Difference between revisions of "Team:ETH Zurich/Sensor Module"

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             <h2>INTRODUCTION:</h2>
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             <h2>OVERVIEW</h2>
 
             <p>
 
             <p>
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                 Our idea was to recognize bowel infection and its possible cause based on the intestine level of Nitric Oxyde (NO) which
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                 Our idea was to identify bowel infection and its possible causes based on the intestine level of nitric oxyde (NO), which
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                 is infection specific, and of Acyl Homoserine-Lactone (AHL) which is microbiota specific. Thus, the simultaneous
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                 is infection specific, and of N-acyl homoserine-lactone (AHL), which is microbiota specific. Thus, the main goal was to detect the simultaneous presence of those two chemicals in an abnormal amount.
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                presence of those two chemicals in an abnormal amount can de detected, and later associated.
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             </p>
 
             </p>
 
             <p>
 
             <p>
−
                 Lactate is also a molecule of interest in IBD research : non only is it playing an important role in metabolism, but recent
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                 Additionally, we found out in our interview with Prof. Christophe Lacroix that lactate is also a molecule of interest in inflammatory bowel disease (IBD) research: lactate plays an important role in microbiome metabolism and recent studies suggest its presence in high amounts in certain cases of severe IBD.
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                studies tend to show that it is present in high amount in certain cases of severe IBD.
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             </p>
 
             </p>
 
             <p>
 
             <p>
−
                 Thus it turns out that two type of sensors are interesting to devellop in order to investigate the causes of IBD. The first
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                 For this reasons, we decided that two type of sensors are interesting to develop in order to investigate the causes of IBD: One sensor to associate the presence of both AHL and NO, and another sensor to associate lactate
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                AND Gate will be able to detect the presence of both AHL and NO, while the second one will detect Lactate
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                 and NO.
 
                 and NO.
 
             </p>
 
             </p>
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                     <img src="https://static.igem.org/mediawiki/2016/6/67/T--ETH_Zurich--sensor2design.svg">
 
                     <img src="https://static.igem.org/mediawiki/2016/6/67/T--ETH_Zurich--sensor2design.svg">
 
                 </a>
 
                 </a>
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                 <p><b>Figure 1:</b>two alternative design for the sensor module</p>
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                 <p><b>Figure 1:</b> Two alternative designs for the sensor module. Left: A sensor module that associates the simultaneous presence of the inflammatory marker nitric oxide (NO) and the microbiotic marker AHL. Right: Association of NO with the microbiotic marker lactate.</p>
 
             </div>  
 
             </div>  
  
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     <div class="sec light_grey">
 
     <div class="sec light_grey">
 
         <div>
 
         <div>
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             <h3> GOALS</h3>
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             <h3>GOALS</h3>
  
 
             <ul>
 
             <ul>
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                 <li>Have an overall overview of the behavior and characteristic of our system</li>
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                 <li>To get an overall overview of the behavior and to compute a dose response curve.</li>
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                 <li>Discuss the specification of our model and see how the design may influence the equations and this the output
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                 <li>To identify how the biological design may influence the the behavior of our system.</li>
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                    behavior
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                 <li>To identify sensitive parameters that can be tuned.</li>
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                </li>
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                 <li>To compare alternative designs.</li>
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                 <li>Define the parameters that can be tuned and that can impact the output of our system so we can control our
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                    system range of working</li>
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                 <li>Compare the different design</li>
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                <li>Infer the input state from the output signal analysis</li>
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             </ul>
 
             </ul>
  
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                     <img src="https://static.igem.org/mediawiki/2016/3/34/T--ETH_Zurich--NorRSystem.svg">
 
                     <img src="https://static.igem.org/mediawiki/2016/3/34/T--ETH_Zurich--NorRSystem.svg">
 
                 </a>
 
                 </a>
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                 <p><b>Figure 1:</b>NorR overview</p>
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                 <p><b>Figure 1:</b> NorR overview.</p>
 
             </div>
 
             </div>
  
 
             <div class="sec white">
 
             <div class="sec white">
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                 <h2>Nitric Oxyde sensor</h2>
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                 <h2>Nitric Oxyde nsor</h2>
 
