Team:Manchester/Model
MODELLING
"From determining which colours our bacteria should produce, to how strong their fragrance should be: modelling has informed all of the choices that make Cutiful the interesting and innovative project it is. The University of Manchester is proud to share with you the thought process behind picking vanillin (proving that logic isn’t always wisdom) and why we advocate green fluorescent hair.
How Modelling influenced Cutiful…
In 6 bullet points:
1.
Integrated Modelling: Chromophore Choice - whilst sfGFP was selected due to its recorded auto-secretion, it has a very high molar extinction coefficient, ϵ. After carefully considering the layer thickness which could be reliably expected to cover hair, and modelling the expected visual effects, amilCP was selected for its equally high ϵ value. (Colour, Prologue)
2.
Integrated Modelling: Odorant Choice - modelling a static isochoric sphere as the headspace, concentrations of various odorants were calculated at detection level. Vanillin held the lowest concentrations of all tested fragrances, and was selected thus. (Fragrance, Prologue)
3.
Modelling Experimental Values: Smell Diffusion linking the estimated rate of bacterial production to various models, including iterative ‘single burst events’ and Fick’s Law, our dynamic modelling shows the spreading of smell through the headspace. This enables calculation of ideal production rate – where the smell is strong enough to be smelled within a 1.2m radius, but weak enough not to overpower the wearer. (Fragrance, Prologue)
4.
Safety and Integrated Human Practices: Kill Switch because Cutiful is made to be used by the general public it needs to be safe by design. In the event that a child might swallow it or if it is improperly discarded: our computational model of the redundant kill switch system shows that our bacteria will be robustly inactivated before they could cause problems. (Human Practices, Act II: The Community Festival)
5.
Integrated Human Practices: Allergenicity - iGEM Baltimore 2017, the Biocrew, developed a method to evaluate BioBricks for allergenicity. Cutiful was born as a method to avoid allergic reactions to bleaching agents in traditional hair dyes, and it has run through the Biocrew’s checklist, coming out clean. Fantastic news for our product, which is fulfilling its primary function more and more accurately as it evolves! (Human Practices, Act V: Conversations with Experts)
6.
Integrated Human Practices: Skin Tests We wanted to offer an ‘allergen-safe’ alternative to dyes – and we have. Not only was Cutiful put through the Biocrew’s checklist, we have also devised a theoretical ‘plaster’, which can be easily applied by the dye’s user, containing small amounts of our product. This gives particularly concerned users the ability to determine whether or not they are allergic to specific components of Cutiful, which might not have been picked up by the Biocrew’s checklist. (Human Practices, Act V: Conversations with Experts)
Modelling – an unending journey
Or: what happens when proto-adults are left with a computer, pop culture, and realise the surface of Venus is covered in lightning. Also: MATLAB, Excel, and foolish quotes.
Prologue
Every project needs to start somewhere, and ours takes form in a windowless room inside the Manchester Institute of Biotechnology – on the mundane, visitor side (think Muggle Charing Cross rather than Platform 9 ¾). It is mid-March, and we have finally settled on what later would come to be called ‘Cutiful’, though in its fledgling stages it is brilliantly named “the hair dye idea”. This Wednesday (every meeting is held on a Wednesday) The Question comes to us. We must advance, and for this we need something concrete.
“So....”, says Professor Breitling brightly, present at the head of the table. The meeting has been underway for a little while now, and everyone is more or less relaxed. (NB: the group is still relatively new, and everyone’s voice trembles: the word ‘relax’ is here being used very, very liberally.) “What colours are we thinking of?” He accompanies this with a friendly smile that turns slightly desperate as no one speaks. The longer no one speaks, the more no one wants to speak. Everyone studies the tables intently.
Silence can be deafening, when it is an entire room holding its breath.
“regular hair colours?” a trembling voice bravely replies. “Brown, black…” and then, after a moment of hesitation: “blonde?”
