This dissertation aims at analyzing complex problems arising in the context of dynamical networks, proteomics, and disease prevention. First, a new graph-based method for proving global stability of synchronization in directed dynamical networks is developed. This method utilizes stability and graph theories to clarify the interplay between individual oscillator dynamics and network topology. Secondly, a graph-theoretical algorithm is proposed to predict Ca2+-binding site in proteins. The new algorithm enables us to identify previously-unknown Ca2+-binding sites, and deepens our understanding towards disease-related Ca2+-binding proteins at a molecular level. Finally, an optimization model and algorithm to solve a disease prevention problem are described at the population level. The new resource allocation model is designed to assist clinical managers to make decisions on identifying at-risk population groups, as well as selecting a screening and treatment strategy for chlamydia and gonorrhea patients under a fixed budget. The resource allocation model and algorithm can have a significant impact on real treatment strategy issues.

Zinc is an essential metal ion for the activity of multiple enzymes and transcription factors. Among many other transporting proteins human serum albumin (HSA) is the main carrier of Zn(II) in the blood plasma. HSA displays multiple ligand binding sites with extraordinary binding capacity for a wide range of ions and molecules including fatty acids. Hence, HSA controls the availability and distribution of those molecules throughout the body. Previous studies have established that the existence of one zinc site with high affinity (MBS-A) that is modulated by the presence of fatty acids. Therefore, the fatty acid concentration in the blood influences zinc distribution which may result in a significant effect on both normal physiological processes and a range of diseases. Based on the current knowledge of HSA's structure and its coordination chemistry with zinc ion, here, we attempted to investigate zinc interactions and coordination with HSA and the effect of different fatty acids on the protein structure, stability and on Zn(II) binding. By NMR titration, we examine the Zn(II) binding to HSA and the spectra show distinct movements of some resonances showing a conformational change has occurred as a result of Zn(II) binding. Isothermal calorimetry titrations study was performed to evaluate zinc binding affinity to HSA in the absence and presence of fatty acids. Free HSA results indicates the existence of one high affinity site and multiple low affinity sites. Upon the binding of fatty acids to HSA, three distinct behaviors of Zn(II) affinity was observed ranging from no effect to moderate to significant depending on the FAs. By the use of circular dichroism, we investigate secondary and tertiary structure of HSA in the presence and absence of FAs and Zn(II). We found albumin is predominately α-helical and the overall conformation of the protein remains unchanged even after interacting with FAs and Zn(II) with some exception. The structural stability of HSA was evaluated by obtaining the denaturation temperature in the presence and absence of fatty acid and we found the thermal denaturation of HSA increases with the increase of amount of fatty acids.