by **Sini Nagpal** (sini.nagpal@elucidata.io)

Many labs continue to develop experimental and computational methods to characterize the flow through metabolic enzyme(s) in cellular context [Weitzel et al].

A critical ingredient of all such efforts is isotope labelling experiments. There is immense variation in the design and scope of labelling experiments [Hellerstein et al]. In some cases of the labelling experiments, we need to calculate the mole fraction of isotopomers of products given the label ratios of the precursors. A manual analysis of such data set can be time taking and error-prone. It would be desirable to have a computational tool which automates this analysis for any given pathway.

We decided to use Rule Bender, a tool for constructing, simulating and analysing rule based biological models in BioNetGen Language (BNGL). Rule Bender has mostly been used for signal transduction pathways and compartmental modelling. Very little literature was available about using it for metabolic pathways [Adam et al]. Hence, we thought this post could be useful to the community.

Analysis of isotopic labelling patterns in metabolic pathways requires tracing atoms from substrate to products for every reaction in the pathway. Atom fate maps trace the position of each carbon atom of a metabolite in reactants and products. These fate maps can be defined using BNGL [Mu et al]. Rule Bender can translate these maps into isotopomer mass-balance equations and simulate the labelling pattern.

**We have used the following toy model pathway to illustrate our approach:**

A —k1—> B —k2—> C

Reaction1: A(C1, N1) —k1—> B(C1, N1)

Reaction2: B(C1, N1) + B(C1, N1) —k2—> C(C1, N1, C2, N2)

Here A, B, C are the metabolites of the metabolic pathway and k1, k2 are the rate constants. B to C is a dimerization reaction. C1, N1, C2, N2 represent the atoms of metabolites which can be either labelled or unlabelled.

Suppose 75% of labelled A is introduced in the pathway. The labelling patterns and the mole fractions of the metabolites can be obtained using rule bender.

**The Rule Bender workflow for the above output is as follows:**

**Describe Parameters:**

begin parameters

v_k1 1 # rate constant for first reaction

v_k2 1 # rate constant for second reaction

v_vi_A_labelled 0.75 # mole fraction of labelled glycine introduced

v_vi_A_unlabelled 0.25 # mole fraction of unlabelled glycine introduced

end parameters

**Describe species and their initial labelled state:**

begin species

A(C1~0,N1~0) 0

B(C1~0,N1~0) 0

C(C1~0,N1~0,C2~0,N2~0) 0

I 1

NULL 0

end species

**Describe reaction rules:**

# Atom Maps:Indices after the ‘%’ indicate the mapping of atoms. Atoms sharing the same index map to each other. In reaction 1, C1 of metabolite A goes to C1 of product B.

begin reaction rules

A(C1%1,N1%2) -> B(C1%1,N1%2) v_k1

B(C1%1,N1%2) + B(C1%3,N1%4) -> C(C1%1,N1%2,C2%3,N2%4) v_k2

# Input Label Patterns and their label ratios:

I -> I + A(C1~0,N1~0) v_vi_A_unlabelled

I -> I + A(C1~1,N1~1) v_vi_A_labelled

end reaction rules

**Describe Observables:**

# Molecules for observation in the results of simulation

begin observables

Molecules A A()

Molecules B B()

Molecules C C()

end observables

**Generate network and simulate ODE:**

# This function generates a network of species and reactions specifying the labelling patterns of each possible species. The network generated can be written in .NET/SBML file. The simulate ODE function provides a timecourse output of concentration of species at different timepoints. This output is obtained in form of a cdat file.

generate_network({overwrite=>1, check_iso=>1});

simulate_ode({prefix=>”equil”,t_end=>10000,n_steps=>10});

setParameter(“v_vi_A_unlabelled”,0.25);

setParameter(“v_vi_A_labelled”,0.75);

simulate_ode({t_end=>200,n_steps=>200});

writeSBML({});

writeMfile({});

writeNET();

From the cdat file, we take the values of concentration at steady state. For our example network, the concentrations of different species as shown in the cdat file is as follows:

**Calculate the mole fraction of the species:
**By using the concentrations of individual isotopomers, we can get the mole fraction of each species. To do this, we wrote a python script to parse the SBML file and group combinations with same number of atoms labelled. Typically, MS methods fail to distinguish the position of the label. For example, all the isotopomers with one atom labelled, irrespective of their position are grouped together for further analysis. The cdat file was used to calculate the mole fraction of all the species.

The advantages of this approach becomes evident for large and complex metabolic pathways. Doing these calculations manually for a large network can quickly become intractable. This method can be efficiently applied to complex metabolic networks with large number of possible labelling patterns.

**References:**

Adam M, Wen Xu. RuleBender: integrated modeling, simulation and visualization for rule-based intracellular biochemistry. *BMC Bioinformatics. *13(Suppl 9):S3: 1-24, 2012.

Hellerstein MK, Neese RA. Mass isotopomer distribution analysis: a technique for measuring biosynthesis and turnover of polymers. *Am J Physiol.* 263(5 Pt 1):E988-1001, 1992

Mu F, William RF. Carbon-fate maps for metabolic reactions. *Bioinformatics*. 23:3193-3199, 2007.

Weitzer M, Noh K. The topology of metabolic isotope labeling networks. *BMC Bioinformatics. *8:315, 2007