Modeling a microbial consortium

“Systems biology is based on the understanding that the whole is greater than the sum of the parts.” ¹

The proposed multi-organisms synthetic biology project implies a complex global behavior that cannot be apprehended intuitively.

Modeling was vital to address these questions:

• 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?
• What parameters should be changed to optimize the response?

A challenging modeling with entities from gene to population

A keystone for our project

After having solved the implementation questions, we have exploited the resulting model to test the feasibility of the system, characterize its emerging properties (e.g. robustness), and ultimately optimize its behaviour by adapting some of the important parameters that we have identified (e.g. the initial concentrations of each microbial specie in the device). This 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 design our device, and how long we have to wait before drinking a non-contaminated water.

The proposed modeling strategy, which integrates several scientific and non-scientific aspects of the project (as illustrated in the impact section), proved to be successfull.

General strategy

Working with a complex biological system involving three microorganisms and several molecules that interact via a broad range of biological and physical processes, the Systems Biology Graphical Notation (SBGN) was a perfect way to ordinate all the elements and represent their interactions. Based on this representation, a system of Ordinary Differential Equations (ODEs) that describes and integrates the individual processes was implemented and solved 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 assess the feasibility of our system and understand its properties using different mathematical tools (such as global sensitivity analyses and an original extension of the metabolic control analysis framework). Following an iterative systems biology approach, the model has been updated with experimental data. In turn, it has driven the wet lab strategy and supported rational design of the device design. Finally, to discuss with non-mathematicians, a user-friendly interface has been created.

Model representation

Our system is composed of several entities (including metabolites, macromolecules and cells) from dinstinct compartments and involved in many biological and physical processes (transcription, translation, signalling, metabolite production, growth, diffusion, etc), and we wondered how we could visualize such a complex system.

Similarly to the representation of technological and electronical devices ¹, we focussed on the Systems Biology Graphical Notation (SBGN), proposed in 2005 to facilitate communication between biochemists, mathematicians and computer scientists. SBGN provides a standard formalism to represent several biochemical and cellular processes.² The original publication about SBGN can be found there.

The SBGN representation was not only a rational way of visualizing and inventoring all the elements we had to consider to build the model; it also allows to present our system to scientific and non-scientific interlocutors (biologist, bioinformatician, mathematician, founders, businessman, contractors, etc).

Abbreviations:

• cqsA: cqsA gene
• CqsS*: engineered CqsS receptor protein
• als: acetolactate synthase gene
• Als: acetolactate synthase enzyme
• S: carbon source
• dac: diacetyl
• Odr10: Odr10 receptor protein
• AMP: antimicrobial peptide
• V_x: reaction x
• deg: degradation
• diff: diffusion

Feasibility study

To assess the feasibility of the project, we needed to simulate the dynamics of our synthetic microbial consortium and its impact on V. cholerae. Based on the SBGN representation of this consortium, each biological and physical process was described mechanistically using appropriate kinetic rate laws which were gathered to constitute the system of ordinary differential equations. Data from publications were used to define initial parameters values, some of them being refined using model-driven experiments (growth characterization). An ODEs solver (from MATLAB R2017a) able to deal with stiff problems was used to simulate the system dynamics.

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

→ Details on the model, its implementation and the simulation results can be found in our simulation page

Understanding and optimizing the system

To understand the emerging properties of the synthetic system, such as robustness and sensitivity, and drive rationally its optimization, we implemented different approaches derived from the fields of metabolic modeling and systems biology:

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

Results indicate that most parameters, including those of the sensor and transmitter modules, have low control on the system (coefficients close to 0, black). They also highlighted the parameters having the strongest influence on the response, most of them being related to the antimicrobial peptide production. Initial level of water contamination as well as the volume of the device were also identified as controlling parameter. Overall, this analysis revealed that the module to optimize is related to AMPs expression, the sensor and transmitter modules having a low impact on the response time.

Based on these results, further simulations were carried out to characterize the system efficiency for different setups of the device (concentrations in Pichia pastoris), under a wide range of contamination levels (concentrations in Vibrio cholerae). Simulation results, represented in the 3D graph shown 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.

→ Details on the methods used to analyse the model and on the results can be found in our model analysis page

An intuitive modeling interface

We wanted this model to be accessible to non-specialists to facilitate discussions and interactions with all the people involved (mathematicians, biologists, founders, entrepreneurs, users, NGOs, etc). This required a user-friendly platform to simulate the behaviour of our synthetic consortium without the use of complex numerical computing environment such as Matlab. Thus, we developed an intuitive visual interface to play with our model.

→ Our visual interface is available on our interface page

Impact of modeling in the project

The model was vital to ensure the success of the project. Initially built ab initio to test its feasibility, the predictive kinetic model has then driven some experiments, which in turn have feed the model, to finally support optimisation of the system and design of the device. The model has also enhanced the collaborative aspect of our project by facilitationg discussions with the different interlocutors. Impact of modeling on each of these aspects is detailed below.

• Project feasibility: When starting the project, we truly believed modeling was a perfect tool to test different aspects of the strategy, hence enhancing our chances of success. We first developed a visual representation of the system, which helped to organize the lab work and the parts we had to construct. When running the first simulations, the model highlighted the feasibility of Croc'n cholera, which enthusiastically encouraged us to go further down that route. See the simulation page.
• Use of experimental data and Design of experiments: Following an iterative systems biology approach, our model has been initially built from data collected in the literature, and has been updated with some preliminary results from wet lab experiments to improve its predictive capabilities. As an example, during our first lab weeks we measured the growth rates of Vibrio harveyi and Pichia pastoris cells inoculated in a common medium, and these parameters were directly updated in the model. Diffusion tests were also carried out on the membrane, and the short diffusion time that we have measured supported our initial hypothesis of a high transfer coefficient which does not slow down the system's dynamics. See the results page.
• Device design: Our predictive model helped us to develop rationally our prototype. As an example, with the estimation of one hour to treat 1 liter with a 20 mL device, it has been possible to dimension our device, and prepare a scale-up to ensure a competitive and robust technology. Our actual prototype would treat 5 liter of water with a 10 cL device. See the device page.
• Entrepreneurship and Communication: More generally, the model was vital to facilitate discussions with all the scientific and non-scientific interlocutors. For instance, the feasibility and robustness analyses helped us to convince some of the sponsors to invest time and money in the project. See the entrepreneurship page.

References

• (1): Institute for Systems Biology, What is Systems Biology, 2017 : https://www.systemsbiology.org/about/what-is-systems-biology/
• (2): Le Novere N, Hucka M, Mi H, Moodie S, Schreiber F, Sorokin A, Demir E, Wegner K, Aladjem MI & Wimalaratne SM (2009) The systems biology graphical notation. Nature biotechnology 27 735–741
  https://www.ncbi.nlm.nih.gov/pubmed/19668183