The Nature of Conformational Correlations in α- and β-Anomers of Nucleic Acid Components in Aqueous Solution by Nuclear Magnetic Resonance

Abstract

The solution distribution of combinations of the sugar ring puckering domains, C2′endo(S), C3′endo(N), and C4′-C5′ rotamers, +sc(g⁺), ap(t), -sc(g^?), in α and β-anomers in ribo- and deoxyribo- pyrimidine nucleic acid components can be determined from vicinal coupling constants (M. Remin, J. Biomol. Str. Dyn. 2, 211 (1984). A general correlation pattern with a conformational constant λ, reflecting an intrinsic physical property of the sugar - side chain ensemble, is developed and expressed in terms of four principles:

I) The +sc rotamer contributes to the C3′endo population to a higher extent (1 - Y_t) than to C2′endo,(l-Y_t-Y_g-/X_s).

II) The ap rotamer contributes to both C2′endo and C3′endo populations to the same extent (Y_t).

III) The—sc rotamer contributes only to the C2′endo population, (Y_g-/X_s).

IV) The molar fractions X_s, Y_t and Y_g- of conformations C2′endo, ap and—sc, respectively, are strongly correlated, λ = (Y_g-/X_s)/Y_t ≈ 0.5, and therefore Y_t is a basic variable parameter which determines all others in the correlation pattern.

In α-anomers, regardless of the type and conformation of the sugar ring and base, the molar fraction Y_t = 0.37 ± 0.02. This finding means that different α-anomers show one correlation pattern free of the influence of the base. In β-anomers, structure and conformation of the base are important factors which modulate (through Y_t) the correlation pattern, conserving its fundamental features. Y_t is considerably increased by a syn-oriented pyrimidine base, but decreases when the base is anti. The transition from anti to syn orientation of the base is followed by destabilization of (C2′endo, +sc) in favor of (C3′endo, ap). The principles of conformational correlations rationalize a variety of correlations observed in the past.     

Confidence intervals for demographic projections based on products of random matrices

This work is concerned with the growth of age-structured populations whose vital rates vary stochastically in time and with the provision of confidence intervals. In this paper a model Y_{t + 1}(ω) = X_{t + 1}(ω)Y_t(ω) is considered, where Y_t is the (column) vector of the numbers of individuals in each age class at time t, X is a matrix of vital rates, and ω refers to a particular realization of the process that produces the vital rates. It is assumed that {X_i} is a stationary sequence of random matrices with nonnegative elements and that there is an integer n₀ such that any product X_{j + n0} ··· X_{j + 1}X_j has all its elements positive with probability one. Then, under mild additional conditions, strong laws of large numbers and central limit results are obtained for the logarithms of the components of Y_t. Large-sample estimators of the parameters in these limit results are derived. From these, confidence intervals on population growth and growth rates can be constructed. Various finite-sample estimators are studied numerically. The estimators are then used to study the growth of the striped bass population breeding in the Potomac River of the eastern United States.     

A Semiparametric Estimator of the Crossing Point in the Two‐Sample Linear Shift Function: Application to Crossing Lifetime Distributions

Let X and Y be two random variables with continuous distribution functions F and G. Consider two independent observations X₁, … , X_m from F and Y₁, … , Y_n from G. Moreover, suppose there exists a unique x* such that F(x) > G(x) for x < x* and F(x) < G(x) for x > x* or vice versa. A semiparametric model with a linear shift function (Doksum, 1974) that is equivalent to a location‐scale model (Hsieh, 1995) will be assumed and an empirical process approach (Hsieh, 1995) is used to estimate the parameters of the shift function. Then, the estimated shift function is set to zero, and the solution is defined to be an estimate of the crossing‐point x*. An approximate confidence band of the linear shift function at the crossing‐point x* is also presented, which is inverted to yield an approximate confidence interval for the crossing‐point. Finally, the lifetime of guinea pigs in days observed in a treatment‐control experiment in Bjerkedal (1960) is used to demonstrate our procedure for estimating the crossing‐point. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The convergence in distribution of some simple epidemics

A group of n susceptible individuals exposed to a contagious disease isconsidered. It is assumed that at each point in time one or more susceptible individuals can contract the disease. The progress of this simple batch epidemic is modeled by a stochastic process X_n(t), t[0, ∞), representing the number of infectiveindividuals at time t. In this paper our analysis is restricted to simple batch epidemics with transition rates given by [α²X_n(t){n −X_n(t) +X_n(0)}]^1/2, t[0, ∞), α(0, ∞). This class of simple batch epidemics generalizes a model used and motivated by McNeil (1972) to describe simple epidemic situations. It is shown for this class of simple batch epidemics, that X_n(t), with suitable standardization, converges in distribution as n→∞ to a normal random variable for all t(0, t₀), and t₀ is evaluated.     

