Steady state enzyme velocities that are independent of [enzyme]: an important behavior in many membrane and particle-bound states

Diffusion and reaction in the cell glycocalyx and the extracellular matrix

Many biologically important macromolecular reactions are assembled and catalyzed at the cell lipid-surface and thus, the extracellular matrix and the glycocalyx layer mediate transfer and exchange of reactants and products between the flowing blood and the catalytic lipid-surface. This paper presents a mathematical model of reaction-diffusion equations that simply describes the transfer process and explores its influence on surface reactivity for a prototypical pathway, the tissue factor (Tf) pathway of blood coagulation. The progressively increasing friction offered by the matrix and glycocalyx to reactants and to the product (coagulation factors X, VIIa and Xa) approaching the reactive surface is simulated and tested by solving the equations numerically with both, monotonically decreasing and constant diffusion profiles. Numerical results show that compared to isotropic transfer media, the anisotropic structure of the matrix and glycocalyx sharply decreases overall reaction rates and significantly increases the mean transit time of reactants; this implies that the anisotropy modifies the distribution of reactants. Results also show that the diffusional transfer, whether isotropic or anisotropic, influences reaction rates according to the order at which the reactants arrive at the boundary. Faster rates are observed when at least one of the reactants is homogeneously distributed before the other arrives at the boundary than when both reactants transfer simultaneously from the boundary.

Hybrid simulations of stochastic reaction-diffusion processes for modeling intracellular signaling pathways

In the intracellular environment, signaling takes place in a nonideal environment that is spatially heterogeneous and that is noisy, with the noise arising from the low copy numbers of the signaling molecules involved. In this paper, we model intracellular signaling pathways as stochastic reaction-diffusion processes and adapt techniques commonly used by physicists to solve for the spatiotemporal evolution of the signaling pathways. We then apply it to study two problems of relevance to the modeling of intracellular signaling pathways. First, we show that, in the limit of small protein diffusion which is typically the case for proteins in the cytosol crowded by other macromolecules, the extent of diffusion control, in the transient regime, on reactions is greater than previous predictions. Second, we show that the presence of scaffold proteins can modify the phosphorylation activity of a mitogen-activated protein kinase cascade, and explain how this activity is modulated by the scaffold protein concentration.

On the validity of the quasi-steady state approximation of bimolecular reactions in solution

Two-step binding kinetics are extensively used to study the relative importance of diffusion in biochemical reactions. Classical analysis of this problem assumes ad hoc that the encounter complex is at quasi-steady state (QSS). Using scaling arguments we derive a criterion for the validity of this assumption in the limit of irreversible product formation. We find that the QSS approximation (QSSA) of two-step binding is only valid if the total ligand and receptor concentrations are much smaller than (k2+k-1)/k1, where k1 and k-1 are, respectively, the forward and reverse diffusion encounter rate constants and k2 is the chemical association rate constant. This criterion can be shown to imply that the average time between encounters is much longer than the half-life of the encounter complex and also guarantees that the concentration of the encounter complex is negligible compared to the reactant and product concentrations. Numerical examples of irreversible and reversible cases corroborate our analysis and illustrate that the QSS may be invalid even if k-2<<k2. Our analysis of the irreversible case is shown to carry through to the more rigorous framework of the Smoluchowski theory of diffusion-controlled reactions. This work underscores the need for exercising greater caution in invoking the QSSA.

Influence of molecular structure on substrate binding to the human organic cation transporter, hOCT1

Organic cation transporters play a critical role in the elimination of therapeutic compounds in the liver and the kidney. We used computational quantitative structure activity approaches to predict molecular features that influence interaction with the human ortholog of the organic cation transporter (hOCT1). [(3)H]tetraethylammonium uptake in HeLa cells stably expressing hOCT1 was inhibited to varying extents by a diverse set of 30 molecules. A subset of 22 of these was used to produce, using Catalyst, a pharmacophore that consisted of three hydrophobic features and a positive ionizable feature. The correlation coefficient of observed versus predicted IC(50) was 0.86 for this training set, which was superior to calculated logP alone (r = 0.73) as a predictor of hOCT1 inhibition. A descriptor-based quantitative structure-activity relationship study using Cerius(2) resulted in an equation relating five molecular descriptors to log IC(50) with a correlation coefficient of 0.95. Furthermore, a group of phenylpyridinium and quinolinium compounds were used to investigate the spatial limitations of the hOCT1 binding site. The affinity for hOCT was higher for 4-phenylpyridiniums > 3-phenylpyridiniums > quinolinium, indicating that substrate affinity was influenced by the distribution of hydrophobic mass. In addition, supraplanar hydrophobic mass was found to increase the affinity for binding hOCT1. These results indicate how a combination of computational and in vitro approaches may yield insight into the binding affinity of transporters and may be applicable to predicting these properties for new therapeutics.

