Tail Order Research Articles

Molecular dynamics simulations of lipid composition and its impact on structural and dynamic properties of skin membrane

The stratum corneum (SC) plays the most important role in the absorption of topical and transdermal drugs. In this study, we developed a multi-layered SC model using coarse-grained molecular dynamics (CGMD) simulations of ceramides, cholesterol, and fatty acids in equimolar proportions, starting from two different initial configurations. In the first approach, all ceramide molecules were initially in the hairpin conformation, and the membrane bilayers were pre-formed. In the second approach, ceramide molecules were introduced in either the hairpin or splayed conformation, with the lipid molecules randomly oriented at the start of the simulation. The aim was to evaluate the effects of lipid chain length on the structural and dynamic properties of SC. By incorporating ceramides and fatty acids of different chain lengths, we simulated the SC membrane in healthy and diseased states. We calculated key structural properties including the thickness, normalized lipid area, lipid tail order parameters, and spatial ordering of the lipids from each system. The results showed that systems with higher ordering and structural integrity contained an equimolar ratio of ceramides (chain length of 24 carbon atoms), fatty acids with chain lengths ≥ of 20 carbon atoms, and cholesterol. In these systems, strong apolar interactions between the ceramide and fatty acid long acyl chains restricted the mobility of the lipid molecules, thereby maintaining a compact lipid headgroup region and high order in the lipid tail region. The simulations also revealed distinct flip-flop mechanisms for cholesterol and fatty acid within the multi-layered membrane. Cholesterol is mostly diffused through the tail-tail interface region of the membrane and could flip-flop in the same bilayer. In contrast, fatty acids flip-flopped between adjacent leaflets of two bilayers in which the tails crossed the thinner headgroup region of the membrane. To conclude, our SC model provides mechanistic insights into lipid mobility and is flexible in its design and composition of different lipids, enabling studies of varying skin conditions.

Measuring Asymmetric Tails Under Copula Distributions

Extensive evidence has been gathered showcasing the prevalence of heavy-tailed distributions and asymmetric tail interdependence within equity and foreign exchange markets, particularly during times of crisis. Tail interdependence in financial markets often manifests as financial contagion, characterized by periods where declining prices and heightened volatility propagate across economic and financial sectors. This phenomenon causes markets that typically exhibit minimal or no correlation to behave similarly, often in opposition to fundamental principles. Instances of unwarranted contagion present a perplexing challenge, suggesting irrationality among market participants and defying conventional risk management strategies and optimal portfolio selections. Our objective is to construct a comprehensive framework for dissecting such occurrences, utilizing a metric of tail-nonexchangeable dependencies employing various copulas with diverse marginal distributions. We offer analytical insights into our measurement of tail order dependence to aid in understanding these events.

New Bivariate Copulas via Lomax Distribution Generated Distortions

We develop a framework for creating distortion functions that are used to construct new bivariate copulas. It is achieved by transforming non-negative random variables with Lomax-related distributions. In this paper, we apply the distortions to the base copulas of independence, Clayton, Frank, and Gumbel copulas. The properties of the tail dependence coefficient, tail order, and concordance ordering are explored for the new families of distorted copulas. We conducted an empirical study using the daily net returns of Amazon and Google stocks from January 2014 to December 2023. We compared the popular Clayton, Gumbel, Frank, and Gaussian copula models to their corresponding distorted copula models induced by the unit-Lomax and unit-inverse Pareto distortions. The new families of distortion copulas are equipped with additional parameters inherent in the distortion function, providing more flexibility, and are demonstrated to perform better than the base copulas. After analyzing the data, we have found that the joint extremes of Amazon and Google stocks are more likely for high daily net returns than for low daily net returns.

Analyzing Lipid Membrane Defects via a Coarse-Grained to Triangulated Surface Map: The Role of Lipid Order and Local Curvature in Molecular Binding.

