Difference between revisions of "Team:INSA-UPS France/Model/Analysis"

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<h1>Model analysis</h1>
 
<h1>Model analysis</h1>
 
<p>
 
<p>
−
After simuling our system and showing the feasibility of our synthetic consortium response, the sensibility and robustness of the system must be evaluated to ensure it adaptability to real life conditions such as parameters variations, and to identify which ones of our wide range of parameters had impacts on our response. Two tools used in metabolic modeling and systems biology were <b>extended to a synthetic microbial population</b>. With <b>global analysis</b>, we determined if our system was sensible to parameters variations (robustness) and with <b>Metabolic Control Analysis (MCA)</b> which are the parameters exerting a major influence in the response time (time to reach a non-pathogenic concentration). This methods, usually perfomed for steady state system, were extended to our dynamic modeL
+
After demonstrating the feasibility of our synthetic consortium, we have characterized some emerging properties that drive its functioning. In particular, we have performed global sensitivity analyses to test the robustness of the system to real life conditions (such as fluctuations of some parameters). To optimize its behaviour and guide its design, we then carried out more detailed analyses by extending the Metaboloic control analysis framework classically used in the fields of metabolic engeneering and systems biology.
 
</p>
 
</p>
 
</section>
 
</section>
  
 
<section>
 
<section>
−
<h1>Global analysis</h1>
+
<h1>Global sensitivity analysis</h1>
−
<p>Biological models are generally based on uncertain parameters that cannot be verified through experiments.(1) Our own model, built with nearly fifty different parameters mostly from publications, confirms this fact. Facing this problem, the global sensitivity analysis was developed to determine the impact of parameters on the model results. This method determines how a metric of interest (here the response time) would evolve if our parameters differ.(1) Many examples of global sensitivity analysis from biochemistry and systems biology are described in <a href="http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0079244">Kent <i>et al.</i>, 2013</a>.
+
<p>All parameter values cannot be known exactely through experiments (1), and our experience in this project, with a model composed by nearly fifty parameters, confirms this fact. As an additional concern, many other sources of variability may impact the efficiency of the system. Variability could emerge from the system itself (living systems are variable by nature) or during each step of the process (manufacturing, transport, storage). Facing this problem, a global sensitivity analysis approach was applied to determine the impact of parameters fluctuations on the response time to reach non-pathogenic concentrations.(1) Many other application of global sensitivity analysis for biochemistry and systems biology are described in <a href="http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0079244">Kent <i>et al.</i>, 2013</a>.
 
</p>
 
</p>
−
<p>For our model, the response time have been calculated 10,000 times under a random variation of each parameter p from 0.9p to 1.1p using a Matlab script (available below). The response time distribution have been analyzed with RStudio (R file available below).
+
<p>To perform this analysis, we generated 10,000 sets of parameters randomly sampled within +- 10% of their reference values, using a uniform distribution, and the response time of the system was calculated for each of these sets (Matlab code available below). Simulation results were analyzed with RStudio (R code available below).
 
</p>
 
</p>
 
<p>Global analysis files: <a href="https://static.igem.org/mediawiki/2017/d/df/T--INSA-UPS_France--iGEM_INSA-UPS_France_2017_Global_Analysis.zip" alt="">Global_Analysis.m + System_of_ODEs.m + Resolution_Function.m + myEventsFcn.m + Global_analysis.R</a></p>
 
<p>Global analysis files: <a href="https://static.igem.org/mediawiki/2017/d/df/T--INSA-UPS_France--iGEM_INSA-UPS_France_2017_Global_Analysis.zip" alt="">Global_Analysis.m + System_of_ODEs.m + Resolution_Function.m + myEventsFcn.m + Global_analysis.R</a></p>
 
<img src="https://static.igem.org/mediawiki/2017/b/b5/T--INSA-UPS_France--Global_analysis.png" alt="">
 
