scholarly journals Macroscopic currents of ionic channels using Mass Action Law: A mathematical model

2021 ◽  
Vol 2 (5) ◽  
pp. 7493-7514
Author(s):  
Torres Jácome Julián ◽  
Martagon-Domínguez Juan Mauricio ◽  
Montes Pérez Areli ◽  
Montiel-Jaen Guadalupe ◽  
García-Garibay Otto ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Ionic Channels ◽  
Mass Action ◽  
System Of Equations ◽  
Law Of Mass Action ◽  
Voltage Dependent ◽  
Mass Action Law ◽  
Experimental Protocols ◽  
Pass Through ◽  
Kinetics Of

In this work it proposes a mathematical model for ion channels based on two concepts, the Hodgkin and Huxley's as well as the Law of Mass Action in addition, we consider the kinetics of channels as a dynamic process of Markov`s chain. With the previous premises, a system of differential equations is proposed that when it is solved, all properties of the macroscopic currents are determined. The activation, deactivation, inactivation, and recovery of the inactivation concepts remain as processes that are part of a chemical reaction. With this system of equations, all the experimental protocols used in electrophysiology to characterize macroscopic currents can be modeled. Another advantage is that the model allows, with the same system of equations, to determine the properties of voltage-dependent channels regardless of the type of ion that pass through in the channel.

scholarly journals Development of a Simple Kinetic Mathematical Model of Aggregation of Particles or Clustering of Receptors

Life ◽  
2020 ◽  
Vol 10 (6) ◽  
pp. 97
Author(s):  
Andrei K. Garzon Dasgupta ◽  
Alexey A. Martyanov ◽  
Aleksandra A. Filkova ◽  
Mikhail A. Panteleev ◽  
Anastasia N. Sveshnikova
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Cluster Formation ◽  
Quantitative Description ◽  
Membrane Receptors ◽  
Mass Action ◽  
Mass Action Kinetics ◽  
Clustering Model ◽  
Mass Action Law ◽  
Kinetics Of

The process of clustering of plasma membrane receptors in response to their agonist is the first step in signal transduction. The rate of the clustering process and the size of the clusters determine further cell responses. Here we aim to demonstrate that a simple 2-differential equation mathematical model is capable of quantitative description of the kinetics of 2D or 3D cluster formation in various processes. Three mathematical models based on mass action kinetics were considered and compared with each other by their ability to describe experimental data on GPVI or CR3 receptor clustering (2D) and albumin or platelet aggregation (3D) in response to activation. The models were able to successfully describe experimental data without losing accuracy after switching between complex and simple models. However, additional restrictions on parameter values are required to match a single set of parameters for the given experimental data. The extended clustering model captured several properties of the kinetics of cluster formation, such as the existence of only three typical steady states for this system: unclustered receptors, receptor dimers, and clusters. Therefore, a simple kinetic mass-action-law-based model could be utilized to adequately describe clustering in response to activation both in 2D and in 3D.

scholarly journals Dynamics of 9-aminoacridine block of sodium channels in squid axons.

1979 ◽  
Vol 73 (1) ◽  
pp. 1-21 ◽  
Author(s):  
J Z Yeh
Keyword(s):  
Ionic Channels ◽  
Na Channel ◽  
Na Channels ◽  
Drug Molecule ◽  
Na Currents ◽  
Voltage Dependent ◽  
A Site ◽  
Kinetics Of ◽  
Block Of Na Channels ◽  
Single Exponential Function

The interactions of 9-aminoacridine with ionic channels were studied in internally perfused squid axons. The kinetics of block of Na channels with 9-aminoacridine varies depending on the voltage-clamp pulses and the state of gating machinery of Na channels. In an axon with intact h gate, the block exhibits frequency- and voltage-dependent characteristics. However, in the pronase-perfused axon, the frequency-dependent block disappears, whereas the voltage-dependent block remains unchanged. A time-dependent decrease in Na currents indicative of direct block of Na channel by drug molecule follows a single exponential function with a time constant of 2.0 +/- 0.18 and 1.0 +/- 0.19 ms (at 10 degrees C and 80 m V) for 30 and 100 microM 9-aminoacridine, respectively. A steady-state block can be achieved during a single 8-ms depolarizing pulse when the h gate has been removed. The block in the h-gate intact axon can be achieved only with multiple conditioning pulses. The voltage-dependent block suggests that 9-aminoacridine binds to a site located halfway across the membrane with a dissociation constant of 62 microM at 0 m V. 9-Aminoacridine also blocks K channels, and the block is time- and voltage-dependent.