What courage, to be found in a fool…
Act I: Colour
“Enter Fool” – stage direction for Shakespeare’s “King Lear”, Act I, Scene 4, Line 624
Although a simple enough ‘pen and paper’ calculation, the modelling of our colours has determined which proteins were selected for Cutiful. Comparison of extinction coefficient data, ϵ, dictated which three of the proposed ten BioBricks Manchester iGEM 2019 has used. With red, orange, brown, violet, dark green, light green, blue, fluorescent red, and fluorescent green at our disposal, BBa_K1321337 (sfGFP - fluoresces green, visibly yellow) and BBa_K592009 (amilCP) were selected for their high extinction coefficients. sfGFP also had a certain degree of auto secretion , which steered our choice in its direction. Out of all the red fluorescent proteins, chosen in order to close the chromatic circle (additive colour theory for UV, subtractive colour theory for visible spectrum), BioBricks BBa_E1010 (mRFP1) was selected (Colour, Prologue). It had been successfully implemented by other iGEM teams, and although having a lower extinction coefficient than, for example, DsRed, mRFP1 matures over 10 times faster: it shows similar brightness in living cells.Below can be found animated models showing the increasing absorbance of each respective chromophore, function of concentration. Shown are the overall effects when the layer is superposed over a light blonde colour, and a dark brown one. Insert is a straight-line graph of absorbance, in arbitrary units, against concentration, in mol dm-3. For modelling purposes, the thickness of the layer has been defined as 1 μm, the approximate thickness of a bacterium.
This model shows…
Relationship between concentration and coverage
• Enabling us to determine that Cutiful is a suitable dye for light hair colours, and will tint darker colours
• Allowing us to estimate the concentrations required for coverage to be noticeable in the white light spectrum (assumption made that, as the sole UV emitter on hair, the fluorescence will visible in the UV spectrum so long as the bacteria express it), and determine whether these might be harmful to our E. coli strain. This is not fundamentally an issue, since the E. coli is expected to secrete the colours, but if the rate of secretion is lower than the rate of production then a build-up of the dye could prove toxic to E. coli.
• Allowing us to estimate the concentrations required for coverage to be noticeable in the white light spectrum (assumption made that, as the sole UV emitter on hair, the fluorescence will visible in the UV spectrum so long as the bacteria express it), and determine whether these might be harmful to our E. coli strain. This is not fundamentally an issue, since the E. coli is expected to secrete the colours, but if the rate of secretion is lower than the rate of production then a build-up of the dye could prove toxic to E. coli.
Act II: Fragrance
“Fly, you fools” – the most misunderstood quote in “Lord of the Rings”, J.R.R.Tolkien. (“Fellowship of the Ring”, Book II, Chapter 5)
Another aspect of our modelling is to accurately represent how secreted smell diffuses through the air. This allows us to predict the concentrations required for an odorant to produce a lasting smell in a defined radius about the user, the benchmarks of which are the ‘personal’, ‘social’, and ‘public’ spheres. The spheres are a function of their radius, and roughly demarcate the average distances an individual will be comfortable having, respectively, a friend, an acquaintance, and a stranger, at.
To this day, the fragrance aspect of our project Cutiful (Fragrance, Prologue) has evolved through two parallel trains of thoughts, expressed in four models:
|
Sphere |
Fick’s Laws |
|---|---|
|
1. Headspace Calculation – amount of odorant required to fill the ‘personal’, ‘social’, and ‘public’ space around a person. |
1. Iterative Smell Diffusion – step wise approximation of the rate of change from the second differential of concentration, with respect to space. |
|
2. Gaussian Distribution – distribution of odorant across space, evolving over time. 
|
2. Fick’s Second Law – solving and dynamically modelling the integral equating the rate of change of concentration over time to the second differential of concentration with respect to space.
 |
Table 1. Explanation of our school of thought, where fragrance modelling is split into two different, though linked, systems, based on differing representations.
The Sphere models are simplified representations of the evolution of smell, not taking into account the continued production of olfactory molecules from bacteria. They are easier to calculate, and more intuitive, though they lack the dynamic realism of models based on Fick’s Laws. In real time, the models were devised in the following order: Headspace Calculation, Iterative Smell, Gaussian Distribution, and Fick’s Second Law.
Scene 1: Sphere
Headspace Calculation
Our modelling begins with a simple, isochoric ‘hard-sphere’ model, which looks at how much vanillin and limonene respectively are required to ‘scent’ the user’s hair. This is a static model, using fixed sphere volumes and odour detection values (ODvanillin = 1.9x10-7 g m-3; ODd-limonene = 2.5x10-3 g m-3) to determine the minimal number of olfactory molecules required to be detectable, expressed as a mass.
