overcoming unknown kinetic data for quantitative modelling ...€¦ · data for quantitative...
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Overcoming Unknown Kinetic Data for Quantitative Modelling of Biological Systems Using Fuzzy Logic and Petri Nets
June 23th2014
Jure Bordon, dr. Miha Moškon, prof. Miha Mraz
University of LjubljanaFaculty of Computer and Information Science
BioPPN’14, Tunis, Tunisia
2June 23, 2014, Tunis, Tunisia
Desired behaviour
Measureddata
Verification
Synthetic biology
BioPPN’14 | Jure Bordon
New biological
system
in vivo implementation
Design and construction
Heiner et al, Petri nets for systems and synthetic biology, 2008
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Desired behaviour
Measureddata
Design and construction
Verification
New biological
system
Model
Synthetic biology
June 23, 2014, Tunis, Tunisia BioPPN’14 | Jure Bordon
Heiner et al, Petri nets for systems and synthetic biology, 2008
4
Modelling approaches
Quantitative Qualitative
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5
Modelling approaches
Quantitative Qualitative
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• Qualitative behavioral properties of the system
• Can be discrete or continuous
• No notion of time and quantity
6
Modelling approaches
Quantitative Qualitative
Time
Co
nce
ntr
atio
n
[s]
[X]
Deterministic(ODEs)
Stochastic(CME)
Accuratekinetic rates?!?
June 23, 2014, Tunis, Tunisia BioPPN’14 | Jure Bordon
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Modelling approaches
Quantitative Qualitative
Deterministic(ODEs)
Stochastic(CME)
Accuratekinetic rates?!?
June 23, 2014, Tunis, Tunisia BioPPN’14 | Jure Bordon
• Parameter estimation only possible when experimental data is available
• Strict limitations in order to get biologically relevant and realistic parameters
• Changing the biological system requires new parameter estimation
• Inconvenient when we want to test multiple GRN topologies (e.g. GRN oscillators)
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Modelling approaches
Fuzzy logic as an alternativeQuantitative Qualitative
Deterministic(ODEs)
Stochastic(CME)
Accuratekinetic rates?!?
• Intuitive qualitative description of system dynamics by using linguistic description
• Can approximate quantitative approaches when kinetic data is known
• More forgiving when we lack accurate kinetic data
• Quantitatively significantly more relevant than qualitative approaches
June 23, 2014, Tunis, Tunisia BioPPN’14 | Jure Bordon
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Petri nets1
Qualitative PNs
Time-free
‐ Qualitative description‐ Behavioural properties
Timed,Quantitative
Stochastic PNs
‐ Molecules‐ Stochastic rates
Discrete State Space Continuous State Space
Fuzzy PNs
‐ Qualitative description
Continuous PNs‐ ODEs (concentrations,
deterministic rates)
‐ Fuzzy PNs (function approximation2; can be used for quantitative modelling even if kinetic data is unknown)
1Heiner et al, Petri nets for systems and synthetic biology, 20082Windhager, Modeling of Dynamic Systems with Petri nets and Fuzzy Logic, PhD thesis, 2013
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Transcription-translation system1
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• Inputs: DNA, transcription resource (TsR), translation resource (TlR)
• Output: Protein concentration
• Processes: transcription, translation, degradation, consumption
DNA mRNA Protein
TsR TlR
ΔProtein
ΔTlR
ΔmRNA
ΔmRNA
ΔTsR
f0 f0
f0
decaydecay
transcription translation
1Windhager, Modeling of Dynamic Systems with Petri nets and Fuzzy Logic, PhD thesis, 2013
11June 23, 2014, Tunis, Tunisia
Transcription-translation system
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• Fuzzy approach for modelling translation
• Other processes are modelled as a system of ODEs1
DNA mRNA Protein
TsR TlR
ΔProtein
ΔTlR
ΔmRNA
ΔmRNA
ΔTsR
f0 f0
f0
decaydecay
transcription translation
1Windhager, Modeling of Dynamic Systems with Petri nets and Fuzzy Logic, PhD thesis, 2013
𝑑[𝑃𝑟𝑜𝑡𝑒𝑖𝑛]
𝑑𝑡=𝑘𝑡𝑙 ⋅ 𝑇𝑙𝑅 ⋅ [𝑚𝑅𝑁𝐴]
𝑚𝑡𝑙 + [𝑚𝑅𝑁𝐴]
12June 23, 2014, Tunis, Tunisia
Modelling translation using Fuzzy logic
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Concentration of mRNA and TlR
How concentration of protein changes depending on concentrations of mRNA and TlR?
Protein concentration change
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Modelling translation using Fuzzy logic
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Modelling translation using Fuzzy logic
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• Fuzzification of mRNA and TlR concentration
(50% Med, 50% High)
950nM 0.45
(50% Low, 50% Med)
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Modelling translation using Fuzzy logic
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Modelling translation using Fuzzy logic
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• Defining IF-THEN rules for protein concentration change
• Rules are very descriptive and intuitive
VS.
𝑑[𝑃𝑟𝑜𝑡𝑒𝑖𝑛]
𝑑𝑡=𝑘𝑡𝑙 ⋅ 𝑇𝑙𝑅 ⋅ [𝑚𝑅𝑁𝐴]
𝑚𝑡𝑙 + [𝑚𝑅𝑁𝐴]
IF (mRNA) is VeryLow AND (TlR) is Low THEN (ConcentrationChange) is VeryLow
17June 23, 2014, Tunis, Tunisia
Modelling translation using Fuzzy logic
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Modelling translation using Fuzzy logic
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• Defuzzification of protein concentration change (Center of gravity)
(80% High, 20% VeryHigh)
20nM
19June 23, 2014, Tunis, Tunisia BioPPN’14 | Jure Bordon
DNA mRNA Protein
TsR TlR
ΔProtein
ΔTlR
ΔmRNA
ΔmRNA
ΔTsR
f0 f0
f0
decaydecay
transcription translation
• One transition is transformed into fuzzy logic Petri net with corresponding input and output
Modelling translation using Fuzzy logic & Petri nets
20June 23, 2014, Tunis, Tunisia BioPPN’14 | Jure Bordon
mRNA concentration
Fuzzification IF-THEN rules Defuzzification
Protein (GFP) concentrationchange
0.72
970
0.28
0
VeryHigh
High
None
.
.
.
0.68
0.32
0.05
VeryHigh
High
None
23.9
314
Protein (GFP) concentration
TlR concentration
0.63
0.83
0.37
0
High
Low
.
.
.
Medium
0None
0
Medium
.
.
.
Modelling translation using Fuzzy logic & Petri Nets
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Simulation
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• Building the model• Matlab Simulink
• Fuzzy logic toolbox
• Simulation run• Matlab engine
• Regards fuzzy logic steps as one step
• Allows an easy way of building fuzzy system
• Simulation run with ODEs and fuzzy logic in the same model
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Simulation
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Results
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Conclusions
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• Fuzzy logic can be used to overcome missing kinetic data
• We lose some accuracy, but still get biologically relevant results
• With more knowledge we can reduce the error
• Can be used with existing methods
• Automatic generation of Petri net based on defined fuzzification/defuzzification/IF-THEN rules?
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Computational Biology Group
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University of Ljubljana, Faculty of computer and information science
http://lrss.fri.uni-lj.si/bio/