ESTROGEN RECEPTOR EXPRESSION ON BREAST CANCER PATIENTS' SURVIVAL UNDER SHAPE RESTRICTED COX REGRESSION MODEL.

For certain subtypes of breast cancer, study findings show that their level of estrogen receptor expression is associated with their risk of cancer death, and also suggests a non-linear effect on the hazard of death. A flexible form of the proportional hazards model, λ(t∣x, z ) = λ(t) exp( z T ß )q(x), is desirable to facilitate a rich class of covariate effect on a survival outcome to provide meaningful insight, where the functional form of q(x) is not specified except for its shape. Prior biologic knowledge on the shape of the underlying distribution of the covariate effect in regression models can be used to enhance statistical inference. Despite recent progress, major challenges remain for the semiparametric shape-restricted inference due to lack of practical and efficient computational algorithms to accomplish non-convex optimization. We propose an alternative algorithm to maximize the full log-likelihood with two sets of parameters iteratively under monotone constraints. The first set consists of the non-parametric estimation of the monotone-restricted function q(x), while the second set includes estimating the baseline hazard function and other covariate coefficients. The iterative algorithm in conjunction with the pool-adjacent-violators algorithm makes the computation efficient and practical. The Jackknife resampling effectively reduces the estimator bias, when sample size is small. Simulations show that the proposed method can accurately capture the underlying shape of q(x), and outperforms the estimators when q(x) in the Cox model is mis-specified. We apply the method to model the effect of estrogen receptor on breast cancer patients' survival.

Multiple free radical scavenging reactions of aurones.

A series of naturally occurring 3',4'-dihydroxy aurones have been studied with regard to multiple free radical scavenging reactions in the gas and two liquid phases using density functional theory (DFT). All of the aurones prefer to perform (2 + n)-HAT mechanism to trap 2 + n free radicals, where n is the sum of the numbers of catechol and guaiacyl units in the gas and benzene phases. The second HAT reaction favours occurring in the same catechol moiety of the first HAT mechanism occurring OH group due to the formation of a stable quinone and the highly exothermic step of the final stable product formation. The catechol and guaiacyl moieties show increased potency for the second and fourth H+/e‒ reactions. In the water phase, aurones can perform multiple H+/e‒ reactions through n1PL-ET-n2HAT-(n+1-n2)ET mechanism, where n1 is the number of OH groups and n2 is the number of guaiacyl moieties.

Structures and non-covalent interaction behaviours of binary systems containing the ionic liquid 1-(2'-hydroxylethyl)-3-methylimidazolium bis(trifluoromethylsulfonyl)imide and chloroform.

Mixtures of ionic liquids (ILs) and molecular solvents can overcome the drawbacks (high viscosity, high polarity, and high cost) of pure ILs and extend their practical use. The structural and interaction properties of ILs form the bases for understanding their properties. In this work, the structural properties of the mixtures of an IL, 1-(2'-hydroxylethyl)-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([C2OHMIM][Tf2N]), with chloroform, a molecular solvent of weak polarity, in various concentrations were analysed using Fourier transform infrared spectroscopy and density functional theory calculations. Excess spectra were used to analyse the infrared spectra. The IL forms a stable ion cluster-CDCl3 complex with CDCl3 in the concentration range investigated. In the ion cluster-CDCl3 complex, the hydrogen atom of CDCl3 forms hydrogen-bonds with the fluorine atoms of the anion. In addition, the chlorine atom of CDCl3 forms a halogen-bond with the oxygen atom of the anion. All the hydrogen and halogen-bonds identified between the [C2OHMIM][Tf2N] ion cluster and CDCl3 exhibit low strength, closed shells, and electrostatically dominant interactions.

Fabrication of Asymmetric Phosphatidylserine-Containing Lipid Vesicles: A Study on the Effects of Size, Temperature, and Lipid Composition.

