Merrin: MEtabolic Regulation Rule INference from time series data

merrin is a Python3 tool to compute metabolic regulatory rules from time series observations. This implementation rely on merrinasp, extension of the Answer Set Programming (ASP) solver clingo with quantified linear constraints.

Quick install

To install the merrin package from the GitHub repository, run the pip command:

python3.X -m pip install git+https://github.com/bioasp/merrin

Usage

merrin can be used in the terminal as follows:

merrin  [-h] -sbml SBML -pkn PKN -obj OBJ -obs OBS [-n NBSOL] [--lpsolver {glpk,gurobi}] [--timelimit TIMELIMIT]
        [--optimization {all,subsetmin}] [--projection {network,node,trace}]

Inferred regulatory rules are displayed in the terminal in CSV format, see examples below.

Mandatory arguments:

-sbml SBML, --SBML SBML
                        Metabolic network in SBML file format.
  -pkn PKN, --PKN PKN   Prior Knowledge Network.
  -obj OBJ, --objective-reaction OBJ
                        Objective reaction.
  -obs OBS, --observations OBS
                        JSON file describing the input timeseries.

Optional arguments:

  -n NBSOL
                        Number of solution to enumerate (default: 0 for all)
  --lpsolver {glpk,gurobi}
                        Linear solver to use (default: glpk)
  --timelimit TIMELIMIT
                        Timelimit for each resolution, -1 if none (default: -1)
  --optimization {all,subsetmin}
                        Select optimization mode: all networks or subset minimal ones only (default: subsetmin)
  --projection {network,node,trace}
                        Select project mode (default: network):
                        - network: enumerate all the rules of each network;
                        - node: enumerate the candidate rules for each node;
                        - trace: enumerate classes of network of equivalent rFBA traces

Input files

Metabolic network

Metabolic network should be in SBML (Systems Biology Markup Language) version 3 format.

Prior Knowledge Network (PKN)

Prior Knowledge Network (PKN) is a text file where each line is such that:

node_1  sign    node_2

with:

• node_1 and node_2 are two components of the regulatory or metabolic systems.
• sign in (0, -1, 1) such that:
  • -1 is an inhibition effect of node_1 on node_2;
  • 1 is an activation effect of node_1 on node_2;
  • 0 is an unknown effect (either activation or inhibition effect) of node_1 on node_2;

Examples

Carbon1	0	RPcl
RPcl	1	Tc2
Tc2	-1	RPcl

In this example, RPcl regulatory rule depends on an unknown interaction with Carbon1 and an inhibition effect of Tc2.

Observations

merrin is compatible with any combination of the following datatypes: kinetics, fluxomics and transcriptomics.

The observations can be noisy. Note that it is preferable not to enter observations that are not certain.

Observations are described in a json file. Each time series observation is defined as follows:

{
    "file": "path/to/the/csv/file",
    "type": ["Kinetics","Fluxomics","Transcriptomics"], <- any non-empty subset
    "constraints": {
        "mutations": {
            "node_u": true, <- forced activation
            "node_v": false, <- forced inhibition
        },
        "bounds": {
            "reaction": [lower_bound, upper_bound]
        }
    }
}

The csv file describing the observation needs to have a Time column with an integer timestamp for each observed time step.

For kinetics and fluxomics data types:

• Metabolites: real-values, modeling the metabolite concentration in the substrate.
• Need to contain a biomass column with the measured value of the biomass.

For fluxomics data types:

• Reaction: real-values, modeling the reaction activity rates in the metabolic network.

For transcriptomics data types:

• All values are binary (0 or 1), modeling the activity (1) or inactivity (0) of a component (metabolite, reaction, regulatory nodes).

Output format

merrin generates a CSV file describing the inferred regulatory networks. A rule set to 1 represents a constant value (i.e. always activated) for which no regulatory rules are necessary to explain the component dynamics.

Remarks 1: If no regulatory networks are returned, then the instance is unsatisfiable. Try to change the max_gap and max_error variables before launching merrin again.

Remarks 2: For unsatisfiable instances with kinetics and/or fluxomics data, launching merrin with the observation declared as transcriptomics data only can sometimes allow inferring some regulatory networks.

Rule syntax and semantics

Regulatory rules are returned in disjunctive normal form (DNF) with the following syntax:

R := 1 || C || (C_1 | ... | C_n)
C := L || (L_1 & ... & L_m)
L := N || !N
N := regulatory component name

with ! denoting the negation, & the logical and, and | the logical or.

Examples

Examples are provided in ./examples.

• The instance ./examples/instances/toy has been generated from the regulatory metabolic network and the experiments described in (Thuillier et al., 2021).
• The instance ./examples/instances/core-regulated has been generated from the regulatory metabolic network and the experiments described in (Covert et al., 2001).
• The instance ./examples/instances/large-scale has been generated from the regulatory metabolic network and the experiments described in (Covert et al., 2002).

To solve the core-regulated instance using the console command, see the bash file: ./examples/run-merrin.sh. It can be executed with:

sh ./examples/run-merrin.sh

To solve the core-regulated instance using a Python script using merrin, check the jupyter notebook: ./examples/notebook-merrin.ipynb.

Inferred rules on the example

Network projection: Infer regulatory networks. Each row of the displayed CSV is a regulatory network and each column is the rules for a given regulatory component.

Example 1: Network projection + All optimization

R2a,R2b,R5a,R5b,R7,R8a,RPO2,RPb,RPcl,RPh,Rres,Tc2
!RPb,1,1,!RPO2,1,!RPh,!Oxygen,R2b,Carbon1,Hext,1,!RPcl
!RPb,1,1,!RPO2,!RPb,!RPh,!Oxygen,R2b,Carbon1,Hext,1,!RPcl
!RPb,1,!RPO2,!RPO2,!RPb,!RPh,!Oxygen,R2b,Carbon1,Hext,1,!RPcl
!RPb,1,!RPO2,!RPO2,!RPb,!RPh,!Oxygen,R2b,Carbon1,Hext,!RPO2,!RPcl
...

Only the first 4 inferred regulatory networks are shown. The node R2b is always set to 1, it does not have any regulatory rules, and so, is always activated.

Example 2: Network projection + Subset minimal optimization

R2a,R2b,R5a,R5b,R7,R8a,RPO2,RPb,RPcl,RPh,Rres,Tc2
!RPb,1,1,1,1,!RPh,!Oxygen,R2b,Carbon1,Hext,1,!RPcl

Node projection: Infer possible regulatory rules for each regulatory component. It will only output 1 row. Each cell contains a set of compatible regulatory rules separated by ';'.

Example 3: Node projection + All optimization

R2a,R2b,R5a,R5b,R7,R8a,RPO2,RPb,RPcl,RPh,Rres,Tc2
!RPb,1,!RPO2;1,!RPO2;1;RPO2,!RPb;1,!RPh,!Oxygen,R2b,Carbon1,Hext,!RPO2;1,!RPcl

The node R5a has 2 possible regulatory rules: !RPO2 or 1 (unregulated).

Example 4: Node projection + Subset minimal optimization

R2a,R2b,R5a,R5b,R7,R8a,RPO2,RPb,RPcl,RPh,Rres,Tc2
!RPb,1,1,1,1,!RPh,!Oxygen,R2b,Carbon1,Hext,1,!RPcl

Trace projection: Infer possible regulatory rules for each rFBA trace compatible with the observations. Each row of the displayed CSV is a class of regulatory networks compatible with an rFBA trace compatible with the observations. Each cell contains a set of compatible regulatory rules separated by ';' for a dedicated node.

Remarks: For the core-regulated instance, it yields the same CSV than the network projection

References

To cite this tool:

Kerian Thuillier, Caroline Baroukh, Alexander Bockmayr, Ludovic Cottret, Loïc Paulevé, Anne Siegel, MERRIN: MEtabolic regulation rule INference from time series data, Bioinformatics, Volume 38, Issue Supplement_2, September 2022, Pages ii127–ii133, https://doi.org/10.1093/bioinformatics/btac479 [pdf]