Enzyme reactions at the surface of living cells. I. Electric repulsion of charged ligands and recognition of signals from the external milieu

The dynamic behaviour of a polyelectrolyte-bound enzyme is studied when diffusion of substrate or diffusion of product is coupled to electric repulsion and to Michaelis-Menten enzyme reaction. The definition of the classical concepts of electric partition coefficients and Donnan potential of a polyelectrolyte membrane has been extended under global non-equilibrium conditions. This extension is permissible when a strong repulsion exists of substrate and product by the fixed negative charges of the membrane. Coupling between product diffusion, electric repulsion and enzyme reaction at constant advancement may result in a hysteresis loop of the partition coefficient as the product concentration is increased in the reservoir. This hysteresis loop vanishes as the rate of product diffusion increases. No hysteresis loop may occur when electric repulsion effects are coupled to substrate diffusion and reaction. The existence of multiple values of the partition coefficient for a fixed concentration of product implies that the membrane may store short-term memory of the former product concentration present in the external milieu. The occurrence of hysteresis generated by coupling enzyme reaction, product diffusion, electric partition effects at constant advancement of the reaction may be viewed as a sensing device of product concentration in the external milieu. Surprisingly, non-linearities required to generate this sensing device come from electrostatic effects and not from enzyme kinetics.     

Spatial order as a source of kinetic cooperativity in organized bound enzyme systems.

When enzyme molecules are distributed within a negatively charged matrix, the kinetics of the conversion of a negatively charged substrate into a product depends on the organization of fixed charges and bound enzyme molecules. Organization is taken to mean the existence of macroscopic heterogeneity in the distribution of fixed charge density, or of bound enzyme density, or of both. The degree of organization is quantitatively expressed by the monovariate moments of charge and enzyme distributions as well as by the bivariate moments of these two distributions. The overall reaction rate of the bound enzyme system may be expressed in terms of the monovariate moments of the charge density and of the bivariate moments of charge and enzyme densities. The monovariate moments of enzyme density do not affect the reaction rate. With respect to the situation where the fixed charges and enzyme molecules are randomly distributed in the matrix, the molecular organization, as expressed by these two types of moments, generates an increase or decrease of the overall reaction rate as well as a cooperativity of the kinetic response of the system. Thus both the alteration of the rate and the modulation of cooperativity are the consequence of a spatial organization of charges with respect to the enzyme molecules. The rate equations have been derived for different types of organization of fixed charges and enzyme molecules, namely, clustered charges and homogeneously distributed enzyme molecules, clustered enzyme molecules and homogeneously distributed charges, clusters of charges and clusters of enzymes that partly overlap, and clusters of enzymes and clusters of charges that are exactly superimposed. Computer simulations of these equations show how spatial molecular organization may modulate the overall reaction rate.     

Ionic control of immobilized enzymes. Kinetics of acid phosphatase bound to plant cell walls.

When an enzyme is bound to an insoluble polyelectrolyte it may acquire novel kinetic properties generated by Donnan effects. It the enzyme is homogeneously distributed within the matrix, a variation of the electrostatic partition coefficient, when substrate concentration is varied, mimics either positive or negative co-operativity. This type of non-hyperbolic behaviour may be distinguished from true co-operativity by an analysis of the Hill plots. If the enzyme is heterogeneously distributed within the polyelectrolyte matrix, an apparent negative co-operativity occurs, even if the electrostatic partition coefficient does not vary when substrate concentration is varied in the bulk phase. If the partition coefficient varies, mixed positive and negative co-operativities may occur. All these effects must be suppressed by raising the ionic strength in the bulk phase. Attraction of cations by fixed negative charges of the polyanionic matrix may be associated with a significant decrease of the local pH. The magnitude of this effect is controlled by the pK of the fixed charges groups of the Donnan phase. The local pH cannot be much lower than the value of this pK. This effect may be considered as a regulatory device of the local pH. Acid phosphatase of sycamore (Acer pseudoplatanus) cell walls is a monomeric enzyme that displays classical Michaelis-Menten kinetics in free solution. However, when bound to small cell-wall fragments or to intact cells, it has an apparent negative co-operativity at low ionic strength. Moreover a slight increase of ionic strength apparently activates the bound enzymes and tends to suppress the apparent co-operativity. At I0.1, or higher, the bound enzyme has a kinetic behavior indistinguishable from that of the purified enzyme in free solution. These results are interpreted in the light of the Donnan theory. Owing to the repulsion of the substrate by the negative charges of cell-wall polygalacturonates, the local substrate concentration in the vicinity of the bound enzyme is smaller than the corresponding concentration in bulk solution. The kinetic results obtained are consistent with the view that there exist at least three populations of bound enzyme with different ionic environments: a first population with enzyme molecules not submitted to electrostatic effects, and two other populations with molecules differently submitted to these effects. The theory allows one to estimate the proportions of enzyme belonging to these populations, as well as the local pH values and the partition coefficients within the cell walls.     

