BIOLOGY
Biochemistry meets mathematics
Professor Johann Rohwer is investigating in vivo-inspired mathematical models to predict enzyme
kinetics in living organisms. Here, he discusses the development of a pioneering technique to
advance this area of study
How did you come to study enzyme kinetics,
and what interests you most within this remit?
What fascinates me about enzyme kinetics is
the ability to calculate and quantitatively predict
the speed of biological reactions under various
conditions. This interest stems from my days
as an undergraduate, when I studied both
mathematics and biochemistry as majors for
my BSc degree. Since then, I’ve been applying
quantitative mathematical frameworks to the
study of molecular biological systems.
Why is an understanding of enzyme kinetics
important in systems biology and, specifically,
the behaviour of enzymes in vivo?
Enzyme kinetics for systems biology aims
to quantitatively describe the behaviour of
enzymes in the context of their pathways, the
emphasis being less on mechanism and more
on an accurate description of the enzyme’s
response towards all substrates, products and
effectors that interact with it. Our group has
developed generic rate equations for systems
biology that are simpler than those of detailed
mechanistic accounts.
Nuclear magnetic resonance (NMR)
spectroscopy is a key method in your most
recent studies. How does this technique work?
NMR spectroscopy is an experimental
technique relying on the magnetic properties
of certain atomic nuclei. When these nuclei
are placed in a strong magnetic field and
excited by an appropriate radio-frequency (RF)
Enzymes fast and slow
Using an advanced spectroscopic approach, biochemists at Stellenbosch University, South Africa,
are exploring enzyme kinetics in the context of their ultimate application – the in vivo environment
PROFESSOR JOHANN ROHWER and his
colleagues at Stellenbosch University are
constructing mathematical frameworks
through which the enzyme kinetics of living
organisms may be modelled. Rohwer’s novel
approach to kinetic modelling will simplify
and make consistent the provision of enzyme
kinetics data, facilitating the construction of
models more accurately representing in vivo
enzyme networks.
ENZYME KINETICS
Enzyme kinetics was originally used to gain
understanding of an enzyme’s mechanism
through performing different kinetic assays.
But this exploration of the chemical reactions
catalysed by enzymes has not always been
a popular topic of study: “In the heyday of
molecular biology in the late 20th Century,
enzyme kinetics went somewhat out of
fashion, as the newly discovered genome
sequences were considered to provide all the
answers,” Rohwer explains. “In the postgenomic era, it is becoming increasingly
apparent that we need quantitative, dynamic
frameworks for understanding biological
systems, and that genomes by themselves
constitute ‘dead’ information.”
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INTERNATIONAL INNOVATION
Enzymes catalyse chemical reactions by
providing an alternative reaction mechanism
of a lesser activation energy, the minimum
energy required for a given reaction to occur.
By analysing the kinetics (rates) of such
reactions, much may be deduced from their
workings. Furthermore, the influence of
specific factors on a reaction’s rate may be
demonstrated and quantified.
IN VIVO VERITAS
Rohwer’s most recent project serves to
evaluate the significance of the in vivo/in
vitro dichotomy in the modelling of enzyme
kinetics. The rationale for this study derives
from the questionable representativeness
of in vitro kinetic models. The in vivo
environment accounts for additional effects
that are not generally taken into account in
these mathematical models, which reduces
their utility to the holistic discipline of
systems biology.
Reductionism is central to the scientific
method, though failure to account for the many
factors involved in a biochemical phenomenon
pixelates the big picture. The bottom-up
approach to constructing a systems-level view
SYSTEMS BIOLOGY
Biological functions stem,
principally, from interactions
between the components of living
organisms. Systems biology
strives to understand the big
picture by exploring how individual
components, like enzymes, act as
parts of grander systems – enzyme
networks, for instance.
In his latest project, Rohwer
resolved to study the extensively
documented Escherichia coli
bacterium and its energy-supplying
central carbon metabolism. This
metabolic pathway relies upon
a complex enzyme network; but
by determining the kinetics of its
constituent enzymes individually,
the system may be understood as
a whole.
ENZYME KINETICS
OBJECTIVE
pulse (the so-called resonance frequency),
they emit an RF signal upon decay (the
so-called free induction decay), which can
be picked up by radio receivers. This signal
is then converted from the time domain to
the frequency domain by Fourier transform,
yielding an NMR spectrum.
Can you explain how you apply this
technique to obtain enzyme parameters for
kinetic modelling?
While the technique of NMR was originally
developed in the 1950s, numerous refinements
and extensions have been developed over
the decades. In our approach, a sample –
consisting of an in vivo cell suspension, an in
situ suspension of permeabilised cells or a
cell lysate – is incubated with the appropriate
substrates and effectors of the pathway under
study. The concentrations of the pathway
intermediates are then followed over time by
acquiring a series of NMR spectra – and this
is repeated for different starting conditions.
