A Distribution-Free Two-Sample Equivalence Test Allowing for Tied Observations

A new testing procedure is derived which enables to assess the equivalence of two arbitrary noncontinuous distribution functions from which unrelated samples are taken as the data to be analyzed. The equivalence region is defined to consist of all pairs (F,G) of distribution functions such that for independent X ∼ F, Y ∼ G the conditional probability of {X > Y} given {X ≠ Y} lies in some short interval around 1/2. The test rejects the null hypothesis of nonequivalence if and only if the standardized distance between the U-statistics estimator of P[X > Y ∣ X ≠ Y] and the center of the equivalence interval (1/2 — ε₁, 1/2 + ε₂) does not exceed a critical upper bound which has to be computed as the α-quantile of a χ²-distribution with one degree of freedom and a random noncentrality parameter proportional to the squared length of that interval. The test is shown to maintain the asymptotic significance level under very weak regularity conditions. Results of an extensive simulation study suggest that its level properties are very satisfactory in small samples as well. The power turns out to be inversely related to the rate P[X = Y] of ties between observations from different samples.     

Optimization of polylactic-co-glycolic acid nanoparticles containing itraconazole using 2<Superscript>3</Superscript> factorial design

This study investigated the utility of a 2³ factorial design and optimization process for polylactic-co-glycolic acid (PLGA) nanoparticles containing itraconazole with 5 replicates at the center of the design. Nanoparticles were prepared by solvent displacement technique with PLGAX ₁ (10, 100 mg/mL), benzyl benzoateX ₂ (5, 20 μg/mL), and itraconazoleX ₃ (200, 1800 μg/mL). Particle size (Y ₁), the amount of itraconazole entrapped in the nanoparticles (Y ₂), and encapsulation efficiency (Y ₃) were used as responses. A validated statistical model having significant coefficient figures (P<.001) for the particle size (Y ₁), the amount of itraconazole entrapped in the nanoparticles (Y ₂), and encapsulation efficiency (Y ₃) as function of the PLGA (X ₁), benzyl benzoate (X ₂), and itraconazole (X ₃) were developed: Y₁=373.75+66.54X₁+52.09X₂+105.06X₃−4.73X₁X₂+46.30X₁X₃; Y₂=472.93+73.45X₁+ 169.06X₂+333.03X₃+62.40X₁X₃+141.49X₂X₃; Y₃= 57.36+6.53X₁+15.52X₂−12.59X₃+1.01X₁X₃+ 1.73X₂X₃.X ₁,X ₂, andX ₃ had a significant effect (P<.001) onY ₁,Y ₂, andY ₃. The particle size, the amount of itraconazole entrapped in the nanoparticles, and the encapsulation efficiency of the 4 formulas were in agreement with the predictions obtained from the models (P<.05). An overlay plot for the 3 responses shows the boundary in whichY ₁ shows the boundary in which a number of combinations of concentration of PLGA, benzyl benzoate, and itraconazole will result in a satisfactory process. Using the desirability approach with the same constraints, the solution composition having the highest overall desirability (D=0.769) was 10 mg/mL of PLGA, 16.94 μg/mL of benzyl benzoate, and 1001.01 μg/mL of itraconazole. This approach allowed the selection of the optimum formulation ingredients for PLGA nanoparticles containing itraconazole of 500 μg/mL.     

Asymptotical Tests on the Equivalence,Substantial Difference and Non‐inferiority Problems with Two Proportions

Let d = p₂ ? p₁ be the difference between two binomial proportions obtained from two independent trials. For parameter d, three pairs of hypothesis may be of interest: H₁: d ≤ δ vs. K₁: d > δ; H₂: d ? (δ₁, δ₂) vs. K₂: d ∈ (δ₁, δ₂); and H₃: d ∈ [δ₁, δ₂] vs. K₃: d ? [δ₁, δ₂], where H_i is the null hypothesis and K_i is the alternative hypothesis. These tests are useful in clinical trials, pharmacological and vaccine studies and in statistics generally. The three problems may be investigated by exact unconditional tests when the sample sizes are moderate. Otherwise, one should use approximate (or asymptotical) tests generally based on a Z‐statistics like those suggested in the paper. The article defines a new procedure for testing H₂ or H₃, demonstrates that this is more powerful than tests based on confidence intervals (the classic TOST – two one sided tests – test), defines two corrections for continuity which reduce the liberality of the three tests, and selects the one that behaves better. The programs for executing the unconditional exact and asymptotic tests described in the paper can be loaded at http://www.ugr.es/~bioest/software.htm. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