<img src="https://static.igem.org/mediawiki/2017/b/b5/T--INSA-UPS_France--Global_analysis.png" alt="">
−
<figcaption><b>Distribution of the response time after random variation of the parameters</b></figcaption>
+
<figcaption><b>Distribution of the response time for 10,000 sets of random parameters</b></figcaption>
−
<p>Distribution analysis of 10,000 response times between 45.46 min (minimum) and 65.05 min (maximum). The median (53.70 min) and the mean (53.87 min) are logically close to the response time without random variation (53.6 min). Visually, we can observe on the graph a high concentration of response time around the median; the standard-deviation value of 3.3 confirms that a majority of response time do not change with parameter random variation.</p>
+
<p>Simulation results indicate that the response times varied between 45.46 min (minimum) and 65.05 min (maximum), with a median of 53.70 min and a mean of 53.87 minclose to the response time of the initial set of parameters (53.6 min).</p>
−
<p>These statistical results from global analysis confirms a global robustness of our model: global variation of parameters, for example because of imprecisions, will not have a significant impact.  
+
<p>These statistical results confirm the global robustness of the system, which will remain efficient even under a reasonable degree of uncertainty.  
 
</p>
 
</p>
 
</section>
 
</section>
  
 
<section>
 
<section>
−
<h1>Extension of MCA</h1>
+
<h1>Metabolic control analysis</h1>
 
<p>
 
<p>
−
<b>Metabolic Control Analysis (MCA)</b> is a mathematical tool widely used in biotechnology to quantify the influence of a specific parameter on the functioning of the system, in terms of fluxes and concentrations. Working with a system governed by a large number of parameters, MCA allows to determine the influence of each of them with respect to a metric of interest.(2)</p><p>Usually used to describe systems at steady state, we had extended the concept of MCA for our dynamic system to analyze the sensitivity and robustness of the response time of the system to each parameter. The response time given by our solver, which is the time before reaching a non-pathogenic <i>Vibrio cholerae</i> concentration, was thus defined as our metric of interest (&tau;). For each parameter (p), the control coefficient (C) was calculated.</p>
+
<b>Metabolic Control Analysis (MCA)</b> is a mathematical tool widely used in biotechnology to quantify the influence of a specific parameter on the functioning of the system, in terms of fluxes and concentrations. Working with a system governed by a large number of parameters, MCA allows to determine the influence of each of them with respect to a metric of interest.(2)</p><p>Usually applied to steady state conditions, we have extended the concepts of MCA to quantify the control exerted by each parameter on the response time (&tau;). For each parameter (p), the control coefficient (C) was calculated.</p>
 
\begin{equation*}
 
\begin{equation*}
 
C = \frac{(\tau(p)-\tau(\delta.p))/\tau}{(p - \delta.p)/p}
 
C = \frac{(\tau(p)-\tau(\delta.p))/\tau}{(p - \delta.p)/p}
 
\end{equation*}
 
\end{equation*}
−
<p>This coefficient quantifies the relative change in the response time &tau; which results from a relative change &delta; of the parameter p. If the response time is not impacted by a variation of the parameter p, the coefficient will be equal to zero. If the response time is reduced by an increase of the parameter p, the coefficient C will be negative. Finally, if the response time is enhanced by an increase of the parameter, the coefficient C will be positive. The variation &delta; was fixed at 0.01. This sensitivity analysis was performed for a wide range of initial concentration of <i>Vibrio cholerae</i>. Results are presented as a heatmap. The Matlab script used to calculated control coefficient and generate a heatmap (SimBiology needed) are available below.</p>
+
<p>This coefficient quantifies the relative change in the response time &tau; which results from a relative change &delta; of the parameter p. If the response time is not impacted by a variation of the parameter p, the coefficient will be equal to zero. A positive (negative) value indicates that an increase in p increases (reduces) the response time.
 +
Control coefficients were calculated by numerical differentiation, by setting &delta; at 0.01. This sensitivity analysis was performed for a wide range of initial concentration of <i>Vibrio cholerae</i>. Results are presented as a heatmap. The Matlab script used to calculated control coefficient and generate a heatmap (SimBiology needed) are available below.</p>
 
