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- ItemProbabilistic models of uORF-mediated ATF4 translation control(Elsevier, 2022) Marasco, Olivia N. J. M.; Roussel, Marc R.; Thakor, NehalATF4 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.
- ItemSmall 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.
- ItemA 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.
- ItemHeineken, 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.
- ItemExchange 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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