The asymmetric distribution of lipids in plasma membranes is closely related to the physiological functions of cells. To improve our previous approach in fabricating asymmetric vesicles, we defined a parameter, asymmetric degree, in this work and investigated the effects of vesicle size, incubation temperature, and lipid composition on the formation process of asymmetric phosphatidylserine (PS)-containing lipid vesicles. The results indicate that all of the three factors have marked but different effects on the time-dependent asymmetric degree of the vesicles as well as the flip and flop rate constants of the PS lipids. However, only vesicle size and PS content show significant influence on the maximal asymmetric degree of the vesicles, while the incubation temperature exhibits negligible effect. This work not only deepens our understanding on the packing property of PS molecules in self-assembled membranes and the formation mechanism of asymmetric vesicles but also practically provides a solution to regulate the asymmetric degree of the PS-containing vesicles using the established kinetic equation. In addition, the method would facilitate researches related to asymmetric vesicles or reconstruction of biological membranes.

Effects of different ester chains on the antioxidant activity of caffeic acid.

Caffeic acid ester derivatives have been widely found in propolis extract and plants. In this work, the effect of ester groups with different aromatic and alkyl chains on the antioxidant activity of caffeic acid was performed on the double H+/e- process using DFT calculations. We found that 1) O3-H3⋯O4 intramolecular hydrogen-bonds exist in the catechol moiety of the investigated compounds, which have the same strength and are closed shell interactions, weak-strength and electrostatic in nature, making the 4-OH more favourable than 3-OH to trap free radicals. 2) In weak polarity phases, caffeic acid and its derivatives prefer to perform the double H+/e- processes via the dHAT mechanism. In the polar phases, the SdPLdET mechanism is more favoured. The first step of these mechanisms is more possible in 4-OH groups. 3) The ester group with different aromatic and alkyl chains would enhance the antioxidant capacities of caffeic acid.

Free radical scavenging potency of ellagic acid and its derivatives in multiple H+/e‒ processes.

The reaction energetics of the multiple free radical scavenging mechanisms of ellagic acid and its derivatives were studied by DFT method. Ellagic acid and its derivatives that bear catechol or guaiacyl moieties can proceed multiple free radical scavenging processes. Intramolecular hydrogen-bonds were found in the most stable geometries of the investigated compounds and can influence the antioxidant activity of the related groups and hydrogen atom/proton loss sequence. The stronger hydrogen-bond, the weaker antioxidant activity of the hydrogen atom/proton-donating group. The preferred mechanisms vary among different phases. All of the investigated compounds prefer to trap free radicals by multiple HAT mechanisms in gas and benzene phases. The second HAT reaction preferably occurs in the same catechol or guaiacyl unit of the first HAT group with the formation of stable quinone or benzodioxole. The catechol and guaiacyl moieties not only retain high free radical scavenging ability of the parent compounds but even show increased potency for the second and fourth H+/e‒ reactions. In water phase, ellagic acid and its derivatives would proceed consecutively PL reactions from the OH groups. The formed di/tri/tetra-anion would proceed one/four electron transfers following with single/double SPLET mechanism and electron donation reactions until forming the stable quinone or benzodioxole.

Role of C‒H bond in the antioxidant activities of rooperol and its derivatives: A DFT study.

Rooperol and its derivatives, derived from the Hypoxis rooperi plant, are polyphenolic and norlignan compounds with excellent antioxidant activities. The reaction enthalpies for the free-radical scavenging by rooperol and its six derivatives were studied using density functional theory. We found that the C-H groups played a significant role in the antioxidant activities in non-polar phases. In the gas and benzene phases, rooperol and its derivatives preferentially underwent the free-radical scavenging process via the 3‒CH group by following the hydrogen atom transfer (HAT) mechanism. In polar phases, the sequential proton loss electron transfer (SPLET) was the most preferred mechanism, and the phenolic O‒H groups played a significant role. Additionally, we found that when the hydrogen atom in the OH group was replaced by a glucose moiety, the antioxidant activity of the adjacent OH group was reduced. ROP, DHROP-I, DHROP-II, ROP-4″-G and ROP-4'G have catechol moiety, they may proceed double step-wise mechanisms to trap free radicals. In the gas and benzene phases, the preferable mechanism is dHAT. In water phase, it is SPLHAT.

Local Acid Strength of Solutions and Its Quantitative Evaluation Using Excess Infrared Nitrile Probes.

