Roussel, Marc

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    Exchange holes in inhomogeneous systems: a coordinate-space model
    (American Physical Society, 1989) Becke, A. D.; Roussel, Marc R.
    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 the proper 1lr asymptotic exchange potential in finite systems. Comparisons of model exchange energies, holes, and potentials with exact Hartree-Fock results in selected atoms are very encouraging.
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    Equilibrium configuration of systems of trapped ions
    (American Physical Society, 1999) Beekman, Richard A.; Roussel, Marc R.; Wilson, P. J.
    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 the global minimum. We have additionally located a number of local minima and some saddle points. A balancing condition between the Coulomb and trapping terms which all of the critical points of the potential energy surface must satisfy was used to estimate the errors in the computed energies.
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    Coordinate files for the equilibrium geometries of ions in an isotropic trap
    (1999) Beekman, Richard A.; Roussel, Marc R.; Wilson, P. J.
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    Synchronization by irregular inactivation
    (American Physical Society, 2000) Closson, Taunia L. L.; Roussel, Marc R.
    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. However, we have discovered that the chaotic state is fragile with respect to random fluctuations in the on time. In the presence of such fluctuations, two uncoupled copies of the system (e.g., two cells) controlled by the same switch rapidly synchronize.
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    Transition from self-replicating behavior to stationary patterns induced by concentration-dependent diffusivities
    (American Physical Society, 2001) Roussel, Marc R.; Wang, Jichang
    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 contrast to the well-known Turing patterns, the obtained time-independent spatial structure has no intrinsic wavelength and the asymptotic state depends exclusively on the initial perturbations. This study illustrates that variable diffusivities can also have profound effects on pattern formation and selection in excitable media.
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    Code and examples for C++ object-oriented differential equation integrators
    (2003) Roussel, Catharine J.; Roussel, Marc R.
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    The scale-free dynamics of eukaryotic cells
    (Public Library of Science, 2008) Aon, Miguel A.; Roussel, Marc R.; Cortassa, Sonia; O'Rourke, Brian; Murray, Douglas B.; Beckmann, Manfred; Lloyd, David
    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 broad frequency distributions and evidence for long-term memory in the observed dynamics. Moreover RDA and PSA showed that the bioenergetic dynamics in both systems show fractal scaling over at least 3 orders of magnitude, and that this scaling obeys an inverse power law. Therefore we conclude that in S. cerevisiae and cardiomyocytes the dynamics are scale-free in vivo. Applying RDA and PSA to data generated from an in silico model of mitochondrial function indicated that in yeast and cardiomyocytes the underlying mechanisms regulating the scale-free behavior are similar. We validated this finding in vivo using single cells, and attenuating the activity of the mitochondrial inner membrane anion channel with 4-chlorodiazepam to show that the oscillation of NAD(P)H and reactive oxygen species (ROS) can be abated in these two evolutionarily distant species. Taken together these data strongly support our hypothesis that the generation of ROS, coupled to redox cycling, driven by cytoplasmic and mitochondrial processes, are at the core of the observed rhythmicity and scale-free dynamics. We argue that the operation of scale-free bioenergetic dynamics plays a fundamental role to integrate cellular function, while providing a framework for robust, yet flexible, responses to the environment.
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    On the distribution of transcription times
    (Biomath Forum, 2013) Roussel, Marc R.
    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 of the rate constants, but a good approximation for long transcription units. An approximate form of the distribution is obtained in which the slow steps are treated exactly and the fast steps are lumped together into a single lag term. This approximate form might be particularly useful as a function to be fit to experimental transcription time distributions. Multi-polymerase effects are also studied by simulation. We find that the analytic model generally predicts the behavior of the multi-polymerase simulations, often quantitatively, provided termination is not rate-limiting.
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    A mathematical model of the biochemical network underlying left-right asymmetry establishment in mammals
    (Elsevier, 2018) Roussel, Catharine J.; Roussel, Marc R.
    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 Lefty and find a wide range of parameters over which bistability (two stable steady states) is observed, with one stable steady state a low-Nodal state corresponding to the right-hand developmental fate, and the other a high-Nodal state corresponding to the left. We find that bistability requires a transcription factor containing two molecules of phosphorylated Smad2. A numerical survey of the full model, including Lefty, shows the effects of Lefty on the potential for bistability, and on the conditions that lead to the system reaching one or the other steady state.
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    Heineken, Tsuchiya and Aris on the mathematical status of the pseudo-steady state hypothesis: a classic from volume 1 of Mathematical Biosciences
    (Elsevier, 2019) Roussel, Marc R.
    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 continues to be studied and mined for insights. This perspective discusses both the strengths and weaknesses of the work presented in this paper. For many, the justification of the pseudo-steady-state approximation using singular perturbation theory is the main achievement of this paper. However, there is so much more material here, which laid the foundation for a great deal of research in mathematical biochemistry in the intervening decades. The parameterization of the equations, construction of the first-order uniform singular-perturbation solution, and an attempt to apply similar principles to the pseudo-equilibrium approximation are discussed in particular detail.
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    A delayed mass-action model for the transcriptional control of Hmp, an NO detoxifying enzyme, by the iron-sulfur protein FNR
    (Springer, 2019) Roussel, Marc R.
    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-action model for the Hmp-FNR network has been developed. This model has 33 parameters, all but three of which were estimated. One of the unknown parameters, the rate of NO inflow into the cell’s cytoplasm, was used as a control parameter in a study of the steady-state structure of this model. This study revealed bistability across a wide range of inflow rates, oxygen concentrations, and values of the unknown parameters. The bistability is caused by substrate inhibition of Hmp by NO, which allows for a high-NO steady state, which would likely be lethal, to coexist with a biologically desirable low-NO steady state.
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    Small binding-site clearance delays are not negligible in gene expression modeling
    (Elsevier, 2020) Trofimenkoff, Elizabeth A. M.; Roussel, Marc R.
    During the templated biopolymerization processes of transcription and translation,a macro molecular 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, and one might think that they could be neglected. However,in the case of transcription, these clearance delays are associated with conservation laws,resulting in surprisingly large effects on the bifurcation diagrams in models of gene expression networks.We study an example of this phenomenon in a model of a gene regulated by a non-coding RNA displaying bistability. Neglecting the binding-site clearance delays in this model can only be compensated for by making ad hoc, unphysical adjustments to the model’s kinetic constants.
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    Probabilistic models of uORF-mediated ATF4 translation control
    (Elsevier, 2022) Marasco, Olivia N. J. M.; Roussel, Marc R.; Thakor, Nehal
    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 the control system that regulates the translation of ATF4, both based on the Vattem-Wek hypothesis. This hypothesis is based on a race to reload, following the translation of a small upstream open reading frame (uORF), the ternary complex that brings the initiator tRNA to the ribosome as the 40S subunit scans along the mRNA, encountering first a start codon for an inhibitory uORF whose reading frame overlaps the start of the ATF4 coding sequence. We develop a pair of simple, analytic, probabilistic models, one of which assumes all nucleotide triplets have identical kinetic properties, while the other recognizes the existence of triplets at which the ternary complex loads more efficiently. We also consider two different functions representing the dependence of the rate of initiation at uORF1 on the ternary complex concentration. In keeping with the theme of this Special Issue, we studied the properties of these models in a Maple document, which can easily be modified to consider different parameters, translation rate initiation functions, and so on.