We built 3 different kinetic models to
understand different key aspects of the muninn project.
CRISPR SHERLOCK - GOLD MEDAL
We have built a kinetics model to understand how different
CPLX1 concentrations impact the time until maximum active GFP was
established. This was vital for the project as it was originally hypothesised that assays containing different CPLX1 mRNA concentrations
allowed to run too long would demonstrate equalised fluorescence yet
measurements taken too early would not demonstrate significant difference in fluorescence. Model findings suggest maximum GFP concentration will be different at
different concentrations of mRNA and the time to reach the maximum
increases with increasing mRNA concentrations, although this relationship occurs in groupings.
How this informed our design can be seen here
We successfully also built a kinetic model that allowed us to
follow glutathione degradation into glycine; however, due to the
lack of modern research on the gcvA:gcvR complex, the model was
not able to be successfully parameterised with high accuracy.
Using findings of our glycine biosensor characterisation, it was noted that the rate of glycine production may be too fast and may kill our cells and so a new construct was designed with a weaker promoter to delay glycine production.
Next, we built an additional model to understand the amount of
RFP produced in the presence of varying concentrations of either
glutathione or eicosane. The amount of RFP produced would be
compared to our standard curve in order to predict
fluorescence. It was through this model that we found our
eicosane system may be more complex than initially expected
which led to us taking a new approach.
The construction of all models was aided by our collaborators at
the University of Waterloo. The Waterloo team provided mentoring on the
most appropriate way to model systems and provided explanations as to why
some equations are more suited than others. Furthermore, the team also provided
troubleshooting advice - particularly with regulated expression in the glutathione model
and logic testing of the CRISPR SHERLOCK model.
CRISPR SHERLOCK Kinetic Model
Rationale & Aims
As we have chosen a CRISPR SHERLOCK system using Leptotrichia wadei Cas13a (Lw2Cas13a) to detect different
levels of CPLX1 mRNA, it was important to understand how our
system operates in silico prior to in vitro work. As the SHERLOCK
system is closed with a finite quenched reporter, the difference
in fluorescence results from the number of cleaved quenched
reporters and not the production of the new reporter.
This means we predicted our system would not produce a greater overall
fluorescence in response to a higher concentration of CPLX1 mRNA
but rather maximum fluorescence is reached faster due to a greater
number of Cas13a molecules being active at once.
The time until maximum GFP concentration depending on mRNA
concentrations is highly important for our system. If measurements
are taken too late, then fluorescence will be equalized whereas if
measurements are taken too early then the number of active Cas13a
complexes may not be significantly different. Through building a
kinetic model we are able to predict a window where the difference is most significant.
The model was built and simulated using COPASI 4.26 . COPASI allows simulation of complex biochemical networks to enable analysis of how systems
function. The model used a series of mass action (Figure 1a) and
Henri-Michealis-Menten (Figure 1b) equations.
Figure 1. A) Mass action equation and B) Henri-Michealis-Menten equations used in all kinetic models.
These equations, as suggested by our collaborators at Waterloo iGEM
, allow simulations of active Cas13a:crRNA complex formation and the
subsequent conversion of quenched GFP to active GFP by the
complex. As such, the model can be broken down into 4 main areas;
these being Cas13a:crRNA complex formation, complex activation,
trans-nuclease activity, and complex degradation via cis-nuclease
activity (Figure 2).
Figure 2. Reactions involved in the detection of CPLX1 mRNA by trans-cleavage activity of Cas13a. A) Formation of Cas13a:crRNA complex; B) Cas13a:crRNA complex activation after CPLX1 binds to the complex; C) Cis-cleavage of CPLX1 by active Cas13a resulting in ribonucleic acids and inactive Cas13a:crRNA complex; D) Trans-cleavage of CPLX1 mRNA and CPLX1 crRNA remaining in the system by active Cas13a resulting in ribonucleic acids; E) Trans-cleavage of quenched GFP by active Cas13a resulting in active GFP and ultimately a fluorescent output.
