Modeling a microbial consortium from gene to population

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 its detection, and finally iii) 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. To describe and predict the behaviour of the microbial consortium, we have developed a mechanistic, dynamic model that can be used to test the feasibility of the system and improve its 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 guessed output, which is the lysis of V. cholerae to reach a non-toxic concentration?

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.

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 the system and represent the interactions between organisms as well as the molecules involved. A system of Ordinary Differential Equations (ODEs) was then written to describe and integrate the individual physical and biological processes and simulate the dynamics of our microbial consortium. Many data gathered from publications and experiments have been used. This mathematical model has been used to simulate the functioning of our system, and analyse its sensitivity and robustness using an extension of Metabolic Control Analysis (MCA). Our model had impacts both on wet lab strategy and device design, and has been updated with experimental data, which is summed up in optimization. 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 example 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 is a way to present our system to different interlocutors (biologist, bioinformatician, mathematician), and to make it reusable and adaptable.

This SBGN representation is also an easy way to visualize and inventory all the elements we had to consider to model our synthetic system with Ordinary Differential Equations (ODEs).

ODEs

The dynamics of our microbial consortium was summed up in twelve differential equations. 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 we needed to wait less than a hour (53.6 minutes) to reach a non-pathogenic concentration.

→ Data, solver files and simulation results can be found in our simulation page

Sensitivity and robustness

Two tools used in metabolic modeling and systems biology were extended to determine if our system was sensible to parameters variations (robustness) and which are the parameters exerting a major influence in the response time (time to reach a non-pathogenic concentration).

Extension of Metabolic Control Analysis (MCA) showed low control coefficients, which prooves that each parameter exerts a limited influence on our model. It highlighted the parameters having the biggest influence: antimicrobial peptides properties, Pichia pastoris and Vibrio cholerae initial concentrations and device volume.

Global sensitivity analysis confirmed the robustness, showing a small variation of the response time when the parameters are varying randomly.

The influence of two major parameters (Pichia pastoris and Vibrio cholerae initial concentrations) is described on the 3D graph above. These two parameters were chosen to create a simulation interface.

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

Visual interface

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

→ 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: Even if our model is mostly a predictive model, some preliminary results from wet lab were implemented in our data to have a more precise simulation. Indeed, we needed to have data of Vibrio harveyi and Pichia pastoris growth in their common medium. During our first lab weeks, we performed growth essays, and the lag time and growth rate results from this experiment were 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