CENTR

FORINTEGRATIVE

BIOINFORMATICSVU

E FluxEs: An R package for metabolic flux quantification

Thomas Binslhttp://www.few.vu.nl/~tbinsl

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Introduction Metabolic fluxes reflect the function and

dynamics of living cells. A number of new techniques for flux

measurement have been developed, which aids for instance dedicated drug development and the design of new efficient bioreactors.

FluxEs is an R computer package that quantifies metabolic fluxes using NMR measurements of isotope labeling experiments. User-/biologist-friendly input format. No isotope steady state necessary.

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Isotope Labeling ExperimentvC2

C1

A

C1D

C2C1

C

C3C2

B

C1v

v

v

vA

CDBv

vv

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Parameter Estimation By performing a computer simulation of the

labeling experiment the NMR multiplets can also be computed…

…and model parameters, like the cycle flux v can be esti-mated by comparing the computed and measured NMR multiplets, e.g. via sum of squares (SSQ) criterion.

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Why R? Free of charge Cross platform, e.g. FluxEs was developed

on a MS Windows machine and runs without any changes on our Linux cluster.

Object oriented Vector based Large variety of additional packages, e.g.

FluxEs uses the “deSolve” package for solving the initial value problem for stiff systems of ordinary differential equations.

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Program Implementation Models are specified in plain text files. The model-files are parsed by the

package and the mathematical representation of the model is derived automatically.

Afterwards, the user is guided through the entire setup process necessary for an optimization, e.g. which parameters should be optimized, which optimization strategy should be used,…

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New grid-polyhedron approach to determine optimal start points for an optimization in parameter space.

Here we see a contour plot of sum-of-squares (SSQ) landscape formed by two parameters p1 and p2.

Optimization Strategy

- Grid points are the vertices of polyhedrons.- SSQ values of the vertices of a polyhedron are averaged and serve as SSQ value of the entire polyhedron.- Polyhedrons are sorted according to these values and the n best are chosen.- For each of the n polyhedrons the best vertex is used as start point for a global parameter estimation.- Additional start points are the n center points and the n best grid points.

p1

p2

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Model of the Tricarboxylic Acid (TCA) cycle

)31,,0(][

))(()(31

0

32

iateKetoglutar

JJateKetoglutarJGlutamateJCitrateCitrateateKetoglutari

exctcaiexcitcaiii

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Results Excellent agreement between the

computed oxygen consumptions and the 'gold standard‘.

Oxygen consumption with the 'gold standard' method is determined for a much larger area than with the isotope labeling method, but the physiological condition in both areas are the same.

Although biological differences between the areas measured and not measured with the isotope labeling method (both included in the blood gas measurement) undoubtedly contribute to deviations from the line of identity, the general correspondence is still surprisingly good.

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Acknowledgements

Hans van Beek

David Alders

Anne-Christin Hauschild

Entire IBIVU Group

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Optimization Strategy (Random Start Points)

Synthetic

data

Noisy data 1

Noisy data 2....

Noisy data 25

10,000 random

start values for

each noisy

data set

30 best (of each data set) used for

re-estimation of true parameter values

Parameter True EstimateJtca 10 29.55 ± 15.05Jexc 10 9.19 ± 5.16Janap 0.6 10.28 ± 7.89Ttrans 0.5 0.79 ± 0.19 Pdil 0.2 0.24 ± 0.04

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Synthetic

data

Noisy data 1

Noisy data 2....

Noisy data 25

30 start points (for each data set) generated using

the grid-polyhedron approach.

Parameter True EstimateJtca 10 12.85 ± 4.09 Jexc 10 10.17 ± 3.68 Janap 0.6 1.89 ± 1.66 Ttrans 0.5 0.59 ± 0.20 Pdil 0.2 0.21 ± 0.04

Optimization Strategy (Grid-Polyhedron)

Estimate29.55 ± 15.059.19 ± 5.1610.28 ± 7.890.79 ± 0.19 0.24 ± 0.04

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Optimization Strategy (Different True Values)

True Parameters Parameter Estimates ± Standard Deviations

J tca J exc J anap T trans P dil J tca J exc J anap T trans P dil

10 10 0.6 0.5 0.2 12.85 ± 4.09 10.17 ± 3.68 1.89 ± 1.66 0.59 ± 0.20 0.21 ± 0.048.5 19.5 3.6 0.6 0.4 8.430 ± 1.27 20.84 ± 9.14 4.08 ± 1.54 0.55 ± 0.20 0.38 ± 0.0413.5 9.5 4 0.5 0.75 11.38 ± 2.81 10.91 ± 3.97 2.35 ± 1.73 0.42 ± 0.20 0.74 ± 0.02

9 7 3 0.7 0.6 7.940 ± 1.56 10.41 ± 6.52 2.11 ± 1.76 0.67 ± 0.20 0.60 ± 0.045 5 2 0.8 0.6 4.640 ± 1.02 6.300 ± 4.21 1.59 ± 1.62 0.71 ± 0.21 0.58 ± 0.05