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REVIEW
Designing and encoding models for
synthetic biology
Lukas Endler*, Nicolas Rodriguez, Nick Juty, Vijayalakshmi Chelliah,
Camille Laibe, Chen Li and Nicolas Le Nove
`re
EMBL—European Bioinformatics Institute, Wellcome Trust Genome Campus, Hinxton,
Cambridge CB10 1SD, UK
A key component of any synthetic biology effort is the use of quantitative models. These
models and their corresponding simulations allow optimization of a system design, as well as
guiding their subsequent analysis. Once a domain mostly reserved for experts, dynamical
modelling of gene regulatory and reaction networks has been an area of growth over the last
decade. There has been a concomitant increase in the number of software tools and
standards, thereby facilitating model exchange and reuse. We give here an overview of the
model creation and analysis processes as well as some software tools in common use. Using
markup language to encode the model and associated annotation, we describe the mining of
components, their integration in relational models, formularization and parametrization.
Evaluation of simulation results and validation of the model close the systems biology ‘loop’.
Keywords: synthetic biology; systems biology markup language; computational biology
1. INTRODUCTION
Synthetic biology has seen an explosive development
over the last decade (Sprinzak & Elowitz 2005;
Andrianantoandro et al. 2006). The engineering of
biological systems has been boosted by the availability
and improvement of wet-lab techniques. Hand in
hand with the development of these experimental
approaches, the use of computational tools and
methods to model and interpret biological systems
has spread and become the mainstream. While at the
end of last century, only a few software tools were
specifically designed to build and interpret gene
regulatory and biochemical reaction networks, today
they number in the hundreds.
Biological systems are highly interconnected, and
their behaviours most often cannot be derived solely
from the properties of single components without the
help of computers. While the dynamics of elementary
interactions and simple regulatory motifs can sometimes
be inferred without the help ofmathematical models, the
behaviour of more complex reaction networks cannot be
unravelled merely by reasoning alone. Therefore, math-
ematical descriptions of biochemical processes and
computational analysis, in combination with experi-
mental results, have become a necessity.
Computer simulations allow the prediction of
system behaviour and can help to elucidate the
mechanisms underlying biological phenomena. An
initial model should be created which is reasonably
faithful to the biological structure, and is capable of
reproducing known behaviours to an acceptable extent.
This can then be used to probe the effects of different
environmental conditions, perturbations and variants
or different designs. For instance, it is possible to use
in silico experiments to screen for possible drug targets
(Undrovinas et al. 2006), to optimize certain aspects of
asystem(e.g.Reijenga et al. 2001), to simulate the
behaviour of mutants (e.g. Bray et al. 1993;Novak &
Tyson 1997) and to analyse the evolvability and
robustness of certain systems (von Dassow et al.
2000). Analyses at this speed and low cost could never
be achieved solely using classical experimental
methods. Finally, and maybe equally important,
models can show us gaps in our understanding of
biological processes and suggest which piece of the
puzzle or experimental data is missing. The modelling
process itself allows one to scrutinize not only the
available data, but also the known or assumed
mechanisms. This often leads to more questions than
answers, and sometimes shows that mechanisms
believed to be established do not actually fit into
observed phenomena or are insufficient to explain
experimental results.
doi:10.1098/rsif.2009.0035.focus
One contribution to a Theme Supplement ‘Synthetic biology: history,
challenges and prospects’.
Electronic supplementary material isavailable at http://dx.doi.org/10.
1098/rsif.2009.0035.focus or via http://rsif.royalsocietypublishing.org.
*Author for correspondence (lukas@ebi.ac.uk).
Received 23 January 2009
Accepted 9 March 2009 This journal is q2009 The Royal Society
J. R. Soc. Interface (2009) 6, S405–S417
S405
Published online 1 April 2009
Modelling has been an integral part of the synthetic
biology work since its inception (Elowitz & Leibler
2000;Gardner et al. 2000). Synthetic biology, indeed,
does not differ from any other engineering activity,
where designing and testing of models are as important
as the building step. This not only allows economy of
time and effort, but also permits optimization of the
final product. However, modelling in biology is most
often an iterative process; the mathematical model has
to be validated by comparison of the model analyses
and simulation results with experimental measure-
ments, and to be refined depending on these compari-
sons. This is especially true for kinetic modelling since a
description of the system’s final state is required
together with its changes over a temporal range.
Figure 1 illustrates the model creation process.
Driven by the needs of the research community,
the availability of more usable software tools and the
existence of community standards, the user population
has shifted from dedicated experts in mathematical
modelling to scientists with different backgrounds and
interests. Computational models have now become
another tool for use in parallel to various experimental
approaches. Modelling, though, still remains a highly
interdisciplinary task. First, it demands a detailed
understanding of the biological and biochemical pro-
cesses to be modelled. This biological knowledge alone
is normally not enough, since encoding it into a
computer readable form requires some mathematical
knowledge and, depending on the tools used, also needs
some computer skills. Model manipulation, evaluation
and prediction generation, on the other hand, require
both computational and biological experience. So while
more and more intuitively usable software tools
emerge, modelling is still a collaborative effort of
experts in different fields or the domain of scientists
with a broader overview and training.
