Revision as of 13:05, 1 November 2017

Model-based design guidelines used to choose our parts rationally

Why do we need to search for functional parameters?

A biological circuit often has different functioning regimes and can only achieve a particular and interesting behavior for a few given combinations of parameters (among which protein expression levels, or promoter sensitivity and leakiness for example). This is why we had to get some insights into the sets of parameters of our circuit and determine a target combination that would make our circuit work, to give out design guidelines for the choice of the parts we would use in the lab.

Please check the full detailed model if you are interested in knowing how our whole model works.

Parameter search

Even before we got our first parts cloned and characterized, we attempted to predict the requirements that they should meet to achieve the criteria previously established from literature data. For this, we extensively explored the parameter space controlling our model, and simulated the response of potential systems to find subsets of parameter combinations satisfying the performance specifications needed to get a sensitive as well as specific tumor sensing circuit.

The parameters satisfying the specifications are called functional space (green ellipse on Figure 1). We selected the biological parts that were the most likely to fall in the functional parameter space.

Different categories of parameters

Our model is relying on a dozen of parameters, some of which we can have a leverage on (typically maximal expression of the proteins, via RBS tuning), and others not (binding constants, promoter leakiness...). Some of these latter parameters have been precisely characterized and others are not very well known. This is why we have chosen to set some parameters to a certain value when we could find a reasonably reliable source in the literature, or when their influence would be redundant with other parameters (such as protein degradation rates and maximal expression rates that can alleviate each other's influence when co-varied), and leave other parameters free to vary to check their influence on our system.

Fixed parameters, because well known

Symbol	Description	Value	Reference
a_AHL	AHL synthesis rate by LuxI	0.01 min^-1	[2]
d_AHL	AHL degradation rate	5x10^-4 min^-1	[4]
D	AHL diffusion coefficient in water	3x10^-8 m²min^-1	[4]
K_LuxR-AHL	LuxR-AHL quadrimer binding constant	5x10^-10 nM^-3	[5]
w	Width of the colonized shell area	5x10^-10 nM^-3	[5]

Fixed parameters, not very well known but redundant with other parameters

Symbol	Description	Value	Reference
d_LuxI	LuxI degradation rate	0.017 min^-1	[4]
d_LuxR	LuxR degradation rate	0.023 min^-1	[4]
d_Azu	Azurin degradation rate	0.1 min^-1	estimated

Parameters allowed to vary because not very well known and which may have a significant effect on our circuit

Symbol	Description	Typical value (initial value in the parameter search)	Reference	Lower bound	Higher bound
a_LuxR	Maximum expression of luxR	5 nM min^-1	iGEM ETH 2014	1x10^-2 nM min^-1	1x10⁴ nM min^-1
a_LuxI	Maximum expression of luxI	1x10³ nM min^-1	[5]	1x10^-2 nM min^-1	1x10⁴ nM min^-1
K_Lac	Half-activation lactate concentration of the hybrid promoter	2x10⁶ nM	Characterized lactate sensing part on which our AND-gate is based	1x10⁴ nM	1x10⁸ nM
k_LuxI	Leakiness of the hybrid promoter	0.01	Characterized lactate sensing part on which our AND-gate is based	0.0001	0.1
K_LuxR	Half-activation LuxR-AHL concentration of the hybrid promoter	5 nM	iGEM ETH 2013	1 nM	100 nM
n_LuxR	Hill coefficient of the hybrid promoter regarding LuxR-AHL concentration	1.7	iGEM ETH 2015	1.1	1.9
n_Lac	Hill coefficient of the hybrid promoter regarding lactate concentration	1.7	iGEM ETH 2015	1.1	1.9
k_Azu-LuxI	Relative expression of azurin compared to LuxR	10 times the luxI expression	estimated	10^-5	10⁵

How do we quantitatively define the functional space?

Cost function

To be able to distinguish systems satisfying the criteria about specificity and azurin production and the ones that do not, we need to use a numerically evaluable condition quantifying how well the criteria are met. Based on this, the script will either accept or discard the parameter set. For this, we will use the following cost function, taking a parameter vector as argument:

\[cost(p) = \max\left(\frac{10\times azu(low\space lac,HIGH\space d_{cell})}{azu(HIGH\space lac,HIGH\space d_{cell})},\frac{10\times azu(HIGH\space lac,low\space d_{cell})}{azu(HIGH\space lac,HIGH\space d_{cell})},\frac{1.10^{6}}{azu(HIGH\space lac,HIGH\space d_{cell})}\right)\]

Each argument of the max function represents in the same order the following criteria:

Specificity of the sensing for lactate
Specificity of the sensing for bacterial cell density
Achieving a large amount of produced azurin

Interpretation of the result of the cost function goes as follows: the smaller the value the better better the criterium is met. If the highest value (e.g. the value for the criterium is met the worst) is below 1, the paramter set is accepted. Over 1, a ratio is not good enough. This monotonicity enables us to rely on optimization algorithms to reach the best combination of parameters available. Also, we can say that every system that has a cost function value below 1 is good enough for us, while "the smaller the better" still applies.

Intermediate modeling result: Analysis of the functional parameter space

Using an optimization toolbox developed for biological systems, MEIGO [6], followed by a package exploring parameter spaces, HYPERSPACE [7], we could obtain the following graphs describing, in the high-dimension space of all possible circuits, a subset of systems satisfying our performance criteria:

On this figure are shown the systems suitable for our application. All the axis are logarithmic, except for n_Lac and n_LuxR. The yellow points are good systems, the blue ones are even better and surpass the specifications that we demand. From this figure, we can draw the following interpretations (see corresponding sub-graphs referred to on the figure).

