Log Pn Research Articles

Effect of solutes structure and pH on the n-octanol/water partition coefficient of ionizable organic compounds.

Liquid-liquid partition coefficient is a useful tool to predict biological and environmental fate of organic compounds, for example bioaccumulation or toxicity of lipophilic contaminants. Conversely, the partitioning of ionizable compounds is poorly studied in contrast to that of neutral compounds. Yet, such topic deserves attention, since numerous organic contaminants are ionizable as well as their degradation products. Hence, the contribution of charged species has to be considered in order to model accurately the mass balance or partition of ionizable compounds. In this context, we investigated the liquid-liquid partition of 13 ionizable compounds (oxalic acid, histidine, benzimidazole, etc.), covering various classes of compounds (carboxylic acids, amino-acids, etc.). The n-octanol/water partition coefficient was measured from pH 1 up to 13, in order to fully gather the distribution of both neutral and charged species. Empirical models describing these results are reviewed and partition parameters adjusted for charged species. The study of benzoic acid derivatives (benzoic, salicylic, ortho- and iso-phthalic acids) provides insights on the influence of chemical groups on the partitioning. In the case of tryptophan, the use of acid/base microconstants allowed to estimate the partition of both the zwitterion and its neutral tautomer. Despite a major zwitterionic form (log PZ(tryptophan)=-1.58±0.30), the minor but neutral tautomer (log PN(tryptophan)=+0.03±0.30) drives the partition equilibrium. Overall, the provided data may be useful to assess the retention of contaminants, its dependency on pH and salinity variations, and thus understanding their environmental fate. Such data may also be useful as well for molecular simulation involving solvation of organic ions in aqueous and non-aqueous solvents.

Multiple linear regression models for predicting the n‑octanol/water partition coefficients in the SAMPL7 blind challenge.

A multiple linear regression model called MLR-3 is used for predicting the experimental n-octanol/water partition coefficient (log PN) of 22 N-sulfonamides proposed by the organizers of the SAMPL7 blind challenge. The MLR-3 method was trained with 82 molecules including drug-like sulfonamides and small organic molecules, which resembled the main functional groups present in the challenge dataset. Our model, submitted as “TFE-MLR”, presented a root-mean-square error of 0.58 and mean absolute error of 0.41 in log P units, accomplishing the highest accuracy, among empirical methods and also in all submissions based on the ranked ones. Overall, the results support the appropriateness of multiple linear regression approach MLR-3 for computing the n-octanol/water partition coefficient in sulfonamide-bearing compounds. In this context, the outstanding performance of empirical methodologies, where 75% of the ranked submissions achieved root-mean-square errors < 1 log P units, support the suitability of these strategies for obtaining accurate and fast predictions of physicochemical properties as partition coefficients of bioorganic compounds.Supplementary InformationThe online version contains supplementary material available at 10.1007/s10822-021-00409-2.

The Order of Edwards and Montgomery Curves

The Elliptic Curve Digital Signature Algorithm (ECDSA) is the elliptic curve analogue of the Digital Signature Algorithm (DSA) [2]. It is well known that the problem of discrete logarithm is NP-hard on group on elliptic curve (EC) [5]. The orders of groups of an algebraic affine and projective curves of Edwards [3, 9] over the finite field Fpn is studied by us. We research Edwards algebraic curves over a finite field, which are one of the most promising supports of sets of points which are used for fast group operations [1]. We construct a new method for counting the order of an Edwards curve [F ] d p E over a finite field Fp . It should be noted that this method can be applied to the order of elliptic curves due to the birational equivalence between elliptic curves and Edwards curves. The method we have proposed has much less complexity 22 O p log p at not large values p in comparison with the best Schoof basic algorithm with complexity 8 2 O(log pn ) , as well as a variant of the Schoof algorithm that uses fast arithmetic, which has complexity 42O(log pn ) , but works only for Elkis or Atkin primes. We not only find a specific set of coefficients with corresponding field characteristics for which these curves are supersingular, but we additionally find a general formula by which one can determine whether a curve [F ] d p E is supersingular over this field or not. The symmetric of the Edwards curve form and the parity of all degrees made it possible to represent the shape curves and apply the method of calculating the residual coincidences. A birational isomorphism between the Montgomery curve and the Edwards curve is also constructed. A oneto- one correspondence between the Edwards supersingular curves and Montgomery supersingular curves is established. The criterion of supersingularity for Edwards curves is found over F pn .