The chosen volumes, referred to as ‘headspace’, are the ‘personal’ sphere (0.4m radius, shown in purple against) and the ‘social’ sphere (1.2m radius, in pink against). Additional calculations for the ‘public’ sphere (2.0m radius, in yellow against) was considered, and discarded, as it was decided that the scent should remain constrained.
Human olfactory receptors being far more sensitive to vanillin than d-limonene, the vastly differing amounts outputted come as no surprise (for personal space: mvanillin=7.1x10-8 g; md-limonene=9.4x10-4 g).
The purple sphere expands from radius 0 – 0.4m, which is traditionally considered the personal sphere. This area of space is closest to the body, and where the scent will be strongest. The concentration of odorants inside the personal sphere cannot exceed a certain concentration, dependent on human nose sensitivity to the molecules, lest the odour becomes overwhelming to the user. This concentration was determined from research through perfumery literature, and comes into meaningful play for the modelling of Fick’s Law.
The pink sphere is associated with the social sphere. It stretches between 0.4m and 1.2m from self, and is the general distance people are allegedly content to interact with acquaintances at. It was decided that the smell emanating from our bacteria should not be detectable beyond the social sphere, as not to importunate strangers passing by. This means that, at the edge of the social sphere, the concentration of odorant should be equal to the OD of the compound. This is shown by the odorant cloud (modelled as the colour filling the sphere) not exceeding the 2.0m radius, at which the public sphere (in yellow) is said to begin.
This model shows…
Relationship between concentration and detection
• Enabling us to establish and clarify the ranges in which we want our fragrances to be detected,
• Giving us a clear, and efficient way of explaining the way we designed our scents, which can be considered backwards: we first decided how strongly and where we wanted each fragrance to be smelt, and then worked our way back to the rate of secretion required for those parameters,
• Allowing us to estimate points in our models where t, x and C are all known. This is a building block in setting up a diffusion model using Fick’s second law, as three limits are required to define the integral of the model.
Gaussian Distribution
Through further research we realised that diffusion can be modelled via a Gaussian distribution, based off the root-mean-square (RMS) displacement from the random walk of individual particles. Using this, a model describing the 1-dimensional diffusion of particles was adapted to work with 3-dimensional diffusion, by altering the RMS calculation and replacing the constant cross-sectional area with an expanding sphere (based on radius).
This model allows for the calculation of odorant concentration at specified distances and time points directly, rather than requiring iterative calculation through incredibly small time steps. However, unlike models based upon Fick’s Laws, this is less effective when extra odorant is being added to the system due to production, as is the case for Cutiful.
Beyond general assumptions such as no directional airflow and the air being in great excess of the odorant, this model assumes that the total amount of odorant is constant. While this constitutes a step towards modelling scent; it is insufficient for a system where our bacteria will be constantly producing odorant. This can be jury-rigged by generating new distributions when new odorant is produced and then summing them at each time point, however this is highly inelegant and inefficient.
The above solution can be modelled via the summation of curves – increasing the processing requirement of the model to beyond feasible within the iGEM timeframe.
This model shows…
Relationship between initial concentration and detection over time
• enabling us to see how quickly odorant is dispersed,
• giving us a simple way to display the approximate effectiveness of our scents,
• allowing us to estimate the detection of different odorants based on their diffusivities and detection thresholds,
• but lacks good production-handling, which lead us to looking at Fick’s Laws.
Scene 2: Fick’s Laws
Iterative Smell Diffusion
Another early model describing the diffusion of smell is an iterative simulation based off Fick’s laws, as adapted from.
Our simulation approximates space as an array of spherical distance bands, each with a concentration of odorant. Second order concentration gradients are estimated and used to calculate the instantaneous movement of molecules from one band to another. This rate of diffusion is applied over sufficiently small time steps to simulate diffusion between time points. The process is repeated, evaluating new concentration gradients and rates of diffusion between each distance band.
