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Some examples of the use of computer-produced contour plots in the fitting of enzyme rate equations to reaction-velocity measurements.

ABSTRACT: The use of computer-based isotach plots, relating reaction velocity to simultaneous variation of two substrates or effectors of an enzyme, in producing estimates of the parameters of enzyme rate equations was investigated. The computer program (;SYMAP') incorporates an interpolation algorithm, and the superiority of this over visual estimation in producing interpolated velocity values for the estimation of parameter values by conventional double-reciprocal plots is described. The usefulness of the SYMAP program in monitoring the process of fitting data obtained by simultaneous changes in two experimental variables is also described. It is shown that if the residual errors are weighted by a procedure described elsewhere (Ottaway, 1971b, 1973), the percentage error of the computed velocity is distributed evenly over a plot which contains a 100-fold variation in the concentration of one substrate and a 500-fold variation in the concentration of Mg(2+), and in which the velocity of the reaction (that catalysed by NAD kinase) varies over a 60-fold range. The two-dimensional percentage error plot was used to assess the limits within which an incomplete inhibition equation is valid, and to detect a discrepancy in an expected good fit, caused by an impurity in one of the substrates.

SUBMITTER: Ottaway JH

PROVIDER: S-EPMC1174525 | biostudies-other | 1972 Dec

REPOSITORIES: biostudies-other

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Project description:By modelling the average activity of large neuronal populations, continuum mean field models (MFMs) have become an increasingly important theoretical tool for understanding the emergent activity of cortical tissue. In order to be computationally tractable, long-range propagation of activity in MFMs is often approximated with partial differential equations (PDEs). However, PDE approximations in current use correspond to underlying axonal velocity distributions incompatible with experimental measurements. In order to rectify this deficiency, we here introduce novel propagation PDEs that give rise to smooth unimodal distributions of axonal conduction velocities. We also argue that velocities estimated from fibre diameters in slice and from latency measurements, respectively, relate quite differently to such distributions, a significant point for any phenomenological description. Our PDEs are then successfully fit to fibre diameter data from human corpus callosum and rat subcortical white matter. This allows for the first time to simulate long-range conduction in the mammalian brain with realistic, convenient PDEs. Furthermore, the obtained results suggest that the propagation of activity in rat and human differs significantly beyond mere scaling. The dynamical consequences of our new formulation are investigated in the context of a well known neural field model. On the basis of Turing instability analyses, we conclude that pattern formation is more easily initiated using our more realistic propagator. By increasing characteristic conduction velocities, a smooth transition can occur from self-sustaining bulk oscillations to travelling waves of various wavelengths, which may influence axonal growth during development. Our analytic results are also corroborated numerically using simulations on a large spatial grid. Thus we provide here a comprehensive analysis of empirically constrained activity propagation in the context of MFMs, which will allow more realistic studies of mammalian brain activity in the future.

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Some examples of the use of computer-produced contour plots in the fitting of enzyme rate equations to reaction-velocity measurements.

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