Prediction of pH-Dependent Hydrophobic Profiles of Small Molecules from Miertus-Scrocco-Tomasi Continuum Solvation Calculations.

Hydrophobicity is a key physicochemical descriptor used to understand the biological profile of (bio)organic compounds as well as a broad variety of biochemical, pharmacological, and toxicological processes. This property is estimated from the partition coefficient between aqueous and nonaqueous environments for neutral compounds (PN) and corrected for the pH-dependence of ionizable compounds as the distribution coefficient (D). Here, we have extended the parametrization of the Miertus-Scrocco-Tomasi continuum solvation model in n-octanol to nitrogen-containing heterocyclic compounds, as they are present in many biologically relevant molecules (e.g., purines and pyrimidines bases, amino acids, and drugs), to obtain accurate log PN values for these molecules. This refinement also includes solvation calculations for ionic species in n-octanol with the aim of reproducing the experimental partition of ionic compounds (PI). Finally, the suitability of different formalisms to estimate the distribution coefficient for a wide range of pH values has been examined for a set of small acidic and basic compounds. The results indicate that in general the simple pH-dependence model of the ionizable compound in water suffices to predict the partitioning at or around physiological pH. However, at extreme pH values, where ionic species are predominant, more elaborate models provide a better prediction of the n-octanol/water distribution coefficient, especially for amino acid analogues. Finally, the results also show that these formalisms are better suited to reproduce the experimental pH-dependent distribution curves of log D for both acidic and basic compounds as well as for amino acid analogues.

Automated potentiometric titrations in KCl/water-saturated octanol: method for quantifying factors influencing ion-pair partitioning.

The knowledge base of factors influencing ion pair partitioning is very sparse, primarily because of the difficulty in determining accurate log PI values of desirable low molecular weight (MW) reference compounds. We have developed a potentiometric titration procedure in KCl/water-saturated octanol that provides a link to log PI through the thermodynamic cycle of ionization and partitioning. These titrations have the advantage of being independent of the magnitude of log P, while maintaining a reproducibility of a few hundredths of a log P in the calculated difference between log P neutral and log P ion pair (diff (log PN − I)). Simple model compounds can be used. The titration procedure is described in detail, along with a program for calculating pKa′′ values incorporating the ionization of water in octanol. Hydrogen bonding and steric factors have a greater influence on ion pairs than they do on neutral species, yet these factors are missing from current programs used to calculate log PI and log D. In contrast to the common assumption that diff (log PN − I) is the same for all amines, they can actually vary more than 3 log units, as in our examples. A major factor affecting log PI is the ability of water and the counterion to approach the charge center. Bulky substituents near the charge center have a negative influence on log PI. On the other hand, hydrogen bonding groups near the charge center have the opposite effect by lowering the free energy of the ion pair. The use of this titration method to determine substituent ion pair stabilization values (IPS) should bring about more accurate log D calculations and encourage species-specific QSAR involving log DN and log DI. This work also brings attention to the fascinating world of nature’s highly stabilized ion pairs.

On possible growths of arithmetical complexity

The arithmetical complexity of infinite words, defined by Avgustinovich, Fon-Der-Flaass and the author in 2000, is the number of words of length n which occur in the arithmetical subsequences of the infinite word. This is one of the modifications of the classical function of subword complexity, which is equal to the number of factors of the infinite word of length n. In this paper, we show that the orders of growth of the arithmetical complexity can behave as many sub-polynomial functions. More precisely, for each sequence u of subword complexity f u (n) and for each prime p > 3 we build a Toeplitz word on the same alphabet whose arithmetical complexity is a(n) = Θ(nf u ([log pn ])).

