Enzyme kinetics

The reason for creating an enzyme kinetic model is to determine the limiting factors in our system to progress the optimization of the production of psilocybin as well as N-terminal modifications of PsiH and CPR tertiary conformational changes prediction in respects to their active sites

In order to create an enzyme kinetics model of the system, the rate constant for the enzymes, the initial concentration of the substrates, and the rate constant for synthesis of substrates were found by reviewing literature. The different values for the substrates and enzymes, can be found in tables 1 and 2 below.

Initial concentration and synthesis rate constant for the substrates

Substrate Initial concentration Rate constant (Km) for the synthesis/diffusion of the substrate
Adenosine triphosphate (ATP) 3 mM 0.226 mM/s
L-tryptophan 3.305 mM 0.31 mM/s
S-adenosyl-L-methionine (SAM) 1 mM 0.12 mM/s
Oxygen 0.25 mM 0.0002 mM/s

Table 1: Shows values for the initial concentration and rate constant for the synthesis of the corresponding substrates.

Rate constant for the enzymes

Enzyme Rate constant (Km)
PsiD 0.729 mM/s
PsiH 0.22 mM/s
PsiK 0.08 mM/s
PsiM 0.165 mM/s

Table 2: Shows values for the rate constants for the four enzymes involved in the biosynthesis of psilocybin.

Modeling Assumptions

While establishing the enzyme kinetic model, different assumptions had to be made. The different assumptions for each value are described in the accordions below.

Initial substrate concentrations

The intracellular ATP concentration of E. coli is reported to be within the interval of 1-5 mM, which is dependent on different environmental factors. We decided to go with an initial concentration of 3 mM in the model, since it is the mean of the interval. [1]

The initial concentration of L-tryptophan is estimated to be 3.036 mM, since literature shows that the L-tryptophan concentration is 0.620 g/L. This is divided by the molecular mass of L-tryptophan, which is 0.20422 g/mmol. [2]

The S-adenosyl-L-methionine concentration is between 1 uM to 10 mM. We decided to use an initial concentration of 1 mM S-adenosyl-L-methionine for our model. [3]

The initial concentration for our system is assumed to be the same as the oxygen concentration in water, which is estimated to be 8 mg/l which corresponds to 0.25 mM. [4]

Rate constants for substrate production

The production of ATP within E. coli has a rate constant of 0.226 mM/s. [5]

The rate constant for the production of L-tryptophan is based on the L-tryptophan synthase in Escherichia coli, which is 0.31 mM/s. The natural use of L-tryptophan is assumed to be equal to the level of L-tryptophan regulated within the E. coli, which means that we assume that our system effectively has the natural rate of L-tryptophan production to use for the reactions. [6]

The rate constant for the production is chosen as a constant flux into the cell at 0.12 mM/s which is from the MetK/MAT enzyme which functions to produce S-adenosyl-L-methionine. The MetK/MAT enzymes originates from E. coli. The rate constant for the consumption of S-adenosyl-L-methionine for other uses is assumed to be as high as what cell regulates. [7]

The rate constant for diffusion into the cell is chosen to be the same as the rate constant for Seawater equilibrium at 25 °C which is 0.0002 mM/s. This value is comparable with the rate constant for the oxygen utilization for aerobic bacteria isolated from marine environments. Diffusion of oxygen out of the cell depends on the systems oxygen usage. Since our system require a relatively high concentration of oxygen, it can be assumed that the oxygen diffusion out of the cell is not very significant. [8]

Rate constants for PsiD/H/K/M

The rate constant for PsiD is assumed to be the same as Ornithine decarboxylase, which is from the organism Capsicum annuum. This organism is not closely related to Psilocybe cyanescens, which could bring an uncertainty to the model. The rate constant is 0.729 mM/s. [9]

The rate constant for this enzyme has yet to be determined. Instead, we use a rate constant of 0.22 mM/s, which is from another cytochrome p450 complex, namely P450BM-3, which uses the substrate Propylbenzene. [10]

The rate constant for this enzyme in psilocybe cyanescens is determined to be 0.08 mM/s. [11]

The rate constant for this enzyme is taken Histone-lysine N-methyltransferase SETD7 in humans. Both enzymes methylate amine. The rate constant for Histone-lysine N-methyltransferase SETD7 is 0.165 mM/s. [12]

Enzyme Kinetics Model

Figure 1: The enzyme kinetics model used to simulate our system.