We propose the concept of local acidity in condensed-phase chemistry in this work. The feature is demonstrated in trifluoroethanol (TFE) by employing two Fourier-transform infrared spectroscopy (FTIR) nitrile probes, acetonitrile (CH3CN) and benzonitrile (PhCN). Specifically, three positive excess peaks were found in the binary systems composed of TFE and a probe using excess spectroscopy. To characterize the local acidity quantitatively, we have tried to correlate the wavenumbers of the positive excess peaks of the probes and the pKa values in water of a series of XH-containing compounds (X = O, N, and C). Good linear relationships were discovered. Accordingly, three different pKa values of TFE were determined based on the three positive excess infrared peaks, which are attributed to the monomer, dimer, and trimer of TFE with the help of quantum-chemical calculations. The concept of local acidity and its quantitative evaluation enrich our knowledge of acid-base chemistry and will shed light on a better understanding of microstructures of solutions.

A combination of FTIR and DFT to study the microscopic structure and hydrogen-bonding interaction properties of the [BMIM][BF4] and water.

The structure and hydrogen-bond interaction property of water and a model ionic liquid (IL): 1-butyl-3-methylimidazolium tetrafluoroborate ([BMIM][BF4]) were studied using the combination of Fourier transform infrared spectroscopy (FTIR) and density functional theory (DFT) calculations. The O‒D stretching vibration region of the deuterated water was an area of special focus. Excess infrared spectroscopy with enhanced resolution was applied to analyse the original infrared spectra of v(O‒D). It is found that: (1) [BMIM][BF4] forms stable hydrogen-bonds with water in the mixture. (2) The hydrogen-bonds are weak strength, closed shell and electrostatic dominant interactions. The preferred interaction site of [BMIM]+ cation is the hydrogen atom at the C2. (3) Cage hexamer water, cyclic tetramer water, cyclic trimer water, ion cluster-water complex, ion pair-water, and anion-water complexes are identified in the mixture. When the mole fraction of D2O (x(D2O)) is larger than 0.9, ion cluster and ion pair were broken apart into individual cations and anions. The cage hexamer water, cyclic tetramer water, and cyclic trimer water disappear at x(D2O) < 0.8, 0.5, and 0.3, respectively. HDO formed by H/D isotope exchange was detected when x(D2O) is less than 0.3.

The structure and interaction properties of two task-specific ionic liquids and acetonitrile mixtures: A combined FTIR and DFT study.

The mixtures of ionic liquid (IL) and acetonitrile (CH3CN) can be used as reaction media, supercapacitors and thermally stable electrolytes. The macroscopic properties of ILs-CH3CN mixtures have been extensively studied. However, some fundamental questions regarding the microscopic properties of ILs-CH3CN mixtures still remain to be answered. In this work, the structure properties and hydrogen-bond interactions of two task-specific ILs, i.e., 1-propylnitrile-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([PCNMIM][Tf2N]) and 1-(2'-hydroxylethyl)-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([C2OHMIM][Tf2N]), and CH3CN were studied using the combination of Fourier transform infrared spectroscopy (FTIR) and density functional theory (DFT) calculations. The aromatic C‒H stretching vibration region of the cation was an area of special focus. Excess infrared spectroscopy with enhanced resolution was applied to analyse the original infrared spectra. It is found that: (1) The two ILs form stable hydrogen-bonds with CH3CN. (2) Ion cluster, ion cluster-acetonitrile, and ion pair-acetonitrile are identified in the mixture. Acetonitrile cannot break apart the strong electronic interaction between the cation and anion in the examined concentration range. (3) The hydrogen-bonds are weak strength, closed shell and electrostatic dominant interactions. (4) The preferred interaction site of [PCNMIM]+ cation is the hydrogen atom at the C2 site, while that of [C2OHMIM]+ cation is the hydrogen atom in the hydroxyl group.

Theoretical insight into the antioxidative activity of isoflavonoid: The effect of the C2=C3 double bond.

