# MODELING

Predict and optimize yield

### Background

The purpose of modeling is to carefully examine the pathways of each intended biosynthetic product, look for ways to optimize production, and understand limiting factors. To accomplish these goals, we used available metabolic pathways for our target organism, and evaluated several different methods to model production of acetaminophen and B_{12} in cyanobacteria. Each of these modeling methods has different assumptions which allow these data to be averaged; providing reasonable quantitative estimates of our biosynthetic products.

### ACETAMINOPHEN

## Acetaminophen Overview

To predict acetaminophen biosynthesis, we analyzed the abundance of the acetaminophen's precursors anthranilate and PABA. Anthranilate comes from chorismate, which is primarily used by the cell to produce the aromatic amino acids phenylalanine, tyrosine, tryptophan, and folate^{[1]}. We used publicly available tryptophan and folate concentrations, estimations from genomic sequences, and ribosomal protein sequences to estimate the amount of precursor available to be made into acetaminophen. Combining this information with enzyme kinetics, we were able to model how much product would be produced per gram biomass of *Arthrospira platensis*. Our results indicate that a backyard culture could produce 200 doses of acetaminophen every 10 days.

*4ABH*metabolize folate precursor PABA and tryptophan precursor anthranilate to make 4-aminophenol which is then processed by

*nhoA*to make acetaminophen, top right.

## Method using Published Tryptophan Data

We used published tryptophan and folate concentration data for *A. platensis* to calculate the moles of the acetaminophen precursors per gram dry mass^{[7,8]}. Tryptophan and folate precursors anthranilate and PABA are the substrates for our enzyme *4ABH*, which converts those precursors to 4-aminophenol before *nhoA* finishes the conversion to acetaminophen. We show several different calculations below using different sources of data.

## Assumptions

- We assumed an even split of precursor at the branch points of PABA and anthranilate, even though enzyme K
_{m}s will affect the amount of precursor going down each pathway. - We assumed the moles of anthranilate produced are equal to the moles of tryptophan, because at least as many moles of anthranilate must be present to make the same ammount of moles tryptophan.
- We assume that folate occurs in such small amounts, coming from 0.21nM of PABA, that its effect on acetaminophen production is neglegible
^{[7]}.

$$\frac{0.442\ µmol\ Trp}{1g\ biomass}\approx \frac{0.442\ µmol\ anth}{1g\ biomass}\times\frac{1\ mol\ acet}{3\ moles\ anth}\times\frac{151g\ acet.}{1 mol acet.}=\frac{2.3mg\ acet.}{1g\ biomass}$$

*Arthrospira platensis*gives us an approximation for acetaminophen's precursor anthranilate (anth.). The starting mass of tryptophan is the average of two literature values for tryptophan concentration

^{[7,8]}and assuming one third of the anthranilate precursor goes to our inserted enzyme,

*4ABH*.

## Sequence Analysis Method

To validate our organism's quantity of tryptophan precursor, we used a custom Python program^{[9]} to convert DNA sequences to amino acids and calculate molar and mass percentages of tryptophan, which can be used to estimate the abundance of the acetaminophen precursor.

## Assumptions

- Using the entire genome sequence to approximate the cellular amino acid composition assumes each codon is expressed in equal concentrations. This does not account for some proteins being less expressed and the resulting skew in amino acid composition.
- Using the ribosomal sequences assumes that the genes encoding ribosomal proteins are representative of the total cellular amino acids ratio.
- The amount of anthranilate and PABA precursors produced are equal to that of their products tryptophan and folate.
- Of the available precursors, one third will go down our pathway. This is based off the idea that the enzymes may have similar affinities for the precursors.
- We assumed that folate occurs at a concentration of 0.21nM,
^{[7]}and comes from at least as many moles of PABA. Thus the small PABA concentration will be neglegible to the total acetaminophen produced.

## Sequence Analysis Details

We ran both the genome and all 55 listed ribosomal protein sequences through a custom Python program, which counted the instances of each amino acid in the sequence, totaled the mass, and calculated the percent tryptophan relative to total mass ^{[4]}. This program showed that tryptophan is 0.9% and 0.6% of total protein for the genome and ribosomal proteins respectively.

$$\frac{0.9\ g\ Trp}{100\ g\ cell\ protein}\times\frac{0.6\ g\ cell\ protein}{1\ g\ biomass}=\frac{0.054\ g\ Trp}{1g\ biomess}$$

^{[7]}. The percentage mass of Trp relative to cellular protein was converted to grams of trp per gram dry biomass.

$$\frac{0.054\ g\ Trp}{1\ biomass}\rightarrow\frac{0.27\ mmol\ Trp}{1\ g\ biomass}\times\frac{1\ mol\ acet}{3\ mol\ Trp}\times\frac{151.163g\ acet}{1\ mol\ acet.}=\frac{13.7mg\ acet.}{1g\ biomass}$$

$$\frac{0.6\ g\ Trp}{100\ g\ cell\ protein}\times\frac{0.6\ g\ cell\ protein}{1\ g\ biomass}=\frac{0.036\ g\ Trp}{1g\ biomess}$$

^{[7]}. The percentage mass of trp relative to cellular protein was converted to grams of trp per gram dry biomass.

$$\frac{0.036 g\ Trp}{1 g\ biomass}\rightarrow \frac{0.175\ mmol\ Trp}{1\ g\ biomass} * \frac{1\ mol\ acet}{3\ mol\ chor} *\frac{151.163\ g}{1 mol\ acet} = \frac{8.8\ mg\ acet}{1 g\ biomass}$$

^{[10].}

## Enzyme Competition

Besides precursor concentrations, the next limiting factor would be how effective our enzyme *4ABH* is at converting precursors from the tryptophan and folate pathways into 4-aminophenol. We can either assume all three competing enzymes will have similar precursor affinity and produce all three products in equal quantities or use ratios of competing enzymes K_{m}s for the limiting intermediates. To make up for unknown enzyme rates and quantities, we made a chorismate metabolic simulation. Since the simulation used data based on K_{m}s from completely different organisms, this enzyme kinetics comparison will be left for later troubleshooting. For that reason, all of the previous calulations were computed using a one third precursor to acetaminophen conversion rate.