Cumulative Damage Survival Models for the Randomized Complete Block Design

A continuous time discrete state cumulative damage process {X(t), t ≥ 0} is considered, based on a non‐homogeneous Poisson hit‐count process and discrete distribution of damage per hit, which can be negative binomial, Neyman type A, Polya‐Aeppli or Lagrangian Poisson. Intensity functions considered for the Poisson process comprise a flexible three‐parameter family. The survival function is S(t) = P(X(t) ≤ L) where L is fixed. Individual variation is accounted for within the construction for the initial damage distribution {P(X(0) = x) | x = 0, 1, …,}. This distribution has an essential cut‐off before x = L and the distribution of L – X(0) may be considered a tolerance distribution. A multivariate extension appropriate for the randomized complete block design is developed by constructing dependence in the initial damage distributions. Our multivariate model is applied (via maximum likelihood) to litter‐matched tumorigenesis data for rats. The litter effect accounts for 5.9 percent of the variance of the individual effect. Cumulative damage hazard functions are compared to nonparametric hazard functions and to hazard functions obtained from the PVF‐Weibull frailty model. The cumulative damage model has greater dimensionality for interpretation compared to other models, owing principally to the intensity function part of the model.     

On the difference between gauss-markov and least squares estimates

For the usual full rank univariate least squares regression model y = XB + e, E(e) = 0, E(ee) = A, the equality of the estimates occurs when B-B^* = (XA^?1X)^?1XA^-1y-(XX)^?1Xy = 0. A necessary and sufficient condition for this equality is that A has some N - k + 1 roots equal where N is the rank of A and k is the rank of X.     

Speciation of phytate ion in aqueous solution. Non covalent interactions with biogenic polyamines

Abstract

The noncovalent interactions of phytate (Phy^6-) with biogenic amines were studied potentiometrically in aqueous solution, at t= 25°C. Several species are formed in the different H+-Phy^6--amine (A) systems, which have the general formula A_p(Phy)H_q^(12-q)-, with p ≤ 3 and 6 ≤ q ≤ 10. The stability of these species is strictly dependent on the charges involved in the formation equilibria. For the equilibrium pH_iAⁱ⁺ + H_j(Phy)⁽¹²-^j)- = A_p(Phy)H_q(^12q)-, (q = pi + j)we found the relationship logK= aζ (ζ is the charge product of reactants), where a= 0.35(0.03, valid for all the amines; this roughly indicates an average free energy contribution per bond -ΔG⁰ = 4.0 ± 0.2 kJ mol^-1. A slightly more sophisticated equation is also proposed for predicting the stability of these species. Owing to the quite high (partially protonated) phytate charge, the stability of A_p(Phy)H_q^(12-q)- species is quite high, making phytate a strong amine sequestering agent in a wide pH range.     

Hierarchical Classification I: Single-Linkage Method

This is the first part of a survey of hierarchical clustering algorithms using joining methods: the Single-Linkage algorithm. Complete-Linkage and general algorithms defined by d(A_i, B) = = α,d(A_i, A_r)±α_sd(A_i, A_s)±βd(A_r, A_s) will be discussed in two subsequent papers.     

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.     

Bubble-column design for growth of fragile insect cells

A mathematical model for the design of bubble-columns for growth of shear-sensitive insect cells is presented. The model is based on two assumptions. First, the loss of cell viability as a result of aeration is a first-order process. Second, a hypothetical volume X, in which all viable cells are killed, is associated with each air bubble during its lifetime. The model merely consists of an equation for k _d, the first-order death-rate constant, and A _min, the minimum specific surface area of the air bubbles to supply sufficient oxygen. In addition to X, the equation for k _d contains the air flow F, the air-bubble diameter d _b, the diameter D and the height H of the bubble column. This equation has been experimentally validated. Comparison of the equations for k _d and A _min shows that especially H is the key parameter to manipulate in bubble-column design in order to meet the demands set by A _min and k _dg, the first-order growth-rate constant. It is concluded that net growth of cells is enhanced as size and height of the bubble column increase.     