<p>MCA files: <a href="https://static.igem.org/mediawiki/2017/e/e0/T--INSA-UPS_France--iGEM_INSA-UPS_France_2017_MCA.zip" alt="">MCA_ev.m + myEventsFcn.m + System_of_ODEs.m</a></p>
 
<p>MCA files: <a href="https://static.igem.org/mediawiki/2017/e/e0/T--INSA-UPS_France--iGEM_INSA-UPS_France_2017_MCA.zip" alt="">MCA_ev.m + myEventsFcn.m + System_of_ODEs.m</a></p>
 
<img src="https://static.igem.org/mediawiki/2017/b/b6/T--INSA-UPS_France--HMnoscale.png" alt="">
 
<img src="https://static.igem.org/mediawiki/2017/b/b6/T--INSA-UPS_France--HMnoscale.png" alt="">
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</li>
 
</li>
 
</ul>
 
</ul>
−
<p>Important conclusions can be reached from this analysis. First, we notice that the initial concentration in <i>Vibrio harveyi</i> and all the strain intrinsic parameters have a weak influence on the response time. <i>V. harveyi</i> works as a simple inducer: a small amount of it is enough to sense CAI-1 and produce enough diacetyl to activate <i>Pichia pastoris</i>. Then, on the contrary, <i>Pichia pastoris</i> concentration (and its intrinsic parameters) have a significant impact on the response time, because a high antimicrobial peptides (AMP) concentration is required to kill <i>V. cholerae</i>. Efforts to optimize the system to accelerate its response could thus consist in engineering <i>P. pastoris</i> to increase the expression of AMPs. Interestingly, the device volume also appears to be a key parameters for our system. For a further development of our system, we should consider carefully AMP properties (death rate, IC50 regarding <i>Vibrio cholerae</i>), <i>Pichia pastoris</i> strain functioning (transcription, translation, gene, promoter) and its concentration in the device.</p>
+
<p>Important conclusions can be reached from this analysis. First, we notice that the initial concentration in <i>Vibrio harveyi</i> as well as most of its parameters have a weak influence on the response time (coefficients close to 0, black). <i>V. harveyi</i> works as a simple inducer: a small number of cells is sufficient to sense CAI-1 and produce enough diacetyl to activate <i>Pichia pastoris</i>. On the contrary, <i>Pichia pastoris</i> concentration and other parameters related to the AMP efficiency (MIC50, Vc kill) have a significant impact on the response time, because a high antimicrobial peptides (AMP) concentration is required to kill <i>V. cholerae</i>. Efforts to optimize the system to speed up its response should thus consist in engineering <i>P. pastoris</i> to increase the expression of AMPs, or to improve the efficiency of AMPs, rather than improving the sensor and transmission parts. Interestingly, the device volume also appears to be a key parameters for our system. For further developments, we should consider carefully AMP properties (death rate, IC50 regarding <i>Vibrio cholerae</i>), <i>Pichia pastoris</i> strain functioning (transcription, translation, gene, promoter) and its concentration in the device.</p>
 
</section>
 
</section>
  
 
<section>
 
<section>
 
<h1>Conclusion</h1>
 
<h1>Conclusion</h1>
−
<p>Our model analysis gave us promising results about our model stability and robustness, and our system functioning.
+
<p>Our model analysis gave us promising results about our the efficiency and robustness of the system.
−
  We reach to the conclusion with have a globaly robust system, and note the different key parameters controling it.
+
  We demonstrated it shows a robust behaviour under fluctuating conditions, and identified the most controlling parameters that should be tune to improve its response, hence guiding the design of an improved system.
−
  For a first study, the <i>Pichia pastoris</i> initial concentration ([<i>Pichia pastoris</i>]<sub>0</sub>) appeared to be the easiest variable to study, because its value can be directly modified without any molecular or microbial engineering approach.</p>
+
  <i>Pichia pastoris</i> initial concentration ([<i>Pichia pastoris</i>]<sub>0</sub>) appeared to be the easiest variable to play with, because its value can be directly adapted without any molecular or microbial engineering approach. We thus simulating the response time for a wide range of Pichia pastoris concentrations, and under a wide range of contamination levels (Vibrio cholerae concentration).</p>
 