2. FORMATS FOR MODEL REPRESENTATION
Biochemical or genetic regulatory networks can be
represented in various forms and formats, ranging from
a crude pathway or an interaction map on a napkin to a
system of ordinary differential equations in a computer
algebra system (plain text file), or to machine execu-
table code producing integrated time courses of a
specific system. Biological reaction networks have
many different logical layers. The first layer comprises
the interacting molecules, as well as all the state
variables. The interactions between the components
and the underlying reaction network define the
topology of the system and form the next logical
layer. The final layer comprises the mathematical
expressions for the interactions, and the fluxes in and
out of the system.
Synthetic biology activities require the incorpor-
ation of as many of these layers as possible in the model.
Static network analysis or creation of deletion mutants
components interactions,
reactions
topology,
design
model
e.g. SBML,
CellML improvement,
optimization
validation
(simulation,
prediction) objectives
(behaviour, yield,
robustness)
experimental
results
biological
realization
evaluation
mathematical
relations,
formularization
primary
literature,
databases
parameters,
quantitative
values
parameter
estimation
Figure 1. Diagram describing the model creation process, centred around the model file. External inputs come from literature,
databases or experiments. Validation and parameter estimation give direct feedbacks on the model, while the predictions can
also guide experimental design. The desired objectives for the system to be designed are part of a mostly in silico design cycle, the
biological implementation and the fitting and comparison of the model to observations are part of the standard systems biology
model development cycle.
Review. Model creation for synthetic biology L. Endler et al.
J. R. Soc. Interface (2009)
S406
of a system requires knowledge of the stoichiometry of
reactions. This cannot always be readily derived from,
for example, ordinary differential equation represen-
tations without additional information. Furthermore,
in some cases, a system has to be interpreted using
different modelling frameworks. For example, in
genetic regulatory networks, a continuous determinis-
tic framework might be useful for bifurcation analysis of
the qualitative behaviour, while a probabilistic discrete
approach could be used to explore robustness and
behaviour at low concentrations of some species
(Elowitz & Leibler 2000).
As dedicated tools, targeted at different tasks, often
use distinct entry formats, their use requires conversion
or reimplementation of the original models into compa-
tible formats. Manual conversion of a model from one
format to another can be a very tedious and error-prone
task, especially for bigger systems. The development of
exchange formats for mathematical models facilitated
the use of different programs and tools and facilitated
their reuse and alteration. Two extensible markup
language (XML) formats, the systems biology markup
language (SBML) (Hucka et al.2003) and cellular
markup language (CellML; Lloyd et al.2004), have
gained broad support in the modelling community. Both
languages store mathematical expressions using content
MathML v. 2.0 (Ausbrooks et al.2003)andusethe
resource description framework (RDF; Beckett 2004)to
incorporate machine-readable metadata.
SBML has been developed as a community effort and
consists of hierarchical lists of elements describing the
compartments of the model, the pools of reacting
entities and the interactions taking place. All elements
can be annotated and commented in both human-
readable and machine-interpretable forms, allowing
extensive documentation and external references to be
directly included in the model file. SBML has been
widely adopted by the modelling community and is
supported by hundreds of tools (see http://sbml.org/
SBML_Software_Guide). A key to the success and
rapid adoption of SBML by developers has been the
availability of a general application programming
interface (API) library, LIBSBML (Bornstein et al.
2008). This allows easy access to all elements of a model
and provides unit and semantic checking of the
SBML file. Tools can therefore use their own internal
representation of a mathematical model, and read and
write the actual model file over the standardized
interface. As LIBSBML also features bindings to
common scripting languages, a computer-literate mod-
eller can use the API for automatic batch manipulation
or simple analysis of SBML files.
Here follows a brief description of the main SBML
elements:
—Compartment. A well-stirred container in which
species reside and reactions take place. This may be,
for example, a two-dimensional membrane or a cell
extending in three dimensions.
—Species. Entities of a certain type residing in a
specific compartment. For example, ATP in the
compartment mitochondrion would constitute a
different species from ATP in the cytosol.
—Parameter. This includes all other kinds of named
quantities. They can be constant or variable and
altered by rules and events. For example, the proton-
motive force or a chemical potential could be defined
as a parameter in a model.
—Reaction. A transformation between one or more
species with specified stoichiometries. This encom-
passes not only chemical reactions, but also trans-
port between compartments, in- and out-flux and so
on. It can contain an expression for a rate law.
—Rule. Mathematical expressions to define relations
between species and parameters. They come in three
different types: assignment rules directly assign the
value of an expression to a variable, rate rules to its
rate of change with time and algebraic rules
define general algebraic equalities between different
variables.
—Function. Definitions of reusable mathematical
functions.
—Event. A discontinuous change taking place when a
trigger condition changes from false to true. The
change can be in all kinds of variables and apply to
more than one.
—Note. Extensive remarks in extensible hypertext
markup language (XHTML), meant to be of human
readable form.
—Annotation. Software-specific metadata and
controlled, machine-readable characterizations in
an RDF format.
