scholarly journals Voltage gating by molecular subunits of Na+ and K+ ion channels: higher-dimensional cubic kinetics, rate constants, and temperature

2015 ◽  
Vol 113 (10) ◽  
pp. 3759-3777 ◽  
Author(s):  
Jürgen F. Fohlmeister
Keyword(s):  
Rate Constants ◽  
Ganglion Cells ◽  
Giant Axon ◽  
Dielectric Surface ◽  
Repetitive Firing ◽  
Strong Temperature Dependence ◽  
Surface Charges ◽  
Activation Gating ◽  
Sodium Inactivation ◽  
Rate Limiting

The structural similarity between the primary molecules of voltage-gated Na and K channels (alpha subunits) and activation gating in the Hodgkin-Huxley model is brought into full agreement by increasing the model's sodium kinetics to fourth order (m3 → m4). Both structures then virtually imply activation gating by four independent subprocesses acting in parallel. The kinetics coalesce in four-dimensional (4D) cubic diagrams (16 states, 32 reversible transitions) that show the structure to be highly failure resistant against significant partial loss of gating function. Rate constants, as fitted in phase plot data of retinal ganglion cell excitation, reflect the molecular nature of the gating transitions. Additional dimensions (6D cubic diagrams) accommodate kinetically coupled sodium inactivation and gating processes associated with beta subunits. The gating transitions of coupled sodium inactivation appear to be thermodynamically irreversible; response to dielectric surface charges (capacitive displacement) provides a potential energy source for those transitions and yields highly energy-efficient excitation. A comparison of temperature responses of the squid giant axon (apparently Arrhenius) and mammalian channel gating yields kinetic Q10 = 2.2 for alpha unit gating, whose transitions are rate-limiting at mammalian temperatures; beta unit kinetic Q10 = 14 reproduces the observed non-Arrhenius deviation of mammalian gating at low temperatures; the Q10 of sodium inactivation gating matches the rate-limiting component of activation gating at all temperatures. The model kinetics reproduce the physiologically large frequency range for repetitive firing in ganglion cells and the physiologically observed strong temperature dependence of recovery from inactivation.

scholarly journals Beyond the Active Site: Mechanistic Investigations of the Role of the Secondary Coordination Sphere and Beyond on Multi-Electron Electrocatalytic Reactions and Their Relations Between Kinetics and Thermodynamics

2020 ◽  
Author(s):  
Vincent Wang
Keyword(s):  
Thermodynamic Parameters ◽  
Coordination Sphere ◽  
Active Site ◽  
Rate Constants ◽  
Reduction Reaction ◽  
Rate Limiting Step ◽  
Limiting Step ◽  
Secondary Coordination Sphere ◽  
Catalytic Rate ◽  
Rate Limiting

<p>The development of an electrocatalyst with a rapid turnover frequency, low overpotential and long-term stability is highly desired for fuel-forming reactions, such as water splitting and CO<sub>2</sub> reduction. The findings of the scaling relationships between the catalytic rate and thermodynamic parameters over a wide range of electrocatalysts in homogeneous and heterogeneous systems provide useful guidelines and predictions for designing better catalysts for those redox reactions. However, such relationships also suggest that a catalyst with a high catalytic rate is typically associated with a high overpotential for a given reaction. Inspired by enzymes, the introduction of additional interactions through the secondary coordination sphere beyond the active site, such as hydrogen-bonding or electrostatic interactions, have been shown to offer a promising avenue to disrupt these unfavorable relationships. Herein, we further investigate the influence of these cooperative interactions on the faster chemical steps, in addition to the rate-limiting step widely examined before, for molecular electrocatalysts with the structural and electronic modifications designed to facilitate the dioxygen reduction reaction, CO<sub>2</sub> reduction reaction and hydrogen evolving reaction. Based on the electrocatalytic kinetic analysis, the rate constants for faster chemical steps and their correlation with the corresponding thermodynamic parameters are evaluated. The results suggest that the effects of the secondary coordination sphere and beyond on these fuel-forming reactions are not necessarily beneficial for promoting all chemical steps and no apparent relation between rate constants and thermodynamic parameters are found in some cases studied here, which may implicate the design of electrocatalysts in the future. Finally, these analyses demonstrate that the characteristic features for voltammograms and foot-of-the-wave-analysis plots are associated with the specific kinetic phenomenon among these multi-electron electrocatalytic reactions, which provides a useful framework to probe the insights of chemical and electronic modifications on the catalytic steps quantitatively (i.e. kinetic rate constants) and to optimize some of critical steps beyond the rate-limiting step.</p>

