
Marc R. Roussel and Talmon Soares (2024) Graphbased,
dynamicspreserving reduction of (bio)chemical systems.
J. Math. Biol. 89, 42.

S. Hossein Hosseini and Marc R. Roussel (2024) Analytic delay
distributions for a family of gene transcription models. Math.
Biosci. Eng. 21, 6225–6262. [Invited paper for a
special issue on
Mathematical modeling and computational methods for gene expression
and protein translation]

Olivia N. J. M. Marasco, Marc R. Roussel and Nehal Thakor (2022)
Probabilistic models of uORFmediated ATF4 translation control.
Math. Biosci. 343, 108762.
[Invited paper for a special issue on
Dynamic
Publication Media in Mathematical Biology]

Justin Eilertsen, Marc R. Roussel, Santiago Schnell and Sebastian
Walcher (2021) On the quasisteadystate approximation in an open
MichaelisMenten reaction mechanism. AIMS Math. 6,
6781–6814. [Special issue on Biochemical Problems, Mathematical Solutions of
Mathematics in Science and
Industry, the official journal of the
Canadian Applied and
Industrial Mathematics Society, currently published via
AIMS Mathematics]

Hakki Ulaş Ünal, Marc R. Roussel, Islam Boussaada and
SilviuIulian Niculescu
(2021) Insights from a qualitative analysis of a gene expression
model. IFACPapersOnLine 54(9), 770–775.
[Invited paper:
24th International Symposium on Mathematical Theory of Networks and
Systems MTNS 2020]
 Marc R. Roussel (2020) Perturbativeiterative computation of
inertial manifolds of
systems of delaydifferential equations with small delays.
Algorithms 13, 209.
[Invited paper for a special issue on
Iterative Algorithms for
Nonlinear Problems: Convergence and Stability]
 Elizabeth A. M. Trofimenkoff and Marc R. Roussel (2020)
Small bindingsite clearance delays are not negligible in gene
expression modeling. Math. Biosci. 325,
108376.
 Marc R. Roussel (2019) A delayed massaction model for the
transcriptional control of Hmp, an NO
detoxifying enzyme, by the ironsulfur protein FNR. In
Giorgio Valmorbida,
Alexandre Seuret, Islam Boussaada and
Rifat Sipahi (Eds.),
Delays and Interconnections: Methodology,
Algorithms and Applications, Advances in Delays and
Dynamics, Vol. 10, Springer, Cham, pp. 215–230.
[Invited paper]
 David Lloyd, Douglas B. Murray, Miguel A. Aon, Sonia Cortassa, Marc
R. Roussel, Manfred Beckmann and Robert K. Poole (2019) Temporal metabolic
partitioning of the yeast and protist cellular networks: the cell is
a global scaleinvariant (fractal or selfsimilar),
multioscillator. J. Biomed. Opt. 24,
051404. [Special issue in
honour of the late Britton Chance]
 Marc R. Roussel (2019) Heineken, Tsuchiya and Aris on the mathematical
status of the pseudosteady state hypothesis: A classic
from volume 1 of Mathematical Biosciences.
Math. Biosci. 318, 108274. [Invited perspective article]
 Marc R. Roussel (2018) The MackeyGlass models, 40 years later.
Biomath Commun. 5, 140–158.
[Invited perspective article]
 Catharine J. Roussel
and Marc R. Roussel (2018) A mathematical model
of the biochemical network underlying leftright asymmetry
establishment in mammals.
BioSystems 173, 281–297. [Invited paper
for a special issue on
Computational, Theoretical, and Experimental Approaches to
Morphogenesis]
 Brian Ingalls, Maya Mincheva and
Marc R. Roussel (2017) Parametric sensitivity analysis of
oscillatory delay systems with an application to gene regulation.
Bull. Math. Biol. 79, 1539–1563.
 Blessing E. Okeke and Marc R. Roussel (2015) An invariantmanifold approach
to lumping.
Math. Model. Nat. Phenom. 10(3), 149–167. [Invited
paper for a special
issue dedicated to Alexander Gorban]
 Md. Ruhul Amin and Marc R. Roussel (2014) Graphtheoretic analysis
of a model for the coupling between photosynthesis and
photorespiration. Can. J. Chem. 92, 85–93.
[Special issue dedicated to Paul Brumer]
 Marc R. Roussel (2013) On the distribution of transcription times.
Biomath 2, 1307247. [Invited paper
associated with Biomath
2013]
 Abir U. Igamberdiev and Marc R. Roussel (2012) Feedforward
nonMichaelisMenten
mechanism for CO_{2} uptake by Rubisco:
Contribution of carbonic anhydrases and photorespiration to
optimization of photosynthetic carbon assimilation.
BioSystems 107, 158–166.
 Marc R. Roussel and Martin J. Slingerland (2012) A biochemically
semidetailed model of auxinmediated vein formation in plant
leaves. BioSystems 109, 475–487.
[Invited paper for a special issue on Biological
Morphogenesis]