Table 1. Concentrations of reaction components for use in mRNA-mediated collateral cleavage of quenched GFP by Lw2Cas13a .
Artificial CPLX1 mRNA
Concentrations (Table 1) were based on values used by Abudayyeh et al. (2017) which also mirrored concentrations used in our own assays. Enzymatic rates (Table 2) were determined from literature. The rates of Cas13a:crRNA complex formation and activation were based on pre-crRNA processing rates  and general activator mRNA dissociation constants . Cleavage rate of ssRNA by the trans-nuclease activity Lw2Cas13a (Kcat) was based on Cas13a from Leptotrichia buccalis (LbuCas13a). Km was obtained by dividing Kcat by catalytic efficiency. These rates were deemed more appropriate than using Cas12a rates as Cas12a possesses nuclease action against DNA rather than RNA and so may operate in a significantly different manner. The rate of cis-ssRNA cleavage by Lw2Cas13a was estimated due to lack of evidence in the literature. Estimates based on the fact that cis-ssRNA is single action and therefore must be slower than trans-ssRNA cleavage, which possesses multiple-turnover activity, as it requires complex reformation to occur again.
Table 2. Enzymatic rates of different cleavage activity by Lw2Cas13a. *Data not in literature and so estimated using related information
Preliminary analysis of the model was completed using a deterministic time course. By using deterministic methods, some accuracy was lost in order to reduce system complexity and computational demand. As rate of GFP production decreases as CPLX1 is degraded, maximum GFP concentration is defined as the point in which 10 consecutive timepoints do not increase by more than 0.01 nM.
The effect of different CPLX1 mRNA concentrations on the time until and amount of GFP produced was investigated. While literature does not indicate the exact concentrations of CPLX1 mRNA in people with and without Parkinson’s Disease, Lahut et al. (2017)  state CPLX1 mRNA concentration and overall expression in the blood of a presymptomatic Turkish cohort is reduced by 67 and 33% respectively. As such, 10 nmol μL-1 was used for a placeholder for individuals without Parkinson’s Disease and a range of values between 6.7 and 3.3 nmol μL-1 were used to account for variation in those with early-stage and late-stage Parkinson’s Disease respectively.
Figure 3. Time-course simulation of changing reactant concentrations within an in vitro CRISPR SHERLOCK system for the detection of 10 nM CPLX1 mRNA. Simulation completed as preliminary scan only.
The time-course of an individual without Parkinson’s Disease (Figure 3
) was used as a benchmark to observe how the model ran. The model indicated a SHERLOCK system using 10 nmol μL-1 CPLX1 mRNA would reach peak GFP concentration within 15.48 seconds. However, no component in the system demonstrated a notable increase in concentration. Furthermore CPLX1 mRNA took 394.32 seconds to be entirely degraded, more than 2500% longer than the time taken until maximum GFP concentration. Established methodology  incubates the system for 1-3 hours which then raises questions regarding the short timescale of GFP increase. Additionally, the concentration of active Cas13a:crRNA complexes does not show a notable increase. This suggested that either the estimated Kcat of cis-cleavage was too high or the rate of activation was too low.
The initial iteration of the model used Kcat and Km of LbuCas13a meaning the first approach to refining the model was to determine if these rates were suitable. UniProt  protein sequence alignment using the Gonnet transition matrix showed 22.3% similarity between LbuCas13a and Lw2Cas13a. Diverse Leptotrichia sp. Cas13a sequence similarity has been noted  , with similarity ranging between 61 and 91% in L. shahii JCM16776 alone. This meant Lw2Cas13a may not be as similar to LbuCas13a as first predicted. The same study also indicated that L. wadei is more closely related to L. shahii than L. buccalis; however, protein sequence alignment of L. shahii Cas13a (LshCas13a) with LwaCas13a2 showed a 16.3% similarity. As a result, both LbuCas13a and LshCas13a Kcat and Km values may not be suitable in place of Lw2Cas13a rates. However, as the LbuCas13a rates are the only available rates, they must be used for the model.
