Monte Carlo simulations of enzymatic reactions in crowded media. Effect of the enzyme-obstacle relative size.

We perform Monte Carlo simulations in three-dimensional (3D) lattice in order to study diffusion-controlled and mixed activation-diffusion reactions following an irreversible Michaelis-Menten scheme in crowded media. The simulation data reveal the rate coefficient dependence on time for diffusion-controlled bimolecular reactions developing in three-dimensional media with obstacles, as predicted by fractal kinetics approach. For the cases of mixed activation-diffusion reactions, the fractality of the reaction decreases as the activation control increases. We propose a modified form of the Zipf-Mandelbrot equation to describe the time dependence of the rate coefficient, k(t)=k0(1+t/τ)(-)(h). This equation provides a good description of the fractal regime and it may be split into two terms: one that corresponds to the initial rate constant (k0) and the other one correlated with the kinetics fractality. Additionally, the proposed equation contains and links two limit expressions corresponding to short and large periods of time: k1=k0 (for t≪τ) that relates to classical kinetics and the well-known Kopelman's equation k∼t(-)(h) (for t≫τ) associated to fractal kinetics. The τ parameter has the meaning of a crossover time between these two limiting behaviours. The value of k0 is mainly dependent on the excluded volume and the enzyme-obstacle relative size. This dependence can be explained in terms of the radius of an average confined volume that every enzyme molecule feels, and correlates very well with the crossover length obtained in previous studies of enzyme diffusion in crowding media.

Macromolecular crowding effect upon in vitro enzyme kinetics: mixed activation-diffusion control of the oxidation of NADH by pyruvate catalyzed by lactate dehydrogenase.

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 with respect to the enzyme present in the reaction. Moreover, we analyzed the influence of macromolecular crowding on the Michaelis-Menten constants, vmax and Km. 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.

Effect of crowding by Dextrans in enzymatic reactions.

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 H2O2 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.

Molecular dynamics simulation of the spherical electrical double layer of a soft nanoparticle: effect of the surface charge and counterion valence.

Molecular dynamics simulations were performed to study the ion and water distribution around a spherical charged nanoparticle. A soft nanoparticle model was designed using a set of hydrophobic interaction sites distributed in six concentric spherical layers. In order to simulate the effect of charged functionalyzed groups on the nanoparticle surface, a set of charged sites were distributed in the outer layer. Four charged nanoparticle models, from a surface charge value of -0.035 C m(-2) to -0.28 C m(-2), were studied in NaCl and CaCl(2) salt solutions at 1 M and 0.1 M concentrations to evaluate the effect of the surface charge, counterion valence, and concentration of added salt. We obtain that Na(+) and Ca(2+) ions enter inside the soft nanoparticle. Monovalent ions are more accumulated inside the nanoparticle surface, whereas divalent ions are more accumulated just in the plane of the nanoparticle surface sites. The increasing of the the salt concentration has little effect on the internalization of counterions, but significantly reduces the number of water molecules that enter inside the nanoparticle. The manner of distributing the surface charge in the nanoparticle (uniformly over all surface sites or discretely over a limited set of randomly selected sites) considerably affects the distribution of counterions in the proximities of the nanoparticle surface.

A semi-grand canonical Monte Carlo simulation model for ion binding to ionizable surfaces: proton binding of carboxylated latex particles as a case study.

In this paper, we present a computer simulation study of the ion binding process at an ionizable surface using a semi-grand canonical Monte Carlo method that models the surface as a discrete distribution of charged and neutral functional groups in equilibrium with explicit ions modelled in the context of the primitive model. The parameters of the simulation model were tuned and checked by comparison with experimental titrations of carboxylated latex particles in the presence of different ionic strengths of monovalent ions. The titration of these particles was analysed by calculating the degree of dissociation of the latex functional groups vs. pH curves at different background salt concentrations. As the charge of the titrated surface changes during the simulation, a procedure to keep the electroneutrality of the system is required. Here, two approaches are used with the choice depending on the ion selected to maintain electroneutrality: counterion or coion procedures. We compare and discuss the difference between the procedures. The simulations also provided a microscopic description of the electrostatic double layer (EDL) structure as a function of pH and ionic strength. The results allow us to quantify the effect of the size of the background salt ions and of the surface functional groups on the degree of dissociation. The non-homogeneous structure of the EDL was revealed by plotting the counterion density profiles around charged and neutral surface functional groups.

New insights into diffusion in 3D crowded media by Monte Carlo simulations: effect of size, mobility and spatial distribution of obstacles.

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 a 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 (α), the crossover time from anomalous to normal diffusion regimes (τ) and the long time diffusion coefficient (D*). Simulation results indicate that there are a more anomalous diffusion (smaller α) and a 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 obstacle excluded volume is a factor to be considered together with the value of the excluded volume itself.

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.

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.

Effect of the surface charge discretization on electric double layers: a Monte Carlo simulation study.

The structure of the electric double layer in contact with discrete and continuously charged planar surfaces is studied within the framework of the primitive model through Monte Carlo simulations. Three different discretization models are considered together with the case of uniform distribution. The effect of discreteness is analyzed in terms of charge density profiles. For point surface groups, a complete equivalence with the situation of uniformly distributed charge is found if profiles are exclusively analyzed as a function of the distance to the charged surface. However, some differences are observed moving parallel to the surface. Significant discrepancies with approaches that do not account for discreteness are reported if charge sites of finite size placed on the surface are considered.