Introduction
Definition of the model
Validation and analysis
Conclusions and future work
Modelling Yeast pre-rRNA Processing
Federica Ciocchetta, Jane Hillston, Martin Kos and David Tollervey
University of Edinburgh
CMSB 2007
20th September 2007
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Introduction
Definition of the model
Outline
Introduction
Definition of the model
Validation and analysis
Conclusions and future work
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Validation and analysis
Conclusions and future work
Introduction
Definition of the model
Validation and analysis
Conclusions and future work
The context
I
RNA plays a fundamental role in the translation of genes into
proteins.
I
The study of RNA synthesis is an area of active research.
I
Eukaryotic cells contain a huge variety of RNA species, almost
all of which are synthesised by post-transcriptional processing.
I
The Tollervey Lab at the University of Edinburgh is
investigating the mechanisms and regulation of ribosomal
RNA processing and turnover, using yeast as a model
organism.
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Introduction
Definition of the model
Validation and analysis
RNA synthesis
From Miller and Beatty (Science, 1969)
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Conclusions and future work
Introduction
Definition of the model
RNA synthesis
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Validation and analysis
Conclusions and future work
Introduction
Definition of the model
Validation and analysis
Conclusions and future work
The rRNA synthesis pathway
NT
transcr
35S
react3
20S
27SA
react5
react6
18S
27SB
react7
7S
25S
react8
5.8S
I
In usual transcription, synthesis proceeds after a fully formed
precursor 35S detaches from the DNA.
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Introduction
Definition of the model
Validation and analysis
Conclusions and future work
The rRNA synthesis pathway
NT
transcrCoTC
20S
27SA
react5
react6
18S
27SB
react7
7S
25S
react8
5.8S
I
When co-transcriptional cleavage (CoTC) occurs, completed
elements of 20S become detached and available for synthesis
whilst transcription is still in progress.
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Introduction
Definition of the model
Validation and analysis
Conclusions and future work
Labelling
I
Radioactive labelling is used to track the progress of synthesis
during the experiments.
I
Rdioactive uracil is introduced into the cell and is
incorporated in the pre-rRNA during transcription.
I
In experiments precursors are separated on a gel according to
their size and the labelling intensity measured, rather than
recording the amounts of different precursors.
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Introduction
Definition of the model
Labelling (1)
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Validation and analysis
Conclusions and future work
Introduction
Definition of the model
Labelling (1)
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Validation and analysis
Conclusions and future work
Introduction
Definition of the model
Labelling (1)
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Validation and analysis
Conclusions and future work
Introduction
Definition of the model
Validation and analysis
Conclusions and future work
Aim of the work
Construction of a computational quantitative model of the
synthesis of pre-rRNA, able to:
I
capture the choice between the usual transcription and CoTC ;
I
represent the labelling process.
The following two points must be investigated:
I
How frequent is the CoTC with respect to transcription
without intermediate cleavage.
I
At what stage of transcription the cleavage occurs.
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Introduction
Definition of the model
Validation and analysis
Conclusions and future work
Dizzy
We used the chemical kinetics simulation package, Dizzy, to
develop our model.
I
Dizzy offers the implementation of well-known and
widely-used simulation algorithms;
I
Its simple input language allowed us to represent our model in
a straightforward way, at the appropriate level of detail;
I
In particular, our study is based on DNA intervals of around
400 bases (the length of DNA transcribed in the time of the
pulse-labelling experiments) instead of single bases which was
readily done in Dizzy.
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Introduction
Definition of the model
Validation and analysis
Conclusions and future work
Assumptions
I
We consider only one cell with approximately 100 copies of the
rDNA sequences responsible of the pre-rRNA transcription.
I
We abstract transcription as a single biological process.
I
We model both the alternative pathways.
I
The current hypothesis assumes that CoTC happens soon
after the transcription of the 20S, but other hypotheses must
be checked.
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Introduction
Definition of the model
Validation and analysis
Conclusions and future work
Usual transcription and CoTC
I
Variables p1 and p2 are introduced, representing the
probabilities of usual transcription and CoTC, respectively.
I
The model distinguishes rDNA sequences of 2 kinds: DNA,
involved in the usual transcription and DNACoTC , involved in
CoTC. We have globally 100 ∗ p1 DNAs and 100 ∗ p2
DNACoTC.
I
In addition, we have 100 ∗ p2 DNAp27SA2, representing the
partially transcribed 27SA2 residuals obtained from cleavage
before the initial time.
I
Current biological knowledge suggest p1 = 0.7 and p2 = 0.3
but this hypthesis is to be tested against experimental data.
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Introduction
Definition of the model
Validation and analysis
Conclusions and future work
Usual transcription and CoTC
I
Variables p1 and p2 are introduced, representing the
probabilities of usual transcription and CoTC, respectively.