Catalytic power of pyruvate decarboxylase. Rate-limiting events and microscopic rate constants from primary carbon and secondary hydrogen isotope effects

1991 ◽  
Vol 113 (22) ◽  
pp. 8402-8409 ◽  
Author(s):  
Francisco J. Alvarez ◽  
Joachim Ermer ◽  
Gerhard Huebner ◽  
Alfred Schellenberger ◽  
Richard L. Schowen
Keyword(s):  
Rate Constants ◽  
Hydrogen Isotope ◽  
Isotope Effects ◽  
Pyruvate Decarboxylase ◽  
Rate Limiting ◽  
Catalytic Power

scholarly journals Control analysis applied to single enzymes: can an isolated enzyme have a unique rate-limiting step?

1993 ◽  
Vol 294 (1) ◽  
pp. 87-94 ◽  
Author(s):  
G C Brown ◽  
C E Cooper
Keyword(s):  
Rate Constants ◽  
General Assumption ◽  
Control Analysis ◽  
Rate Limiting Step ◽  
Limiting Step ◽  
Steady State Rate ◽  
Carbamate Kinase ◽  
State Rate ◽  
Rate Limiting ◽  
Control Coefficients

Control analysis is used to analyse and quantify the concept of a rate-limiting step within an enzyme. The extent to which each rate constant within the enzyme limits the steady-state rate of the enzyme and the levels of enzyme intermediate species are quantified as flux and concentration control coefficients. These coefficients are additive and obey summation theorems. The control coefficients of triose phosphate isomerase, carbamate kinase and lactate dehydrogenase are calculated from literature values of the rate constants. It is shown that, contrary to previous assumption, these enzymes do not have a unique rate-limiting step, but rather flux control is shared by several rate constants and varies with substrate, product and effector concentrations, and with the direction of the reaction. Thus the general assumption that an enzyme will have a unique rate-limiting step is unjustified.

scholarly journals The Deoxyglucose Method in the Ferret Brain. II. Glucose Utilization Images and Normal Values

1989 ◽  
Vol 9 (1) ◽  
pp. 43-52 ◽  
Author(s):  
C. Redies ◽  
M. Diksic ◽  
Y. L. Yamamoto
Keyword(s):  
Rate Constants ◽  
Glucose Utilization ◽  
Normal Values ◽  
Brain Size ◽  
Experimental Period ◽  
Brain Structures ◽  
Rate Limiting Step ◽  
Rate Limiting ◽  
The Brain ◽  
Deoxyglucose Method

To measure cerebral glucose utilization with the autoradiographic deoxyglucose method, the tracer transfer rate constants and lumped constants must be known. 2-Deoxyglucose (2-DG) and fluorodeoxyglucose (FDG) constants were determined in 18 gray and white matter brain structures of the anesthetized ferret. The ferret is a domestic carnivore particularly suitable for deoxyglucose studies because of its small brain size and low body weight. The average gray matter rate constants for tracer transfer across the blood-brain barrier are similar for 2-DG and FDG in the ferret brain ( K*1 = 0.21 ml/g/min and k*2 = 0.39 min−1). The rate constant for the rate-limiting step of tracer phosphorylation, k*3, is 1.6 times higher for FDG than for 2-DG (0.21 vs. 0.13 min−1). Loss of metabolized tracer is about 1–1.5%/min throughout the ferret brain for both tracers as estimated for a 180 min experimental period. Taking into account this loss, the lumped constant is 0.92 for FDG and 0.68 for 2-DG. Glucose utilization values in the brain of the anesthesized ferret range from 33 μmol/100 g/min in the corpus callosum to 104 μmol/100 g/min in the caudate nucleus. Representative glucose utilization images of coronal sections of the ferret brain are shown. Brain structures are identified on the same slices counterstained with thionin.

scholarly journals Equilibrium and Kinetic Properties of the Interaction between Tetrodotoxin and the Excitable Membrane of the Squid Giant Axon

1970 ◽  
Vol 55 (3) ◽  
pp. 309-335 ◽  
Author(s):  
Leon Andres Cuervo ◽  
William J. Adelman
Keyword(s):  
Dissociation Constant ◽  
Rate Constants ◽  
Sodium Current ◽  
Giant Axon ◽  
Kinetic Properties ◽  
Bathing Solution ◽  
Thermodynamic Quantities ◽  
Partial Recovery ◽  
Reactive Site ◽  
Membrane Complex

