2 1. Define zero and first order Markov models for the sequence (seqeuence1_A2) provided in the course content. Sequence1_A2 is Mycobacterium tuberculosis gene mtb48 (15 pts) Sequence: ggacgaattggacccgcatgtcgcccgggcgttgacgctggcggcgcggtttcagtcggccctagacgggacgctcaatcagatgaacaacggatcc ttccgcgccaccgacgaagccgagaccgtcgaagtgacgatcaatgggcacca gtggctcaccggcctgcgcatcgaagatggtttgctgaagaagctgggtgccgaggcggtggctcagcgggtcaacgaggcgctgcacaatgcgca ggccgcggcgtccgcgtataacgacgcggcgggcgagcagctgaccgctgcgtt atcggccatgtcccgcgcgatgaacgaaggaatggcctaagcccattgttgcggtggtagcgactacgcaccgaatgagcgccgcaatgcggtcattc agcgcgcccgacacggcgtgagtacgcattgtcaatgttttgacatggatcg gccgggttcggagggcgccatagtcctggtcgccaatattgccgcagctagctggtcttaggttcggttacgctggttaattatgacgtccgttacca Zero Order Markov Model: Defined by P (i) where I equals A, T, G, or C) P (A) = 106/548 P (T) = 101/548 P (G) = 183/548 P (C) = 158/548 First Order Markov Model: P (A|A) = 22 P (A|T) =28 P (A|G) = 26 P (A|C) = 29 P (T|A) = 15 P (T|T) =20 P (T|G) = 37 P (T|C) = 0 P (G|A) = 38 P (G|T) = 32 P (G|G) = 39 P (G|C) = 65 P (C|A) = 31 P (C|T) = 19 P (C|G) = 0 P (C|C) = 30 2. Using models you derived in (1) determine the probability of DNA fragment AGTAGCTTCCAG (this fragment was also used in A1) (25 pts) Zero Order Markov Model: Defined by P (i) where I equals A, T, G, or C) P (A) = 3/12 = 25% P (T) = 3/12 = 25% P (G) = 3/12 = 25% P (C) = 3/12 = 25% First Order Markov Model: Defined by P(i|i) where i equals A T G or C P (A|A) = 0/6 P (A|T) =0/6 P (A|G) = 3/6 P (A|C) = 0/6 P (T|A) = 1/6 P (T|T) =1/6 P (T|G) = 0 P (T|C) = 1/6 P (G|A) = 0/6 P (G|T) = 1/6 P (G|G) = 0/6 P (G|C) = 1/6 P (C|A) = 1/6 P (C|T) = 1/6 P (C|G) = 0/6 P (C|C) = 1/6