<img src="https://static.igem.org/mediawiki/2017/a/a8/T--INSA-UPS_France--3Dfig.png" alt="">
 
<img src="https://static.igem.org/mediawiki/2017/a/a8/T--INSA-UPS_France--3Dfig.png" alt="">
 
<figcaption><b>Response time depending on two major parameters: <i>Vibrio cholerae</i> and <i>Pichia pastoris</i> concentrations</b></figcaption>
 
<figcaption><b>Response time depending on two major parameters: <i>Vibrio cholerae</i> and <i>Pichia pastoris</i> concentrations</b></figcaption>
−
<p>To plot the figure above, response time was calculated for different range of <i>Vibrio cholerae</i> and <i>Pichia pastoris</i> initial concentrations. We can conclude from this figure that the response time will stay acceptable for a wide range <i>Pichia pastoris</i> initial concentration: we would no pass above 120 minutes, even at low <i>Pichia pastoris</i> initial concentrations, and on realistic <i>Vibrio cholerae</i> initial concentration (less than 10<sup>8</sup> cell/L (3)), we are above 80 minutes.</p>
+
<p>Under all the situations tested here, the response time remains below 120 minutes, even at low <i>Pichia pastoris</i> initial concentrations.</p>
 
<p>This two parameters seemed to be the two more interesting to show the dynamic of our system to non-mathematicians.</p>
 
<p>This two parameters seemed to be the two more interesting to show the dynamic of our system to non-mathematicians.</p>
 
<h2><b>&rarr;</b> Our visual interface is available on <a href="https://2017.igem.org/Team:INSA-UPS_France/Model/Interface">our interface page</a>
 
<h2><b>&rarr;</b> Our visual interface is available on <a href="https://2017.igem.org/Team:INSA-UPS_France/Model/Interface">our interface page</a>

Revision as of 17:50, 18 October 2017

Croc'n Cholera
iGEM UPS-INSA Toulouse 2017

Analysis

Model analysis

After demonstrating the feasibility of our synthetic consortium, we have characterized some emerging properties that drive its functioning. In particular, we have performed global sensitivity analyses to test the robustness of the system to real life conditions (such as fluctuations of some parameters). To optimize its behaviour and guide its design, we then carried out more detailed analyses by extending the Metaboloic control analysis framework classically used in the fields of metabolic engeneering and systems biology.

Global sensitivity analysis

All parameter values cannot be known exactely through experiments (1), and our experience in this project, with a model composed by nearly fifty parameters, confirms this fact. As an additional concern, many other sources of variability may impact the efficiency of the system. Variability could emerge from the system itself (living systems are variable by nature) or during each step of the process (manufacturing, transport, storage). Facing this problem, a global sensitivity analysis approach was applied to determine the impact of parameters fluctuations on the response time to reach non-pathogenic concentrations.(1) Many other application of global sensitivity analysis for biochemistry and systems biology are described in Kent et al., 2013.

To perform this analysis, we generated 10,000 sets of parameters randomly sampled within +- 10% of their reference values, using a uniform distribution, and the response time of the system was calculated for each of these sets (Matlab code available below). Simulation results were analyzed with RStudio (R code available below).

Global analysis files: Global_Analysis.m + System_of_ODEs.m + Resolution_Function.m + myEventsFcn.m + Global_analysis.R

Distribution of the response time for 10,000 sets of random parameters

Simulation results indicate that the response times varied between 45.46 min (minimum) and 65.05 min (maximum), with a median of 53.70 min and a mean of 53.87 minclose to the response time of the initial set of parameters (53.6 min).

These statistical results confirm the global robustness of the system, which will remain efficient even under a reasonable degree of uncertainty.