An example of a regular inbreeding system with cubic ancestral growth that preserves some genetic variability

A specific regular inbreeding system of quadruple half-second cousin mating is considered. A regular inbreeding system can be thought of as a graph which satisfies certain natural homogeneity properties. Random walks X _n and Y _n are introduced on the nodes of the graph; the event {X _n=Y_n} is a renewal event by the homogeneity properties. In Arzberger (1985) it is shown that 1) graphs associated with left cancellative semigroups are regular, and 2) for regular systems, the population becomes genetically uniform if and only if the event {X _n=Y_n} is recurrent. In Arzberger (1986) the system of quadruple half-second cousin mating is associated with a cancellative semigroup, thus the system is regular. In this paper we show that 1) A_n is asymptotically of the form cn ³, where A _n is the number of ancestors n generations into the past, 2) {X _n=Y_n} is not recurrent (this is shown by associating (X _n, Y _n) with a random walk in Z ³, 3) P[X _3n =Y _3n ] is asymptotically of the form cn ^–3/2. Thus, in this example, genetic heterogeneity is maintained, with a cubic rate of growth for A_n, not by an exponential growth rate, as in all previous examples of regular inbreeding systems in which genetic heterogeneity is maintained.     

Estimation of a Conditional Mean in a Linear Regression Model

Consider the two linear regression models of Y_ij on X_ij, namely Y_ij = β_io + β_il X_ij + ε_ij,j = 1,2,…,n_i, i = 1,2, where ε_ij are assumed to be normally distributed with zero mean and common unknown variance σ². The estimated value of a mean of Y₁ for a given value of X₁ is made to depend on a preliminary test of significance of the hypothesis β₁₁ = β₂₁. The bias and the mean square error of the estimator for the conditional mean of Y₁ are given. The relative efficiency of the estimator to the usual estimator is computed and is used to determine a proper choice of the significance level of the preliminary test.     

Response surface methodology for optimization and characterization of limonene-based coenzyme Q10 self-nanoemulsified capsule dosage form

The aim of this study was to systematically obtain a model of factors that would yield an optimized self-nanoemulsified capsule dosage form (SNCDF) of a highly lipophilic model compound, Coenzyme Q10 (CoQ). Independent variables such as amount of R-(+)-limonene (X ₁), surfactant (X ₂), and cosurfactant (X ₃), were optimized using a 3-factor, 3-level Box-Behnken statistical design. The dependent variables selected were cumulative percentage of drug released after 5 minutes (Y ₁) with constraints on drug release in 15 minutes (Y ₂), turbidity (Y ₃), particle size (Y ₄), and zeta potential (Y ₅). A mathematical relationship obtained,Y ₁=78.503+6.058X ₁ +13.738X ₂+5.986X ₃−25.831X ₁ ² +9.12X ₁X₂−26.03X ₁X₃−38.67X ₂ ² +11.02X ₂X₃−15.55X ₃ ³ (r ²=0.97), explained the main and quadratic effects, and the interaction of factors that affected the drug release. Response surface methodology (RSM) predicted the levels of factorsX ₁,X ₂, andX ₃ (0.0344, 0.216, and 0.240, respectively), for a maximized response ofY ₁ with constraints of >90% release onY ₂. The observed and predicted values ofY ₁ were in close agreement. In conclusion, the Box-Behnken experimental design allowed us to obtain SNCDF with rapid (>90%) drug release within 5 minutes with desirable properties of low turbidity and particle size.     

Self-assembly of four three-dimensional reduced molybdenum(V) phosphates decorated with transitional metal complexes

