Use and abuse of the quasi-steady-state approximation

The transient kinetic behaviour of an open single enzyme, single substrate reaction is examined. The reaction follows the Van Slyke-Cullen mechanism, a spacial case of the Michaelis-Menten reaction. The analysis is performed both with and without applying the quasi-steady-state approximation. The analysis of the full system shows conditions for biochemical pathway coupling, which yield sustained oscillatory behaviour in the enzyme reaction. The reduced model does not demonstrate this behaviour. The results have important implications in the analysis of open biochemical reactions and the modelling of metabolic systems.     

The total quasi-steady-state approximation is valid for reversible enzyme kinetics

The Briggs-Haldane approximation of the irreversible Michaelis-Menten scheme of enzyme kinetics is cited in virtually every biochemistry textbook and is widely considered the classic example of a quasi-steady-state approximation. Though of similar importance, the reversible Michaelis-Menten scheme is not as well characterized. This is a serious limitation since even enzymatic reactions that go to completion may be reversible. The current work derives a total quasi-steady-state approximation (tQSSA) for the reversible Michaelis-Menten and delineates its validity domain. The tQSSA allows the derivation of uniformly valid approximations for the limit of low enzyme concentrations, ET相似文献   

A quasi-steady-state approximation method for diffusion problems: I. Concentration dependent diffusion coefficients

A generalization of Landahl's approximation method (H. D. Landahl,Bull. Math. Biophysics,15, 49–61, 1953) for non-linear diffusion problems is suggested. The method is applied to sorption, desorption, and free diffusion problems involving concentration-dependent diffusion coefficients. With some limitations, the results compare favorably with those obtained by numerical methods.     

An extended first approximation model for the amygdaloid kindling phenomenon

A first approximation model, which accounts for the strongest phenomena defining kindling is suggested. It is based on an excitatory-inhibitory coupling of neural aggregates, to which a self-stimulation element for the excitatory aggregate was added. The functional linking hypothesis views the representation of kindling as a process of gradual transition through structural changes from a stable system to a system showing stability for small perturbations and an oscillatory orbit for larger perturbations, to a purely oscillatory system. The anatomical linking hypothesis views the excitatory aggregate as representing the hypothalamus, the inhibitory aggregate as representing the hippocampal-septal-preoptic complex, and the selfstimulating element of the excitatory aggregate as representing the amygdaloid-pyriform complex. The model was realized on a digital computer with graphic capabilities and showed good qualitative agreement with the experimental data related to kindling. In addition, the use of the model for generating new experiments is discussed.     

The enzymatic and chemical reduction of extended biliverdins

The substrate specificity of rat liver biliverdin reductase was probed using helical and extended biliverdins. The former were the ZZZ-all-syn biliverdins IX alpha and IX gamma, and the latter were the 5Z-syn, 10Z-syn, 15Z-anti; 5Z-anti, 10E-anti, 15E-anti biliverdins. It was found that the reduction rates of the biliverdins increased with the progressive stretching of their conformations. The most extended biliverdin was reduced at a higher rate than biliverdin IX alpha. The chemical reduction rates to bilirubins followed a similar pattern. Nucleophilic addition of 2-mercaptoethanol to the C10 methine was also favored in the extended biliverdins.     

Model of reduction of actin polymerization forces by ATP hydrolysis

The effects of hydrolysis of ATP-actin to ADP-actin on actin polymerization-based force generation are calculated using a multifilament two-state Brownian ratchet model. The model treats an ensemble of rigid parallel filaments growing against a hard, inert, diffusing obstacle held in an optical trap. The filaments stochastically grow, depolymerize and undergo transitions between polymerizing and depolymerizing tip states. The parameters in the model are obtained from literature values and a fit to the measured dependence of the polymerization rate on the free-actin concentration. For more than two filaments, the stall force per filament near the critical concentration is much less than the equilibrium ATP-actin stall force. By reducing the availability of free monomers, the obstacle causes filament tips to convert to the depolymerizing state, so that only a small fraction of the filaments contact the obstacle at a given time.     

Experimental evaluation of a quasi-steady-state controller for yeast fermentation

The quasi-steady-state (QSS )controller whose implementation on a computer-coupled laboratory fermentor was presented earlier is briefly reviewed. The slow rate of approach to QSS of the uncontrolled process is verified experimentally. The ability of the control system to rapidly force the system to QSS is demonstrated by a run in which three different QSS points are achieved in a single 12 hr fermentation. The nonlinear nature of the process and the ability of the control system to handle this is demonstrated by comparing the response times to command inputs of different sizes. Noninteraction between cell and substrate response modes is demonstrated. The ability of the system to manipulate substrate concentration in the vessel without a direct measure of it is shown.     

Midface fractures: advantages of immediate extended open reduction and bone grafting

Experience with 240 midface (Le Fort and zygoma) fractures in multiple trauma patients has emphasized that superior aesthetic results are obtained by immediate extended open reduction with primary bone grafting. Internal fixation of 110 zygomatic and 130 Le Fort fractures was performed in the lower midface (zygomaticomaxillary and nasomaxillary buttresses). Open reduction of the condyle was employed in five concomitant Le Fort and subcondylar fractures with a loss of ramus height to prevent superior and posterior displacement of the middle and lower face. Bone grafts were utilized in 74 patients. They were most frequently employed in the orbit and less frequently in the lower midface. Bone graft survival paralleled that observed under elective conditions, and a slightly higher infection rate was observed. Extended open reduction and immediate bone grafting adds a new dimension to the aesthetic results obtained from facial fracture treatment. Structural bony integrity and pre-injury facial architecture may be restored in the absence of soft-tissue contracture. Restoration of the pre-injury facial architecture (the essence of facial fracture treatment) is more accurately accomplished when these techniques are utilized.     