The Lipophilicity Behavior of Three Catechol-O-methyltransferase (COMT) Inhibitors and Simple Analogues

The ionization and lipophilicity properties of the second-generation catechol-O-methyltransferase (COMT) inhibitors entacapone (1), nitecapone (2), and tolcapone (3) which share the same nitrocatechol structure but have remarkably different pharmacokinetic profiles are investigated to identify relationships between some of these physicochemical parameters and the blood-brain-barrier (BBB) passage. In addition, the lipophilicity behavior of the simpler, structurally related analogues 4–11 is studied. Combined descriptors such as Δlog P (difference between log P in two different solvent systems) and diff(log PN−I) (difference between log P of two different electrical forms of a given solute in the same system) provide insight into inter- and intramolecular interactions characteristic of the analyzed compounds.

Early full blood count and severity of disease in neonates with necrotizing enterocolitis.

Thrombocytopaenia occurs during necrotizing enterocolitis (NEC), and nadir platelet count is associated with extent of disease. In paediatric meningococcal disease, the product of neutrophil and platelet count at admission is prognostically useful. We therefore aimed to determine whether the first full blood count (FBC) after diagnosis of NEC is useful as a score for poor outcome and severity of disease. Between 1987 to 2001, neutrophils (N), platelets (P) and their product (PN) was available in 187 neonates treated for NEC at our institution. Neonates with NEC were grouped according to the extent of disease (no gangrene, focal, multifocal and pan-intestinal). Data were not normally distributed so Mann-Whitney U test or analysis of variance (ANOVA) on logged data were used ( p<0.05 was considered significant). Receiver operating characteristics (ROC) curves were used to examine the relationship between specificity and sensitivity. A perfect test would have an ROC curve area of 1. Initial P count and PN product of non-survivors were both significantly lower than in survivors ( p<0.0001), whereas N was not different ( p<0.08). Low Log(10)PN was significantly associated with greater extent of disease (ANOVA; no gangrene vs multifocal, p<0.01, vs panintestinal, p<0.0005), suggesting that the initial FBC could be prognostically useful. Area under the ROC survival curve for neutrophils was 0.58, for platelets 0.75 and for PN product 0.71; thus, although no test performed extremely well, initial platelet count and NP product could be useful in evaluating disease severity in neonates with NEC and for further monitoring.

Contacts in self-avoiding walks and polygons

We prove several results concerning the numbers of n-edge self-avoiding polygons and walks in the lattice Zd which had previously been conjectured on the basis of numerical results. If the number of n-edge self-avoiding polygons (walks) with k contacts is pn(k) (cn(k)) then we prove that κ0 ≡ limn→∞ n-1 log pn(k) = limn→∞ n-1 log cn(k) exists for all fixed k and is independent of k. For polygons in Z2, we prove that there exist two positive functions B1 and B2, independent of n but depending on k, such that B1nkpn(0) ≤ pn(k) ≤ B2nkpn(0) for fixed k and n large. Also, provided the limit exists, we prove that 0 < limn→∞ kn/n < 1. In addition, we consider the number of polygons with a density of contacts, i.e. k = αn, and show that the corresponding connective constant, κ(α), exists and is a concave function of α. For d = 2, we prove that limα→0+ κ(α) = κ0 and the right derivative of κ(α) at α = 0 is infinite.

On Monotone Almost (P, μ) - u. d. Mod 1 Sequence

Using the result of almost u.d. mod 1 and G. Hoheisel [6] and Emdös's result, Akiyama [1] gave a different proof of the Erdös and Turán result [4], i.e., Δ2 log pn changes its sign infinitely many times, where pn is the n-th prime number and Δ2 f(n) = Δ(Δf(n)), Δf(n) = f(n + 1)-f(n). In this paper, we show the neceasary condition for monotone almost uniform distribution mod 1. We give Fejér's type theorem for almost uniform distribution mod 1 and give a similar result of Niederreiter [8]. Also we obtain the converse of its result with some conditions. As an application, we give a simple proof [1] of Erdös and Turán's result using Erdös's result [cf. 3, 9, 10, 11, and 21. Also we obtain the condition of P(n) that Δ2 log P(n) changes its sign infinitely many times.