Isoflavonoids are one of the most important groups of naturally occurring antioxidants. Their structural features are important for evaluating their antioxidative activity. In this work, density functional theory (DFT) methods were applied to investigate the influence of the C2=C3 double bond on the antioxidative activity of isoflavonoids based on three currently accepted radical scavenging mechanisms from the viewpoint of thermodynamics. The C2=C3 double bond can make the compounds more flat, which would extend the conjugated system in the molecule and make the isoflavonoids higher antioxidant activity. The C2=C3 double bond would not alter the strongest antioxidative hydroxyl group of the isoflavonoids. In the gas, benzene and CHCl3 phases, the C2=C3 double bond will enhance the antioxidative activity of isoflavonoids by lowering the bond dissociation enthalpies of the hydroxyl groups in the B ring that are the strongest antioxidative sites for the hydrogen atom transfer (HAT) mechanism. In polar phases, a similar result is obtained by weakening the proton affinity of 7-OH that is the strongest antioxidative hydroxyl group in the sequential proton loss electron transfer (SPLET), mechanism. Thus, the C2=C3 double bond will enhance the antioxidative activity of isoflavonoids irrespective of the studied phases.

The structure and hydrogen-bond behaviours of binary systems containing ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate and methanol/ethanol.

Mixing ionic liquids (ILs) with a molecular cosolvent can largely reduce the high viscosities, high polarities, and high costs of ILs. The macroscopic properties of IL-cosolvent mixtures have been studied extensively. However, some fundamental questions regarding the microscopic properties of the binary mixtures still remain to be answered. In this work, the structural and hydrogen-bond features of binary systems containing 1-butyl-3-methylimidazolium tetrafluoroborate ([BMIM][BF4]) and methanol/ethanol were studied by using the combination of Fourier-transform infrared spectroscopy (FTIR) and density functional theory (DFT) calculations. Excess infrared absorption spectroscopy with enhanced spectral resolution was used to analyse the original IR spectra. The alcohol tetramer/larger multimers, alcohol trimer, anion-alcohol, ion pair-alcohol, and ion cluster-alcohol complexes were identified in the excess spectra. With the increasing [BMIM][BF4], the alcohol multimers gradually broke out from the larger multimers into smaller multimers. The hydrogen-bonded complex related with anion [BF4]- and alcohol gradually changes from anion-alcohol complex to ion pair-alcohol complex. The ion cluster-alcohol appears when the x(alcohol) is <0.50. The most stable optimized geometries of anion-alcohol, ion pair-alcohol, and ion cluster-alcohol were carefully analysed, and the hydrogen-bonds were identified. All of the hydrogen-bonds in these studied complexes had weak strength, closed shells and electrostatically dominant interactions.

Effect of Imidazolium-Based Ionic Liquids on the Structure and Phase Behavior of Palmitoyl-oleoyl-phosphatidylethanolamine.

Among various applications, ionic liquids (ILs) have been used as antimicrobial agents in laboratories, possibly through induction of the leakage of bacteria. A molecular-level understanding of the mechanism that describes how ILs enhance the permeation of membranes is still lacking. In this study, the effects of imidazolium-based ILs with different alky chain lengths on the structure and phase behavior of 1-palmitoyl-2-oleoyl-phosphatidylethanolamine (POPE), which is a representative bacteria-membrane-rich lipid, have been investigated. By employing differential scanning calorimetry and synchrotron small- and wide-angle X-ray scattering techniques, we found that ILs with longer alkyl chains influenced the phase behavior more effectively, and lower IL concentrations are needed to induce phase separation for both lamellar liquid crystalline phase and nonlamellar inverted hexagonal phase of POPE. Interestingly, the IL with an alkyl chain of 12 carbon atoms ([C12mim]Cl) shows a difference. It exhibits a stronger disturbing effect on the POPE bilayer structure than [C16mim]Cl, indicating that the ability of ILs to influence the membrane structures is dependent not only on the alkyl chain length of ILs, but also on the degree of matching of the alkyl chain lengths of ILs and lipids. The new lamellar and nonlamellar structures induced by ILs both have smaller repeat distances than that of pure POPE, implying thinner membrane structures. Data of the fluorescence-based vesicle dye leakage assay are consistent with these results, particularly the defects caused by IL-induced phase separation can enhance the membrane permeability markedly. The present work may shed light on our understanding of the antimicrobial mechanism of ILs.

