# Marc R RousselUniversity of Lethbridge · Department of Chemistry & Biochemistry

Marc R Roussel

Ph.D.

## About

89

Publications

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Introduction

Marc R Roussel works at the Department of Chemistry & Biochemistry, University of Lethbridge. Marc's research includes the development of methods for modeling biochemical systems and for the analysis of biochemical methods, as well as applications of these methods. Marc is one of the founding members of the Alberta RNA Research and Training Institute.

Additional affiliations

July 2005 - present

February 2005 - May 2005

September 2004 - January 2005

Education

May 1990 - June 1994

## Publications

Publications (89)

ATF4 is a key transcription factor that activates transcription of genes needed to respond to cellular stress. Although the mRNA encoding ATF4 is present at constant levels in the cell during the initial response, translation of ATF4 increases under conditions of cellular stress while the global translation rate decreases. We study two models for t...

The conditions for the validity of the standard quasi-steady-state approximation in the Michaelis--Menten mechanism in a closed reaction vessel have been well studied, but much less so the conditions for the validity of this approximation for the system with substrate inflow. We analyze quasi-steady-state scenarios for the open system attributable...

The conditions for the validity of the standard quasi-steady-state approximation in the Michaelis-Menten mechanism in a closed reaction vessel have been well studied, but much less so the conditions for the validity of this approximation for the system with substrate inflow. We analyze quasi-steady-state scenarios for the open system attributable t...

Delay-differential equations belong to the class of infinite-dimensional dynamical systems. However, it is often observed that the solutions are rapidly attracted to smooth manifolds embedded in the finite-dimensional state space, called inertial manifolds. The computation of an inertial manifold yields an ordinary differential equation (ODE) model...

During the templated biopolymerization processes of transcription and translation, a macromolecular machine, either an RNA polymerase or a ribosome, binds to a specific site on the template. Due to the sizes of these enzymes, there is a waiting time before one clears the binding site and another can bind. These clearance delays are relatively short...

Volume 1, Issue 1 of Mathematical Biosciences was the venue for a now-classic paper on the application of singular perturbation theory in enzyme kinetics, "On the mathematical status of the pseudo-steady state hypothesis of biochemical kinetics" by F. G. Heineken, H. M. Tsuchiya and R. Aris. More than 50 years have passed, and yet this paper contin...

In Escherichia coli, an enzyme called Hmp is a key contributor to the detoxification of nitric oxide (NO). In the absence of NO, the transcription of the hmp gene is repressed by an iron-sulfur protein called FNR. NO damages the iron-sulfur cluster of FNR, weakening the repression of hmp and allowing expression of Hmp to high levels. A delayed mass...

This book uses a hands-on approach to nonlinear dynamics using commonly available software, including the free dynamical systems software Xppaut, Matlab (or its free cousin, Octave) and the Maple symbolic algebra system.
Detailed instructions for various common procedures, including bifurcation analysis using the version of AUTO embedded in Xppaut...

Britton Chance, electronics expert when a teenager, became an enthusiastic student of biological oscillations, passing on this enthusiasm to many students and colleagues, including one of us (DL). This historical essay traces BC's influence through the accumulated work of DL to DL's many collaborators. The overall temporal organization of mass-ener...

In 1977, Michael Mackey and Leon Glass published a short paper that presented and analyzed three delay-differential physiological models, one of which, now known as the Mackey-Glass equation, was shown to generate chaotic behavior. This paper also introduced the concept of a dynamical disease. In this perspective article, I attempt to place the Mac...

The expression of the TGF-β protein Nodal on the left side of vertebrate embryos is a determining event in the development of internal-organ asymmetry. We present a mathematical model for the control of the expression of Nodal and its antagonist Lefty consisting entirely of realistic elementary reactions. We analyze the model in the absence of Left...

A parametric sensitivity analysis for periodic solutions of delay differential equations is developed. Because phase shifts cause the sensitivity coefficients of a periodic orbit to diverge, we focus on sensitivities of the ex-trema, from which amplitude sensitivities are computed, and of the period. Delay-differential equations are often used to m...

