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Optimizing enzyme ratios in the tagatose synthesis pathway
enzyme ratio optimization
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We searched for the constants for the first-step reaction and got the following results.
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V
max=8.87mmol/s
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K
m = 0.51 mM
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What follows are the constants for the Michaelis-Menten equation.
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V
max=225±13(nkat*mg
-1)
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K
m = 25 ±4(mM)
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So, if the estimate v=V
max valid, the concentration of galactose is required to be over 100 K
m(2.5mol·L
-1) when v=0.99V
max.
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However, it is a concentration impossible to reach in vivo.
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However, we did not find constants for RIGDH measured in an environment similar to the in vivo one, which is explained by the instability of NADH in lower pH.
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And the K
m is 8.8 mM, K
cat is 13.5 U under pH 9.0 and 37℃
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According to the figure "Effect of pH on the activity of RIGDH", the activity of RIGDH is reduced to about 20%, consequently, we estimate K
cat to be 13.5 * 20% U under pH 6.5-7.0.
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We employed an optimization algorithm that contains initiation, target function calculation, iteration with mutation, and result evaluation.
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For initiation, we chose random distribution to initial the ratio of the enzymes. This initiation is done 50 or more times to create a group of particles, each representing a certain ratio. With this group of particles, we could achieve the effect of Particle Swam Optimization.
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Then we consider the concentration of tagatose in a pre-determined time as the target value.
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We iterate the ratio of enzymes in two ways. First, in a certain possibility, we made all of the particles move toward the best ratio in a recent situation. Otherwise, a random search is made to avoid being stuck to a local optimization.
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We iterate about 50 times and plot the ratio of every particle as a result. A single particle's ratio change and corresponding target value were also plotted for observation.
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