Elevated function of blood clotting factor VIIa mutants that have enhanced affinity for membranes. Behavior in a diffusion-limited reaction

Blood clotting factor VIIa is involved in the first step of the blood coagulation cascade, as a membrane-associated enzyme in complex with tissue factor (TF). Factor VIIa is also an important therapeutic agent for hemophilia where its function may include TF-independent as well as TF-dependent mechanisms. This study compared the activity of wild type factor VIIa (WT-VIIa) with that of a mutant with elevated affinity for membrane (P10Q/Q32E, QE-VIIa). Phospholipid and cell-based assays showed the mutant to have up to 40-fold higher function than WT-VIIa in both TF-dependent and TF-independent reactions. Tissue factor-dependent reactions displayed the maximum enhancement when binding had reached equilibrium in competition with another TF-binding protein. In liposome-based assays, the association rate of WT-VIIa with TF occurred at a physical maximum and could not be improved by site-directed mutagenesis. A practical consequence was identical function of WT-VIIa and QE-VIIa in assays that depended entirely on assembly kinetics. Thus, factor VIIa mutants provided unique reagents for probing the mechanism of factor VIIa action. They may also offer superior agents for therapy.

Exosite binding tethers the macromolecular substrate to the prothrombinase complex and directs cleavage at two spatially distinct sites

The prothrombinase complex, composed of the proteinase, factor Xa, bound to factor Va on membranes, catalyzes thrombin formation by the specific and ordered proteolysis of prothrombin at Arg(323)-Ile(324), followed by cleavage at Arg(274)-Thr(275). We have used a fluorescent derivative of meizothrombin des fragment 1 (mIIaDeltaF1) as a substrate analog to assess the mechanism of substrate recognition in the second half-reaction of bovine prothrombin activation. Cleavage of mIIaDeltaF1 exhibits pseudo-first order kinetics regardless of the substrate concentration relative to K(m). This phenomenon arises from competitive product inhibition by thrombin, which binds to prothrombinase with exactly the same affinity as mIIaDeltaF1. As thrombin is known to bind to an exosite on prothrombinase, initial interactions at an exosite likely play a role in the enzyme-substrate interaction. Occupation of the active site of prothrombinase by a reversible inhibitor does not exclude the binding of mIIaDeltaF1 to the enzyme. Specific recognition of mIIaDeltaF1 is achieved through an initial bimolecular reaction with an enzymic exosite, followed by an active site docking step in an intramolecular reaction prior to bond cleavage. By alternate substrate studies, we have resolved the contributions of the individual binding steps to substrate affinity and catalysis. This pathway for substrate binding is identical to that previously determined with a substrate analog for the first half-reaction of prothrombin activation. We show that differences in the observed kinetic constants for the two cleavage reactions arise entirely from differences in the inferred equilibrium constant for the intramolecular binding step that permits elements surrounding the scissile bond to dock at the active site of prothrombinase. Therefore, substrate specificity is achieved by binding interactions with an enzymic exosite that tethers the protein substrate to prothrombinase and directs cleavage at two spatially distinct scissile bonds.

Lag-burst kinetics in phospholipase A(2) hydrolysis of DPPC bilayers visualized by atomic force microscopy

The lag-burst phenomenon in the phospholipase A(2) mediated hydrolysis of phospholipid bilayers is for the first time demonstrated in an atomic force microscopy (AFM) study. Simultaneous AFM measurements of the degree of bilayer degradation and the physical-chemical state of the membrane reveals growing nanoscale indentations in the membrane during the lag phase. It is argued that these indentations are domains of hydrolysis products (lysoPC/PC) which eventually trigger the burst. The rate of the rapid hydrolysis following the burst is found to be proportional to the length of the edge between membrane adsorbed and desorbed to the mica base. The observed maximal rate of membrane degradation is approx. 0.2 mmol lipid/min/mol lipase in solution.

Significance of reduced dimensionality in reaction kinetics: impact of multi-site particles

This review examines novel kinetic properties of enzymes on membrane surfaces or states of restricted diffusion. A leading feature is the presence of multiple enzymes and/or substrates per particle. In these states, enzymes can be influenced by parameters such as the number of substrates or enzymes per particle, particle size, the rates of exchange of substrate or enzyme from the particle, or substrate diffusion to the particle. These steps are independent of the enzyme site parameters which are described by classical enzymology. The results make it clear that non-classical behaviors are important to biological systems, are the basis for some enzyme expression levels and are determinants of cellular design. To identify more unique functions of these states, descriptions of catalysis in the non-solution state should become a part of kinetic education in biology.