Figure 4. Time-course simulation of changing reactant concentrations within an in vitro CRISPR SHERLOCK system for the detection of 10 nM CPLX1 mRNA after refining initial reaction concentrations
The first step to refining the model was to convert from nmol/mL to nmol/L to allow easier conversion of experimental results which are typically given in molarity. As part of conversion, the concentrations of reactants were converted to nM and the reaction volume was changed to reflect L instead of mL. This had an immediate effect on the model (Figure 4), which now predicts maximum GFP within 2.26 seconds, likely suggesting original concentrations had been miscalculated due to complex units. By updating the concentrations the change in GFP concentration no longer ended with an abrupt change much rather the curve ends in a sigmoidal-like manner as would be predicted in an enzyme system.
As some parameters were miscalculated, it was important to check all other parameters used in the model. Whilst checking parameters concerning Cas13a:crRNA complex formation, activation, and deactivation, it was observed that the rates of formation and activation used were also inaccurate. In the original model, a rate constant of 0.29 nM s-1 was used to observe Cas13a:crRNA complex activation. Under closer observation it was noted that the value was only a concentration as it had not been divided by 60 to produce a rate and so this error was rectified. Furthermore, the rate for complex formation was also incorrect as it did not consider concentration. This was corrected by first dividing the processing rate by 60 to obtain the processing rate per seconds before dividing the experimental concentration  by the rate per second. After observing the rates of Cas13a:crRNA complex formation and activation, it was hypothesised that exact complex degradation rate may not vital. This is as in vitro degradation rate will likely always be order of magnitudes greater than formation and activation. Due to this hypothesis, the rate of degradation was increased to be closer in line with trans-ssRNA cleavage.
Table 3. Corrected parameters developed during CRISPR SHERLOCK kinetic model refinement
Cas13a:crRNA complex formation
Cas13a:crRNA complex activation
Cas13a:crRNA complex degradation
Upon correcting these parameters (Table 3), the model now predicts that maximum GFP will be reached in 17.84 seconds (Figure 5).
Figure 5. Refined Time-course simulation of changing reactant concentrations within an in vitro CRISPR SHERLOCK system for the detection of 10 nM CPLX1 mRNA. Data shown until point of plateau.
After presenting the model to our collaborators at Waterloo, it was noted that the model would give a more true reflection of the system if crRNA degradation by trans-cleavage was also included. Rates used were equal to degradation of CPLX1 mRNA degradation and GFP activation. Inclusion of crRNA degradation did not impact time until maximum GFP concentration (Figure 6).
Figure 6. Final time-course simulation of changing reactant concentrations within an in vitro CRISPR SHERLOCK system for the detection of 10 nM CPLX1 mRNA. Model changed to include crRNA degradation by Cas13a ssRNA-trans cleavage. Data shown until point of plateau.
The predicted times until maximum GFP concentration changed as a result of model refinement. Overall, the model predicts that time until maximum GFP does not change in the same manner as first hypothesised (Table 4). The model predicts that time until maximum fluorescence increases at semi-regular intervals between 3.33 and 6.67; however, there is a sudden decline between 6.67 and 7.33. After this decline, time until maximum begins to increase at a regular interval once again. The cause behind the decrease is unclear as it would be predicted that time would continue to increase at the regular interval as no other parameter has been changed. Unforeseen interactions may provide an explanation; however, it is not currently possible to identify the interactions with current level of understanding. Regardless, reaction run time should reflex the maximum time until fluorescence across all CPLX1 mRNA concentrations and so reactions should run for 25 to 30 seconds.