Model reduction using a posteriori analysis

Mathematical models in biology and physiology are often represented by large systems of non-linear ordinary differential equations. In many cases, an observed behaviour may be written as a linear functional of the solution of this system of equations. A technique is presented in this study for automatically identifying key terms in the system of equations that are responsible for a given linear functional of the solution. This technique is underpinned by ideas drawn from a posteriori error analysis. This concept has been used in finite element analysis to identify regions of the computational domain and components of the solution where a fine computational mesh should be used to ensure accuracy of the numerical solution. We use this concept to identify regions of the computational domain and components of the solution where accurate representation of the mathematical model is required for accuracy of the functional of interest. The technique presented is demonstrated by application to a model problem, and then to automatically deduce known results from a cell-level cardiac electrophysiology model.     

Validity of quasi-steady-state and transfer-function representations for input-output relation in a Michaelis-Menten reaction

In relation to the input-output characteristics of enzymatic reactions in the cellular metabolism and biochemical reactors, the validity of the quasi-steady-state and transfer-function representations of reaction velocity has been examined for a basic Michaelis-Menten reaction employing computer simulation, that is, numerical integration of the rate equation. The well-known S-v relationship (relationship between substrate concentration and reaction velocity)derived on the quasi-steady-state assumption is found to be in general a good approximation to the actual velocity throughout the temporal progress of the reaction. The validity of the approximation depends on a ratio of the Michaelis constant to the total enzyme concentration in the reaction system rather than on the individual rate constants. A transfer-function representation is derived on assuming an exponential change in the reaction velocity for the indicial response to the substrate influx rate. The representation has a wider valid region with a decrease in influx rate than with an increase in the influx rate. The validity is most dependent on a ratio of total enzyme concentration to the steady-state concentration of the substrate. The analysis of the linear sensitivity of the reaction velocity to rate constants reveals that the characteristics of these valid representations in systems analysis change according to the phase of the reaction.     

Effect of error of the quasi-steady-state approximation on the estimation of Km and Vm from a single time curve

For an irreversible, one-substrate enzyme mechanism, post-transient time curves of the substrate and the product are approximately described by different equations of the steady-state type. The magnitude of error of these approximations is shown to be small either at low enzyme/substrate or at low enzyme/ Michaelis-constant ratios. The effect of error on the kinetic parameters estimated from a single time curve is evaluated. It is shown that a set of well-separated substrate con centrations (which are still high relative to the concentration of enzyme) is crucial for obtaining accurate estimates of the parameters.     

Plasmid copy number control: a case study of the quasi-steady-state assumption.

Perelson & Brendel (1989, J. molec. Biol. 208, 245-255) have proposed kinetic models for the control of plasmid copy number, based on experiments by J. Tomizawa and his associates. The quasi-steady-state assumptions (QSSA) made in the analysis of these models are justified in the present paper, thereby providing an example of how QSSA can provide a powerful and reliable tool in the analysis of biological kinetics.     

Chromate reduction by Rhodobacter sphaeroides

Rhodobacter sphaeroides grew in the presence of up to 43 μM chromate and reduced hexavalent chromium to the trivalent form under both aerobic and anaerobic conditions. Reduced chromium remained in the external medium. Reductase activity was present in cells of R. sphaeroides independent of whether chromate was present or not in the growth medium. The reducing activity was found in the cytoplasmic cell fraction and was dependent on NADH. The chromate-reducing enzyme was purified by anion exchange, hydroxyapatite and hydrophobic interaction chromatography, and gel filtration. The molecular weight of the enzyme was 42 kDa as determined by gel filtration. The optimum of the reaction is at pH 7.0 and 30°C. The enzyme activity showed a hyperbolic dependence on the concentrations of both substrates, NADH and chromate, with a maximum velocity at 0.15 mM NADH. A K _m of 15±1.3 μM CrO₄ ²⁻ and a V _max of 420±50 μmol min⁻¹ mg protein⁻¹ was determined for the enzyme isolated from anaerobically grown cells and 29±6.4 μM CrO₄ ²⁻ and 100±9.6 μmol CrO₄ ²⁻ min⁻¹ mg protein⁻¹ for the one from aerobically grown ones. Journal of Industrial Microbiology & Biotechnology (2000) 25, 198–203. Received 05 January 2000/ Accepted in revised form 27 May 2000     

Acetylene reduction by rumen microflora

Summary Acetylene reduction to ethylene by filtrates of rumen contents has been studied. The Km values for acetylene are comparable to those reported for nitrogenase enzymes from N₂ fixing bacteria. The enhancement of ethylene production from acetylene by phosphate and pyruvate suggests that the reduction was carried out by anaerobic microorganisms. Acetylene reduction occurred in the rumen only when a high nitrogen diet was fed to the sheep. Some microorganisms isolated from the rumen contents were grown anaerobically under N₂ gas on agar not supplemented with combined nitrogen. Methane production by filtrates of rumen contents was found to be inhibited by acetylene.