The advantage of this model is its ease to connect to a secretion/production model: odorant can be dynamically added at each time point, in line with whatever function or series of data available. This model, however, proves wieldy due to the sheer amount of computation required. As the time steps between time points must be very small, such that the instantaneous rate of diffusion remains sufficiently accurate, time is computed very slowly. In order to model ca. 5min reliably, months of processing using relatively powerful domestic computers would be required. As a result, this model was dropped in favour of a calculus driven model.
This model shows…
Relationship between concentrations across distance bands diffusing over time
• enabling us to see how an odorant behaves in air without complex maths,
• however, has an unreasonable demand for computational power,
• which directs us towards using more intensive mathematics,
• leading to further research into the assumptions and calculations of Fick’s Laws
Fick’s Second Law
Fick’s Second Law relates the rate of change of concentration, dC/dt, to the second differential of concentration with respect to space, ∇²C. We made the assumption, based on the isochoric hard-sphere model, that at time t=0, distance x=0, the concentration of odorant would be function of the rate of bacterial production. Since we desired the smell to go no further than the upper limit of the ‘social’ sphere, we assumed that at t=∞, x=1.2, C=OD, the odour detection threshold (so that, at x>1.2, C
Using our solution to Fick’s second law of diffusion, derived from integrating between the limits mentioned above, we modelled the change in concentration over time and space as a three-dimensional surface. Insert is a concentration profile dependent on time, where the red line (if visible) represents the maximum concentration (calculated from values in Engineering Perfumes, Mata V., Gomes P. and Rodrigues A.) and the green the Odour Detection Threshold (OD, from Odor Thresholds for Chemicals with Established Health Standards, 2nd Edition, AIHA). These are the values we initially set as limits for x=1.2m and x=0.4m respectively, for any time t. From the model, it can be seen that at the secretion rates used (Bacterial Cell Production Calculations.xlsx, Appendix II Scene 2, varying for vanillin and limonene) the thresholds are not exceeded, and indeed well underneath the desired values for the wanted concentrations. In order to obtain the effects stipulated in the hard-sphere model, we would require five-fold higher bacterial production rates of. However, GC-MS results from laboratory experiments have shown that 0.6μg L-1 of limonene were produced by our bacterial cultures, which is clearly above the detection threshold. We recognise that, therefore, the secretion rates calculated were drastic underestimates. (Fragrance, Prologue)
This model shows…
Relationship between time, space and odorant concentration
• A three dimensional surface mapping the concentration (z axis) at different time points and distances from the user’s head.
• Enabling us to predict the way concentration will change over a period of nine hours (the longest we assumed someone to stand still – when sleeping)
• And allowing us to determine the required rate of bacterial secretion of our odorants in order to fulfil the stipulations laid out by the hard-sphere model (ie: for any time t: at x=1.2m, C=< OD; at x=0.4m, C=< Coverwhelming)
Act III: Kill Switch
“Self-confidence, my friends call it” – Edgar Allan Poe
This model shows…
• Integration of public concerns regarding biosafety.
• Kinetic modelling showing a stable steady state which can rapidly transition towards cell lethality.
• Mutation analysis showing kill switch functionality over a realistic time course.
GMOs are generally a concern of the public. Through our human practices activities, it became especially clear that there is a concern about our bacteria living on longer than they should, escaping the hair or, in the worst-case scenario, going on to cause infection (Human Practices, Act II: The Community Festival). To address this very valid concern, we propose the implementation of a kill switch, such that if the bacteria escapes the hair or is no longer wanted on the hair it can be easily killed. Making reliable kill switches is difficult: they often result in bacteria having to transcribe more RNA and produce more protein, and if they work, they will result in cell death; this leads to strong selection pressure inherently against kill switches. To avoid this, there are multiple schools of thought: 1) You can design a kill switch to have minimal metabolic burden, hence lessening the selection pressure against it; 2) You can design a kill switch for redundancy, hence reducing the chance that any individual mutation would lead to complete inactivation of the kill switch. Consequently, we have designed a highly redundant kill switch with minimal additional basal expression to combine with a supplementary shampoo required to maintain the bacterial colony.
