- Elizabeth A. M. Trofimenkoff and Marc R. Roussel (2020)
Small binding-site clearance delays are not negligible in gene
expression modeling. Math. Biosci. 325,
108376.
- Marc R. Roussel (2019) A delayed mass-action model for the
transcriptional control of Hmp, an NO
detoxifying enzyme, by the iron-sulfur 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]
- Marc R. Roussel (2019) Heineken, Tsuchiya and Aris on the mathematical
status of the pseudo-steady state hypothesis: A classic
from volume 1 of Mathematical Biosciences.
Math. Biosci. 318, 108274. [Invited perspective article]
- Marc R. Roussel (2018) The Mackey-Glass 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 left-right asymmetry
establishment in mammals.
BioSystems 173, 281–297. [Invited paper
for a
special issue on
Computational, Theoretical, and Experimental Approaches to
Morphogenesis]
- David Lloyd, Douglas B. Murray, Miguel A. Aon, Sonia Cortassa, Marc
R. Roussel, Manfred Beckmann and Robert K. Poole (2018) Temporal metabolic
partitioning of the yeast and protist cellular networks: the cell is
a global scale-invariant (fractal or self-similar),
multioscillator. J. Biomed. Opt. 24,
051404. [Special issue in
honour of the late Britton Chance]
- 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 invariant-manifold approach
to lumping.
Math. Model. Nat. Phenom. 10, 149–167. [Invited
paper for a special
issue dedicated to Alexander Gorban]
- Md. Ruhul Amin and Marc R. Roussel (2014) Graph-theoretic 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
non-Michaelis-Menten
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
semi-detailed model of auxin-mediated 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) Turing-Hopf 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
scale-free dynamics of eukaryotic cells.
PLoS ONE 3, e3624.
- Marc R. Roussel and David Lloyd (2007) Detection of a chaotic metabolic
attractor by real-time monitoring of a
multi-oscillatory 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) Graph-theoretic 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) Graph-theoretic 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 single-enzyme
single-substrate 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 graph-theoretic 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 low-dimensional 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)
Reaction-diffusion models of development with state-dependent
diffusion coefficients.
Prog. Biophys. Mol. Biol. 86, 113–160.
[Invited paper]
- Marc R. Roussel and Jichang Wang (2004)
Pattern formation in excitable media with
concentration-dependent diffusivities.
J. Chem. Phys. 120, 8079–8088.
- Catharine J. Roussel and Marc R. Roussel (2003)
Generic object-oriented 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
light-dark cycle. J. Theor. Biol. 214,
577–597.
- Marc R. Roussel and Jichang Wang (2002)
The influence of concentration-dependent 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 self-replicating behavior to stationary patterns
induced by concentration-dependent 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) Delay-differential
equations and the model equivalence problem in chemical
kinetics.
Physics in Canada 57, 114–120. [Invited paper]
- Marc R. Roussel and Jichang Wang (2001)
Phase synchronization of nonidentical light-sensitive
Belousov-Zhabotinsky systems induced by variability in a high-low
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 light-sensitive
Belousov-Zhabotinsky 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 free-running 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
long-lived damped oscillations.
J. Theor. Biol. 195, 233–244.
- Marc R. Roussel (1998) Approximating state-space manifolds which
attract solutions of systems of delay-differential equations.
J. Chem. Phys. 109, 8154–8160.
- Marc R. Roussel (1997) Forced-convergence 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 delay-differential equations
in chemical kinetics. J. Phys. Chem. 100,
8323–8330.
- Marc R. Roussel and Carmay Lim (1995) Discrete, dynamic polymer
modeling: A pseudo-diatomic 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) Phase-plane 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 steady-state
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 steady-state
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 coordinate-space model. Phys. Rev. A
39, 3761–3767.