Squid giant axons were treated with tetrodotoxin (TTX) in concentrations ranging from 1 nM to 25 nM and the resulting decrease in sodium current was followed in time using the voltage clamp technique. The removal of TTX from the bathing solution produced only partial recovery of the sodium current. This suggests that the over-all interaction is more complex than just a reversible reaction. By correcting for the partial irreversibility of the decrease in sodium current, a dissociation constant of 3.31 x 10-9 M was calculated for the reaction between TTX and the reactive site of the membrane. The data obtained fit a dose-response curve modified to incorporate the correction for partial irreversibility when calculated for a one-to-one stoichiometry. The fit disagreed with that calculated for a reaction between two molecules of TTX with a single membrane-reactive site, but neither supported nor disproved the possibility of a complex formed by two reactive sites with one molecule of TTX. Values of the rate constants for the formation and dissociation of the TTX-membrane complex, k1 and k2, respectively, were obtained from the kinetic data. The values are: k1 = 0.202 x 108 M-1, and k2 = 0.116 min-1. The magnitude of the dissociation constant derived from these values is 5.74 x 10-9 M, which has the same order of magnitude as that obtained from equilibrium measurements. Arrhenius plots of the rate constants gave values for the thermodynamic quantities of activation.

The nature of the transition state in diarylmethyl cation – nucleophile combination reactions as probed by secondary α-deuterium isotope effects

2001 ◽  
Vol 79 (12) ◽  
pp. 1887-1897
Author(s):  
Thuy Van Pham ◽  
Robert A McClelland
Keyword(s):  
Transition State ◽  
Isotope Effect ◽  
Rate Constant ◽  
Rate Constants ◽  
Flash Photolysis ◽  
Isotope Effects ◽  
Equilibrium Constants ◽  
Bond Formation ◽  
Kinetic Isotope ◽  
Rate Limiting

Transition-state structures for the carbocation–nucleophile combination reactions of (4-substituted-4'- methoxydiphenyl)methyl cations with water, chloride, and bromide ions in acetonitrile–water mixtures have been investigated by measuring the secondary α-deuterium kinetic and equilibrium isotope effects. Rate constants in the combination direction were measured with laser flash photolysis. Equilibrium constants were measured for the water reaction by a comparison method in moderately concentrated sulfuric acid solutions, for the bromide reaction via the observation of reversible combination, and for the chloride reaction from the ratio of the combination rate constant and the rate constant for the ionization of the diarylmethyl chloride product. The fraction of bond making in the transition state has been calculated as the ratio log (kinetic isotope effect):log (equilibrium isotope effect). For the water reaction, there is 50–65% bond making in the transition state; this is also true for cations that are many orders of magnitude less reactive. The same conclusions, 50–65% bond formation in the transition state independent of reactivity, have previously been made in correlations of log kw vs. log KR. Thus, two quite different measures of transition structure provide the same result. The kH:kD values for the halide combinations in 100% acetonitrile are within experimental error of unity. This is consistent with suggestions that these reactions are occurring with diffusional encounter as the rate-limiting step. Addition of water has a dramatic retarding effect on the halide reactions, with rate constants decreasing steadily with increased water content. Small inverse kinetic isotope effects are observed (in 20% acetonitrile:80% water) indicating that carbon—halogen bond formation is rate-limiting. Comparison of the kinetic and equilibrium isotope effects shows ~25 and ~40% bond formation in the transition states for the reactions with bromide and chloride, respectively.Key words: carbocation, isotope effect, transition state, halide.