Lipid packing defects are known to serve as quantitative indicators for protein binding to lipid membranes. This paper presents a protocol for mapping molecular lipid detail onto a triangulated continuum leaflet representation. Besides establishing the desired forward counterpart to the existing inverse TS2CG map, this coarse-grained to triangulated surface (CG2TS) map enables straightforward extraction of the defect characteristics for any membrane geometry found in nature. We have applied our protocol to investigate the role of local curvature and varying lipid packing on the defect constant π. We find that the defect size is greatly influenced by both factors, arguing strongly against the usual assignment of a single defect constant in the case of more realistic membrane conditions. An important discovery is that lipids in the gel phase produce larger defects, or a higher π, in domains of high (local) curvature than the same lipid in a liquid phase of any curvature. This finding suggests that membranes featuring very ordered lipid packing can bind proteins via large defects in curved regions. Finally, we propose a route for estimating defect constants directly from the standard membrane properties. Identifying the precise role of composition, lipid (tail) order, and (local) curvature in defects for the irregular lipid structures that are (temporally) present in many biological processes is instrumental for obtaining fundamental insight as well as for a rational design of membrane binding targets.

Origin of the nonlinear structural and mechanical properties in oppositely curved lipid mixtures.

Structural and mechanical properties of membranes such as thickness, tail order, bending modulus and curvature energetics play crucial role in controlling various cellular functions that depend on the local lipid organization and membrane reshaping. While behavior of these biophysical properties are well understood in single component membranes, very little is known about how do they change in the mixed lipid membranes. Often various properties of the mixed lipid bilayers are assumed to change linearly with the mole fractions of the constituent lipids which, however, is true for "ideal" mixing only. In this study, using molecular dynamics simulations, we show that structural and mechanical properties of binary lipid mixture change nonlinearly with the lipid mole fractions, and the strength of the nonlinearity depends on two factors - spontaneous curvature difference and locally inhomogeneous interactions between the lipid components.

Extreme Behaviors of the Tail Gini-Type Variability Measures

AbstractFor a bivariate random vector $(X, Y)$, suppose $X$ is some interesting loss variable and $Y$ is a benchmark variable. This paper proposes a new variability measure called the joint tail-Gini functional, which considers not only the tail event of benchmark variable $Y$, but also the tail information of $X$ itself. It can be viewed as a class of tail Gini-type variability measures, which also include the recently proposed tail-Gini functional. It is a challenging and interesting task to measure the tail variability of $X$ under some extreme scenarios of the variables by extending the Gini's methodology, and the two tail variability measures can serve such a purpose. We study the asymptotic behaviors of these tail Gini-type variability measures, including tail-Gini and joint tail-Gini functionals. The paper conducts this study under both tail dependent and tail independent cases, which are modeled by copulas with so-called tail order property. Some examples are also shown to illuminate our results. In particular, a generalization of the joint tail-Gini functional is considered to provide a more flexible version.

Phospholipid Monolayer/Graphene Interfaces: Curvature Effect on Lipid Morphology and Dynamics.

Phospholipids are an important class of lipids that are widely used as model platforms for the study of biological processes and interactions. These lipids can form stable interfaces with solid substrates, such as graphene, and these interfaces have potential applications in biosensing and targeted drug delivery. In this paper, we perform molecular dynamics simulations of graphene-supported lipid monolayers to characterize the lipid properties of such interfaces. We observed substantial differences between the supported monolayer and free-standing bilayer in terms of the lipid properties, such as the tail order parameters, density profiles, diffusion rates, and so on. Furthermore, we studied these interfaces on sinusoidally deformed graphene substrates to understand the effect of curvature on the supported lipids. Here, we observed that the nature of the substrate curvature, that is, concave or convex, can locally affect the lipid/substrate adhesion strength and induce structural and dynamic changes in the adsorbed lipid monolayer. Together, these results help characterize the properties of lipid/graphene interfaces and provide insights into the substrate curvature effect on these interfaces, which can enable the tuning of lipid properties for various sensor devices and drug delivery applications.