Marc R. Roussel (2012) Further studies of the functional equation
truncation approximation. Can. Appl. Math. Q.
20, 209–227. [Special issue dedicated to Herb
Friedman]
 Marc R. Roussel and Terry Tang (2012) Simulation of mRNA diffusion in
the nuclear environment. IET Syst. Biol. 6,
125–133.
[Invited paper for a special issue on ``Modelling noise in
biochemical reaction networks'']
 Maya Mincheva and Marc R. Roussel (2012) TuringHopf instability
in biochemical reaction networks arising from pairs of
subnetworks. Math. Biosci. 240, 1–11.
 Marc R. Roussel and Abir U. Igamberdiev (2011) Dynamics and
mechanisms of oscillatory photosynthesis.
Biosystems 103, 230–238.
[Special issue on
Computational Models of Photosynthesis]
 Taunia L. L. Closson
and Marc R. Roussel (2009) The flattening phase
transition in systems of trapped ions.
Can.
J. Chem. 87, 1425–1435.
[Invited paper for a special issue dedicated to
Professor Tom Ziegler]
 Miguel A. Aon,
Marc R. Roussel, Sonia Cortassa, Brian O'Rourke,
Douglas B. Murray, Manfred Beckmann and David Lloyd (2008) The
scalefree dynamics of eukaryotic cells.
PLoS ONE 3, e3624.
 Marc R. Roussel and David Lloyd (2007) Detection of a chaotic metabolic
attractor by realtime monitoring of a
multioscillatory state in a yeast continuous culture.
FEBS J. 274, 1011–1018.
Follow this link for the data sets.
 Maya Mincheva and Marc R. Roussel (2007) Graphtheoretic methods for the
analysis of chemical and biochemical networks. I. Multistability
and oscillations in ordinary differential equation models.
J. Math. Biol. 55, 61–86.
 Maya Mincheva and Marc R. Roussel (2007) Graphtheoretic methods for the
analysis of chemical and biochemical networks. II.
Oscillations in networks with delays.
J. Math. Biol. 55, 87–104.
 Marc R. Roussel, Alexander A. Ivlev
and Abir U. Igamberdiev (2007) Oscillations of the internal
CO_{2} concentration in tobacco leaves transferred to
low CO_{2}. J. Plant Physiol.
164, 1188–1196.
 Marc R. Roussel and Rui Zhu (2006) Stochastic kinetics description
of a simple transcription model. Bull.
Math. Biol. 68, 1681–1713.
 Santiago Schnell, Michael J. Chappell, Neil D. Evans and
Marc R. Roussel (2006) The mechanism distinguishability
problem in biochemical kinetics: The singleenzyme
singlesubstrate reaction as a case study.
C. R. Biologies 329, 51–61.
 Kevin L. Davis and Marc R. Roussel (2006) Optimal observability
of sustained stochastic competitive inhibition oscillations
at organellar volumes.
FEBS J. 273, 84–95.
 Maya Mincheva and Marc R. Roussel (2006) A graphtheoretic method for
detecting potential Turing
bifurcations. J. Chem. Phys. 125,
204102.
Included in the Dec. 1, 2006 issue of the compilation
Virtual Journal of Biological Physics Research.
 Marc R. Roussel and Terry Tang (2006) The functional equation
truncation method for approximating slow invariant manifolds: A
rapid method for computing intrinsic lowdimensional manifolds.
J. Chem. Phys. 125, 214103.
 Marc R. Roussel and Rui Zhu (2006) Validation of an algorithm for delay
stochastic simulation of
transcription and translation in prokaryotic gene expression.
Phys. Biol. 3, 274–284.
 Marc R. Roussel and Rui Zhu (2004) Reducing a chemical master equation
by invariant manifold methods.
J. Chem. Phys. 121, 8716–8730.
Included in the Nov. 1, 2004 issue of the compilation
Virtual Journal of Biological Physics Research.
 Catharine J. Roussel and Marc R. Roussel (2004)
Reactiondiffusion models of development with statedependent
diffusion coefficients.
Prog. Biophys. Mol. Biol. 86, 113–160.
[Invited paper]
 Marc R. Roussel and Jichang Wang (2004)
Pattern formation in excitable media with
concentrationdependent diffusivities.
J. Chem. Phys. 120, 8079–8088.
 Catharine J. Roussel and Marc R. Roussel (2003)
Generic objectoriented differential equation integrators.
C/C++ Users J. 21(11), 18–23.
Code and examples
(zip file)
 Didier Gonze, Marc R. Roussel and Albert Goldbeter (2002)
A model for the enhancement of fitness in cyanobacteria based on
resonance of a circadian oscillator with the external
lightdark cycle. J. Theor. Biol. 214,
577–597.
 Marc R. Roussel and Jichang Wang (2002)
