RNA2D3D: a program for generating, viewing, and comparing 3-dimensional models of RNA

Using primary and secondary structure information of an RNA molecule, the program RNA2D3D automatically and rapidly produces a first-order approximation of a 3-dimensional conformation consistent with this information. Applicable to structures of arbitrary branching complexity and pseudoknot content, it features efficient interactive graphical editing for the removal of any overlaps introduced by the initial generating procedure and for making conformational changes favorable to targeted features and subsequent refinement. With emphasis on fast exploration of alternative 3D conformations, one may interactively add or delete base-pairs, adjacent stems can be coaxially stacked or unstacked, single strands can be shaped to accommodate special constraints, and arbitrary subsets can be defined and manipulated as rigid bodies. Compaction, whereby base stacking within stems is optimally extended into connecting single strands, is also available as a means of strategically making the structures more compact and revealing folding motifs. Subsequent refinement of the first-order approximation, of modifications, and for the imposing of tertiary constraints is assisted with standard energy refinement techniques. Previously determined coordinates for any part of the molecule are readily incorporated, and any part of the modeled structure can be output as a PDB or XYZ file. Illustrative applications in the areas of ribozymes, viral kissing loops, viral internal ribosome entry sites, and nanobiology are presented.     

RNA2D3D: A program for Generating,Viewing, and Comparing 3-Dimensional Models of RNA

Abstract

Using primary and secondary structure information of an RNA molecule, the program RNA2D3D automatically and rapidly produces a first-order approximation of a 3-dimensional conformation consistent with this information. Applicable to structures of arbitrary branching complexity and pseudoknot content, it features efficient interactive graphical editing for the removal of any overlaps introduced by the initial generating procedure and for making conformational changes favorable to targeted features and subsequent refinement. With emphasis on fast exploration of alternative 3D conformations, one may interactively add or delete base-pairs, adjacent stems can be coaxially stacked or unstacked, single strands can be shaped to accommodate special constraints, and arbitrary subsets can be defined and manipulated as rigid bodies. Compaction, whereby base stacking within stems is optimally extended into connecting single strands, is also available as a means of strategically making the structures more compact and revealing folding motifs. Subsequent refinement of the first-order approximation, of modifications, and for the imposing of tertiary constraints is assisted with standard energy refinement techniques. Previously determined coordinates for any part of the molecule are readily incorporated, and any part of the modeled structure can be output as a PDB or XYZ file. Illustrative applications in the areas of ribozymes, viral kissing loops, viral internal ribosome entry sites, and nanobiology are presented.     

Applications of a Vectorized MANOVA-Model

If the observation matrix of n independent p-dimensional normal vectors with common covariance matrix is transformed into an np-vector, linear models and hypotheses on the expectations can be formulated, that are not attainable in standard MANOVA or GMANOVA models. The distribution of an earlier proposed test procedure for this vectorized model is derived for p = 2, and its application is demonstrated for crossover and repeated measurement designs. Numerical results are compared in situations, in which both the standard and the vectorized model are applicable.     

A nonparametric test for association with censored data

A nonparametric procedure is proposed for the problem of testing association between two continuous variables when one is subject to arbitrary censoring. The motivation for the procedure derives from our finding that Cox's likelihood procedure may not adequately control the size of the test. The proposed procedure allows the censoring mechanism to depend on the independent variable, is simple computationally, and provides accurate control over the size of the test even for quite small samples. Asymptotic results suggest that it may provide a sensitive alternative to Cox's procedure. An example dealing with survival following operation for myasthenia gravis is provided, wherein a method for testing after adjustment for covariate information is described.     

The half-life of a drug in relation to its therapeutic index

A procedure is given for the determination of the effective half-life of a drugin vivo with respect to an arbitrary response. If the half-life of the drug with respect to toxicity is different from that for therapy, the therapeutic index would be expected to depend on the temporal spacing of the dose. Equations are derived for this variation for a special case. This work was carried out under contract with the Medical Division of the Chemical Warfare Service.     