The other widely used XML format, CellML, provides
a more modular structure. A model description consists
of components and lists of connections between them.
This leads to a greater flexibility, especially for multi-
scale models, and allows for easier reuse of components
at the expense of biochemical semantics. The language is
mostly developed by the Physiome Project and Bioengi-
neering Institute at the University of Auckland. To date,
there have been fewer tools supporting CellML (http://
www.cellml.org/tools) than SBML, but tools exist to
interconvert between both formats (see http://www.ebi.
ac.uk/compneur-srv/sbml/convertors/SBMLConvertors.
html;Schilstra et al.2006), offering users the
possibility to choose from a broad range of evaluation
software programs.
An important, though often neglected, part of
mathematical models is descriptions and character-
izations of its components. It can be very valuable to
include references and comments directly in the model
file, especially for bigger models. Here, entities and
relations can become hard to assign to their corre-
sponding biological species and processes, and the
original sources can be hard to keep track of. Therefore,
extensive documentation of the model, and the
references for its components, should always be kept
with the model file, especially if more than one person is
involved in the modelling process. Traditionally, a
model is described by an accompanying text physically
separated from the file containing it. While it is
essential to have a verbose description of the model,
direct annotation of the elements is very useful for
exchange and reuse of models, as well as during
the creation process itself. A reporting standard for
Review. Model creation for synthetic biology L. Endler et al.
J. R. Soc. Interface
407
(2009)
S
the curation and validation of biological models—
MIRIAM or minimal information requested in the
annotation of biochemical models (Le Nove
`re et al.
2005)—not only gives rules an encoded model to
comply with, but also defines a form for controlled
annotations. This scheme for annotations consists of a
stable identifier in the form of a uniform resource
identifier (URI; Berners-Lee et al. 2005) for each piece
of information and a qualifier indicating the relation of
this information to the annotated element. A catalogue
of resources (such as controlled vocabularies or
databases) is provided in MIRIAM resources
(Laibe & Le Nove
`re 2007), as well as a set of online
services, which include creation and resolution of model
annotations in URI form. The ability to include not
only the mathematical description, but also reference
and biological information in the same file simplifies
exchange and reuse of models and eases collaborative
work of groups of people on one model. Using a formal
modelling language such as SBML, the process of
modelling can easily become a collaborative effort, with
different people using different tools to insert key
players and reactions, annotations, kinetic rate laws,
mathematical expressions and parameter values into a
common model file.
3. GATHERING BITS AND PIECES
Prior to the creation of a detailed kinetic model, one
needs to list the main elements. These are the key
interacting species and other observables of the system
one wants to model (and synthesize afterwards). In
addition, one must gather their known regulatory
interactions and chemical reactions from the scientific
literature and databases. The kind of databases to mine
depends very much on the system to be modelled.
Apart from the general list given in the yearly nucleic
acid research database issue (Galperin & Cochrane
2009), an overview of resources more specific to
modelling is given in Ng et al. (2006) and Wierling
et al. (2007). For biological pathways and reactions, the
Kyoto Encyclopedia of Genes and Genomes (KEGG;
Kanehisa et al. 2008), Reactome ( Vastrik et al. 2007;
Matthews et al.2008), Panther (Mi et al. 2007) and the
Meta- and BioCyc (Caspi et al. 2008) databases are
especially useful, as they either directly export in
generally used computer-readable formats (such as
SBML) or their outputs can be converted to them.
Complementary to searching through databases,
text mining tools can help to confine the number of
articles to screen and also reveal valuable information
on interactions or relationships between components.
Among the tools available, IHOP (http://www.ihop-
net.org/;Hoffmann & Valencia 2004) and Chilibot
(http://www.chilibot.net;Chen & Sharp 2004) have
been valuable for us in identifying potential protein and
gene-regulatory interactions. A general overview of
text mining and some of the available tools is given in
Krallinger et al. (2008) and Ananiadou et al. (2006),
for example.
Another possibility is to start with existing models
that one can access through databases and repositories
such as the Biomodel database ( Le Nove
`re et al. 2006;
figure 2), Java web simulation ( JWS) online (Snoep &
Olivier 2002) or the CellML model repository (Lloyd
et al. 2008). For more specific models, although still
quite remote from synthetic biology projects, one can
use dedicated repositories such as the database of
Quantitative Cellular Signalling (Sivakumaran et al.
2003) and ModelDB (Hines et al. 2004). The models
Figure 2. Biomodels database is a resource offering curated and annotated versions of models published in peer-reviewed
literature. The models can be browsed, downloaded or directly simulated online, as shown here for the repressilator.
Review. Model creation for synthetic biology L. Endler et al.
J. R. Soc. Interface (2009)
S408
stored in these databases not only give an idea of the
interactions and species one may need to model a given
biological process, but also provide an overview of the
mathematical relations used by other researchers. The
models, or parts of them, can then be used as starting
points or modules for new modelling efforts. Some of
these databases, such as Biomodels database, directly
allow creation and retrieval of complete submodels
based on user-selected components. Another possibility
for creating models from existing ones is to use an online
modelling environment such as WEBCELL (Lee et al.
