Markov state models (MSM) are used to model the kinetics of processes sampled by molecular dynamics (MD) simulations. MSM reduce the high dimensionality inherent to MD simulations as they partition the free energy landscape into discrete states, generating a kinetic model as a series of uncorrelated jumps between states. Here, we detail a new method, called GRadient Adaptive Decomposition, which optimizes coarse-grained MSM by refining borders with respect to the gradient along the free energy surface. The proposed method requires only a small number of initial microstates because it corrects for errors produced by limited sampling. Whereas many methods rely on fuzzy partitions for proper statistics, GRAD retains a crisp decomposition. Two test studies are presented to illustrate the method and assess its accuracy: the first analyzes MSM of idealized model potentials, while the second is a study of the dynamics of unstacking of the deoxyribose adenosine monophosphate dinucleotide.

their dysregulation in disease. However, the molecular mechanisms that drive these phase transitions, the biophysical properties of the resulting droplets, and the way their properties impact biological function, remain poorly understood. Here, we focus on LAF-1, an essential DEAD-box RNA helicase associated with P granules in the C. elegans germline. We find that purified LAF-1 can phase separate into liquid droplets at near physiological (low mM) concentrations. LAF-1 droplet formation is driven by its disordered N-terminal RGG domain, which is both necessary and sufficient for droplet formation. We combine microrheology, FRAP, and single molecule imaging approaches to reveal the local viscoelastic properties and molecular dynamics inside the droplets. Our results provide mechanistic and structural insight into the phase transition-driven assembly of liquid-like organelles, and suggest that the biophysics of intracellular phase separation can sensitively control molecular dynamics and function.

Reverse gyrase, found in hyperthermophiles, is the only enzyme known to overwind (introduce positive supercoils into) DNA. The ATP-dependent activity, detected at >70 C, has so far been studied solely by gel electrophoresis, and thus the reaction dynamics remain obscure. Here we image the overwinding reaction at 71 C under a microscope, using DNA containing consecutive 30 mismatched base pairs that serve as a well-defined substrate site. A single reverse gyrase molecule processively winds the DNA for >100 turns. Bound enzyme shows moderate temperature dependence, retaining significant activity down to 50 C. Unloaded reaction rate at 71 C exceeds 5 turns s À1 , which is >10 2 -fold higher than hitherto indicated but lower than the ATPase rate measured in bulk of 20 s À1 , indicating loose coupling. The overwinding reaction sharply slows down as the torsional stress accumulates in DNA, and ceases at stress of mere~5 pN,nm, where one more turn would cost only six times the thermal energy. The enzyme would thus keep DNA in a slightly overwound state to protect, but not overprotect, the genome of hyperthermophiles against thermal melting. Overwinding activity is also highly sensitive to DNA tension, with an effective interaction length exceeding the size of reverse gyrase, implying requirement for slack DNA. All results point to the mechanism where strand passage relying on thermal motions, as in topoisomerase IA, is actively, but loosely, biased toward overwinding.