Almost Uniform Distribution Modulo 1 and the Distribution of Primes

Let (an), n = 1, 2, ... be a sequence of real numbers which is related with number theoretic functions such as Pn, the n-th prime. We study the distribution of the fractional parts of (an) using the concept of "almost uniform distribution" defined in [9]. Then we can show a generalization of the results of [2] on the convex property of log Pn. The method may be extended as well to other oscillation problems of number theoretical interest.

Insight into the lipophilicity of the aromatic N-oxide moiety.

A systematic study to assess the influence of N-oxygenation on the lipophilicity of aromatic weak bases was performed. The methods used were experimental (CPC and shake-flask techniques) and computational (AMI semi-empirical method). The intrinsic increment in the log P(oct) system for an oxygen atom added to form an aromatic N-oxide, designated as diff(log PN(O) -N), was -1.91, but the presence of para-substituents markedly affected this value. The good linear relationship (r2 = 0.92) between diff(log PN(O) - N), and the electronic density on the oxygen atom suggests that H-bond acceptor basicity is the main structural factor responsible for the variations in lipophilicity of aromatic N-oxides. Partition coefficients of aromatic N-oxides in dodecane/buffer and chloroform/buffer systems also support this hypothesis. The solvent-dependent polarity of the N-oxide moiety is mainly due to its marked H-bond acceptor basicity.

Schur properties of convolutions of exponential and geometric random variables

Convolutions of random variables which are either exponential or geometric are studied with respect to majorization of parameter vectors and the likelihood ratio ordering (⩾lr) of random variables. Let Xλ, …, Xλn be independent exponential random variables with respective hazards λi (means 1/λi), i = 1 …, n. Then if λ = (λ1, …, λn) ⩾m (λ1′, …, λn′) = λ′, it follows that Σi = 1n Xλ ⩾lr Σi = 1n Xλ′1. Similarly if Xp1, …, Xpn are independent geometric random variables with respective parameters p1, …, pn, then p = (p1, …, pn) ⩾m(p′1, …, p′n) = p′ or log p = (log p1, …, log pn) ⩾ m (log p1, …, log pn) = log p′ implies Σi = 1n Xpl ⩾ lr Σi = 1n XP′1. Applications of these results are given yielding convenient upper bounds for the hazard rate function of convolutions of exponential (geometric) random variables in terms of those of gamma (negative binomial) distributions. Other applications are also given for a server model, the range of a sample of i.i.d. exponential random variables, and the duration of a multistate component performing in excess of a given level.

The dimension of random ordered sets

AbstractLet P = (X, &lt;) be a finite ordered set and let |P| denote the cardinality of the universe X. Also let Δ(P) denote the maximum degree of P, i.e., the maximum number of points comparable to any one point of P. Füredi and Kahn used probabilistic methods to show that the dimension of P satisfies dim(P)≦ c1 Δ(P)log|P| and dim(P) ≦ c2Δ(P) log2Δ(P) where c, and c2 are positive absolute constants. In this article, we consider the probability space Ω(n, p) of bipartite ordered sets having n minimal elements and n maximal elements, where the events that any minimal element is less than any maximal element are independently distributed and each has probabilityp =p(n). We show that for every ϵ &gt;0, there exist δ, c &gt; 0 so that: (1) if (log1+ϵn)/n&lt;p &lt; 1/log n, then dim(P)∈ Ωpn log pn for almost all P∈ Δ(n, p); and (2) if 1/log n ≦ &lt; 1 − n−1+ϵ, then dim(P) &gt;n‐ cnlp log n for almost all P ∈Ω(n, p). The first inequality is best possible up to the value of the constant δ when p &gt; (log2+en)/n. As to the accuracy of the second inequality, we have the trivial upper bound dim(P)≦n for all P∈Ω(n, p). We then develop a nontrivial upper bound which holds for almost all P ∈Ω(n, p), when p ≧ 1 /log n. This upper bound has the same form as the lower bound when p is constant. We also study the space ℒ︁(n) of all labelled ordered sets on n points and show that there exist positive constants c1, c2 so that n/4 ‐ c1n/log n &lt; dim(P) &lt;c2 n/4 ‐ c2n/log n for almost all P ∈ ℒ︁(n).