2006). In addition to offering multiple analysis
methods, WEBCELL also allows import and modification
of models from Biomodels database and JWS online.
An interesting approach is adopted by SYCAMORE
(Weidemann et al. 2008), which merges a database of
quantitative enzyme kinetics—SABIO-RK (Wittig
et al. 2006)—with the ability to create models via a
web front end. These can subsequently be downloaded
in the SBML format.
To keep track of the resources and references used for
model components, as mentioned above, they can be
stored in a separate text file or as metadata in the XML
file directly. SBML offers two possibilities for the latter:
(i) the notes and (ii) annotation elements. Both provide
further information regarding model elements in
human-readable or a machine-friendly format, respect-
ively. Notes are encoded in XHTML, providing
flexibility and human readability. Annotations, on the
other hand, contain machine-readable metadata in
various XML formats, which may be software-specific
information or standard pointers, such as MIRIAM
annotation in RDF. Many SBML-supporting tools,
such as SBML editor (Rodriguez et al. 2007), COMPLEX
PATHWAY SIMULATOR (COPASI, Hoops et al. 2006)
and CELLDESIGNER (Funahashi et al. 2003), allow notes
or annotations to be kept.
4. MODEL CREATION
Having identified the key components of the system,
reacting entities and topology, one needs to design the
biochemical structure of the model. While the former
steps have dealt with biology, the current one deals
with chemistry. This step is still independent of a
specific mathematical framework or formulation used.
While stoichiometry and qualitative influence of the
species can be sketched at this stage, no mathematical
expressions and quantitative information are necessary
for creating a static model of the system. Still, this kind
of a model has already been used to do basic structural
analysis, for example for building steady-state models
of metabolism (for reviews see Klamt & Stelling 2003;
Llaneras & Pico
´2008;Planes & Beasley 2008), studying
logical networks (Glass & Kauffman 1973;Thomas
1973) or looking for network motifs in regulatory
networks (Alon 2007).
SBML supports this stage, especially with the
reactions element. This element is not solely destined
for simple chemical reactions, but encompasses all forms
of transformations between physical entities as well as
transport, in- and outflows. Each reaction needs to have
at least one reactant or product with a given
stoichiometry. Furthermore, it can also contain a species
called modifiers, which are not consumed by the reaction,
but they influence its rate in some form. To further
characterize the role of involved reactants and modifiers,
it is helpful to use controlled vocabularies. SBML allows
the inclusion of identifiers pointing to terms from the
systems biology ontology (SBO; Le Nove
`re et al.2007)to
add a layer of semantics on the components of a model.
SBO is a set of six controlled vocabularies that cover, in
the context of systems biology, elements such as
interactions, mathematical expressions, modelling frame-
works and quantitative parameters. In the repressilator
model, for e.g., LacIp might be labelled as an inhibitor
(SBO:0000020) in the transcription of the tetR gene.
Concerning electrical circuit diagrams, a graphical
representation of a biochemical system can be very helpful
at this stage. Unlike the engineering disciplines, however,
the biological community has yet to adopt a unique and
standardized graphical language for the display of
biological networks. The Systems Biology Graphical
Notation (SBGN) is a recently proposed visual language
for the representation of biological networks (Le Nove
`re
et al. 2008). It allows unambiguous representation of a
process diagram of the reaction network. A number of
modelling tools allow one to lay out systems graphically
and store them in SBML. CELLDESIGNER (Funahashi et al.
2003), for example, is a platform-independent graphical
editor for biological networks, into which existing models
in SBML format can be imported and modified. Notes can
also be added and mathematical equations entered for the
different interactions. Substrates, products and modifiers
can be added either directly by drawing and setting the
appropriate connections on the canvas or by entering
them in the corresponding lists. Information about the
graphical layout is stored in a CELLDESIGNER-specific
format in the annotation elements of the newly created
SBML file. A possible SBGN compliant layout of
the repressilator and CELLDESIGNER’s interface are
shown in figure 3.
While CELLDESIGNER is mainly an editor, it has some
built-in deterministic integration capability features,
based on a third party ODE SOLVER, SBMLODESOLVER
(Machne
´et al. 2006). For a more thorough analysis,
such as stochastic interpretations or structural
analysis, the simulation package COPASI (Hoops et al.
2006) and the large group of tools contained in the
systems biology workbench (SBW; Sauro et al.2003)can
be used directly from the program. Using SBML as its
native format CELLDESIGNER generates models that can
be used by the whole family of SBML aware tools.
While being intuitive and visually appealing,
graphical representations can quickly become cluttered
and confusing for large or densely connected networks.
Another possibility for creating and editing models in
SBML format is purely form-based editors, which
provide scalability while retaining precision. We
would just wish to mention a few different approaches
at this point. For instance, JIGCELL (Vass et al. 2004),
developed at the Virginia Polytechnic Institute & State
University, uses a model builder in the form of a
spreadsheet. This gives a nice overview even in cases of
complex and dense networks. Meanwhile COPASI
(Hoops et al. 2006) uses a tree-like representation of
Review. Model creation for synthetic biology L. Endler et al.
