Marc Roussel's publications

Books

  1. Marc R Roussel (2023) Foundations of Chemical Kinetics: A Hands-On Approach, IOP Publishing, Bristol.
  2. Marc R Roussel (2019) Nonlinear Dynamics: A Hands-On Introductory Survey, Morgan & Claypool, San Rafael, CA (IOP Concise Physics series).
  3. Marc R. Roussel (2012) A Life Scientist's Guide to Physical Chemistry, Cambridge University Press, Cambridge.

Refereed papers

  1. Marc R. Roussel and Talmon Soares (2024) Graph-based, dynamics-preserving reduction of (bio)chemical systems. J. Math. Biol. 89, 42.
  2. 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]
  3. Olivia N. J. M. Marasco, Marc R. Roussel and Nehal Thakor (2022) Probabilistic models of uORF-mediated ATF4 translation control. Math. Biosci. 343, 108762. [Invited paper for a special issue on Dynamic Publication Media in Mathematical Biology]
  4. Justin Eilertsen, Marc R. Roussel, Santiago Schnell and Sebastian Walcher (2021) On the quasi-steady-state approximation in an open Michaelis-Menten 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]
  5. Hakki Ulaş Ünal, Marc R. Roussel, Islam Boussaada and Silviu-Iulian Niculescu (2021) Insights from a qualitative analysis of a gene expression model. IFAC-PapersOnLine 54(9), 770–775. [Invited paper: 24th International Symposium on Mathematical Theory of Networks and Systems MTNS 2020]
  6. Marc R. Roussel (2020) Perturbative-iterative computation of inertial manifolds of systems of delay-differential equations with small delays. Algorithms 13, 209. [Invited paper for a special issue on Iterative Algorithms for Nonlinear Problems: Convergence and Stability]
  7. 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.
  8. 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]
  9. 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 scale-invariant (fractal or self-similar), multioscillator. J. Biomed. Opt. 24, 051404. [Special issue in honour of the late Britton Chance]
  10. 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]
  11. Marc R. Roussel (2018) The Mackey-Glass models, 40 years later. Biomath Commun. 5, 140–158. [Invited perspective article]
  12. 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]
  13. 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.
  14. Blessing E. Okeke and Marc R. Roussel (2015) An invariant-manifold approach to lumping. Math. Model. Nat. Phenom. 10(3), 149–167. [Invited paper for a special issue dedicated to Alexander Gorban]
  15. 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]
  16. Marc R. Roussel (2013) On the distribution of transcription times. Biomath 2, 1307247. [Invited paper associated with Biomath 2013]
  17. Abir U. Igamberdiev and Marc R. Roussel (2012) Feedforward non-Michaelis-Menten mechanism for CO2 uptake by Rubisco: Contribution of carbonic anhydrases and photorespiration to optimization of photosynthetic carbon assimilation. BioSystems 107, 158–166.
  18. 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]
  19. 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]
  20. 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'']
  21. Maya Mincheva and Marc R. Roussel (2012) Turing-Hopf instability in biochemical reaction networks arising from pairs of subnetworks. Math. Biosci. 240, 1–11.
  22. 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]
  23. 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]
  24. 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.
  25. 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.

  26. 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.
  27. 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.
  28. Marc R. Roussel, Alexander A. Ivlev and Abir U. Igamberdiev (2007) Oscillations of the internal CO2 concentration in tobacco leaves transferred to low CO2. J. Plant Physiol. 164, 1188–1196.
  29. Marc R. Roussel and Rui Zhu (2006) Stochastic kinetics description of a simple transcription model. Bull. Math. Biol. 68, 1681–1713.
  30. 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.
  31. Kevin L. Davis and Marc R. Roussel (2006) Optimal observability of sustained stochastic competitive inhibition oscillations at organellar volumes. FEBS J. 273, 84–95.
  32. 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.

  33. 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.
  34. 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.
  35. 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.

  36. 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]
  37. Marc R. Roussel and Jichang Wang (2004) Pattern formation in excitable media with concentration-dependent diffusivities. J. Chem. Phys. 120, 8079–8088.
  38. 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)

  39. 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.
  40. 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.
  41. 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.
  42. Marc R. Roussel and Simon J. Fraser (2001) Invariant manifold methods for metabolic model reduction. Chaos 11, 196–206. [Invited paper]
  43. 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 for a special issue on Nonlinear Dynamics]
  44. 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.
  45. 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.
  46. Taunia L. L. Closson and Marc R. Roussel (2000) Synchronization by irregular inactivation. Phys. Rev. Lett. 85, 3974–3977.
  47. 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.
  48. Marc R. Roussel (1999) Redesigning the quantum mechanics curriculum to incorporate problem solving using a computer algebra system. J. Chem. Ed. 76, 1373–1377.
  49. 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.
  50. 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

