A BASIC program for the numerical solution of the transient kinetics of complex biochemical models

Hecht, Pedro; Nikonov, J.M.; Alonso, Guillermo

doi:10.1016/0169-2607(90)90018-5

Cited by 12 publications

(7 citation statements)

References 15 publications

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“…The kinetic behavior of the models was simulated with a computer program based on the Runge-Kutta algorithm [7] implemented in Borland-Delphi software. The simulated reaction of the Scheme I model, with either k p = 0 or 1 s -1 , starts by addition of 25 µM ATP to 1 µM Ca-ATPase equilibrated with 50 µM Ca.…”

Section: Guillermo L Alonso and Débora A Gonzálezmentioning

confidence: 99%

Activation free energies in partial steps of the sarcoplasmic reticulum Ca-ATPase cycle during the transient states of the reaction

Alonso¹,

González²

2014

asb

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The step-by-step free energy (ΔG) profile of the sarcoplasmic reticulum Ca-ATPase cycle during the transient state of simulated reactions was analyzed previously by Alonso and Hecht (1990). ΔG was negative at all the steps. Here we calculated the step-by-step activation energies (ΔG) in the same model according the transition state theory. Transient species were introduced as chemical intermediates at each step; they react with enzyme species accordingly with the mass law, decaying at 6.56x10 12 s-1. Other rate constants are as in the referenced paper. The transient evolution of the model was followed with a computer program. The evolution of the ligands concentrations agree with experimental results. Enzymatic species concentrations lie within 10-10-10-6 M, transient species lie within 10-19-10-17 M, at 0.1 s, when the reaction is in a cuasi-steady-state. These differences preclude the use of the standard (ΔG o) or basic (ΔG basic) free energies, to describe ΔG fall along the cycle. Forward and backward ΔG are shown for 10 and 100 ms of simulated reaction; both are negative in forward cycles, at any reaction time, and their sum equals the partial ΔG. The results show the absence of any activation energy hill to be surmounted upon the reaction advance. Similar results were obtained for the successive binding of 2 Ca ions to the enzyme through (+)cooperative reactions.

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Section: Guillermo L Alonso and Débora A Gonzálezmentioning

confidence: 99%

Activation free energies in partial steps of the sarcoplasmic reticulum Ca-ATPase cycle during the transient states of the reaction

Alonso¹,

González²

2014

asb

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“…1) was followed, applying the set of differential equations given in Appendix 1. The concentration values of the species were calculated for different cumulative reaction times with a computer program [6] adapted to Borland-Delphi software.…”

Section: Methodsmentioning

confidence: 99%

“…Taking into account (6) and the invariance of all k i values, the transport velocities calculated from the transport of *L in a system containing the unlabelled ligand in equilibrium (V 0 *) should be always lower than those calculated from the initial transport of the unlabeled ligand into an initially empty compartment (V 0 ). This is a consequence of the law of mass action applied to the partial steps participating in the uptake reaction.…”

Section: Looking For the Trans Effect In An Equilibrated Systemmentioning

confidence: 99%

In Silico Kinetic Study of the Glucose Transporter

Alonso

González

2007

J Biol Phys

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Glucose transport in plasma membranes is the prototypic example of facilitated diffusion through biological membranes, and transport in erythrocytes is the most widely studied. One of the oldest and simplest models describing the kinetics of the transport reaction is that of alternating conformers, schematized in a cycle of four partial reactions where glucose binds and dissociates at two opposite steps, and the transporter undergoes transconformations at the other two opposite steps. The transport kinetics is entirely defined by the forward and backward rate constants of the partial reactions and the glucose and transporter concentrations at each side of the membrane, related by the law of mass action. We studied, in silico, the effect of modifications of the variables on the transient kinetics of the transport reaction. The simulations took into account thermodynamic constraints and provided results regarding initial velocities of transport, maximal velocities in different conditions, apparent influx and efflux affinities, and the turnover number of the transporter. The results are in the range of those experimentally reported. Maximal initial velocities are obtained when the affinities of the ligand for the transporter are the same at the extraand intracellular binding sites and when the equilibrium constants of the transconformation steps are equal among them and equal to 1, independently of the obvious effect of the increase of the rate constant values. The results are well adjusted to Michaelis-Menten kinetics. A larger initial velocity for efflux than for uptake described in human erythrocytes is demonstrated in a model with the same dissociation constants at the outer and inner sites of the membrane. The larger velocities observed for uptake and efflux when transport occurs towards a glucose-containing trans side can also be reproduced with the alternating conformer model, depending on how transport velocities are measured.

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“…When cytoplasmic Ca is reduced by transport, Mn has more chance to bind to E.Mn and the rate of Mn uptake (through cycle 3) increases. We simulated numerically4 the temporal evolution of Ca and Mn uptake, assigning kinetic constants to the model. Our results reproduce the pattern of the experimental curves (inset in panel A of Fig.…”

mentioning

confidence: 99%

A Model Accounting for the Simultaneous Transport of Calcium and Manganese in Sarcoplasmic Reticulum Membranes

González

Ostuni

Lacapère

et al. 2003

Annals of the New York Academy of Sciences

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A BASIC program for the numerical solution of the transient kinetics of complex biochemical models

Cited by 12 publications

References 15 publications

Activation free energies in partial steps of the sarcoplasmic reticulum Ca-ATPase cycle during the transient states of the reaction

Activation free energies in partial steps of the sarcoplasmic reticulum Ca-ATPase cycle during the transient states of the reaction

In Silico Kinetic Study of the Glucose Transporter

A Model Accounting for the Simultaneous Transport of Calcium and Manganese in Sarcoplasmic Reticulum Membranes

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