Lipid demixing and protein-protein interactions in the adsorption of charged proteins on mixed membranes

The adsorption free energy of charged proteins on mixed membranes, containing varying amounts of (oppositely) charged lipids, is calculated based on a mean-field free energy expression that accounts explicitly for the ability of the lipids to demix locally, and for lateral interactions between the adsorbed proteins. Minimization of this free energy functional yields the familiar nonlinear Poisson-Boltzmann equation and the boundary condition at the membrane surface that allows for lipid charge rearrangement. These two self-consistent equations are solved simultaneously. The proteins are modeled as uniformly charged spheres and the (bare) membrane as an ideal two-dimensional binary mixture of charged and neutral lipids. Substantial variations in the lipid charge density profiles are found when highly charged proteins adsorb on weakly charged membranes; the lipids, at a certain demixing entropy penalty, adjust their concentration in the vicinity of the adsorbed protein to achieve optimal charge matching. Lateral repulsive interactions between the adsorbed proteins affect the lipid modulation profile and, at high densities, result in substantial lowering of the binding energy. Adsorption isotherms demonstrating the importance of lipid mobility and protein-protein interactions are calculated using an adsorption equation with a coverage-dependent binding constant. Typically, at bulk-surface equilibrium (i.e., when the membrane surface is "saturated" by adsorbed proteins), the membrane charges are "overcompensated" by the protein charges, because only about half of the protein charges (those on the hemispheres facing the membrane) are involved in charge neutralization. Finally, it is argued that the formation of lipid-protein domains may be enhanced by electrostatic adsorption of proteins, but its origin (e.g., elastic deformations associated with lipid demixing) is not purely electrostatic.     

Electrostatic effects and calcium ion concentration as modulators of acid phosphatase bound to plant cell walls

At 'low' ionic strength, acid phosphatase bound to plant cell walls exhibits an apparent negative co-operativity, whereas it displays classic Michaelis-Menten kinetics in free solution. Conversely, at 'high' ionic strength, the bound enzyme and the soluble enzyme behave identically. This apparent negative co-operativity is explained by the existence of an electrostatic partition of the charged substrate by the fixed negative charges of the cell wall. Raising the ionic strength suppresses these electrostatic repulsion effects. Calcium may be removed from the cell walls by acid treatment and the acid phosphatase is apparently strongly inhibited. This inhibition occurs together with an increased apparent negative co-operativity of the enzyme. Incubating cell wall fragments previously depleted of calcium with CaCl2 restores the initial behaviour of the enzyme. Calcium, which tightly binds to cell wall pectic compounds, has by itself no effect on the enzyme in free solution. It affects the net charge of the cell wall and therefore the amplitude of electrostatic repulsion effects. Non-linear least-square fitting methods make it possible to estimate the density of fixed negative charges as well as the electrostatic partition coefficient, for both the 'native' and 'calcium-deprived' cell wall fragments. It may be shown directly that calcium loading and unloading in the cell wall controls the electrostatic effects, by monitoring proton extrusion from cell wall fragments upon raising the ionic strength. Proton outflux in the bulk phase is considerably enhanced upon removal of calcium from the cell walls. The main conclusion is that loading and unloading of calcium during cell elongation and division may regulate the activity of cell wall enzymes.     