Optical effects on the surrounding structure during quantitative analysis using indocyanine green videoangiography: A phantom vessel study

Various reports have been published regarding quantitative evaluations of intraoperative fluorescent intensity studies using indocyanine green (ICG) with videoangiography (VAG). The effects of scattering and point‐spread functions (PSF) on quantitative ICG‐VAG evaluations have not been investigated. Clinically, when ICG is administered through the peripheral vein, it reaches the tissue intra‐arterially. To achieve more reliable intraoperative quantitative intensity evaluations, we examined the impact of high‐intensity structures on close areas. The study was conducted using a phantom model and surgical fluorescent microscope. A region of interest (ROI) was created for the vessel model and another ROI was created within 3 cm of that. With an ROI of 6.8 mm in the vessel phantom model, 10% intensity was confirmed, even though there was no fluorescent structure. Intensity decreased gradually as the ROI moved further from the vessel model. Our study results suggest that the presence of a high‐intensity structure and the size of the ROI may affect quantitative intensity evaluations using ICG‐VAG. Results of linear regression analysis indicate that the relationship of intensity (Y) and distance (X) is as follows: Y(real/A) = 29 Exp(?0.062X) + 164.3 Exp(?1.81X). The optical effect should be considered when performing an intraoperative intensity study with a surgical microscope.      

Almost-one Parameter Hypothesis of Individuality in Height Growth

Thus far an individual height growth curve h_ij(t) of the i-th person in the j-th period, t being his (or her) age, has been studied as a function of t associated with its velocity curve. In this note we introduce a natural scale X(t) in place of t, which linearizes this personal curve and facilitates its analysis, in the sense that this equation of growth contains apparently two personal parameters for one period but one of them plays an essential role. The effectiveness of this approach will be seen in four figures.     

Theory of transport in linear biological systems: I. Fundamental integral equation

The conditions under which the output,γ _b (t), of a biological system is related to the input,γ _a (t), by an integral equation of the typeγ _b (t) = ∫ ₀ ^t γ _a (ω)w(t−ω)dω, where ω(t) is a transport functioncharacteristic of the system, are analyzed in detail. Methods of solving this type of integral equation are briefly discussed. The theory is then applied to problems in tracer kinetics in which input and output are sums of exponentials, and explicit formulae, which are applicable whether or not the pool is uniformly mixed, are derived for “turnover time” and “pool” size.     

On Admissible Estimators in a Linear Model

Let Y be observable random vector such that EY=Xβ and D(Y)=ρ²V. Linear estimation of a parameter p′β under the squared loss is considered. RAO, 1976 and 1979, obtained a necessary and sufficient condition for admissibility of an estimator t′Y in the case X=I. This result will be extended for arbitrary X. AMS 1970 subject classifications. Primary 62J05; secondary 62C15.     

Practical design equations for trickling-filter process

The concept of solid retention time (SRT) was applied in the trickling-filter process. A rational model of the trickling-filter process employing activated-sludge-process operational parameters was presented. The design equation was developed as follows; 1/SRT = [(S₀ ? S_n)/X ]·(F/V)·Y ? k_d, where SRT is the sludge retention time, S₀ is the influent substrate concentration; S_n is the effluent substrate concentration; X is the total cell mass retained per unit filter volume; V is the total volume of the filter; F is the influent flow rate; Y is the cell yield, and k_d is the cell decay rate. A laboratory-scale trickling-filter pilot plant treating synthetic sucrose waste-water was studied to verify the present design equation. The solid retention time was evaluated from the total slime mass (active and inactive) retained and the sludge wasted daily. It was found that the present design equation could be applied for designing the trickling-filter process by the application of SRT employed in the activated sludge process. Also, the SRT could be related to the hydraulic loading and influent substrate concentration for a given filter medium. The variation of SRT by the hydraulic loading at constant organic loading was observed and could be expressed by the mechanistic model. When SRT was maintained more than 12 days, it provided the highest five-day biological oxygen demand (BOD₅) removal, minimum sludge production, and lowest sludge volume index (SVI) value. The present model does include both microbial growth kinetic concepts, which can be more practical and meaningful for the design of a trickling filter.     

ALGORITHM FOR APPLICATION OF FOURIER ANALYSIS FOR BIORHYTHMIC BASELINES OF PHARMACODYNAMIC INDIRECT RESPONSE MODELS

The change of an indirect pharmacological response R(t) can be described by a periodic time-dependent production rate k_in (t) and a first-order loss constant k_out. If k_in(t) follows some biological rhythm (e.g., circadian), then the response R(t) also displays a periodic behavior. A new approach for describing the input function in indirect response models with biorhythmic baselines of physiologic substances is introduced. The present approach uses the baseline (placebo) response R_b(t) to recover the equation for k_in(t). Fourier analysis provides an approximate equation for R_b(t) that consists of terms (usually two or three) of the Fourier series (harmonics) that contribute most to the overall sum. The model differential equation is solved backward for k_in(t), yielding the equation involving R_b(t). A computer program was developed to perform the square L²-norm approximation technique. Fourier analysis was also performed based on nonlinear regression. Cortisol suppression after inhalation of fluticasone propionate (FP) was modeled based on the inhibition of the secretion rate k_in(t) using ADAPT II. The pharmacodynamic parameters k_out and IC₅₀ were estimated from the model equation with k_in(t) derived by the new approach. The proposed method of describing the input function needs no assumption about the behavior of k_in(t), is as efficient as methods used previously, and is more flexible in describing the baseline data than the nonlinear regression method. (Chronobiology International, 17(1), 77–93, 2000)     

