Naoto Sakamoto

Effect of enzyme concentration on the dynamic behavior of a membrane-bound enzyme system

Abstract The dynamic behavior of the reaction-diffusion system, composed of glucose oxidase (EC 1.1.3.4) immobilized at a uniform concentration in a membrane, used as a glucose electrode is represented by a diffusion equation with a nonlinear reaction-term in one-dimensional space. The mathematical model is analyzed by computer simulation, that is, numerical integration of the equation under various initial and boundary conditions, to examine the effect of enzyme concentration on the response characteristics (responsiveness and linearity in response) of the electrode. The analysis of the responses of the system to stepwise changes in the boundary value (glucose concentration in simple solution) infers that the enzyme concentration governs the patterns of the spatial distributions of the substrates (glucose and dissolved oxygen) in steady states and transient responses. It is also revealed that the response characteristics of the electrode are optimized with concentration of immobilized enzyme and that the system establishes the steady states at the same spatial distributions of the substrates, regardless of the boundary value. The diffusion of the substrates and the oxygen concentration also have significant effects on the response characteristics of the electrode.

Kinetics of membrane-bound enzymes: Validity of quasi-steady-state approximation for a Michaelis-Menten-type reaction

Abstract The dynamic behavior of a reaction-diffusion system with a Michaelis-Menten-type enzyme immobilized at a uniform concentration in a membrane is analyzed to examine the validity of the quasi-steady-state approximation at nonsteady state in a heterogeneous and open system. The conditions for validity are evaluated for the well-known S - v relationship (Michaelis equation) in the membrane-bound enzyme system by comparison with the actual reaction velocity determined from computer simulation. The analysis of the responses of the system to stepwise changes in substrate influx rate infers that the validity is governed rather by the ratios of the Michaelis constant to the total enzyme concentration ( K m / E T and to the maximum velocity ( K m / V max ) than by the individual rate constants. Throughouts the course of the responses, the Michaelis equation is reliable, with an error below 1% when the ratio K m / E T is higher than 100. This same accuracy cannot be attained when the ratio K m / E T is less than 1. In the case the ratio K m / E T is approx. 10 the error exceeds 1% only for the very early phase of the responses. The ratio of K m / E max is related to the characteristics of the dynamic behavior of the system, affecting the time for the maximum error to occur in the Michaelis equation during the response.

A two-dimensional compartment model for the reaction-diffusion system of acetylcholine in the synaptic cleft at the neuromuscular junction

A minimal compartment model of the reaction-diffusion system (RD system) of a neurotransmitter in a two-dimensional space of axis-symmetrical disc is proposed to represent the chemical transmission process of a quantum of acetylcholine (ACh) in the synaptic cleft at the neuromuscular junction. The behavior of the RD system for ACh is expressed by a two-dimensional diffusion equation with nonlinear reaction terms due to the rate processes for ACh receptor and acetylcholinesterase. The simulation analysis of the RD system reveals that the radial diffusion process of ACh has more distinctive effects on spontaneous generation of the miniature endplate current (MEPC) than the transverse process. The anisotropic diffusion is effective in the RD system since the diffusion coefficient of ACh in the radial direction is evaluated to be about 1.0 x 10(-6) cm2 sec-1 for appropriate characterization of the MEPC, on which the diffusion coefficient in the transverse direction larger than 2.0 x 10(-6) cm2 sec-1 has virtually no effects. The compartment model is thus appropriately constructed to comprise three elements on the transverse coordinate and ten elements on the radial coordinate in the disc with 500 nm of radius and 50 nm of height.

Strong control on the transit time in metabolic channelling

A suite of different characteristic times is used to describe the temporal behavior of a metabolic pathway. Here we focus on the ‘transit’ time that is the average time it takes for a molecule entering the steady‐state pathway as a substrate to exit the pathway as a product. We show that metabolic channelling results in dramatic changes in control exerted by pathway enzymes on the transit time. In an ‘ideal’ pathway a doubling of the enzyme concentrations halves the transit time. In a dynamic channel such an increase can reduce the transit time by a factor of four or more.

Simulation analysis of the effects of the simultaneous release of quanta of acetylcholine on the endplate current at the neuromuscular junction

Arrival of an action potential to a nerve terminal at the neuromuscular junction induces the release of a few hundred quanta of acetylcholine (ACh) into the synaptic cleft, resulting in depolarization of the muscle cell which is observed as the endplate current (EPC). The release of each quantum of ACh invokes the miniature endplate current (MEPC), so that an EPC could be generated by summation of the MEPCs both in time during evolution of the EPC and in space for a certain area of the post-synaptic membrane. In this study, a mathematical model for EPC generation is developed as a reaction-diffusion system (RD system) which represents the dynamic behavior of ACh in the chemical transmission process with the simultaneous quantum release of ACh. The RD system for ACh is mathematically expressed by a two-dimensional diffusion equation with nonlinear reaction terms due to the rate processes for acetylcholinesterase (AChE) and ACh receptor (AChR). Numerical solution of the governing equation with the method of lines and the Gear method yields temporal changes in relative concentrations of the open channel form of AChR which is assumed to be equivalent to the EPC. Analysis of the behavior of the RD system with respect to the various distances between the release sites of ACh on the pre-synaptic membrane demonstrates that the amplitude of EPC is quite sensitive to the distances around 0.5 µm, but independent of the values of the diffusion coefficient of ACh in the synaptic cleft.