Molecular dynamics simulations of the human ocular lens with age and cataract

The human ocular lens consists primarily of elongated, static fibers characterized by high stability and low turnover, which differ dramatically in their composition and properties from other biological membranes. Cholesterol (Chol) and sphingolipids (SL) are present at high concentrations, including saturated SLs, such as dihyrosphingomyelin (DHSM). Past molecular dynamics simulations demonstrated that the presence of DHSM and high Chol concentration contributes to higher order in lipid membranes. This current study simulated more complex models of human lens membranes. Models were developed representing physiological compositions in cataractous lenses aged 74 ± 6 years and in healthy lenses aged 22 ± 4, 41 ± 6, and 69 ± 3 years. With older age, Chol and ceramide concentrations increase and glycerophospholipid concentration decreases. With cataract, ceramide concentration increases and Chol and glycerophospholipid concentrations decrease. Surface area per lipid, deuterium order parameters (SCD), sterol tilt angle, electron density profiles, bilayer thickness, chain interdigitation, two-dimensional radial distribution functions (2D-RDF), lipid clustering, and hydrogen bonding were calculated for all simulations. All systems exhibited low surface area per lipid and high bilayer thickness, indicative of strong vertical packing. SCD parameters suggest similarly, with saturated tails in the hydrophobic core of the membrane having elevated order. Vertical packing and acyl tail order increased with both age and cataract condition. Lateral diffusion decreased with age and cataracts, with the older and cataractous models demonstrating increased long-range structure by the 2D-RDF analysis. In future work examining the membrane proteins of the lens, these models can serve as a physiologically accurate representation of the lens lipidome.

Stochastic comparisons on extremes of burr type XII samples associated with Archimedean copula and heterogeneous shape parameters

This study deals with random variables from Burr Type XII samples having heterogeneous shape parameters and homogeneous frailty parameters. For samples whose survival copula (whose copula) is Archimedean copula, sufficient conditions based on the heterogeneity of shape parameter vector for the stochastic tail ordering and usual stochastic ordering between sample minimums (sample maximums) are provided. As for independent samples, the convex transform order and tail hazard rate order (tail reversed hazard rate order) between sample minimums (maximums) are discussed. Several numerical examples are also presented to illustrate the theoretical findings.

Bacterial Membranes Are More Perturbed by the Asymmetric Versus Symmetric Loading of Amphiphilic Molecules.

Characterizing the biophysical properties of bacterial membranes is critical for understanding the protective nature of the microbial envelope, interaction of biological membranes with exogenous materials, and designing new antibacterial agents. Presented here are molecular dynamics simulations for two cationic quaternary ammonium compounds, and the anionic and nonionic form of a fatty acid molecule interacting with a Staphylococcus aureus bacterial inner membrane. The effect of the tested materials on the properties of the model membranes are evaluated with respect to various structural properties such as the lateral pressure profile, lipid tail order parameter, and the bilayer’s electrostatic potential. Conducting asymmetric loading of molecules in only one leaflet, it was observed that anionic and cationic amphiphiles have a large impact on the Staphylococcus aureus membrane’s electrostatic potential and lateral pressure profile as compared to a symmetric distribution. Nonintuitively, we find that the cationic and anionic molecules induce a similar change in the electrostatic potential, which points to the complexity of membrane interfaces, and how asymmetry can induce biophysical consequences. Finally, we link changes in membrane structure to the rate of electroporation for the membranes, and again find a crucial impact of introducing asymmetry to the system. Understanding these physical mechanisms provides critical insights and viable pathways for the rational design of membrane-active molecules, where controlling the localization is key.

Remarks on the tail order on moment sequences

We consider positively supported Borel measures for which all moments exist. On the set of compactly supported measures in this class a partial order is defined via eventual dominance of the moment sequences. Special classes are identified on which the order is total, but it is shown that already for the set of distributions with compactly supported smooth densities the order is not total. In particular we construct a pair of measures with smooth density for which infinitely many moments agree and another one for which the moments alternate infinitely often. This disproves some recently published claims to the contrary. Some consequences for games with distributional payoffs are discussed.

