Team:Macquarie Australia/Modeling

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Basic Principle-

One of the aims of this project was to re-engineer E.coli to produce chlorophyll a which E.coli does not naturally produce. It produces heme which shares the same precursor as a chlorophyll a, Protoporphyrin IX (PPIX) (figure 1) (Willows, 2004). The PPIX pathway begins from aminolevulinic acid (ALA), which is produced naturally in E.coli but can be also be added to increase the production of PPIX (Willows, 2004).

Fig 1: Biosynthetic pathway from ALA to the first coloured intermediate protoporphyrin IX. a. ALA dehydratase; b. porphobilinogen deaminase; c. uroporphyrinogen III synthase; d. uroporphyrinogen decarboxylase; e. coproporphyrinogen oxidase; f. protoporphyrinogen oxidase (Willows, 2004) .

Our initial aim was to model the pathway from ALA to PPIX in native E. coli cells to determine what concentration of ALA would give us the optimal yield of PPIX. Ultimately, we (plan to) model the entire Chlorophyll a biosynthesis pathway, and the production of H2 gas (link to PSII model).

Mathematical Model Overview-

Michaelis-­Menten type enzyme kinetics were studied first prior to establishing appropriate parameters from reported literature to propose our models. The adopted kinetic equation was then used to determine enzyme concentration through first-hand experiments and then to create feedback on our model which contains an arbitrary amount of enzyme concentrations.

The initial velocity of the reaction (V_i) directly depends on the rate of the conversion of ES to P. It is also dependent on the total enzyme concentration (Keleti & Kramer, 1986). By using the following formula, the total enzyme concentration can be determined from the experimental values of V_i and S, which also corresponds to initial ALA concentration. (Keleti & Kramer, 1986)

Our Model

(use table)

• Abbreviations used-
• ALA -δ-aminolevulinic acid
• PPBS-porphobilinogen synthase
• PPB -porphobilinogen
• PPBD-porphobilinogen deaminase
• HMB-hydrymethylbilane
• UROS-uroporphyrinogen III synthase
• URO-uroporphyrinogen III
• UROD-uroporphyrinogen decarboxylase
• CPO-coproporphyrinogen
• CPOO-coproporphyrinogen oxidase
• POIX-protoporphyrinogen IX
• POO-protoporphyrinogen oxidase
• PPIX-protoporphyrin IX

In our modelling experiment, the initial concentration of ALA, [ALA]0, was used as a known independent variable while initial enzyme concentration, [E]0, was used as a dependent variable . We assumed that all the substrates and products had a concentration of 0 at time 0 sec (t=0). [ALA]0 was varied from 1mM to 5mM to 10 mM to 20mM. [E]0 was arbitrarily chosen in a realistic interval of 0.1 µM to 1 µM. This is the natural concentration of enzyme seen in E.coli . Moreover, we assume that there is no inhibition involved and that ALA to PPIX only follows this biosynthesis pathway. Should inhibition be involved it will significantly reduce or prevent PPIX production.

First model

In this model we considered the following reaction for ALA to PPIX transformation:

Table 1- Table displaying enzyme properties involved.

The above equations were used to obtain the following graphs via Matlab. The above equation was replicated for all the intermediates. In this equation, S1 denotes the substrate and S2 denotes the intermediate produced from that substrate. For example, for the first step of reaction, ALA to porphobilinogen, S1 denotes ALA and S2 denotes porphobilinogen. Again, for the following step of the reaction, porphobilinogen to hydroxymethylbilane, S1 denotes porphobilinogen and S2 denotes hydroxymethylbilane. This was done for the entire reaction cycle until PPIX production.

Graph 1: The above graph was plotted using initial ALA concentration of 1mM and 0mM of the remaining intermediates, enzyme and products involved. From the graph, it was observed that [ALA] became 0 at an accelerated rate and [PPIX] reached its peak value in approximately 0.7h . Combined values of Kcat for all the intermediates contribute to the time for formation of PPIX. This peak [PPIX] value was 1/8th of [ALA]0, which was expected as the conjugation of eight ALA molecules yields one protoporphyrin IX (PPIX) molecule(Wachowska et al., 2011).

Graph 2: This consists of graph 1 zoomed in to view the change in concentration of the intermediates involved at the initial stage of the reaction. PPB was the first intermediate produced, thus it appeared first and began to decrease as HMB was produced. As Uroporphyrinogen III synthase has a very high Kcat (500/s) , URO production from HMB was almost instant, hence, HMB was rapidly consumed.