Differential equation models of chemical or biochemical systems usually display multiple, widely varying time scales, i.e. they are stiff. After the decay of transients, trajectories of these systems approach low-dimensional invariant manifolds on which the eventual attractor (an equilibrium point in a closed system) is approached, and in which thi...

We develop and analyze a mathematical model based on a previously enunciated hypothesis regarding the origin of rapid, irregular oscillations observed in photosynthetic variables when a leaf is transferred to a low-CO2 atmosphere. This model takes the form of a set of differential equations with two delays. We review graph-theoretical methods of an...

A previously studied model of prokaryotic transcription [Roussel and Zhu, Bull. Math. Biol. 68 (2006) 1681--1713] is revisited. The first four moments of the distribution of transcription times are obtained analytically and analyzed. A Gaussian is found to be a poor approximation to this distribution for short transcription units at typical values...

A mathematical model is devised to study the diffusion of mRNA in the nucleus from the site of synthesis to a nuclear pore where it is exported to the cytoplasm. This study examines the role that nuclear structure can play in determining the kinetics of export by considering models in which elements of the nuclear skeleton and confinement by chroma...

Network conditions for Turing instability in biochemical systems with two biochemical species are well known and involve autocatalysis or self-activation. On the other hand general network conditions for potential Turing instabilities in large biochemical reaction networks are not well developed. A biochemical reaction network with any number of sp...

We present here a model intended to capture the biochemistry of vein formation in plant leaves. The model consists of three modules. Two of these modules, those describing auxin signaling and transport in plant cells, are biochemically detailed. We couple these modules to a simple model for PIN (auxin efflux carrier) protein localization based on a...

The approximation of invariant manifolds has important applications for understanding dynamical systems, as well as for model reduction. The intrinsic low-dimensional manifold (ILDM) method constructs an approximation to a slow invariant manifold of a set of autonomous ordinary differential equations by finding the locus of points at which the rate...

Rubisco, the most abundant protein serving as the primary engine generating organic biomass on Earth, is characterized by a low catalytic constant (in higher plants approx. 3s(-1)) and low specificity for CO(2) leading to photorespiration. We analyze here why this enzyme evolved as the main carbon fixation engine. The high concentration of Rubisco...

The transient and steady-state behaviour of the reversible Michaelis–Menten mechanism [R] and Competitive Inhibition (CI) mechanism is studied by analysis in the phase plane. Usually, the kinetics of both mechanisms is simplified to give a modified Michaelis–Menten velocity expression; this applies to the CI mechanism with excess inhibitor and to m...

We classify mathematical models that can be used to describe photosynthetic oscillations using ideas from nonlinear dynamics, and discuss potential mechanisms for photosynthetic oscillations in the context of this classification. We then turn our attention to recent experiments with leaves transferred to a low CO₂ atmosphere which revealed stochast...

When the anisotropy of a harmonic ion trap is increased, the ions eventually collapse into a two-dimensional structure consisting of concentric shells of ions. This collapse generally behaves like a second-order phase transition. A graph of the critical value of the anisotropy parameter vs. the number of ions displays substructure closely related t...

Cardiomyocyte NAD(P)H oscillations. Movie of NAD(P)H oscillations (autofluorescence) in a cardiomyocyte recorded using a two photon laser scanning microscope (Bio-Rad MRC-1024MP) with excitation at 740 nm. Whole cell oscillations (100 s period) were triggered with a laser flash in an isolated cardiomyocyte in the absence of any other fluorophore. N...

Yeast NAD(P)H oscillations. Movie of NAD(P)H oscillations (autofluorescence) in spontaneously synchronized oscillations (ca. 100 s) in a contiguous layer of S. cerevisiae cells, recorded with a two photon laser scanning microscope (Bio-Rad MRC-1024MP) with excitation at 740 nm. The layer of yeast cells was perfused with aerated PBS, pH 7.4, in the...

