1. Methods of identification and localization of the DNA coding sequences Jacek Leluk Interdisciplinary Centre for Mathematical and Computational Modelling, Warsaw University Jacek Leluk Interdisciplinary Centre for Mathematical and Computational Modelling Warsaw University

2. Periodic asymmetry index Position asymmetry Codon usage Markov models Codon prototype Measures dependent on a model of coding DNA Measures independent of a model of coding DNA Identification of coding/non-coding sequences in genome oligonucleotide counts base compositional bias between codon positions dependence between nucleotide positions base compositional bias between codon positions periodic correlation between nucleotide positions Average mutual information Fourier spectrum Amino acid usage Codon preference Hexamer usage based on: Jacek Leluk Interdisciplinary Centre for Mathematical and Computational Modelling, Warsaw University

3. The notation used S – DNA sequence of length l, while S i ( i=1... l ) denotes the individual nucleotides C – sequence of codons; C j – the codon occupying position j in the sequence - denotes the sequence of codons that results when the grouping of nucleotides from sequence S into codons starts at nucleotide i or, - denotes the codon occupying position j in the decomposition i of the sequence S [k] - the nucleotide occupying position k in the codon Jacek Leluk Interdisciplinary Centre for Mathematical and Computational Modelling, Warsaw University

4. Examples Jacek Leluk Interdisciplinary Centre for Mathematical and Computational Modelling, Warsaw University

5. The notation used Measures based on a model of coding DNA probability of the sequence of nucleotides S, given that S is coding in frame i (i=1, 2, 3) probability of the non-coding DNA sequence (randomly generated) Likelihood ratio The ratio of the probability of finding the sequence of nucleotides S, if S is coding in frame i over the probability of finding the sequence of nucleotides S, if S is non-coding Jacek Leluk Interdisciplinary Centre for Mathematical and Computational Modelling, Warsaw University

6. The notation used Measures based on a model of coding DNA Log-likelihood ratio coding potential of sequence S in frame i given the model of coding DNA the probability of the sequence of nucleotides S is higher assuming that S is coding in frame i, than assuming that S is non-coding in frame i the probability of S is higher assuming that S does not code in frame i than assuming that S is coding in frame i The log-likelihood ratios is computed for all three possible frames. If the sequence is coding, the log-likelihood ratio will larger for one of the frames than for the other two. Jacek Leluk Interdisciplinary Centre for Mathematical and Computational Modelling, Warsaw University

7. Codon usage Measures based on a model of coding DNA Measures based on oligonucleotide counts frequency (probability) of codon C in the genes of the considered species (the codon usage table) probability of finding the sequence of codons C knowing that C codes for a protein P 0 (C)=(1/64) m probability of finding the non-coding sequence Jacek Leluk Interdisciplinary Centre for Mathematical and Computational Modelling, Warsaw University

8. Amino acid usage Measures based on a model of coding DNA Measures based on oligonucleotide counts the observed probability of the amino acid encoded by codon C in the existing proteins This value can be directly derived from a codon usage table by summing up the probabilities of synonymous codons wheremeans c’ synonymous to c probability of finding the amino acid sequence resulting of translating the sequence in coding open reading frame frequency of the „non-coding amino acids”; n c – number of codons synonymous to C Jacek Leluk Interdisciplinary Centre for Mathematical and Computational Modelling, Warsaw University

9. Codon preference Measures based on a model of coding DNA Measures based on oligonucleotide counts relative probability in coding regions of codon C among codons synonymous to C probability of the sequence S encoding the particular amino acid sequence in frame i probability of codon C in non-coding DNA In non-coding regions there is no preference between „synonymous codons”. Then: Jacek Leluk Interdisciplinary Centre for Mathematical and Computational Modelling, Warsaw University

10. Hexamer usage Measures based on a model of coding DNA Measures based on oligonucleotide counts This approach is based on the hexamer usage table for i=1, 2, 3,..., 4096. In this case there are six reading frames to be analyzed. The probability of a sequence of hexanucleotides, in the coding frame of a coding sequence is Jacek Leluk Interdisciplinary Centre for Mathematical and Computational Modelling, Warsaw University

11. Codon prototype Measures based on a model of coding DNA Measures based on base compositional bias between codon positions Let f(b,r) be the probability of nucleotide b at codon position r, as estimated from known coding regions. Then: P 2 (S) and P 3 (S) are computed in similar way is the probability of codon c in coding regions, assuming independence between adjacent nucleotides probability of for all triplets c in non-coding DNA Example: Jacek Leluk Interdisciplinary Centre for Mathematical and Computational Modelling, Warsaw University