Four new three-dimensional materials built from reduced molybdenum(V) phosphates as building blocks and transitional metal (Co, Zn and Cd) complexes as linkers, (Hbpy)₂[Co(bpy)(H₂O)]₂[Co(H₂PO₄)₂ (HPO₄)₆(MoO₂)₁₂(OH)₆] (1), [Co(H₂O)₄]₂[Co(Hbpy)(H₂O)]₂[Co(bpy)][Co(HPO₄)₄(PO₄)₄(MoO₂)₁₂(OH)₆] · 6H₂O (2), Na₂[Zn(Hbpy)(H₂O)₂]₂[Zn(Hbpy)]₂[Zn(HPO₄)₂(PO₄)₆(MoO₂)₁₂(OH)₆] · 4H₂O (3), (H₂bpy)₂[Cd(bpy)(H₂O)]₂[Cd(bpy)(H₂O)₂]₂[Cd(HPO₄)₄(PO₄)₄(MoO₂)₁₂(OH)₆] · 2H₂O (4) (bpy = 4,4′-bipyridine), have been synthesized and characterized by elemental analyses, IR, TG, and single crystal X-ray diffraction. The 3-D framework of 1 is constructed from Co[P₄Mo₆]₂ dimers bonded together with [Co(bpy)]_n coordination polymer chains. In compound 2, the Co[P₄Mo₆]₂ dimers are linked by both [Co(bpy)] complex chains and the cobalt dimers to form a 3-D framework. Compounds 1 and 2 represent the first examples of reduced molybdenum(V) phosphates decorated with transition metal complexes chains. The 3-D framework of 3 is constructed from Zn[P₄Mo₆]₂ dimers bonded together with [Zn(bpy)] coordination complexes and [Zn(bpy)(H₂O)₂] complexes. In compound 4, the Cd[P₄Mo₆]₂ dimers are coordinated with [Cd(bpy)(H₂O)] and [Cd(bpy)(H₂O)₂] complexes to construct a 3-D structure. To our best knowledge, it is the first time that linear ligand 4,4′-bpy molecules have been grafted into the backbone of reduced molybdenum phosphates. Furthermore, the magnetic properties of compounds 1 and 2 are reported.     

Oxygen uptake does not increase linearly at high power outputs during incremental exercise test in humans

A group of 12 healthy non-smoking men [mean age 22.3 (SD 1.1) years], performed an incremental exercise test. The test started at 30 W, followed by increases in power output (P) of 30 W every 3 min, until exhaustion. Blood samples were taken from an antecubital vein for determination of plasma concentration lactate [La⁻]_pl and acid-base balance variables. Below the lactate threshold (LT) defined in this study as the highest P above which a sustained increase in [La⁻]_pl was observed (at least 0.5 mmol · l⁻¹ within 3 min), the pulmonary oxygen uptake (V˙O₂) measured breath-by-breath, showed a linear relationship with P. However, at P above LT [in this study 135 (SD 30) W] there was an additional accumulating increase in V˙O₂ above that expected from the increase in P alone. The magnitude of this effect was illustrated by the difference in the final P observed at maximal oxygen uptake (V˙O_2max) during the incremental exercise test (P _max,obs at V˙O_2max) and the expected power output at V˙O_2max(P _max,exp at V˙O_2max) predicted from the linear V˙O₂-P relationship derived from the data collected below LT. The P _max,obs at V˙O_2max amounting to 270 (SD 19) W was 65.1 (SD 35) W (19%) lower (P<0.01) than the P _max,exp at V˙O_{2max .} The mean value of V˙O_2max reached at P _max,obs amounted to 3555 (SD 226) ml · min⁻¹ which was 572 (SD 269) ml · min⁻¹ higher (P<0.01) than the V˙O₂ expected at this P, calculated from the linear relationship between V˙O₂ and P derived from the data collected below LT. This fall in locomotory efficiency expressed by the additional increase in V˙O₂, amounting to 572 (SD 269) ml O₂ · min⁻¹, was accompanied by a significant increase in [La⁻]_pl amounting to 7.04 (SD 2.2) mmol · l⁻¹, a significant increase in blood hydrogen ion concentration ([H⁺]_b) to 7.4 (SD 3) nmol · l⁻¹ and a significant fall in blood bicarbonate concentration to 5.78 (SD 1.7) mmol · l⁻¹, in relation to the values measured at the P of the LT. We also correlated the individual values of the additional V˙O₂ with the increases (Δ) in variables [La⁻]_pl and Δ[H⁺]_b. The Δ values for [La⁻]_pl and Δ[H⁺]_b were expressed as the differences between values reached at the P _max,obs at V˙O_2max and the values at LT. No significant correlations between the additional V˙O₂ and Δ[La⁻]_pl on [H⁺]_b were found. In conclusion, when performing an incremental exercise test, exceeding P corresponding to LT was accompanied by a significant additional increase in V˙O₂ above that expected from the linear relationship between V˙O₂ and P occurring at lower P. However, the magnitude of the additional increase in V˙O₂ did not correlate with the magnitude of the increases in [La⁻]_pl and [H⁺]_b reached in the final stages of the incremental test. Accepted: 30 October 1997     