## Assumptions

- We assume that our genes were designed, inserted, and translated successfully and in non-limiting quantities.
- We assume K
_{m}values for*Arthrospira platensis*are the same as other organisms' enzyme K_{m}s. - We assume that enzyme rate and quantity is the same for each
*4ABH, folp1, and TrpD*, else we could not compare K_{m}ratios and calculate approximate the K_{m}of*4ABH*for anthranilate.

## Acetaminophen Conclusion

These numbers show that there will probably be enough precursor to produce a useful, detectable quantity of acetaminophen. Based on literature and sequence estimates of tryptophan, we can assume there would be at least that many moles of anthranilate precursor for our inserted pathway to push towards acetaminophen. The three calculations above can be averaged to finally predict 8.26mg ± 2.77mg acetaminophen per gram of *Arthrospira platensis* biomass or 8.26µg per mL. This would be significantly above the limit of detection for our HPLC, at 50ng per ml, and serve as a starting point for optimizing production. This means that one 325mg dose of acetaminophen could be obtained in ~39g of biomass, meaning a 3 by 12 foot round pool could produce enough acetaminophen for more than 200 doses every 10 days. While 39 grams isn't an ideal amount of medicine to consume, it does show that *Arthrospira platensis* has significant potential as a molecular factory for acetaminophen.

### VITAMIN B_{12}

The quantity of DMB B_{12} produced depends on a successful production and integration of the active B_{12} lower ligand, composed of 5,6-dimethylbenzimidazole (5,6-DMB) and α-ribazole 5’-phosphate. For cyanobacteria in the wild, cobalt is often the limiting factor for growth and production of B_{12}^{[26,27]}. Both *ssuE* and *bluB* genes are engineered to be regulated using a strong PtrC promoter, creating an abundance of the activating portion of the lower ligand, 5,6-DMB. Due to the abundant synthesis of 5,6-DMB, it should not act as the limiting factor for DMB B_{12}^{[25]}. *Synechococcus elongatus* PCC 7942 and *Arthrospira platensis* C1 both have the *cobS* gene which codes for a protein that binds the α-ribazole within the 5,6-dimethylbenzimidazolyl nucleotide moiety to the cobalt-containing adenosylcobinamide-GDP complex^{[14,15]}. Previous research involving the DMB B_{12} pathway suggests that a lower ligand constructed with 5,6-DMB has a 100 fold higher binding affinity for cobalt than that of one constructed with adenine^{[16, 17, 27]}. Due to the high binding affinity and abundance of 5,6-DMB as a lower ligand when compared to adenine, we assume a 100:1 ratio for DMB B_{12} to adenine B_{12}; for every 100 active DMB B_{12} synthesized, there will be 1 inactive adenine B_{12} synthesized.

$$\frac{2.5µg\ B_{12}\ analog}{1g\ drymass} * \frac{100\ DMB\ bindings}{100\ DMB\ bindings+1\ adenine\ binding} = \frac{2.47µg\ DMB\ B_{12}}{1g\ biomass}$$

_{12}analogs to active DMB B

_{12}. This equation assumes the cobalt binding affinity ratio of

*cobS*for DMB and adenine in

*Arthrospira platensis*are the same as their orthologs present in the researched

*Propionibacterium freudenreichii*.

## Assumptions

- Cobalt is the primary limiting factor of DMB B
_{12}synthesis^{[11,12]}. - The PtrC promoter is a strong promoter in
*S. elongatus*7942^{[25]}. - Gene inserts will be expressed, oxidizing FMN to FMNH
_{2}, then catalyzing the synthesis of 5,6-DMB in excess^{[13]}. - The
*cobS*protein in*A. platensis*will attach the α-ribazole part of the 5,6-DMB lower ligand to cobalt-containing adenosylcobinamide-GDP complex at rates similar to those assayed in*Propionibacterium freudenreichii*^{[14,15]}. - Cobalt will be provided in excess of 0.3mM according the BG-11 recipe, ensuring maximum precursor availability
^{[16,17]}. - There will be a 100:1 conversion of inactive adenine B
_{12}analogs to active DMB B_{12}given the 100 fold higher binding affinity for 5,6-DMB as a lower ligand^{[16, 17, 27]}.

## B_{12} Conclusion

Published HPLC results show that *Arthrospira platensis* produces between 1.5-2.5µg B_{12} analogs per gram dry weight^{[18]}. Considering the assumed ratio for conversion of B_{12} analogs to DMB B_{12}, we predict 1.49-2.47µg DMB B_{12} per gram dry weight of our engineered *A. platensis*, thus meeting the USDA’s recommended daily value of 6µg in one 2-4g serving.