Team:Valencia UPV/Model

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MODELING

INDEX

Introdiction
- Deterministic and Stochastic Models
Overview
- What We Are Modeling?
- Modeling Software Modules
Human-Plant: Optogenetic Circuit
Plant-Human: Sensor Circuit
- Deterministic
- Stochastic
Experimental Data
- Optogenetic Circuit
- Sensor Circuit
Validation
Conclusions

INTRODUCTION

Modeling our gene circuits is of paramount importance since it provides us with deep insight and prediction capability of the biological processes taking place in ChatterPlant. This way, we aim to break the traditional wall imposed by trial-error approaches, which often result in unnecessary or inconclusive experiments.

Mathematical models in synthetic biology contribute not only to generate empirically contrastable hypothesis but also to manage laboratory time and hardware resources efficiently. Furthermore, because of the understanding and foresight provided by modeling, tuning and programing ChatterPlant according to the necessities of certain situations is possible more than ever.

DETERMINISTIC AND STOCHASTIC MODELS

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:

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.

The type of deterministic model that we implement is a system of Ordinary Differential Equations (ODEs)
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

OVERVIEW

WHAT WE ARE MODELING?

The SynBio-based design integrated in ChatterPlant is composed by two gene circuits. The analysis of both their single performance and their interaction with several factors (e.g. the cell medium, environment and ChatterBox), is basic to reach one of our main goals: a new sustainable and efficient agriculture system.

Our model comprises of:

Optogenetic circuit. How long has to remain the light pulse in order to get a certain protein amount? How could be optimized the energetic supply of LEDs light in order to maximize a cycle of protein production? These questions among others arose to our minds as we were designing the LED’s system.
Sensor circuit. Bearing in mind the time span during which the biological sensor is transiently ON, it is mandatory to design a sampling rate test according to the plant’s periodic security necessities.

MODELING SOFTWARE MODULES

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.

HUMAN-PLANT: OPTOGENETIC CIRCUIT

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.

DETERMINISTIC

REACTIONS

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

REACTIONS

Considerations in the model:

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.
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.
Transcription reaction is faster than translation reaction, so can be considered in the equilibrium state.
The conformation change is instantaneous.

REACTIONS

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.

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