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Explore the thermodynamic principles governing complex formation between proteins and polyelectrolytes in this 29-minute conference lecture from the Workshop on "Charged Soft Matter: Bridging Theory and Experiment" at the Erwin Schrödinger International Institute. Examine a comprehensive thermodynamic analysis that quantifies the main driving forces in protein-polyelectrolyte interactions, specifically counterion release and hydration effects. Discover how this analysis provides quantitative understanding of Hofmeister effects on polyelectrolyte-protein interactions and learn about its applications to biocondensates and phase separation in mixtures of oppositely charged proteins. Delve into a detailed case study analyzing the binary complex formation between the highly positively charged linker histone H1 (+53 charge) and the highly negatively charged chaperone prothymosin α (ProTα, -44 charge), which form high-affinity complexes at physiological salt concentrations. Understand how counterion release from ProTα serves as the primary driving force in this interaction, while hydration effects play minimal roles, and examine the strongly negative heat capacity change (-0.87 kJ/(K mol)) attributed to loss of conformational degrees of freedom. Gain insights into the fundamental importance of charge-charge interactions in biologically relevant systems through this theoretical and experimental analysis.