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We simulated nine datasets corresponding to different network structures (Fig 1): a network of 4 genes with a branching structure and inhibition feedback loop (FN4); a network of 5 genes with a cycling structure (CN5); a network of 8 genes with multiple branching structure and feedback loops (FN8); a network of 8 genes with branching trajectories (BN8); networks with a tree structure of 5, 10, 20, 50, and 100 genes (Trees). These networks represent the main types of network structures that have been used for benchmarking GRN inference algorithms [17]. Overall, the objective was to reproduce time-course experiments in which single-cell profiling is performed after a given stimulus, typically a change of medium [22, 24, 25]. This stimulus was therefore taken into account in all the simulations, in the form of a virtual gene defined as being inactive before the beginning of the experiment and fully activated afterwards.

For each network, inference is performed on ten independently simulated datasets, each dataset containing the same 10 timepoints with 100 cells per timepoint (1000 cells sampled per dataset). The performance on each dataset is then measured as the area under the precision-recall curve (AUPR), based on the unsigned inferred weights of edges. Finally, the performance of each method is summarized as a box plot of the corresponding AUPR values, or the average AUPR value for the tree-structure activation networks (Trees). For each plot, the dashed gray line indicates the average performance of the random estimator (assigning to each edge a weight 0 or 1 with 0.5 probability). For the Trees networks, each dataset corresponds to a random tree structure of fixed size (5, 10, 20, 50, and 100 genes) sampled from the uniform distribution over trees of this size. (A) Performance of all methods when considering only undirected interactions. (B) Performance of the methods able to infer directed interactions. (C) Performance of the SCRIBE inference method for the same networks, in three conditions: when one has access to real single-cell trajectories (in brown), when pseudo-trajectories are reconstructed from time-stamped data using a coupling method similar to Waddington-OT (in pink), and when a single pseudo-trajectory is reconstructed using the pseudotime algorithm SLINGSHOT (in light green). For the last two conditions, the datasets used are therefore the same as those used for the other methods.

When computing the average runtime of each algorithm on the tree-like networks, we observed that except for SCRIBE, all algorithms are suitable for inferring GRN with a realistic number of genes (see S1 Table). Thus, due to this computational limit and its poor performances when using time-stamped data, we did not consider SCRIBE for further analysis.

We then investigated the limit performances with respect to the number of cells and/or timepoints. We observed that the performances of the first five algorithms decrease for the tree-like networks when the number of genes increases (Fig 2). This can be due to three main factors:

We therefore investigated the effects of these three factors on the accuracy of the algorithms by studying their performances in terms of AUPR for ten datasets generated from ten randomly-generated tree-like network of ten genes, when varying the number of cells at each timepoint (Fig 3A), the length of the interval for a fixed time gap between each timepoint (Fig 3B), and the density of the sequence of timepoints for an interval with fixed length (Fig 3C). As anticipated, all these conditions have an impact on the quality of the inference: augmenting their values tends to produce a better quality of inference. We also observed that the number of sampled cells seems less critical than the other factors, confirming that few cells at a sequence of timepoints which is dense and long-enough is preferable to many cells on a sequence of timepoints which is too coarse and/or too short. This should be kept in mind when designing single-cell transcriptomics experiments aiming at GRN inference.

For simplicity, only the case of undirected interactions is considered here and the datasets are restricted to 10-gene tree-structure networks (see Fig 2 for the general benchmark). Inference is performed for each method and condition on ten independently simulated datasets and summarized by box plots of AUPR values as in Fig 2. For each plot, the dashed gray line indicates the average performance of the random estimator (assigning to each edge a weight 0 or 1 with 0.5 probability). (A) Performance as a function of the number of cells per timepoint, while keeping the same timepoints. (B) Performance as a function of the length of the measurement period, while keeping the same gap between timepoints and the same total number of cells. (C) Performance as a function of the gap between timepoints, while keeping the same final timepoint and the same total number of cells. 59ce067264

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