Due to time constraints we have not had time to construct or test our kill switch designs. Instead, we are using primarily existing iGEM biobricks which have been shown to function and we underpin the quality of our designed system via modelling both: the kill switch action, as well as the chance for our kill switch to mutate and lose its function. The action of our two kill switches has been kinetically modelled primarily through mass-action kinetics. Mutation chances have then been estimated based off of all possible single point mutations and approximated consequential failure. Finally, as to not introduce allergens into our product, we also scanned our kill switch proteins for common allergenic epitopes. This modelling has thus shown our kill switch to be effective and relatively long lasting while not adding an allergenic profile to our product. Our kill switch constitutes a strong response towards public concern and provides a good start point for further teams to add onto and develop.
Scene 1: Kill Switch Mechanism
Our kill switch will be highly redundant, such that it is less likely for the cell to fully inactivate the kill switch. To achieve this, we propose incorporating two independent kill switch mechanisms which can both on their own kill the cell and will both trigger when needed. Additionally, our cytotoxic proteins are negatively controlled; this means, if a mutation occurs in the regulatory regions it is likely to trigger the death of the cell. As a result, to inactivate the kill switch very specific proteins would have to be mutated.
To reduce the chance of kill switch loss we plan to have the kill switch incorporated into the bacterial chromosome between two essential genes to prevent loss via homologous recombination. This would help protect the kill switch from large-scale deletions or translocation events or homologous recombination as it is likely that these would also result in damage to essential genes which would prevent the passing on of these changes.
Both of our kill switches will rely on repeated supplementation from a specific shampoo. In the hair dye industry, it is common practice to use colour-protecting shampoos, so this is par for the course. By using supplementation from a defined shampoo, we can control the environment our bacteria are in and hence constrain them only to be able to live in this environment. By choosing to control our kill switch by supplementation allowed us to use simpler triggering mechanisms which do not require complex and metabolically taxing sensing systems. As our bacteria will function on human heads, we have directed our choice of supplements towards safe non-irritant/carcinogenic inducers.
Mechanism 1 – Mg2+/ColE2
Our first kill switch mechanism uses a Mg2+ riboswitch which controls production of the DNase ColE2. ColE2 is naturally produced by E. coli to kill other E. coli strains not containing the immunity protein (Im). In standard conditions, on our supplemented hair, where there is ~10mM Mg2+, the repressor BM3R1 will prevent transcription of ColE2. To ensure against premature cell death Im will be weakly constitutively expressed to neutralise ColE2 leakage. When the Mg2+ concentration drops, the ORF2 repressor will be successfully translated. This will lead to repression of BM3R1 and expression of ColE2 sufficient to overcome the immunity protein. In addition to the toxicity of ColE2, ORF2 is also toxic at achievable levels. As a result, if ColE2 gains a loss of function mutation, this kill switch will still function (See fig. 1).
The main benefit of this kill switch is that ColE2 is a coliform bacteria specific endonuclease; this means that when killed by this mechanism, the DNA within the cell will be destroyed. This significantly reduces the chance of any horizontal DNA transfer after death. Additionally, if ColE2 is used rather than the mini-colicin, it would be able to infiltrate other E. coli cells; this means that if some cells mutate but non-mutated cells still remain, they would all still be killed off. This could be used to reduce the chance of a colony becoming fully immune to the kill switch; however, this could also cause temporary damage to the local microbiome depending on ColE2 susceptibility. This is still preferable to antibiotic solutions which would be less specific, and over time the local microbiome would likely recover and so the harm is relatively low.
The primary weak spot of this killswitch is ORF2; if this mutates to prevent expression or to lose function then the mechanism will likely fail. As the riboswitch inhibits the translation of the mRNA, it is likely that a mutation within the riboswitch is more likely to lead to a loss of function, hence cell death. This means that for failure the most likely situations are:
• a mutation in the ORF2 promoter,
• or a mutation in the ORF2 repressor removing both repressor function and cytotoxicity.
Mechanism 2 – Arabinose/Holin
Our second kill switch mechanism uses an arabinose and CAP-regulated promoter which is used to inhibit production of Holin. Holin is a protein taken from lambda phage, forming complexes at the inner bacterial membrane to create pores. These pores compromise membrane integrity severely, disrupting respiration and other vital systems. Similarly to ColE2 there is an immunity protein for Holin, called Anti-holin, this will be weakly constituently expressed to cover leakage. By using an arabinose and CAP-regulated promoter we can check for the presence of arabinose and lack of glucose. Hair is unlikely to have high glucose concentrations on the surface while it can be supplemented by arabinose. If the arabinose concentration were to drop or glucose to rise then the repressor would cease production and Holin would be expressed, overcoming the low immunity protein concentration and killing the cell.
