The Krebs cycle dataset

Motivation

This dataset contains simulated time series that mimic Kreb's cycle. The intent of the datasets is for causal discovery from multivariate time series data, provide ground truth causal relationships as well as allow testing on multiple scenarios, including many short time series,

few long time series, as well as relative data instead of absolute values.

The dataset was created at the Czech Technical University in Prague as part of the CoDiet project https://www.codiet.eu/, which focuses on the relationship between diet and non-transmittable diseases.

The contents of this repository are also described in the following paper: (TODO, we will provide a bibtex reference, once published)

Causal Learning in Biomedical Applications
Petr Ryšavý, Xiaoyu He, Jakub Mareček

Dataset composition

There are four datasets, each differing in the type of time series. The basic characteristics are described in the table below. Each of the datasets is contained in one of the subdirectories of this repository.

Dataset	N. features	Lenght	N. series	Initialization	Concentrations
KrebsN	16	500	100	Normal distribution	Absolute
Krebs3	16	500	120	Excitation of three	Relative
KrebsL	16	5000	10	Normal distribution	Absolute
KrebsS	16	5	10000	Normal distribution	Absolute

Each of the datasets was sampled using a simulator of the Krebs cycle. Individual compounds were created in a bounding box and spread throughout the box at random locations. In each time step, the molecules move in the box, and once a reaction can happen, the reactants are removed, and the product is created. As a result, the concentrations of the particles change, resulting in one data point per time step of the simulator.

Each of the time series is in its individual file, with a name connected to the type of the series and the seed (timestamp) used for the dataset generation. Each of the rows in each of the time series files contains concentrations of one compound, where individual time steps are separated by tab character \t. The files with the individual time series are, therefore, in the TSV format (tab-separated-values) and can be opened in any text editor or tabular editor.

The features in the dataset correspond to the following molecules:

• GTP - Guanosine triphosphate,
• H20 - Water,
• CIS-ACONITATE - Aconitic acid,
• MALATE - Malic acid,
• OXALOACETATE - Oxaloacetic acid,
• FAD - Flavin adenine dinucleotide,
• SUCCINYL-COA - Succinyl-coenzyme A,
• NAD - Nicotinamide adenine dinucleotide,
• A-K-GLUTARATE - α-Ketoglutaric acid,
• GDP - Guanosine diphosphate,
• NADH - Nicotinamide adenine dinucleotide,
• CITRATE - Citric acid, the molecule that has given the cycle one of its names,
• SUCCINATE - Succinic acid,
• ISOCITRATE - Isocitric acid, and
• ACETY-COA - Acetyl coenzyme A.

Whenever the concentrations are absolute (please see the table above), the features show the number of individual molecules in the mix. Whenever the concentrations are relative, the concentrations are normalized to zero-one interval.

The dataset contains no missing data. The source of randomness in the data comes from the initialization of the compound's concentrations and randomness of the location of the compounds in the bounding box. Despite the fact that it is unlikely, the datasets can contain repeated time series. The datasets are self-contained.

If needed for testing, the recommended train-test split is so that the first x % of the dataset is used for training, and the remaining 1-x% is used for testing. The order in which individual time series are considered is at the root of the repository.

The datasets do not contain any confidential, offensive, or similar type of data.

Dataset collection

The dataset is simulated, meaning that the data were generated by a computer program. The simulator is based on the Chemistry Engine repository (https://github.com/AugustNagro/Chemistry-Engine) by August Nagro. You can find the code used to generate the dataset in github repository at https://github.com/petrrysavy/krebsgenerator/.

Uses

The dataset is intended for testing and developing causal discovery algorithms. From the time series, one would naturally ask questions of whether higher levels of FURMATE in one-time step imply higher levels of MALATE in the next step, in an ideal case leading to the discovery of the whole cycle of reactions. The usage is, however, not limited to causal discovery; it is possible to predict concentrations at the next level or do any similar time-series analyses.

Distribution

The dataset is available at the HuggingFace repository at https://huggingface.co/datasets/petrrysavy/krebs/tree/main. The dataset is available under the CC-BY-3.0 license. The authors bear all responsibility in case of violation of rights. To download the dataset, use

git clone [email protected]:datasets/petrrysavy/krebs/

The metadata to the project in JSON format can be found at https://huggingface.co/api/datasets/petrrysavy/krebs/croissant.

Example of Usages in Custom Projects

An example usage of the dataset can be found at github repository at https://github.com/petrrysavy/krebsdynotears. The repository shows usage of the dataset to evaluate DyNoTears (see https://arxiv.org/abs/2002.00498), a State-of-the-art method for dynamic Bayesian networks. The repository also provides an example of how to load the code into Python language, here:

import os
import pandas as pd

with open("krebsN.txt", "r") as file:
    lines = file.readlines()
files = ["krebsN" + os.sep + line.strip() for line in lines]

data = [pd.read_table(path + os.sep + file, header=None, index_col=0).transpose() for file in files]

# data now contains a list of pandas data frames, one per single time-series
# columns of the data frames are concentrations of one of the 16 compounds
# rows correspond to individual time-steps, sorted by increasing time

Maintenance

With queries, requests, and errands about the dataset, please contact either Petr Ryšavý [email protected], or Jakub Mareček [email protected]. The authors of the repository are open to proposed changes and extensions of the dataset; the simplest way to do so is to open a pull request in HuggingFace, which will be merged after validation. The history of the dataset can be seen in the commit history at https://huggingface.co/datasets/petrrysavy/krebs/commits/main.