From this, we performed our first experiment with measurements at time intervals of 5, 10, 20, 30, 60 and 120 minutes. However, no brown coloured solution was observed to indicate PPIX formation, which was also verified with nanodrop absorbance readings.

Based on this, we constructed a second model taking into account the intermediates consisting of enzyme complexes.

In order to quantify the number of enzymes involved in the ALA to PPIX pathway, we measured the concentrations for each of the pathway’s intermediates.

The E. coli cultures were grown overnight with shaking at 300 rpm at 37°C. The cells were harvested by centrifugation, supernatant discarded. The cells were resuspended in 5 mL of 0.1 mM glucose in 1 mM ALA, then incubated in the dark for 14 days. Approximately 250 uL of cells were extracted each time over 24 hour intervals, and lysed with lysis buffer and neutralized with neutralization buffer (Sigma plasmid prep kit). The precipitates were separated by centrifugation for 10 mins, and the absorbance of the supernatant measured with the nanodrop (Thermoscientific Nanodrop 2000 spectrophotometer). The absorbance maxima of PPIX is 404 nm.

Second Model-

When the intermediates (enzyme complexes) were added, the following reactions were obtained:

The first reaction was translated into a mathematical equation to give:-

The second mathematical model was then based on these equations.

Fig 2 : 2 ALA molecules combine to produce 1 PPB molecule. 4 PGB molecules form 1 HMB molecule (Ryter & Tyrrell, 2000).

The stoichiometric relationships displayed in figure 2 were introduced into matlab and used to obtain the following graph:

Graph 3: This graph was obtained with 1mM [ALA]0 and 0.1 µM of initial enzyme concentration. [PPIX] reached its peak after approximately 7 days. From our first experiment, a significant concentration of PPIX was observed after 1 week. After a further 2 weeks, [PPIX] was found to reach its peak (shown in experimental part).

The second experiment

The second experiment enabled us to examine the effect of cell concentration on PPIX production. It was initially speculated that the intracellular and extracellular concentration of ALA was consistent, and our model assumed that the cells occupied the entire space. That is, we assumed that the added ALA solution enters directly into the cells, which is not the case. Thus, we took this into consideration and remodeled our code to take into account the fact that cells only occupy a certain percentage of the total volume. Here are the explanations:

Notations:

• 1 =solution with which we resuspended cells (ALA)
• 2=cells
• Vi=volume of the media i
• V=volume total = V1 + V2
• xvol=proportion of cells in the media
• Ci(t)=i concentration at t
• ni(t)=molar quantity of the media i at t
• de=molar quantity which enter in cells between t and t+dt
• dc=molar quantity which is consumed between t and t+dt
• We know dc and we want to find de knowing that C1(t) = C2(t) at any time:


Thereby, we obtained the following graph with an enzyme concentration of 0.3 µM by taking into account of the above cell percentage:





Graph 4- Concentrations of product and intermediates produced over time using enzyme concentration of 0.3 µM, 1mM initial ALA concentration and considering effects of cell concentration.




Experiments

The importance of gaining feedback on models and testing the influence of several parameters cannot be overstressed. It was observed from first hand experiments that altering some key factors could significantly increase the production of PPIX.




With this in mind, several experiments were performed with the aim of optimising the production of PPIX. The initial experiment involved the resuspension of our E.coli cells in a solution of 1mM ALA. The formation of PPIX is indicated by a colour change from clear to brown which took approximately one week before the first traces of PPIX were observed. Several assumptions were made and then new experiments were carried out with slight changes to the original experiments including a decrease in cell concentration, varying the ALA concentration and the addition of zinc and magnesium to the cell culture.




FIRST EXPERIMENTS (16/07-29/07)

Protocol1

Tools:

• LB Media (250 mL)
• E.coli cells
• lysis solution (200 µL doses)
• Binding buffer (350 µL doses)
• 0.1 mM glucose in 1 mM ALA (5 mL)

Methods:

In order to quantify the number of enzymes involved in the ALA to PPIX pathway, we measured the concentrations for each of the pathway’s intermediates.




The E. coli cultures were grown overnight with shaking at 300 rpm at 37°C. The cells were harvested by centrifugation, supernatant discarded. The cells were resuspended in 5 mL of 0.1 mM glucose in 1 mM ALA, then incubated in the dark for up to 14 days. 250 uL of cells were extracted each time over 24 hour intervals and lysed with lysis buffer (Sigma plasmid prep kit) and neutralized (buffer). The precipitates were separated by centrifugation for 10 mins, and the absorbance of the supernatant measured with the nanodrop (Thermoscientific Nanodrop 2000 spectrophotometer). The absorbance maxima of PPIX is 404 nm.