Construction of analytically solvable models for interacting species

By observing that the n-tuple of rate functionsQ(c) is orthogonal to the c-space gradients of each of the (n - 1) constants of the motion Φ _v (c), a generic canonical expression for the rate functions is given in terms of the exterior product of the gradients of the (n - 1) Φ _v 's. For models withQ so prescribed from the outset, an analytical general solution is obtainable directly for the system of autonomous ordinary differential equations dc/dt =Q(c). Thus, the generic canonical expression for the rate functions can be utilized to construct analytically solvable models for interacting biological species, as ilIus~rated by examples here.     

Additive genetic variance within populations derived by single-seed descent and pod-bulk descent

Summary Breeders of self-pollinated legumes commonly use single-seed descent (SSD) or pod-bulk descent (PBD) to produce segregating populations of highly inbred individuals. We presented equations for the expected value of the additive genetic variance within populations derived by SSD (E(V _A)_SSD) and PBD (E(V _A)_PBD) in terms of the initial population size (N ₀), the number of seed harvested per pod (M), the probability of survival of an individual (), and the generation at which the population is evaluated (S _t). Differences between (E(V _A)_SSD) and (E(V _A)_PBD) are due to differences in the expected amount of random drift which occurs with the two methods after the S ₀ generation. With both methods, random drift occurs when progeny are sampled from heterozygous parents. An additional component of random drift occurs when sampled progeny fail to survive during SSD, or when sampling occurs amoung families during PBD. For values of N ₀, M, , and S _t that are typical of soybean (Glycine max (L.) Merr.) breeding programs, (E(V _A)_SSD) will be greater than (E(V _A)_PBD). The ratio of (E(V _A)_SSD) to (E(V _A)_PBD) will: (1) increase as M and increase; (2) approach a value of 1.00 as N ₀ increases; and (3) be a curvilinear function of S _t. Plant breeders should compare SSD and PBD based upon values of (E(V _A)_SSD) and (E(V _A)_PBD) and the expected cost of carrying out the two methods.Contribution No. 2910 of the South Carolina Agricultural Experiment Station, Clemson University     

Dynamic light-scattering studies of internal motions in DNA. I. Applicability of the rouse-zimm model

The intermediate scattering function G(K,t) for any polymer model obeying a linear separable Langevin equation can be expressed in terms of the eigenvalues and eigenvectors of its normal coordinate transformation. An algorithm for the extract numerical evaluation of G(K,t) for linear Rouse-Zimm chains in the presence of hydrodynamic interaction has been developed. The computed G(K,t)² were fit to C(t) = A exp(?t/τA) + B, and apparent diffusion coefficients calculated according to D_app ≡ 1/(2τ_AK²). G(K,t)² was surprisingly well-fit by single-exponential decays, especially at both small and large values of Kb, where K is the scattering vector and b the root-mean-squared subunit extension. Plots of D_app vs K² in-variably showed a sigmoidal rise from D₀ at K² = O up to a constant plateau value at large K²b². Analytical expression for G(K,t), exact in the limit of short times, were obtained for circular Rouse-Zimm chains with and without hydrodynamic interaction, and also for free-draining linear chains, and in addition for the independent-segment-mean-force (ISMF) model. The predicted behaviors for G(K,t) at large Kb (or KR_G) was found in all cases to be single-exponential with 1/τ ∝ K² at large Kb, in agreement with the computational results. A simple procedure for estamating all parameter of the Rouse-Zimm model from a plot of D_app vs K² is proposed. Experimental data for both native and pH-denatured calf-thymus DNA in 1.0M Nacl with and without EDTA clearly plateau behavior of D_app at large values of K, in harmony with the present Rouse-Zimm and ISMF theories, and in sharp contrast to previous predictions based on the Rouse-Zimm model.     

A Property of Second Order Differential Equations with Application to Formal Kinetics

It is shown that if x(t) is the solution of a second order differential equation, with real negative characteristic roots (not necessarily distinct), which exhibits an extremum at t = T, then T|x(T)|/|A| [UNK] 1/e where A is the area under the x(t) curve. This result is compared to a special case previously derived by M. Morales and applications of the theorem to formal kinetic problems are discussed.