J. R. Soc. Interface
409
(2009)
S
the different models elements, spreadsheets to quickly
list elements of a given type and more detailed forms
to precisely alter each element. While potentially
slower than entering reactions in a pure spreadsheet,
it facilitates the definition of complex reactions and
performs extensive checking in the background. A third
approach is taken by SBMLEDITOR (Rodriguez et al.
2007;figure 4), a low-level SBML editor, currently
without any simulation or evaluation capabilities.
SBMLEDITOR is more closely based on the SBML
format itself and supports the entire language. It has
been up to now one of the few that permit direct
entering of MIRIAM and SBO annotations.
Lately, some tools specifically aimed for synthetic
biology have been created. One approach has been to
create gene-regulatory networks from reusable modules
similar to those stored in the MIT Registry of Standard
Biological Parts (Endy 2005). An effort using quantitative
modules in CellML format has been presented at the
SysBioSys 2007 conference (Rouilly et al. 2007). Some
recent tools have allowed the export in SBML format,
such as the command line tool ASMPARTS (Rodrigo et al.
2007), synthetic biology software suite (Hill et al. 2008), as
well as an extension (Marchisio & Stelling 2008)written
for the PROMOT (Ginkel et al. 2003) suite. These tools and
efforts are still in the early stages, but they have already
seemed to be quite usable, even if they do not offer the full
range of biological parts available in the registry.
5. ENTERING MATHEMATICAL RELATIONS
AND NUMERICAL VALUES
Once a potential network structure is created, a
mathematical framework has to be chosen to develop
a kinetic version. As different frameworks allow for
complementary analysis and interpretation, it is often
useful to keep the model interpretable by more than
Figure 3. The CELLDESIGNER interface provides an ample selection of graphical elements and editing options to design biochemical
and mathematical models. The repressilator is represented in CELLDESIGNER’s graphical notation, a derivative of SBGN. The
raised window is the editing form for the kinetic law of a single reaction.
Figure 4. SBMLEDITOR allows detailed manipulation of all
elements of SBML. Here the main overview, the species editing
form, a MIRIAM annotation dialogue and the MathML code of
the kinetic law shown in figure 2 are displayed.
Review. Model creation for synthetic biology L. Endler et al.
J. R. Soc. Interface (2009)
S410
one formalism. The simultaneous use of alternative
frameworks has proved beneficial, especially for gene
regulatory networks. This can be seen in one of
the landmark papers of synthetic biology describing
the repressilator (Elowitz & Leibler 2000). A determi-
nistic approach was used to analyse the qualitative
behaviour in dependence of key parameters, while a
stochastic version permitted testing of the robustness of
the design to transcriptional noise. In this section, we
will concentrate on these two frameworks.
As chemical and biological processes are inherently
stochastic, it seems natural to take this into account for
modelling. However, stochastic simulations are generally
computationally much more intensive, and for bigger
models or greater numbers of interacting components,
this burden quickly becomes limited. For metabolic
processes, and in general reactions involving more than a
few hundred molecules, the continuous deterministic
approach provides a fairly good approximation.
The adequate forms of the mathematical expressions
describing interactions and reaction velocities are often
difficult to find at first, and sometimes different kinetic
laws have to be tried out. In general, one can apply
expression derived from first principles or, if the
mechanism of reaction is not well defined or completely
unknown, resort to generic or empirical rate laws. One
of the most general approaches is to employ rate laws
derived according to the law of mass action kinetics. In
these equations, reaction rates are directly proportional
to the activities of the reactants (e.g. concentrations in
dilutions and partial pressures in gas phase) to a power,
called the order of the reaction for this reactant, which
is equal to its stoichiometry. This allows automatic
generation of kinetic expressions for bigger reaction
networks with only stoichiometric information, by
fitting experimental datasets (sometimes leading to
reaction orders that differ from stoichiometries). While
this approach is widely applied in chemical systems and
also has been quite successfully used in signal transduc-
tion, it leads to a high number of parameters and
intermediary steps, and needs the explicit inclusion of
catalysing enzymes. For enzyme-catalysed reactions
with a known reaction mechanism, mechanistic rate
laws using quasi steady-state or rapid equilibrium
assumptions can be applied. The most common rate
laws can be looked up in reference books (e.g. Segel
(1993) or Cornish-Bowden (2004)) or derived using
methods such as the graph-based one derived by King &
Altman (King & Altman 1956;Chou 1989). However, for
this approach a detailed knowledge of the reaction
mechanisms and modifying effectors is essential. Each
reaction has also to be treated individually, which might
not be feasible for larger models. As an alternative,
generic expressions can be used, which show the general
behaviour of enzyme-catalysed reactions for varying
ranges around reference states of the system. These
allow the inclusion of experimentally derived parameters,
activators or inhibitors to some extent, even if the exact
mechanisms are not known. The simplest forms of
these are the irreversible Michaelis–Menten and Hill-
like rate laws. However, as many reactions cannot be
assumed to be mostly unidirectional (Cornish-Bowden &
Cardenas 2001), generic reversible forms for the most
commonly used biochemical rate laws have been pro-
posed. Examples are the convenience rate law (Lieber-
meister & Klipp 2006) and the reversible Hill equation
(Rohwer et al.2007). These rate laws also allow one to
include thermodynamic constants, which are easier to
measure than kinetic constants, and to easily adopt
experimentally determined parameters, while displaying
behaviours similar to more detailed mechanisms over a
broad range of concentrations.