Reactions of 1-substituted 2,4,6-trinitrobenzenes with nucleophiles

1979 ◽  
Vol 44 (5) ◽  
pp. 1453-1459 ◽  
Author(s):  
Jaromír Kaválek ◽  
Ahmad Ashfaq ◽  
Vojeslav Štěrba
Keyword(s):  
Methyl Ether ◽  
Rate Constants ◽  
Equilibrium Constants ◽  
Nucleophilic Aromatic Substitution ◽  
Aromatic Substitution ◽  
Phenyl Ester ◽  
Methyl Derivative ◽  
Rate Limiting Step ◽  
Limiting Step ◽  
Rate Limiting

Rate constants have been determined of nucleophilic aromatic substitution of 2,4,6-trinitrophenyl methyl ether (Ia), 2,4,6-trinitrophenyl ethanoate (Ic), 2,4,6-trinitrochlorobenzene (Ib), 2,4,6-trinitrodiphenyl ether (Id), 2,4,6-trinitro-4'-bromodiphenyl ether (Ie), 2,3',4,6-tetranitrodiphenyl ether (If) and 2,4,4',6-tetranitrodiphenyl ether (Ig) with methoxide, ethanoate and methyl cyanoethanoate (II) anions in methanol. For the compounds Ia,b rate and equilibrium constants of addition of the anion II(-) at positions 3 and 5 have been measured, too. In reactions of the compounds Ia to Ig with ethanoate anion the first (rate-limiting) step produces the phenyl ester Ic which reacts with a further ethanoate anion to give 2,4,6-trinitrophenol (Ih) and ethanoic anhydride. In reactions of the bromo derivative Ie and, to a still larger extent, compound Id the methyl derivative Ia is formed besides the compound Ih.

scholarly journals Catalysis by acetylcholinesterase in two-hydronic-reactive states. Integrity of deuterium oxide effects and hydron inventories

1992 ◽  
Vol 285 (2) ◽  
pp. 451-460 ◽  
Author(s):  
E Salih
Keyword(s):  
Kinetic Parameters ◽  
Conformational Change ◽  
Rate Constants ◽  
Literature Abstract ◽  
Deuterium Oxide ◽  
Ph Dependence ◽  
Reversible Inhibitor ◽  
Induced Fit ◽  
Rate Limiting ◽  
Hydrolysis Of

Low 2H2O effects (1.0-1.5) for the parameter k(cat.)/Km in the hydrolysis of various substrates by acetylcholinesterase (AcChE) is due to normal 2H2O effects (1.8-2.8) for the parameter k(cat.) and 2H2O effects of 1.0-2.5 for the parameter Km. The analyses and interpretations of 2H2O effects in the literature utilizing the parameter k(cat.)/Km, which led to the proposal of ‘isotope insensitivity’ of the catalytic steps and the hypothesis of a rate-limiting substrate-induced-fit conformational change, are incorrect. Since k(cat.) is the only parameter that can represent the hydron-transfer step solely, the 2H2O effect can most appropriately be evaluated by using this parameter. Calculations and comparison of acylation (k+2) and deacylation (k+3) rate constants show that acylation is rate-determining for most substrates and the improved binding -0.84 to -2.09 kJ/mol (-0.2 to -0.5 kcal/mol) in 2H2O obscures the normal 2H2O effect on k(cat.) when the ratio k(cat.)/Km is utilized. Consistent with this, measurements of the inhibition constant (KI(com.)) for a reversible inhibitor, phenyltrimethylammonium, lead to KI(com.)H2O = 39 +/- 3 microM and KI(com.)2H2O = 24.5 +/- 3.5 microM, an 2H2O effect of 1.59 +/- 0.26. pH-dependence of k(cat.) in 2H2O is subject to variability of the pK(app.) values, as evaluated in terms of the two-hydronic-reactive states (EH and EH2) of AcChE, and is due to an uneven decrease in 2H2O of the kinetic parameters k'cat. for the EH2 state relative to k(cat.) for the EH state, thus leading to variable shifts in pK(app.) values of between 0.5 and 1.2 pH units for this parameter. The observed pH-independent limiting rate constants for k(cat.)/Km(app.) are made to vary between 0.5 and 1.0 in 2H2O by effects on kinetic parameters for the EH2 state, k'cat./K'm varying between 0.2 and 0.7 relative to the EH state, with k(cat.)/Km varying between 0.4 and 1.0. The effects observed on k(cat.)/Km(app.) are ultimately the result of variable effects of 2H2O on k'cat. and K'm for the EH2 state relative to k(cat.) and Km for the EH state of AcChE. These effects are responsible for the variable shifts and more than 0.5 pH unit of the pK(app.) values in 2H2O for pH-k(cat.)/Km profiles. The upward-bowing hydron inventories for k(cat.)/Km are the result of linear hydron inventories for k(cat.) and downward-bowing on Km and are not due to the rate-limiting substrate-induced fit process as claimed in the literature.(ABSTRACT TRUNCATED AT 400 WORDS)

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