Team:TU-Delft/Modeling/StochasticSensitivitySpecificityAnalysis

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= Stochastic Model =  
= Stochastic Model =  
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In Saccharomyces cerevisiae, stochasticity (noise) arising from transcription contributes significantly to the level of heterogeneity within a eukaryotic clonal population [[Team:TU-Delft/Modeling/SingleCellModel#Ref7|[7]]].[[File:TUDHybridModel.png|400px|left|thumb|'''Figure 11''': Hybrid model of the modified yeast pathway]] In order to investigate the effects of this stochasticity, we decided to build a stochastic model of the pathway using a '''Hybrid ODE-SDE''' framework (where SDE stands for stochastic differential equation). Data from [[Team:TU-Delft/Modeling/SingleCellModel#Ref7|[5]]] suggests that the Pheromone signalling is robust against cell to cell variations. Motivated by this fact, we assume the dynamics until the activation of the transcription factor to be deterministic rather than stochastic. As a result of the gene expression being noisy, we build a hybrid stochastic model consisting of deterministic semantics until the activation of the transcription factor ''Ste12'' and treat it as a time varying parameter modulating the reaction based gene expression module interpreted with stochastic semantics using the stochastic differential equations approach [[Team:TU-Delft/Modeling/SingleCellModel#Ref7|[8]]], the schematic of which is given in Figure 11.
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In Saccharomyces cerevisiae, stochasticity (noise) arising from transcription contributes significantly to the level of heterogeneity within a eukaryotic clonal population [[Team:TU-Delft/Modeling/SingleCellModel#Ref1|[1]]].[[File:TUDHybridModel.png|400px|left|thumb|'''Figure 1''': Hybrid model of the modified yeast pathway]] In order to investigate the effects of this stochasticity, we decided to build a stochastic model of the pathway using a '''Hybrid ODE-SDE''' framework (where SDE stands for stochastic differential equation). Motivated by the fact that the Pheromone signalling is robust against cell to cell variations., we assume the dynamics until the activation of the transcription factor to be deterministic rather than stochastic. As a result of the gene expression being noisy, we build a hybrid stochastic model consisting of deterministic semantics until the activation of the transcription factor ''Ste12'' and treat it as a time varying parameter modulating the reaction based gene expression module interpreted with stochastic semantics using the stochastic differential equations approach [[Team:TU-Delft/Modeling/SingleCellModel#Ref2|[2]]], the schematic of which is given in Figure 1.
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Twenty simulations were done for each three different input concentrations. The results of which are in the figure below.
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Twenty simulations were done for different input concentrations. The results of which are in the figure below.
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[[File:CLE20nM.png|575px|left|thumb|'''Figure 1''': Stochastic Simulation of the System for 20nM Ligand concentration]]
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[[File:CLE20nM.png|575px|left|thumb|'''Figure 2''': Stochastic Simulation of the System for 20nM Ligand concentration]]
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[[File:CLE200nM.png|575px|left|thumb|'''Figure 2''': Stochastic Simulation of the System for 200nM Ligand concentration]]
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[[File:CLE200nM.png|575px|left|thumb|'''Figure 3''': Stochastic Simulation of the System for 200nM Ligand concentration]]
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=== conclusion ===
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= Sensitivity and Specificity =
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* The mean of the stochastic simulation runs closely follow the deterministic solutions.
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* It helped us assess the degree of variablity that is present within the system
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Using an input ligand concentration of 200uM (this corresponds to the quantity of ''Methyl Nicotinate'' in TB sample), we used the single cell pathway model to set the threshold to the maximum GFP output that was produced. We then used a sample population of 1000 people and a input ligand concentration varying over a range from 0 - 2uM to perform the test. The results from the tests are presented below.
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* The time duration of the project limited further applications of this model, the proposed use of which is presented in the future works section.</div>
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= Results =
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[[File:FN.png|260px|left|thumb|'''Figure 4''': False Negative Analysis]]
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[[File:FP.png|260px|right|thumb|'''Figure 5''': False Positive Analysis]]
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= Conclusion =
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The results indicate that the proposed device has a sensitivity of 87% and a specificity of 74%, which shows that there is a great potential for further improvement. Towards which we are currently making use of the structural model to investigate ways by which better ligand binding affinities can be achieved.
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= MATLAB Codes =
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=== Stochastic Model & False positive;False negative tests ===
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[[File:TUD-Download.png|50px|link=File:FalsePositiveFalseNegativeTest.zip|left]]
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<br clear="all" />
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= References =
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{|style="margin: 1em auto 1em auto;" class="wikitable sortable" width="90%"
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!style="white-space: nowrap; width: 1px;"|
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!class="unsortable"|Source
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|-
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|style="text-align: center"|<span id="Ref1">[1]</span>
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|[http://www.nature.com/ng/journal/v31/n1/pdf/ng869.pdf Ozbudak, E. M., Thattai, M., Kurtser, I., Grossman, A. D. & van Oudenaarden, <br>'''Regulation of noise in the expression of a single gene''', <br>Nature Genet. 31, 69-73 (2002)]
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|-
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|style="text-align: center"|<span id="Ref2">[2]</span>
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|[http://epubs.siam.org/doi/pdf/10.1137/060666457 Desmond J.Hingham<br>'''Modeling and Simulating Chemical Reactions''',<br>SIAM Rev., 50(2), 347–368]
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Latest revision as of 03:38, 27 October 2012