P2Y purinoceptors induce changes in intracellular calcium in acinar cells of rat lacrimal glands

Adenosine 5′-triphosphate (ATP) is an extracellular signal that regulates various cellular functions. Cellular secretory activities are enhanced by ATP as well as by cholinergic and adrenergic stimuli. The present study aimed to determine which purinoceptors play a role in ATP-induced changes in the intracellular concentration of calcium ions ([Ca²⁺]_i) and in the fine structure of acinar cells of rat lacrimal glands. ATP induced exocytotic structures, vacuolation and an increase in [Ca²⁺]_i in acinar cells. The removal of extracellular Ca²⁺ or the use of Ca²⁺ channel blockers partially inhibited the ATP-induced [Ca²⁺]_i increase. U73122 (an antagonist of PLC) and heparin (an antagonist of IP₃ receptors) did not completely inhibit the ATP-induced [Ca²⁺]_i increase. P1 purinoceptor agonists did not induce any changes in [Ca²⁺]_i, whereas suramin (an antagonist of P2 receptors) completely inhibited ATP-induced changes in [Ca²⁺]_i. A P2Y receptor agonist, 2-MeSATP, induced a strong increase in [Ca²⁺]_i, although UTP (a P2Y_2,4,6 receptor agonist) had no effect, and reactive blue 2 (a P2Y receptor antagonist) resulted in partial inhibition. The potency order of ATP analogs (2-MeSATP > ATP ⋙ UTP) suggested that P2Y₁ played a significant role in the cellular response to ATP. BzATP (a P2X₇ receptor agonist) induced a small increase in [Ca²⁺]_i, but α,β-meATP (a P2X_1,3 receptor agonist) had no effect. RT-PCR indicated that P2X_2,3,4,5,6,7 and P2Y_1,2,4,12,14 are expressed in acinar cells. In conclusion, the response of acinar cells to ATP is mediated by P2Y (especially P2Y₁) as well as by P2X purinoceptors.     

Novel trans-platinum complexes of the histone deacetylase inhibitor valproic acid; synthesis, in vitro cytotoxicity and mutagenicity

The first examples of Pt complexes of the well known anti-epilepsy drug and histone deacetylase inhibitor, valproic acid (VPA), are reported. Reaction of the Pt(II) am(m)ine precursors trans-[PtCl₂(NH₃)(py)] and trans-[PtCl₂(py)₂] with silver nitrate and subsequently sodium valproate gave trans-[Pt(VPA_−1H)₂(NH₃)(py)] and trans-[Pt(VPA_−1H)₂(py)₂], respectively. The valproato ligands in both complexes are bound to the Pt(II) centres via the carboxylato functionality and in a monodentate manner. The X-ray crystal structure of trans-[Pt(VPA_−1H)₂(NH₃)(py)] is described. Replacement of the dichlorido ligands in trans-[PtCl₂(py)₂] and trans-[PtCl₂(NH₃)(py)] by valproato ligands (VPA_−1H) to yield trans-[Pt(VPA_−1H)₂(py)₂] and trans-[Pt(VPA_−1H)₂(NH₃)(py)] respectively, significantly enhanced cytotoxicity against A2780 (parental) and A2780 cisR (cisplatin resistant) ovarian cancer cells. The mutagenicity of trans-[Pt(VPA_−1H)₂(NH₃)(py)] and trans-[Pt(VPA_−1H)₂(py)₂] was determined using the Ames test and is also reported.     

Two luminescent alkali-silver heterometallic sulfonates

Systematic survey on the reactions of silver nitrate with H₃Ssal ligand (H₃Ssal = 5-sulfo-salicylic acid) accompanying with different alkali metal ions under alkali conditions leads to two novel luminescent alkali-silver heterometallic sulfonates, [KAg(HSsal)(H₂O)₃]_n (1) with a 3-D structure constructed by [K₂O₁₀] binuclear units linking 1-D_∞¹[Ag₂(HSsal)₂] double chains, [NaAg(HSsal)(H₂O)₃]_n (2) with a 3-D structure constructed by the [Ag₂(HSsal)₂] dimers connecting 1-D_∞¹[NaO₆] chains, and also reveals the coordination strength of the alkali metal cations and Ag⁺ towards the sulfonate groups with K⁺ > Na⁺ > Ag⁺ > Li⁺ order. The two compounds show intense blue emissions in both solid state and water solution.     