Temporal organization of biological processes requires massively parallel processing on a synchronized time-base. We analyzed time-series data obtained from the bioenergetic oscillatory outputs of Saccharomyces cerevisiae and isolated cardiomyocytes utilizing Relative Dispersional (RDA) and Power Spectral (PSA) analyses. These analyses revealed bro...

Measurement of the internal CO(2) concentration (Ci) in tobacco leaves using a fast-response CO(2) exchange system showed that in the light, switching from 350 microLL(-1) to a low CO(2) concentration of 36.5 microLL(-1) (promoting high photorespiration) resulted in the Ci oscillating near the value of CO(2) compensation point (Gamma*). The oscilla...

A chemical mechanism is a model of a chemical reaction network consisting of a set of elementary reactions that express how molecules react with each other. In classical mass-action kinetics, a mechanism implies a set of ordinary differential equations (ODEs) which govern the time evolution of the concentrations. In this article, ODE models of chem...

Delay-differential equations are commonly used to model genetic regulatory systems with the delays representing transcription and translation times. Equations with delayed terms can also be used to represent other types of chemical processes. Here we analyze delayed mass-action systems, i.e. systems in which the rates of reaction are given by mass-...

We monitored a continuous culture of the yeast Saccharomyces cerevisiae by membrane-inlet mass spectrometry. This technique allows very rapid simultaneous measurements (one point every 12 s) of several dissolved gases. During our experiment, the culture exhibited a multioscillatory mode in which the dissolved oxygen and carbon dioxide records displ...

A slow manifold is a low-dimensional invariant manifold to which trajectories nearby are rapidly attracted on the way to the equilibrium point. The exact computation of the slow manifold simplifies the model without sacrificing accuracy on the slow time scales of the system. The Maas-Pope intrinsic low-dimensional manifold (ILDM) [Combust. Flame 88...

The quantitative modeling of gene transcription and translation requires a treatment of two key features: stochastic fluctuations due to the limited copy numbers of key molecules (genes, RNA polymerases, ribosomes), and delayed output due to the time required for biopolymer synthesis. Recently proposed algorithms allow for efficient simulations of...

The conditions for diffusion-driven (Turing) instabilities in systems with two reactive species are well known. General methods for detecting potential Turing bifurcations in larger reaction schemes are, on the other hand, not well developed. We prove a theorem for a graph-theoretic condition originally given by Volpert and Ivanova [Mathematical Mo...

We study a stochastic model of transcription kinetics in order to characterize the distributions of transcriptional delay and of elongation rates. Transcriptional delay is the time which elapses between the binding of RNA polymerase to a promoter sequence and its dissociation from the DNA template strand with consequent release of the transcript. T...

A theoretical analysis of the distinguishability problem of two rival models of the single enzyme-single substrate reaction, the Michaelis-Menten and Henri mechanisms, is presented. We also outline a general approach for analysing the structural indistinguishability between two mechanisms. The approach involves constructing, if possible, a smooth m...

When molecules are present in small numbers, such as is frequently the case in cells, the usual assumptions leading to differential rate equations are invalid and it is necessary to use a stochastic description which takes into account the randomness of reactive encounters in solution. We display a very simple biochemical model, ordinary competitiv...

In the small-number limit, we must abandon the description of chemical systems in terms of continuous concentration variables which evolve according to deterministic rate equations in favor of a discrete stochastic formulation. The probability distribution for the molecular populations however does obey a deterministic equation called the chemical...

We study invariant manifold methods for reducing chemical master equations using the Michaelis-Menten mechanism as an example. We try Fraser's functional iteration method first, but find that it is difficult to use for master equations of high dimension. Using the insights gained from Fraser's method, we develop a technique to produce reduced chemi...

We study methods for reducing chemical master equations using the Michaelis-Menten mechanism as an example. The master equation consists of a set of linear ordinary differential equations whose variables are probabilities that the realizable states exist. For a master equation with s(0) initial substrate molecules and e(0) initial enzyme molecules,...