Molecular organization and clustering of cell-wall-bound enzymes as a source of kinetic apparent co-operativity

When fixed charges and enzyme molecules are not homogeneously distributed in a matrix, the degree of organization of charges, of enzyme molecules and of charges with respect to enzyme molecules modulate the enzyme reaction rate. The overall reaction velocity of the bound enzyme system may be expressed in terms of monovariate moments of the charge density distribution and of the bivariate moments of the charge and enzyme density distributions. With respect to the situation where fixed charges and enzyme molecules are randomly distributed in the matrix, the molecular organization, as expressed by the monovariate and bivariate moments results in an increase or a decrease, of the overall reaction rate, as well as in the appearance of a kinetic cooperativity. The degree of spatial organization of objects may be expressed quantitatively through the concept of minimal spanning tree. This concept may thus be applied to the quantification of the degree of order that may exist in the bidimensional distribution of enzyme molecules in a charged matrix. Primary walls of isolated plant cells in sterile culture behave as a polyanion and contain different enzymes. The spatial distribution in sycamore cell walls of an acid phosphatase has been studied through the concept of minimal spanning tree and shown to be non-randomly distributed in the polyanionic matrix, but clustered in that matrix. This spatial organization results in a modulation of the reaction rate of the cell-wall-bound phosphatase reaction. Both the theoretical and experimental results presented in this study leave little doubt as to the validity of the idea that in situ the organization of fixed charges and enzyme molecules modulate the overall dynamics of enzyme reactions.     

Electrostatics of mesophilic and psychrophilic trypsin isoenzymes: qualitative evaluation of electrostatic differences at the substrate binding site

A qualitative evaluation of electrostatic features of the substrate binding region of seven isoenzymes of trypsin has been performed by using the continuum electrostatic model for the solution of the Poisson-Boltzmann equation. The sources of the electrostatic differences among the trypsins have been sought by comparative calculations on selective charges: all charges, conserved charges, partial charges, unique cold trypsin charges, and a number of charge mutations. As expected, most of the negative potential at the S(1) region of all trypsins is generated from Asp(189), but the potential varies significantly among the seven trypsin isoenzymes. The three cold active enzymes included in this study possess a notably lower potential at and around the S(1)-pocket compared with the warm active counterparts; this finding may be the main contribution to the increased binding affinity. The source of the differences are nonconserved charged residues outside the specificity pocket, producing electric fields at the S(1)-pocket that are different in both sign and magnitude. The surface charges of the mesophilic trypsins generally induce the S(1) pocket positively, whereas surface charges of the cold trypsins produce a negative electric field of this region. Calculations on mutants, where charged amino acids were substituted between the trypsins, showed that mutations in Loop2 (residues 221B and 224) and residue 175, in particular, were responsible for the low potential of the cold enzymes.     

Electrostatic effects on the kinetics of bound enzymes.

1. The effect of the interaction between the charged matrix and substrate on the kinetic behaviour of bound enzymes was investigated theoretically. 2. Simple expression is derived for the apparent Km. 3. The apparent Km can only be used for the characterization of the electrostatic effect of the ionic strength does not vary with the substrate concentration. 4. The deviations from Michaelis-Menton kinetics are graphically illustrated for cases when the ionic strength varies with the substrate concentration. 5. The inhibition of the bound enzyme by a charged inhibitor at constant ionic strength is characterized by an apparent Ki. 6. When both the inhibitor concentration and the ionic strength change there is no apparent Ki, and the inhibition profile is graphically illustrated for this case. 7. Under certain conditions the electrostatic effects manifest thenselves in a sigmoidal dependence of the enzyme activity on the concentration of the substrate or inhibitor.     