Computational Study on the Microscopic Adsorption Characteristics of Linear Alkylbenzene Sulfonates with Different Chain Lengths on Anthracite Surface

In order to explore the influence of different lengths of hydrophobic carbon chains on the diffusion characteristics of surfactants on the surface of anthracite, six linear alkyl benzene sulfonates with different hydrophobic carbon chain lengths were selected (mC, m = 8, 10, 12, 14, 16, 18; m represents the numbers of carbon atoms in the hydrophobic carbon chain), and molecular dynamics (MD) simulations were adopted. Models of surfactant-anthracite, surfactant-graphite layer, and water-surfactant-anthracite were constructed. After analyzing a series of properties such as adsorption energy, diffusion coefficient, radial distribution function (RDF), and hydrophobic tail order parameters, it was found that 12C had the highest adsorption strength on the surface of anthracite; the reason was that 12C had the highest degree of aggregation near the oxygen-containing functional groups on the surface of anthracite. Further studies had found that the hydrophobic tail chain of 12C had the strongest isotropy. The study fills the gap in the systematic study of the diffusion characteristics of linear alkylbenzene sulfonates (LAS) with different chain lengths on the surface of anthracite, enriches and develops the basic theory of coal wettability, and also provides technical ideas for the design of new surfactants and new dust suppression agents.

Tail dependence functions of the bivariate Hüsler–Reiss model

The tail dependence coefficient, a special case of the tail dependence function, measures extremal dependence between two random variables. It is known that the tail dependence coefficient of bivariate Gaussian random vectors with constant correlation coefficient |ρ|<1 is zero with rate satisfying regular variation at zero. In this note, we consider the tail dependence function of bivariate Gaussian random vectors with dynamic correlation coefficient ρn satisfying the Hüsler–Reiss condition. We also establish the convergence rates to the tail dependence functions under some refined Hüsler–Reiss conditions. By-products are the tail orders and tail order functions with related expansions.

Stochastic comparison of parallel systems with Pareto components

AbstractPareto distribution is an important distribution in extreme value theory. In this paper, we consider parallel systems with Pareto components and study the effect of heterogeneity on skewness of such systems. It is shown that, when the lifetimes of components have different shape parameters, the parallel system with heterogeneous Pareto component lifetimes is more skewed than the system with independent and identically distributed Pareto components. However, for the case when the lifetimes of components have different scale parameters, the result gets reversed in the sense of star ordering. We also establish the relation between star ordering and dispersive ordering by extending the result of Deshpande and Kochar [(1983). Dispersive ordering is the same as tail ordering. Advances in Applied Probability 15(3): 686–687] from support $(0, \infty )$ to general supports $(a, \infty )$, $a &gt; 0$. As a consequence, we obtain some new results on dispersion of order statistics from heterogeneous Pareto samples with respect to dispersive ordering.

Tail dependence and heavy tailedness in extreme risks

In the modeling of multivariate extreme risks, the tail dependence and the heavy tailedness are the two key factors. Heavy tailedness are usually defined through the regular variation. Tail dependence can be modeled by copulas with the so-called tail order property. In this paper, we propose a new risk measure called the Joint Expected Shortfall (JES) as an alternative of quantifying extreme risks. The JES, which can be viewed as a consolidation of both Expected Shortfall (ES) and Marginal Expected Shortfall (MES) risk measures, has the desirable property of measuring risk by jointly capturing both tail dependence and heavy tailedness. The asymptotic analysis of JES is conducted to provide a simple and transparent way of studying the interplay between tail dependence and heavy tailedness. Various examples are presented to illuminate our results. In particular, risk measures such as ES and MES that ignore the joint effect of dependence and heavy tailedness may severely underestimate the underlying risk.