12. Markov Models Measures based on a model of coding DNA Measures based on dependence between nucleotide positions In the Markov models the probability of a nucleotide at a particular codon position depends on the nucleotide(s) preceding it. The Markov models of order 1 is the simplest of the Markov models. The probability of a nucleotide depends only on the preceding nucleotide. In this case, the model of coding DNA is based on the probabilities of the four nucleotides at each codon position, depending on the nucleotide occurring at the preceding codon position (technically called the transition probabilities). Thus, instead of one single matrix, as in Codon Prototype, three 4x4 matrices (the transition matrices) are required, F 1, F 2, and F 3, each one corresponding to a different codon position. There are used Markov models of the order 1 to 5 Jacek Leluk Interdisciplinary Centre for Mathematical and Computational Modelling, Warsaw University

13. Position asymmetry Measures independent of a model of coding DNA Measures based on base compositional bias between codon positions The goal is to measure how asymmetric is the distribution of nucleotides at the three triplet positions in the sequence. the relative frequency of nucleotide b at codon r position in the sequence S, as calculated from one of the three decompositions of S in codons (any of them) average frequency of nucleotide b at the three codon positions asymmetry in the distribution of nucleotide b Jacek Leluk Interdisciplinary Centre for Mathematical and Computational Modelling, Warsaw University

14. Position asymmetry (continued) Measures independent of a model of coding DNA Measures based on base compositional bias between codon positions Position Asymmetry of the sequence Jacek Leluk Interdisciplinary Centre for Mathematical and Computational Modelling, Warsaw University

15. Periodic asymmetry index Measures independent of a model of coding DNA Measures based on periodic correlation between nucleotide positions This approach considers three distinct probabilities: - the probability P in of finding pairs of the same nucleotide at distances k=2, 5, 8,... - the probability P 1 out of finding pairs of the same nucleotide at distances k=0, 3, 6,... - the probability P 2 out of finding pairs of the same nucleotide at distances k=1, 4, 7,... The tendency to cluster homogeneous di-nucleotides in a 3-base periodic pattern can be measured by the Periodic Asymmetry Index: Jacek Leluk Interdisciplinary Centre for Mathematical and Computational Modelling, Warsaw University

16. Average mutual information Measures independent of a model of coding DNA Measures based on periodic correlation between nucleotide positions absolute number of times when nucleotide i is followed by nucleotide j at a distance of k positions Correlation between nucleotides i and j at a distance of k positions probability that nucleotide i is followed by nucleotide j at a distance of k positions where p i and p j are probabilities of nucleotide i and j occurrence in sequence S Jacek Leluk Interdisciplinary Centre for Mathematical and Computational Modelling, Warsaw University

17. Average mutual information (continued) Measures independent of a model of coding DNA Measures based on periodic correlation between nucleotide positions Mutual Information function quantifies the amount of information that can be obtained from one nucleotide about another nucleotide at a distance k Jacek Leluk Interdisciplinary Centre for Mathematical and Computational Modelling, Warsaw University

18. Average mutual information (continued) Measures independent of a model of coding DNA Measures based on periodic correlation between nucleotide positions the in-frame mutual information at distances k=2, 5, 8,... Average Mutual Information the out-frame mutual information at distances k=0, 1, 3, 4,... Jacek Leluk Interdisciplinary Centre for Mathematical and Computational Modelling, Warsaw University

19. Fourier analysis Measures independent of a model of coding DNA Measures based on periodic correlation between nucleotide positions No such ``peak'' is apparent for non-coding sequences DNA coding regions reveal the characteristic periodicity of 3 as a distinct peak at frequency f =1/3 The partial spectrum of a DNA sequence S of length l corresponding to nucleotide b is defined as: where U b (S j )=1 if S j =b, and otherwise it is 0, and f is the discrete frequency, f =k/l, for k=1, 2,...,l/2 Jacek Leluk Interdisciplinary Centre for Mathematical and Computational Modelling, Warsaw University

20. Summary of results Jacek Leluk Interdisciplinary Centre for Mathematical and Computational Modelling, Warsaw University

21. List of Gene Identification programs and Internet access (part 1) Jacek Leluk Interdisciplinary Centre for Mathematical and Computational Modelling, Warsaw University

22. List of Gene Identification programs and Internet access (part 2) Jacek Leluk Interdisciplinary Centre for Mathematical and Computational Modelling, Warsaw University

23. Thank you for your attention