Difference between revisions of "Team:Valencia UPV/Model"

In ChatterPlant we aim to understand and program our synbio device according to the necessities of certain situations.

Modeling our gene circuits provides us with deep insight and prediction capability of the biological processes taking place in ChatterPlant.

Furthermore, mathematical models in synthetic biology contribute not only to generate empirically contrastable hypothesis, but also to manage resources efficiently, skipping unnecessary experiments imposed by trial-error approaches.

The SynBio-based design integrated in ChatterPlant is composed by two gene circuits. In order to set ChatterPlant as a new sustainable and efficient agriculture system, we analyzed both their single performance and their interaction with several factors (e.g. the cell medium, environment and ChatterBox).

Our model comprises of:

1. HUMAN-PLANT: Optogenetic circuit. . How to tune the synbio circuit parameters to get the desired plant response to red light stimulus? How long has to remain the LEDs system switched ON in order to get a certain protein amount?

Check our Optogenetic circuit model

2. PLANT-HUMAN: AND gate. How much GP3 is necessary to let the color be expressed? Which is the optimal proportion between recombinases and GP3?

Check our AND gate model

In our in silico experiments, we analysed empirical data and used optimization algorithms in order to set the optimal conditions which ensure a smooth bidirectional communication between plants and humans.

In ChatterPlant we analyze the dynamic behavior of our biological system considering the biochemical species involved in a certain set of reactions. According to the degree of approximation to capture the dynamic behavior, we can differentiate two approaches:

1. Deterministic. Deterministic models do not take into account the natural randomness of the reactions. For each chemical species, the amount of molecules transformed within reactions only depends on the initial amount of molecules, reaction rates and stoichiometry relations.

Check our Deterministic Optogenetic Model

Check our Deterministic Recombinase-GP3 Model

2. Stochastic. Inherent noise due to random events plays a relevant role in the dynamics. As a deterministic model does not capture noise, we use stochastic linear differential equations.

We start building the genetic circuits from basic modules, coupling them to generate the mathematical model of the whole system. As UPV_iGEM is an interdisciplinary team, most of the models generated in ChatterPlant are included in the modeling software tool and are represented by modules in an artistic graphic interface, for the purpose of introducing researchers to a more realistic conception of the engineering in biology, meanly, SynBio.

Two constitutive modules express the E-PIF6 and PhyB-VP64 fusion proteins that regulate the output expression.

Constitutive modules representation of the fusion proteins E-PIF6 and PhyB-VP64.

E-PIF6 binds to the promoter’s operator. When red light (660 nm wavelength) LEDs are switched on, PhyB changes its conformation (PhyB*) and binds to PIF6. Consequently, the transcription of the desired protein starts because of the RNAp recruitment by VP64.

Expression regulated by the transcriptional factors.

Far red light (740 nm wavelength) reverts PhyB* to its natural conformation (PhyB). This change stops de transcriptional activity of the third optogenetic circuit’s module.

Switch off.

Now we take into account the principal reactions in each module representing them both graphic design and formal reactions.

E-PIF6 expression

PhyB-VP64 expression

Regulated expression

Constitutive module A=E-PIF6

Constitutive module B=PhyB-VP64

Regulated module

Considerations in the model:

1. The c_RNAp constant considers that the cell has the sufficient free RNAp in excess to be utilized by all the active genes that are transcribing simultaneously in the cell, including the gene of interest. Under this conception, the free RNAp vary in an almost unappreciable way in time, so can be defined as the C_RNApFree constant and consequently the sum of the RNAp linked to the DNA and the free RNAp as the c_RNAp constant.
2. The RNAp binding-unbinding reactions to the promoter are much faster than the elongation and degradation reactions, so can be considered in the equilibrium state.
3. Transcription reaction is faster than translation reaction, so can be considered in the equilibrium state.
4. The conformation change is instantaneous.

After a mathematical development (download here for more information), we obtained the following equations, which define the constitutive and regulated expression respectively (where sub P is a generalization to name the protein)

Constitutive expression production is directly proportional to the translation rate (k_x), to the transcription effective rate (k_mxe), to the gene copy number (c_nx) and inverse proportional to the mRNA degradation rate (d_mx). The protein degradation is defined by the protein degradation rate in the cellular medium.

Regulated expression is proportional to the translation rate (kp), to the transcription rate (km), to the gene copy number (cnP) and inverse proportional to the mRNA degradation rate (dmP).

Alphas and betas are defined by rates (see supplementary). When red light is off (y2=0), the expression becomes as:

The basal expression depends on the E-PIF6 production. With the model obtained we discovered that the leakage can be reduced with a strong promoter on E-PIF6 :

An overview about the theory behind this type of models is addressed at the Stochastic chapter of our downloadable Modeling detailed explanation. Basically, instead of using deterministic reaction rates, we use probabilistic reaction rates. These rates define the probability per time unit of one chemical changes to other or disappear.

In general terms, the next equation represents the production of proteins under the assumption of a white Gaussian noise, i.e. null mean and unitary variance:

SIMULATIONS AND CONCLUSIONS