Unconditional Confidence Interval for the Difference between Two Proportions

In applied statistics it is customary to have to obtain a one‐ or two‐tail confidence interval for the difference d = p₂ – p₁ between two independent binomial proportions. Traditionally, one is looking for a classic and non‐symmetric interval (with respect to zero) of the type d ∈ [δ_L;δ_U], d ≤ δ₀ or d ≥ δ₀. However, in clinical trials, equivalence studies, vaccination efficacy studies, etc., and even after performing the classic homogeneity test, intervals of the type |d| ≤ Δ₀ or |d| ≥ Δ₀, where Δ₀ > 0, may be necessary. In all these cases it is advisable to obtain the interval by inverting the appropriate test. The advantage of this procedure is that the conclusions obtained using the test are compatible with those obtained using the interval. The article shows how this is done using the new exact and asymptotic unconditional tests published. The programs for performing these tests may be obtained at URL http://www.ugr.es/~bioest/software.htm.     

Trans-pyridine tetraammine complexes of RuII and RuIII with N7-coordninated purine nucleosides

 The synthesis, spectroscopic, and electrochemical properties of trans-[L(Pyr)(NH₃)₄Ru^II/III] (Pyr=py, 3-phpy, 4-phpy, 3-bnpy, or 4-bnpy; L=H₂O, Guo, dGuo, 1MeGuo, Gua, Ino, or G⁷-DNA) are reported. As expected, the Pyr ligand slows DNA binding by trans-[(H₂O)(Pyr)(NH₃)₄Ru^II]²⁺ relative to [(H₂O)(NH₃)₅Ru^II]²⁺ and favors reduction of Ru^III by about 150 mV. The pyridine ligand also promotes the disproportionation of Ru^III to afford the corresponding complexes of Ru^II and, presumably, Ru^IV. For L=Ino, disproportionation follows the rate law: d[Ru^II]/dt=k ₀[Ru^III]+k ₁[OH^–][Ru^III], k ₀=(2.7±0.7)×10^–4s^–1 and k ₁=70±1 M^–1s^–1. Received: 11 May 1998 / Accepted: 3 March 1999     

On a Characterization of the Exponential Distribution by Weak Homoscedasticity of Record Values

A sequence {X_n, n≤1} of independent and identically distributed random values with continuous cumulative distribution function F(x) is considered. X_j is a record value of this sequence if X_j ≤ max (X₁, X₂, …, X_j?1). We define L(n)=min.(j!j>L(n?1.), X_j<X_L(n?1)), with L(0) = 1. Let Z_n=X_L(n)? X_L(n?1), n ≤ 1. We will show that the conditional variance of Z_n given X_L(n?1)=x does not depend on × if and only if F(x) is exponential.     

Observer design for differential-algebraic model of an aerobic culture of a recombinant yeast

