechanism?
Persistence as a phenotypic switch
• Recent work due to Balaban et al showed that there are two types of
persisters:


Type I – generated by an external triggering event such as passage
through stationary phase
Type II – generated spontaneously from cells exhibiting ‘normal’ phenotype
Stringent response and growth control
Triggered by adverse conditions, e.g. starvation
Transcription control (p)ppGpp:




Lack of nutrients
Stalled ribosomes
ppGpp synthesis
Reprogramming of transcription
Translation shutdown




Proteases
(p)ppGpp involved
Activation of toxin-antitoxin modules
Toxin reversibly disables ribosomes
ppGpp
Lon
TRANSCRIPTION
Toxins
RAC
TRANSLATION
GROWTH
NUTRIENT
AVAILABILITY
Tox
Ant
mRNA
Ribosome
Ribosome
Ribosome
Toxin
tmRNA
Antitoxin
Toxin-antitoxin modules
•
•
•
•
Toxin and antitoxin are part of an operon
Overexpression of toxin leads to ‘stasis’
Toxin cleaves mRNA at the stop codon
Cleaved mRNA disables translating
ribosomes
• Ribosomes can be ‘rescued’ by tmRNA
• One example: RelB and RelE
(Gerdes 2003)
Toxin-antitoxin modules
• TA module provides an emergency brake
• Normally all toxin is bound to antitoxin
 Antitoxin
binds toxin at a ratio > 1
 Antitoxin has a shorter half-life
• Shutdown can be triggered by fluctuations:
Toxin excess  reduced translation  more
excess toxin .. translation shutdown
• Recovery from shutdown facilitated by
tmRNA which reverses
Reaction kinetics
Variables:
• T = Toxin concentration
• A = Antitoxin concentration
• R = ribosome activity
Transcription:
Reaction kinetics
Translation:
Reaction kinetics
Ribosome dynamics:
Deterministic simulation result
Toxin
Antitoxin
Ribosome activity
Stochastic simulation result
Toxin
Antitoxin
Ribosome activity