                 <p>
 
                 <p>
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                     In the absence of NO, NorR is produced constitutively and binds repressively to the PnorV promoter, preventing gene transcription.
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                     In the absence of NO, NorR is produced constitutively and binds to the PnorV promoter, which leads to a repression of the gene transcription.
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                     When NO is present in the medium, it binds cooperatively to the hexameric form of NorR,and activate the
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                     When NO is present in the medium, it binds cooperatively to the hexameric form of NorR and activates the promoter.
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                    promoter.
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                 </p>
 
                 </p>
 
             </div>
 
             </div>
  
 
             <div class="sec white">
 
             <div class="sec white">
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                 <h3>ASSUMPTION</h3>
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                 <h3>ASSUMPTIONS</h3>
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                 <p> We considered here that the binding of NO to NorR and PnorV_{i} does not affect the other species binding.
+
                 <p> We considered here the binding of NO to NorR and PnorV_{i} does not affect the other species binding.
 
                     Thus the reactions \begin{align*} NorR+NO&amp;\rightleftharpoons NorR_{NO}\\ \end{align*} and \begin{align*}
 
                     Thus the reactions \begin{align*} NorR+NO&amp;\rightleftharpoons NorR_{NO}\\ \end{align*} and \begin{align*}
 
                     PnorV_{NorR}+NO&amp;\rightleftharpoons NorR_{NO}\\ \end{align*} have the same reaction rate. Under those
 
                     PnorV_{NorR}+NO&amp;\rightleftharpoons NorR_{NO}\\ \end{align*} have the same reaction rate. Under those

Revision as of 00:15, 19 October 2016

PAVLOV'S COLI

SENSOR MODULE

OVERVIEW

Our idea was to identify bowel infection and its possible causes based on the intestine level of nitric oxyde (NO), which is infection specific, and of N-acyl homoserine-lactone (AHL), which is microbiota specific. Thus, the main goal was to detect the simultaneous presence of those two chemicals in an abnormal amount.

Additionally, we found out in our interview with Prof. Christophe Lacroix that lactate is also a molecule of interest in inflammatory bowel disease (IBD) research: lactate plays an important role in microbiome metabolism and recent studies suggest its presence in high amounts in certain cases of severe IBD.

For this reasons, we decided that two type of sensors are interesting to develop in order to investigate the causes of IBD: One sensor to associate the presence of both AHL and NO, and another sensor to associate lactate and NO.

SENSOR MODULE

Figure 1: Two alternative designs for the sensor module. Left: A sensor module that associates the simultaneous presence of the inflammatory marker nitric oxide (NO) and the microbiotic marker AHL. Right: Association of NO with the microbiotic marker lactate.

GOALS

  • To get an overall overview of the behavior and to compute a dose response curve.
  • To identify how the biological design may influence the the behavior of our system.
  • To identify sensitive parameters that can be tuned.
  • To compare alternative designs.

Figure 1: NorR overview.

Nitric Oxyde nsor

In the absence of NO, NorR is produced constitutively and binds to the PnorV promoter, which leads to a repression of the gene transcription. When NO is present in the medium, it binds cooperatively to the hexameric form of NorR and activates the promoter.

ASSUMPTIONS

We considered here the binding of NO to NorR and PnorV_{i} does not affect the other species binding. Thus the reactions \begin{align*} NorR+NO&\rightleftharpoons NorR_{NO}\\ \end{align*} and \begin{align*} PnorV_{NorR}+NO&\rightleftharpoons NorR_{NO}\\ \end{align*} have the same reaction rate. Under those assumption, the system of equation can thus be simplified as follows:

REACTIONS

Reaction

NOrR SYSTEM:

\begin{align*} &\rightarrow NorR\\ NO+NorR&\rightleftharpoons NorR_{NO}\\ 2NorR_{NO}&\rightleftharpoons DNorR_{NO2}\\ 2NorR &\rightleftharpoons DNorR\\ DNorR+NO&\rightleftharpoons DNorR_{NO1}\\ DNorR_{NO1}+NO&\rightleftharpoons DNorR_{NO2}\\ DNorR_{NO2}+PnorV0&\rightleftharpoons PnorV1\\ DNorR_{NO2}+PnorV1&\rightleftharpoons PnorV2\\ DNorR_{NO2}+PnorV2&\rightleftharpoons PnorV3\\ PnorV3&\rightarrow mRNA_{Bxb1}\\ NorR&\rightarrow\\ DNorR&\rightarrow \\ DNorR_{NO1}&\rightarrow\\ DNorR_{NO2}&\rightarrow\\ NorR_{NO}&\rightarrow\\ mRNA_{Bxb1}&\rightarrow\\ \end{align*}
Species Description
NO Nitric Oxyde produced from DETA/NO reaction
NorR NorR constitutively produced insideE. coli cells
NorR NO NorR with No boundE. coli cells
DNorR Dimer of NorR , regulatory protein PnorV operon
DNorR NO1 Dimer with one NO bound to one of its site
DNorR NO2 Dimer two NO bound to it
PnorV i PnorV promoter with i sites occupied by DNoR NO2
PnorV 3 PnorV3 is the active promoter

RESULTS

The sensor module must be able to finely sense the different species, and in the rigth amount of concentrations. In this section we will explain how the model was used to provide useful insights for the biological system parameters.

REQUIREMENTS

NO sensor sensitivity range = [2 uM - 200 uM] Dynamic range : the system must be as fast as possible

KEY IDEA

We want to make the sensitivity range of the sensor and the activation range of the hybrid promoter match, so it propagates information relative to the inflammatory and candidate species to the switch and thus to the reporter. Under FACS and fluorescence distribution analysis the level of inflammation could then be inferred

PARAMETERS OF INTEREST

  • transcription rate of NorR
  • translation rate of NorR (RBS concentration)
  • Degradatioin rate of NorR

those parameters will allow us to set with the kinetic and the steady-state concentration of NorR in the system.

SENSITIVITY ANALYSIS
DOSE RESPONSE

HEAT MAP

Figure 3:This simulation was run with an input concentration of NO of 2 uM. As explained before we would like to match the range of activation of the NO sensor module with the required dynamic range, in order to propagate through the genetic circuit all the information relative to the degree of activation of the sensor. Here, in order to avoid false negative results during the learning phase we would like an activation between 20% and 60% at the limit of detection. Which implies to keep a ratio between the degradation rate and the transcription rate (Kd) between 1.2 nM and 0.65 nM

Figure 4:This simulation was run with an input concentration of NO of 200 uM, the ideal upper limit of the sensor dynamic range. At this point we want a full activation of the sensor, which means at least a ratio of 0.8 activated promoter. Here it means a production rate superior to 2.5 nM min-1

This is the optimal limit of detection of our system. However, as we can see it is hard to adjust this limit of detection, As the system seems extremely stiff. As we can see for those concentration of NO, we already reach the full activation independently of the transcription rate. The behaviour of the sensor at 2uM or 200uM is similar. At first view, it seems that we can only choose between full activation for both those concentration (all-or-nothing behaviour), or a weak activation. Thus it does not seem possible to play with the tunable parameters to adjust the behaviour of the system on the range of interest. However, in order to get a deeper insight on the model, it will be interesting to look at a more detailed dose response simulation.

Figure 5:In order to more precisely tune our system, we wanted to look more into details into the dose reponse behaviour of the module. Providing the model with a range of different production rates, and degradation rtaes respecting the previously defined ratio constrain, we plot the dose response of the sensor.

DOSE RESPONSE

However, the output of the NO module is the number of PnorV promoter activated by the NO. This number, at a cell level is between 1 and 15, so noise may play an important role in the system behavior, that is why a stochastic simulation may, in case of low NO level, be interested in order to get deeper insight on the system response to NO.

HEAT MAP

Figure 6:Plotting the concentration corresponding to the maximum of the derivative of the previous dose response curve we compute the limit of detection of the system as a function of the transcription rate, assuming a degradation rate respecting the previous ratio constrain.