Based on the substrates and products of PsiD/H/K/M, an illustration of the enzyme kinetics model used to predict psilocybin production is made, which can be seen in figure 1. Note that a lot of our values for initital concentration and rate constants are based on assumtions, which means that the model will deviate a lot from practical reality.

Enzymatic plot

The initial concentrations and rate constants from table 1 and 2 were used to generate plots of the substrates, the intermediates, and the product, psilocybin, over a period of 160 seconds. The reason for 160 seconds is to illustrate some of the limiting factors within our system, according to our enzyme kinetic model. Some of these plots are shown in figure 2 through 6.

Figure 2: Shows the enzyme kinetic plot with the values from table 1 and 2 over a time period of 160 seconds with the intent of investigation the systems dependency on oxygen.

The plot from figure 2 indicates that oxygen might be a limiting factor in our system, since low levels are observed for both oxygen and 4-Hydroxytryptamine, and the production of this intermediate is dependent on oxygen.

Figure 3: Shows the enzyme kinetic plot with the values from table 1 & 2 over a time period of 160 seconds with unlimited oxygen levels.

Figure 3 illustrates our model when there is an overabundance of oxygen within the cell. This is to determine if unlimited oxygen would yield a higher production of psilocybin during the 160 seconds time frame. And between this model and the one from figure 2, the production of psilocybin increases from 0.10 mmol/L to 0.15 mmol/L, which is a 50 % increase in the production of psilocybin. This shows the potential for optimizing the diffusion of oxygen into the cell to increase the yield of psilocybin. However, this percentage can change with different time frames, since the concentrations of the substrates and intermediates are closer to reaching equilibrium after 1 hour as opposed to 1 second.

Figure 4: Shows the enzyme kinetic plot with the values from table 1 and 2 over a time period of 3600 seconds for the enzymatic production of psilocybin with both unlimited and normal oxygen.

When plotting the enzyme kinetics model with a 3600 second time frame, the substrates and intermediates are closer to reaching equilibrium than when plotting with a 160 second time frame, and in figure 4, the production of psilocybin is seemingly linear after approximately 540 seconds. Although, after calculating and plotting the fold increase between the production of psilocybin with normal and unlimited oxygen, it is clear that the production is not entirely linear yet. With a fold increase of more than 7 after 1 hour, we can determine that increasing the oxygen concentration within the cell will increase the production of psilocybin.

Therefore, we wanted to find a way of optimizing the oxygen levels. This is what our hardware part is designed for, which can be accessed through the link above

Figure 5: Shows the enzyme kinetic plot with the values from tables 1 and 2 over a time period of 300 seconds with the intent of investigation of L-tryptophan concentration.

We also wanted to determine if the cells natural concentration of L-tryptophan would be a limiting factor. Figure 5 is plot of our enzyme kinetics model with a 300 second time frame, where the curve for L-tryptophan concentration is depicted. From figure 5, we have determined that L-tryptophan is not a limiting factor within our system since the equilibrium concentration is higher than the intermediates and does not move towards zero.

Figure 6: Shows the enzyme kinetic plot with the values from table 1 and 2, unlimited oxygen, and a 160 second time frame to investigate other potentially limiting factors within our system.

Another concern was if perhaps one of the enzymes are limiting the production of psilocybin. The plot in figure 5 is made with the same data as from figure 3, that being with unlimited oxygen and with a timeframe of 160 seconds, except all the intermediates, psilocybin, L-tryptophan and S-adenosyl-L-methionine are shown here. Even with unlimited oxygen L-tryptophan isn’t fully depleted while the concentration of tryptamine steadily increases. There is an abundance of 4-hydoxytryptamine-4-phosphate and S-adenosyl-L-methionine, with relatively little Psilocybin being produced, which indicates that the enzyme PsiM is likely a limiting factor. 4-Hydroxytryptamine is also at very low concentration, which indicates that either the enzyme PsiH is a limiting factor, or that PsiK is very efficient at catalyzing the transfer of phosphate from ATP to 4-Hydroxytryptamine.