Only some given combination of expression of LuxI and LuxR are suitable for our needs. This is expected as the tuning of the bacterial cell density at which the quorum sensing is triggered is mainly done with these two proteins
High amounts of azurin are more easily achieved when LuxI maximal expression is high: then the expression of azurin does not need to be that much more compared to luxI to reach the desired level.
The tipping point of the lactate sensing must be either around or above the lactate levels to be distinguished (1 mM in healthy tissues and 5mM in tumors). The first possibility makes sense as the promoter should ideally be unactivated at low lactate level and activated above. However, the combination of this lactate sensing and quorum sensing into the hybrid promoter seems to allow for a second possibility: that the full activation of the promoter happens at much higher concentrations. In both cases, the differential expression at 1 mM and 5 mM plays the role of "increasing the leakiness" of the promoter in regard to luxR so that the quorum sensing is more easily activated in presence of lactate.
The leakiness is a very important parameter to be able to achieve a good performance for our system. The smaller the leakiness, the more probable it is to find a good system.
The Hill coefficient of our hybrid promoter in regard to lactate will allow more or less possibilities of systems: when over 1.5, a population of systems is present (more on the yellow side) that allows for a larger set of a_LuxR/a_LuxI combinations (see also n_Lac vs a_LuxR and n_Lac vs a_LuxI graphs). As we won't be able to tune it, we should prepare for the worst and try to aim for the best systems (the blue ones) on graph 1 to keep a security margin
K_LuxR and n_LuxR don't have a significant influence on our system, we can stop studying them

Final modeling result: Experimental guidelines used for circuit design

From these observations, we can deduce guidelines regarding the parameters on which we can exert an active control, that is to say the expression level of the genes LuxI and LuxR (a_LuxR and a_LuxI here) as well as a judicious choice of a previously characterized lactate sensor circuit (comprising lldR and lldP genes) among the iGEM ETH 2015 part collection .

Target parameters and restrictions

To translate these insights into experimental results in the lab, we need to chose a target in the range of parameters that works for our application. With the help of the previously characterized initial values for a_LuxR (5 nMmin^-1) and a_LuxI (1x10³ nMmin^-1), we can hope to tune our system and reach our target in the parameter space via simple RBS tuning which is supported by the Salis Lab RBS Calculator [7].

As it turned out, the regulatory sequence in front of the luxR gene on the part at our disposal induced already a relatively high expression level. It was hard to get more than 10 times more expression for this gene on the Salis calculator, this is why the range a_LuxR > 1x10² nMmin^-1 is inaccessible to us (grey area), and that we have to choose LuxI in consequence. We also get to chose K_Lac among the ones available in the promoter collection of parts ranging from BBa_K1847002 to BBa_K1847009: between 0.3 mM and 2.4mM.

Taking into account the experimental constraints (forbidden grey area), the targeted parameters (red squares) were chosen on the following plot, with an extensive compatibility for different potential leakiness of our hybrid promoter (red frame):

Parameter search iteration 2 — Parameter space of vectors of parameters satisfying our criteria (cost below 1). Yellow points are good enough systems, blue ones are even better and surpass the specifications that we demand. Red features highlight our choice for the operating choice that we will implement in the lab through genetic design guidelines.

With a_LuxR = 1x10² nMmin^-1, a_LuxI = 1x10⁴ nMmin^-1 and K_Lac = 1x10⁶ nM, we should be at a suitable operating point for our system and still have some security margin in case the genetic design does not yield the exact expression levels that we would expect from it. To achieve these parameters, we gave the following directions for the design of our parts:

HERE NEED A BIG HIGHLIGHT OF THE FOLLOWING LIST, SOME FRAME OR SOMETHING

Use a 10 times stronger RBS than on the piG0047 sequence of iGEM ETH 2014 team for the expression of LuxR
Use a 10 times stronger RBS than on the piG0050 sequence of iGEM ETH 2014 team for the expression of LuxI
Use the BBa_K1847008 part with J23118-B0034 regulatory sequences, giving K_lac = 1.8 mM

These value were the basis for the design of our parts and the subsequent experimentations.

Sanity check: in silico behavior for the chosen target parameters

We can validate on our model that they would work well to distinguish the specific levels dictated by our application:

System response after optimization — Expected behavior of the circuit for the chosen parameter set target: intracellular azurin concentration (in nM) depending on both lactate level and bacterial cell density. The white lines correspond to low levels of lactate and bacterial cell density (in healthy tissues) and the black lines represent the high levels (in tumor tissues). The output level of azurin is only significant if both inputs are high, which is the behavior that suits our application.

We can confirm that the obtained parameter set target would lead to a functioning circuit.

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      <p> From these observations, we can deduce guidelines regarding the parameters on which we can exert an active control, that is to say the expression level of the genes LuxI and LuxR (<em>a</em><sub>LuxR</sub> and <em>a</em><sub>LuxI</sub> here) as well as a judicious choice of a previously characterized lactate sensor circuit (comprising lldR and lldP genes) among the <a href="https://2015.igem.org/Team:ETH_Zurich/Part_Collection">iGEM ETH 2015 part collection </a>.
      </p>
-<div class="multi-summary">
+<div class="multi-summary" id="experiment_guidelines">
 <details>
      <summary>Target parameters and restrictions</summary>

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