Molecular Simulations of Ocular Lens Membranes at Various Stages of Age and Cataract

The human ocular lens consists primarily of elongated, static fibers characterized by high stability and low turnover, which differ dramatically in their composition and properties from other biological membranes. Cholesterol (Chol) and sphingolipids (SL) are present at high concentrations, including saturated SLs, such as dihyrosphingomyelin. Past molecular dynamics (MD) simulations demonstrated that the presence of DHSM and high Chol concentration contributes to higher order in lipid membranes. Using the CHARMM36 all-atom force field, this study simulated more complex models of human lens membranes with the inclusion of lysolipids and plasmanyl lipids. Models were developed representing physiological compositions in cataractous lenses aged 74±6 years and in healthy lenses aged 22±4, 41±6, and 69±3 years. With older age, Chol and ceramide concentrations increase and glycerophospholipid concentration decreases. With cataract, ceramide concentration increases and Chol and glycerophospholipid concentrations decrease. Surface area per lipid, deuterium order parameters (SCD), sterol tilt angle, electron density profiles (EDP), bilayer thickness, chain interdigitation, two-dimensional radial distribution functions (2D-RDF), mean-square displacement, lipid clustering, and hydrogen bonding were calculated for all simulations. All systems exhibited low surface area per lipid and high bilayer thickness, indicative of strong vertical packing. SCD parameters suggest similarly, with saturated tails in the hydrophobic core of the membrane having order parameter exceeding 0.4. Vertical packing and acyl tail order increased with both age and cataract. Lateral diffusion decreased with age and cataracts, with the older and cataractous models demonstrating increased long-range structure by the 2D-RDF analysis. Experimental results have found crystallization of Chol in older lenses, which similarly indicates increased order. In future work examining the membrane proteins of the lens, these models can serve as physiologically accurate representations of the lens lipidome.

Physical mechanism analysis of cholesterol concentration effect on asymmetric phospholipid membrane

Cell membrane is a multi-component complex system containing large number of membrane proteins and various types of sterols, so its properties are closely relevant to the interaction of sterols with phospholipid membranes. In this paper, we use the molecular dynamics method to investigate the effect of cholesterol concentration on asymmetric phospholipid system. To describe the membrane with the complex lipid components, we employ the coarse-grained model and choose three types of saturated phospholipids, DPPC, DPPE and DPPS, as the membrane components. The different concentrations of cholesterol are represented by five systems, so different physical influences on asymmetric phospholipid membrane can be exhibited. After enough time of the molecular simulation, the structural properties of the membrane, such as lipid accumulation, lipid tail sequence, lipid diffusion and cholesterol turnover, are obtained. The analysis on the total energy of the system, the L-J and electrostatic interaction between cholesterol molecules and phospholipid membrane system shows that the effect of cholesterol concentration on asymmetric phospholipid membrane is through changing the fluidity of asymmetric phospholipid membrane. Meanwhile, the distribution of cholesterol molecules in phospholipid membrane shows that most of them are concentrated in the inner side of phospholipid membrane, which also leads to the increase in tail order parameter and the thickness of phospholipid membrane. At the same time, we take into account the stress of cholesterol molecules to analyze the turnover of cholesterol molecules in different concentrations in the phospholipid membrane, and find that there is no obvious law of the stress on cholesterol molecules at different concentrations. Therefore, the turnover frequency of cholesterol molecules is mainly due to the stronger fluidity of the phospholipid membrane when the concentration of cholesterol increases. Our research can provide some help for a better understanding of the basic characteristics of the structure and kinetics of membranes containing cholesterol.

Simulation Study of Breast Cancer Lipid Changes Affecting Membrane Oxygen Permeability: Effects of Chain Length and Cholesterol.