The main advantage of this kill switch is the co-operative nature of Anti-holin. Anti-holin functions as an immunity protein because it forms heterodimers with Holin; these can’t enter polarised membranes and so cannot form pores. However, when the Holin concentration becomes sufficient to form enough homodimers to form pores, the membrane becomes uncharged and the heterodimers may enter and establish further pores. This positive feedback should help accelerate the killing.
The most likely way for this kill switch to be inactivated is losing expression or function of Holin/endolysin. This is likely to occur either by the promoter losing function or Holin/endolysin acquiring loss of function mutations.
Figure 2: Holin Regulation System. The Arabinose/Holin system is shown here both in active (-Arabinose +Glucose) and in dormant (+Arabinose -Glucose) states. The weak production of anti-holin has been excluded for clarity.
Kinetic Modelling:
To model the kill switches, kinetic models were constructed based on the transcription, translation and degradation values in MATLAB’s Simbiology examples. Wherever possible these models used mass-action kinetics.
Mass action kinetics
Where kf and kr refer to the forward and reverse rate constants respectively. A, B and X refer to species for which a, b, and x are stoichiometric coefficients.
Initially, repressors were modelled as switching between a bound and unbound state on the DNA. This, however, produced data which made the repressors appear “stickier” to the DNA than they should be. As a result, a reduced model of DNA repression was used to approximate translation from the amount and nature of the repressors.
Reduced Model for DNA Repression
Where kt refers to the unrepressed rate constant of transcription. Bg refers to the effective dimer-operator association constant, for TetR Bg = 108M. ηm is the multimerization efficiency of the repressor, as TetR family repressors act almost exclusively as dimers ηm ≃ 1. Data and model taken from
Furthermore, specific kinetics could not be found for the repressors used in the kill switch; as these repressors are of the same family as the TetR repressor, they were assumed to have similar kinetics and modelled accordingly. These models assume that neither NTPs nor amino acids are limited and that the rates of transcription/translation, without repressors/riboswitches, are constant. Finally, these models assume that no movement is required between compartments; as bacteria do not have membrane-bounded compartments, this is a reasonable assumption and drastically simplifies the models.
Mg2+/ColE2
The Mg2+/ColE2 kill switch model describes the whole genetic circuit using the reduced repressor model. To produce only a small amount of the Im2 protein, a promoter with 10% strength and an RBS with 30% strength have been modelled. ColE2 and Im2 then have their interactions modelled via standard reversible mass-action kinetics. Due to the lack of available data, the ColE2 and Im2 interaction is approximated to the ColE9 Im9 reaction, as these are in the same protein families. Finally, the effect of magnesium on the riboswitch is approximated via an estimated Hill-Langmuir equation obtained from.
Where EC50 refers to the concentration of Mg2+ where half inhibition is seen, this was estimated from to be approximately 0.134mM.
Figure 3: Simbiology Diagram of Mg2+/ColE2 kill switch. Grey blobs refer to quantities of objects. Yellow circles indicate reactions where arrows indicate products and reactants, dotted lines are used to refer to reactants that are not consumed in the reaction. Reactions with the backwards/forwards arrows are reversible. Mg2+ is a parameter which controls the amount of uninhibited ORF2 mRNA.
Figure 4: Mg2+/ColE2 Kill switch plot. The dashed line shows when the Mg2+ concentration was reduced. Before 20 seconds, the stable baseline condition is shown, where leakage is sufficiently managed by Im2 production. Following 20 seconds, the Mg2+ concentration drop leads to kill switch activation. ORF2 and ColE2 drastically increase leading to cell death.
The results of this modelling show our kill switch can reach a steady state; upon Mg2+ removal, the kill switch rapidly switches towards cell death. The increase of ColE2-Im2 complexes and drop of Im2 protein suggests that under in vivo conditions the cells would have excess immunity protein so should be relatively safe from premature cell death. When ColE2 becomes unrepressed, its production overcomes what the immunity protein can inactivate resulting in cell death.