Protein structure prediction of PsiH and CPR

Since we wanted to modify the N-terminals of PsiH and CPR, because it acts as an anchor to the endoplasmic reticulum which bacteria doesn’t have, it is likely that the modification may change the tertiary structure and the active sites of the proteins.

Figure 7: Shows the predicted PsiH enzyme from RoseTTAFold.

To predict the tertiary structures of the proteins we used RoseTTAFold. RoseTTAFold is a program that can use the amino acid sequence to predict the tertiary structure of an enzyme. Illustrations of this can be seen below on figure 7 and 8 with the predicted structure of PsiH from RoseTTAFold.

Figure 8: Shows the alignment between PsiH Wildtype and PsiH with N-terminal modification 4. Red indicate a low Qres score, and blue indicate a high Qres score.

We aligned the different predicted proteins structures with modification to their respective predicted Wildtype in VDM, to see their structural differences. An example of this can be seen in figure 8.

Figure 9: Illustrates the Qres scores for the alignment between the PsiH wild type and the PsiH with N-term. 4. Qres score on the y-axis and the amino acid residue on the x-axis.

It is difficult to pinpoint the exact location and alignment score in figure 8. Therefore, figures 9 and 10 were made to show the Qres alignment scores between PsiH Wildtype and PsiH N-terminal modification 4 and between CPR Wildtype and CPR N-terminal modification 6. The Qres alignment score can be determined by the score on the Y-axis and the amino acid residue on the X-axis. The Qres alignment score indicates the similarity between the tertiary structure of two enzymes. Within a region of two enzymes, a Qres score of 1 means the structural alignment is identical and a Qres score of 0 indicates that the structural alignment is extremely different.

Figure 10: Illustrates the Qres scores for the alignment between the CPR Wild type and the CPR with N-term. 6. Qres score on the y-axis and the amino acid residue on the x-axis.

From the Qres scores in figures 9 and 10, there are a few structural differences within the tertiary structures of the proteins from RoseTTAFolds predictions. The lowest Qres scores are at the approximate residue intervals 280-290 and 550-560 for PsiH N-term. 4 and CPR N-term. 6. However, the question remains of whether or not these structural differences is at the active site.
The active sites of PsiH and CPR is not known in UniProt. Therefore, we decided to align different 4-monooxygenase and different cytochrome P450 reductase from UniProt to find their active site. This is under the assumption that the active sites of different 4-monooxygenase and different cytochrome P450 reductase are relatively conserved compared to the rest of their amino acid sequence. The alignment of PsiH with different 4-monooxygenase and alignment of CPR with different cytochrome P450 reductase can be seen in figure 11 below.

Figure 11: Shows the alignment from UniProt of PsiH with different 4-monooxygenase and CPR with different cytochrome P450 reductase. Green color indicates the assumed active site. Orange color indicates the amino acid residues where a low Qres value was seen within the Qres score from figures 9 and 10. Stars indicate the same amino acid is present for all of the sequences and dots indicate a slight variation in amino acid.

From figure 11 we see the alignment of different 4-monooxygenase and different cytochrome P450 reductase. Orange color indicates were Qres score of PsiH N-term. 4 and CPR N-term. 6 is low, meaning that a change in the tertiary structure is predicted. Green color indicates where we assume the active site of the enzyme is. PsiH N-term. 4 does not seem to have its tertiary structure changed much at the active site, however, CPR N-term. 6 have its tertiary structure changed at the active site, which might decrease its enzymatic function.

The above folding prediction, alignment and analysis is an example of the steps one could take to determine if a N-terminal modification is interfering with the active site or not.

This table shows which N-terminal modifications is conserved within their assumed active sites and which modification is predicted to change within the active sites. As the table shows, most of the modified versions of PsiH seem to be conserved in what has been estimated to be the active site except from PsiH N-term. 10, which therefore was excluded from the process. It appears to be very differently when looking at CPR, in which one the two known catalytic domains consequently change a result of the modification in each case. The fact that CPR is much more sensitive might be due to the fact that this enzyme is much better characterized making it easier to point out the active sites in contrary to PsiH. Using PubMed, the flavodoxin-like and FAD-binding FR-type domains could be found and used as a reference. The different N-terminals can be found under Experiments- introduction


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