With advances in single-cell techniques, measuring gene dynamics at cellular resolution has become practicable. In contrast, the increased complexity of data has made it more challenging computationally to unravel underlying biological mechanisms. Thus, it is critical to develop novel computational methods capable of dealing with such complexity and of providing predictive deductions from such data. Many methods have been developed to address such challenges, each with its own advantages and limitations. We present an iterative regression algorithm for inferring a mechanistic gene network from single-cell data, especially suited to overcoming problems posed by measurement outliers. Using this regression, we infer a developmental model for the gene dynamics in Drosophila melanogaster blastoderm embryo. Our results show that the predictive power of the inferred model is higher than that of other models inferred with least squares and ridge regressions. As a baseline for how well a mechanistic model should be expected to perform, we find that model predictions of the gene dynamics are more accurate than predictions made with neural networks of varying architectures and complexity. This holds true even in the limit of small sample sizes. We compare predictions for various gene knockouts with published experimental results, finding substantial qualitative agreement. We also make predictions for gene dynamics under various gene network perturbations, impossible in non-mechanistic models.
