Mathematical modeling for protein folding devices. Applications …ivorra/pres/Engopt2010.pdf ·...
Transcript of Mathematical modeling for protein folding devices. Applications …ivorra/pres/Engopt2010.pdf ·...
07/09/2010 ENGOPT 2010 - p. 1/16
Mathematical modeling for protein foldingdevices. Applications to high pressure
processing and microfluidic mixers .
Ivorra Benjamin1 & Angel Manuel Ramos1
Microlfuidic mixer: Juana López Redondo2 & Pilar Martínez Ortigosa2
High pressure processing: Juan-Antonio Infante1,Jose Maria Rey1 & Nadia Smith1
Protein folding modeling: Juan Bello Rivas1
1- - Universidad Complutense de Madrid
2- Supercomputación: Algoritmos - Universidad de Almeria
In part funded by:
Outlines
Part I: Protein folding
Part II: Microfluidic mixer
optimization
Conclusions and perspectives
07/09/2010 ENGOPT 2010 - p. 2/16
Outlines
• Protein folding
-Principle
-Some interesting applications
• Microfluidic mixer optimization
-Device description
-Optimization Problem
-Results
• Conclusions and perspectives
Outlines
Part I: Protein folding
Definition
Industrial applications
Interesting mathematical
problems
Part II: Microfluidic mixer
optimization
Conclusions and perspectives
07/09/2010 ENGOPT 2010 - p. 3/16
Part I: Protein folding
Outlines
Part I: Protein folding
Definition
Industrial applications
Interesting mathematical
problems
Part II: Microfluidic mixer
optimization
Conclusions and perspectives
07/09/2010 ENGOPT 2010 - p. 4/16
Definition
What are proteins? They are organic compounds (enzymes,DNA, ...) that catalyze chemical reactions (fermentation, vitalsupport, ...).
For instance:
What is protein folding? it is a process that consists of achange in the protein structure from a folded state (canperform chemical reaction) to an unfolded state (inactive).
Representation:
Outlines
Part I: Protein folding
Definition
Industrial applications
Interesting mathematical
problems
Part II: Microfluidic mixer
optimization
Conclusions and perspectives
07/09/2010 ENGOPT 2010 - p. 5/16
Industrial applications
How protein folding process occurs? When energy is appliedto protein provoking a perturbation of the proteinconformational equilibrium. It can be performed, for instance,by using changes in temperature and/or pressure or changesin chemical potential (such as concentration changes).
CONFIGURATION
Intermediate State
Folded State
Unfolded State
Intermediate State
EN
ER
GY
What are the protein folding interests? The range of industrialapplications is wide: DNA sequencing, drug moleculescreation, food treatment, etc.
Outlines
Part I: Protein folding
Definition
Industrial applications
Interesting mathematical
problems
Part II: Microfluidic mixer
optimization
Conclusions and perspectives
07/09/2010 ENGOPT 2010 - p. 6/16
Interesting mathematical problems
Inside the consortium , we are interested in threemain problematics: Design of microfluidic mixers: This part will be developed
here. Modeling, simulation and optimization of
High-Pressure/Temperature food treatment:
Published in: ’On the Modelling and Simulation of HighPressure Processes and Inactivation of Enzymes in FoodEngineering’. Math. Models and Meth. in Appl. Sciences.
Modeling and simulation of protein folding at chemical level:Work in progress (PhD).
Outlines
Part I: Protein folding
Part II: Microfluidic mixer
optimization
Device description
Knight mixer
Industrial problem
Shape parameterization
Mathematical modeling
Optimization problem
Some results
Conclusions and perspectives
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Part II: Microfluidic mixer optimization
Outlines
Part I: Protein folding
Part II: Microfluidic mixer
optimization
Device description
Knight mixer
Industrial problem
Shape parameterization
Mathematical modeling
Optimization problem
Some results
Conclusions and perspectives
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Device description
Principle: Microfluidic mixers are used to mix, as fast aspossible, a protein solution with a solvent provoking a rapidchange in chemical potential resulting in the unfold of certainproteins.
Example of microfluidic mixer: There exist a wide range oftechniques to create microfluidic mixers.
