A Framework of Nonequilibrium Statistical Mechanics. I. Role and Types of Fluctuations

Understanding the fluctuations by which phenomenological evolution equations with thermodynamic structure can be enhanced is the key to a general framework of nonequilibrium statistical mechanics. These fluctuations provide an idealized representation of microscopic details. We consider fluctuation-enhanced equations associated with Markov processes and elaborate the general recipes for evaluating dynamic material properties, which characterize force-flux constitutive laws, by statistical mechanics. Markov processes with continuous trajectories are conveniently characterized by stochastic differential equations and lead to Green–Kubo-type formulas for dynamic material properties. Markov processes with discontinuous jumps include transitions over energy barriers with the rates calculated by Kramers. We describe a unified approach to Markovian fluctuations and demonstrate how the appropriate type of fluctuations (continuous versus discontinuous) is reflected in the mathematical structure of the phenomenological equations.

Arginine-enriched mixed-charge domains provide cohesion for nuclear speckle condensation

Low-complexity protein domains promote the formation of various biomolecular condensates. However, in many cases, the precise sequence features governing condensate formation and identity remain unclear. Here, we investigate the role of intrinsically disordered mixed-charge domains (MCDs) in nuclear speckle condensation. Proteins composed exclusively of arginine/aspartic-acid dipeptide repeats undergo length-dependent condensation and speckle incorporation. Substituting arginine with lysine in synthetic and natural speckle-associated MCDs abolishes these activities, identifying a key role for multivalent contacts through arginine’s guanidinium ion. MCDs can synergise with a speckle-associated RNA recognition motif to promote speckle specificity and residence. MCD behaviour is tuneable through net-charge: increasing negative charge abolishes condensation and speckle incorporation. By contrast, increasing positive charge through arginine leads to enhanced condensation, speckle enlargement, decreased splicing factor mobility, and defective mRNA export. Together, these results identify key sequence determinants of MCD-promoted speckle condensation, and link the speckle’s dynamic material properties with function in mRNA processing.