Some modelling tools offer predefined rate laws. For
instance, COPASI and WEBCELL have a wide range of
enzyme and general kinetic laws which can be easily
incorporated into the model or used to create more
elaborate ones if necessary. Another interesting feature
offered by COPASI is the ability to transform all
reversible reactions in a model into pairs of irreversible
ones. While this of course only works for simple rate
laws, it facilitates the use of subsequent stochastic
evaluations, as these require the use of probabilities for
elementary molecular events.
A convenient way to try out different rate laws for
larger models is shown by SBMLSQUEEZER (Dra
¨ger et al.
2008), a plug-in for CELLDESIGNER. It allows one to choose
single or groups of reactions, and to apply different
kinetic laws from a list of formalisms. In order to assign
the adequate rate law and use the correct reactants,
products and modifiers, it analyses the diagram created
by CELLDESIGNER (a derived form of SBGN) and takes
SBO annotations of the species, parameters and reactions
into account. While this still needs some user interaction,
it is a commendable improvement that greatly facilitates
the creation of larger and complex models.
Various mathematical formalisms are employed to
model gene-regulatory networks (reviewed in de Jong
2002). While there is evidence for the stochastic nature
of transcriptional regulation (Fiering et al. 2000;
Elowitz et al. 2002), deterministic approaches are
often chosen due to their easier evaluation, and for
simplicity of qualitative analysis. In our example, the
repressilator, the authors used a Hill-type regulation
function to simulate transcriptional repression, and
first-order mass action rate laws for modelling trans-
lation, transcription and decay. Hill-type functions are
often used to model gene expression or signal transduc-
tion as they are a subset of logistic functions, and they
provide a sigmoid or step-like dose response to
modulators, as found in some experimental results
(Yagil & Yagil 1971;Rosenfeld et al. 2005;Kaplan et al.
2008). Sometimes, the Hill coefficient can be justified by
cooperative binding behaviour—as in the case of the
repressilator. In other cases, it can be due to dimen-
sional restriction or more complex mechanisms, sub-
sumed into a single step. Transcription and translation,
while actually being composed of multiple reactions,
are modelled as single first-order reactions. For the
stochastic simulations, repressor binding had to be
unravelled into single steps. COPASI allows one to
interpret the model using different algorithms. Both a
sample stochastic and deterministic time-course evalu-
ation is shown in figure 5.
Some problems cannot be sufficiently described
without taking spatial inhomogeneities into account.
Although many intracellular processes have been
Review. Model creation for synthetic biology L. Endler et al.
J. R. Soc. Interface
411
(2009)
S
described with the assumption of a well-stirred reaction
environment, this approach is insufficient for processes
involving intracellular or extracellular gradients or
heterogeneous populations of molecules (Kholodenko
2006). While some tools exist to help with the creation
and simulation, there are no standard formats for
interchange of models involving diffusional processes up
to now. An exhaustive survey of the various spatial
modelling approaches is beyond the scope of this paper.
Different software tools and formalisms commonly
employed are reviewed in Lemerle et al. (2005),
Takahashi et al. (2005) and Tolle & Le Nove
`re (2006).
Another problem plaguing modelling, in particular
of signalling processes, is the combinatorial explosion
resulting from alternative non-covalent binding of
proteins, and molecular entities existing under different
states (conformations, covalent modifications, etc.)
One approach to avoid the problem is to use agent-
based models of populations. In these methods,
interactions between autonomous individuals are
simulated. They have been successfully employed to
simulate, for instance, bacterial chemo-taxis (Shimizu
et al. 2003), tissue formation and developmental
processes (reviewed in Thorne et al. 2007) and cancer
growth (Wang et al. 2007;Zhang et al. 2009). A related
approach is the use of rule-based models, where actual
reactions are not described, but only the rules to
generate them during simulations (e.g. Blinov et al.
2004;Lok & Brent 2005). As with spatial modelling,
there are still few software tools supporting these
frameworks, specifically for biology.
6. FINDING AND FITTING PARAMETERS
To create a quantitative model, values for the various
constants and parameters used in mathematical
relations have to be derived. While there exist a vast
amount of experimentally derived values in scientific
literature, it is often hard to find the relevant ones in
the multitude of publications.
For enzyme-catalysed reactions, there exist various
databases helping to identify the appropriate values.
Two databases providing kinetic parameters are
BRENDA (Chang et al. 2008) and the above mentioned
SABIO-RK (Wittig et al. 2006). Both offer a wide range
of parameters and reactions extracted from primary
literature, with powerful search options. SABIO-RK
additionally offers the mechanism assumed in the
original source and the ability to export reactions in
SBML format. Help with directly searching the primary
literature is offered by KMedDB (http://sysbio.molgen.
mpg.de/KMedDB;Hakenberg et al.2004). It allows
PubMed abstracts to be searched for various kinetic
parameters in combination with compound, organism or
enzyme reaction identifiers. Further information on the
thermodynamics of biological reactions is available at
the TECRDB (Goldberg et al.2004). Another helpful
source of general interaction parameters is given by the
Kinetik Data of Biomolecular Interaction database
(Kumar et al.2008).
