1. Stochastic simulation algorithms
ESE680: Systems Biology

2. 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 Chemical Kinetics”
Friday 23 Mar, 2-3pm, Berger Auditorium

3. Chemical reactions are random eventsB B A A
A + B AB
A + B AB

4. Poisson process
Poisson process is used to model the occurrences of random events.
Interarrival times are independent random variables, with exponential distribution.
Memoryless property.
event
event
event
time

5. 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

6. Stochastic reaction kineticsAB
time
reaction
reaction
reaction
time

7. Multiple reactions A + B  AB
Multiple reactions are seen as concurrent Poisson processes.
Gillespie simulation algorithm: determine which reaction happens first. k 1
A + B  AB k 2
Rate 1
Rate 2

8. Multiple reactions A AB
time
reaction 1
reaction 2
reaction 1
time

9. t – leaping scheme A AB
time r2 r1 r2 r1 r1 r2 r1 D D D D
time

10. Erlang distribution

11. Erlang  Gaussian

12. Stochastic simulation with Gaussian rv

13. Stochastic simulation with Gaussian rv
Ito stochastic integral

14. Chemical Langevin equation
White noise driving the original system

15. Stochastic fluctuations triggered persistence in bacteria
ESE680: Systems Biology

17. 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 ( )
(from Balaban et al, Science, 2003)

18. 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?

19. 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

21. 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
Toxins
RAC
TRANSCRIPTION
TRANSLATION
GROWTH
NUTRIENT
AVAILABILITY

22. Tox
Ant
mRNA
tmRNA
Ribosome
Ribosome
Ribosome
Toxin
Antitoxin

23. 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)

24. 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

25. Reaction kinetics Variables: T = Toxin concentration
A = Antitoxin concentration
R = ribosome activity
Transcription:

26. Reaction kinetics
Translation:

27. Reaction kinetics
Ribosome dynamics:

28. Deterministic simulation result
Toxin
Antitoxin
Ribosome activity

29. Stochastic simulation result
Toxin
Antitoxin
Ribosome activity