Table 4. Time until maximum GFP concentration in seconds and maximum GFP concentration produced by ssRNA-mediated trans-cleavage of quenched GFP by Lw2Cas13a in the presence of different concentrations of CPLX1 activator mRNA. Time until maximum GFP concentration reached when 10 consecutive timepoints do not increase by more than 0.01 nM.
mRNA Concentration (nM)
Time until Maximum GFP Concentration (s)
Maximum GFP Concentration (nM)
The new time reflects findings by East-Seletsky et al. (2016) . Gel electrophoresis results were highly similar after either 30 seconds or 10 minutes of incubation. It may be suggested that current methodology adopts a 'just in case' approach to ensure that a response is elucidated. This ideology is suitable for current SHERLOCK systems designed to distinguish between viruses - such as Zika - at strain level . Longer incubations than needed could be used as a precaution to confirm responses due to the potential impact of false negatives so it may be argued that reaction run time should be doubled - particularly as time until maximum is not as important as initially thought.
The model highlighted that maximum GFP concentration changes depending on CPLX1 mRNA concentration (Figure 7a). This outcome was not originally predicted; however, it is logical after considering how the system operates. At higher concentrations, more Cas13a is activated thus more GFP is activated before all Cas13a complexes are degraded. At low concentrations, less GFP can be activated before all active Cas13a complexes are degraded. Regression analysis (Figure 7b) revealed a positive correlation (R2=0.9979, P <0.05) between maximum GFP concentration and CPLX1 mRNA concentration.
Figure 7. a) Change in GFP concentration over 30 seconds at different concentrations of CPLX1 mRNA concentration indicative of persons without (10.00 nM), early stage 6.67 nM, and late stage (3.33 nM) Parkinson's Disease. b) Maximum concentration of GFP produced by trans-ssRNA cleavage activity of Cas13a at different concentrations of CPLX1 mRNA. Trendline represents regression (R2=0.9955, P <0.0001)
The discovery of a positive correlation between CPLX1 mRNA concentration and GFP concentration and the lack of correlation between CPLX1 mRNA concentration and time until maximum GFP concentration disproves the original hypothesis. As a result, the approach towards methodology development was changed. The model demonstrated that a 60 second reaction run time allows maximum GFP concentration to be reached in all assayed conditions. Furthermore, it was revealed that all samples can be assayed at the same time as fluorescence will be different depending on starting CPLX1 mRNA concentration.
Figure 8. Maximum concentration of GFP produced by trans-ssRNA cleavage activity of Cas13a at different concentrations of quenched GFP. Trend line represents regression (R2=0.8459)
During parameter testing, it was also found that quenched GFP was in excess in the system. Lowering quenched GFP concentration increased the time until maximum GFP concentration and has negligible impact on maximum GFP concentration - increasing final concentration by as much as 0.09 nM. As a result, it may be possible to reduce the cost per reaction without compromising the efficacy of the assay by reducing the amount of quenched GFP added per reaction. This is only plausible because the change in concentration does not have significant effect on maximum GFP. The model suggests that the system would still be functional using 10 nM quenched GFP rather than 125 nM (Figure 8). As with reaction runtime, this value ought to be doubled to ensure response.
As the model output was GFP concentration, the model could be tested using standard curves which plot fluorescence against known concentrations of the same GFP and then comparing experimental fluorescence to calculate actual GFP concentration and compare. Providing the concentration predicted by the model was correct, this highlights the potential to standardise the system across different by plotting concentration against relative fluorescence to fluorescein. By doing so, error can be reduced as relative fluorescence should remain somewhat unchanged between plate readers and laboratories.
Glutathione Detection Kinetic Model
Rationale & Aims
Like the preceding eicosane detection model, it was important to understand how the degradation of glutathione into glycine and cysteine resulted in a dose dependant response. However, due to the involvement of multiple enzymes, this model primarily sought to identify bottlenecks in the glutathione degradation pathway. Bottleneck identification allows for improved construct design by utilising different promoters and ribosome binding sites (RBS) in order to reduce metabolic burden on the cell as well as optimising the system to produce a more defined response at different concentrations.
As previously, the model was constructed on COPASI 4.26 using Henri Michaelis-Menten kinetics to describe enzyme activity, and mass action to describe transcription and translation.
Reaction volume (0.492 μL) was based on cell volume of E. coli and system was parameterised to use mM concentrations. Glutathione concentration (1,150 μM) was based on concentrations at 50 years old - 10 years before the average age where Parkinson’s Disease symptoms present .