I
The model distinguishes rDNA sequences of 2 kinds: DNA,
involved in the usual transcription and DNACoTC , involved in
CoTC. We have globally 100 ∗ p1 DNAs and 100 ∗ p2
DNACoTC.
I
In addition, we have 100 ∗ p2 DNAp27SA2, representing the
partially transcribed 27SA2 residuals obtained from cleavage
before the initial time.
I
Current biological knowledge suggest p1 = 0.7 and p2 = 0.3
but this hypthesis is to be tested against experimental data.
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Introduction
Definition of the model
Validation and analysis
Conclusions and future work
Usual transcription and CoTC
I
Variables p1 and p2 are introduced, representing the
probabilities of usual transcription and CoTC, respectively.
I
The model distinguishes rDNA sequences of 2 kinds: DNA,
involved in the usual transcription and DNACoTC , involved in
CoTC. We have globally 100 ∗ p1 DNAs and 100 ∗ p2
DNACoTC.
I
In addition, we have 100 ∗ p2 DNAp27SA2, representing the
partially transcribed 27SA2 residuals obtained from cleavage
before the initial time.
I
Current biological knowledge suggest p1 = 0.7 and p2 = 0.3
but this hypthesis is to be tested against experimental data.
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Introduction
Definition of the model
Validation and analysis
Conclusions and future work
Usual transcription and CoTC
I
Variables p1 and p2 are introduced, representing the
probabilities of usual transcription and CoTC, respectively.
I
The model distinguishes rDNA sequences of 2 kinds: DNA,
involved in the usual transcription and DNACoTC , involved in
CoTC. We have globally 100 ∗ p1 DNAs and 100 ∗ p2
DNACoTC.
I
In addition, we have 100 ∗ p2 DNAp27SA2, representing the
partially transcribed 27SA2 residuals obtained from cleavage
before the initial time.
I
Current biological knowledge suggest p1 = 0.7 and p2 = 0.3
but this hypthesis is to be tested against experimental data.
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Introduction
Definition of the model
Validation and analysis
Conclusions and future work
Usual transcription and CoTC
I
Variables p1 and p2 are introduced, representing the
probabilities of usual transcription and CoTC, respectively.
I
The model distinguishes rDNA sequences of 2 kinds: DNA,
involved in the usual transcription and DNACoTC , involved in
CoTC. We have globally 100 ∗ p1 DNAs and 100 ∗ p2
DNACoTC.
I
In addition, we have 100 ∗ p2 DNAp27SA2, representing the
partially transcribed 27SA2 residuals obtained from cleavage
before the initial time.
I
Current biological knowledge suggest p1 = 0.7 and p2 = 0.3
but this hypthesis is to be tested against experimental data.
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Introduction
Definition of the model
Validation and analysis
Conclusions and future work
Usual transcription and CoTC
I
Variables p1 and p2 are introduced, representing the
probabilities of usual transcription and CoTC, respectively.
I
The model distinguishes rDNA sequences of 2 kinds: DNA,
involved in the usual transcription and DNACoTC , involved in
CoTC. We have globally 100 ∗ p1 DNAs and 100 ∗ p2
DNACoTC.
I
In addition, we have 100 ∗ p2 DNAp27SA2, representing the
partially transcribed 27SA2 residuals obtained from cleavage
before the initial time.
I
Current biological knowledge suggest p1 = 0.7 and p2 = 0.3
but this hypthesis is to be tested against experimental data.
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Introduction
Definition of the model
Validation and analysis
Conclusions and future work
Description of the labelling process (1)
The following assumptions about the labelling are made:
1. The radioactive uracil is introduced into the cell at time
t0 = 0;
2. The labelling equilibration is very fast and so not considered;
3. The radioactive uracil is in large quantity and does not lose
radioactivity, i.e. it is in constant supply and all additions to
polymerase chains after t0 will incorporate it.
Initially, nascent transcripts may exhibit different levels of labelling
depending on their stage of transcription when the uracil was
introduced. After some time only fully-labelled elements occur.
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Introduction
Definition of the model
Validation and analysis
Conclusions and future work
Description of the labelling process (2)
To model the different steps in the transcription and the resulting
different levels in the labelling, the whole rDNA sequence is
discretized into regions:
CoTC
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
It is split into 400 -base regions, corresponding to the bases
transcribed in 10s (the time period of observations). As the total
sequence has approx. 6660 bases, 17 regions are obtained.
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Introduction
Definition of the model
Validation and analysis
Conclusions and future work
Definition of the model in Dizzy: species
I
Each species used in the reaction must be defined in the
model by a species symbol.
I
Different symbols are defined to represent the species at
different levels of labelling and transcription. The suffix li is
used to indicate the initial transcription situation/the level of
labelling.
