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Flux Balance AnalysisFlux Variability Analysis
Metabolic network analysisOptimization-based methods
Laszlo David
Mathematics in Life SciencesFreie Universität Berlin
29 October, 2010
Laszlo David Optimization-based methods
Flux Balance AnalysisFlux Variability Analysis
1 Flux Balance Analysis
2 Flux Variability Analysis
Laszlo David Optimization-based methods
Flux Balance AnalysisFlux Variability Analysis
Linear Programming
What is linear programming?
Linear programming is a technique for the optimization of alinear objective function, subject to linear equality and linearinequality constraints.
A linear program in standard form
min ctxs.t . Ax = b
x ≥ 0
Laszlo David Optimization-based methods
Flux Balance AnalysisFlux Variability Analysis
Linear Programming
What is linear programming?
Linear programming is a technique for the optimization of alinear objective function, subject to linear equality and linearinequality constraints.
A linear program in standard form
min ctxs.t . Ax = b
x ≥ 0
Laszlo David Optimization-based methods
Flux Balance AnalysisFlux Variability Analysis
Optimization-based methods
Laszlo David Optimization-based methods
Flux Balance AnalysisFlux Variability Analysis
Flux Balance Analysis
MotivationGiven a metabolic network find the most suitable fluxdistribution for a certain task.
Example tasksOptimal flux distribution for biomass production (growth).Minimize ATP production to guarantee optimal metabolicenergy efficiency.Maximize the production of a chosen metabolite todetermine production capabilities of a given network.
Laszlo David Optimization-based methods
Flux Balance AnalysisFlux Variability Analysis
Flux Balance Analysis
MotivationGiven a metabolic network find the most suitable fluxdistribution for a certain task.
Example tasksOptimal flux distribution for biomass production (growth).Minimize ATP production to guarantee optimal metabolicenergy efficiency.Maximize the production of a chosen metabolite todetermine production capabilities of a given network.
Laszlo David Optimization-based methods
Flux Balance AnalysisFlux Variability Analysis
Flux Balance Analysis
MotivationGiven a metabolic network find the most suitable fluxdistribution for a certain task.
Example tasksOptimal flux distribution for biomass production (growth).Minimize ATP production to guarantee optimal metabolicenergy efficiency.Maximize the production of a chosen metabolite todetermine production capabilities of a given network.
Laszlo David Optimization-based methods
Flux Balance AnalysisFlux Variability Analysis
Flux Balance Analysis
MotivationGiven a metabolic network find the most suitable fluxdistribution for a certain task.
Example tasksOptimal flux distribution for biomass production (growth).Minimize ATP production to guarantee optimal metabolicenergy efficiency.Maximize the production of a chosen metabolite todetermine production capabilities of a given network.
Laszlo David Optimization-based methods
Flux Balance AnalysisFlux Variability Analysis
Method
Step 1.Identify an objective function Z .
Step 2.
Set bounds on the flux variables ( vmini ≤ vi ≤ vmax
i for alli ∈ {1, ...,n})
Step 3.Solve the linear program:min Z tvs.t . Sv = 0
vmin ≤ v ≤ vmax
Laszlo David Optimization-based methods
Flux Balance AnalysisFlux Variability Analysis
Method
Step 1.Identify an objective function Z .
Step 2.
Set bounds on the flux variables ( vmini ≤ vi ≤ vmax
i for alli ∈ {1, ...,n})
Step 3.Solve the linear program:min Z tvs.t . Sv = 0
vmin ≤ v ≤ vmax
Laszlo David Optimization-based methods
Flux Balance AnalysisFlux Variability Analysis
Method
Step 1.Identify an objective function Z .
Step 2.
Set bounds on the flux variables ( vmini ≤ vi ≤ vmax
i for alli ∈ {1, ...,n})
Step 3.Solve the linear program:min Z tvs.t . Sv = 0
vmin ≤ v ≤ vmax
Laszlo David Optimization-based methods
Flux Balance AnalysisFlux Variability Analysis
FBA’s method in pictures
Laszlo David Optimization-based methods
Flux Balance AnalysisFlux Variability Analysis
FBA’s method in pictures
Laszlo David Optimization-based methods
Flux Balance AnalysisFlux Variability Analysis
FBA’s method in pictures
Laszlo David Optimization-based methods
Flux Balance AnalysisFlux Variability Analysis
FBA’s method in pictures
Laszlo David Optimization-based methods
Flux Balance AnalysisFlux Variability Analysis
1 Flux Balance Analysis
2 Flux Variability Analysis
Laszlo David Optimization-based methods
Flux Balance AnalysisFlux Variability Analysis
Flux Variability analysis
QuestionWhat happens when there are multiple flux distributions withthe same ’best’ objective value? (i.e. the set of solution is aface of the polyhedron)
ImportanceThe biological conclusions drawn fromdifferent optima can be different.
Laszlo David Optimization-based methods
Flux Balance AnalysisFlux Variability Analysis
Flux Variability analysis
QuestionWhat happens when there are multiple flux distributions withthe same ’best’ objective value? (i.e. the set of solution is aface of the polyhedron)
ImportanceThe biological conclusions drawn fromdifferent optima can be different.
Laszlo David Optimization-based methods
Flux Balance AnalysisFlux Variability Analysis
Flux Variability analysis
Idea 1Find all flux distributions that have the same ’best’ objectivevalue. (Computationally expensive)
Idea 2Instead of finding all flux distributions, find the range in whichthe fluxes vary. (Flux variability analysis)
Laszlo David Optimization-based methods
Flux Balance AnalysisFlux Variability Analysis
Flux Variability analysis
Idea 1Find all flux distributions that have the same ’best’ objectivevalue. (Computationally expensive)
Idea 2Instead of finding all flux distributions, find the range in whichthe fluxes vary. (Flux variability analysis)
Laszlo David Optimization-based methods
Flux Balance AnalysisFlux Variability Analysis
Example
Flux variability analysis
Solve the linear program for all j ∈ {1, ...,n}:min/max vj
s.t . Sv = 0vmin ≤ v ≤ vmax
Z tv = Zobj
Laszlo David Optimization-based methods
Flux Balance AnalysisFlux Variability Analysis
Example
Laszlo David Optimization-based methods
Flux Balance AnalysisFlux Variability Analysis
Summary: Optimization based methods
Advantages
For an objective function we get a ’fast’ answer what theoptimal flux distribution is.Successfully employed for several microorganisms.
DrawbacksSensitivity to the definition of objective function.Optimal flux distribution might not be unique.Microorganisms could use different optimization criteriadepending on their environment.The exploration of all suitable objective function is a difficulttask.
Laszlo David Optimization-based methods
Flux Balance AnalysisFlux Variability Analysis
Summary: Optimization based methods
Advantages
For an objective function we get a ’fast’ answer what theoptimal flux distribution is.Successfully employed for several microorganisms.
DrawbacksSensitivity to the definition of objective function.Optimal flux distribution might not be unique.Microorganisms could use different optimization criteriadepending on their environment.The exploration of all suitable objective function is a difficulttask.
Laszlo David Optimization-based methods
Flux Balance AnalysisFlux Variability Analysis
Summary: Optimization based methods
Advantages
For an objective function we get a ’fast’ answer what theoptimal flux distribution is.Successfully employed for several microorganisms.
DrawbacksSensitivity to the definition of objective function.Optimal flux distribution might not be unique.Microorganisms could use different optimization criteriadepending on their environment.The exploration of all suitable objective function is a difficulttask.
Laszlo David Optimization-based methods
Flux Balance AnalysisFlux Variability Analysis
Summary: Optimization based methods
Advantages
For an objective function we get a ’fast’ answer what theoptimal flux distribution is.Successfully employed for several microorganisms.
DrawbacksSensitivity to the definition of objective function.Optimal flux distribution might not be unique.Microorganisms could use different optimization criteriadepending on their environment.The exploration of all suitable objective function is a difficulttask.
Laszlo David Optimization-based methods
Flux Balance AnalysisFlux Variability Analysis
Summary: Optimization based methods
Advantages
For an objective function we get a ’fast’ answer what theoptimal flux distribution is.Successfully employed for several microorganisms.
DrawbacksSensitivity to the definition of objective function.Optimal flux distribution might not be unique.Microorganisms could use different optimization criteriadepending on their environment.The exploration of all suitable objective function is a difficulttask.
Laszlo David Optimization-based methods
Flux Balance AnalysisFlux Variability Analysis
Summary: Optimization based methods
Advantages
For an objective function we get a ’fast’ answer what theoptimal flux distribution is.Successfully employed for several microorganisms.
DrawbacksSensitivity to the definition of objective function.Optimal flux distribution might not be unique.Microorganisms could use different optimization criteriadepending on their environment.The exploration of all suitable objective function is a difficulttask.
Laszlo David Optimization-based methods
Flux Balance AnalysisFlux Variability Analysis
Questions
Questions?
Laszlo David Optimization-based methods
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