Arabinose/Holin
The Arabinose/Holin model is very similar to the Mg2+/ColE2 model in being largely mass-action based and repression being modelled through the reduced model. The pBAD promoter of the phIF gene is controlled such that at a specific time point transcription will stop to indicate either removal of arabinose or addition of glucose. Due to the complexity and the lack of information of the specific assembly of Holin/anti-holin monomers this has not been modelled; however, the relative concentrations should be sufficient to demonstrate lysis capability.
Figure 5: Simbiology diagram of Arabinose/holin killswitch
Grey blob refer to quantities of objects. Yellow circles indicate reactions where arrows indicate products and reactants, dotted lines are used to refer to reactants that are not consumed in the reaction. Reactions with the backwards/forwards arrows are reversible.
Figure 6: Arabinose/Holin Plot
The dashed line shows when the pBAD promoter was disabled. Before 20 seconds the stable standard condition is shown, where phIF is produced repressing Lysozyme and Holin production. Following 20 seconds, the phIF concentration drops due to protein degredation and Lysozyme and Holin become expressed and build to lethal levels.
The results of this modelling again show our kill switch can reach a steady state then when the pBAD promoter shuts down the system will move towards cell death as lysozyme and holin production dramatically increases. Although there is a longer lag period predicted by this model it may still kill faster due to the positive feedback of holin heterodimers.
Scene 2: Mutation Modelling
Loss of function of our kill switches is most likely due to a promoter/RBS or protein loss of function. By modelling how readily these can be mutated we can approximate how long it will take for a significant amount of a bacterial population to become resistant. In order for a bacterium to survive it must inactivate both kill switches; however, there are multiple likely ways to for each kill switch to inactivate. For the purposes of this modelling we will only look at single point mutations for the purpose of simplicity. Furthermore, we ignore gain of function mutations leading to kill switch inactivation due to the low likelihood as well as the difficulty in predicting these. Additionally, the mutation rate of E. coli can be very variable based on environmental conditions, due to the approximate nature of this modelling we applied a standard value throughout. Finally, we are also ignoring lethal mutations which lead to pre-emptive kill switch activation as these will likely just lead to the bacteria being replaced.
There is a large diversity of promoters and RBSs that function in E. coli as demonstrated by the wealth of the Biobrick library. To simplify matters we will look at the promoter and RBSs together, and assume that when three-point mutations occur across the promoter/RBS the function will be sufficiently disrupted as to cause failure.
To model the loss of function of proteins is significantly more complex: many proteins have hypervariable regions where mutations make little difference; mutations from one amino acid to another can be more or less detrimental based on the type of amino acids exchanged – Glu for Asp is generally less detrimental than Glu for Ile; many proteins may have certain regions which must have certain properties such as hydrophobicity in a transmembrane domain. As a result, applying a blanket probability across a protein seems like an oversimplification. To support this, we have developed a tool which tries to predict the probability of a protein to get a loss of function mutation over time. This tool incorporates the above issues by allowing you to define regions with specific rules or levels of vulnerability as well as essential amino acids such as catalytic residues or start codons. The tool then takes these as well as amino acid characteristics into account to predict the chance of the loss of function of a protein. Using an online motif Blast-style tool as well as databases such as Uniprot we identified specific regions and amino acids within our proteins to assign increased vulnerability to mutation and thus approximated the chance for mutation over time.
Figure 7: MiniColicin and ORF2 Motif alignment
Motif alignments taken from. Protein sequences are aligned to common motifs highlighting likely areas of importance for protein function.
Effects of selection pressure across generations have not been included in our modelling due to complexity. Depending on how much metabolic burden our kill switch puts on the cell this could result in an underestimate. However, in order to successfully reduce metabolic burden without killing the cell, first the kill switch must be inactivated then the repressors and immunity proteins causing the burden. This indirect order reduces the chance of cells getting the correct mutations to allow selection pressure to help propagate kill switch-inactivated bacteria.