The influence of concentrationdependent diffusivities on wave
stability. Phys. Chem. Chem. Phys. 4,
1310–1314; errata, ibid. 3152–3153.
 Marc R. Roussel and Jichang Wang (2001)
A transition from selfreplicating behavior to stationary patterns
induced by concentrationdependent diffusivities.
Phys. Rev. Lett. 87, 188302; errata, ibid.
90, 119902.
 Marc R. Roussel and Simon J. Fraser (2001) Invariant manifold methods
for metabolic model reduction.
Chaos 11, 196–206. [Invited paper]
 Catharine J. Roussel and Marc R. Roussel (2001) Delaydifferential
equations and the model equivalence problem in chemical
kinetics.
Physics in Canada 57, 114–120. [Invited
paper for a special issue on Nonlinear Dynamics]
 Marc R. Roussel and Jichang Wang (2001)
Phase synchronization of nonidentical lightsensitive
BelousovZhabotinsky systems induced by variability in a highlow
illumination program.
J. Phys. Chem. A 105, 7371–7380.
 Marc R. Roussel and Jichang Wang (2000) Onset and synchronization of
complex dynamical behavior in the lightsensitive
BelousovZhabotinsky reaction with periodic and nearly periodic
switching. J. Phys. Chem. A 104, 11751–11756.
 Taunia L. L. Closson and Marc R. Roussel (2000) Synchronization
by irregular inactivation.
Phys. Rev. Lett. 85, 3974–3977.
 Marc R. Roussel, Didier Gonze and Albert Goldbeter (2000)
Modeling the differential fitness of cyanobacterial strains
whose circadian oscillators have different freerunning periods:
Comparing the mutual inhibition and substrate depletion
hypotheses. J. Theor. Biol. 205, 321–340.
 Marc R. Roussel (1999) Redesigning the quantum mechanics
curriculum to incorporate problem solving using a computer
algebra system.
J. Chem. Ed. 76, 1373–1377.
 Robert A. Marriott, Andrew W. Hakin, Jin Lian Liu and Marc R.
Roussel (1999) Automated statistical analysis of
high temperature and pressure vibrating tube densimeter data.
Computers & Chem. 23, 487–492.
 Richard A. Beekman, Marc R. Roussel and P. J. Wilson (1999) Equilibrium
configurations of systems of trapped ions.
Phys. Rev. A 59, 503–511.
Coordinate
files for
the equilibrium geometries
 Marc R. Roussel (1998) Slowly reverting enzyme inactivation: A
mechanism for generating
longlived damped oscillations.
J. Theor. Biol. 195, 233–244.
 Marc R. Roussel (1998) Approximating statespace manifolds which
attract solutions of systems of delaydifferential equations.
J. Chem. Phys. 109, 8154–8160.
 Marc R. Roussel (1997) Forcedconvergence iterative schemes for the
approximation of
invariant manifolds. J. Math. Chem. 21,
385–393.
 Lan G. Ngo and Marc R. Roussel (1997) A new
class of biochemical oscillator models based on competitive
binding. Eur. J. Biochem. 245, 182–190.
 Marc R. Roussel (1997) An analytic center manifold for a simple
epidemiological model. SIAM Rev. 39, 106–109.
 Marc R. Roussel (1996) The use of delaydifferential equations
in chemical kinetics. J. Phys. Chem. 100,
8323–8330.
 Marc R. Roussel and Carmay Lim (1995) Discrete, dynamic polymer
modeling: A pseudodiatomic model of lignin.
J. Comp. Chem. 16, 1181–1191.
 Marc R. Roussel and Carmay Lim (1995) Dynamic
model of lignin growing in restricted spaces.
Macromolecules 28, 370–376.
 Simon J. Fraser and Marc R. Roussel (1994) Phaseplane geometries
in enzyme kinetics. Can. J. Chem. 72, 800–812.
 Marc R. Roussel and Simon J. Fraser (1993) Global analysis
of enzyme inhibition kinetics. J. Phys. Chem. 97,
8316–8327; errata, ibid. 98, 5174.
 Marc R. Roussel and Simon J. Fraser (1991) Accurate steadystate
approximations: Implications for kinetics experiments and
mechanism. J. Phys. Chem. 95, 8762–8770.
 Marc R. Roussel and Simon J. Fraser (1991) On the geometry of transient
relaxation. J. Chem. Phys. 94, 7106–7113.
 Marc R. Roussel and Simon J. Fraser (1990) Geometry of the steadystate
approximation: Perturbation and accelerated convergence
methods. J. Chem. Phys. 93, 1072–1081.
 W. Ross Hastings, Marc R. Roussel and Michael C. Baird (1990)
Mechanism of the conversion of [Ru(CO)_{5}] to
[Ru_{3}(CO)_{12}]. J. Chem. Soc., Dalton
Trans. 1990, 203–205.
 A.D. Becke and M.R. Roussel (1989) Exchange holes in inhomogeneous
systems: A coordinatespace model. Phys. Rev. A
39, 3761–3767.