Reaction-diffusion models are widely used to model developmental processes. The great majority of current models invoke constant diffusion coefficients. However, the diffusion of metabolites or signals through tissues is frequently such that this assumption may reasonably be questioned. We consider several different physical mechanisms leading to e...

We study a model of pattern formation in an excitable medium with concentration-dependent diffusivities. The reaction terms correspond to a two-variable Gray-Scott model in which the system has only one stable steady state. The diffusion coefficients of the two species are assumed to have a functional relationship with the concentration of the auto...

Investigations on the onset of wave instability in excitable reaction–diffusion media have mainly focused on the effects of reaction kinetics and the relative diffusivity of activator and inhibitor. In this study, we characterize wave stability in a medium in which a diffusion coefficient depends on the local concentration of a reagent. Calculation...

Fitness enhancement based on resonating circadian clocks has recently been demonstrated in cyanobacteria [Ouyang et al. (1998). Proc. Natl Acad. Sci. U.S.A.95, 8660-8664]. Thus, the competition between two cyanobacterial strains differing by the free-running period (FRP) of their circadian oscillations leads to the dominance of one or the other of...

Introduction Data analysis is a transformative process which takes some measured quantities and transforms them in some way into other values. This transformation can be one-to-one (the end product is a single value computed from a single measurement) , many-to-one (one final value computed from a number of experimental measurements) or many-to-man...

In this Letter, we report the observation of a transition from self-replicating behavior to stationary spatial structures induced by concentration-dependent diffusivities in the excitable Gray-Scott medium. Notably, the transition occurs even though there is no change in the relative diffusivities between the activator and the inhibitor. In contras...

Phase synchronization of two systems with different dynamical parameters driven by a common external signal is studied using a model of the photosensitive Belousov−Zhabotinsky reaction. Complex dynamics, including chaos, arise when the external light intensity is periodically switched between two levels. Two dynamical conditions are investigated he...

After the decay of transients, the behavior of a set of differential equations modeling a chemical or biochemical system generally rests on a low-dimensional surface which is an invariant manifold of the flow. If an equation for such a manifold can be obtained, the model has effectively been reduced to a smaller system of differential equations. Us...

In this paper we studied the behavior of a model of a periodically driven photosensitive Belousov−Zhabotinsky reaction. The computations were carried out with a two-variable Oregonator model modified to account for photosensitivity. The external light intensity was periodically switched between two levels. By keeping the total cycle length fixed wh...

Many natural and technological systems have on/off switches. For instance, mitosis can be halted by biochemical switches which act through the phosphorylation state of a complex called mitosis promoting factor. If switching between the on and off states is periodic, chaos is observed over a substantial portion of the on/off time parameter plane. Ho...

In a recent experimental study, Ouyang et al. (1998, Proc. Natl. Acad. Sci. U.S.A.95, 8660-8664) have shown that, in direct competition, cyanobacterial strains whose circadian clocks have free-running periods (FRPs) which match the period of an imposed light/dark (LD) cycle exclude strains whose FRPs are out of resonance with the LD cycle. These di...

In early embryonic development, the cell cycle is paced by a biochemical oscillator involving cyclins and cyclin-dependent kinases (cdks). Essentially the same machinery operates in all eukaryotic cells, although after the first few divisions various braking mechanisms (the so-called checkpoints) become significant. Haase and Reed have recently sho...

One of the traditional obstacles to learning quantum mechanics is the relatively high level of mathematical proficiency required to solve even routine problems. Modern computer algebra systems are now sufficiently reliable that they can be used as mathematical assistants to alleviate this difficulty. In the quantum mechanics course at the Universit...

A recently developed vibrating tube densimeter has been used to measure relative densities of aqueous sodium bromide from 373 to 523 K over a pressure range of 10–30 MPa. The instrument produces time period data consisting of both baseline and sample plateau regions. The number of samples injected into the instrument is known. The time period data...

We have computed the equilibrium conformations of clusters of up to 100 ions in a spherically symmetric harmonic trap by a simple optimization strategy called seeding in which ions are added or removed from previously discovered minima. In each case, we have found at least as good a minimum as was previously known and believe that we have located t...

