Team:Edinburgh/Modelling/Bacterial

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Overview: Modelling bacterial BRIDGEs

The second Kappa model created for the project attempted to realise the original vision we held for the system: a composite device based on the tried and tested Elowitz repressilator, combined with light-producing and light-sensing pathways for three different wavelengths. The primary objective of the modelling would then be to confirm that the three systems interacted with one another in roughly the manner expected, without undue interference or trouble. A secondary objective would involve use of the model in understanding the structure of the system and possibly to compare different proposed subsystems against one another, to analyse which one would work better.

The following sections describe, in turn: the repressilator model that forms the core of the system, the red light production and signal transduction pathways, the blue light production and signal transduction pathways, the green light production and signal transduction pathways, the results obtained by running the simulation, and finally the analysis of the results obtained.

The Repressilator

The core of the model is formed by the Elowitz repressilator designed by Ty Thomson in 2009 (available to view here). This was one of the first to incorporate the concept of standardised biological parts (i.e. BioBricks) into a modelling context, attempting to "introduce a modular framework for modelling BioBrick parts and systems using rule-based modelling". The idea was to model at the level of individual parts, such that systems could be constructed using different components by paying a cost upfront with the construction of models of the parts, and thus making modular construction of specific models practically effort free - similar, in fact, to the idea of characterised and composable BioBricks used in the design and construction of synthetic circuits.

The framework as described by Thomson establishes a concise set of Kappa rules necessary to incorporate new BioBricks into such a model, by dividing them into four wide-ranging categories - promoter sequences, coding sequences, ribosome binding sites, and terminators. For example, a promoter sequence must define how repressor proteins and RNA polymerases bind with it, how transcription is initiated, and what happens when readthrough occurs and the promoter sequence is transcribed. A coding sequence must define its transcription, translation initiation and actual translation, and degradation of the translated protein (the action of the protein itself is not necessary, with the exception of its repressor activity which would be described in the corresponding promoter sequence). Finally, a ribosome binding site must define how a ribosome may bind with the site and how the RBS is transcribed, and a terminator must define how termination occurs, and what happens if termination fails (i.e. terminator readthrough).

The framework also describes what rates are necessary for the complete characterisation of the model. These roughly correspond to the rules given above, and include: promoter binding affinities and rate of RNAP recruitment; rate of transcription and rate of recruitment for ribosome binding sites; rates of transcription, translation, and degradation for protein coding sequences; and terminator percentage of successful termination. Although very few, if any, of the BioBricks in the Registry are characterised to this extent of modelling utility, such a framework at least provides something that we can be aiming for.

Thomson's model of the Elowitz repressilator was created as a working example of this framework, and is capable of fully simulating the interactions that occur within the system. The rules within fully satisfy the above framework for the repressilating reactions involving lacI, lambda-cI, and tetR and their associated BioBricks: BBa_B0034, BBa_R0051, BBa_R0040, BBa_R0010, BBa_C0051, BBa_C0040, BBa_C0012, and BBa_B0011.

For details of Ty Thomson's repressilator model, readers are directed to the aforementioned RuleBase link as well as the actual Kappa model.

The Red Light Pathway

The red light production pathway consists of a BioBricked red luciferase production gene coupled to the lacI promoter (BBa_R0010); the presence of LacI in the system inhibits the production of red luciferase. The assumption is then made that red luciferase translates directly into red light - essentially, that substrates such as luciferin are constitutively expressed, and that there is no need to include them within the model.

The red light sensor pathway, depicted in Figure 2, is a signal transduction pathway involving Cph8 (which can have either 'on' or 'off' state and can bind to OmpR) and OmpR (which can be either phosphorylated or unphosphorylated and can bind to either Cph8 or one of the ompC and ompF promoters). The assumption is made that there is a relatively static amount of Cph8 and OmpR within the system, and that there is no need to model their creation via transcription and translation or their degradation. Assumptions are also made regarding the balance between the concentration of on / off Cph8 and phosphorylated / unphosphorylated OmpR when the system is stable, as well as the fact that OmpR can only change phosphorylation state when not bound to any of Cph8, ompC, or ompF.

When red light is not present in the system, an equilibrium exists between 'on' and 'off' Cph8 (heavily biased towards the 'on' state) and phosphorylated and unphosphorylated OmpR (heavily biased towards the phosphorylated state). When the red light sensing pathway is activated by bursts of photons at the correct wavelength, the Cph8 sensor is almost all turned 'off', which leads to OmpR almost fully unphosphorylated.

The ompC promoter is activated by phosphorylated OmpR in sufficient quantity, and is coupled to the BioBricked protein coding sequence BBa_C0040 that produces TetR. The ompF promoter is activated by minimal amounts of phosphorylated OmpR (and is inhibited by its presence in large quantities); when active, it stimulates production of LacI>. The presence of increased amounts of LacI in the system will act to inhibit the lacI promoter, which also controls expression of TetR as per the standard repressilator. Minor assumptions are made regarding the kinetic rates related to the ompF and ompC promoters within the model.

