Model overview

Modeling a microbial consortium

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

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.

To understand, predict and ultimately control the behaviour of the synthetic microbial consortium, we have developed a mechanistic, dynamic model. When developing the model, we had to tackle several issues that were particularly challenging: the proposed microbial consortium involves several entities going from the molecular level (including genes, RNAs, proteins, and metabolites) up to the cellular level, several intracellular and extracellular compartments, and a wide range of biological and physical processes (including transcription, translation, signalling, growth or diffusion). 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.

General strategy

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 tool for model representation

Our system is composed of several entities (including metabolites, macromolecules and cells) involved in many processes (transcription, translation, signalling, metabolite production, growth, 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/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

To assess the feasibility of the project, we needed to simulate the dynamics of all the components of our synthetic microbial consortium. Based on the SBGN representation of this consortium, each 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 kinetics essay). 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 strenghtening the feasibility of the project.

→ Details on the model, implementation and 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 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 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 indicates that most parameters, including those of the sensor and transmitter modules, have low control on the systel(coefficients close to 0, white). They also highlighted the parameters having the stongest influence on the response, 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 water contamination (Vc_0) 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.

→ 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 to facilitate discussions and interactions with all the people involved (mathematicians, biologists, founders, entrepreneurs, users, etc). This required a user-friendly platform to simulate the behaviour of our synthetic system 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 modelling in the project

The model was vital to ensure the success of the project. Initially build ab initio, modelling results have driven some experiments, which in turn have feed the model, to finally support the design of the device:

• Use of experimental data and Design of experiments: Using an iterative approach, 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 predictive capabilities. 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 dimension our device, and prepare a scale-up to ensure 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