Bayesian mapping of quantitative trait loci under the identity-by-descent-based variance component model

Variance component analysis of quantitative trait loci (QTL) is an important strategy of genetic mapping for complex traits in humans. The method is robust because it can handle an arbitrary number of alleles with arbitrary modes of gene actions. The variance component method is usually implemented using the proportion of alleles with identity-by-descent (IBD) shared by relatives. As a result, information about marker linkage phases in the parents is not required. The method has been studied extensively under either the maximum-likelihood framework or the sib-pair regression paradigm. However, virtually all investigations are limited to normally distributed traits under a single QTL model. In this study, we develop a Bayes method to map multiple QTL. We also extend the Bayesian mapping procedure to identify QTL responsible for the variation of complex binary diseases in humans under a threshold model. The method can also treat the number of QTL as a parameter and infer its posterior distribution. We use the reversible jump Markov chain Monte Carlo method to infer the posterior distributions of parameters of interest. The Bayesian mapping procedure ends with an estimation of the joint posterior distribution of the number of QTL and the locations and variances of the identified QTL. Utilities of the method are demonstrated using a simulated population consisting of multiple full-sib families.     

Homogeneous nets of neuron-like elements

Propagation and reverberation of excitation patterns are investigated for 1-dimensional and 2-dimensional homogeneous nets of neuron-like elements. A 1-dimensional net has a proper set of excitation patterns which only can be conducted in the net. Such a net has an ability of discriminating and shaping stimulus signals. Two types of self-reproducing reverberatory excitation patterns are shown for 2-dimensional homogeneous nets. An algebraic theory of general homogeneous nets is also developed.     

The Escherichia coli 30S ribosomal subunit; an optimized three-dimensional fit between the ribosomal proteins and the 16S RNA.

We have generated a computerized fit between the 3-dimensional map of the E.coli 30S ribosomal proteins, as determined by neutron scattering, and the recently published 3-dimensional model for the 16S RNA. To achieve this, the framework of coordinates for RNA-protein cross-link sites on the phosphate backbone in the RNA model was related to the corresponding framework of coordinates for the mass centres of the proteins by a least squares fitting procedure. The resulting structure, displayed on a computer graphics system, gives the first complete picture of the E.coli 30S ribosomal subunit showing both the proteins and the double-helical regions of the RNA. The root mean square distance between cross-link sites and protein centres is 32 A. The position of the mass centre of the combined double-helical regions was calculated from the model and compared with the position of the mass centre of the complete set of proteins. The two centres are displaced relative to one another by 20 A in the model structure, in good agreement with the experimental value of 25 A found by neutron scattering.     

Mapping quantitative trait loci using the MCMC procedure in SAS

The MCMC procedure in SAS (called PROC MCMC) is particularly designed for Bayesian analysis using the Markov chain Monte Carlo (MCMC) algorithm. The program is sufficiently general to handle very complicated statistical models and arbitrary prior distributions. This study introduces the SAS/MCMC procedure and demonstrates the application of the program to quantitative trait locus (QTL) mapping. A real life QTL mapping experiment in wheat female fertility trait was used as an example for the demonstration. The fertility trait phenotypes were described under three different models: (1) the Poisson model, (2) the Bernoulli model and (3) the zero-truncated Poisson model. One QTL was identified on the second chromosome. This QTL appears to control the switch of seed-producing ability of female plants but does not affect the number of seeds produced once the switch is turned on.     

General multistage gatekeeping procedures

A general multistage (stepwise) procedure is proposed for dealing with arbitrary gatekeeping problems including parallel and serial gatekeeping. The procedure is very simple to implement since it does not require the application of the closed testing principle and the consequent need to test all nonempty intersections of hypotheses. It is based on the idea of carrying forward the Type I error rate for any rejected hypotheses to test hypotheses in the next ordered family. This requires the use of a so-called separable multiple test procedure (MTP) in the earlier family. The Bonferroni MTP is separable, but other standard MTPs such as Holm, Hochberg, Fallback and Dunnett are not. Their truncated versions are proposed which are separable and more powerful than the Bonferroni MTP. The proposed procedure is illustrated by a clinical trial example.     