Steady-state enzyme kinetics in the Escherichia coli periplasm: a model of a whole cell biocatalyst

This study provided analysis of in vivo enzyme kinetics in a model system which consisted of alkaline phosphatase in the periplasm of Escherichia coli. Modeling of complete substrate titration curves was achieved for a wide range of intraperiplasmic enzyme levels and outer membrane permeabilities. The results helped to identify the features most important to optimize in vivo reaction velocity. For many situations, a surprising finding was that maximum enzyme expression was not a major concern. For example, for moderate enzyme expression levels and moderate substrate levels (ca 0-5 mM), the limiting step for the enzyme in the periplasm was substrate (para-nitrophenylphosphate) diffusion through the outer membrane. In vivo reaction velocity was directly proportional to substrate concentration, outer membrane permeability, and the cell concentration. Velocity was also quite insensitive to a potent inhibitor of the enzyme. Even though diffusion-limited, periplasmic reaction velocity was quite sensitive to temperature, suggesting that the conformation of porin proteins in the E. coli outer membrane governed the average size of the pore. This model system therefore defined important features of bacterial whole cell biocatalyst design, which may also apply to other reactors using intact cells as catalysts.

Regulation of tissue plasminogen activator activity by cells. Domains responsible for binding and mechanism of stimulation

A number of cell types have previously been shown to bind tissue plasminogen activator (tPA), which in some cases can remain active on the cell surface resulting in enhanced plasminogen activation kinetics. We have investigated several cultured cell lines, U937, THP1, K562, Molt4, and Nalm6 and shown that they bind both tPA and plasminogen and are able to act as promoters of plasminogen activation in kinetic assays. To understand what structural features of tPA are involved in cell surface interactions, we performed kinetic assays with a range of tPA domain deletion mutants consisting of full-length glycosylated and nonglycosylated tPA (F-G-K1-K2-P), DeltaFtPA (G-K1-K2-P), K2-P tPA (BM 06.022 or Reteplase), and protease domain (P). Deletion variants were made in Escherichia coli and were nonglycosylated. Plasminogen activation rates were compared with and without cells, over a range of cell densities at physiological tPA concentrations, and produced maximum levels of stimulation up to 80-fold with full-length, glycosylated tPA. Stimulation for nonglycosylated full-length tPA dropped to 45-60% of this value. Loss of N-terminal domains as in DeltaFtPA and K2P resulted in a further loss of stimulation to 15-30% of the full-length glycosylated value. The protease domain alone was stimulated at very low levels of up to 2-fold. Thus, a number of different sites are involved in cell interactions especially within finger and kringle domains, which is similar to the regulation of tPA activity by fibrin. A model was developed to explain the mechanism of stimulation and compared with actual data collected with varying cell, plasminogen, or tPA concentrations and different tPA variants. Experimental data and model predictions were generally in good agreement and suggest that stimulation is well explained by the concentration of reactants by cells.

Two soluble glycosyltransferases glycosylate less efficiently in vivo than their membrane bound counterparts

Many Golgi glycosyltransferases are type II membrane proteins which are cleaved to produce soluble forms that are released from cells. Cho and Cummings recently reported that a soluble form of alpha1, 3-galactosyltransferase was comparable to its membrane bound counterpart in its ability to galactosylate newly synthesized glycoproteins (Cho,S.K. and Cummings,R.D. (1997) J. Biol. Chem., 272, 13622-13628). To test the generality of their findings, we compared the activities of the full length and soluble forms of two such glycosyltransferases, ss1,4 N-Acetylgalactosaminyltransferase (GM2/GD2/ GA2 synthase; GalNAcT) and beta galactoside alpha2,6 sialyltransferase (alpha2,6-ST; ST6Gal I), for production of their glycoconjugate products in vivo . Unlike the full length form of GalNAcT which produced ganglioside GM2 in transfected cells, soluble GalNAcT did not produce detectable GM2 in vivo even though it possessed in vitro GalNAcT activity comparable to that of full length GalNAcT. When compared with cells expressing full length alpha2,6-ST, cells expressing a soluble form of alpha2,6-ST contained 3-fold higher alpha2,6-ST mRNA levels and secreted 7-fold greater alpha2,6-ST activity as measured in vitro , but in striking contrast contained 2- to 4-fold less of the alpha2,6-linked sialic acid moiety in cellular glycoproteins in vivo . In summary these results suggest that unlike alpha1,3-galactosyltransferase the soluble forms of these two glycosyltransferases are less efficient at glycosylation of membrane proteins and lipids in vivo than their membrane bound counterparts.