Figure 7:With regards to all the previous simulation it appears that a promoter strength of 3 nM for example is enough to see a 4 fold promoter activation under 200 uM of NO system stimulation. We wanted to determine which concentration of the NO species this promoter strength would represent. It appears that the NOrR concnetration remains quite low and similar to the concentration of native NorR in the E.Coli. In order to make the circuit as easy to implement as possible. It was suggested tu thus only use the native NorR naturally present in the cell. This would simplify the circuit to reducing the amount of sequence to inject inside the plasmids.

PARAMETER ESTIMATION

In order to provide the biologists more accurate information for an efficient system tuning, we decided to estimate the parameters of the real system. As the NO sensor already worked pretty well and shows a nice behaviour on the plate reader tests, we decided to fit the parameters of our model based on one of those plate reader experiments.

Figure 7:curve fitting for the NO sensor. Each curve correspond to a time response to a certain concentration of nitric oxide induction. we used MEIGO for the fitting. MEIGO uses metaheuristic and Bayesian methods to fit data to a system of differential equations.

Figure 17: Dose response of the NO sensor with the estimated parameters.

Figure 8: AHL Sensor overview

AHL SENSOR

In the absence of AHL, EsaR is constitutively produced, dimerizes and bind as a dimer to the esaBox situated downstream the promoter, preventing transcription as a roadblock. When a higher than normal amount of AHL is present in the gut, it binds to the EsaR dimer, and free the promoter, allowing transcription. Later on, several EsaBox can be added, in order to tune the sensor sensitivity.

ASSUMPTION

We assume a very fast dimerization of EsaR

REACTIONS

EsaR Hybrid Promoter System:

\begin{align*} &\rightarrow EsaR\\ 2 EsaR & \rightleftharpoons DEsaR\\ AHL+DEsaR &\rightleftharpoons DEsaR_{AHL1}\\ AHL+DEsaR_{AHL1}&\rightleftharpoons DEsaR_{AHL2}\\ Pesar1+AHL&\rightleftharpoons Pesar1_{AHL1}\\ Pesar1_{AHL1}+AHL&\rightleftharpoons Pfree +DEsaR_{AHL2}\\ Pfree &\rightarrow mRNA_{GFP}\\ EsaR&\rightarrow\\ DEsaR&\rightarrow \\ DEsaR_{AHL1}&\rightarrow\\ DEsaR_{AHL2}&\rightarrow\\ mRNA_{GFP} &\rightarrow\\ \end{align*}
Esar Reporter System:

\begin{align*} &\rightarrow EsaR\\ 2 EsaR & \rightleftharpoons DEsaR\\ AHL+DEsaR&\rightleftharpoons DEsaR_{AHL1}\\ AHL+DEsaR_{AHL1} & \rightleftharpoons DEsaR_{AHL2}\\ Pesar2+AHL&\rightleftharpoons Pesar2_{AHL1}\\ Pesar2_{AHL1}+AHL&\rightleftharpoons Pout+DEsaR_{AHL2}\\ Pout &\rightarrow mRNA_{GFP}\\ EsaR&\rightarrow \\ DEsaR&\rightarrow \\ DEsaR_{AHL1}&\rightarrow\\ DEsaR_{AHL2}&\rightarrow\\ mRNA_{GFP} &\rightarrow\\ \end{align*}
Species Description
AHL Acyl Homocerine Lactone introduced in the medium
EsaR EsaR constitutively produced insideE. coli cells
DEsaR Dimer of EsaR , regulatory protein binding to Esaboxes situated downstream the promoter
DEsaR AHL1 Dimer with one AHL bound to one of its site
DEsaR AHL2 Dimer with two AHL bound to one of its site
DNorR NO2 Dimer two NO bound to it
Pesar i Pesar1 correspond to the hybrid promoter. Pesar1 is the reporter promoter. They are independant
Pfree Pout respectively promoter freed from the road block constituted by the EsaR bound to the downstream esaboxes

RESULTS

The sensor module must be able to finely sense the different species, and in the rigth amount of concentrations. In this section we will explain how the model was used to provide useful insights for the biological system parameters.