Single-enzyme systems can undergo weakly damped concentration oscillations if the enzyme can be converted to an inactive form which only slowly reverts to the active form. Inactivation can take many forms, including a simple (hysteretic) conformational change of the enzyme. This observation may provide an explanation for the damped oscillations see...

Although the theory of delay-differential equations (DDEs) is generally best set in a function space, some systems of DDEs have solutions which, after the decay of transients, lie on a low-dimensional manifold in their state space. When the delay is small, highly accurate approximations to the state-space manifold which attracts the solutions can b...

In many dynamical systems, an invariant manifold attracts the phase‐space flow. These manifolds can be approximated by an In many dynamical systems, an invariant manifold attracts the phase‐space flow. These manifolds can be approximated by an
iterative method based on a functional equation treatment. However, a convergent mapping is not automatica...

It has been noted that single-enzyme systems can undergo strongly damped transient oscillations. In this paper, we present a nonlinear dynamics analysis of oscillations in undriven chemical systems. This analysis allows us to classify transient oscillations into two groups. In the first group, oscillations arise from rapid oscillatory relaxation to...

A simple epidemiological model whose dynamics are described by a pair of nonlinearly coupled Lotka--Volterra oscillators is shown to have a two-dimensional center manifold. This center manifold turns out to be identical to the center eigenspace and is thus analytically determinable. On the center manifold, the system is reduced to a single Lotka--V...

The concept of a chemically acceptable model is developed. Chemically acceptable models are causal and maintain the nonnegativity of concentrations. An extension of the law of mass action allowing delayed effects is described and shown to lead to chemically acceptable models. Delayed variable enzyme catalysis and Oregonator models are studied and s...

We have developed a novel simulation strategy based on cellular automata methods which can be used to simulate a variety of physicochemical processes, including those involved in polymerization. Our approach leads to dynamic, parallel models. This strategy can address several classes of questions in technologically or scientifically important syste...

A discrete, dynamic model of lignification most suited to studying lignin growing in highly restricted spaces is presented. This model satisfactorily reproduces many known properties of lignin. It is argued that the model therefore produces spatially realistic structures for lignin. The effects of hemicellulose binding on lignification are studied....

Simple enzyme mechanisms are capable of a surprisingly rich variety of behavior. This paper presents a global analysis of this behavior for several inhibition mechanisms, For instance, in competitive inhibition one can vary the system parameters (typically total inhibitor concentration); then the ordinary differential equations describing this mech...

A theoretical analysis of accurate steady-state experiments is presented. In principle, mechanisms can be distinguished and all rate constants found independently by using this approach. The method is illustrated by comparing two enzyme-catalysis mechanisms originally proposed by Henri: the usual enzyme-complex model, and a bimolecular model. It is...

Coupled chemical reactions are often described by (stiff) systems of ordinary differential equations (ODEs) with widely separated relaxation times. In the phase space Γ of species concentration variables, relaxation can be represented as a cascade through a nested hierarchy of smooth hypersurfaces (inertial manifolds) {Σ}: If d is the number of ind...

The time evolution of two model enzyme reactions is represented in phase space Γ. The phase flow is attracted to a unique trajectory, the slow manifold M, before it reaches the point equilibrium of the system. Locating M describes the slow time evolution precisely, and allows all rate constants to be obtained from steady‐state data. The line set M...

The conversion of [Ru(CO)5] into [Ru3(CO)12] in cyclohexane at 294–308 K has been shown to involve initial carbon monoxide dissociation to give the intermediate [Ru(CO)4]; the latter then combines further with [Ru(CO)5] in a series of fast steps to form ultimately the trimer [Ru3(CO)12]. The mechanism is thus closely related to the dissociative mec...

We present a new coordinate-space model of spherically averaged exchange-hole functions in inhomogeneous systems that depends on local values of the density and its gradient and Laplacian, and also the kinetic energy density. Our model is completely nonempirical, incorporates the uniform-density electron gas and hydrogenic atom limits, and yields t...