As cytosol-specific dipeptidase (pepD) and glutathione-specific gamma-glutamylcyclotransferase (ChaC) expression was constitutive, transcription rate of mRNA was based on E. coli transcription elongation rate at 37 °C– approximately 42 bp.sec-1  . To calculate rate, the number of nucleotides was divided by 42 before dividing 1 by the result. Translation rate was based on E. coli ß-galactosidase translation rate – 14.5 amino acids.sec-1  . Translation rate, again, was calculated by dividing the number of amino acids by 14.5 then dividing 1 by the result.
mRNA degradation rate was based on half-lives of total mRNA in E. coli – approximately 6.8 minutes . Protein degradation was based on average E. coli protein half life which is approximately 20 hours .
Table 5. Enzyme rates for pepD and chaC in Mus musculus used in the glutathione model. Rates obtained from BRENDA .
Enzyme rates (Table 5) were determined using the BRENDA database . However, Kcat and Km were not available for either enzyme. As values for both enzymes were available for Mus musculus and so these values were used for consistency. However, as the rates for E. coli become available, they should be substituted into the model.
The model found that all glutathione is converted into glycine within 548.6 seconds (Figure 9). However, it was noted that the cleavage of the dipeptide into glycine and cysteine by pepD occurred at a drastically fast rate than the cleavage of glutathione into 5-oxo-L-proline and dipeptide by ChaC.
Figure 9. Time course over 600 seconds showing the conversion of glutathione into cysteine-glycine dipeptide via chaC followed by the hydrolysis of the dipeptide into glycine and cysteine (not shown) by pepD.
When observing the enzyme rates used in the model for each enzyme it became clear that pepD has a much lower Km than ChaC. This means needs less dipeptide to achieve half the maximum velocity and so the slow rate of ChaC creates a bottleneck.
The solution to this problem was to design a pepD construct with weak expression as to limit the amount of pepD in the system. Through doing this, the time until conversion from glutathione to glycine can be increased and so reduce the stress on cell and allow a response. Although we did not have time to assemble this construct, it was designed. This construct can be seen here.
Future Model Improvements
As previously mentioned, the model should be re-parameterised in the future to include enzyme rates for E. coli become available.
The model, in its current state, acts as a base to model the rest of the system. By monitoring the conversion of glutathione into glycine, it is possible to monitor the change in RFP expression under the control of gcvB promoter. Waterloo iGEM proposed a series of reversible mass action equations (Figure 10) which would allow modelling of the gcvA/gcvR interaction before gcvA interacts with the gcvB promoter – as discussed in our glutathione biosensor.
Figure 10. Modelling equations provided by Waterloo iGEM team as part of modelling mentoring for the construction of kinetic models.
Although this could not currently be implemented, due to a lack of research on the rate of association and dissociation between each component, the equations would allow for exploration of dose-dependent responses. It may also provide insight as to how other parts of the system may be adapted to produce a more distinguishable result between glutathione concentrations.
Eicosane Detection Kinetic Model
Rationale & Aims
Unlike the CRISPR SHERLOCK system, the detection of eicosane via the expression of RFP was an in vivo system. As a result, a different kinetic model was needed to understand how different concentrations of eicosane impact RFP expression as RFP was to be produced rather than converted from an inactive state to an active state. The overall aims of the model slightly differ from CRISPR SHERLOCK as the model sought to identify a dose-dependant response in a system not limited by being closed.
A dose-dependant response would drastically reduce the importance of measuring results within specific timeframes as the response will not equalised as originally hypothesised in the closed CRISPR SHERLOCK system
By constructing a kinetic mode we will be able to predict RFP concentration in response to different alcohol concentrations. Through studying the effect of each unit, such as eicosanol production and RFP transcription, we would be able to identify any bottlenecks which may reduce the efficacy of our system.
The model was constructed and simulated, again, using COPASI 4.26  and used Henri Michaelis-Menten kinetics to study the hydration of eicosane into eicosanol by long chain monooxygenase A (LadA), and mass action to describe transcription and translation.
