Phase Phenomena of Proteins in Living Matter

Proteins must fold and function in the immensely complex environment of a cell, i.e. the cytoplasm—this is far from the ideal test-tube setting of a dilute solution. Here, this thesis answers an important question at the interface of physics and biology: how does the crowded cellular environment influence the dynamics of individual proteins and their folding phases? This thesis is presented in two parts. First, we review protein folding and investigate the effects of hydrostatic pressure using coarse-grained molecular simulations. There are two common forms of pressure-dependent potentials of mean force (PMFs) derived from hydrophobic molecules available for coarse-grained molecular simulations of protein folding and unfolding under hydrostatic pressure. We investigated the two different pressure-dependencies on the desolvation potential in a structure-based protein model using coarse-grained molecular simulations. We compared the simulation results to the known behavior of proteins based on experimental evidence. We showed that the protein’s folding transition curve on the pressure–temperature phase diagram depends on the relationship between the potential well minima and pressure. For a protein that reduces its total volume under pressure, the PMF needs to carry the feature that the direct contact well is less stable than the water-mediated contact well at high pressure. In the second part we move toward understanding the effects of crowded environment of the cell. Proteins have properties that are exhibited by systems near a critical point, where distinct phases merge. This concept goes beyond previous studies that propose proteins have a well-defined folded and unfolded phase boundary in the pressure-temperature plane. Here, by modeling the protein phosphoglycerate kinase (PGK) on the temperature ($T$), pressure ($P$), and crowding volume-fraction ($\varphi$) phase diagram, we demonstrate a critical transition where phases merge, and PGK exhibits large structural fluctuations. Above the critical temperature ($Tc$), the difference between the intermediate and unfolded phases disappears. When $\varphi$ increases, the $Tc$ moves to a lower $T$. With experiments mapping the $T$--$P$--$\varphi$ space, we verify the calculations and reveal a critical point at 305 K and 170 MPa that moves to a lower $T$ as $\varphi$ increases. Crowding shifts PGK closer to a critical line in its natural parameter space, where large conformational changes can occur without costly free-energy barriers. Specific structures are proposed for each phase based on the simulation. To understand the ``quniary'' interaction between cells, we examine the interplay between folding and inter-domain interactions of engineered FiP35 WW domain repeat proteins with $n=1$ through 5 repeats using a coarse-grained simulated annealing with the AWSEM Hamiltonian. According to our simulations, misfolded structures become increasingly prevalent as one proceeds from monomer to pentamer, with extended inter-domain beta sheets appearing first, then multi-sheet `intramolecular amyloid' structures, and finally novel motifs containing alpha helices. Finally, in developing principles of protein behavior \emph{in vivo}, we discuss the implications and connection to the organization and dynamics of the cytoplasm, unifying the single protein scale with the many-protein architectures at the subcellular scale.