One of the basic characteristics of every living system is the ability to respond to extracellular signals. This is carried out through a limited number of protein-based signaling networks, whose function is not based only on simple transmission of the received signals, but incorporates the processing, encoding and integration of both, external and internal signals. The results than lead to different changes in gene expression, regulate cell growth, differentiation, embryo development, and stress responses in mammalian cells, whereas the malfunction is in correlation with diseases. Commonly observed instance of signal transduction through a series of protein kinase reactions are the kinases of the mitogen activated protein kinase (MAPK) cascades. These pathways are found in almost all eukaryotes and play an important role in controlling different cellular processes, including fundamental functions. In order to understand better the nature of this regulation and to gain greater insight into the mechanisms that determine the function of cells, MAPK cascades have been intensively studied using mathematical modeling and computational simulations. The primary aim is to faithfully describe the system and to be able to predict the system behavior. Synergistically with experimental analysis, reported observations have identified properties of these pathways, such as rapid induction, noise resistance, amplification capability, threshold induction mechanism etc. Here, we investigate one class of approaches for analyzing the relationship between network structure and functional behavior and the overall idea involves applying optimization techniques. By manipulating the desired functional behavior and by monitoring the corresponding parameter values, one can learn how model parameters and functions are related, and then be in a position to discover new design principles. The primary motivation was to explore if there is any trade-off while promoting simultaneously large amplification and fast signal propagation. We identified the competing parameters in the linear tricyclic cascade and their values for the optimal design for minimal response times and given amplification. We also incorporated “ultrasensitivity”, in order to analyze interplay between this steady-state property and dynamic behavior of the system. Special emphasis is placed on the robustness of the resulting tricyclic cascades in the face of variations in kinase and phosphatase concentration ratios.