Using generic rate equations, a kinetic model
of the pathway is then fitted to the NMR
concentration time courses to obtain the
kinetic parameters.
In the next five to 10 years, what impact do you
foresee your research having?
The construction of kinetic models for
computational systems biology is hampered
by a lack of kinetic data; even when such data
are available, they are frequently not from a
consistent source. I hope that my work will
pave the way for researchers to more easily
acquire large sets of consistent enzyme-kinetic
parameters with reduced effort. This should
facilitate the construction of kinetic models
on larger scales – the sizes of such models
have been lagging behind purely structural
metabolic network models, which have been
available on genome-wide scales for more
than a decade.
To utilise nuclear magnetic resonance (NMR)
spectroscopic technology for in vivo modelling of
enzyme kinetics.
KEY COLLABORATORS
Enzyme kinetics and modelling of various cellular
pathways: Professor Jannie Hofmeyr; Professor
Jacky Snoep; Professor Ann Louw, Department of
Biochemistry, Stellenbosch University, South Africa
Modelling redox networks: Dr Ché Pillay, University of
KwaZulu-Natal, South Africa
Enzyme kinetics for systems biology: Dr Gertien Smits,
University of Amsterdam, Netherlands
Modelling plant isoprenoid metabolism: Professor
Jonathan Gershenzon; Dr Lawrie Wright, Max Planck
Institute for Chemical Ecology, Germany
PARTNERS
Beilstein-Institut zur Förderung der Chemischen
Wissenschaften, Germany
International Study Group for Systems Biology, UK
South African Society of Biochemistry and Molecular
Biology, South Africa
FUNDING
South African National Research Foundation
Alexander von Humboldt Foundation
CONTACT
Johann Rohwer
Professor of Molecular Systems Biology; Head of the
Department of Biochemistry
Stellenbosch University
JC Smuts Building
Variation in substrate and product
concentrations (left panel) and calculated
reaction rates (right panel) determined
from a time-course of nuclear magnetic
of enzyme kinetics involves compiling data
representing the kinetics of individual reactions.
While this approach is not inherently flawed, it
does necessitate the derivation of consistent,
representative experimental data – typically a
costly and labour-intensive requirement.
AN INNOVATIVE APPROACH
By applying the latest in nuclear magnetic
resonance (NMR) spectroscopic technology,
Rohwer’s in vivo aspirations became possible.
NMR spectra can be acquired in a real-time,
non-invasive manner, mitigating the sampling
requirements typical of conventional assays,
as Rohwer highlights: “NMR is an online
technique, which means that samples do not
need to be quenched or extracted prior to
analysis, as is often the case with traditional
assays”. NMR spectroscopy also acquires a
richer dataset, meaning fewer experiments,
and thus less time and money, are required to
determine reaction kinetics.
By collecting NMR data describing the
changing concentrations of effectors (molecular
regulators of biological activity), substrates
Van der Bijl Street
Stellenbosch
Western Cape 7600
South Africa
resonance spectra collected for the E. coli
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phosphoglucoisomerase reaction
E [email protected]
(substances metabolised by a given enzyme)
and metabolites (the products of enzymatic
reactions) during a metabolic process, the
kinetics of this process may be calculated.
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http://bit.ly/RG_Johann_Rohwer
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JOHANN ROHWER is Professor in
A NUMBERS GAME
Recognising the model to be only as good
as the maths, Rohwer’s group also sought
to develop and employ a more universal
equation. Where traditional approaches began
as overly complex, and were simplified to a
point of compromise, the generic reversible
Hill equation (GRHE), on which Rohwer’s
calculations were based, makes no unjustified
assumptions and is easier to interpret in the
context of experimental data.
the Laboratory for Molecular Systems
Biology and, since 2015, Head of
the Department of Biochemistry
at Stellenbosch University, South
Africa. He obtained his PhD in 1997 from the University
of Amsterdam, Netherlands, under the supervision of
Hans Westerhoff. His main research interests are the
construction of kinetic models of cellular function,
with a particular emphasis on plant and microbial
central carbon metabolism, cellular redox networks
and glucocorticoid receptor signalling. To aid model
construction, his lab has developed a method applying
The modified GRHE therefore copes well
with enzymatic behaviours such as allosteric
regulation, wherein a regulatory molecule may
bind to a region of the enzyme distinct from its
active site to influence its activity. This marks a
great improvement over the popular MichaelisMenten equation, which assumes there to be no
allostericity, cooperativity or product inhibition
at play.
NMR spectroscopy to obtain enzyme kinetics.
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