For instance:
Considered mixer: Knight mixer
Outlines
Part I: Protein folding
Part II: Microfluidic mixer
optimization
Device description
Knight mixer
Industrial problem
Shape parameterization
Mathematical modeling
Optimization problem
Some results
Conclusions and perspectives
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Knight mixer
Outlines
Part I: Protein folding
Part II: Microfluidic mixer
optimization
Device description
Knight mixer
Industrial problem
Shape parameterization
Mathematical modeling
Optimization problem
Some results
Conclusions and perspectives
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Industrial problem
Objective: optimize the mixer to reduce the time needed toreach a certain protein concentration.
Previous work (collaborators: Stanford Microfluidics Lab. ): Aonly shape optimization of the mixer have been done andvalidated by experiments: ’Semi–deterministic and geneticalgorithms for global optimization of microfluidic protein foldingdevices’, Intern. Journal of Num. Method in Engineering.
(8µs) ⇒ (1.2µs)
Current work: solve a more complex optimization problemconsidering more geometrical variables and the inlet velocities.
Outlines
Part I: Protein folding
Part II: Microfluidic mixer
optimization
Device description
Knight mixer
Industrial problem
Shape parameterization
Mathematical modeling
Optimization problem
Some results
Conclusions and perspectives
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Shape parameterization
px
lc
h2
(cx2,cy2)
l2
ls
(cx1,cy1)
h1l1
le
θ
us
Axi
al s
ymm
etry
exit
Center inlet
Side inlet
Ω
uc
Outlines
Part I: Protein folding
Part II: Microfluidic mixer
optimization
Device description
Knight mixer
Industrial problem
Shape parameterization
Mathematical modeling
Optimization problem
Some results
Conclusions and perspectives
07/09/2010 ENGOPT 2010 - p. 12/16
Mathematical modeling
Steady equations:
C
C30
90
+Convective−Diffusion
Navier−Stokes
Outlines
Part I: Protein folding
Part II: Microfluidic mixer
optimization
Device description
Knight mixer
Industrial problem
Shape parameterization
Mathematical modeling
Optimization problem
Some results
Conclusions and perspectives
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Optimization problem
We are interested in minimizing:
J(xparam) =
∫
c
xparam
30
c
xparam
90
dy
uxparam(y) · t
, (1)
where cxparam
90 , cxparam
30 and uxparam are computed by solving
numerically (considering a FEM) the following system:
−∇ · (η(∇u + (∇u)⊤)) + ρ(u · ∇)u + ∇p = 0 in Ω,
∇ · u = 0 in Ω,
∇ · (−D∇c + cu) = 0 in Ω,
+ boundary conditions.
(2)
This optimization problem is solved by using the GlobalOptimization Platform software with a genetic algorithm as thecore algorithm and where the initial population is generatedusing the secant method.
Outlines
Part I: Protein folding
Part II: Microfluidic mixer
optimization
Device description
Knight mixer
Industrial problem
Shape parameterization
Mathematical modeling
Optimization problem
Some results
Conclusions and perspectives
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Some results
Outlines
Part I: Protein folding
Part II: Microfluidic mixer
optimization
Conclusions and perspectives
Conclusions and perspectives
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Conclusions and perspectives
Outlines
Part I: Protein folding
Part II: Microfluidic mixer
optimization
Conclusions and perspectives
Conclusions and perspectives
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Conclusions and perspectives
• Importance of the protein folding process in industrialapplications.
• For each application, our modeling/simulation are validatedby posteriori prototyping.
• The new parameterization allows to improve existingmicrofluidic mixers.
• Perspectives: Direct modeling of the folding process,creations of new patents...
Outlines
Part I: Protein folding
Part II: Microfluidic mixer
optimization
Conclusions and perspectives
Conclusions and perspectives
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Conclusions and perspectives
Global Optimization Platform
http://www.mat.ucm.es/momat/software.htm
Outlines
Part I: Protein folding
Part II: Microfluidic mixer
optimization
Conclusions and perspectives
Conclusions and perspectives
07/09/2010 ENGOPT 2010 - p. 16/16
Conclusions and perspectives
!!! Thank You !!!