Model overview

Modeling a microbial consortium from genes to populations

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

Our general strategy involves i) the detection of Vibrio 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 V. 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? Modeling was vital to address these questions since this cannot be done intuitively.

Therefore, to understand, predict and ultimately control the behaviour of the synthetic microbial consortium, we have developed a mechanistic, dynamic model. This model has been exploited 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 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 we 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 assess the feasibility of our system and understand its properties by analyzing its sensitivity and robustness using different mathematical tools (global sensitivity analyses and an original 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 the optimization section. Finally, to discuss with non-mathematicians, a user-friendly interface has been created.

SBGN: a standard representation of models in systems biology

Our system is composed of microorganisms interacting by responding to stimulations (inputs) and producing a molecular response (outputs) through a network composed of 12 entities and 24 reactions. This is a perfect illustration of a systematic use of biological material, at the scale of both a unique microorganism and a microbial consortium, and we wondered how can we visualize such system.

Systems biology tools have been developed to represent biological systems (such as networks transforming inputs into outputs) that can be modeled mathematically, similarly to technological and electronical devices.(1) The SBGN (Systems Biology Graphical Notation) project, launched in 2005 to facilitate communication between biochemists, mathematicians and computer scientists, consists in a standard notation to represent biochemical and cellular processes, and to easily share biological systems within the community.(2) The original publication about SBGN can be found there.

We thus developed a SBGN representation of this complex system as a rational way of visualizing and inventoring all the elements we had to consider to build the model. This representation also allows to present our system to scientific and non-scientific interlocutors (biologist, bioinformatician, mathematician, founders, businessman, contractors, etc), and to make it reusable and adaptable.

Abbreviations:

• cqsA: cqsA gene
• CqsS*: engineered CqsS receptor protein
• als/ALS: acetolactate synthase
• S: carbon source (e.g. glucose)
• dac: diacetyl
• Odr10: Odr10 receptor protein
• AMP: antimicrobial peptide
• V_x: reaction x
• deg: degradation
• diff: diffusion

Simulating the system's dynamics

The dynamics of our microbial consortium was summed up in 12 differential equations determining the concentrations of all the components (from genes to populations) and their dynamics. All the biological and physical processes were described mechanistically, and the resulting kinetic rate laws were gathered to constitute our system of ODEs. Data from publications and from preliminary experiments (growth kinetics essay) were used to define the 46 parameters values. 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 emerging 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 developed and 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 stongest influence, most 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) as well as the volume of the device were also identified as controlling 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 this model to be accessible to non-specialists. This required a platform to perform simulations of 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

An iterative modelling approach to design a functional device

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

• Use of experimental data and Design of experiments: Our model has been initially build using data collected from the literature, and has been updated with some preliminary results from wet lab to improve its predictions, hence driving the type of experiments that had to be carried out. 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 greatly helped us to develop our prototype. With the estimation of one hour to treat 1 liter with 20 mL of device, it has been possible to design our device, and anticipate 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