A microscopic model of enzyme kinetics

Extensions to Michaelis-Menten Kinetics for Single Parameters

Biochemical transformation kinetics is based on the formation of enzyme-substrate complexes. We developed a robust scheme based on unit productions of enzymes and reactants in cyclic events to comply with mass action law to form enzyme-substrate complexes. The developed formalism supports a successful application of Michaelis-Menten kinetics in all biochemical transformations of single parameters. It is an essential tool to overcome some challenging healthcare and environmental issues. In developing the formalism, we defined the substrate [S]= [Product]3/4 and rate of reaction based on rate and time perspectives. It allowed us to develop two quadratic equations. The first, represents a body entity that gave a useful relationship of enzyme E = 2S0.33, and the second nutrients/feed, each giving [Enzymes] and [Enzyme-substrate complexes], simulating rate of reaction, [substrate], and their differentials. By combining [Enzymes] and [Enzyme-substrate complexes] values, this quadratic equation derives a Michaelis-Menten hyperbolic function. Interestingly, we can derive the proportionate rate of reaction and [Enzymes] values of the quadratics resulting in another Michaelis-Menten hyperbolic. What is clear from these results is that between these two hyperbolic functions, in-competitive inhibitions exist, indicating metabolic activities and growth in terms of energy levels. We validated these biochemical transformations with examples applicable to day to day life.

A cellular automaton model of crystalline cellulose hydrolysis by cellulases

BACKGROUND

Cellulose from plant biomass is an abundant, renewable material which could be a major feedstock for low emissions transport fuels such as cellulosic ethanol. Cellulase enzymes that break down cellulose into fermentable sugars are composed of different types - cellobiohydrolases I and II, endoglucanase and β-glucosidase - with separate functions. They form a complex interacting network between themselves, soluble hydrolysis product molecules, solution and solid phase substrates and inhibitors. There have been many models proposed for enzymatic saccharification however none have yet employed a cellular automaton approach, which allows important phenomena, such as enzyme crowding on the surface of solid substrates, denaturation and substrate inhibition, to be considered in the model.

RESULTS

The Cellulase 4D model was developed de novo taking into account the size and composition of the substrate and surface-acting enzymes were ascribed behaviors based on their movements, catalytic activities and rates, affinity for, and potential for crowding of, the cellulose surface, substrates and inhibitors, and denaturation rates. A basic case modeled on literature-derived parameters obtained from Trichoderma reesei cellulases resulted in cellulose hydrolysis curves that closely matched curves obtained from published experimental data. Scenarios were tested in the model, which included variation of enzyme loadings, adsorption strengths of surface acting enzymes and reaction periods, and the effect on saccharide production over time was assessed. The model simulations indicated an optimal enzyme loading of between 0.5 and 2 of the base case concentrations where a balance was obtained between enzyme crowding on the cellulose crystal, and that the affinities of enzymes for the cellulose surface had a large effect on cellulose hydrolysis. In addition, improvements to the cellobiohydrolase I activity period substantially improved overall glucose production.

CONCLUSIONS

Cellulase 4D simulates the enzymatic hydrolysis of cellulose to glucose by surface and solution phase-acting enzymes and accounts for complex phenomena that have previously not been included in cellulose hydrolysis models. The model is intended as a tool for industry, researchers and educators alike to explore options for enzyme engineering and process development and to test hypotheses regarding cellulase mechanisms.

A model for the stoichiometric regulation of blood coagulation

We have developed a model of the extrinsic blood coagulation system that includes the stoichiometric anticoagulants. The model accounts for the formation, expression, and propagation of the vitamin K-dependent procoagulant complexes and extends our previous model by including: (a) the tissue factor pathway inhibitor (TFPI)-mediated inactivation of tissue factor (TF).VIIa and its product complexes; (b) the antithrombin-III (AT-III)-mediated inactivation of IIa, mIIa, factor VIIa, factor IXa, and factor Xa; (c) the initial activation of factor V and factor VIII by thrombin generated by factor Xa-membrane; (d) factor VIIIa dissociation/activity loss; (e) the binding competition and kinetic activation steps that exist between TF and factors VII and VIIa; and (f) the activation of factor VII by IIa, factor Xa, and factor IXa. These additions to our earlier model generate a model consisting of 34 differential equations with 42 rate constants that together describe the 27 independent equilibrium expressions, which describe the fates of 34 species. Simulations are initiated by "exposing" picomolar concentrations of TF to an electronic milieu consisting of factors II, IX, X, VII, VIIa, V, and VIIII, and the anticoagulants TFPI and AT-III at concentrations found in normal plasma or associated with coagulation pathology. The reaction followed in terms of thrombin generation, proceeds through phases that can be operationally defined as initiation, propagation, and termination. The generation of thrombin displays a nonlinear dependence upon TF, AT-III, and TFPI and the combination of these latter inhibitors displays kinetic thresholds. At subthreshold TF, thrombin production/expression is suppressed by the combination of TFPI and AT-III; for concentrations above the TF threshold, the bolus of thrombin produced is quantitatively equivalent. A comparison of the model with empirical laboratory data illustrates that most experimentally observable parameters are captured, and the pathology that results in enhanced or deficient thrombin generation is accurately described.

Biocatalytic membrane reactors: applications and perspectives

Membranes and biotechnological tools can be used for improving traditional production systems to maintain the sustainable growth of society. Typical examples include: new and improved foodstuffs, in which the desired nutrients are not lost during thermal treatment; novel pharmaceutical products with well-defined enantiomeric compositions; and the treatment of waste-water, wherein pollution by traditional processes is a problem.

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.