Team:TUDelft/CSSLaksh Menu

Single Cell Model


Biological functions are inherently stochastic in nature, which leads to a wide degree of variability not only at the population level but also at the level of individual cells, which makes it important to test the reliability of our system. Towards this, we first built a stochastic model of the pathway and then used it to assess the specificity and the sensitivity of our device.

Contents

Stochastic Model

In Saccharomyces cerevisiae, stochasticity (noise) arising from transcription contributes significantly to the level of heterogeneity within a eukaryotic clonal population [1].
Figure 1: Hybrid model of the modified yeast pathway
In order to investigate the effects of this stochasticity, we decided to build a stochastic model of the pathway using a Hybrid ODE-SDE framework (where SDE stands for stochastic differential equation). Motivated by the fact that the Pheromone signalling is robust against cell to cell variations., we assume the dynamics until the activation of the transcription factor to be deterministic rather than stochastic. As a result of the gene expression being noisy, we build a hybrid stochastic model consisting of deterministic semantics until the activation of the transcription factor Ste12 and treat it as a time varying parameter modulating the reaction based gene expression module interpreted with stochastic semantics using the stochastic differential equations approach [2], the schematic of which is given in Figure 1.

Twenty simulations were done for different input concentrations. The results of which are in the figure below.

Figure 2: Stochastic Simulation of the System for 20nM Ligand concentration
Figure 3: Stochastic Simulation of the System for 200nM Ligand concentration

Sensitivity and Specificity

Using an input ligand concentration of 200uM (this corresponds to the quantity of Methyl Nicotinate in TB sample), we used the single cell pathway model to set the threshold to the maximum GFP output that was produced. We then used a sample population of 1000 people and a input ligand concentration varying over a range from 0 - 2uM to perform the test. The results from the tests are presented below.

Results

Figure 4: False Negative Analysis
Figure 5: False Positive Analysis

Conclusion

The results indicate that the proposed device has a sensitivity of 87% and a specificity of 74%, which shows that there is a great potential for further improvement. Towards which we are currently making use of the structural model to investigate ways by which better ligand binding affinities can be achieved.

MATLAB Codes

Stochastic Model & False positive;False negative tests

TUD-Download.png


References

Source
[1] [http://www.nature.com/ng/journal/v31/n1/pdf/ng869.pdf Ozbudak, E. M., Thattai, M., Kurtser, I., Grossman, A. D. & van Oudenaarden,
Regulation of noise in the expression of a single gene,
Nature Genet. 31, 69-73 (2002)]
[2] [http://epubs.siam.org/doi/pdf/10.1137/060666457 Desmond J.Hingham
Modeling and Simulating Chemical Reactions,
SIAM Rev., 50(2), 347–368]


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