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Register a new userModel of separated form factors for unilamellar vesicles
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Authors
M. A. Kiselev
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New model of separated form factors is proposed for the evaluation of small-angle neutron scattering curves from large unilamellar vesicles. The validity of the model was checked by comparison to the model of hollow sphere. The model of separated form factors and hollow sphere model give reasonable agreement in the evaluation of vesicle parameters.
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The desire to create cell-like models for fundamental science and applications has spurred extensive effort towards creating giant unilamellar vesicles (GUVs). However, a route to selectively self-assemble GUVs in bulk has remained elusive. In bulk solution, membrane-forming molecules such as phospholipids, single-tailed surfactants, and block copolymers typically self-assemble into multilamellar, onion-like structures. So although self-assembly processes can form nanoscale unilamellar vesicles, scaffolding by droplets or surfaces is required to create GUVs. Here we show that surprisingly, it is possible to bulk self-assemble cell-sized GUVs with almost complete selectivity over other vesicle topologies. The seemingly paradoxical pair of features that enables this appears to be having very dynamic molecules at the nanoscale, that create unusually rigid membranes. The resultant self-assembly pathway enables encapsulation of molecules and colloids, and can also generate model primitive cells that can grow and divide.
We study the Ising model two-point diagonal correlation function $ C(N,N)$ by presenting an exponential and form factor expansion in an integral representation which differs from the known expansion of Wu, McCoy, Tracy and Barouch. We extend this expansion, weighting, by powers of a variable $lambda$, the $j$-particle contributions, $ f^{(j)}_{N,N}$. The corresponding $ lambda$ extension of the two-point diagonal correlation function, $ C(N,N; lambda)$, is shown, for arbitrary $lambda$, to be a solution of the sigma form of the Painlev{e} VI equation introduced by Jimbo and Miwa. Linear differential equations for the form factors $ f^{(j)}_{N,N}$ are obtained and shown to have both a ``Russian doll nesting, and a decomposition of the differential operators as a direct sum of operators equivalent to symmetric powers of the differential operator of the elliptic integral $ E$. Each $ f^{(j)}_{N,N}$ is expressed polynomially in terms of the elliptic integrals $ E$ and $ K$. The scaling limit of these differential operators breaks the direct sum structure but not the ``Russian doll structure. The previous $ lambda$-extensions, $ C(N,N; lambda)$ are, for singled-out values $ lambda= cos(pi m/n)$ ($m, n$ integers), also solutions of linear differential equations. These solutions of Painleve VI are actually algebraic functions, being associated with modular curves.
Ligand-receptor binding and unbinding are fundamental biomolecular processes and particularly essential to drug efficacy. Environmental water fluctuations, however, impact the corresponding thermodynamics and kinetics and thereby challenge theoretical descriptions. Here, we devise a holistic, implicit-solvent, multi-method approach to predict the (un)binding kinetics for a generic ligand-pocket model. We use the variational implicit-solvent model (VISM) to calculate the solute-solvent interfacial structures and the corresponding free energies, and combine the VISM with the string method to obtain the minimum energy paths and transition states between the various metastable (dry and wet) hydration states. The resulting dry-wet transition rates are then used in a spatially-dependent multi-state continuous-time Markov chain Brownian dynamics simulations, and the related Fokker-Planck equation calculations, of the ligand stochastic motion, providing the mean first-passage times for binding and unbinding. We find the hydration transitions to significantly slow down the binding process, in semi-quantitative agreement with existing explicit-water simulations, but significantly accelerate the unbinding process. Moreover, our methods allow the characterization of non-equilibrium hydration states of pocket and ligand during the ligand movement, for which we find substantial memory and hysteresis effects for binding versus unbinding. Our study thus provides a significant step forward towards efficient, physics-based interpretation and predictions of the complex kinetics in realistic ligand-receptor systems.
Lipid bilayers composed of non-alpha hydroxy sphingosine ceramide (CER NS), cholesterol (CHOL), and free fatty acids (FFA), which are components of the human skin barrier, are studied via molecular dynamics simulations. Since mixtures of these lipids exist in dense gel phases with little molecular mobility at physiological conditions, care must be taken to ensure that the simulations become decorrelated from the initial conditions. Thus, we propose and validate an equilibration protocol based on simulated tempering in which the simulation takes a random walk through temperature space, allowing the system to break out of metastable configurations and hence become decorrelated form its initial configuration. After validating the equilibration protocol, the effects of the lipid composition and ceramide tail length on bilayer properties are studied. Systems containing pure CER NS, CER NS + CHOL, and CER NS + CHOL + FFA, with the CER fatty acid tail length varied within each CER NS-CHOL-FFA composition, are simulated. The bilayer thickness is found to depend on the structure of the center of the bilayer, which arises as a result of the tail length asymmetry between the lipids studied. The hydrogen bonding between the lipid headgroups and with water is found to change with the overall lipid composition, but is mostly independent of the CER fatty acid tail length. Subtle differences in the lateral packing of the lipid tails are also found as a function of CER tail length. Overall, these results provide insight into the experimentally observed trend of altered barrier properties in skin systems where there are more ceramides with shorter tails present.
When DNA molecules are heated they denature. This occurs locally so that loops of molten single DNA strands form, connected by intact double-stranded DNA pieces. The properties of this melting transition have been intensively investigated. Recently there has been a surge of interest in this question, caused by experiments determining the properties of partially bound DNA confined to nanochannels. But how does such confinement affect the melting transition? To answer this question we introduce, and solve a model predicting how confinement affects the melting transition for a simple model system by first disregarding the effect of self-avoidance. We find that the transition is smoother for narrower channels. By means of Monte-Carlo simulations we then show that a model incorporating self-avoidance shows qualitatively the same behaviour and that the effect of confinement is stronger than in the ideal case.
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