The mathematical model of an aerobic culture of recombinant yeast presented in work by Zhang et al. (1997) is given by a differential-algebraic system. The classical nonlinear observer algorithms are generally based on ordinary differential equations. In this paper, first we extend the nonlinear observer synthesis to differential-algebraic dynamical systems. Next, we apply this observer theory to the mathematical model proposed in Zhang et al. (1997). More precisely, based on the total cell concentration and the recombinant protein concentration, the observer gives the online estimation of the glucose, the ethanol, the plasmid-bearing cell concentration and a parameter that represents the probability of plasmid loss of plasmid-bearing cells. Numerical simulations are given to show the good performances of the designed observer.Symbols C ₁ activity of pacing enzyme pool for glucose fermentation (dimensionless) - C ₂ activity of pacing enzyme pool for glucose oxidation (dimensionless) - C ₃ activity of pacing enzyme pool for ethanol oxidation (dimensionless) - E ethanol concentration (g/l) - G glucose concentration (g/l) - k _a regulation constant for (g glucose/g cell h^–1) - k _b regulation constant for (dimensionless) - k _c regulation constant for (g glucose/g cell h^–1) - k _d regulation constant for (dimensionless) - K _m1 saturation constant for glucose fermentation (g/l) - K _m2 saturation constant for glucose oxidation (g/l) - K _m3 saturation constant for ethanol oxidation (g/l) - L ( t) time lag function (dimensionless) - p probability of plasmid loss of plasmid-bearing cells (dimensionless) - P recombinant protein concentration (mg/g cell) - q _G total glucose flux culture time (g glucose/g cell h) - t culture time (h) - t _lag lag time (h) - X total cell concentration (g/l) - X ⁺ plasmid-bearing cell concentration (g/l) - Y ^F _{X / G} cell yield for glucose fermentation pathway (g cell/g glucose) - Y ^O _{X / G} cell yield for glucose oxidation pathway (g cell/g glucose) - Y _{X / E} cell yield for ethanol oxidation pathway (g cell/g ethanol) - Y _{E / X} ethanol yield for fermentation pathway based on cell mass (g ethanol·g cell) - ₂ glucoamylase yield for glucose oxidation (units/g cell) - ₃ glucoamylase yield for ethanol oxidation (units/g cell) - µ₁ specific growth rate for glucose fermentation (h^–1) - µ₂ specific growth rate for glucose oxidation (h^–1) - µ₃ specific growth rate for ethanol oxidation (h^–1) - µ_1max maximum specific growth rate for glucose fermentation (h^–1) - µ_2max maximum specific growth rate for glucose oxidation (h^–1) - µ_3max maximum specific growth rate for ethanol oxidation (h^–1)     

Microcalorimetric Study of <Emphasis Type="Italic">Tetrahymena</Emphasis> Growth Affected by Copper(II) Complexes

By means of microcalorimetry, the effect of four copper(II) complexes on Tetrahymena growth was investigated. The extent and duration of the inhibitory effect on the metabolism, judged by the rate constant, k, and the half inhibition concentration, IC₅₀, varied with the different complexes. The results showed that the half inhibition concentrations IC₅₀ of CuCl₂, (C₉H₆NO)₂Cu and [Cu(phen)₂]Cl₂⋅6H₂O were 9.9 × 10⁻⁴, 2.0 × 10⁻⁴, and 2.6 × 10⁻⁴ mol/L, respectively. The sequence of antibiotic activity of these three complexes was: (C₉H₆NO)₂Cu > [Cu(phen)₂]Cl₂⋅6H₂O > CuCl₂. The growth rate constants of [Cu(phen)₃]Cl₂⋅6H₂O did not change obviously with the increase of concentrations, but [Cu(phen)₃]Cl₂⋅6H₂O also can prolong the time of Tetrahymena growth.     

Polyoxometalate/laccase-mediated oxidative polymerization of catechol for textile dyeing

The synergistic effect between polyoxometalates (POMs), namely K₅[SiW₁₁V^VO₄₀]·11H₂O and H₅[PMo₁₀V^V ₂O₄₀]·13H₂O and laccase from ascomycete Myceliophthora thermophila has been employed for the first time in oxidative polymerization of catechol. Such a laccase-mediator system allowed the formation of a relatively high molecular weight polycatechol as confirmed by size exclusion chromatography and electrospray ionization mass spectrometry (ESI-MS) (3990 Da when using K₅[SiW₁₁V^VO₄₀]·11H₂O and 3600 Da with H₅[PMo₁₀V^V ₂O₄₀]·13H₂O). The synthesized polymers were applied as dyes for the dyeing of flax fabrics. The color intensity of flax fabrics colored with polymer solutions was evaluated by diffuse reflectance spectrophotometry via k/s measurements (+10% of fixation ratio). A new synthetic process allowed a dyeing polymer, provided upon flax coloration, better color fixation and color resistance when compared to that obtained by conventional synthesis with laccase solely or with addition of organic mediator (1-hydroxybenzotriazole).     

