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From 2012.igem.org

Our modeling team has developed tools to understand and predict better the processes involved in our biosystem.

1) In first place we adapted a metabolic model of Synechococcus with the functions we included with our constructs. We transformed a wildtype Synechococcus elongatus with the luciferase genes (luxAB) regulated by the promoter psbA. The reactions of bioluminescence expressed by the LuxAB construct were introduced as follows:

LuxE8  : octanoic acid + ATP + NADPH -> octanal + AMP + NADP+ + diphosphate
LuxAB8 : octanal + FMNH2 + oxygen -> FMN + H2O + octanoic acid + light
LuxE14  : tetradecanoic acid + ATP -> tetradecanal + AMP + NADP+ + diphosphate
LuxAB14 : tetradecanal + FMNH2 + oxygen -> FMN + H2O + tetradecanoic acid + light
LuxE16  : hexadecanoic acid + ATP -> hexadecanal + AMP + NADP+ + diphosphate
LuxAB16 : hexadecanal + FMNH2 + O2 -> FMN + H2O + hexadecanoic acid + luz
FMN_red : FMNH2 + NADP+ <-> FMN + NADPH

May be noted that the luciferin (FMNH2) is reduced (regenerated) by the reaction FMN_red, which is not naturally present in Synechococcus, but which we added to our model to ensure light production in a persistent way. As a future aim, we plan to include luciferin regeneration gene cassettes to this wildtype. If we didn’t insert this adjustment, the model would calculate flow 0, as luminescence would extinguish in a few seconds with the scarce FMNH2, so the model has no solutions for infinite time flow. Moreover, we used here bioluminescence functions with 3 types of fatty acid (8, 14 and 16 carbon chain length), which are abundant in the cyanobacterial cell an can be used as ‘fuel’ with greatest probability, inside the luciferase chain length operation range.
This yielded results as we optimized the model’s algorithm to maximize light production, by adjusting the flow rates of the other reaction of the metabolism under certain restrictions which make it a biologically reasonable maximum value.
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In second place, we adapted the wildtype model with the sucrose export induced by the expression of the cscB transporter gene included in our transformed strain from Harvard. Here we modeled the maximum values of sucrose export for 2 different growth restrictions, 0.09mmol Biomass/gDCW*/h (a value near to the maximum growth, similar to an averaged exponential phase culture) and 1x10^-6mmol Biomass/gDCW/h (a negligible growth value which will keep all the vital reactions working but not divert a significant amount of fixed carbon to increasing biomass, as in an averaged dynamic equilibrium of a stationary phase culture).
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As we planned to transform this cscB strain to express luxI, the protein that synthesizes AHL (Vibrio autoinducer molecule), we introduced the reaction in the model as follows:

ahl: Hexanoyl-(acyl carrier protein) + S-adenosyl-L-methionine -> ahl + S-methyl-5'-thioadenosine + an acyl-carrier protein

As we know, this biomachine has 2 functions inserted, for which we have an interest of flow maximization. Unfortunately, export of sucrose and export of AHL, both carbon based molecules, sets a biochemical competition for carbon redirection. Therefore we came out with 3 modeled outputs: Parabolic curve of maximization of AHL+Sucrose (fig a), and the linear functions of AHL vs. Sucrose production in both growth scenarios (fig b, c).

(Figs a, b, c)

As in reality we have a much more copious sucrose requirement to keep our biolamp module alive than AHL to induce it (just 1 or 2 molecules per cell of Aliivibrio fischeri – (reference)), we cut the graph of high growth scenario at the sucrose export value at the salt stress we set in our design (150nm NaCl) for the scenario of maximum growth (as the forward idea is to keep the bioreactor in a continuous exponential phase), which corresponds to a flow of 0.00974 mmol/g DCW/h (units adapted from Ducat et al, 2012). This imposes a constant flux of sucrose and AHL, which is optimum for our system. The answer of the model to this constant export of sucrose is a flow of 0.015mmol/g DCW/h, which is a pretty high value. As you will see later, this value of AHL export is fundamental for the development of our next model.

-*: DCW=Dry Cell Weight, where an average Synechococcus cell has a dry weight of 1.53pg.

2) We achieved our main goal of integrating and connecting all the system into a single model capable of predicting the luminescence of the consortium system in different bioreactor setting scenarios, assuming fast diffusion mechanisms of substances in the medium with a pump system and skimmer control of population density in both Synechococcus and Aliivibrio modules.
The main part is based on the model of bioluminescence regulation developed by Belta et al. 2001, a hybrid model of 9 differential equations which predicts the behavior of the whole regulatory mechanism of luciferase expression (including cAMP, AHL, LuxR and LuxI expression) in Aliivibrio fischeri. We modified this model to restrict the growth of the Aliivibrio population to a constrained volume (biolamp compartment) meanwhile we adopted a greater volume for the dilution of the autoinducer (AHL). Such volume represents the annexing of the photobioreactor of Synechococcus and the extra volume from tubing and pumping systems where the medium flows.
We gave the system a new input oh AHL derived from the Synechococcus population, which has a Ks (constant rate of AHL production/cell resultant from the previous model) multiplying the number of cells (culture density x culture volume – of the photobioreactor compartment). The model still counts with the AHL produced by the Aliivibrio population, and the degradation half-life in the cells. As we said above, the diffusion speed of AHL is considered instantaneous (as the rate’s scale is very high compared with other variables, such as cell growth or gene expression).
The application of this model is focused in the optimization in the design of the future bioreactor which may contain the system. We are looking for the values of compartment volumes, relative volume, population densities and total volume which can assure a diel control of luminescence (in 12h cycles, considering export rates and the AHL half-life of 10h) by the light induced activity of our Synechococcus biomachine; and, within those values, the settings with maximum luminescence values.
A second filter is be applied to the group of solutions obtained from these premises, with the result of our further model on export and consumption rates of sucrose. This filter aims to discard the settings where insufficient sucrose is exported to the culture to sustain the growth of the Aliivibrio population. Although this requires additional experimental work that unfortunately we didn’t have time to carry out in our lab, we managed to adapt some experimental values extracted from the literature:

The export of sucrose from our cyanobacteria is: 0.0000536nmol/cell/s (units adapted from Ducat et al, 2012)
The consumption of sucrose by Aliivibrio fischeri is: 0.00000150nmol/cell/s (units adapted from oxygen consumption rates at maximum bioluminescent activity, at normal glycolytic route assumptions in aerobic conditions, from Makemson 1985)

This amendment model sets the total volume of dilution, the compartmental volumes of occupation and the cell densities for S. elongatus cscB and for A. fischeri (cell densities in a range between 0 and 10^9 cell/ml) as controlled variables.
The output gives the multivariate scenarios where the rate of change of sucrose concentration in the common broth is 0 or positive, so that the energy budget is not deficitary: