Search

The liquid-liquid phase separation (LLPS) of Tau has been postulated to play a role in modulating the aggregation property of Tau, a process known to be critically associated with the pathology of a broad range of neurodegenerative diseases including Alzheimer's Disease. Tau can undergo LLPS by homotypic interaction through self-coacervation (SC) or by heterotypic association through complex-coacervation (CC) between Tau and binding partners such as RNA. What is unclear is in what way the formation mechanisms for self and complex coacervation of Tau are similar or different, and the addition of a binding partner to Tau alters the properties of LLPS and Tau. A combination of in vitro experimental and computational study reveals that the primary driving force for both Tau CC and SC is electrostatic interactions between Tau-RNA or Tau-Tau macromolecules. The liquid condensates formed by the complex coacervation of Tau and RNA have distinctly higher micro-viscosity and greater thermal stability than that formed by the SC of Tau. Our study shows that subtle changes in solution conditions, including molecular crowding and the presence of binding partners, can lead to the formation of different types of Tau condensates with distinct micro-viscosity that can coexist as persistent and immiscible entities in solution. We speculate that the formation, rheological properties and stability of Tau droplets can be readily tuned by cellular factors, and that liquid condensation of Tau can alter the conformational equilibrium of Tau., (© 2021 The Protein Society.)

Free energy evaluation in molecular simulations of both classical and quantum systems is computationally intensive and requires sophisticated algorithms. This is because free energy depends on the volume of accessible phase space, a quantity that is inextricably linked to the integration measure in a coordinate representation of a many-body problem. In contrast, the same problem expressed as a field theory (auxiliary field or coherent states) isolates the particle number as a simple parameter in the Hamiltonian or action functional and enables the identification of a chemical potential field operator. We show that this feature leads a “direct” method of free energy evaluation, in which a particle model is converted to a field theory and appropriate field operators are averaged using a field-theoretic simulation conducted with complex Langevin sampling. These averages provide an immediate estimate of the Helmholtz free energy in the canonical ensemble and the entropy in the microcanonical ensemble. The method is illustrated for a classical polymer solution, a block copolymer melt exhibiting liquid crystalline and solid mesophases, and a quantum fluid of interacting bosons.

ABSTRACT We investigate the directed self-assembly (DSA) of cylinder-forming block copolymers inside extended guiding templates of different sizes and shapes. We focus in particular on templates that promote the formation of linear arrays of two or three cylinders for contact hole multiplication. Using self-consistent field theory (SCFT) simulations, we uncover the existence windows for two- and three-cylinder arrays and assess their stability relative to other defective morphologies present in the templates. From SCFT simulations, templates in which three DSA cylinders are the lowest free energy configuration are more prone to defective morphologies in comparison to narrower templates with a two cylinder ground state. The size, placement and pitch of the defect-free structures are estimated for different template sizes and shapes. Beyond the thermodynamic description of the self-assembly process and the ensuing equilibrium properties, we also consider the equally important issue of the kinetics of melting of defects into perfect structures. Using the string method, we compute the most probable kinetic pathways that anneal elementary defects into a desired perfect array of cylinders. Similar to our findings on defectivity levels, defects in three-cylinder-friendly templates are associated with high kinetic barriers > 8 kT while their counterparts in narrower templates more readily dissipate into two-cylinder states after crossing barriers < 2 kT. © 2014 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys. 2015, 53, 317-326 [ABSTRACT FROM AUTHOR]

ABSTRACT We use self-consistent field theory to study the self-assembly of cylinder-forming diblock copolymers confined in a cylindrical prepattern. This situation arises in contact holes-the hole shrink problem-where the goal is to produce a cylindrical hole with reduced dimensions relative to a guiding prepattern. In this study, we focus on systems with a critical prepattern dimension ranging from 50 nm to 100 nm that consequently lead to the formation of a single cylinder in the middle of the hole. We find that a variety of defect morphologies arise from the self-assembly process and are strongly governed by the prepattern dimensions, wetting conditions as well as the polymer molecular weight. We also consider blends of diblock copolymers and homopolymers and determine optimal blending configurations that not only favor the formation of the desired cylindrical morphology but also extend the processing window relative to the pure diblock case. When defective structures form inside the prepattern, we compute their formation energy and use the string method to examine the kinetic pathways for the transition from the defective state to the perfect cylindrical state. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015, 53, 142-153 [ABSTRACT FROM AUTHOR]

We use three-dimensional self-consistent field theory (SCFT) to study the directed self-assembly (DSA) of cylinder-forming block copolymers in a peanut-shaped (also called egg-box) prepattern. The design of the prepattern shape will target the pitch reduction of the contact holes. The idea is that the DSA of block copolymers will not only lead to reduced critical dimensions relative to the template but will also repair defects in the guiding prepatterns and produce defect-free contact holes. We also study blends of block copolymers and homopolymers with various lengths and volume fractions. Using SCFT simulations, we establish the effects of the added homopolymer on defectivity, the process window, and the properties of the formed cylinders. In an attempt to quantify the effect of thermal fluctuations on the placement of the cylinders, we resort to complex Langevin simulations and perform a stochastic sampling of the assembled morphologies. [ABSTRACT FROM AUTHOR]

We report a stable and efficient complex Langevin sampling scheme for performing approximation-free numerical simulations directly on the path-integral coherent-states field theory for an assembly of interacting bosons. We apply the method to generate the λ line of critical phase transitions associated with Bose-Einstein condensation in a model ϕ4 scalar field theory. The new approach enjoys near-linear scaling in the resolved (d+1) spatial and imaginary-time dimensions and should be particularly efficient for the study of dense systems at low temperature. [ABSTRACT FROM AUTHOR]

Advances in synthetic polymer chemistry have unleashed seemingly unlimited strategies for producing block polymers with arbitrary numbers (n) and types (k) of unique sequences of repeating units. Increasing (k,n) leads to a geometric expansion of possible molecular architectures, beyond conventional ABA-type triblock copolymers (k = 2, n = 3), offering alluring opportunities to generate exquisitely tailored materials with unparalleled control over nanoscale-domain geometry, packing symmetry, and chemical composition. Transforming this potential into targeted structures endowed with useful properties hinges on imaginative molecular designs guided by predictive theory and computer simulation. Here, we review recent developments in the field of block polymers. [ABSTRACT FROM AUTHOR]