Previous studies have suggested that positive feedback loops and ultrasensitivity are prerequisites for bistability in covalent modification cascades. However, it was recently shown that bistability and hysteresis can also arise solely from multisite phosphorylation. Here we analytically demonstrate that double phosphorylation of a protein (or other covalent modification) generates bistability only if: (a) the two phosphorylation (or the two dephosphorylation) reactions are catalyzed by the same enzyme; (b) the kinetics operate at least partly in the zero‐order region; and (c) the ratio of the catalytic constants of the phosphorylation and dephosphorylation steps in the first modification cycle is less than this ratio in the second cycle. We also show that multisite phosphorylation enlarges the region of kinetic parameter values in which bistability appears, but does not generate multistability. In addition, we conclude that a cascade of phosphorylation/dephosphorylation cycles generates multiple steady states in the absence of feedback or feedforward loops. Our results show that bistable behavior in covalent modification cascades relies not only on the structure and regulatory pattern of feedback/feedforward loops, but also on the kinetic characteristics of their component proteins.

Traditionally, studies on the diffusion-controlled reaction of biological macromolecules have been carried out in dilute solutions (in vitro). However, in an intracellular environment (in vivo), there is a high concentration of macromolecules, which results in non-specific interactions (macromolecular crowding). This affects the kinetics and thermodynamics of the reactions that occur in these systems. In this paper, we study the crowding effect of large macromolecules on the reaction rates of the hydrolysis of Nsuccinyl-L-phenyl-Ala-p-nitroanilide catalyzed by alpha-chymotrypsin, by adding Dextrans of various molecular weights to the reaction solutions. The results indicate that the volume occupied by the crowding agent, but not its size, plays an important role in the rate of this reaction. A v max decay and a K m increase were obtained when the Dextran concentration in the sample was increased. The increase in K m can be attributed to the slowing of protein diffusion, due to the presence of crowding. Whereas the decrease in v max could be explained by the effect of mixed inhibition by product, which is enhanced in crowded media. As far as we know, this is the first reported experiment on the crowding effect in an enzymatic reaction with a mixed inhibition by product.

Analytical solutions for the steady-state flux arriving at an active surface from a mixture (in which one active species reacts with non-active ligands in the medium) can be helpful in a variety of problems: voltammetric techniques, heterogeneous processes in reactors, toxic or nutrient uptake, techniques of diffusive gradients in thin films (DGT), etc. Under any geometry that sustains steady-state, a convenient combination of the reaction-diffusion equations leads to a simpler formulation of the problem for arbitrary diffusivities of the species and arbitrary rate constants of the first order conversion between the active species and the non-active species. The resulting problem can be characterised in terms of a list of dimensionless parameters involving the kinetic and mobility properties of each species. A lability degree for each 1:1 complex in terms of the surface concentrations leads to: i) a lability criterion specific for each complex in the mixture and ii) the assessment of the relative contribution of each complex to the resulting flux. Semi-infinite spherical diffusion (as in the Gel Integrated MicroElectrode, GIME, biouptake modelling of microorganisms , etc.) is specifically considered and some consequences of its full analytical solutions are discussed.

Covalent modification cycles are ubiquitous. Theoretical studies have suggested that they serve to increase sensitivity. However, this suggestion has not been corroborated experimentally in vivo. Here, we demonstrate that the assumptions of the theoretical studies, i.e., irreversibility and absence of product inhibition, were not trivial: when the conversion reactions are close to equilibrium or saturated by their product, ''zero-order'' ultrasensitivity disappears. For high sensitivities to arise, not only substrate saturation (zero-order) but also high equilibrium constants and low product saturation are required. Many covalent modification cycles are catalyzed by one bifunctional 'ambiguous' enzyme rather than by two independent proteins. This makes high substrate concentration and low product concentration for both reactions of the cycle inconsistent; such modification cycles cannot have high responses. Defining signal strength as ratios of modified (e.g., phosphorylated) over unmodified protein, signal-to-signal response sensitivity equals 1: signal strength should remain constant along a cascade of ambiguous modification cycles. We also show that the total concentration of a signalling effector protein cannot affect the signal emanating from a modification cycle catalyzed by an ambiguous enzyme if the ratio of the two forms of the effector protein is not altered. This finding may explain the experimental result that the pivotal signal transduction protein PII plus its paralogue GlnK do not control steady-state N-signal transduction in Escherichia coli. It also rationalizes the absence of strong phenotypes for many signal-transduction proteins. Emphasis on extent of modification of these proteins is perhaps more urgent than transcriptome analysis.