REQUIREMENTS

AHL sensor sensitivity range = [10 nM - 1 uM] Dynamic range : the system must be as fast as possible

KEY IDEA

We want to make the sensitivity range of the sensor and the activation range of the hybrid promoter match, so it propagates information relative to the inflammatory and candidate species to the switch and thus to the reporter. Under FACS and fluorescence distribution analysis the level of inflammation could then be inferred

PARAMETERS OF INTEREST

  • transcription rate of NorR
  • translation rate of NorR (RBS concentration)
  • Degradatioin rate of NorR

those parameters will allow us to set with the kinetic and the steady-state concentration of NorR in the system.

SENSITIVITY ANALYSIS
HEAT MAP

Figure 9:The activation of the promoter was simulated under a constant AHL simulation of 100 nM with varying translation and transcription rates of Esar. As we can see it seems that they have similar impact on the circuit behaviour

As we can see on the graph below, translation and transcription have similar effect on promoter activation. Thus we decided to play with promoter strength rather than rbs level inside each cells. Later on we decided to only play with the promoter strength (transcription rate), as a entire collection of biobrick promoters is available, and thus spare to the lab to work on a rbs library in order to modify the cell translation rate.

Figure 10:We simulated the effect on the transcription and degradation rate on the AHL sensor promoter activity under 100 nM (ideal lower limit of detection) As before we want to match the detection and dynamic range of the sensor to propagate the level of inflammation through the genetic circuit. Here it implies that the ratio (Kd) must stay between 0.1 nM and 0.5 nM

Figure 11:The same analysis performed on the AHL sensor system with the ideal upper detection limit 1 uM diplays the heatmap above. To guarantee a activation superior to 90% at the input level, we need a Kd < 0.66 nM

DOSE RESPONSE

However the output is a amount of freed promoter at a cell level. As our cells only contain around 15 plasmid so stochastic modelling may be interesting.

Figure 12:The same dose response analysis was performed on the AHL sensor to finely tune our system in order to make it behave as ideally as possible. a range of different Esar production rate were tested on the circuit while simulated the dose response, assuming the ration constrained respected.

PARAMETERS ESTIMATION

Using the previous analysis, we now want to be able to give insights for the real system we have. The first step consists in estimated the actual parameters of our circuit. Actually we can only play with a few parameters, as most of them are chemical reactions rate on which we do not have any impacts. We used MEIGO, a optimisation tool, to infer the parameters.

Figure 13: We performed a parameters deterministic estimation using MEIGO. The Estimation was perform using facs datas. Meigo is an optimization toolbox that includes metaheuristic methods and a Bayesian inference method for parameter estimation.

We have some trouble with the plate reader test during the first part of our lab project. In particular with the AHL sensor that presented an unexpected behaviour at some concentration of AHL. Therefore, we decided to perform this parameter estimation in order to get a deeper understanding of the chemical mechanism, and to try to find an explanation and give to the biologists some clues to improve the system. As before the number of parameters the biologists can play with is rather restricted. We thus decided to focus on the two following parameters : EsaR production and degradation rate, which are easily tunable.

Figure 14: A plate reader experiment presenting "unexpected behaviour"

Figure 15: Simulation of the same plate reader experiment. As we can see, there is a "fall" of GFP activity for AHL concentrations of 10 and 100 nM. See the dose response plots below for more explanations

The number of parameters the biologists can play with is rather restricted. We thus decided to focus on the two following parameters : EsaR production and degradation rate, which are easily tunable. On the graphs below we simulated the influence of degradation and production rate of EsaR on the dose response.

Figure 14: Influence of EsaR production rate on the dose response of the system. As stated above our ideal range of sensitivity to AHL is between 10 nM and 10 uM. The "bump" at low concnetration must be attenuated in order to avoid false positive. The results above suggests the the bump is attenuated at low production rate, but then the lack of road block preventing the GFP transcription decrease the limit of detection, And the system became sensitive to 1 nM of AHL. Another solution would be to increase EsaR production rate, but as shown on the graph, activation disappear even at very high AHL concentration

Figure 15: Influence of EsaR degradation rate on the dose response of the system. Unlike Esar production rate, when Esar degradation rate decreases, the "low-concentration bump" decreases as well, but the activation at higher AHL concentration is not decreased. Therefore, the model tends to suggest that decreasing EsaR degradation rate could improve the circuit accuracy