  51. Marc R. Roussel (1998) Slowly reverting enzyme inactivation: A mechanism for generating long-lived damped oscillations. J. Theor. Biol. 195, 233–244.
  52. Marc R. Roussel (1998) Approximating state-space manifolds which attract solutions of systems of delay-differential equations. J. Chem. Phys. 109, 8154–8160.
  53. Marc R. Roussel (1997) Forced-convergence iterative schemes for the approximation of invariant manifolds. J. Math. Chem. 21, 385–393.
  54. 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.
  55. Marc R. Roussel (1997) An analytic center manifold for a simple epidemiological model. SIAM Rev. 39, 106–109.
  56. Marc R. Roussel (1996) The use of delay-differential equations in chemical kinetics. J. Phys. Chem. 100, 8323–8330.
  57. Marc R. Roussel and Carmay Lim (1995) Discrete, dynamic polymer modeling: A pseudo-diatomic model of lignin. J. Comp. Chem. 16, 1181–1191.
  58. Marc R. Roussel and Carmay Lim (1995) Dynamic model of lignin growing in restricted spaces. Macromolecules 28, 370–376.
  59. Simon J. Fraser and Marc R. Roussel (1994) Phase-plane geometries in enzyme kinetics. Can. J. Chem. 72, 800–812.
  60. Marc R. Roussel and Simon J. Fraser (1993) Global analysis of enzyme inhibition kinetics. J. Phys. Chem. 97, 8316–8327; errata, ibid. 98, 5174.
  61. Marc R. Roussel and Simon J. Fraser (1991) Accurate steady-state approximations: Implications for kinetics experiments and mechanism. J. Phys. Chem. 95, 8762–8770.
  62. Marc R. Roussel and Simon J. Fraser (1991) On the geometry of transient relaxation. J. Chem. Phys. 94, 7106–7113.
  63. 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.
  64. W. Ross Hastings, Marc R. Roussel and Michael C. Baird (1990) Mechanism of the conversion of [Ru(CO)5] to [Ru3(CO)12]. J. Chem. Soc., Dalton Trans. 1990, 203–205.
  65. A.D. Becke and M.R. Roussel (1989) Exchange holes in inhomogeneous systems: A coordinate-space model. Phys. Rev. A 39, 3761–3767.

Non-refereed articles

  1. Marc R. Roussel and Moisés Santillán (2022) Editorial: Biochemical Problems, Mathematical Solutions. AIMS Math. 7, 5662–5669. [Editorial to accompany a special issue of Mathematics in Science and Industry on this theme]
  2. D. Lloyd, E. L. Rossi and M. R. Roussel (2008) Introduction: The temporal organization of living systems from molecule to mind. In David Lloyd and Ernest Rossi (Eds.), Ultradian Rhythms from Molecules to Mind, Springer, Berlin, pp 1–8.
  3. Marc R. Roussel (2007) Step sizes in simulations of diffusion. A comment on "Modeling the signaling endosome hypothesis: Why a drive to the nucleus is better than a (random) walk" by Charles L. Howe (2005) Theor. Biol. Med. Model. 2, 43.
  4. Marc R. Roussel and Rui Zhu (2006) Exactly reduced chemical master equations. In Alexander N. Gorban, Nikolaos K. Kazantzis, Ioannis G. Kevrekidis, Hans Christian Öttinger and Constantinos Theodoropoulos (Eds.), Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena, Springer, Berlin, pp 295–315. [Invited paper]
  5. Rui Zhu and Marc R. Roussel (2005) Chemical master equation reduction methods. In Andrei Ludu, Nathan R. Hutchings and Darrell R. Fry (Eds.), ISIS International Symposium on Interdisciplinary Science (AIP Conf. Proc. vol. 755), American Institute of Physics, Melville, NY, pp 172–176.
  6. Marc R. Roussel (2003) Reduction of biochemical models using functional iteration. In R. Gauges, U. Kummer, J. Pahle and U. Rost (Eds.), 3rd Workshop on Computation of Biochemical Pathways and Genetic Networks, Logos Verlag, Berlin, pp 17–26. [Invited paper]
  7. Marc R. Roussel (2001) Book review: An Introduction to Mathematical Physiology and Biology, 2nd ed., by J. Mazumdar. Physics in Canada 57, 216–217.
  8. Marc R. Roussel (2000) An autonomous cell-cycle oscillator involved in the coordination of G1 events. BioEssays 22, 3–5. [Invited comment]

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