Metabolic Modeling - Why?
Models - why?
Building models of a system helps us improve our understanding.
It is also a way of checking our understanding, as comparison
of a model with reality is the way to prove whether the model
works.
Models of metabolic pathways - why?
They will help us bridge the gap from genotype to phenotype.
The genomic sequences available are not enough to determine
the phenotype.
The availability of expression data offers us a window to the
dynamic events occurring in the cell.
Genomic information + expression data models
phenomics
Categorising methods (Hatzimanikatis and Bailey)
Categorising models according to the interaction between a
subsystem and its cellular enviroment.
Isolated mechanism
complexity
fixed interactions
Isolated mechanism + specific growth rate
one way interaction
Single input-multiple output coupling
specific growth rate = f (C)
biochemical detail in one direction
Multiple input-multiple output
spectrum of interactions
Categorising methods (Giuseppin and van Riel)
“Engineering” approach: Input and output fluxes are measured and
used to determine the internal net fluxes through the metabolic
pathways. These methods are static; they describe fluxes at given
conditions and do not allow for extrapolation to other conditions and
transients.
Example: Metabolic Flux Analysis (MFA), Flux Balance Analysis
(FBA).
Cybernetic approaches. Based on the hypothesis that cells react to their
environment using an optimal response for survival and competition.
Example: Optimal Metabolic Control Theory.
Treat metabolism as a limited set of enzymes with interactions that can
be described in terms of substrate, enzyme and product levels.
Example: Metabolic Control Analysis.
Dynamic Optimal Metabolic Control
DATA
(metabolic flux info on
steady states of continuous
cultures of an organism)
MFA
Identify the steady stases and
fluxes as the OPTIMAL states under
given growth rates and conditions
Constraints are now visible.
Upper /lower limits for fluxes
Identify strategies related to growth, substrate
uptake and homeostasis. These form the cybernetic
heart of the model.
Steady-state and dynamic modelling method. Needs data on:
relevant stoichiometric matrix
fluxes
compound concentrations
Molecular versus System Level Approaches
Qualitative verbal models have been dominant
in biochemistry - a young science studying
unknown and complex systems.
Reductionist approaches have been popular
because they provided us with ever-increasing
knowledge of the biochemical details
of metabolic networks
(pathways=>enzymes=>genes)
Quantitative systems approach
builds a mathematical
description of the system
properties based on information
about general features
of the molecular structure.
Metabolic Steady States
Living organisms have the ability to maintain a relatively constant composition whilst
taking in nutrients from the environment and excreting products.
There is a constant flux of matter and energy through the metabolic pathways =>
dynamic equilibrium.
Intermediates in the pathway must not be allowed to accumulate, so:
rate of formation = rate of degradation
1
Glucose
2
Glc6P
3
Fru6P
rate 1 = rate 2 = rate 3 = ...
....
Ethanol
+
CO2
The quest for the rate-limiting step
When a process is conditioned as to its rapidity by a number of separate factors
the rate of the process is limited by the pace of the slowest factor.
This statement is wrong if taken literally. In a linear metabolic
pathway all reactions operate at the same rate in the steady state.
What was really meant was that the rate of a pathway could be altered
only by changing the activity of one particular enzyme.
Despite the fact that experimental data has often contradicted this concept,
much of the work on the control of metabolism has been centred around the
search for potential regulatory enzymes.
Regulatory enzymes were expected to:
- be found at the beginning of a pathway
- be non-equilibrium enzymes
- show changes in activity caused not just by their own substrates
- directly affect the metabolic flux
Problems with rate-limiting step approaches
The rate of a sequence of simple chemical reactions could depend to varying degrees
on the rate constants of all the reactions. (1930s)
The rate of a sequence of unsaturated enzymes depends non-linearly on the kinetic
parameters of all the enzymes. (Waley, 1964)
The increase in amount of rate-limiting enzymes using gene cloning techniques did not
always result in an increase of the rate of the pathway. (glycolysis experiment, 1986)
Replacing the question:
Is this enzyme rate-limiting?
with
How does this enzyme’s activity affect the metabolic flux?
Use of sensitivity analysis (introduced into metabolic biochemistry by Higgins, 1960s).
Biochemical Systems Theory, developed based on sensitivity analysis (Savageau, 1969).
Metabolic Control Analysis (Theory) (Kacser and Burns, Heinrich and Rapoport, 1970s).
Metabolic Control Analysis - Basics
X
source
E1
S1
Y
...
En
Sn ...
Jn
J1
Z
product
ln(Jn)
Flux control coefficient CE1Jn = lnJn / ln[E1]
For small enzyme concentration changes,
the flux control coefficient can be used to
calculate the flux using a power law:
J = a [E]C
ln([E1])
Summation Kacser and Burns found that the coefficients for all enzymes that affect a
particular metabolic flux in a cell, must add up to 1:
theorem
n
J
C
 i 1
i 1
Metabolic Control Analysis - Basics (2)
ln(rate v)
Elasticity e  ln|v| / ln[S]
ln([S])
Connectivity
theorem
Elasticities measure the influence of metabolites on
enzymes, and are thus related to the kinetic properties
of the enzymes.
Elasticities are properties of individual enzymes and
not of the metabolic system.
Elasticities can also be defined with respect to external
effectors (=> response coefficients).
The sum of the products of flux control coefficients with elasticities for
all enzymes in the system is zero:
n
J i
C
 i eS  0
i 1
Metabolic Control Analysis - Problems
Chief intellectual achievements of MCA (Kell and Mendes, 1999):
•Each step in a linear pathway at steady state contributes quantitatively to the control
of flux in a manner expressed by the summation theorem.
•The flux-control coefficients are consequently necessarily small
•The activities of many steps must be changed simultaneously if fluxes are to be enhanced
substantially.
Implicit and explicit assumptions in MCA:
All cells are the same
Heterogeneity is greater than normally assumed.
Simple models are adequate
Many more genes than we know the functions
of contribute to fitness in a cell.
The “universal method”
proposed for large changes
in parameters is adequate
for any metabolic system.
It doesn’t work if a) the end-product inhibits its
own synthesis and b) if there are interactions
involving moiety-conserved cycles.
Coefficients of MCA for very
large changes are similar
to those for small changes