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The quasi-steady-state approximation is widely used to develop simplified deterministic or stochastic models of enzyme catalyzed reactions. In deterministic models, the quasi-steady-state approximation can be mathematically justified from singular perturbation theory. For several closed enzymatic reactions, the homologous extension of the quasi-steady-state approximation to the stochastic regime, known as the stochastic quasi-steady-state approximation, has been shown to be accurate under the analogous conditions that permit the quasi-steady-state reduction of the deterministic counterpart. However, it was recently demonstrated that the extension of the stochastic quasi-steady-state approximation to an open Michaelis--Menten reaction mechanism is only valid under a condition that is far more restrictive than the qualifier that ensures the validity of its corresponding deterministic quasi-steady-state approximation. In this paper, we suggest a possible explanation for this discrepancy from the lens of geometric singular perturbation theory. In so doing, we illustrate a misconception in the application of the quasi-steady-state approximation: timescale separation does not imply singular perturbation., Comment: 19 pages, 1 Figure

Intrinsically disordered proteins and protein regions lack a stable three-dimensional structure under physiological conditions. Several proteomic investigations of intrinsic disorder have been performed to date and have found disorder to be prevalent in eukaryotic proteomes. Here we present descriptive statistics of intrinsic disorder features for ten model eukaryotic proteomes that have been calculated from computational disorder prediction algorithms. The data descriptor also provides consensus disorder annotations as well as additional physical parameters relevant to protein disorder, and further provides protein existence information for all proteins included in our analysis. The complete datasets can be downloaded freely, and it is envisaged that they will be updated periodically with new proteomes and protein disorder prediction algorithms. These datasets will be especially useful for assessing protein disorder, and conducting novel analyses that advance our understanding of intrinsic disorder and protein structure.

We consider a diffusion model with limit cycle reaction functions. In an unbounded domain, diffusion spreads pattern outwards from the source. Convection adds instability to the reaction–diffusion system. We see the result of the instability in a readiness to create pattern. In the case of strong convection, we consider that the first-order approximation may be valid for some aspects of the solution behaviour. We employ the method of Riemann invariants and rescaling to transform the reduced system into one invariant under parameter change. We carry out numerical experiments to test our analysis. We find that most aspects of the solution do not comply with this, but we find one significant characteristic which is approximately first order. We consider the correspondence of the Partial Differential Equation with the Ordinary Differential Equation along rays from the initiation point in the transformed system. This yields an understanding of the behaviour.

Reactions in the intracellular medium occur in a highly organized and heterogenous environment rendering invalid modeling approaches based on the law of mass action or its stochastic counter-part. This has led to the recent development of a variety of stochastic microscopic approaches based on lattice-gas automata or Brownian dynamics. The main disadvantage of these methods is that they are computationally intensive. We propose a mesoscopic method which permits the efficient simulation of reactions occurring in the complex geometries typical of intracellular environments. This approach is used to model the transport of a substrate through a pore in a semi-permeable membrane, in which its Michaelis–Menten enzyme is embedded. We find that the temporal evolution of the substrate is a sensitive function of the spatial heterogeneity of the environment. The spatial organization and heterogeneities of the intracellular medium seem to be playing an important role in the regulation of biochemical reactions.

We consider single enzyme–substrate reaction mechanisms involving multiple complexes and demonstrate that these are equivalent to a distributed delay system without complexes. The distribution of the delay is determined by the number of intermediates and the relative sizes of the rates of the individual reaction mechanisms. We also consider the limit where there are a large number of intermediate complexes, and the conditions under which a number of known reaction mechanisms are equivalent. The present formalism brings forth new perspectives in the implementation of experimental techniques to rule out particular reaction mechanisms by studying the distribution of the delay between reactant mixing and product formation.

We present a method to determine the reaction type and kinetic constants for enzyme inhibitors that decreases the number of experimental assays by at least a factor of five. It is based on a new theoretical formalism in terms of concentrations that dismisses the requirement of estimating initial velocities. Expressions for the time evolution of the concentrations of all the reactants are also given.

An analytic formalism developed earlier to describe the time evolution of the basic enzyme reaction is extended to fully competitive systems. Time-dependent closed form solutions are derived for the three nominal cases of competition: even, slow and fast inhibitors, allowing for the first time the complete characterization of the reactions. In agreement with previous work, the time-independent Michaelis-Menten approach is shown to be inaccurate when a fast inhibitor is present. The validity of the quasi-steady-state approximation on which the present framework is based is also revised.

An innovative theoretical approach that enables the complete characterisation of enzyme–substrate and enzyme–substrate–competitor reactions is generalised to systems with multiple alternative substrates. Based on the quasi‐steady‐state assumption, time‐dependent closed form solutions are presented for cases with even, weak and mixed substrate competition. The analytic framework should facilitate the development of computational fitting procedures for progress curves, simplifying the measuring process and increasing the reliability of reaction constant estimates.