Results



Graph 5- PPIX was observable after approximately one week of incubation and continued to increase for a further 6 days. The theoretical absorbance value for a complete conversion of ALA to PPIX was calculated to be 2.0625. At 14th day, 2.0625 mM concentration of PPIX was produced.




As a result of conducting these experiments, an approximation for the time needed to produce a significant quantity of PPIX was established which is 14 days. Optimal concentration of PPIX was produced in 14 days. Considering the first traces of PPIX were detected 1 week after the beginning of the experiment, several possible optimisation strategies were examined:



• Cell concentration - oxygen is a key requirement for this pathway. If the current oxygen levels were maintained while reducing the quantity of the cells that are present, more oxygen is available for each cell and could increase the rate of the reaction.
• ALA concentration - the substrate concentration greatly influences the final concentration of the product. By varying the concentration of ALA, an optimum value can be determined for the production of PPIX.
• Addition of Zinc, Magnesium and PBS - ALA dehydratase catalyzes the first step of the PPIX biosynthesis from ALA. It exists mainly as a high activity octamer or a low activity hexamer (Lawrence, Ramirez, Selwood, Stith, & Jaffe, 2009). Magnesium acts as an allosteric regulator of ALA dehydratase and contains a binding site only in the octamer. As well as this, it has been demonstrated that the absence of magnesium promotes the formation of these low activity hexamers (Breinig et al., 2003) However, ALA dehydratase purifies with eight Zn2+ ions per octamer(Jaffe, Martins, Li, Kervinen, & Dunbrack, 2001).
• This suggests that the addition of both zinc and magnesium would promote the formation of the more active octamers and hence increase the rate of the first step of the PPIX biosynthesis
• Perform an in vitro experiment: this allows us to check the assumption [ALA]int = [ALA]ext
  
  

SECOND EXPERIMENTS (from 03/08)

Protocol2

Tools:

• LB Media (250 mL)
• E.coli cells
• Lysis solution (20 µL)
• ALA (20 mM)
• glucose (20 mM)
• PBS solution
• ZnCl2 (10 µM)
• MgCl or MgSO4 (2 mM)

Methods:

As performed in protocol 1, we measured the concentrations for each of the pathway’s intermediates to quantify the number of enzymes involved in the ALA to PPIX pathway.

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The E. coli cultures were grown overnight with shaking at 300 rpm at 37°C. The cells were harvested by centrifugation, supernatant discarded. The cells were resuspended in a solution of PBS(to define), Zinc(10µM) and Mg(2mM), then incubated in the dark for up to 19 days. The cultures were adjusted to an OD of 0.2 and 0.02 to observe the effect of cell concentration on PPIX output. Four concentrations of ALA were tested against these conditions as follows:





Approximately 25 uL of cells were extracted each time over 24 hour intervals, and lysed with lysis buffer (20 uL) (Sigma plasmid prep kit) and neutralized (neutralisation buffer). The precipitates were separated by centrifugation for 10 mins and the absorbance of the supernatant measured with the nanodrop (Thermoscientific Nanodrop 2000 spectrophotometer).




Results



Graph 6 - Shows concentration of PPIX produced from various initial concentration of ALA for E.coli cell culture of 0.2mM concentration. For 5 mM of initial ALA concentration most PPIX was produced which is due to substrate inhibition (shown in figure 2 below).





Graph 7 - Shows concentration of PPIX produced from various initial concentration of ALA for E.coli cell culture of 0.02mM concentration. For 5 mM of initial ALA concentration most PPIX was produced which is due to substrate inhibition (shown in figure 2 below).




Discussion

5mM of initial concentration of ALA produced optimum concentration of PPIX. This is due to substrate inhibition where Protoporphyrinogen IX inhibits conversion of ALA to porphobilinogen via porphobilinogen synthase (Stamford, Capretta, & Battersby, 1995).




Moreover, change in concentration of cells did not change the production of PPIX ensuring oxygen availability did not affect the PPIX production that much. Adding of glucose resulted a little increase in PPIX production which ensured. Hence, we can say that it doesn’t affect PPIX production that much.A little difference was seen between experimental PPIX formation and predicted PPIX formation. We predicted formation of 0.12 mM PPIX (shown in Graph 1) form 1 mM ALA but only 0.065 mM PPIX was produced experimentally (shown in Graph 7 ).