scholarly journals DOES THE KINETICS OF TRYPSIN DIGESTION DEPEND ON THE FORMATION OF A COMPOUND BETWEEN ENZYME AND SUBSTRATE

1922 ◽  
Vol 4 (5) ◽  
pp. 487-509 ◽  
Author(s):  
John H. Northrop
Keyword(s):  
Experimental Evidence ◽  
Substrate Concentration ◽  
Relative Velocity ◽  
Mass Action ◽  
Law Of Mass Action ◽  
Rate Of Hydrolysis ◽  
Gelatin Concentration ◽  
Kinetics Of ◽  
Hydrolysis Of ◽  
Substrate Concentrations

1. The velocity of hydrolysis of gelatin by trypsin increases more slowly than the gelatin concentration and finally becomes nearly independent of the gelatin concentration. The relative velocity of hydrolysis of any two substrate concentrations is independent of the quantity of enzyme used to make the comparison. 2. The rate of hydrolysis is independent of the viscosity of the solution. 3. The percentage retardation of the rate of hydrolysis by inhibiting substances, is independent of the substrate concentration. 4. There is experimental evidence that the enzyme and inhibiting substance are combined to form a widely dissociated compound. 5. If the substrate were also combined with the enzyme, an increase in the substrate concentration should affect the equilibrium between the enzyme and the inhibiting substance. This is not the case. 6. The rate of digestion of a mixture of casein and gelatin is equal to the sum of the rates of hydrolysis of the two substances alone, as it should be if the rate is proportional to the concentration of free enzyme. This contradicts the saturation hypothesis. 7. If the reaction is followed by determining directly the change in the substrate concentration, it is found that this change agrees with the law of mass action; i.e., the rate of digestion is proportional to the substrate concentration.

Thermodynamic evaluation using the law of mass action under consideration of the activity coefficients in the system NdCl3-HCl (or NaOH)-H2O-DEHPA-kerosene

2018 ◽  
Vol 115 (6) ◽  
pp. 614
Author(s):  
Christiane Scharf ◽  
André Ditze
Keyword(s):  
Activity Coefficients ◽  
Earth Metal ◽  
Mass Action ◽  
Thermodynamic Evaluation ◽  
Law Of Mass Action ◽  
Neodymium Chloride ◽  
Mass Action Law ◽  
Extensive Experimental Data ◽  
Hydroxide Water ◽  
Metal Solvent

For the recovery of neodymium, an important rare earth metal, solvent extraction using DEHPA as extractant is a possible process for winning and recycling. A preceding study by the authors has provided extensive experimental data of the system neodymium-chloride-hydrochloric acid (or sodium hydroxide)-water-di-(2-ethylhexyl)phosphoric acid (DEHPA)-kerosene. It was found that the description of the reaction Nd3++3(DEHPA)2 ⇄ Nd(DEHP‧DEHPA)3+3H+ by an ideal mass action law is only partly satisfactory. This article investigates the contribution of several parameters to non-ideality. On this basis, expressions for activity coefficients of neodymium in the aqueous phase as well as DEHPA and neodymium in the organic phase are derived. The resulting equations are shown to represent the system with considerably better accuracy than previously possible.

Far-from-equilibrium kinetic processes

2015 ◽  
Vol 40 (4) ◽  
Author(s):  
J. Miguel Rubí ◽  
Agustin Pérez-Madrid
Keyword(s):  
Reaction Rate ◽  
Driving Forces ◽  
Mass Action ◽  
Law Of Mass Action ◽  
Equilibrium Conditions ◽  
Activated Processes ◽  
Far From Equilibrium ◽  
Kinetics Of ◽  
External Driving ◽  
Good Agreement

AbstractWe analyze the kinetics of activated processes that take place under far-from-equilibrium conditions, when the system is subjected to external driving forces or gradients or at high values of affinities. We use mesoscopic non-equilibrium thermodynamics to show that when a force is applied, the reaction rate depends on the force. In the case of a chemical reaction at high affinity values, the reaction rate is no longer constant but depends on affinity, which implies that the law of mass action is no longer valid. This result is in good agreement with the kinetic theory of reacting gases, which uses a Chapman–Enskog expansion of the probability distribution.

scholarly journals Study of Reversible Platelet Aggregation Model by Nonlinear Dynamics

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 759
Author(s):  
Grigorii A. Vasilev ◽  
Aleksandra A. Filkova ◽  
Anastasia N. Sveshnikova
Keyword(s):  
Nonlinear Dynamics ◽  
Mathematical Model ◽  
Steady State ◽  
Platelet Aggregation ◽  
Mass Action ◽  
Influence Area ◽  
Platelet Aggregate ◽  
Mass Action Law ◽  
Type Node