Magnetic braking, ambipolar diffusion, cloud cores, and star formation - Natural length scales and protostellar masses

view Abstract Citations (187) References (79) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Magnetic Braking, Ambipolar Diffusion, Cloud Cores, and Star Formation: Natural Length Scales and Protostellar Masses Mouschovias, Telemachos Ch. Abstract Magnetic braking is essential for cloud contraction and star formation. Ambipolar diffusion is unavoidable in self-gravitating, magnetic clouds and leads to single-stage (as opposed to hierarchical) fragmentation (or core formation) and protostar formation. Magnetic forces dominate thermal-pressure and centrifugal forces over scales comparable to molecular cloud radii. Magnetic support of molecular clouds and the imperfect collisional coupling between charged and neutral particles introduce a critical magnetic length scale (λM,cr = 0.62υAτff) and an Alfvén length scale ((λA = πυAτni), respectively, in the problem which together with a critical thermal length scale (λT,cr = 1.09Caτff) explain naturally the formation of fragments (or cores) in otherwise quiescent clouds and determine the sizes and masses of these fragments during the subsequent stages of contraction. (The quantity υA is the Alfvén speed, τni the mean neutral-ion collision time, Ca the adiabatic speed of sound, and τff the free4all time scale.) Numerical calculations based on new adaptive-grid techniques follow the formation of fragments by ambipolar diffusion and their subsequent collapse up to an enhancement in central density above its initial equilibrium value by a factor ≃106 with excellent spatial resolution. The results confirm the existence and relevance of the three length scales and extend the analytical understanding of fragmentation and star formation derived from them. The ultimately bimodal opposition to gravity (by magnetic forces in the envelope and by thermal-pressure forces in the core) introduces a break in the slope of the log pn -log r profile. The relation Bc ∞ pkc between the magnetic field strength and the gas density in cloud cores holds with K = 0.4 - 0.5 even in the presence of ambipolar diffusion up to densities ∼109 cm-3 for a wide variety of clouds. The value K ≃ ½ is fairly typical. At the late stages of evolution, for example, at a central density of about 3 × 108 cm-3, a typical core is relatively uniform, contains 0.1 Msun and a magnetic field ≃ 3 mG, and is surrounded by a spatially rapidly decreasing, highly nonspherical (disklike) density distribution. The amount of mass available for accretion onto the compact core is limited by magnetic forces, and is typically ≃1 Msun. These results are built into the detailed scenario for star formation described recently elsewhere. Publication: The Astrophysical Journal Pub Date: May 1991 DOI: 10.1086/170035 Bibcode: 1991ApJ...373..169M Keywords: Ambipolar Diffusion; Interstellar Magnetic Fields; Interstellar Matter; Magnetic Clouds; Space Plasmas; Star Formation; Computational Astrophysics; Molecular Clouds; Protostars; Stellar Mass; diffusion; hydromagnetics; interstellar: magnetic fields; interstellar: matter; Astrophysics; DIFFUSION; HYDROMAGNETICS; INTERSTELLAR: MAGNETIC FIELDS; INTERSTELLAR: MATTER; PLASMAS; STARS: FORMATION full text sources ADS |

Amiodarone Partitioning with Phospholipid Bilayers and Erythrocyte Membranes

The apparent partition coefficient (P) of amiodarone between aqueous buffer and lipid vesicles or erythrocyte ghosts was determined by equilibrium distribution using [125I]amiodarone as a tracer. The lipid vesicles consisted of total lipids extracted from erythrocyte or of egg phosphatidylcholine alone or mixed with a varying amount of stearic acid, phosphatidylethanolamine, sphingomyelin, phosphatidylserine, or cholesterol. All the conditions yielded a similar value of P (P≅ 17,000). The log value of the partition coefficient of the neutral form of the drug is log PN=5.95. The value of the extrapolated 1 -octanol–buffer partition coefficient is log PN,oct=6.66. Partition coefficient measurements on erythrocyte ghosts suggested that amiodarone partitioned to a similar extent in the protein and lipid content of the membrane.