Our mutation analysis suggests that kill switch mutation would occur very slowly. This is very positive for preventing infection based on getting product into eyes or taking it up orally during application as over the short time course the kill switch should be active in virtually every cell and should drastically reduce bacterial populations preventing infection getting hold. However, over the course of 1 year, approximately 0.01% of bacteria would have fully inactivated kill switches. Although this is a small proportion of the overall population, this could easily constitute bacteria on the order of 104 across a head with approximately 300g of hair. As a result, over a prolonged period of time it may make sense to recommend not supplementing the bacteria to induce death, then replacing with new bacteria at regular time intervals to reduce the number of bacteria that have single kill switch knockouts to reduce the number of double knockout bacteria. Additionally, this provides an argument for the use of the full Colicin E2 rather than the mini Colicin, so as to allow non-inactivated bacteria to help kill the immune bacteria.
Figure 8: Proportion of bacteria with inactive kill switches over a year
Across a year the single kill switch mechanisms reach approximately 0.1% inactivation across bacteria populations. Using a double kill switch system total inactivation reaches 0.01% across populations after a year. In short term usage the double kill switch boasts very low mutation rates and shows dramatic improvements over the single system.
Scene 3: Allergen Prediction
To find out if adding our kill switch would be likely to result in allergic reactions, we used the allergenonline blast. Using the sliding 80mer window function we were able to scan our proteins for any epitopes that are known to be allergenic. In all cases similarity was less than <35% and as a result insignificant. From this modelling we conclude it is unlikely for our kill switch to cause any allergic effects.
Aside: Conclusion
Our kill switch is theoretically plausible, resilient and likely non-allergenic. Our kill switch is likely to be sufficiently and robustly effective against any possibility of infection from our bacteria, which should help to address legitimate public concerns identified in our discussions with potential users of our product. Furthermore, our kill switch should be sufficient to reduce bacterial release as after long time periods there is still a relatively low proportion of bacteria lacking active kill switches; this means the probability one gets the chance to escape, space to grow and does not have an active kill switch is rather low. Our kill switch will help prevent our bacteria lasting longer than desired; however, if used for a long time, on the order of years, the effectiveness of the kill switch might become reduced and they may be harder to remove. Beyond replacing bacteria to remove bacteria with single inactivated kill switches, the prevalence of existing commensal bacteria could play a large part in supporting our kill switches. As the kill switches reduce colony size and other produced proteins reduce fitness, commensal bacteria are likely to slowly outcompete our bacteria hence helping clear our bacteria. We believe this kill switch system is a strong answer to the concern identified in our stakeholder interviews and drastically increases the viability of our project by adding safety and security mechanisms to our bacteria.
Act IV: Allergens
“Every poet, but not every fool.” – Samuel T. Coleridge, if he had known Twitter. (inspired from Epigram)
Cutiful was created with in mind the idea of making hair dyes safer for users (Human Practices, Act II: The Community Festival). This includes checking that the molecules we are substituting alleged carcinogens and allergens with, are themselves harmless; a process for which we have decided to rely on existent iGEM teams’ work. In choosing to apply iGEM 2017 Baltimore Biocrew’s Allergenicity Checklist, we want to make Cutiful a safer alternative which keeps in the spirit of iGEM by relying on the work of previous teams. The Allergenicity Checklist states to run our amino acid sequence through BLAST, to compare to the sequences present in known allergens. We then report a percentage match, stating which allergen our constructs are most similar to.
Below can be found our results, summarised. We considered that, since certain parts of our BioBricks were common to multiple constructs, only a select representation should be tested. PepG with a hydrophobic tag was not submitted to the check, for example, because PepG had already been tested (and come back with 0 matching sequences) and the hydrophobic tag had also undergone comparison, in the colour constructs (which had also come back with 0 matching sequences).
| Part | Known allergen match? | Allergenic? |
|---|---|---|
| mRFP1 – alone | 0/146 | No |
| mRFP1 – N (OmpA) & His tag | 0/172 | No |
| mRFP1 – C (HylA) & His tag | 0/212 | No |
| sfGFP – alone | 0/159 | No |
| sfGFP – N (OmpA) & His tag | 0/184 | No |
| sfGFP – C (HylA) & His tag | 0/224 | No |
| sfGFP – His tag | 0/164 | No |
| amilCP – alone | 0/142 | No |
| amilCP – N (OmpA) & His tag | 0/168 | No |
| amilCP – C (HylA) & His tag | 0/208 | No |
| PepG – alone | E>1 | No |
| PepG – N (OmpA) | E>1 | No |