As the system was in vivo, the production of proteins - LadA and RFP - had to be modelled. Transcription rate of LadA was given as a single rate which incorporated RNA polymerase recruitment and elongation. Rate predicted to occur at 42 nucleotides per second  and so the number of transcribed products produced per second was determined by dividing 1 by the nucleotide length divided by 42. All translation rates were given as a single rate, 14.5 amino acids per second , which incorporates ribosome recruitment and polypeptide extension. The number of translated products produced per second was determined by dividing 1 by the polypeptide chain length which was divided by 14.5.
The Kcat and Km of LadA, 0.02 and 9.1 respectively, were sourced from the BRENDA database; however, only the rates for hexadecane hydration by Geobacillus thermodenitrificans were available. However, hexadecane is a smaller molecule than eicosane meaning actual Kcat is likely even lower. Furthermore, the G. thermodenitrificans and enzymes operate at a temperature that would kill Escherichia coli and as such the Kcat and Km values may not be suitable for the final iteration of the model
When it came to modelling the regulated transcription of RFP under control of the alcohol dehydrogenase promoter, adhEp2, there was minimal information available on how the promoter operates. The original source material for adhEp2 lists the promoter as having 2 regions; an upstream silencer region and downstream fnr binding region. During the design of our RFP expression construct, it was hypothesised that 1-eicosanol would interact with components that allowed Fnr to bind to a 5' truncated variant of the promoter. This 5' truncate was selected due to evidence that Fnr can only regulate adhEp2 if the silencer is removed. The truncated variant was also chosen to remove the upstream silencer region .
However, under further analysis it became apparent that there is a lack of evidence to support the claim that 1-eicosanol will initial RFP transcription in the designed system. This is particularly due to the lack of evidence that fnr and 1-eicosane interact. As such, there appears to have been a misconception during the design phase that the system would be activated in the presence of any alcohol. This misconception likely occurred as fnr is heavily involved in anaerobic lifestyle and as E. coli can produce alcohols via fermentation then a link may have been made increasing alcohol concentration interacts with fnr to induce alcohol dehydrogenase to allow NADH production via redox reactions.
Due to the lack of evidence to support our system, model design was postponed until our constructed system was tested. This was because if the system was functional then the approach for modelling regulated RFP expression would have to be reevaluated as understanding would be incorrect.
Model-based Hypotheses and Experimental Findings
Due to the lack of evidence to support our system, it thus became important to test our system before model construction continued. The system was assembled and tested in E. coli DH5alpha by exposing cells to different alcohols including 1-eicosanol, ethanol, butanol, and propanol. From our model, it was predicted that the system should not work as the adhEp2 promoter does not operate as initially understood. If experimental findings demonstrated the construct was functional, then modelling the system via a different path would be plausible; however, if the system did not work then the model successfully prevented waste of resources and time. Through either result, the model allowed greater understanding of the system and careful consideration for the other two systems to ensure both would be functional.
The results of characterisation showed that the system was non-functional in the presence of 1-eicosanol. As it may be argued that the system was non-functional as 1-eicosanol is a large molecule thus unable to diffuse into the cell, the system was also unresponsive to ethanol and other shorter alcohols. As it was originally hypothesised that any alcohol would interact with adhEp2 to induce RFP expression, the system was shown not to function as expected - the outcome which the model research predicted.
While construction of the eicosane kinetics model was not possible, the findings of the model research were highly important to the rest of the project. Through identifying that our system was not going too be activated by 1-eicosanol - and further proving this experimentally - we were able to redirect time and resources into improving other models. In order to successfully express RFP in the presence of eicosane, a different approach must be taken. One method may be to bind eicosane to a small-chain variable fragment to allow protein interactions which enables a greater array of detection mechanisms such as ELISA or high performance liquid chromatography.
Content: Connor Trotter
Figures: Connor Trotter and Matthew Rogan
Proofreading: Connor Trotter, Dr Alice Banks, Bradley Brown
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