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MCA |
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Back to the MCA homepage.
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In previous sections it was described how to obtain the control
coefficients of a metabolic pathway knowing the values of the enzyme
elasticities, using the summation thoerems,
the connectivity relations and
several additional relations. For several reasons,
it is useful if those operations can be tied up together and applied in one
uniform way. Several matrix methods have been developed that fulfil this task.
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The Matrix Method of Reder |
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Reder (1988) developed a matrix
method which is general and complete. In this method the matrices
are reduced to become invertible, the operations that lead to such
invertible matrices are equivalent to the special theorems developed
for complex structures (see above). Reder's
method is based on finding the structural properties of the pathway,
that is the properties which are not dependent on the values of the
elasticities but only on the stoichiometric relationships. This method,
albeit requiring some advanced knowledge of linear algebra, is the most
straightforward to incorporate in
computational applications.
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The Matrix Method of Cascante et al. |
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Cascante et al. (1989a,
b) focused on the similarities between
MCA and Savageau's Biochemical Systems Theory (BST) and developed a
matrix method in which one constructs a matrix of global properties and a
matrix of local properties. This is, of course, similar to the two other
methods cited above, in which one obtains the matrix of global properties (control coefficients) by inversion of the matrix of local
properties (elasticity coefficients).
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Recent Developments in Matrix Methods |
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More recently, Westerhoff et al.
(1994) developed a matrix method that
accomplishes the reverse of the previous ones. With it one can determine the
values of the enzyme elasticities from know values of the control coefficients.
This is a potentially very useful method as enzyme elasticities are very
difficult to measure in vivo or in situ while the control
coefficients are rather more easy (but still have many difficulties, see
next section).
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Group |
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