Banaji, Murad

Donnell, Pete

Marginean, Anca

Pantea, Casian

English

Portsmouth University Research Portal (Pure)

BIOINFORMATICS Vol. 00 no. 00 2013Pages 1–2
CoNtRol: an open source framework for the analysis of
chemical reaction networks
Pete Donnell 1∗, Murad Banaji 1, Anca Marginean 2 and Casian Pantea 3
1 Department of Mathematics, University of Portsmouth, Portsmouth, UK.
2 Computer Science Department, Technical University of Cluj-Napoca, Cluj-Napoca, Romania.
3 Department of Mathematics, West Virginia University, Morgantown, WV, USA.
Received on XXXXX; revised on XXXXX; accepted on XXXXX
Associate Editor: XXXXXXX
ABSTRACT
Summary: We introduce CoNtRol, a web based framework for
analysis of chemical reaction networks (CRNs). It is designed to
be both extensible and simple to use, complementing existing CRN-
related tools. CoNtRol currently implements a number of necessary
and/or sufficient structural tests for multiple equilibria, stable periodic
orbits, convergence to equilibria and persistence, with the potential
for incorporation of further tests.
Availability: Reference implementation: reaction-networks.
net/control/. Source code and binaries, released under
the GPLv3: reaction-networks.net/control/download/.
Documentation: reaction-networks.net/wiki/CoNtRol.
Contact: pete.donnell@port.ac.uk
1 INTRODUCTION
Differential equation models of chemical reaction networks
(CRNs), encompassing many ecological, epidemiological and
related nonnegative systems, are almost universally complicated
by parameter uncertainty. However, dynamical properties of large
classes of CRN models are remarkably robust to changes in
parameter values, leading to a range of results relating network
structure to dynamical behaviour. Such parameter-free approaches
to the analysis of CRNs fall into the scope of chemical reaction
network theory (Horn and Jackson, 1972; Feinberg, 1972, 1979).
Fuelled in part by its implications to systems biology (Bailey, 2001;
Shinar and Feinberg, 2010), chemical reaction network theory has
seen a surge of interest in recent years, attacking questions about
multistationarity (Craciun et al., 2006; Conradi et al., 2007; Banaji
et al., 2007; Banaji and Craciun, 2009; Shinar and Feinberg, 2012),
global stability (Craciun et al., 2009; Angeli et al., 2010; Anderson,
2011; Donnell and Banaji, 2013), oscillatory behavior (Angeli et al.,
2013) and persistence (Angeli et al., 2007; Pantea, 2012).
Many of the results in chemical reaction network theory lend
themselves to algorithmic implementation, which is useful for
large networks. In this note we introduce CoNtRol (CRN tool),
a new, fully open source platform, currently coded in C, Java,
Octave and PHP, to perform computations on CRNs without the
need for any proprietary software. CoNtRol has a web based
front end interfacing with a suite of modular tests, to which users
∗to whom correspondence should be addressed
may add new tests in any language. With its array of features,
CoNtRol complements existing software tools. The Chemical
Reaction Network Toolbox (Ellison et al., 2011) is a proprietary
Windows program which implements the results of deficiency
theory (Feinberg, 1979), as well as checking for concordance
(Shinar and Feinberg, 2012), equivalent to network injectivity. It
applies to various types of kinetics, including mass action, and
generates detailed information about network properties, multiple
and degenerate steady states, and their stability. ERNEST (Soranzo
and Altafini, 2009) and CRNreals (Szederke´nyi et al., 2012)
are MATLAB toolboxes aimed at testing multistationarity, and
respectively, distinguishability and identifiability of CRNs. Tests
for multistationarity of CRNs are also implemented in Maple (Feliu
and Wiuf, 2013). While not all criteria included in these tools are
currently tested in CoNtRol, its extensible nature allows for their
future inclusion.
2 FEATURES AND FUNCTIONALITY
CoNtRol has an intuitive user interface where a list of reactions can
be input manually or uploaded in a variety of formats. While the
focus so far has been on developing the framework for extensible
functionality, a number of tools for the analysis of CRNs have also
been implemented and tested.
2.1 Network Analysis
The current functionality of CoNtRol includes a number of
necessary and/or sufficient structural tests for multiple equilibria,
stable oscillation, convergence to equilibria, and persistence,
assuming mass action or more general kinetics. In particular the
following are checked: sufficient conditions for convergence to
equilibria based on the theory of monotone dynamical systems
(Angeli et al., 2010; Donnell and Banaji, 2013); conditions
of the deficiency zero and deficiency one theorems (Feinberg,
1987), resulting in claims about local stability of equilibria,
absence of multiple positive equilibria, and absence of periodic
orbits, primarily for mass action kinetics; structural conditions
for persistence (Angeli et al., 2007; Donnell and Banaji, 2013)
based on examining the siphons of the system; and a large number
of sufficient/necessary conditions for injectivity and absence of
multistationarity gathered from the literature and developed in
c© Oxford University Press 2013. 1
Donnell et al
S
1
2
EF
3
ES
4
P
FP
Fig. 1. Futile cycle DSR graph
{
E + S 
 ES → E + P
F + P 
 FP → F + S
(Banaji and Pantea, 2013). The outputs are cross-referenced to
the documentation of CoNtRol, where each conclusion and its
implications are described in detail. We note that some of the
multistationarity results of CoNtRol are similar to those of The
Chemical Reaction Network Toolbox (Ellison et al., 2011).
2.2 DSR graph generation
A useful tool in the parameter-free study of CRNs is the DSR
graph: a bipartite graph with signed, labelled, and sometimes
directed edges. CoNtRol includes a Java Web Start application
for drawing DSR graphs. The graph layout is highly customisable,
and the “export to LATEX” feature generates TikZ code for the
resulting DSR diagram. An example is illustrated in Figure
1. Easily checked structural conditions on the DSR graph can
imply, or contribute towards, powerful conclusions regarding
multistationarity, asymptotic stability, or oscillatory behavior in
a CRN (Craciun et al., 2006; Banaji and Craciun, 2009; Angeli
et al., 2010, 2013; Shinar and Feinberg, 2013). Several of these are
implemented or lend themselves naturally to future implementation.
2.3 Batch processing
This feature allows users to analyse a number of networks in a
single run, thus generating statistics about the occurrence of certain
behaviours. An archive containing individual files describing each
network is uploaded, and the user is emailed a link to the output
once it is complete. For example, the table below summarises the
results of some injectivity tests implemented in CoNtRol, applied
to the database of all 4082 nonisomorphic bimolecular CRNs with
three species and three reactions (Deckard et al., 2009).
GKα GKβ MAα MAβ
44% 45% 45% 47%
GK: general kinetics. MA: mass action kinetics. α: the system is
injective on the relative interior of each nontrivial stoichiometry
class. β: the fully open system is injective on the nonnegative
orthant. For example, with mass action kinetics, 45% (MAα) of the
networks were injective on the relative interior on each nontrivial
stoichiometric class, only slightly more than with general kinetics
(GKα). See (Banaji and Pantea, 2013) for more details.
2.4 Miscellaneous
A number of features that further improve usability have been
implemented. These include multiple input formats, the option to
receive the output via email, and automatic generation of LATEX code
(e.g., list of reactions, stoichiometric matrix).
3 CONCLUSION
We have written CoNtRol aiming for a user friendly tool with
maximal functionality, implementing state of the art theory on
CRNs. We expect future inclusion of further results from the rich
theory of CRNs, with contributions from the research community.
Funding: CP’s work was supported by Leverhulme grant F/07
058/BU; PD’s work was supported by EPSRC grant EP/J008826/1.
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2