Fig 3- Protoporphyrinogen IX inhibiting conversion of ALA to porphobilinogen via porphobilinogen synthase (Stamford, Capretta, & Battersby, 1995). This is a process of substrate inhibition which allows a certain concentration of ALA to produce optimum amount of PPIX which in our case was 5mM (Stamford, Capretta, & Battersby, 1995).




Conclusion

Our experiments enabled us to get a better understanding of how the pathway from ALA to PPIX worked. Substantial amount of PPIX was produced from ALA and the ratio of ALA:PPIX concentration produced was 1:8 as expected (Wachowska et al., 2011). ALA seemed to pass through the membrane passively. As no excess energy was needed to introduce ALA to E.coli. Oxygen availability did not have a massive impact on the PPIX production as change in concentration of cells did not affect the concentration of PPIX produced. Moreover, due to substrate inhibition, 5mM initial ALA concentration produced higher concentration of PPIX compared to other concentrations. We didn’t find the enzyme concentration as we expected as the experiments were too long and we didn’t have time to measure other concentration such as those of the intermediates





References

• Alwan, A. F., Mgbeje, B., & Jordan, P. M. (1989). Purification and properties of uroporphyrinogen III synthase (co-synthase) from an overproducing recombinant strain of Escherichia coli K-12. Biochem. J, 264, 397-402.
• Boynton, T. O., Daugherty, L. E., Dailey, T. A., & Dailey, H. A. (2009). Identification of Escherichia coli HemG as a novel, menadione-dependent flavodoxin with protoporphyrinogen oxidase activity. Biochemistry, 48(29), 6705-6711.
• Breckau, D., Mahlitz, E., Sauerwald, A., Layer, G., & Jahn, D. (2003). Oxygen-dependent coproporphyrinogen III oxidase (HemF) from Escherichia coli is stimulated by manganese. Journal of Biological Chemistry , 278(47), 46625-46631.
• Breinig, S., Kervinen, J., Stith, L., Wasson, A. S., Fairman, R., Wlodawer, A., . . . Jaffe, E. K. (2003). Control of tetrapyrrole biosynthesis by alternate quaternary forms of porphobilinogen synthase. Nature Structural & Molecular Biology, 10(9), 757-763.
• Camadro, J.-M., Matringe, M., Scalla, R., & Labbe, P. (1991). Kinetic studies on protoporphyrinogen oxidase inhibition by diphenyl ether herbicides. Biochem. J, 277, 17-21.
• Dixon, J. M., Taniguchi, M., & Lindsey, J. S. (2005). PhotochemCAD 2: A Refined Program with Accompanying Spectral Databases for Photochemical Calculations¶. Photochemistry and photobiology, 81(1), 212-213.
• Jaffe, E. K., Martins, J., Li, J., Kervinen, J., & Dunbrack, R. L. (2001). The molecular mechanism of lead inhibition of human porphobilinogen synthase. Journal of Biological Chemistry, 276(2), 1531-1537.
• Keleti, T., & Kramer, M. (1986). Basic enzyme kinetics: Akademiai Kiado Budapest.
• Lawrence, S. H., Ramirez, U. D., Selwood, T., Stith, L., & Jaffe, E. K. (2009). Allosteric inhibition of human porphobilinogen synthase. Journal of Biological Chemistry, 284(51), 35807-35817.
• Maneli, M. H., Corrigall, A. V., Klump, H. H., Davids, L. M., Kirsch, R. E., & Meissner, P. N. (2003). Kinetic and physical characterisation of recombinant wild-type and mutant human protoporphyrinogen oxidases. Biochimica et Biophysica Acta (BBA)-Proteins and Proteomics, 1650(1), 10-21.
• Ryter, S. W., & Tyrrell, R. M. (2000). The heme synthesis and degradation pathways: role in oxidant sensitivity: heme oxygenase has both pro-and antioxidant properties. Free Radical Biology and Medicine , 28(2), 289-309.
• Stamford, N. P. J., Capretta, A., & Battersby, A. R. (1995). Expression, purification and characterisation of the product from the Bacillus subtilis hemD gene, uroporphyrinogen III synthase. European Journal of Biochemistry , 231(1), 236-241.
• Willows, R. (2004). Chlorophylls.
• Wachowska, M., Muchowicz, A., Firczuk, M., Gabrysiak, M., Winiarska, M., Wańczyk, M., . . . Golab, J. (2011). Aminolevulinic acid (ALA) as a prodrug in photodynamic therapy of cancer. Molecules, 16(5), 4140-4164.

PHOTOSYSTEM II