Blood cell platelets form aggregates upon vessel wall injury. Under certain conditions, a disintegration of the platelet aggregates, called “reversible aggregation”, is observed in vitro. Previously, we have proposed an extremely simple (two equations, five parameters) ordinary differential equation-based mathematical model of the reversible platelet aggregation. That model was based on mass-action law, and the parameters represented probabilities of platelet aggregate formations. Here, we aimed to perform a nonlinear dynamics analysis of this mathematical model to derive the biomedical meaning of the model’s parameters. The model’s parameters were estimated automatically from experimental data in COPASI software. Further analysis was performed in Python 2.7. Contrary to our expectations, for a broad range of parameter values, the model had only one steady state of the stable type node, thus eliminating the initial assumption that the reversibility of the aggregation curve could be explained by the system’s being near a stable focus. Therefore, we conclude that during platelet aggregation, the system is outside of the influence area of the steady state. Further analysis of the model’s parameters demonstrated that the rate constants for the reaction of aggregate formation from existing aggregates determine the reversibility of the aggregation curve. The other parameters of the model influenced either the initial aggregation rate or the quasi-steady state aggregation values.

scholarly journals THE KINETICS OF ENZYME REACTIONS: SCHÜTZ'S LAW

1930 ◽  
Vol 13 (3) ◽  
pp. 323-334 ◽  
Author(s):  
E. A. Moelwyn-Hughes ◽  
J. Pace ◽  
W. C. M. Lewis
Keyword(s):  
Experimental Results ◽  
Mass Action ◽  
Law Of Mass Action ◽  
Enzyme Reactions ◽  
Adsorption Theory ◽  
The Law ◽  
Kinetics Of ◽  
Hydrolysis Of ◽  
Tryptic Hydrolysis ◽  
Made In

1. A review of the applicability of Schütz's Law to enzymic reactions is given. 2. The theoretical deductions of the Law, (a) on the basis of the law of mass action, (b) on the basis of the adsorption theory, are given and the significance of the assumptions made in these deductions pointed out. 3. It is shown that the true critical increment for an enzymic reaction is equal to twice the critical increment calculated from the Schütz constant ks, if the heat of decomposition of the enzyme-products complex be neglected. 4. Experiments are described on the tryptic hydrolysis of casein at 30°C. and 404C. The foregoing considerations are applied to the experimental results obtained.

scholarly journals A model of carbon dioxide dissolution and mineral carbonation kinetics

2009 ◽  
Vol 466 (2117) ◽  
pp. 1265-1290 ◽  
Author(s):  
Mark J. Mitchell ◽  
Oliver E. Jensen ◽  
K. Andrew Cliffe ◽  
M. Mercedes Maroto-Valer
Keyword(s):  
Carbon Dioxide ◽  
Mass Action ◽  
Mineral Carbonation ◽  
Leading Order ◽  
Full System ◽  
Mass Action Law ◽  
Gaseous Carbon Dioxide ◽  
Equilibrium Concentrations ◽  
Kinetics Of ◽  
Independent Parameters

The kinetics of the dissolution of carbon dioxide in water and subsequent chemical reactions through to the formation of calcium carbonate, a system of reactions integral to carbon sequestration and anthropogenic ocean acidification, is mathematically modelled using the mass action law. This group of reactions is expressed as a system of five coupled nonlinear ordinary differential equations, with 14 independent parameters. The evolution of this system to equilibrium at 25 ° C and 1 atm, following an instantaneous injection of gaseous carbon dioxide, is simulated. An asymptotic analysis captures the leading-order behaviour of the system over six disparate time scales, yielding expressions for all species in each time scale. These approximations show excellent agreement with simulations of the full system, and give remarkably simple formulae for the equilibrium concentrations.

scholarly journals The effect of enzyme loading, alcohol/acid ratio and temperature on the enzymatic esterification of levulinic acid with methanol for methyl levulinate production: a kinetic study

RSC Advances ◽  
2021 ◽  
Vol 11 (25) ◽  
pp. 15054-15059
Author(s):  
Miaojia Song ◽  
Xiaohui Di ◽  
Yu Zhang ◽  
Yongming Sun ◽  
Zhongming Wang ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Kinetic Study ◽  
Levulinic Acid ◽  
Mass Action ◽  
Enzymatic Esterification ◽  
Law Of Mass Action ◽  
Enzyme Loading ◽  
Methyl Levulinate ◽  
Acid Ratio ◽  
The Law

Based on reaction reversibility and the law of mass action, a mathematical model was developed. By the developed model, the effect of enzyme loading, molar alcohol/acid ratio, and temperature on methyl levulinate yield was kinetically analyzed.

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