Model overview

Modeling a microbial consortium from genes to populations

Our general strategy is based on i) the detection of V. cholerae using as input signal a quorum sensing molecule, ii) a molecular communication between two organisms thanks to the production of a signaling metabolite, and eventually iii) the detection of this signal to activate the production of antimicrobial peptides as output, at a lethal dose for Vibrio cholerae. Compared to synthetic biology approaches based on a single microorganism, multi-organisms synthetic biology implies a more complex global behaviour.

Would the quorum sensing molecule (CAI-1) induce a sufficient response to activate the sensor (Vibrio harveyi)? Would the receptor be able to produce enough molecular message (diacetyl) to transmit the signal to the effector Pichia pastoris? Would the effector produce enough antimicrobial peptides to deliver the expected output, which is the death of V. cholerae to reach a non-toxic concentration?

To understand, predict and ultimately control the behaviour of the microbial consortium, we have developed a mechanistic, dynamic model. This model allowed to test the feasibility of the system, characterize its properties (e.g. robustness), and ultimately optimize its behaviour by adapting some of the parameters that we can control (e.g. the initial concentrations of each microbial specie).

A model was also crucial regarding the entrepreneurship and the integrated human practices parts of our project: we needed to show to clients and investors, but also to citizens, how our system works, how we will dimensionate our device, and how long do you have to wait before drinking a non-contaminated water.

Modeling approaches

Working with a complex biological system involving three microorganisms and several molecules, the Systems Biology Graphical Notation (SBGN) was a perfect way to ordinate all the elements and represent their interactions. A system of Ordinary Differential Equations (ODEs) was then written to describe and integrate the individual physical and biological processes to simulate the dynamics of our microbial consortium. Many data gathered from publications and experiments have been used to build the resulting kinetic model. This model has been used to simulate the functioning of our system and understand its properties by analyzing its sensitivity and robustness using different mathematical tools (global sensitivity analyses, extension of the metabolic control analysis framework). Following an iterative systems biology approach, it has been updated with experimental data. In turn, it has driven both the wet lab strategy and the device design, which is summed up in optimization section. Finally, to discuss with non-mathematicians, a user-friendly interface has been created.

SBGN: a standard representation of models in systems biology

“Systems biology is based on the understanding that the whole is greater than the sum of the parts.”(1) Systems biology is a new approach to understand and to manipulate biological material. It proposes to represent biological systems such as networks transforming inputs into outputs that could be modeled mathematically, similarly to technological and electronical devices.(1) It requires communication between biochemists, mathematicians and computer scientists. The SBGN (Systems Biology Graphical Notation) project has been launched in 2005 to facilitate this communication. It proposes a standard notation to represent biochemical and cellular processes, and to easily share biological systems to the community.(2) The standard notation can be found there.

Our system is composed of microorganisms interacting by responding to stimulations (inputs) and producing a molecular response (outputs). This is a perfect illustration of a systematic use of biological material, at the scale of both a unique microorganism and a microbial consortium.

Abbreviations:

• cqsA: cqsA gene
• CqsS*: engineered CqsS receptor protein
• als/ALS: acetolactate synthase
• S: substrate for diacetyl production
• dac: diacetyl
• Odr10: Odr10 receptor protein
• AMP: antimicrobial peptide
• V: velocity
• deg: degradation
• diff: diffusion

Our SBGN representation allows to present our system to different interlocutors (biologist, bioinformatician, mathematician), and to make it reusable and adaptable.

This SBGN representation is also an rational way to visualize and inventory all the elements we had to consider to build the equation system.

Simulating the system's dynamics

The dynamics of our microbial consortium was summed up in twelve differential equations determining the concentrations of all the components (from genes to populations) and their dynamics. Every biological or physical process was described mathematically, and was gathered to constitute our system of ODEs. Data from publications and from preliminary experiments (growth kinetics essay) were used to define our parameters. An ODEs solver from MATLAB R2017a was used to simulate the system.

Under realistic conditions, simulation showed that the response time of the system (i.e. the time to reach a non-pathogenic concentration) remains below 1 hour (53.6 minutes), hence demonstrating the feasibility of the project.

→ The data, model and simulation results can be found in our simulation page

Understanding and optimizing the system

Different approaches used in metabolic modeling and systems biology were implemented to analyze different properties of the synthetic system, such as robustness and sensitivity, and understand how we can control it:

• Global sensitivity analyses were carried out to determine if our system was robust to random perturbations of parameters around their reference value. As shown below, the small variation in the response time indicate that the synthetic system is robust to parameter fluctuations that can arise during the manufacturing process, the transport, etc, or originate from living organisms themselves.

• An extension of the Metabolic control analysis framework was then applied to identify the parameters that exerts strong control on the response time, and ultimately optimize the device functioning.

Results indicated that most parameters have low control (coefficients close to 0, black), and highlighted the parameters having the biggest influence, all of them being related to the antimicrobial peptide: initial concentration of the producer Pichia pastoris, and AMP efficiency (Vc_death_rate and MIC50). Initial level of contamination of water (Vc_0) is also an important parameter.

Further simulations were thus carried out to evaluate the system efficiency for different concentrations in Pichia pastoris, under a wide range of contamination levels (concentrations in Vibrio cholerae). Simulation results, represented in the 3D graph below, indicate that the response time remains low (< 120 min) even at very high contamination levels. These two parameters, which exerts most of the control on the system, were selected as tunable parameters when creating a user-friendly simulation interface that can show their influence on the system to non-specialists.

→ Sensitivity analysis methods and their results are described in our model analysis page

An intuitive modeling interface for non-specialists

We wanted to show the behaviour of our synthetic system without the use of complex numerical computing environment such as Matlab. Thus, we developed a visual interface with Javascript to show the kinetics of Vibrio cholerae death depending of the two major parameters determined previously.

→ Our visual interface is available on our interface page

Model driven optimization

Our mathematical model was useful for different parts of our project, and was also implemented by other parts:

• Use of experimental data: Our model has been initially build using data collected from the literature, and has been continuously updated with some preliminary results from wet lab to improve its predictions. As an example, we needed to characterize the growth rate of Vibrio harveyi and Pichia pastoris in a common medium. During our first lab weeks, we performed growth essays, and the lag time and growth rate results from these experiments were thus directly implemented in our model. See the results page.
• Device design: Our predictive model served for our technology development. With the estimation of one hour to treat 1 liter with 20 mL of device, it has been possible to design our device, and think about a scale-up to develop a competitive technology. See the device page.

References

• (1): Institute for Systems Biology, What is Systems Biology, 2017 : https://www.systemsbiology.org/about/what-is-systems-biology/
• (2): Le Novère N. et al. The Systems Biology Graphical Notation. Nature Biotechnology (2009), 27: 735-741