Prediction of locally optimal splice sites in plant pre-mRNA with applications to gene identification in Arabidopsis thaliana genomic DNA.

Prediction of splice site selection and efficiency from sequence inspection is of fundamental interest (testing the current knowledge of requisite sequence features) and practical importance (genome annotation, design of mutant or transgenic organisms). In plants, the dominant variables affecting splice site selection and efficiency include the degree of matching to the extended splice site consensus and the local gradient of U- and G+C-composition (introns being U-rich and exons G+C-rich). We present a novel method for splice site prediction, which was particularly trained for maize and Arabidopsis thaliana. The method extends our previous algorithm based on logitlinear models by considering three variables simultaneously: intrinsic splice site strength, local optimality and fit with respect to the overall splice pattern prediction. We show that the method considerably improves prediction specificity without compromising the high degree of sensitivity required in gene prediction algorithms. Applications to gene identification are illustrated for Arabidopsis and suggest that successful methods must combine scoring for splice sites, coding potential and similarity with potential homologs in non-trivial ways. A WWW version of the SplicePredictor program is available at http:/gnomic.stanford.edu/volker/SplicePredi ctor.html/     

Statistical Analysis of Nonrectangular Family Data

MINQUE (Minimum Norm Quadratic Unbiased Estimators) theory is applied to the problem of estimation of variance components in family data (siblings) with variable family size. Using this approach, the traditional iterative maximum likelihood estimators are shown to be asymptotically normal, even though the data come from non-identical parent distributions. Asymptotic expressions are also obtained for the variance of the MINQUE estimators which hold even if the data are decidedly non-normal (e.g. a mixture of normals). In the case of normal data, exact small-sample variance estimates are derived. Simulations demonstrate the fast rate of convergence to asymptotic properties as the number of families increases. These desirable qualities suggest that the easy to compute MINQUE class of estimators may provide a useful alternative method for modelling familial aggregation.     

The joint distribution of patterns in random sequences with application to the RC-measure for expressivity

A method previously developed for computation of pattern probabilitiesin random sequences under Markov chain models. We extend thismethod to the calculation of the joint distribution for twopatterns. An application yields the distribution of the rightchoice measure for expressivity and how significance boundsdepend on sequence length. These bounds are used to show thatthe choice of pyrimidine in codon position 3 of Escherichiacoli genes deviates considerably from a general Markov processmodel for coding regions. We also derive some statistical evidencethat this significant deviation is limited to codon position3.     

First and second moment of counts of words in random texts generated by Markov chains

An exact expression for the variance of random frequency thata given word has in text generated by a Markov chain is presented.The result is applied to periodic Markov chains, which describethe protein-coding DNA sequences better than simple Markov chains.A new solution to the problem of word overlap is proposed. Itwas found that the expected frequency and overlapping propertiesdetermine most of the variance. The expectation and varianceof counts for triplets are compared with experimental countsin Escherichia coli coding sequences.     

Exact computation of pattern probabilities in random sequences generated by Markov chains

Observed patterns in macromolecular sequences are often consideredas words and compared with their probabilities of occurringin random sequences. Calculation of these probabilities, however,often lacks rigour. We have developed an algorithm for exactcomputation of such probabilities for stochastic sequences thatfollow a Markov chain model. The method is applicable to thecase that a random sequence contains one out of two given patternsP and Q, or both simultaneously. Another application yieldsthe probability Junction P(x) that a sequence contains patternP exactly x times. An application to patterns that include wild-cardcharacters yields probabilities for homonucleotide clustersof a given length. We prove the probability of multiple runsof single nucleotides in the SV40 genome to be in accordancewith the dinucleotide composition of the sequence, althoughit is in conflict with mononucleotide composition. Received on January 10, 1990; accepted on April 23, 1990