Metabolic control analysis

Metabolic Control Analysis (MCA) is a mathematical tool widely used in biotechnology to quantify the influence of a specific parameter on the functioning of the system, in terms of fluxes and concentrations. Working with a system governed by a large number of parameters, MCA allows to determine the influence of each of them with respect to a metric of interest.(2)

Usually applied to steady state conditions, we have extended the concepts of MCA to quantify the control exerted by each parameter on the response time (τ). For each parameter (p), the control coefficient (C) was calculated.

\begin{equation*} C = \frac{(\tau(p)-\tau(\delta.p))/\tau}{(p - \delta.p)/p} \end{equation*}

This coefficient quantifies the relative change in the response time τ which results from a relative change δ of the parameter p. If the response time is not impacted by a variation of the parameter p, the coefficient will be equal to zero. A positive (negative) value indicates that an increase in p increases (reduces) the response time. Control coefficients were calculated by numerical differentiation, by setting δ at 0.01. This sensitivity analysis was performed for a wide range of initial concentration of Vibrio cholerae. Results are presented as a heatmap. The Matlab script used to calculated control coefficient and generate a heatmap (SimBiology needed) are available below.

MCA files: MCA_ev.m + myEventsFcn.m + System_of_ODEs.m

Heatmap representing each parameter influence on the response time, using a MCA approach
  • Red: parameters favouring a short response time
  • Green: parameters favouring a long response time
  • White: parameters with no significant influence

Important conclusions can be reached from this analysis. First, we notice that the initial concentration in Vibrio harveyi as well as most of its parameters have a weak influence on the response time (coefficients close to 0, black). V. harveyi works as a simple inducer: a small number of cells is sufficient to sense CAI-1 and produce enough diacetyl to activate Pichia pastoris. On the contrary, Pichia pastoris concentration and other parameters related to the AMP efficiency (MIC50, Vc kill) have a significant impact on the response time, because a high antimicrobial peptides (AMP) concentration is required to kill V. cholerae. Efforts to optimize the system to speed up its response should thus consist in engineering P. pastoris to increase the expression of AMPs, or to improve the efficiency of AMPs, rather than improving the sensor and transmission parts. Interestingly, the device volume also appears to be a key parameters for our system. For further developments, we should consider carefully AMP properties (death rate, IC50 regarding Vibrio cholerae), Pichia pastoris strain functioning (transcription, translation, gene, promoter) and its concentration in the device.

Conclusion

Our model analysis gave us promising results about our the efficiency and robustness of the system. We demonstrated it shows a robust behaviour under fluctuating conditions, and identified the most controlling parameters that should be tune to improve its response, hence guiding the design of an improved system. Pichia pastoris initial concentration ([Pichia pastoris]0) appeared to be the easiest variable to play with, because its value can be directly adapted without any molecular or microbial engineering approach. We thus simulating the response time for a wide range of Pichia pastoris concentrations, and under a wide range of contamination levels (Vibrio cholerae concentration).

Response time depending on two major parameters: Vibrio cholerae and Pichia pastoris concentrations

Under all the situations tested here, the response time remains below 120 minutes, even at low Pichia pastoris initial concentrations.

This two parameters seemed to be the two more interesting to show the dynamic of our system to non-mathematicians.

→ Our visual interface is available on our interface page

References

  • (1): Kent E, Neumann S, Kummer U, Mendes P, What can we learn from global sensitivity analysis of biochemical systems? PLoS ONE, 8 (2013), p. e79244 http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0079244
  • (2): Moreno-Sánchez R, Saavedra E, Rodríguez-Enríquez S, Olín-Sandoval V, Metabolic control analysis a tool for designing strategies to manipulate metabolic pathways. J. Biomed. Biotechnol., 2008 (2008), p. 597913 https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2447884/
  • (3): Huq A., West, P. A., Small, E. B., Huq, M. I., and Colwell, R. R., Influence of water temperature, salinity and pH on survival and growth of toxigenic Vibrio cholerae serovar O1 associated with live copepods in laboratory microcosms, Appl. Environ. Microbiol. 1984, 48: 420–424.