We have chosen to use Pseudomonas sp. as a chassis organism due to its rapid and abundant colonisation abilities within the rhizosphere. To ensure Pseudomonas sp. can colonise effectively, the metabolic load and resource drain of our system on the cell must be kept to a minimum in order to conserve natural homeostasis and minimise waste. As our system utilises enzymes found in flavonoid production, our naringenin synthesis pathway will be most taxing on resources used to maintain the natural homeostasis of flavonoid pathways. Some of these resources (ATP, CoA and Malonyl CoA, for example) are included but not restricted to flavonoid production. If we are to program a cell to produce an amount of naringenin per unit time, we need to consider what range of output works best in terms of maintaining the cells homeostasis.

On top of maintaining the cells homeostasis, sufficient naringenin needs to be produced by the pathway to attract the desired nitrogen fixing bacteria. The results of our chemotaxis experiments and previous research have shown higher concentrations of naringenin to inhibit growth of multiple soil microbes (1). It is therefore important that production by our system is stable in variable environmental conditions such that there are no detrimental effects on the rhizosphere community. By creating an enzymatic model of the pathway, we aimed to alter the operon design in order to minimise resource drain and stabilise naringenin production as a means of increasing system optimisation and robustness.

The chemotaxis modelling and wetware element to our project characterise the production rate of naringenin required for chemotaxis to occur. When the production rates of naringenin by our endophytic chassis have been characterised, the pathway model will give us the tools to alter the operon in order to optimise production.

Naringenin, our chemoattract of choice, is synthesised from L-tyrosine via the enzymatic action of tyrosine ammonia lyase (TAL), 4-coumarayl ligase (4CL), chalcone synthase (CHS) and chalcone isomerase (CHI) (Figure1). These four enzymes are contained within the iGEM part BBa_1497017. Within this part all four enzymes are under the control of a single strong T7 promoter (BBa_I712074), with each enzyme having the same strong RBS (BBa_B0034). This system gives equal expression of each of the four enzymes. Previous research has identified that changing relative expression of each enzyme in the pathway improved naringenin production (2). We intended to optimise our system by using a model to explore how we could redesign the operon in order to maximise flux through the pathway whilst minimising resource consumption and waste.

The model was built on Matlab using differential equations which employ mass action kinetics to describe the behaviour of reactants and products for each reaction step. Mass action kinetics describes the behaviour between a substrate and reactant as an equation where the velocity or rate of a chemical reaction is directly proportional to the concentration of the reactants. These kinetics are used for substrate binding in which substrate and enzyme diffuse towards each other to dimerise via the formation of a covalent bond, and catalysis in which the covalent bond breaks to produce two or more products (excluding the reverse reaction of substrate binding which represents failed substrate binding).

Mass Action kinetics are used due to the fact that we have not fully characterised all aspects of molecular biology with respect to enzyme mechanics. Mass action kinetics are also deterministic in contrast to the stochastic nature of biochemical systems. Deterministic models don’t account for the variety of outcomes that can occur when a low molecular count is used as the probability of collision changes under low molecular counts due to the fact that conversion become event dependant and not rate dependant (5).

Enzymatic rates were obtained from literature via the BRENDA enzyme database (6). Enzymatic rates from the origin species of each gene in the operon were used and are displayed in Table 1. Where more than one figure was available, the most cited value was used. The CHI enzyme in the operon originates from Gerbera sp. No rates were identified from this species so the only available rate from Eubacterium rumulus was used.

Table 1. KM constant for each substrate of the four enzymes coded for by the naringenin synthesis operon BBa_1497017 and the source literature used to identify each value.

Transcription and Translation

It was critical to include the effects of changing both promoters and ribosome binding sites as naringenin production and steady state metabolite concentrations are dependent on enzyme abundance. This was done by modelling both transcription and translation as regulatory mechanisms such that the expression of genes could be tuned relative to one another. Transcription was spilt into two reactions for each enzyme, the first reaction being transcription initiation by recruitment of the RNA polymerases to the promoter site and the second reaction synthesis of mRNA, which was set to 40 nucleotides a second (13).

Translation was also split into two separate reactions, recruitment of the ribosome and translation, which was 16.5 AA per second, based on Escherichia coli poly-peptide elongation (14). Changing the promoter and RBS would change the rate of recruitment of RNA polymerase and ribosomes and so affect rate of change of mRNA and Protein with respect to time.

Since the RNA polymerase and ribosome concentration would remain constant and non-limiting, the rate of transcription and translation had to be defined for each of the four enzymes. Transcription rates were based on the average prokaryotic transcription rate of approximately 40 nucleotides per second (15). The number of nucleotides for each enzyme was calculated by multiplying the number of amino acids by three. This was then divided by 40 to give the transcription time. The transcription rate was calculated by dividing one by the transcription time. Therefore, as TAL has the longest amino acid sequence its transcription time is the longest. Translation times were calculated using a rate of 16.5 amino acids per second (14).

Degradation rates were included in the model to consider natural degradation of both mRNA and proteins over time. mRNA degradation rates were based on mean mRNA half-lives (16). Protein degradations were calculated assuming a protein half-life time of 20 hours (17).

Model Results