A transfer-function representation for regulatory responses of a controlled metabolic pathway

A transfer-function representation for the response of a controlled metabolic pathway to the changes in influx and efflux rates of metabolites is formulated to describe analytically and approximately the regulatory behavior of the pathway around a steady state. The pathway model analyzed is an open and homogeneous system which consists of two consecutive enzymatic reactions catalyzed by an allosteric enzyme of Monod-Wyman-Changeux (MWC) dimeric model and a Michaelis-Menten-type enzyme, respectively, and undergoes the feedback inhibition by the end product. The rate equation for the system (a system of ordinary differential equations) is linearized about a steady state, so that the responses of the reaction rates to the changes in influx rate of the substrate and efflux rate of the end product are expressed in a form of transfer function. The formulation leads to the transfer function for the response of production rate of the end product to the change in its efflux rate to clarify the regulatory response of feedback mechanism in controlled metabolic pathways. The relationship among the chemical species in the system at steady states also supports a reasonable assumption that the regulatory mechanisms in metabolic pathways are to control the production of end product against the change in its demand from the cellular environments.

A transfer-function representation for the input-output relation in consecutive Michaelis-Menten-type reactions

A transfer-function representation is devised to describe analytically and approximately the reaction velocity (output) in response to the substrate influx rate (input) in single and two consecutive Michaelis-Menten-type reactions in an open and homogeneous system. The transfer function for single reactions has an expression of first-order system, the time constant of which is dependent on the kinetic parameters and flow rate (steady-state value of the input and output), but independent of the magnitude of the input change. The transfer function for the two-reaction system can be formed with successive multiplication of the transfer functions for the first and second reactions. The validity of the representation is examined with variation in the kinetic parameters and flow rate by comparing the output of the transfer function with the actual response obtained from the computer simulation, that is, numerical integration of the rate equation. The analysis of the indicial responses indicates that the transfer functions for single and two consecutive reactions are valid within a certain error for the response around a steady state.

Validity of transfer-function representation of input-output relation in allosteric models☆

A transfer-function representation of reaction velocity is devised to describe analytically and approximately an input-output response of allosteric enzyme around a steady state. The transfer function is derived on assuming an exponential change in reaction velocity for the indicial response to substrate influx rate. The validity of the representation with variation in the kinetic parameters and flow rates is examined for the response of Koshland-Nemethy-Filmer (KNF) and Monod-Wyman-Changeux (MWC) dimeric models by comparing with the exact response obtained from the computer simulation, that is, by numerical integration of the rate equation. The representation has a wider valid region with a decrease in influx rate than with an increase. For the KNF model the representation is valid for negative cooperativity, but invalid for positive cooperativity. For the MWC model the validity decreases with stronger cooperativity. With the transfer functions valid for the Michaelis-Menten and allosteric reactions, we may derive the transfer-function representation for many metabolic pathways.

Localization effects of acetylcholine release from a synaptic vesicle at the neuromuscular junction

A two-dimensional compartment model devised for the appropriate representation of the transient process of the spontaneous generation of miniature endplate current (MEPC) at the neuromuscular junction is applied for clarifying the biochemical significance of the quantal release mechanism of acetylcholine (ACh), a typical neurotransmitter, in the synaptic chemical transmission process. The simulation analysis with the model demonstrates that the localization of the ACh release due to the fusion of a synaptic vesicle with the presynaptic membrane has significant effects on the amplitude of MEPC and that the stronger effects are caused with the smaller diffusion coefficients of ACh in the cleft. The sharpest and highest response of MEPC is achieved when the release area is about 4 times to the natural release through the narrow pore. On the other hand, the actual localization corresponding to the natural release of ACh makes the amplitude of MEPC higher by a factor about 2.5 compared with that in the most extended release of ACh examined, implying that the natural release mechanism works as an amplifier of the MEPC with the fixed amount of ACh available.

Association between Excessive Alcohol Use and Alcohol-Related Injuries in College Students: A Multi-Center Cross-Sectional Study in Japan.

Alcohol-related injuries in college students are a major public health problem worldwide. We clarified the association between excessive drinking and alcohol-related injuries in Japanese college students. This was a cross-sectional study with a self-administered questionnaire. From January to March 2013, we sampled all college students and graduate students aged 20 years or older during annual health examinations at three colleges in Mie Prefecture in Japan. The questionnaire assessed the frequency of alcohol drinking, amount of alcohol consumed per day, binge drinking during the past year, alcohol-related injuries during the past year, and demographic data. Logistic regression analysis was conducted on the association between excessive alcohol use and alcohol-related injuries. A total of 2,842 students underwent health examinations, of whom 2,177 (76.6%) completed the questionnaire. Subjects included 1,219 men (56.0%) and 958 women (44.0%). Eighty-eight men (7.2%) and 93 women (9.7%) were classified as excessive weekly drinkers, while 693 men (56.8%) and 458 women (47.8%) were determined to be binge drinkers. Eighty-one men (6.6%) and 26 women (2.7%) had experienced alcohol-related injuries during the past year. In the logistic regression analysis, binge drinkers (odds ratio 25.6 [8.05-81.4]) and excessive weekly drinkers (odds ratio 3.83 [2.41-6.09]) had a history of significantly more alcohol-related injuries, even after adjusting for age and sex. In conclusion, alcohol-related injuries in college students in Japan were strongly associated with excessive drinking. As a strategy for preventing such injuries in this population, an interventional study is required to identify effective methods for reducing excessive alcohol use.