Electrostatic repulsion of ion penetrable charged membranes: role of Donnan potential

A model is proposed for the electrostatic repulsion between two ion-penetrable charged membranes in which fixed charges are uniformly distributed. This model assumes that the electric potential far inside the membrane is always equal to the Donnan potential, independent of the membrane separation. In this respect the present model completely differs from usual models for the electrostatic interaction of colloidal particles which assume that the surface potential or the surface charge density remains constant during interaction. It is shown that the rise in potential in the interacting membranes caused by their approach is greatly suppressed so that the potential in the membrane does not exceed the Donnan potential. Numerical results of the calculation of the repulsion by the non-linear Poisson-Boltzmann equation are displayed as a function of the membrane separation and an approximate formula is also derived.     

An additional circulatory system: Vascular-Interstitial closed electric circuits (VICC)

The construction and activation of a previously described additional circulatory system for long-distance transport in tissue is summarized. Metabolism or injury produces electrochemical polarization of tissue. This driving force produces exchange of material by electrophoresis and dielectrophoresis in tissue and cellular matrices with fixed surface charges. These transports are described over vascular-intersititial closed electric circuits (VICC) because blood vessels function as relatively insulated conducting cables and connect with the conducting tissue fluids over capillaries. Necessary electron tranfer takes place at sites of segmental capillary contractions by the superimposed electric field via globular proteins known to exchange electrons in the endothelial cellular membranes. The effect of field-activated VICC is here demonstrated by accumulation of granulocytes in vivo as an electrophoretic process, which gives a mechanistic and energetic logical explanation of so-called leukotaxis.     

Electric interactions at the lipid membrane surface

This work presents the results of an experimental study and of computer simulations concerning electric interactions in the surface layer of egg yolk lecithin (EYL) liposome membranes. The surface layer is formed by EYL polar heads, which possess features of electric dipoles, and positive charged polar heads belonging to admixtures of quaternary ammonium salts (AS). The results of the experimental study are in good agreement with the ones of the computer simulations. It was found that fluidity of the membranes, at a given concentration of AS, obtains the extremal (minimal) value. Similarly, the binding energy of the dipoles-positive charges system behaves like that in computer simulations. Moreover, the locations of the fluidity extremum and those of the binding energy depend on the charge of the AS polar heads as well as on the degree of electric interactions screening by the environment. At a certain optimal value of the screening coefficient, the energy of the system is the lowest (the most negative) and together with the rise in AS charge, the minimum of the energy moves towards its higher concentrations.     

Enzyme reactions at the surface of living cells. II. Destabilization in the membranes and conduction of signals

The dynamics of a bound-enzyme reaction is studied when the diffusion of both the substrate and the product is coupled to their electric repulsion and to enzyme reaction. Contrary to what is occurring when substrate diffusion is uncoupled with electric repulsion and enzyme reaction, no hysteresis loop of the partition coefficient exists. The electric partition coefficient monotonically declines as substrate or product concentration is increased in the reservoir. The random perturbation of a steady state may generate a localized destabilization of substrate and product concentration. This destabilization must propagate in the membrane and may be viewed as the conduction of a signal. These conduction phenomena are entirely due to electric effects. In the absence of these effects, the system is homeostatic, that is it returns back to its initial steady state after a perturbation. Obviously under these conditions conduction of signals cannot occur. Increasing the ionic strength of the external milieu tends to stabilize the system and to suppress conduction effects in the membrane.     

Reversible binding of substance P to artificial lipid membranes studied by capacitance minimization techniques

Interaction of substance P with electrically neutral, planar lipid bilayers prepared from 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine and with anionic bilayers prepared from mixtures of 1,2-dioleoyl-sn-glycero-3-phosphocholine and brain phosphatidylserine was measured using the capacitance minimization method for monitoring the membrane surface potential caused by the positive charges and electric dipole moment of adsorbed peptide. Substance P bound to the electrically neutral bilayers from 9 mM KCl (buffered to pH 5.5 with 2.0 mM 2-(N-morpholino)ethanesulfonate) with a maximal binding density of about 1 x 10(-2) molecules per nm2 and a dissociation constant of about 2 x 10(-4) M. Measurement of the surface potential at different ionic strengths (shielding of surface charges) allowed distinction between the fixed-charge surface potential and a dipole potential. Ascribing this dipole potential to membrane-bound substance P would imply an effective dipole moment normal to the bilayer surface of about 20 Debye per molecule. Magnitude and polarity are consistent with an alpha-helical domain at the C-terminal end of substance P which is oriented normal to the surface of the membrane, and inserted so as to be inaccessible to the aqueous phase. Consistent measurements were obtained with anionic membranes at low substance P concentrations (10(-7)-10(-6) M; pH 7.2). They indicated electrostatic accumulation of the triply charged peptide on the surface of the membrane followed by hydrophobic interaction with the same parameters as for neutral membranes. The results agree with the membrane structure of substance P determined with infrared attenuated total reflection spectroscopy, circular dichroism measurements, and thermodynamic estimations.     

