Francesc Mas

Bistability from double phosphorylation in signal transduction. Kinetic and structural requirements.

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.

Product dependence and bifunctionality compromise the ultrasensitivity of signal transduction cascades

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.

Pattern morphologies in zinc electrodeposition

Abstract A systematic experimental study of quasi two-dimensional zinc electrodeposition in an electrochemical cell with parallel electrodes is reported. The well-known different growth regimes, from anisotropically dendritic to irregularly disordered fractal, described previously in radial cells, are shown together with a novel mixed texture composed of dendritic backbones with ramified open branches. Experiments conducted by varying the cell thickness and electrode separation show significant effects by the current on the pattern morphology. Finally, the self-similarity of the electrodeposits is examined for two different growth regimes.

Effect of crowding by dextrans on the hydrolysis of N-Succinyl-L-phenyl-Ala-p-nitroanilide catalyzed by α-chymotrypsin

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 nonspecific 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 N-succinyl-L-phenyl-Ala-p-nitroanilide catalyzed by α-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.

Lability and mobility effects on mixtures of ligands under steady-state conditions

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 micro-organisms, etc.) is specifically considered and some consequences of its full analytical solutions are discussed.

Physical constraints in the synthesis of glycogen that influence its structural homogeneity: a two-dimensional approach.

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.

Two representations in multifractal analysis

Two representations in multifractal analysis, the so-called q and tau representations, are discussed theoretically and computed practically. Complementary to the standard q-representation, the so-called tau -representation is especially suited to resolving the most rarified subsets of the distributed measure. Moreover, these two representations are especially adapted, respectively, to the well known fixed-size and fixed-mass box-counting algorithms. Both strategies are first applied to iteratively constructed mathematical measures. Once tested in this way, we use them to analyse the mass distribution and the growth probability distribution of an experimental electrodeposited pattern.

Induced reactant adsorption in normal pulse polarography of labile metal polyelectrolyte systems part 1. Study of current-potential relationship assuming potential-independent adsorption parameters

Abstract A model for the interpretation of the normal pulse polarographic reduction of a metal ion in a metal polyelectrolyte system, including both the polyelectrolyte adsorption and the induced adsorption of the metal ion, is developed. The influence of the physical parameters included in the model on the maximum and limiting currents has received special attention. This knowledge is of great importance for the development of a physical picture of the behaviour of the system. The following restrictions have been assumed: (i) large excess of the macromolecular ligand; (ii) labile complex; (iii) reversible charge transfer; (iv) Langmuirian adsorption of both the complex and the ligand species; and (v) the adsorption coefficients of the ligand and the complex are potential-independent.

Study of a simple redox system with adsorption of both reactant and product at the DME when a time dependent potential is applied. Pulse polarography

Abstract A rigorous theory is developed to obtain a current—potential—time relationship when an arbitrary potential is applied to the DME and a reversible diffusion-controlled reaction occurs with adsorption of both reactant and product of the reaction. The development has been made generalizing the procedure followed in th epotentiostatic case, where the differential diffusion equations are transformed into integral equations. In particular, the case of pulse polarography has been considered. The rigorous solution and also several approximations are analyzed for this case and their accuracy is discussed.

Diffusion of alpha-Chymotrypsin in solution-crowded media. A fluorescence recovery after photobleaching study

Fluorescence recovery after photobleaching (FRAP) is one of the most powerful and used techniques to study diffusion processes of macromolecules in membranes or in bulk. Here, we study the diffusion of alpha-chymotrypsin in different crowded (Dextran) in vitro solutions using a confocal laser scanning microscope. In the considered experimental conditions, confocal FRAP images could be analyzed applying the uniform circular disk approximation described for a nonscanning microscope generalized to take into account anomalous diffusion. Considering the slow diffusion of macromolecules in crowded media, we compare the fitting of confocal FRAP curves analyzed with the equations provided by the Gaussian and the uniform circular disk profile models for nonscanning microscopes. As the fitted parameter variation with the size and concentration of crowders is qualitatively similar for both models, the use of the uniform circular disk or the Gaussian model is justified for these experiments. Moreover, in our experimental conditions, alpha-chymotrypsin shows anomalous diffusion (alpha < 1), depending on the size and concentration of Dextran molecules, until a high concentration and high size of crowding agent are achieved. This result indicates a range of validity of the idealized fitting expressions used, beyond which other physical phenomena must be considered.