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A mixture of proteins and polyelectrolytes are widely used in applications such as food systems, biosensors, protein purification, drug delivery. Experiments have demonstrated that the structures and phase behavior of protein-polyelectrolyte mixture can be dependent on a variety of factors, including the physical and chemical characteristics of proteins, polyelectrolytes, properties of solution, and temperature. Despite extensive experimental studies, there is still a lack of a theoretical framework to understand the fundamental physics which is capable of capturing the complexities of the phase behavior of protein-polyelectrolyte mixtures and be able to predict the impact of the component properties on the structure of these mixtures. Motivated by the lack of studies, in this thesis, we have built a single chain in mean-field based coarse-grained multibody simulation framework to study the phase behavior of protein and polyelectrolyte complexes. We have explored the influence of features such as the dielectric difference between the protein and the solvent, charge distribution of proteins, and the solution pH. Our results demonstrate that the pattern of charge heterogeneities can exert a significant influence on the resulting characteristics of the aggregates, in some cases leading to a transformation from polymer-bridged complexes to direct protein aggregates driven by attraction between oppositely charged patches. Later, we appended the framework to capture the influence of variable charge on proteins and polyelectrolytes due to variation in their dissociation characteristics in the presence of other charged species and properties of the solution. We …