Another common way of finding quantitative infor-
mation is going through papers describing modelling
efforts in the relevant fields. These can be a valuable
source of pointers to relevant primary literature, and
can also help with deriving or adapting experimental
parameters to the form needed for the model. The
above-mentioned databases and repositories of models
are quite useful in this respect, as they not only give an
overview of existing parametrized models, but also offer
links to the primary literature.
Most of the parameters derived from the literature
can nevertheless be taken only as guideline values for
Figure 5. COPASI offers various methods for evaluating dynamic models and displaying the results. Time courses of the protein
numbers of the repressilator are shown here, calculated using a deterministic (LSODA) and a stochastic (Gibson–Bruck)
method. The deterministic solution is also represented as the phase plane of the tetR and the LacI proteins, showing the
convergence to a limit cycle. In a separate window, the MIRIAM annotations of the model element are shown.
Review. Model creation for synthetic biology L. Endler et al.
J. R. Soc. Interface (2009)
S412
modelling. If measured time courses or steady-state
data exist for the system to be described, several
algorithms have been implemented for parameter
estimation and refinement. For a short overview and
comparison of some of these methods see Moles et al.
(2003) and Rodriguez Fernandez et al. (2006).An
intuitive and useful interface that features numerous
global and local estimation methods is offered by
COPASI. It allows simultaneous fitting of a subset of
parameters to different sets of experimental values.
Unfortunately, COPASI up to now has not included
support for events. To estimate parameters in models
containing events, the tool PET (http://mpf.biol.vt.edu/
pet), closely connected with the JIGCELL suite, offers a
convenient graphical interface also allowing multiple
time series to be fitted simultaneously. Another tool
supporting events is the command line-driven SBML-
PET (Zi & Klipp 2006). For users of the commercial
Matlab (The MathWorks, MA, USA) environment,
SBTOOLBOX2(Schmidt & Jirstrand 2006), a free package
with SBML support, offers various estimation and
optimization methods.
A completely different approach to search for
adequate parameters is subsumed under the term
optimization. While similar in its methods to parameter
estimation, it differs in that it tries to reach a global
goal rather than fit a given set of parameters, and is
widely used in the engineering of metabolic systems.
For a comprehensive review see Banga (2008). Again
COPASI offers a range of different algorithms for
minimization of a given target objective function.
Another interesting approach is inverse bifurcation
analysis (Lu et al. 2006). It can be used to find
parameter values exhibiting certain qualitative
behaviours. For example, it can help in finding regimes
that display certain kinds of switching behaviour, or
creating more robust oscillators with a given system.
Unfortunately, the tools available for this approach up
to now have used MATHEMATICA (Wolfram Research,
Inc., IL, USA) or Matlab, and have still required quite
some expert knowledge and skill. Hopefully, more user-
friendly tools will be developed for this promising
approach in the future.
7. VALIDATION AND EVALUATION
OF THE MODEL
Once a model has been created that can be run, it still
has to prove its ability to reproduce experimental
results up to a required accuracy and predict interest-
ing and non-trivial observables.
Validation of a model can be performed in two stages.
Observation of the qualitative behaviour of the model can
be very informative in models having multiple steady
states and showing switch-like or oscillatory behaviours.
The qualitative behaviour can be studied either over
small parts of the parameter space, by simply scanning
over defined ranges of parameters and initial conditions,
or by doing global bifurcation analyses. While the first
procedure is easily accessible in many software
packages, the second one requires more dedicated tools.
CELLDESIGNER offers simple scanning over a range of
parameters through SBMLODESOLVER, while COPASI
offers more sophisticated possibilities. Using loops and
combinations of tasks, scans over more than one
condition or parameter are possible. For analysing the
global qualitative behaviour of a model, numerical
bifurcation analysis is one of the most widely used
methods. Among the tools available, the free tools XPP-
AUT (Ermentrout 2002)andOSCILL8(http://oscill8.
sourceforge.net/), both using the AUTO continuation
library (Doedel 1981), have been used in biological
modelling (e.g. Csika
´sz-Nagy et al.2006). Converters
from SBML to the format used by XPP-AUT and OSCILL8
are integrated in JIGCELL, COPASI, SBW, SBTOOLBOX2
and Biomodels database. OSCILL8 can also be integrated
into the SBW, allowing to seamlessly analyse models in
this framework.
Model checking, originally used in computer science
(Clarke & Emerson 1982;Queille & Sifakis 1982), is a
different approach to validate the qualitative behaviour
of systems. It allows one to test whether the system can
fulfil certain objectives, for example reachability of
certain states, the consecutive temporal activation of
certain species or oscillatory behaviour. While support
for quantitative dynamical models is still insufficient,
BIOCHAM (Calzone et al. 2006) has limited SBML
support and offers model checking capabilities. ROVER
GENE(Batt et al. 2007), a free add-on to the
commercial Matlab environment, has been more
specifically aimed at the needs of synthetic biology.