DFT Studies on the Antioxidant Activity of Naringenin and Its Derivatives: Effects of the Substituents at C3.

The radical scavenging activity of a flavonoid is largely influenced by its structure. The effects of the substituents at C3 position on the antioxidant activity of naringenin were carried out using the density functional theory (DFT) method. The reaction enthalpies related with the three well-established mechanisms were analyzed. Excellent correlations were found between the reaction enthalpies and Hammett sigma constants. Equations obtained from the linear regression can be helpful in the selection of suitable candidates for the synthesis of novel naringenin derivatives with enhanced antioxidant properties. In the gas and benzene phases, the antioxidant activity of naringenin was enhanced by the electron-donating substituents via weakening the bond dissociation enthalpy (BDE). In the water phase, it was strengthened by electron-withdrawing groups-via lowering the proton affinity (PA). The electronic effect of the substituent on the BDE of naringenin is mainly governed by the resonance effect, while that on the ionization potential (IP) and PA of naringenin is mainly controlled by the field/inductive effect.

A DFT-based study of the hydrogen-bonding interactions between myricetin and ethanol/water.

Flavonoids are vital constituents of propolis that are responsible for its medicinal activity. Flavonoid extraction commonly employs ethanol and water as solvents. In the extraction reaction, hydrogen-bonding interactions play a crucial role. In this study, hydrogen-bonding interactions between myricetin-an abundant flavonoid in propolis-and ethanol or water were studied theoretically using density functional theory (DFT) methods. The molecular geometry and charge properties of the myricetin monomer were analyzed first. After careful optimization, nine stable myricetin-CH3CH2OH/H2O complex geometries were obtained. Hydrogen bonds were confirmed to exist in these optimized structures. The most stable structures were found to be those with hydrogen bonds involving the hydrogen atoms of hydroxyl groups and the oxygen atom of the keto group of myricetin. The characteristics of the hydrogen-bonding interactions in the optimized structures were carefully analyzed. The hydrogen bonds in the optimized geometries were shown to be closed-shell-type interactions. H5' in ring B of myricetin presented the strongest interaction. The hydrogen bonds were found to be Coulombic interactions. Those between the hydrogen atoms of the hydroxyl groups in myricetin and the oxygen atoms in CH3CH2OH and H2O were of moderate strength and had some covalent character, while the others were weak and were dominantly electrostatic in character.

The influence of the H5⋯OC4 intramolecular hydrogen-bond (IHB) on the antioxidative activity of flavonoid.

Flavonoids widely found in natural foods are characterized by acting as antioxidants compounds. There are close relationship between the antiradical activities and structural properties of flavonoids. In this work, density functional theory (DFT) methods were applied to investigate the influence of the H5⋯OC4 intramolecular hydrogen-bond (IHB) on the antiradical activity of flavonoid based on three prevalently accepted radical scavenging mechanisms: hydrogen atom transfer (HAT), single electron transfer-proton transfer (SET-PT) and sequential proton-loss electron-transfer (SPLET). The thermodynamic properties: bond dissociation enthalpy (BDE), ionization potential (IP), proton dissociation enthalpy (PDE), proton affinity (PA) and electron transfer enthalpy (ETE) related with these mechanisms were calculated to elucidate the antiradical activity. The results showed that the 5-OH group is most influenced and its antiradical capacity was weakened by the H5⋯OC4 IHB. In the gas, benzene and chloroform phases, H5⋯OC4 IHB would reduce the antiradical activity of flavonoid via increasing the bond dissociation enthalpy. While, in the DMSO and H2O phases, the opposite result occurs by lowering the proton affinity.

Substituent Effects on the Radical Scavenging Activity of Isoflavonoid.

