A mathematical model of ageing yeast

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A mathematical model of ageing yeast

• Colin Gillespie

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Outline

• Explain the purpose of a mathematical model
• Background description of yeast
• Bakers/ budding yeast/ saccharomyces cerevisiae
• Highlight the key areas in modelling ageing yeast
• Conclusions

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What we mean by old yeast

• Sterile
• A slowing of the cell cycle
• An accumulation of budding scars in the cell and
  an increase in overall cell size
• Daughters from old mothers inherit aging
  characteristics
• An accumulation of extrachromosomal
• rDNA circles (ERCs) (Sinclair Guarente,
  1997)
• It has been suggested that ERCs are one
• cause of ageing
• ERCs are not the only cause of ageing,
• just an important one!

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Whats the point of building a mathematical model?

• To sharpen our understanding of the biological
  process or hypothesis under consideration
• To highlight gaps in current knowledge
• To develop the capacity to make clear, testable
  predictions

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What are ERCs?

• The yeast ribosomal DNA (rDNA) locus on
  chromosome XII consists of 100-200 of a 9.1kb
  repeat
• Approximately half of the rDNA repeats are
  transcriptionally active at any one time
• ERCs are formed by circular rDNA molecules that
  have been excised from the rDNA array
• ERCs can then replicate via the ARS present in
  each rDNA repeat
• Approximately 15 generations after an ERC has
  formed or been introduced, the cell senesces

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What data do we have?

• When an ERC was introduced into a virgin cell,
  the cell senesced after 15 generations
• It is believed that after 15 generations, the
  cell contains 500 to 1000 ERCs death by
  overcrowding!
• There is a strong mother cell bias of ERC
  inheritance
• Unlikely to be passive process
• 80 of the time, all ERCs are retained by the
  mother
• An old mother may give birth to an old daughter
• This can easily be explained if the mother cell
  passes on a significant number of ERCs
• An ERC is formed, on average, after 8 generations
• Average lifespan of WT yeast is 24 generations
  compared to 15 generations when an ERC is been
  introduced

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Putting it all together
Two Possible yeast paths
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Life span curve of yeast

• A "shoulder" on the left, reflecting the low rate
  of death of young individuals
• A steep decline in survival past the shoulder,
  which accounts for the majority of death amongst
  the cells
• A "tail" on the right for a few long lived
  individuals

A modelling interpretation
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How fast do ERCs replicate?
The rate of death is approximately constant, so
it seems reasonable that ERCs replicate at a
constant rate

• After an ERC is introduced into a healthy cell,
  the cell senesces after 15 divisions
• It is estimated that there are a 1000 ERCs
  present when a cell senesces
• Hence a replication rate of between 0.5 and 0.7
  seems likely.

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Segregation properties of yeast cells
mother gains an ERC
We know how often a mother cell passes on some
ERCs approx 78 - but not how many ERCs it
passes on!
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Segregation properties of yeast cells

• Constant probability of an ERC being retained
• To fit the data, we need to set the probability
  of an ERC being retained at 0.999. So only 1 per
  1000 ERCs is passed on to the daughter cells.
• However, since when the mother cell does pass on
  an ERC, it is likely to a single ERC.
• This creates a middle-aged daughter, who will
  live another 15 generations.
• Instead we need an old daughter

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Segregation properties of yeast cells(2)

• A ERC dependent segregation construct.
• This is similar to an age-dependent segregation
  structure
• When a cell has few ERCs (lt750), the mother cell
  retains each ERC with probability 0.998
• Each ERC over the 750 threshold has a 0.5
  probability of being retained.

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How many ERCs can kill a cell?

• It is believed that about 1000 ERCs causes a cell
  to stop replicating
• In our simulation, a cell senesces when the ERC
  level is greater than 1000
• We investigated other possibilities, but it made
  little difference since we are interested in the
  survival curve

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Whats the probability that an ERC is formed each
generation?

• On average, an ERC is formed after 7 to 8
  generations
• It is unlikely that the ERCs formed through
  excision contribute much to the 1000 ERCs needed
  for cell senescence.
• However, it does kick-start the process!
• We consider three mechanisms for ERC formation
  constant, linear and quadratic.

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3 mechanisms of ERC formation
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Putting it all together

• Commence the simulation with a healthy mother
  cell 0 ERCs
• Determine if an ERC is generated through excision
• Calculate how many ERCs are replicated
• If the number of ERCs is greater than 1000, the
  cell dies
• Cell divides with mother cell segregation bias
• Return to step ii

To calculate the survival curve, we follow the
daughter cells of the above cell and then the
grand-daughters. This allows yeast cells to begin
with a non-zero ERC population.
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The results
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So?

• The segregation of ERCs breaks down in older
  mother cells.
• The formation of ERCs cannot be constant, but
  rather depends on the age of the yeast cell.
• Hence, there must be another mechanism(s), in
  addition to ERC accumulation which underlies
  yeast ageing.

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The Sir2 effect

• An additional copy of Sir2 increases lifespan
• What could explain this increase in lifespan, in
  terms of ERCs
• Altered segregation of ERCs
• Unlikely, as it only affects a few individuals
• Replication of ERCs
• A possibility, but could not fit the data
• ERC formation
• Yes well maybe

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Altering of ERC Formation rate
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Acknowledgements

• The BASIS team
• Carole Proctor
• Tom Kirkwood
• Richard Boys
• Darren Wilkinson
• Daryl Shanley

Thanks also to Leonard Guarente