Using piecewise affine, or for a better fit multi-affine,
functions to model transcriptional regulation, it allows
users to check whether a genetic regulatory system can
exhibit a desired dynamical property or behaviour in a
given range of parameters and initial conditions. More
relevant to the design of networks, the tool can also be
used to find parameters showing a desired behaviour
and to test the robustness of the behaviour around these
parameter values.
Qualitative analysis can also give hints as to which
parameters offer the best success in achieving a desired
behaviour or whether a certain design can exhibit the
wanted function at all. Identifying the most promising
parameters to change, of course, depends not only on
the mathematical analysis, but also on the biological
feasibility. While some characteristics such as promoter
strength, transcript and protein stability are quite
variable, enzymatic activities, for example, might be
harder to tweak. Also as changes in the characteristics
of biological components can at best be qualitative, it is
important to find parameter ranges that show
behaviour robust to variations. In the repressilator
example mentioned above, the qualitative analysis led
to the identification of a few key properties important
for obtaining stable oscillations—strong promoters
with tight cooperative repression and comparable
mRNA and protein half-lives, with the protein half-
lives mainly determining the period length. Apart from
helping to choose the right biological components, these
criteria also led the authors of the paper to introduce
tags for proteases into the repressor sequences.
Model validity can also be checked by comparison of
the results of simulation runs with quantitative
experimental data, such as time courses or steady-
state concentrations and fluxes. These can sometimes
Review. Model creation for synthetic biology L. Endler et al.
J. R. Soc. Interface
413
(2009)
S
be derived from the literature, or retrieved from
databases, for example, quantification of mRNA or
metabolites. If the model satisfactorily reproduces
experimental results and displays the desired behaviours,
it can further be tested by experimental verification of its
predicted results and behaviour. JIGCELL features a
dedicated tool, the COMPARATOR (described in Allen
et al.2003), to automatize this comparison. Using user-
defined objective functions,it compares a model’s results
and transformations thereof with given sets of experi-
mental data and assertions on model variables. It also
allows different models or versions of a modelto be tested
to the same data and assertions and then to compare
their performance.
8. CONCLUSION AND OUTLOOK
The tools already available for model creation are quite
sufficient for most applications. Use of inter-convertible
formats such as SBML or CellML endows scientists
with a rich toolkit supporting nearly all aspects of
model evaluation, interpretation and refinement. Most
of these tools are freely available for academic users,
allowing scientists to try and use more than one
program for each task. The ample annotation possibi-
lities of these XML-based formats allow the models to
be thoroughly described, which helps in collaborative
model building and interpretation, as well as in model
exchange and reuse.
Nevertheless, as most of the tools have been designed
for systems biology purposes, with a slightly different
modelling process in mind, they lack some of the
features desirable in synthetic biology. Firstly, they
hardly support the modular building process used in
some efforts to create synthetic gene regulatory
systems. Some tools try to include the available
resources targeting synthetic biology—such as the
MIT’s registry of standard biological parts—as model
building resources. While this looks quite promising,
they currently offer only a few modules of the available
biological elements. Although some of them support
general exchange formats and thereby allow for easy
export to other tools, they are restricted to only a small
number of mathematical formulations, and lack inte-
gration of metabolism and signal transduction cascades.
Another feature barely supported up to now is the
ability to use qualitative behaviour prediction to guide
the design process. Tools that deduce possible
behaviours and suggest feasible layouts could be very
helpful in the first stages of a synthetic biology project.
BIOCHAM offers this facility to some extent, but more
tools for deterministic and stochastic kinetic modelling
would be desirable. While parameter estimation and
optimization are integrated in many programs with
intuitive interfaces, qualitative analysis capabilities are
mostly found in separate dedicated tools, requiring
more mathematical skills and expertise. Efforts to make
these tools more accessible to mathematically less
proficient scientists would be very useful for both the
systems and synthetic biology communities.
A general problem in both systems and synthetic
biology is the lack of tools supporting standardized
annotation of model elements and biological entities.
Some standards have only recently been agreed upon by
a broader part of the community, so some time may still
be needed until widespread adoption. We believe the
use of such a standardized annotation is a necessary
development for the interchange and reuse of models
and modules by different scientists and tools. One very
successful effort in developing a standard, publicly
available database of biological parts for synthetic
biology has been created in the BioBrick registry of
standard biological parts (http://partsregistry.org/).
In a recent publication, Canton et al.(2008)proposed a
promising way to represent quantitative characteristics
of biological devices in the form of a data sheet and
demonstrate it on a device composed of BioBrick parts.
Mathematical modelling and in silico design of systems
would profit very much from the adoption of such
standards by the community.
As the vibrant and quickly growing communities of
synthetic and systems biology have produced a
plethora of tools and algorithms, we are optimistic
that the features mentioned above will be implemented
soon. The use of open standard formats and community-
based development has proved to be of great value in
biological modelling and hopefully this successful trend
will continue and widen to newly emerging fields.
The authors are thankful to Dominic Tolle for discussions.
This work was partly supported by the British Biotechnology
and Biological Sciences Research Council.
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