Composite Degrees Of Freedom Research Articles

Kinetic control of shape deformations and membrane phase separation inside giant vesicles.

A variety of cellular processes use liquid-liquid phase separation (LLPS) to create functional levels of organization, but the kinetic pathways by which it proceeds remain incompletely understood. Here in real time, we monitor the dynamics of LLPS of mixtures of segregatively phase-separating polymers inside all-synthetic, giant unilamellar vesicles. After dynamically triggering phase separation, we find that the ensuing relaxation-en route to the new equilibrium-is non-trivially modulated by a dynamic interplay between the coarsening of the evolving droplet phase and the interactive membrane boundary. The membrane boundary is preferentially wetted by one of the incipient phases, dynamically arresting the progression of coarsening and deforming the membrane. When the vesicles are composed of phase-separating mixtures of common lipids, LLPS within the vesicular interior becomes coupled to the membrane's compositional degrees of freedom, producing microphase-separated membrane textures. This coupling of bulk and surface phase-separation processes suggests a physical principle by which LLPS inside living cells might be dynamically regulated and communicated to the cellular boundaries.

High stress twinning in a compositionally complex steel of very high stacking fault energy

Deformation twinning is rarely found in bulk face-centered cubic (FCC) alloys with very high stacking fault energy (SFE) under standard loading conditions. Here, based on results from bulk quasi-static tensile experiments, we report deformation twinning in a micrometer grain-sized compositionally complex steel (CCS) with a very high SFE of ~79 mJ/m2, far above the SFE regime for twinning (<~50 mJ/m2) reported for FCC steels. The dual-nanoprecipitation, enabled by the compositional degrees of freedom, contributes to an ultrahigh true tensile stress up to 1.9 GPa in our CCS. The strengthening effect enhances the flow stress to reach the high critical value for the onset of mechanical twinning. The formation of nanotwins in turn enables further strain hardening and toughening mechanisms that enhance the mechanical performance. The high stress twinning effect introduces a so far untapped strengthening and toughening mechanism, for enabling the design of high SFEs alloys with improved mechanical properties.

Nonequilibrium Self-Organization of Lipids into Hierarchically Ordered and Compositionally Graded Cylindrical Smectics.

When a dry mass of certain amphiphiles encounters water, a spectacular interfacial instability ensues: It gives rise to the formation of ensembles of fingerlike tubular protrusions called myelin figures─tens of micrometers wide and tens to hundreds of micrometers long─representing a novel class of nonequilibrium higher-order self-organization. Here, we report that when phase-separating mixtures of unsaturated lipid, cholesterol, and sphingomyelin are hydrated, the resulting myelins break symmetry and couple their compositional degrees of freedom with the extended myelinic morphology: They produce complementary, interlamellar radial gradients of concentrations of cholesterol (and sphingomyelin) and unsaturated lipid, which stands in stark contrast to interlamellar, lateral phase separation in equilibrated morphologies. Furthermore, the corresponding gradients of molecule-specific chemistries (i.e., cholesterol extraction by methyl-β-cyclodextrin and GM1 binding by cholera toxin) produce unusual morphologies comprising compositionally graded vesicles and buckled tubes. We propose that kinetic differences in the information processing of hydration characteristics of individual molecules while expending energy dictate this novel behavior of lipid mixtures undergoing hydration.

All twist and no bend makes raft edges splay: Spontaneous curvature of domain edges in colloidal membranes.

Using theory and experiments, we study the interface between two immiscible domains in a colloidal membrane composed of rigid rods of different lengths. Geometric considerations of rigid rod packing imply that a domain of sufficiently short rods in a background membrane of long rods is more susceptible to twist than the inverse structure, a long-rod domain in a short-rod membrane. The midplane tilt at the interdomain edge forces splay, which, in turn, manifests as spontaneous edge curvature with energetics controlled by the length asymmetry of constituent rods. A thermodynamic model of such tilt-curvature coupling at interdomain edges explains a number of experimental observations, including annularly shaped long-rod domains, and a nonmonotonic dependence of edge twist on domain radius. Our work shows how coupling between orientational and compositional degrees of freedom in two-dimensional fluids gives rise to complex shapes of fluid domains, analogous to shape transitions in 3D fluid vesicles.

Pulsatile Lipid Vesicles under Osmotic Stress

The response of lipid bilayers to osmotic stress is an important part of cellular function. Recent experimental studies showed that when cell-sized giant unilamellar vesicles (GUVs) are exposed to hypotonic media, they respond to the osmotic assault by undergoing a cyclical sequence of swelling and bursting events, coupled to the membrane’s compositional degrees of freedom. Here, we establish a fundamental and quantitative understanding of the essential pulsatile behavior of GUVs under hypotonic conditions by advancing a comprehensive theoretical model of vesicle dynamics. The model quantitatively captures the experimentally measured swell-burst parameters for single-component GUVs, and reveals that thermal fluctuations enable rate-dependent pore nucleation, driving the dynamics of the swell-burst cycles. We further extract constitutional scaling relationships between the pulsatile dynamics and GUV properties over multiple timescales. Our findings provide a fundamental framework that has the potential to guide future investigations on the nonequilibrium dynamics of vesicles under osmotic stress.