Tumor radiotherapy relies on intracellular oxygen (O2) to generate reactive species that trigger cell death, yet hypoxia is common in cancers of the breast. De novo lipid synthesis in tumors supports cell proliferation but also may lead to unusually high levels of the 16:1 palmitoleoyl (Y) phospholipid tail, which is two carbons shorter than the 18:1 oleoyl (O) tail abundant in normal breast tissue. Here, we use atomic resolution molecular dynamics simulations to test two hypotheses: (1) the shorter, 16:1 Y, tail of the de novo lipid biosynthesis product 1-palmitoyl,2-palmitoleoyl-phosphatidylcholine (PYPC) promotes lower membrane permeability relative to the more common lipid 1-palmitoyl,2-oleoylphosphatidylcholine (POPC), by reducing oxygen solubility in the interleaflet region, and (2) cholesterol further lessens the permeability of PYPC by reducing overall O2 solubility and promoting PYPC tail order adjacent to the rigid cholesterol ring system. The simulationsconducted here indicate that PYPC has a permeability of 14±1cm/s at 37°C, comparable to 15.4±0.4cm/s for POPC. Inclusion of cholesterol in a 1:1 ratio with phospholipid intensifies the effect of chain length, giving permeabilities of 10.2±0.2cm/s for PYPC/cholesterol and 11.0±0.6cm/s for POPC/cholesterol. These findings indicate that PYPC maynot substantiallyinfluence membrane-level oxygen flux and is unlikely to hinder breast tissue oxygenation.

Effect of alcohol on the phase separation in model membranes

The discovery of coexisting liquid-ordered and liquid-disordered phases in multicomponent lipid bilayers has received widespread attention due to its potential relevance for biological systems. One of the many open questions is how the presence of additional components affects the nature of the coexisting phases. Of particular interest is the addition of alcohols because their anesthetic properties may arise from modulating bilayer behavior. We use coarse-grained Molecular Dynamics simulations to gain insight into the partitioning preferences of linear n-alcohols into ordered and disordered bilayers alongside their effects on local membrane structure. We find that alcohols cause only small changes to membrane composition alongside a lack of significant effects on membrane thickness and lipid tail order. Cholesterol and n-alcohol trans-bilayer motion is measured and found to be near or within the range of previous atomistic results. The cholesterol flip-flop rates increase with both n-alcohol length and concentration for octanol, dodecanol, and hexadecanol, indicating a decrease in lipid order. Umbrella sampling simulations of removing cholesterol from tertiary membranes find no significant difference with or without n-alcohols at various concentrations. Simulations of a phase-separated bilayer show that octanol preferentially partitions into the liquid-disordered phase in a ratio of approximately 3:1 over the liquid-ordered phase. Furthermore, partition coefficients of alcohol in single-phase membranes show a preference for longer alcohols (dodecanol and hexadecanol) to partition preferentially into the liquid-ordered phase, while decreasing the length of the alcohol reverses this trend. Our work tests experimental results while also investigating the ability for coarse-grained MARTINI simulations to capture minute differences in model membrane spatial arrangements on the nanoscale level.

The Surface and Hydration Properties of Lipid Droplets

Lipid droplets (LDs) are energy storage organelles composed of neutral lipids, such as triacylglycerol (TG) and sterol esters, surrounded by a phospholipid (PL) monolayer. Their central role in metabolism, complex life cycle, and unique lipid monolayer surface have garnered great attention over the last decade. In this article, results from the largest and longest all-atom simulations to date suggest that 5–8% of the LD surface is occupied by TG molecules, a number that exceeds the maximal solubility reported for TGs in PL bilayers (2.8%). Two distinct classes of TG molecules that interact with the LD monolayer are found. Those at the monolayer surface (SURF-TG) are ordered like PLs with the glycerol moiety exposed to water, creating a significant amount of chemically unique packing defects, and the acyl chains extended toward the LD center. In contrast, the TGs that intercalate just into the PL tail region (CORE-TG) are disordered and increase the amount of PL packing defects and the PL tail order. The degree of interdigitation caused by CORE-TG is stable and determines the width of the TG-PL overlap, whereas that caused by SURF-TG fluctuates and is highly correlated with the area per PL or the expansion of the monolayer. Thus, when the supply of PLs is limited, SURF-TG may reduce surface tension by behaving as a secondary membrane component. The hydration properties of the simulated LD systems demonstrate ∼10 times more water in the LD core than previously reported. Collectively, the reported surface and hydration properties are expected to play a direct role in the mechanisms by which proteins target and interact with LDs.