The Arkin model of the lysis-lysogeny decision of phage lambda

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The Arkin model of the lysis-lysogeny decision of
phage lambda

• Tom Evans

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Introduction

• Phage injects its DNA into an E. coli cell
• Replicates either via lysis or lysogeny
• A molecular switching mechanism determines which
  pathway is selected
• The model of Arkin et al (1998) for phage lambda
  contains the important genes and proteins
  involved in the molecular switch

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The model

• Model contains five genes
• cI, cro, n, cII, cIII
• These genes code for the proteins
• CI, Cro, N, CII, CIII
• The number of molecules of each protein is
  modelled stochastically over 0,T
• At time T, compare (CI) and (Cro) to see
  whether lysis or lysogeny has occurred

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What happens

• Assume only one phage infects the bacterium
• To begin with, only the cro and n genes are on.
• Usually, the amount of Cro will increase over the
  35 minute cell cycle, leading to lysis

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What happens

• However, the N protein can switch on the CII
  gene.
• If, by chance, enough CII is produced in the
  early stages of the infection, then the cI gene
  will be switched on.
• If the level of CI exceeds that of Cro, then
  lysogeny will occur.
• The probability of lysogeny increases as MOI
  increases.

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Gene expression

• Two stages
• Transcription gene RNAP mRNA
• Translation mRNA ribosome protein

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Transcription

• RNAP enzyme binds to promoter upstream of the
  gene
• RNAP moves along DNA until it gets to the start
  of the gene
• RNAP moves along the gene, building an mRNA
  transcript
• When RNAP reaches the end of the gene, the mRNA
  transcript is released

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Translation

• Ribosome binds to RBS binding site on the mRNA
  transcript
• Ribosome moves along the mRNA transcript,
  building the protein
• When ribosome reaches the end of the transcript,
  the protein is released

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Example transcription of the cI gene
RNAP
start
stop
PRM (promoter)
cI (gene)
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Example transcription of the cI gene
RNAP
start
stop
PRM (promoter)
cI (gene)
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Example transcription of the cI gene
RNAP
start
stop
PRM (promoter)
cI (gene)
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Example transcription of the cI gene
RNAP
start
stop
PRM (promoter)
cI (gene)
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Example transcription of the cI gene
MCI
RNAP
start
stop
PRM (promoter)
cI (gene)
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Example translation of CI
Rib
RBS
MCI
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Example translation of CI
Rib
RBS
MCI
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Example translation of CI
Rib
RBS
MCI
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Example translation of CI
CI
Rib
RBS
MCI
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Results (I)
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Results (II)
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Results (III)
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Model complexity

• From the model description, it doesnt sound too
  bad
• Only 5 genes and 5 proteins
• But the average gene length is 350 nucleotides
  (G, C, A, T)
• Each movement of an RNAP or ribosome molecule
  from one nucleotide to the next is modelled
  individually (exponential distribution)
• So need to generate around 700 exponential random
  numbers just to simulate production of one
  protein molecule.

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A simplification

• Gibson and Bruck (2000) used the well known
  result that a sum of exponential random variables
  has a gamma distribution to write a simplified
  version of the Arkin model.
• Movement of RNAP / ribosome can now be modelled
  with a single gamma random number
• Their model allows RNAP / ribosome molecules to
  overtake each other (this doesnt happen in
  reality)
• But their results are similar to those of Arkin
  et al (1998)

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Gibson-Bruck results
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What Im doing

• I have written the Gibson-Bruck version of the
  algorithm in Matlab
• Reproduce the lambda results
• Modify the algorithm for Stx phage
• Generate Stx results and compare with lambda

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My results for MOI1