Osmotic Pulsations of Lipid Vesicles under Hypotonic Stress

The response of lipid bilayers to osmotic stress is an important part of cellular function. It has been shown that cell-sized giant unilamellar vesicles (GUVs) exposed to hypotonic media, respond to the osmotic assault by undergoing a cyclical sequence of swelling and bursting events, coupled to the membrane's compositional degrees of freedom. In this work, we seek to establish a fundamental and quantitative understanding of the essential pulsatile behavior of GUVs under hypotonic conditions, by advancing a comprehensive theoretical model for vesicle dynamics. We combine experimental and theoretical approaches to characterize the swell-burst cycles of GUVs under hypotonic conditions. We first focus on the membrane rupture mechanism, and show that thermal fluctuations enable stochastic pore nucleations, leading to a dependence of the lytic strain on the load rates. Second, we emphasize the role of solute diffusion in the leak-out process, responsible for the slowdown of the pulsatile dynamics. Finally, we unravel new scaling relationships between the pulsatile dynamics and the GUV properties. Our findings provide a fundamental framework that has the potential to guide future investigations on the non-equilibrium dynamics of vesicles under osmotic stress.

Effect of short-range interactions on the quantum critical behavior of spinless fermions on the honeycomb lattice

We present a functional renormalization group investigation of an Euclidean three-dimensional matrix Yukawa model with U(N) symmetry, which describes N = 2 Weyl fermions that effectively interact via a short-range repulsive interaction. This system relates to an effective low-energy theory of spinless electrons on the honeycomb lattice and can be seen as a simple model for suspended graphene. We find a continuous phase transition characterized by large anomalous dimensions for the fermions and composite degrees of freedom. The critical exponents define a new universality class distinct from Gross-Neveu type models, typically considered in this context.

Renormalization flow of bound states

A renormalization group flow equation with a scale-dependent transformation of field variables gives a unified description of fundamental and composite degrees of freedom. In the context of the effective average action, we study the renormalization flow of scalar bound states which are formed out of fundamental fermions. We use the gauged Nambu--Jona-Lasinio model at weak gauge coupling as an example. Thereby, the notions of a bound state or fundamental particle become scale dependent, being classified by the fixed-point structure of the flow of effective couplings.

The Phase Behavior of Cationic Lipid–DNA Complexes

We present a theoretical analysis of the phase behavior of solutions containing DNA, cationic lipids, and nonionic (helper) lipids. Our model allows for five possible structures, treated as incompressible macroscopic phases: two lipid–DNA composite (lipoplex) phases, namely, the lamellar (L α C) and hexagonal (H II C) complexes; two binary (cationic/neutral) lipid phases, that is, the bilayer (L α ) and inverse-hexagonal (H II) structures, and uncomplexed DNA. The free energy of the four lipid-containing phases is expressed as a sum of composition-dependent electrostatic, elastic, and mixing terms. The electrostatic free energies of all phases are calculated based on Poisson–Boltzmann theory. The phase diagram of the system is evaluated by minimizing the total free energy of the three-component mixture with respect to all the compositional degrees of freedom. We show that the phase behavior, in particular the preferred lipid–DNA complex geometry, is governed by a subtle interplay between the electrostatic, elastic, and mixing terms, which depend, in turn, on the lipid composition and lipid/DNA ratio. Detailed calculations are presented for three prototypical systems, exhibiting markedly different phase behaviors. The simplest mixture corresponds to a rigid planar membrane as the lipid source, in which case, only lamellar complexes appear in solution. When the membranes are “soft” (i.e., low bending modulus) the system exhibits the formation of both lamellar and hexagonal complexes, sometimes coexisting with each other, and with pure lipid or DNA phases. The last system corresponds to a lipid mixture involving helper lipids with strong propensity toward the inverse-hexagonal phase. Here, again, the phase diagram is rather complex, revealing a multitude of phase transitions and coexistences. Lamellar and hexagonal complexes appear, sometimes together, in different regions of the phase diagram.

Getting the supersymmetric unification scale from quantum confinement with chiral symmetry breaking

Two models which generate the supersymmetric Grand Unification Scale from the strong dynamics of an additional gauge group are presented. The particle content is chosen such that this group confines with chiral symmetry breaking. Fields that are usually introduced to break the Grand Unified group appear instead as composite degrees of freedom and can acquire vacuum expectation values due to the confining dynamics. The models implement known solutions to the doublet-triplet splitting problem. The SO(10) model only requires one higher dimensional representation, an adjoint. The dangerous coloured Higgsino-mediated proton decay operator is naturally suppressed in this model to a phenomenologically interesting level. Neither model requires the presence of gauge singlets. Both models are only technically natural.

Dual descriptions of SO(10) supersymmetric gauge theories with arbitrary numbers of spinors and vectors

We examine the low-energy structure of $\mathcal{N}=1$ supersymmetric SO(10) gauge theory with matter chiral superfields in ${N}_{Q}$ spinor and ${N}_{f}$ vector representations. We construct a dual to this model based upon an $\mathrm{SU}{(N}_{f}{+2N}_{Q}\ensuremath{-}7)\ifmmode\times\else\texttimes\fi{}\mathrm{Sp}{(2N}_{Q}\ensuremath{-}2)$ gauge group without utilizing deconfinement methods. This product theory generalizes all previously known Pouliot-type duals to $\mathrm{SO}{(N}_{c})$ models with spinor and vector matter. It also yields large numbers of new dual pairs along various flat directions. The dual description of the SO(10) theory satisfies multiple consistency checks including an intricate renormalization group flow analysis which links it with Seiberg's duality transformations. We discuss its implications for building grand-unified theories that contain all standard model fields as composite degrees of freedom.