Early pulmonary granulocyte recruitment in response to Streptococcus pneumoniae.

Although polymorphonuclear leukocytes (PMN) are a conspicuous histologic feature of clinical and experimental pneumococcal pneumonia, neither the mechanism nor the magnitude of recruitment of these cells to the lung following lesser pneumococcal challenge is known. We have, therefore, investigated the early process of recruitment of PMN to alveolar spaces after pulmonary inoculation of Streptococcus pneumoniae in doses less than those causing pneumonia. We injected Balb/c mice with water and varying inoculums of pneumococci via an endobronchial catheter. Bronchoalveolar lavage (BAL) was performed on the inoculated lung at 0, 2, or 4 h after injection. Cellular response was measured and chemotactic activity was assayed on BAL supernatants at each time interval using the migration of human PMN through 3-micron filters in modified Boyden chambers by the leading front techniques. The BAL of normal and control animals (inoculum of sterile water only used for the control animals) yielded 5.03 +/- 1.51 X 10(2) and 0.17 +/- 0.04 X 10(5) PMN, respectively. The PMN recruitment at 4 h as a function of pneumococcal inoculum was described by the following equation: log PMN = 0.751 log Pn + 1.119 (r2 = 0.82, p less than 0.001). The PMN were, therefore, recruited in a dose-dependent manner. That recruitment may be caused by chemotactic substance(s) was suggested by the significant correlation between the PMN response and the distance of in vitro migration: log PMN = 0.057 micron + 0.52 (r = 0.77, p less than 0.005). We have defined quantitatively the recruitment of PMN to the lung after pneumococcal challenge.(ABSTRACT TRUNCATED AT 250 WORDS)

Decomposition pressure of YN and UN-YN solid solutions

Decomposition pressure-temperature relations have been determined experimentally for YN and U 1− x Y x N ( x = 0.25, 0.5, 0.75). The results are: log PN 2[ YN] = 12.8 − 3.51 × 10 4/ T, 2400–2750 K; log pN 2[ U 0.25 Y 0.75 N] = 12.6 − 3.54 × 10 4/ T, 2450–2800 K; log pN 2[ U 0.5 Y 0.5 N] = 12.3 − 3.61 × 10 4/ T, 2550–2850 K; log pN 2[ U 0.75 Y 0.25 N] = 12.1 − 3.65 × 10 4/ T, 2600–3000 K. These results agree well with the theoretical equation: log pN 2[ U 1− x Y x N] = (1 − x) log PN 2 [ UN] + x logPN 2[ YN], which may be derived from thermodynamic considerations of the decomposition reaction of U 1− x Y x N based on the reaction: U 1−xY xN(s) = U 1−xY x(1) + 1 2 N 2(g) . Statistical thermodynamic calculations based on the linearity of the isotherms in the log PN 2[ U 1− x Y x N] vs. YN mole fraction show that the interaction between U and N and that between Y and N in U 1− x Y x N may be attractive, having the same order of magnitude.

Equilibrium nitrogen pressures and thermodynamic properties of uranium sesquinitride

Equilibrium nitrogen pressures over the two-phase region UN + U 2N 3 were measured between 750° and 1050 °C. Nitrogen pressures were also determined in the single-phase region of U 2N 3. The U-rich phase boundary was obtained as 1.542 of the N/U atom ratio from the tensiometric measurement. The decomposition pressure of U 2N 3 was given by log pN 2 (atm) = 7.201 −11736/ T. The standard heat of the decomposition, UN 1.54 = UN + 0.27 N 2, was calculated to be ΔH 0 298=16.74 kcal/mole.

On a theorem of Erdös and Turán

changes its sign an infinite number of times. The aim of the present paper is to prove an improvement of this theorem. It shall be proved that the total curvature of the polygonal line having the vertices n+i log Pn (n = 1, 2, 3, ***) in the complex z-plane is infinite. This implies that Pnu?lPn-1 -p2 changes its sign an infinite number of times, but our result also contains some quantitative information regarding the oscillations of the sequence Pn+IPPn-lp.2 The total curvature G of a finite polygonal line situated in the complex z-plane may be defined as follows: