Pathway analysis is widely used to gain mechanistic insights from high-throughput omics data. However, most existing methods do not consider signal integration represented by pathway topology, resulting in enrichment of convergent pathways when downstream genes are modulated. Incorporation of signal flow and integration in pathway analysis could rank the pathways based on modulation in key regulatory genes. This implementation can be facilitated for large-scale data by discrete state network modeling due to simplicity in parameterization. Here, we model cellular heterogeneity using discrete state dynamics and measure pathway activities in cross-sectional data. We introduce a new algorithm, Boolean Omics Network Invariant-Time Analysis (BONITA), for signal propagation, signal integration, and pathway analysis. Our signal propagation approach models heterogeneity in transcriptomic data as arising from intercellular heterogeneity rather than intracellular stochasticity, and propagates binary signals repeatedly across networks. Logic rules defining signal integration are inferred by genetic algorithm and are refined by local search. The rules determine the impact of each node in a pathway, which is used to score the probability of the pathways modulation by chance. We have comprehensively tested BONITA for application to transcriptomics data from translational studies. Comparison with state-of-the-art pathway analysis methods shows that BONITA has higher sensitivity at lower levels of source node modulation and similar sensitivity at higher levels of source node modulation. Application of BONITA pathway analysis to previously validated RNA-sequencing studies identifies additional relevant pathways in in-vitro human cell line experiments and in-vivo infant studies. Additionally, BONITA successfully detected modulation of disease specific pathways when comparing relevant RNA-sequencing data with healthy controls. Most interestingly, the two highest impact score nodes identified by BONITA included known drug targets. Thus, BONITA is a powerful approach to prioritize not only pathways but also specific mechanistic role of genes compared to existing methods. BONITA is available at: https://github.com/thakar-lab/BONITA.