A new computational method for cable theory problems.

We discuss a new computational procedure for solving the linear cable equation on a tree of arbitrary geometry. The method is based on a simple set of diagrammatic rules implemented using an efficient computer algorithm. Unlike most other methods, this technique is particularly useful for determining the short-time behavior of the membrane potential. Examples are presented and the convergence and accuracy of the method are discussed.     

The propagation of a cultural or biological trait by neutral genetic drift in a subdivided population

We study fixation probabilities and times as a consequence of neutral genetic drift in subdivided populations, motivated by a model of the cultural evolutionary process of language change that is described by the same mathematics as the biological process. We focus on the growth of fixation times with the number of subpopulations, and variation of fixation probabilities and times with initial distributions of mutants. A general formula for the fixation probability for arbitrary initial condition is derived by extending a duality relation between forwards- and backwards-time properties of the model from a panmictic to a subdivided population. From this we obtain new formulae(formally exact in the limit of extremely weak migration) for the mean fixation time from an arbitrary initial condition for Wright's island model, presenting two cases as examples. For more general models of population subdivision, formulae are introduced for an arbitrary number of mutants that are randomly located, and a single mutant whose position is known. These formulae contain parameters that typically have to be obtained numerically, a procedure we follow for two contrasting clustered models. These data suggest that variation of fixation time with the initial condition is slight, but depends strongly on the nature of subdivision. In particular, we demonstrate conditions under which the fixation time remains finite even in the limit of an infinite number of demes. In many cases-except this last where fixation in a finite time is seen--the time to fixation is shown to be in precise agreement with predictions from formulae for the asymptotic effective population size.     

Generalized n-dimensional biomechanical field analysis using statistical parametric mapping

A variety of biomechanical data are sampled from smooth n-dimensional spatiotemporal fields. These data are usually analyzed discretely, by extracting summary metrics from particular points or regions in the continuum. It has been shown that, in certain situations, such schemes can compromise the spatiotemporal integrity of the original fields. An alternative methodology called statistical parametric mapping (SPM), designed specifically for continuous field analysis, constructs statistical images that lie in the original, biomechanically meaningful sampling space. The current paper demonstrates how SPM can be used to analyze both experimental and simulated biomechanical field data of arbitrary spatiotemporal dimensionality. Firstly, 0-, 1-, 2-, and 3-dimensional spatiotemporal datasets derived from a pedobarographic experiment were analyzed using a common linear model to emphasize that SPM procedures are (practically) identical irrespective of the data's physical dimensionality. Secondly two probabilistic finite element simulation studies were conducted, examining heel pad stress and femoral strain fields, respectively, to demonstrate how SPM can be used to probe the significance of field-wide simulation results in the presence of uncontrollable or induced modeling uncertainty. Results were biomechanically intuitive and suggest that SPM may be suitable for a wide variety of mechanical field applications. SPM's main theoretical advantage is that it avoids problems associated with a priori assumptions regarding the spatiotemporal foci of field signals. SPM's main practical advantage is that a unified framework, encapsulated by a single linear equation, affords comprehensive statistical analyses of smooth scalar fields in arbitrarily bounded n-dimensional spaces.     