I
The only species initially different from zero are the ones that
refer to the rDNA regions where the nascent transcripts are
close to the end of transcription at t0 .
I
Unlabelled elements are not considered as they cannot be
detected in the experiments.
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Introduction
Definition of the model
Validation and analysis
Conclusions and future work
Definition of the model in Dizzy: reactions
I
The reactions in the two pathways are captured in reaction
statements in Dizzy.
I
For each biological reaction in the two pathways we have as
many reactions as the number of levels of labelling for that
reactant.
I
For instance, consider usual transcription. In Dizzy it is
represented by the following set of reaction statements:
transcrli
DNAli → DNAli+1 + El35Sli , rt;
transcrl17
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
i = 1, 2, ..., 16
DNAl17 → DNAl17 + El35Sl17 , rt;
Introduction
Definition of the model
Validation and analysis
Conclusions and future work
Derivation of rates
I
Current experimental data are sparse and application of some
parameter estimation algorithms led to large approximation
errors.
I
Some information can be obtained from the literature.
I
The transcription/labelling rate is assumed to be rt = 0.25s −1
— the transcription of each region happens in 10s and
produces an average of 2.5 transcripts.
I
Other constant reaction rates are derived from the estimated
duration (rate = 1/time).
I
N.B. The rate of a reaction does not depend on the labelling.
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Introduction
Definition of the model
Validation and analysis
Conclusions and future work
Validation: introduction
I
In order to validate the model, we simulate the model and
compare the resulting curves with the known behaviours.
I
We are interested in reproducing results consistent with the
knowledge of the model and not necessarily perfectly fitting
the experimental data.
I
The variability of the experimental data is presumed to be
relatively high, on average in the range of 10%. This does not
change the overall shape of the curves.
I
Gillespie’s Direct Method was the simulation algorithm used.
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Introduction
Definition of the model
Validation and analysis
Conclusions and future work
Validation: pulse labelling
Pulse-labelling is used to measure the quantity of the elements.
Pulse time [s]
The derived data represent the radioactive density for some of the
elements in the pathway, normalised by the total amount of uracil.
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Introduction
Definition of the model
Validation: results (1)
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Validation and analysis
Conclusions and future work
Introduction
Definition of the model
Validation: results (2)
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Validation and analysis
Conclusions and future work
Introduction
Definition of the model
Validation: results (3)
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Validation and analysis
Conclusions and future work
Introduction
Definition of the model
Validation and analysis
Conclusions and future work
Validation: results (4)
I
100 replications were made of each 500s simulation run. Each
run takes only a few minutes.
I
The simulation results are largely in agreement with the
expected behaviours. The steady-state values obtained are
comparable with the experimental data.
I
There are some discrepancies — these may be due to unknown
biological phenomena and further experiments are needed.
I
To judge the quality of the simulation, we evaluated the
confidence intervals for each simulation time point. With
confidence coefficient α = 0.05, the confidence interval width
is 3% − 15% of the steady state value of the element.
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Introduction
Definition of the model
Validation and analysis
Conclusions and future work
Analysis: usual transcription vs CoTC
We plot 20S for different values of the frequencies p1 and p2.
Results support the hypothesis that the frequency of CoTC is
non-null and has a value close to the one chosen in the model
(30%).
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Introduction
Definition of the model
Validation and analysis
Conclusions and future work
Analysis: CoTC point
Altering the cleavage position for CoTC has a marked effect on the
synthesis of 20S.
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Introduction
Definition of the model
Validation and analysis
Conclusions and future work
Analysis: CoTC point
However the impact on 27S which is synthesised further down the
pathway is negligible.
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Introduction
Definition of the model
Validation and analysis
Conclusions and future work
Summary
I
In this paper we have presented a model describing the
synthesis of pre-rRNA. In particular we focus on two aspects:
the description of the process of labelling and on the choice
between usual transcription and CoTC.
I
Dizzy was chosen as the modelling and simulation framework
for our study.
I
The validation and the analysis have been made by means of
stochastic simulation (Gillespie).
I
The model is able to reproduce the expected results and the
simulations of the main elements are comparable with the
experimental data.
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing
Introduction
Definition of the model
Validation and analysis
Conclusions and future work
Future investigations and study
I
One topic for future investigation will be the derivation of
more precise rates, obtained by applying parameter estimators
to a set of experimental data.
I
We will try changing some of the hypotheses we have made.
For example, our current model assumes that rates are
constant, and that reactions follow a mass action kinetics.
I
We aim to use our model to answer further biological
questions about the synthesis pathway.
I
We are also developing a PRISM model of the system and will
investigate the data which can be derived from it.
Ciocchetta, Hillston, Kos and Tollervey
Modelling Yeast pre-rRNA Processing