Computer algebra approaches to enzyme kinetics

AbstractA Logistic-Normal random variable (Y) is obtained from a Normal random variable (X) by the relation Y = (ex)/(1 + ex). In Monte-Carlo analysis of decision trees, Logistic-Normal random variates may be used to model the branching probabilities. In some cases, the probabilities to be modeled may not be independent, and a method for generating correlated Logistic-Normal random variates would be useful. A technique for generating correlated Normal random variates has been previously described. Using Taylor Series approximations and the algebraic definitions of variance and covariance, we describe methods for estimating the means, variances, and covariances of Normal random variates which, after translation using the above formula, will result in Logistic-Normal random variates having approximately the desired means, variances, and covariances. Multiple simulations of the method using the Mathematica computer algebra system show satisfactory agreement with the theoretical results.

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Kinetic Aspects of the Interaction of Blood Clotting Enzymes

Thrombosis and Haemostasis ◽

10.1055/s-0038-1651214 ◽

1968 ◽

Vol 19 (03/04) ◽

pp. 364-367 ◽

Cited By ~ 4

Author(s):

H. C Hemker ◽

P. W Hemker

Keyword(s):

Enzyme Kinetics ◽

Blood Clotting ◽

Competitive Inhibition ◽

Competitive Inhibitor ◽

Kinetics Of

SummaryThe enzyme kinetics of competitive inhibition under conditions prevailing in clotting tests are developed and a method is given to measure relative amounts of a competitive inhibitor by means of the t — D plot.

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Kinetic Aspects of the Interaction of Blood Clotting Enzymes

Thrombosis and Haemostasis ◽

10.1055/s-0038-1656222 ◽

1965 ◽

Vol 13 (01) ◽

pp. 155-175 ◽

Cited By ~ 4

Author(s):

H. C Hemker ◽

P.W Hemker ◽

E. A Loeliger

Keyword(s):

Kinetic Analysis ◽

Enzyme Kinetics ◽

Blood Clotting ◽

Enzyme System ◽

Enzyme Kinetic ◽

Clotting Time ◽

Standard Methods

SummaryApplication of the methods of enzyme-kinetic analysis to the results of clotting tests is feasible and can yield useful results. However, the standard methods of enzyme kinetics are not applicable without modifications imposed by the peculiarities of the blood-clotting enzyme system. The influence of the following complicating circumstances is calculated :1. Substrate is not present in excess.2. Only relative measures exist for concentrations of substrate or enzymes.3. Enzymes and substrates are often added together.4. Reagents are not pure.5. Clotting-time is our only measure for clotting-velocity.Formulas are deduced, which makes it possible to recognize the effect of these complications.

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