Formulation of Dacarbazine-loaded Cubosomes—Part II: Influence of Process Parameters

The purpose of this study was to investigate the combined influence of three-level, three-factor variables on the formulation of dacarbazine (a water-soluble drug) loaded cubosomes. Box–Behnken design was used to obtain a second-order polynomial equation with interaction terms to predict response values. In this study, the selected and coded variables X ₁, X ₂, and X ₃ representing the amount of monoolein, polymer, and drug as the independent variables, respectively. Fifteen runs of experiments were conducted, and the particle size (Y ₁) and encapsulation efficiency (Y ₂) were evaluated as dependent variables. We performed multiple regression to establish a full-model second-order polynomial equation relating independent and dependent variables. A second-order polynomial regression model was constructed for Y ₁ and confirmed by performing checkpoint analysis. The optimization process and Pareto charts were obtained automatically, and they predicted the levels of independent coded variables X ₁, X ₂, and X ₃ (−1, 0.53485, and −1, respectively) and minimized Y ₁ while maximizing Y ₂. These corresponded to a cubosome formulation made from 100 mg of monoolein, 107 mg of polymer, and 2 mg with average diameter of 104.7 nm and an encapsulation efficiency of 6.9%. The Box–Behnken design proved to be a useful tool to optimize the particle size of these drug-loaded cubosomes. For encapsulation efficiency (Y ₂), further studies are needed to identify appropriate regression model.     

Intracellular signalling by nucleotide receptors in PC12 pheochromocytoma cells

The effect of extracellular ATP was studied in PC12 cells, a neurosecretory line that releases ATP. The addition of micromolar concentrations of ATP to PC12 cells evoked a transient increase in the cytosolic free Ca²⁺ concentration ([Ca²⁺]_i), as measured with the Ca²⁺-dye fura 2. AMP and adenosine were without effect, ruling out the involvement of P₁ receptors in mediating this response. The increase in [Ca²⁺]_i was reduced in calcium-free media and virtually eliminated by the addition of EGTA, suggesting that calcium influx was the primary response initiated by extracellular ATP. Nucleotide triphosphates such as UTP and, to a lesser degree, ITP also evoked an increase in [Ca²⁺]_i while GTP and CTP had little effect. In order to identify the receptor subtype mediating this response, the efficacy of ATP and ATP cogeners was assessed. The rank order potency was ATP > adenosine 5′-[γ-thio]triphosphate > ADP > 2-methylthioadenosine triphosphate (2-MeSATP) ～ adenosine 5′-[β-thio]diphosphate ? adenosine 5′-[αβ-methylene] triphosphate, adenosine 5′-[βγ-imido]triphosphate. This profile is not characteristic of either the P_2X or the conventional P_2Y receptors. The Ca²⁺ response exhibited desensitization to ATP that was dependent on the extracellular metabolism of ATP. UTP was equally effective in desensitizing the response. ATP, UTP, ITP, and to a much lesser extent 2MeSATP increased inositol phosphate production in a dose-dependent manner, suggesting receptor coupling to phosphatidylinositol-specific phospholipase C. These data are consistent with the view that PC12 cells express a class of non-P_2Y nucleotide receptors (P_2N) that mediate calcium influx and the accumulation of inositol phosphates. © 1993 Wiley-Liss, Inc.     

Optimization of Hydrogels for Transdermal Delivery of Lisinopril by Box–Behnken Statistical Design

The aim of this study was to investigate the combined influence of three independent variables on the permeation kinetics of lisinopril from hydrogels for transdermal delivery. A three-factor, three-level Box–Behnken design was used to optimize the independent variables, Carbopol 971 P (X ₁), menthol (X ₂), and propylene glycol (X ₃). Fifteen batches were prepared and evaluated for responses as dependent variables. The dependent variables selected were cumulative amount permeated across rat abdominal skin in 24 h (Q ₂₄; Y ₁), flux (Y ₂), and lag time (Y ₃). Aloe juice has been first time investigated as vehicle for hydrogel preparation. The ex vivo permeation study was conducted using Franz diffusion cells. Mathematical equations and response surface plots were used to relate the dependent and independent variables. The regression equation generated for the cumulative permeation of LSP in 24 h (Q ₂₄) was Y ₁ = 1,443.3–602.59X ₁ + 93.24X ₂ + 91.75X ₃ − 18.95X ₁ X ₂ – 140.93X ₁ X ₃ – 4.43X ₂ X ₃ – 152.63X ₁ ² – 150.03X₂ ² − 213.9X ₃ ². The statistical validity of the polynomials was established, and optimized formulation factors were selected by feasibility and grid search. Validation of the optimization study with 15 confirmatory runs indicated high degree of prognostic ability of response surface methodology. The use of Box–Behnken design approach helped in identifying the critical formulation parameters in the transdermal delivery of lisinopril from hydrogels.