Conformational Dynamics of Protein Side Chains and Enzyme-Substrate Interaction

Abstract

The electric interaction of charged and polar protein side chains with dipole moments of the bonds of substrate molecules bound in enzyme active sites is considered. The conformational motion of the side chains leads to the fact that the electric interaction, besides a constant (electrostatic) part, contains a fluctuating one, which is a random force (noise) exerted on the substrate molecule. On the time scale of enzyme turnovers this noise can be considered as the white one with good approximation. The noise is external, and the explicit expression for its intensity has been obtained. The possible functional role of the noise as an activating factor in enzyme catalysis is discussed.     

Conservation of local electric fields in the evolution of Cu,Zn superoxide dismutase

The trend of the electric field and the value of the electric field flux, sensed by the superoxide substrate in the proximity of the active site, were found to be constant in three highly homologous Cu,Zn superoxide dismutases from ox, pig and sheep, which display large differences in net protein charge and distribution of electrically charged surface residues but very similar catalytic rate constants. The spatial relationship of charges on the protein surface apparently has been conserved during the evolution of this enzyme to create electrostatic facilitation of catalysis.     

Phospholipase A2 at the bilayer interface.

Interfacial catalysis is a necessary consequence for all enzymes that act on amphipathic substrates with a strong tendency to form aggregates in aqueous dispersions. In such cases the catalytic event occurs at the interface of the aggregated substrate, the overall turnover at the interface is processive, and it is influenced the molecular organization and dynamics of the interface. Such enzymes can access the substrate only at the interface because the concentration of solitary monomers of the substrate in the aqueous phase is very low. Moreover, the microinterface between the bound enzyme and the organized substrate not only facilitates formation of the enzyme-substrate complex, but a longer residence time of the enzyme at the substrate interface also promotes high catalytic processivity. Binding of the enzyme to the substrate interface as an additional step in the overall catalytic turnover permits adaptation of the Michaelis-Menten formalism as a basis to account for the kinetics of interfacial catalysis. As shown for the action of phospholipase A2 on bilayer vesicles, binding equilibrium has two extreme kinetic consequences. During catalysis in the scooting mode the enzyme does not leave the surface of the vesicle to which it is bound. On the other hand, in the hopping mode the absorption and desorption steps are a part of the catalytic turnover. In this minireview we elaborate on the factors that control binding of pig pancreatic phospholipase A2 to the bilayer interface. Binding of PLA2 to the interface occurs through ionic interactions and is further promoted by hydrophobic interactions which probably occur along a face of the enzyme, with a hydrophobic collar and a ring of cationic residues, through which the catalytic site is accessible to substrate molecules in the bilayer. An enzyme molecule binds to the surface occupied by about 35 lipid molecules with an apparent dissociation constant of less than 0.1 pM for the enzyme on anionic vesicles compared to 10 mM on zwitterionic vesicles. Results at hand also show that aggregation or acylation of the protein is not required for the high affinity binding or catalytic interaction at the interface.     

Influence of charge and molecular size on membrane stabilization

We have reported that the antihaemolytic effect of low concentrations of chlorpromazine is decreased after enzymic removal of sialopeptides from red cell membranes, suggesting that an interaction between negatively charged sialic acids and positively charged chlorpromazine is involved in its membrane stabilizing effect. We have now investigated the antihaemolytic action of simpler molecules with different charges Removal of membrane sialopeptides did not affect the membrane stabilizing actions of simple aliphatic mono- or diamines nor of similar aliphatic molecules carrying strong positive or negative charges, where those positively charged were more potent than those with negative charges. It appears, therefore, that membrane stabilizing activity is determined primarily by lipophilicity and secondarily by polarity and that it does not depend on interactions with enzymically accessible sialopeptides on the outer surface of biological membranes.     