The interior of the living cell is highly concentrated and structured with molecules that have different shapes and sizes. Almost all experimental biochemical data have been obtained working in dilute solutions, situations which do not reflect the in vivo conditions. The consequences of such crowding upon enzymatic reactions remain unclear. In this paper we have studied and compared the initial velocity of the hydrolysis of N-succinyl-L-phenyl-Ala-p-nitroanilide catalyzed by alpha-chymotrypsin, the oxidation of ABTS by H 2 O 2 catalyzed by HRP; and the oxidation of NADH in presence of pyruvate catalyzed by LDH. These reactions were chosen as model enzymatic processes occurring in different in vitro crowded media. The systems crowding has been built by introducing Dextran of several concentrations and sizes. Our results indicate that the volume occupied by the crowding agent, but not its size, plays an important role on the initial velocity of reactions involving tiny enzymes. However, the enzyme size is another important factor influencing the velocity of the reactions of large enzymes occurring in Dextran crowded media. In this situation, the reaction initial velocity depends on both occupied volume and dimension of the crowding agent that is present in the reaction media.

Abstract. Particle diffusion in crowded media was studied through Monte Carlo simulations in 3D obstructed lattices. Three particular aspects affecting the diffusion, not extensively treated in three-dimensional geometry, were analysed: the relative particle-obstacle size, the relative particle-obstacle mobility and the way of having the obstacles distributed in the simulation space (randomly or uniformly). The results are interpreted in terms of the parameters that characterize the time dependence of the diffusion coefficient: the anomalous diffusion exponent (a), the crossover time from anomalous to normal diffusion regimes (τ) and the long time diffusion coefficient (D*). Simulation results indicate that there is a more anomalous diffusion (smaller a) and lower long time diffusion coefficient (D*) when obstacle concentration increases, and that, for a given total excluded volume and immobile obstacles, the anomalous diffusion effect is less important for bigger size obstacles. However, for the case of mobile obstacles, this size effect is inverted yielding values that are in qualitatively good agreement with in vitro experiments of protein diffusion in crowded media.These results underline that the pattern of the spatial partitioning of the obstacleexcluded volume is a factor to be considered together with the value of the excluded volume itself.

Enzyme kinetics studies have been usually designed as dilute solution experiments, which differ substantially from in vivo conditions. However, cell cytosol is crowded with a high concentration of molecules having different shapes and sizes. The consequences of such crowding in enzymatic reactions remain unclear. The aim of the present study is to understand the effect of macromolecular crowding produced by Dextran of different sizes and at diverse concentrations in the well-known reaction of oxidation of NADH by pyruvate catalyzed by L-Lactate Dehydrogenase (LDH). Our results indicate that the reaction rate is determined by both the occupied volume and the relative size of Dextran obstacles in respect to the enzyme present in the reaction.Moreover, we analyzed the influence of macromolecular crowding on the MichaelisMenten constants, ‫ݒ‬ ௫ and ‫ܭ‬ . The obtained results show that only high concentrations and large sizes of Dextran reduce both constants suggesting a mixed activation-diffusion control of this enzymatic reaction due to the Dextran crowding action. From our knowledge, this is the first experimental study that depicts mixed activation-diffusion control in an enzymatic reaction due to the effect of crowding.

Several aspects of glycogen optimization as an efficient fuel storage molecule have been studied in previous works: the chain length and the branching degree. These results demonstrated that the values of these variables in the cellular molecule are those that optimize the structure-function relationship. In the present work we show that structural homogeneity of the glycogen molecule is also an optimized variable that plays an important role in its metabolic function. This problem was studied by means of a two-dimensional approach, which allowed us to simplify the very complicated structure of glycogen. Our results demonstrate that there is a molecular size limit that guarantees the structural homogeneity, beyond which the structure of the molecule degenerates, as many chains do not grow. This strongly suggests that such a size limit is precisely what the molecule possesses in the cell.