Phospholipid bilayers constitute the primary structural element of biological membranes, and as such, they play a central role in biochemical and biophysical processes at the cellular level, including cell protection, intercellular interactions, trans-membrane transport, cell morphology, and protein function, to name a few. The properties of phospholipid bilayers are thus of great interest from both experimental and theoretical standpoints. Although experiments have provided much of the macroscopic functions and properties of biological membranes, insight into specific mechanisms at the molecular level are seldom accessible by conventional methods. To obtain a better understanding of biochemical and biophysical processes at the molecular level involving phospholipid bilayers, we apply molecular simulation methods to investigate the complexity of the membrane matrix using atomistic models. Here, we discuss three specific biological processes that are associated with biological membranes: 1) membrane stabilization, 2) membrane phase behavior, and 3) fatty acid-induced toxicity in cell membranes. For membrane stabilization, molecular dynamics studies were performed for mixed phospholipid bilayers containing two of the most prevalent phospholipids (phosphatidylcholine and phosphatidylethanolamime) in biological membranes. We presented structural and dynamics properties of these systems, as well as the effect of stabilizing agents, such as trehalose, on their properties. Furthermore, we performed a comprehensive analysis of the phase transition of lipid bilayers and investigated the interactions of stabilizing agents (glucose or trehalose) with lipid bilayers under dehydrated conditions to understand the mechanisms for preservation of cellular systems. For membrane phase behavior, a comprehensive study of the structural properties of saturated and monounsaturated lipid bilayers near the main phase transition were investigated using molecular dynamics simulations. In this study, we demonstrated that atomistic simulations are capable of capturing the phase transformation process of lipid bilayers, providing a valuable set of molecular and structural information at and near its transition state. Lastly, the third study investigated the mechanism for fatty acid-induced toxicity by integrating in vitro and in silico experiments to reveal the biophysical interactions of saturated fatty acid (palmitate) with the cellular membranes and the role of trehalose and unsaturated fatty acids (oleate and linoleate) in preventing changes to the membrane structure. Knowledge gained from this study is essential in the prevention and treatment of obesity-associated cirrhosis diseases. / Ph. D.