Dr' Eduardo Mendoza

1
Lecture 9
MC2 Analysis of the Yeast Trehalose Module

• Dr. Eduardo Mendoza
• Oct 22, 2003 Physics Department
• Mathematics Department Center for
  NanoScience
• University of the Philippines
  Ludwig-Maximilians-University
• Diliman Munich, Germany
• eduardom_at_math.upd.edu.ph
  Eduardo.Mendoza_at_physik.uni-muenchen.de

2
Topics to be covered

• 9.1Features of the Trehalose Module
• 9.2 Canonical Model for the Trehalose Module
• 9.3 Normal Conditions Response
• 9.4 MC2 Analysis Basics
• 9.5 MC2 Analysis for Trehalose
• 9.6 Heat Shock Response

3
References

• R. Alves, M. Savageau Comparing systemic
  properties of ensembles of biological networks by
  graphical and statistical methods, Bioinformatics
  16/6 2000
• E.O. Voit Biochemical and genomic regulation of
  the trehalose cycle in yeast review of
  observations and canonical model analysis,
  Journal of Theoretical Biology 223, 2003

4
9.1 Features of the Trehalose Module

• Trehalose Facts
• disaccharide found in bacteria, eukaryotic
  microorganisms, plants, insects, invertebrates
• crucial defense mechanism that stabilizes
  proteins and biological membranes under a variety
  of stress conditions (increased temperature,
  hydrostatic pressure, dessication, nutrient
  starvation, osmotic or oxidative stress, exposure
  to toxic chemicals)
• important target for biotechnology (for food
  manufacturing, vaccine protection in hot
  climates, cosmetic products,...)

5
The Trehalose Module

• consists only of a few metabolites that form a
  substrate cycle
• exhibits surprisingly complex regulation (s. next
  two slides)
• not readily addressed with an experimental
  approach
• Mathematical model is an effective alternative

6
Yeast Model (Curto et al, 1995)
The Trehalose Module
7
The Trehalose Module (Voit, 2003)
8
9.2 Canonical Model for the Trehalose Module

Voit, p. 56
9
Dependent Variables
10
Independent Variables
11
Trehalose S-System Model
Note Xo external glucose concentration
12
9.3 Normal Conditions Response

• Yeast cycle under different conditions
• Low glucose ? most of it used for glycolysis
• High glucose ? most stored as glycogen
• Rising temperature ? first responsibility is to
  produce sufficient amounts of trehalose for
  protection

13
Baseline analysis (wild type)

• Obs (ervations)
• ATP, trehalose other metabolites decrease
  within 15 minutes after depletion of external
  carbon source
• Both glycogen and trehalose serve as storage
  carbohydrates under glucose abundance, they
  accumulate dramatically and can make up to 20 of
  dry cell mass

• YM (Yeast Model)
• The model with parameter specs from the
  literature exhibits similar dynamic features
• If the input of glucose is permanently doubled ,
  glycolytic flux increases by 80, trehalose by
  40 but the glyogen pool grows five-fold
• The model exhibits stable steady state
  (eigenvalue analysis), the right ranges in log
  gains and parameter sensitivity

14
Genes involved in the trehalose module
15
Baseline Analysis (mutants)

• Mutants are represented in the system through
  strong or total reduction in enzyme activity
• Model solution and comparison with observations
  show that the model captures mutations in key
  enzymes and their observed ramifications well

16
Example of mutant analysis

• Obs (ervations)
• A mutation in TPS2 leads to a strong reduction in
  the activitiy of T6P phostaphase, which leads to
  a significant and toxic accumulation of T6P and
  the depletion of the trehalose pool
• This causes a problem under heat where TPS2
  mutants show increased sensitivity and fail to
  grow.
• As a secondary effect, hexokinase activity and
  G6P accumulation are reduced

• YM (Yeast Model)
• The TPS2 mutation is readily implemented in the
  model as reduced activity of the T6P phosphatase
  step. As expected, this alteration results in a
  greatly expanded T6P pool and in a trehalose
  concentration that corresponds to just 1 of the
  wild type model
• G6P and the glycolytic flux are slightly reduced

17
Summary (baseline/mutant)
18
9.4 MC2 Analysis Basics

• Steps in MC2 Analysis
• Formulate mathematical models for the alternative
  designs being compared
• More complex model is designated the reference,
  the other the alternative
• Establish internal equivalence
• Each process in the alternative model that is
  identical to one in the reference model is
  assigned a set of parameter values identical to
  the corresponding set in the reference model

19
MC2 Analysis Steps (contd)

• 3. Establish external equivalence
• Each process in the alternative model that is
  different from the corresponding process in the
  reference model will have a set of parameter
  values that is unique to the alternative model
• Establish contraints by equating the expressions
  for a systemic property common to the two models
  and solving for the unique parameters of the
  alternative in terms of those of the reference
• 4. Analyze the differences between the models
  that remain

20
Basic MC2 Analysis for S-Systems

• Steady state equations (and various systemic
  properties) can be solved analytically ? explicit
  constraint equations formed and solved
• Comparative analysis (Step 4) thru ratios of
  systemic properties such as
• Concentrations
• Fluxes
• Logarithmic gains
• Parameter sensitivities
• Stability margins

21
9.6 MC2 Analysis for Trehalose

• Approach compare for each regulatory signal YM
  to an alternative, otherwise equivalent model AM
• Overall results suggest that various signals
  cooperate synergistically, thereby achieving two
  goals
• they aid in the control of the internal glucose
  pool and
• Facilitate efficient channeling of glucose
  towards glycolysis, glycogen or trehalose
  depending on physiological demands
• If anyone of these signals is missing, the cell
  doesnt seem to run into disastrous difficulties,
  but each signal offers a slight advantage over an
  unregulated system, and taken together, the
  regulated structure is better suited to handle
  perturbations than an alternative, less regulated
  system

22
Example
23
Overview of MC2 Results
24
9.6 Heat Shock Response (s)
msn2, msn4
HSPs
Sphingo- lipids
m
25
(No Transcript)
26
Example
27
Summary of up-regulation responses
28
Thanks for your attention !

• Questions?