arXiv subjects

Xiao-jun Li

Publications and source records attributed to Xiao-jun Li.

10 recordsLinked to original sources

arXiv2001

Molecular theory of hydrophobic mismatch between lipids and peptides

Effects of the mismatch between the hydrophobic length, d, of transmembrane alpha helices of integral proteins and the hydrophobic thickness, D_h, of the membranes they span are studied theoretically utilizing a microscopic model of lipids. In particular, we examine the dependence of the period of a lamellar phase on the hydrophobic length and volume fraction of a rigid, integral, peptide. We find that the period decreases when a short peptide, such that d D_h, is inserted. The effect is due to the replacement of extensible lipid tails by rigid peptide. As the peptide length is increased, the lamellar period continues to increase, but at a slower rate, and can eventually decrease. The amount of peptide which fails to incorporate and span the membrane increases with the magnitude of the hydrophobic mismatch |d-D_h|. We explicate these behaviors which are all in accord with experiment. Predictions are made for the dependence of the tilt of a single trans-membrane alpha helix on hydrophobic mismatch and helix density.

cond-mat.soft↗

arXiv2001

Theory of tunable pH sensitive vesicles of anionic and cationic lipids or anionic and neutral lipids

The design of vesicles which become unstable at an easily tuned value of pH is of great interest for targeted drug delivery. We present a microscopic theory for two forms of such vesicles. A model of lipids introduced by us previously is applied to a system of ionizable, anionic lipid, and permanently charged, cationic lipid. We calculate the pH at which the lamellar phase becomes unstable with respect to an inverted hexagonal one, a value which depends continuously on the system composition. Identifying this instability with that displayed by unilamellar vesicles undergoing fusion, we obtain very good agreement with the recent experimental data of Hafez et al., Biophys. J. 2000 79: 1438-1446, on the pH at which fusion occurs vs. vesicle composition. We explicate the mechanism in terms of the role of the counter ions. This understanding suggests that a system of a neutral, non lamellar forming lipid stabilized by an anionic lipid would serve equally well for preparing tunable, pH sensitive vesicles. Our calculations confirm this. Further, we show that both forms of vesicle have the desirable feature of exhibiting a regime in which the pH at instability is a rapidly varying function of the vesicle composition.

cond-mat.soft↗

arXiv2000

Phenomenological Theory for Phase Turbulence in Rayleigh-Bénard Convection

We present a phenomenological theory for phase turbulence (PT) in Rayleigh-Bénard convection, based on the generalized Swift-Hohenberg model. We apply a Hartree-Fock approximation to PT and conjecture a scaling form for the structure factor $S(k)$ with respect to the correlation length $ξ_2$. We hence obtain {\it analytical} results for the time-averaged convective current $J$ and the time-averaged mean square vorticity $Ω$. We also define power-law behaviors such as $J \sim ε^μ$, $Ω\sim ε^λ$ and $ξ_2 \sim ε^{-ν}$, where $ε$ is the control parameter. We find from our theory that $μ= 1$, $ν\ge 1/2$ and $λ= 2 μ+ ν$. These predictions, together with the scaling conjecture for $S(k)$, are confirmed by our numerical results.

cond-mat.stat-mech↗

arXiv2000

Fluctuations in mixtures of lamellar- and nonlamellar-forming lipids

We consider the role of nonlamellar-forming lipids in biological membranes by examining fluctuations, within the random phase approximation, of a model mixture of two lipids, one of which forms lamellar phases while the other forms inverted hexagonal phases. To determine the extent to which nonlamellar-forming lipids facilitiate the formation of nonlamellar structures in lipid mixtures, we examine the fluctuation modes and various correlation functions in the lamellar phase of the mixture. To highlight the role fluctuations can play, we focus on the lamellar phase near its limit of stability. Our results indicate that in the initial stages of the transition, undulations appear in the lamellae occupied by the tails, and that the nonlamellar-forming lipid dominates these undulations. The lamellae occupied by the head groups pinch off to make the tubes of the hexagonal phase. Examination of different correlations and susceptibilities makes quantitative the dominant role of the nonlamellar-forming lipids.

cond-mat.soft↗

arXiv2000

Distribution of lipids in non-lamellar phases of their mixtures

We consider a model of lipids in which a head group, characterized by its volume, is attached to two flexible tails of equal length. The phase diagram of the anhydrous lipid is obtained within self-consistent field theory, and displays, as a function of lipid architecture, a progression of phases: body-centered cubic, hexagonal, gyroid, and lamellar. We then examine mixtures of an inverted hexagonal forming lipid and a lamellar forming lipid. As the volume fractions of the two lipids vary, we find that inverted hexagonal, gyroid, or lamellar phases are formed. We demonstrate that the non-lamellar forming lipid is found preferentially at locations which are difficult for the lipid tails to reach. Variations in the volume fraction of each type of lipid tail are on the order of one to ten per cent within regions dominated by the tails. We also show that the variation in volume fraction is correlated qualitatively with the variation in mean curvature of the head-tail interface.

cond-mat.soft↗

arXiv1999

Theory of Lipid Polymorphism: Application to Phosphatidylethanolamine and Phosphatidylserine

We introduce a microscopic model of a lipid with a charged headgroup and flexible hydrophobic tails, a neutral solvent, and counter ions. Short-ranged interactions between hydrophilic and hydrophobic moieties are included as are the Coulomb interactions between charges. Further, we include a short-ranged interaction between charges and neutral solvent, which mimics the short-ranged, thermally averaged interaction between charges and water dipoles. We show that the model of the uncharged lipid displays the usual lyotropic phases as a function of the relative volume fraction of the headgroup. Choosing model parameters appropriate to dioleoylphosphatidylethanolamine in water, we obtain phase behavior which agrees well with experiment. Finally we choose a solvent concentration and temperature at which the uncharged lipid exhibits an inverted hexagonal phase and turn on the headgroup charge. The lipid system makes a transition from the inverted hexagonal to the lamellar phase which is related to the increased waters of hydration correlated with the increased headgroup charge via the charge-solvent interaction. The polymorphism displayed upon variation of pH mimics that of the behavior of phosphatidylserine.

cond-mat.soft↗

arXiv1997

Nature of Roll to Spiral-Defect-Chaos Transition

We investigate the nature of the parallel-roll to spiral-defect-chaos (SDC) transition in Rayleigh-Benard convection, based on the generalized Swift-Hohenberg model. We carry out extensive, systematic numerical studies by, on one branch, increasing the control parameter gradually from the parallel roll regime to the SDC regime and, on the other branch, decreasing it in the opposite manner. We find that the data of several time-averaged global quantities all form hysteretic loops from the two branches. We also discuss several possible scenarios for the transition and analyze our data for SDC accordingly. We conclude that the roll-to-SDC transition is first-order in character and that the correlation length diverges at the conduction to convection onset. We further postulate that this transition can be understood somewhat similar to the hexagon-to-roll transition in non-Boussinesq fluids. Finally we comment on the differences between our conclusion and those in two experiments.

patt-sol↗

arXiv1997

Phenomenological Theory for Spatiotemporal Chaos in Rayleigh-Benard Convection

We present a phenomenological theory for spatiotemporal chaos (STC) in Rayleigh-Benard convection, based on the generalized Swift-Hohenberg model. We apply a random phase approximation to STC and conjecture a scaling form for the structure factor $S(k)$ with respect to the correlation length $ξ_2$. We hence obtain analytical results for the time-averaged convective current $J$ and the time-averaged vorticity current $Ω$. We also define power-law behaviors such as $J \sim ε^μ$, $Ω\sim ε^λ$ and $ξ_2 \sim ε^{-ν}$, where $ε$ is the control parameter. We find from our theory that $μ= 1$, $ν\ge 1/2$ and $λ= 2 μ+ ν$ for phase turbulence and that $μ= 1$, $ν\ge 1/2$ and $λ= 2 μ+ 2 ν$ for spiral-defect chaos. These predictions, together with the scaling conjecture for $S(k)$, are confirmed by our numerical results. Finally we suggest that Porod's law, $S(k) \sim 1/ξ_2 k^3$ for large $k$, might be valid in STC.

patt-sol↗

arXiv1997

Direct Transition to Spatiotemporal Chaos in Low Prandtl Number Fluids

We present the first large scale numerical simulation of three-dimensional Rayleigh-Bénard convection near onset, under free-free boundary conditions for a fluid of Prandtl number $σ=0.5$. We find that a spatiotemporally chaotic state emerges immediately above onset, which we investigate as a function of the reduced control parameter $ε$. We conclude that the transition from conduction to spatiotemporal chaos is second order and of ``mean field'' character. We also present a simple theory for the time-averaged convective current. Finally, we show that the time-averaged structure factor satisfies a scaling behavior with respect to the correlation length near onset.

patt-sol↗

arXiv1996

Dynamical Properties of Multi-Armed Global Spirals in Rayleigh-Benard Convection

Explicit formulas for the rotation frequency and the long-wavenumber diffusion coefficients of global spirals with $m$ arms in Rayleigh-Benard convection are obtained. Global spirals and parallel rolls share exactly the same Eckhaus, zigzag and skewed-varicose instability boundaries. Global spirals seem not to have a characteristic frequency $ω_m$ or a typical size $R_m$, but their product $ω_m R_m$ is a constant under given experimental conditions. The ratio $R_i/R_j$ of the radii of any two dislocations ($R_i$, $R_j$) inside a multi-armed spiral is also predicted to be constant. Some of these results have been tested by our numerical work.

patt-sol↗