Elastic, electrostatic and electrokinetic forces influencing membrane curvature

Many cellular and intracellular processes critically depend on membrane shape, but the shape generating mechanisms are still to be fully understood. In this study we evaluate how electrostatic/electrokinetic forces contribute to membrane curvature. Membrane bilayer had finite thickness and was either elastically anisotropic or anisotropic overall, but isotropic per sections (heads and tails). The physics of the situation was evaluated using a coupled system of elastic and electrostatic/electrokinetic (Poisson-Nernst-Planck) equations. The fixed charges present only on the upper membrane surface lead to the accumulation of counter-ions and depletion of co-ions that decay spatially very rapidly (Debye length<1nm), as does the potential and electric field. Spatially uneven electric field and the permittivity mismatch also induce charges at the membrane-solution interface, which are not fixed but influence the electrostatics nevertheless. Membrane bends due to - Coulomb force (caused by fixed membrane charges in the electric field) and the dielectric force (due to the non-uniform electric field and the permittivity mismatch between the membrane and the solution). Both act as membrane surface forces, and both depend supra-linearly on the fixed charge density. Regardless of sign of the fixed charges, the membrane bends toward the charged (upper) surface owing to the action of the Coulomb force, but this is opposed by the smaller dielectric force. The spontaneous membrane curvature becomes very pronounced at high fixed charge densities, leading to very small spontaneous radii (<50nm). In conclusion the electrostatic/electrokinetic forces contribute significantly to the membrane curvature.     

Substrate ground state binding energy concentration is realized as transition state stabilization in physiological enzyme catalysis

Previously published kinetic data on the interactions of seventeen different enzymes with their physiological substrates are re-examined in order to understand the connection between ground state binding energy and transition state stabilization of the enzyme-catalyzed reactions. When the substrate ground state binding energies are normalized by the substrate molar volumes, binding of the substrate to the enzyme active site may be thought of as an energy concentration interaction; that is, binding of the substrate ground state brings in a certain concentration of energy. When kinetic data of the enzyme/substrate interactions are analyzed from this point of view, the following relationships are discovered: 1) smaller substrates possess more binding energy concentrations than do larger substrates with the effect dropping off exponentially, 2) larger enzymes (relative to substrate size) bind both the ground and transition states more tightly than smaller enzymes, and 3) high substrate ground state binding energy concentration is associated with greater reaction transition state stabilization. It is proposed that these observations are inconsistent with the conventional (Haldane) view of enzyme catalysis and are better reconciled with the shifting specificity model for enzyme catalysis.     

Immobilized enzymes: Electrokinetic effects on reaction rates under external diffusion

The rates of reactions catalyzed by enzymes immobilized on a nonporous solid surface have been computed employing a Nernst film model. The Nernst-Planck equations for the transport of the charged substrate and product species in the film and the Poisson equation for the distribution of electrical potential are solved numerically with the appropriate boundary conditions. The electrical charge at the surface is assumed to arise from the dissociation equilibria of the acidic and basic surface groups of the enzyme. The pH at the surface affects both the surface charge as well as the intrinsic kinetics of the enzyme-catalyzed reaction. Factors which determine the pH at the surface include the pH in the bulk solution and the release of H(+) ions in the enzyme-catalyzed reaction. The latter causes a lowering of pH at the surface, causing the reaction rate to differ from that computed assuming an equilibrium distribution of electrical potential. Another kind of nonequilibrium contribution is caused by unequal charges or diffusivities of the substrate and products, which results in a diffusion potential being set up. Two moduli are introduced to evaluate the significance of the reaction-generated lowering of pH and the diffusion potential effect. The effect of changing various parameters, e.g., reaction rate constant, substrate concentration, enzyme concentration, pH, etc., on the overall reaction rate are studied.