Proteins are versatile biopolymers in living systems; they exhibit a great diversity of functions depending on the order in which their amino acids are arranged. Most protein functions, like mechanical or regulatory functions, only emerge from the interactions with other proteins and macromolecules. This dissertation describes how we have developed and adapted new computational models to investigate emergent structural and dynamic properties of protein interactions. Chapter 1 presents a review of the two systems of interest to be explored in successive chapters: the regulation of the actin cytoskeleton and the control of DNA transcription by the nuclear factor kappa B (NF-κB). It also introduces some models developed to study the interactions of proteins with actin filaments and with DNA. Chapters 2 and 3 focus on protein interactions in the actin cytoskeleton network. Chapter 2 describes how we have estimated the mechanical and dynamical properties of actin networks using polymer theory. We developed a simplified mathematical mean-field model of F-actin polymerization, cross-linking, and branching based on mass action kinetics. Then we obtained an analytical solution to the connectivity, rigidity, and force percolation transitions using a generalized version of the Flory-Stockmayer theory. Chapter 3 describes how we used a computational mechano-chemical model to simulate the conditions where the actin networks exhibit rare sudden movements. We show that actin networks containing Arp2/3 undergo sudden releases of strain known as “cytoquakes”. Chapters 4 and 5 focus on DNA-protein interactions. Chapter 4 describes a new implementation to simulate protein and DNA dynamics for large systems that we developed. This new procedure retains the accuracy of previous methods our group developed with a 30-fold speedup and eases the introduction of new potential energy terms. Chapter 5 describes how we used this protein a