EXPLANATION AND OUTLOOK

This behaviour was totally unexpected as we never witnessed any information about it on litterature describing Esar and esaboxes systems. Therefore, our biologists spend quite along time trying to figure out the reason of this bumpy like dose response, thinking they did something wrong during experiment settings. However once we set a proper FACS analysis, we managed to estimate the parameters and plugged them in the model. Then, it appears that all our experoiment were totally fine, just displaying a counter-intuitive behaviour. To explain it, one has to take a closer look to the equation: bothe AHL and Esar are involved in different equations : AHL presence shift forward the equilibrium of DEsaR_{AHL} production and \begin{align*} Pesar1_{AHL1}+AHL&\rightarrow Pfree +DEsaR_{AHL2}\\\end{align*}. However an increase of EsaR concentration also increase the production of DEsaR_{AHL} which shifts the last reaction on the opposite direction. Therefore there a particular range of AHL/EsaR ratio for which the activation is stronger than the repression, which explains the "bumpy behavior" for intermediate AHL concentrations.

Figure 13: Lactate Sensor overview

LACTATE SENSOR

The promoter if flanked of two LldR specific binding sites : O1 and O2. In the absence of of lactate, LldR and LldD are constitutively produced. LldR then binds to O1 and O2 as a dimer, forms a DNA loop and preventing transcription. When Lactate (Lac) is present, it binds to the LldR complex and free the promoter. LldD lowers the concentration of Lactate inside the cell by catalyzing its transformation into pyruvate. The idea is to set a tunable treshold to the Lactate sensor, as this species, just like AHL, is anyway always present in the gut, and we only want to sense abnormal concentration.

ASSUMPTIONS

LldR exists as a dimer in solution. 2 molecules of lactate bind to one LldR dimer (L2). Lldr dimer bind to the two operator sites when no LldR is present. Lactate releases the binding of LldR dimer to the operators.

Reaction

Lactate system:

\begin{align*} &\rightarrow LldD\\ &\rightarrow LldR\\ LldD+Lac&\rightleftharpoons Pyr+LldD\\ 2LldR&\rightleftharpoons DLldR\\ DLldR+ G_on&\rightleftharpoons G_off\\ DLldR + Lac&\rightleftharpoons DLldR_{Lac1}\\ DLldR_{Lac1}+Lac&\rightleftharpoons DLldR_{Lac2}\\ G_off + Lac&\rightleftharpoons G_off_1\\ G_off_1 + Lac&\rightleftharpoons G_on + DLldR_{Lac2}\\ G_on&\rightleftharpoons mRNA_{GFP}\\ LldD&\rightarrow\\ LldR&\rightarrow\\ DLldR&\rightarrow\\ DLldR_{Lac1}&\rightarrow\\ DLldR_{Lac2}&\rightarrow\\ \end{align*}
Species Description
LldR regulatory protein of the Lac system, acts as a repressor
DLldR Dimer of LldR
Lac Lactate introduced in the medium. Forms a complex with LldR, preventing it from repressing the Promoter. Acts thus as an activatorE. coli cells
Pyr NO Pyruvate, inactive form of lactateE. coli cells
LldD Regulatory protein, catalyse the oxydation of Lactate into Pyruvate
G_on NO1 Active promoter
G_off NO2 Promoter repressed by LldR binding
G_off_1 NO2 Repressed promoter with 1 lactate molecule bound
DLldR_Lac1 i DLldR with one Lactate molecule bound NO2
DLldR_Lac2 3 DLldR with two Lactate molecule bound

REQUIREMENTS

NO sensor sensitivity range = [100 uM - 100 mM] Dynamic range : the system must be as fast as possible

KEY IDEA

As before, we want to make the sensitivity range of the sensor and the activation range of the hybrid promoter match, so it propagates information relative to the inflammatory and candidate species to the switch and thus to the reporter. Under FACS and fluorescence distribution analysis the level of inflammation could then be inferred. ETH-Zurich previous team already worked on a Lactate sensor. Thus we tried to improve their work and adapt the sensor sensitivity to our system. It appears that their system is too sensitive for our purpose. As a consequence we decided to add to the plasmid LldR which is constitutively produced and, by inactivating Lactate, artificially lower the concentration of active Lactate that would be able to bind the LLdR complex that inhibits gene transcription.