Understanding the role of substituents is of great importance for the preparation of novel phenolic compounds with enhanced antioxidative properties. In this work, the antioxidative activity of isoflavonoid derivatives with different substituents placed at the C2 position was determined by density functional theory (DFT) calculations. The bond dissociation enthalpy (BDE), ionization potential (IP), and proton affinity (PA) related to hydrogen atom transfer (HAT), single electron transfer-proton transfer (SET-PT), and sequential proton loss electron transfer (SPLET) mechanisms were calculated. The strongest antioxidative group of isoflavonoid is not altered by the substituents. Excellent correlations were found between the BDE/IP/PA and Hammett sigma constants. Equations obtained from linear regression can be useful in the selection of suitable candidates for the synthesis of novel isoflavonoids derivatives with enhanced antioxidative properties. In the gas and benzene phases, the electron-donating substituents would enhance the antioxidative activity of isoflavonoids via weakening the BDE of 4'-OH. In water phase, they will reduce the antioxidative by strengthening the PA of 7-OH. Contrary results occur for the electron-withdrawing groups. In addition, the electronic effects of substituents on the BDE/IP/PA have also been analyzed.

The influence of C2C3 double bond on the antiradical activity of flavonoid: Different mechanisms analysis.

Flavonoids widely found in bee products are excellent antioxidants. The structural features are important in evaluating the antiradical activity of flavonoid. In this work, the density functional theory (DFT) methods were applied to investigate the influence of C2C3 double bond on the antiradical activity of flavonoid based on three prevalently accepted radical scavenging mechanisms from the thermodynamic aspect. It is found that the hydroxyl groups in different rings are affected variously by the C2C3 double bond and the 3OH group is most influenced. For the compounds that only differ with the C2C3 double bond, the antiradical activity of flavone or flavonol (possessing C2C3 double bond) is not always stronger than that of flavanone: in the weak polarity phases, only the antiradical activities of chrysin, galangin and morin are stronger than those of pinocembrin, pinobanksin and dihydro-morin, respectively. In polar phases, the C2C3 double bond would weaken the antiradical activity of flavonoid via enlarging the proton affinity and the antiradical activity of flavone or flavonol is weaker than that of flavanone.

The antioxidative activity of piceatannol and its different derivatives: Antioxidative mechanism analysis.

The naturally occurring stilbenes piceatannol and its derivatives are excellent antioxidants. In this work, the antioxidative activities of piceatannol and different piceatannol derivatives have been investigated using the density functional theory (DFT) method based on three widely accepted radical scavenging mechanisms, namely, the hydrogen atom transfer (HAT), single electron transfer followed by proton transfer (SET-PT) and sequential proton loss electron transfer (SPLET). The gas and four solvent phases, namely, bond dissociation enthalpy (BDE), ionization potential (IP), proton dissociation enthalpy (PDE), proton affinity (PA) and electron transfer enthalpy (ETE), related to these mechanisms were calculated to elucidate the antioxidative capacities of the investigated compounds. This work focuses specifically on the thermodynamically preferred mechanism, antioxidative site and antioxidative activity order of the investigated stilbenes. The substituted effects of the methyl group and prenyl group on the chemical properties of the remaining OH and CH groups are also analysed. This work confirms the vital role of the OH and CH groups on free radical scavenging of piceatannol and its derivatives.

The Substituent Effect on the Radical Scavenging Activity of Apigenin.

Flavonoids widely found in natural foods are excellent free radical scavengers. The relationship between the substituent and antioxidative activity of flavonoids has not yet been completely elucidated. In this work, the antioxidative activity of apigenin derivatives with different substituents at the C3 position was determined by density functional theory (DFT) calculations. The bond dissociation enthalpy (BDE), ionization potential (IP), and proton affinity (PA) were calculated. Donator acceptor map (DAM) analysis illustrated that the studied compounds are worse electron acceptors than F and also are not better electron donors than Na. The strongest antioxidative group of apigenin derivatives was the same as apigenin. Excellent correlations were found between the BDE/IP/PA and Hammett sigma constants. Therefore, Hammett sigma constants can be used to predict the antioxidative activity of substituted apigenin and to design new antioxidants based on flavonoids. In non-polar phases, the antioxidative activity of apigenin was increased by the electron-withdrawing groups, while it was reduced by the electron-donating groups. Contrary results occurred in the polar phase. The electronic effect of the substituents on BDE(4'-OH), BDE(5-OH), PA(4'-OH), and IP is mainly controlled by the resonance effect, while that on BDE(7-OH), PA(5-OH), and PA(7-OH) is governed by the field/inductive effect.