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

07/09/2010 ENGOPT 2010 - p. 7/16

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

07/09/2010 ENGOPT 2010 - p. 8/16

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

07/09/2010 ENGOPT 2010 - p. 9/16

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

07/09/2010 ENGOPT 2010 - p. 10/16

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

07/09/2010 ENGOPT 2010 - p. 11/16

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

07/09/2010 ENGOPT 2010 - p. 13/16

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

07/09/2010 ENGOPT 2010 - p. 14/16

Some results

Outlines

Part I: Protein folding

Part II: Microfluidic mixer

optimization

Conclusions and perspectives

Conclusions and perspectives

07/09/2010 ENGOPT 2010 - p. 15/16

Conclusions and perspectives

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

• 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

07/09/2010 ENGOPT 2010 - p. 16/16

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 !!!