Modeling of biological signal pathways forms the basis of systems biology. Also, network models have been important representations of biological signal pathways. In many biological signal pathways, the underlying networks over which the propagations spread are unobserved so inferring network structures from observed data is an important procedure to study the biological systems. In this paper, we focus on protein regulatory networks which are sparse and where the time series measurements of protein dynamics are available. We propose a method based on compressive sensing (CS) for reconstructing a sparse network structure based on limited time-series gene expression data without any a priori information. We present a set of numerical examples to demonstrate the method. We discuss issues of coherence in the data set, and we demonstrate that incoherence in the sensing matrix can be used as a performance metric and a guideline for designing effective experiments.