Thus, in standard conditions involving the isolated pathway, large amounts of TetR are produced due to the action of the phosphorylated OmpR promoter, whilst similarly the production of LacI is inhibited. When red light activates the signal transduction pathway, however, the concentration of unphosphorylated OmpR increases, which allows greater amounts of LacI to be produced, which in turn inhibits the production of TetR.

The graph in Figure 3 shows the results of simulating the red light sensing pathway, after inducing a short period of red light expression at t=100. This red light then stimulates an increased level of LacI within the system (in comparison to the control simulation in Figure 4), which acts to repress the amount of TetR present. The time units in the simulation are arbitrary but controlled by the kinetic rates used, which means that with further characterisation data, it would be possible to optimise the response of the pathway to actual conditions.

The Blue Light Pathway

The blue light production pathway consists of a BioBricked blue luciferase production gene coupled to the pTet promoter (BBa_R0040); the presence of TetR in the system inhibits the production of blue luciferase. The assumption is then made that blue luciferase translates directly into blue light - essentially, that substrates such as LuxCDE and lumazine are constitutively expressed, and that there is no need to include them within the model.

The blue light sensor, depicted in Figure 5, is the hybrid LovTAP protein, which can be in either a 'light' state or a 'dark' state and can bind to the trp promoter BioBricked as BBa_K191007. Assumptions were made regarding the rate of change in LovTAP rates when activated by light, as well as the fact that LovTAP can only change state when not bound.

When blue light is not present in the system, LovTAP remains in the 'dark' state. When blue light is present, LovTAP changes configuration to the 'light' state, which allows it to bind to the trp promoter and thus inhibit the production of lambda-CI. Again, assumptions were made regarding the kinetic rates at which these interactions occur.

Thus, in standard conditions, large amounts of lambda-CI are produced. However, when blue light activates the signal transduction pathway, the concentration of activated LovTAP increases, which then represses the production of lambda-CI in the system until the effect wears off.

The graph in Figure 6 shows the results of simulating the blue light sensor pathway, after inducing a short period of blue light expression at t=100. This blue light then represses the production of lambda-CI within the system for a short period of time (in comparison to the control simulation in Figure 7), before the effect wears off and transcription / translation are allowed to occur once more. Again, the time units in the simulation are arbitrary but controlled by the kinetic rates used, and could be optimised further using better characterisation data.

The Green Light Pathway

The green light production pathway consists of a BioBricked green luciferase production gene coupled to the lambda-CI promoter (BBa_R0040); the presence of lambda-CI in the system inhibits the production of green luciferase. The assumption is then made that blue luciferase translates directly into blue light - essentially, that any substrates are constitutively expressed and that there is no need to include them within the model.

The hypothetical green light sensor, is composed of a proposed fusion between the CcaS receptor and the PhoR response regulator, the action of which would be similar to that of the red light sensor depicted above. The fusion protein can be either 'on' or 'off' depending on whether or not it senses light of the appropriate wavelength; when 'on', it acts to phosphorylate the response protein PhoB. The phosphorylated PhoB can then act as an inhibitory transcription factor on a hypothetical promoter possibly based on one of the phoA, phoS, or ugpB genes. This pathway as a whole is depicted in Figure 8.

Many assumptions are made in the modelling of this pathway - for example, PhoB is generally characterised as an activator rather than a repressor, and thus some form of negation (i.e. a 'NOT' gate similar to the inverter built into the red light transduction pathway) will have to be built into the system, either as part of the pathway itself or by creating a hypothetical repressive promoter. The second approach was chosen when modelling the pathway, for the simplicity it offers.

When green light is not present in the system, the CcaS-PhoR fusion remains in the 'off' state. When green light is present, however, the fusion changes configuration to the 'on' state, which then proceeds to cascade a signal down the transduction pathway by phosphorylating PhoB, which then acts as a transcription factor.

Thus, in standard conditions for the isolated pathway, large amounts of LacI are produced by the uninhibited promoter. On the other hand, when blue light activates the signal transduction pathway, CcaS-PhoR activation is followed by an increase in the concentration of phosphorylated PhoB, which represses the production of LacI in the system until the effect wears off.

The graph in Figure 9 shows the results of simulating the green light sensing pathway, after inducing a short period of green light expression at t=100. This green light then represses the production of LacI within the system for a short period of time (in comparison to the control simulation in Figure 10), before the effect wears off and transcription / translation are allowed to occur once more. Again, the time units in the simulation are arbitrary but controlled by the kinetic rates used, and could be optimised further using better characterisation data.

Problems Encountered and Overcome

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Results

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Analysis

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