Long-term evolution of multilocus traits

 We analyze monomorphic equilibria of long-term evolution for one or two continuous traits, controlled by an arbitrary number of autosomal loci and subject to constant viability selection. It turns out that fitness maximization always obtains at long term equilibria, but in the case of two traits, linkage determines the precise nature of the fitness measure that is maximized. We then consider local convergence to long term equilibria, for two multilocus traits subject to either constant or frequency dependent selection. From a model of long-term dynamics near an equilibrium we derive a criterion of local long-term stability for 2-dimensional equilibria. It turns out that mutation can be a decisive factor for stability. Received 26 January 1994; received in revised form 26 September 1994     

Three-dimensional visualization and quantitative analysis of cervical cell nuclei with confocal laser scanning microscopy

OBJECTIVE: To develop a method for the acquisition and processing of 3-dimensional images based on confocal laser scanning microscopy for the purpose of 3-dimensional visualization and quantitative analysis of cell nuclei. STUDY DESIGN: A contour-based surface rendering method was used, and volume rendering was implemented according to the basic volume rendering pipeline. To extract quantitative features, a 3-dimensional labeling method based on slice information was used. After applying the labeling algorithm, the measurements for 3-dimensional quantitative analysis of nuclei were extracted: nuclear volume, surface area and spherical shape factor. We compared the 3-dimensional features of normal and abnormal cervical cell nuclei. RESULTS: Comparison of the size of 3-dimensional cervical cell nuclei between normal and abnormal revealed a statistically significant difference. The proposed method could overcome the limitation inherent in 2-dimensional analysis and could become a way of improving the accuracy and reproducibility of quantification of cell nuclei. CONCLUSION: Three-dimensional visualization and quantification of cell nuclei provide valuable medical information that can lead to a more objective diagnosis.     

Exact and efficient inference procedure for meta-analysis and its application to the analysis of independent 2 x 2 tables with all available data but without artificial continuity correction

Recently, meta-analysis has been widely utilized to combine information across comparative clinical studies for evaluating drug efficacy or safety profile. When dealing with rather rare events, a substantial proportion of studies may not have any events of interest. Conventional methods either exclude such studies or add an arbitrary positive value to each cell of the corresponding 2 x 2 tables in the analysis. In this article, we present a simple, effective procedure to make valid inferences about the parameter of interest with all available data without artificial continuity corrections. We then use the procedure to analyze the data from 48 comparative trials involving rosiglitazone with respect to its possible cardiovascular toxicity.     

On the probability of reaching a threshold in a stochastic mammillary system

The multivariate distribution over time of a particular stochastic mammillary compartmental model is obtained for any point in time. The maximum expectation of the peripheral compartments is then derived and used to determine lower bounds on the probability that the maximum of the peripheral compartments reaches any arbitrary threshold level. A bound on the probability is illustrated by an example and some of its implications are explored.     

Integrate and fire neural networks, piecewise contractive maps and limit cycles

We study the global dynamics of integrate and fire neural networks composed of an arbitrary number of identical neurons interacting by inhibition and excitation. We prove that if the interactions are strong enough, then the support of the stable asymptotic dynamics consists of limit cycles. We also find sufficient conditions for the synchronization of networks containing excitatory neurons. The proofs are based on the analysis of the equivalent dynamics of a piecewise continuous Poincaré map associated to the system. We show that for efficient interactions the Poincaré map is piecewise contractive. Using this contraction property, we prove that there exist a countable number of limit cycles attracting all the orbits dropping into the stable subset of the phase space. This result applies not only to the Poincaré map under study, but also to a wide class of general n-dimensional piecewise contractive maps.     

Multilevel models for survival analysis with random effects

A method for modeling survival data with multilevel clustering is described. The Cox partial likelihood is incorporated into the generalized linear mixed model (GLMM) methodology. Parameter estimation is achieved by maximizing a log likelihood analogous to the likelihood associated with the best linear unbiased prediction (BLUP) at the initial step of estimation and is extended to obtain residual maximum likelihood (REML) estimators of the variance component. Estimating equations for a three-level hierarchical survival model are developed in detail, and such a model is applied to analyze a set of chronic granulomatous disease (CGD) data on recurrent infections as an illustration with both hospital and patient effects being considered as random. Only the latter gives a significant contribution. A simulation study is carried out to evaluate the performance of the REML estimators. Further extension of the estimation procedure to models with an arbitrary number of levels is also discussed.