Gene regulatory network reconstruction using time-delayed S-system model

The advent of microarray technology and the availability of high-throughput timeseries gene expression data has gradually led to the emergence of system biologists’ proficiency in determining cellular dynamics, thus enabling the reverse engineering of Gene Regulatory Networks (GRNs). However, the curse of dimensionality, i.e., very few observations available for a large number of genes, is still considered one of the key factors affecting the inferring of GRNs from time-series data. Amongst the available models to infer GRNs, S-system formalism is considered to be an excellent compromise between accuracy and mathematical flexibility. Although the S-system model has the ability to represent the regulations very accurately, due to the higher number of parameters, it is currently limited to reconstructing small-and medium-scale GRNs. Evolutionary algorithms, a sub-field of computational intelligence, have been widely used for optimization in reverse engineering GRNs (and specifically with the S-system model) because of its computational simplicity and its capacity to cater difficult and intractable problems. As one of its objectives, this research aims to develop efficient evolutionary optimization techniques for S-system based GRN modeling. For implementing evolutionary optimization, Differential Evolution (DE) and its variants show promise in the complex multi-modal search landscape which exist during the process of reverse engineering GRNs. However, considering that for large-scale GRNs the performance of DE can deteriorate and cause the algorithm to frequently stall or become stuck in local minima, as the first step to achieve the objective of efficient algorithm design, we incorporate the domain knowledge in the initial population generation and a new mutation operation (Flip Operation or FO) in the optimization process. Incorporation of knowledge allows the population to commence with good seeds, while the proposed FO allows the optimization to search for global solutions by not getting potentially trapped in local minima. A refinement algorithm is also included as a post-processing operation to eliminate possible false regulations from the near optimal candidate solutions. Further, domain knowledge is also incorporated to develop a novel cardinality based fitness criteria that is motivated with the biologically relevant power-law distribution of genes’ in-degrees. The adaptive nature of the maximum and minimum in-degrees allows dynamic reduction of search space, thereby resulting in a skeletal structure of the network with accurate parameters values. In other words, the new approach improves the search technique and reaches the solution more quickly compared to the existing methods in the literature. The cardinality values are updated adaptively to further narrow down the search space to obtain superior results quickly. In addition, the method is further improvised so that it can cope with the absence of microRNA (miRNA) expression profiles during the inference process. A critical analysis is also presented on the influence of miRNAs regulations on the GRN, in spite of a lack of miRNA data. Since the traditional S-system models genetic interactions with non-time-delayed ordinary differential equations, all reverse engineering methods using the S-system model can only infer instantaneous regulations. Thus, time-delayed regulations, whose existence is obvious in the GRNs, are either missed completely or these are inferred with incorrect regulatory weight and/or direction by the existing methods. In this research, by including time-delays to be part of the S-system parameters, a novel time-delayed S-system (TDSS) model is proposed to overcome limitations of the existing S-system model. Moreover, we have further improved our inference method developed earlier to reconstruct the network by simultaneously inferring instantaneous and time-delayed regulations present in the GRNs. Due to the large number of parameters to infer, the current state-of-the-art S-system modeling approaches are limited to reconstructing small-and medium-scale GNRs. Exploiting the biological interactions of a GRN and the knowledge about genes, we show that a GRN can be naturally decoupled and incorporated in our proposed time-delayed S-system modeling. In the process, the previous fitness function is also enhanced to work more effectively to infer model parameters (including time-delays) of very large-scale GRNs. We also demonstrate how a domain knowledgebased clustering technique can be applied to develop a local search procedure that is very effective while inferring regulations of large-scale GRNs.