Search for: All records

Variational flooding is an enhanced sampling method for obtaining kinetic rates from molecular dynamics simulations. This method is inspired by the idea of conformational flooding that employs a boost potential acting along a chosen reaction coordinate to accelerate rare events. In this work, we show how the empirical distribution of crossing times from variational flooding simulations can be modeled with analytical Kramers’ time-dependent rate (KTR) theory. An optimized bias potential that fills metastable free energy basins is constructed from the variationally enhanced sampling (VES) method. This VES-derived flooding potential is then augmented by a switching function that determines the fill level of the boost. Having a prescribed time-dependent fill rate of the flooding potential gives an analytical expression for the distribution of crossing times from KTR theory that is used to extract unbiased rates. In the case of a static boost potential, the distribution of barrier crossing times follows an expected exponential distribution, and unbiased rates are extracted from a series of boosted simulations at discrete fill levels. Introducing a time-dependent boost that increases the fill level gradually over the simulation time leads to a simplified procedure for fitting the biased distribution of crossing times to analytical theory. We demonstrate the approach for the paradigmatic cases of alanine dipeptide in vacuum, the asymmetric SN2 reaction, and the folding of chignolin in explicit solvent. 

Coacervation is a common phenomenon in natural polymers and has been applied to synthetic materials systems for coatings, adhesives, and encapsulants. Single-component coacervates are formed when block polyampholytes exhibit self-coacervation, phase separating into a dense liquid coacervate phase rich in the polyampholyte coexisting with a dilute supernatant phase, a process implicated in the liquid–liquid phase separation of intrinsically disordered proteins. Using fully fluctuating field-theoretic simulations using complex Langevin sampling and complementary molecular-dynamics simulations, we develop molecular design principles to connect the sequenced charge pattern of a polyampholyte with its self-coacervation behavior in solution. In particular, the lengthscale of charged blocks and number of connections between oppositely charged blocks are shown to have a dramatic effect on the tendency to phase separate and on the accessible chain conformations. The field and particle-based simulation results are compared with analytical predictions from the random phase approximation (RPA) and postulated scaling relationships. The qualitative trends are mostly captured by the RPA, but the approximation fails catastrophically at low concentration. 

Proteins make up much of the machinery of cells and perform many roles that are essential for life. Some important proteins – known as intrinsically disordered proteins – lack any stable three-dimensional structure. One such protein, called tau, is best known for its ability to form tangles in the brain, and a buildup of these tangles is a hallmark of Alzheimer’s disease and many other dementias. Tau is also one of a number of proteins that can undergo a process called liquid-liquid phase separation: essentially, a solution of tau separates into a very dilute solution interspersed with droplets of a concentrated tau solution, similar to an oil-water mixture separating into a very watery solution with drops of oil. Understanding the conditions that lead to spontaneous liquid-liquid phase separation might give insight into how the tau tangles form. However, it was not known whether it is possible in principle for liquid-liquid phase separation of tau to occur in a living brain. Lin, McCarty et al. have now used an advanced computer simulation method together with experiments to map the conditions under which a solution containing tau undergoes liquid-liquid phase separation. Temperature as well as the concentrations of salt and the tau protein all influenced how easily tau droplets formed or dissolved, and the narrow range of conditions that encouraged droplet formation fell within the normal conditions found in the body, also known as “physiological conditions”. This suggested that tau droplets might form and dissolve easily in living systems, and possibly in the brain, depending on the precise physiological conditions. To explore this possibility further, tau protein was added to a dish containing living cells. As the map suggested, slightly adjusting temperature or protein concentrations caused tau droplets to form and dissolve, all while the cells remained alive. The map provided by this study may offer guides to researchers looking for liquid-liquid phase separation in the brain. If liquid-liquid phase separation of tau occurs in living brains, it may be important for determining whether and when damaging tau tangles emerge. For example, the high concentration of tau in droplets might speed up tangle formation. Ultimately, a better understanding of the conditions and mechanism for liquid-liquid phase separation of tau can help researchers understand the role of protein droplet formation in living systems. This may be a process that promotes, or possibly a regulatory mechanism that prevents, the formation of tau tangles associated with dementia.