Figure 13: Lactate Sensor overview

PARAMETERS OF INTEREST

  • transcription rate of LldD
  • transcription rate of LldR
  • Degradation rate of LldD

those parameters will allow us to set with the kinetic and the steady-state concentration of Lactate in the system. However in term of modularity, it turns out it is easier for the biologist to play with the constitutive promoters involved in LldR and LldD production.

Figure 14:The behavior of the lactate sensor with LldD was simulated. The lactate input was set on the lower bound of the ideal sensitive range, namely 100 uM. For this concentration we wish to set the proper LldD concentration that allow a small activation (ideally <30%), so there is no risk of false negative.

Figure 15:The same analysis performed, with the ideal upper detection limit 100mM. To guarantee this concentration is very high, and we can see we have full activation, whatever are the production rates values.

Figure 13: In the graph above, we plotted the dose response curve for a large range of LldR production rate. This shows that one can easily tune the system and adjust the limit of detection, by increasing or decreasing the production rate of the LldR protein.

Figure 13: As for the LldR plot, the LldD production rate can modify the limit of detection and the range of sensitivity of the lactate sensor. Therefore for a more precise tuning, playing with the LldD production rate is a possible way to tune the circuit.

To quickly summarize the difficulties met with the lactate sensor: We based our model and design on the ETH_Zurich iGem team 2015. In their project, they also use a lactate sensitive circuit, So we decided to use the datas they already have for our sensor. However, last year sensor proved to be by far too sensitive for our purpose: they were able to sense up to only a few nM of Lactate in the system while we need tosense between 100 uM and 100 mM. Thus we needed to tune the circuit such that it meet our requirements. To do that we propose the following method: As the more accessible parameters biologists can play with are protein production and degradation rate, we decided to simulate the influence of those parameters on the limit of sensitivity and dynamic range of our system. It appears that aas LldR is a repressor protein to the promoter, increasing its production rate and/or decreasing its degradation rate shift the limit of detection to the right, decreasing the sensitivity of our circuit. However the amount of available promoter is limited, and do is their strength. We came up with the idea of introducing the LldD specie in the design. LldD catalyse the degradation of lactate into Pyruvate. So its presence artificially decrease the concentration of Lactate available to activate the reporter inside the cell. Based on parameters found on litterarure, we figured out that the more you increase its production rate the less sensitive is the sensor. There fore playing with the different constitutive promoter strength allows the biologists to finely tune the system and make it fit our sensitivity requirements.

Figure 13: Plotting the maximum of the derivative of the dose response curves for the range of LldD production rate, we are able to define the limit of detection of the lactate sensor.

Figure 8: Full AND Gate overview

Full AND Gate

Now it is time to link the two previous modules together in order to create the full AND Gate. Ideally, we would like to keep the model as modular as possible. In a first part, our way to proceed in order to recreate the hybrid promoter behavior from the two simple PnorV+Esabox promoter will be described. Then we propose a second model which takes into account all the different states of the promoter under NO and AHL/lactate binding, that can be stochastically simulated.

We developed two models to simulate the and gate. The first one is based on the modular model and consider both systems (NO sensor part and AHL sensor part) as independent. It was developed in the idea to keep everything inter-operable, interchangeable and modular. However, this require a strong assumption, namely that there is no influence of one of the module on the other one. In order to keep the precision of our model, we developed a second model formed of 61 equation that takes into account all the interactions between in the AND gate. Therefor, we have two models for the AND gate, the first one which allow modularity and gives you a quick but slightly approximated overview of the full AND gate circuit, and a Second model, more complex, and longer to implement and to simulate, but that keep the high precision in term of mass action equations, and which is interesting in term of tuning, but sacrifices modularity.