A computational method to preclude multistationarity in networks of interacting species.

A Petri net approach to the study of persistence in chemical reaction networks.

A proof of the global attractor conjecture in the single linkage class case.

Chemical reaction network structure and the stability of complex isothermal reactors–I. the deficiency zero and deficiency one theorems.

Combinatorial approaches to Hopf bifurcations in systems of interacting elements.

Complex balancing in general kinetic systems.

Complex biology with no parameters.

Concordant chemical reaction networks and the Species-Reaction graph.

Concordant chemical reaction networks.

CRNreals: a toolbox for distinguishability and identifiability analysis of biochemical reaction networks.

Enumeration and online library of mass-action reaction networks.

ERNEST: a toolbox for chemical reaction network theory.

General mass action kinetics. Archive for Rational Mechanics and Analysis,

Graph-theoretic approaches to injectivity and multiple equilibria in systems of interacting elements.

Graph-theoretic characterizations of monotonicity of chemical networks in reaction coordinates.

Lectures on chemical reaction networks. Lectures delivered at the Mathematics Research

Local and global stability of equilibria for a class of chemical reaction networks.

On the persistence and global stability of mass-action systems.

P matrix properties, injectivity, and stability in chemical reaction systems.

Some results on injectivity and multistationarity in chemical reaction networks.

Structural sources of robustness in biochemical reaction networks.

Subnetwork analysis reveals dynamic features of complex (bio) chemical networks.

The chemical Reaction Network Toolbox ver.

Toric dynamical systems.

Understanding bistability in complex enzyme-driven reaction networks.

CoNtRol:an open source framework for the analysis of chemical reaction networks

CoNtRol:an open source framework for the analysis of chemical reaction networks

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