Metastability of energy state
The liquid condensate state of MLOs is energeticallymetastable , namely, resides in a local minimum of Gibbs free energy (Figure 1A ). A thermodynamic system will spontaneously minimize the free energy to attain states with higher stability. As such, liquid condensate state can spontaneously transit to more energetically favorable states, namely, other local minima with lower free energy or the global minimum, simply over longer time16–18 or expedited by disease-associated mutations10–13,19. For example, liquid condensates can evolve into reversible hydrogels or irreversible amyloid-like aggregates, which has lower free energy and higher stability. Additionally, LLPS can be an intermediate process to facilitate nucleation and lower the free energy of crystallization and aggregation18,20,29–32,21–28. To maintain the liquid condensate state, specific quality control machineries 33 are required to stop them from spontaneous solidification34–37, including post-translational modification (PTM) 38,39, RNA binding 40, chaperon 11,41–45, hydrotrope 46and disaggregase 47.
In cell biology, proteins are commonly hydrophilic biomacromolecules dispersed in the state of dilute solution. How can the metastable liquid condensates form from the dispersed solution thermodynamically? Basically, there are two types of interactions in a dispersed protein solution, namely, the homotypic interactions between two biomolecules (e.g., protein or nucleic acid) and two water molecules, as well as the heterotypic interactions between a biomolecule and a water molecule48. The phase transition from dispersed state to phase-separated state can occur if the homotypic interactions are favored over heterotypic interactions. The enthalpy and entropy change of this phase transition can be categorized into four quadrants (Figure 1B ). The formation of liquid condensates is thermodynamically favored within two quadrants (Figure 1B , highlighted with green color), namely, when\(\Delta H\bullet\Delta S>0\). When \(\Delta H>0\) and\(\Delta S>0\), \(\Delta G\) is only negative at high temperature. This means the LLPS is spontaneous when temperature is higher than a threshold value, thus exhibiting a lower critical solution temperature (LCST) phase behavior, which has been found in extracellular IDPs including elastin, elastin-like polypeptide 49 and histidine-rich squid beak proteins 50–52. When\(\Delta H<0\) and \(\Delta S<0\), \(\Delta G\) is only negative at low temperature. This means the LLPS is spontaneous when temperature is lower than a threshold value, thus exhibiting an upper critical solution temperature (UCST) phase behavior, which has been found in intracellular IDPs including Ddx4 53, LAF-1 54, FUS 55, TDP-43 56 and hnRNP17 protein. By contrast, the formation of liquid condensates is thermodynamically disfavored within two quadrants (Figure 1B , highlighted with red color), namely, when\(\Delta H\bullet\Delta S<0\). When \(\Delta H>0\) and\(\Delta S<0\), phase separation is always thermodynamically unfavorable, and solution remains in the dispersed state because\(\Delta G\) is always positive. When \(\Delta H<0\) and\(\Delta S>0\), phase separation is always thermodynamically favorable. Dispersed solution will form irreversible phase separation spontaneously, either liquid-solid phase separation or LLPS, as\(\Delta G\) is always negative.