MODULAR MODEL

Figure 16:AND gate simulation using the modular model. As we can see, the rage of sensitivity is not totally the expected one. However, this corresponds to our expectations, since we decided to assume the NO sensor set of reaction and the AHL one independent. We obtain the above results by multiplying the fraction of active promoters of each sensor part, and consider the resulting fraction as the fraction of active hybrid promoter, leading to mRNA and protein production.

FULL STATE MODEL

Figure 17: T plot was obtain using a more detailed model, taking into account all the interaction and overlapping between the NO sensor and the AHL sensor. As describe above, it is composed of 61 equations and takes into account all the binding/unbinding reaction of the different species to and from the hybrid promoter ( PnorV + esaboxes ) As you can see above, it displays for our ideal AND Gate, a better range of sensitivity.

AND GATE SIMULATION WITH THE ESTIMATED PARAMETERS

In order to be able to predict our AND Gate behaviour, we need to simulate it with the fitted parameters. Thus we are able to compare the "real" AND gate dose response with the ideal system. The fitted AND Gate simulation provide allow us to predict our system behaviour, to confirm their experiments and provide some insights in order to improve the circuit and stick closer to the ideal range of input species we want to detect.

MODULAR MODEL

Figure 16:AND gate simulation using the modular model, using the fitted parameters. Here, we decided to use the parameters estimated from the test of the NO and AHL sensor separately tested and characterized. For simplicity, we assume that those parameters are not modified by the presence of the other sensor ( AHL and NO sensor respectively ). As you can see, the AND Gate present an activation at low concentration of AHL. Although it doesnt behave as an AND gate in the full range of possible input, it shows consistency with the previously characterized sensor. This "early activation" actually corresponds to teh bumpy dose response of the AHL sensor for the current parameters.

FULL STATE MODEL

Figure 17:AND gate simulation using the full model, with the fitted parameters. As stated above, while the modular model provide flexibility and reasonably consistent results, it still lacks precision due to the assumptions. As the behaviour of our AND Gate is unusual, we decided to run the simulation using the full model, which provides more accurate results. As we can see the bump is attenuated. This could be explained by the fact that the shifting of equilibrium due to the AHL/EsaR ratio is attenuated by the presence of the NO sensor part. For more information please refer to the AHL sensor module part.

ADDITIONAL LINKS AND INFORMATIONS

FULL-MODEL

For additional information about the full model, please check the link below.

DETERMINISTIC OVER STOCHASTIC MODEL

At the beginning of the project, we wanted to a model as precise as possible that would allow us to tune finely our system in order to get a response as close to the ideal one as possible. In addition, we also decided to go first for a full stochastic model. Thus FACS analysis and comparison as well as fitting would assure us a good parameter estimation. Moreover, we wished that looking at the reporter distribution would help us to get some additional information about the input of the circuit. As the system is thought as a detector, and its application (travelling through the gut which is seen as a black box to get activated eventually by the presence of both NO and specific AHL) is to express a reporter, we wished that by simply looking at he distribution of mean and variance of the reporter could give us enough information in order to reconstitute the input. Thus in a medical application, a simple FACS analysis of the remaining E.Coli harvesting from the faeces, would be enough to determine the acuteness of the inflammation and a quantitative data on the microbiota disbalance. However, it appeared after several staochastic simulation that the fluctuation of the ratio of activated promoter, for one trajectory, was to fast to have any influence of the reporter protein expression, as binding and unbinding of protein and ligand to and from DNA strand are quick reaction compared to mRNA and protein production and folding. As shown on the graph below. Thus we decided to go for simple deterministic simulation for the AND gate characterization.

Figure 18:We compare the behavior of the model under deterministic and stochastic simulations. As we can see the mean behavior remains similar. The fluctuations around the mean value due to the stochasticity can be neglected at a promoter scale because protein-ligand binding-unbinding reaction is extremely fast compare to protein/mRNA production and folding. Thus choosing a deterministic approach here does not represent a loss of information neither for the kinetic nor for the concentration at steady state.

ADDITIONAL LINKS AND INFORMATIONS

MODEL-BRICK

For additional information, please check our public Git repository. All our codes are available there. As the spirit of iGem is information and knowledge sharing, we tried to make our codes as easily usable as possible.

Thanks to the sponsors that supported our project: