Investigation of Genetic Code Optimality for Overlapping Protein Coding Sequences. Presented by Martin Bossert
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1 Ulm University Institute of ommunications Engineering Investigation of enetic ode Optimality for Overlapping Protein oding Sequences Presented by Martin Bossert 8th International Symposium on urbo odes & Iterative Information Processing, ugust 18th to 22nd, 2014, Bremen, ermany Katharina Mir and Steffen Schober enetic ode Optimality 1
2 DF priority program InKoMBio Ulm University Institute of ommunications Engineering Finding new overlapping genes and their theory (FO heory) Find and verify new overlapping protein-coding DN-sequences in prokaryotes and understand the underlying mechanisms using models from information and communication theory Motivation nalysis of overlapping genes revealed interesting statistical findings regarding long ORFs in alternative reading frames re these statistical findings a consequence of the genetic code? Is the genetic code optimized for the existence of long overlapping gene pairs? Katharina Mir and Steffen Schober enetic ode Optimality 2
3 Information is Stored in the DN Ulm University Institute of ommunications Engineering DN double helix (Deoxyribonucleic acid) Picture: modified from Katharina Mir and Steffen Schober enetic ode Optimality 3
4 Information is Stored in the DN Ulm University Institute of ommunications Engineering DN double helix (Deoxyribonucleic acid) Nucleotides = {,,,} Picture: modified from Katharina Mir and Steffen Schober enetic ode Optimality 3
5 Information is Stored in the DN Ulm University Institute of ommunications Engineering DN double helix (Deoxyribonucleic acid) Base pair base pairs Escherichia coli Nucleotides = {,,,} Pictures: modified from Katharina Mir and Steffen Schober enetic ode Optimality 3
6 Information is Stored in the DN Ulm University Institute of ommunications Engineering DN double helix (Deoxyribonucleic acid) Base pair base pairs Escherichia coli base pairs Human being Nucleotides = {,,,} Pictures: modified from Katharina Mir and Steffen Schober enetic ode Optimality 3
7 Information is Stored in the DN Ulm University Institute of ommunications Engineering DN double helix (Deoxyribonucleic acid) ene ene expression Protein = hain of amino acids (aa) (20 different aa exist) Example E.coli: Length of proteins 30 to 5000 amino acids Pictures: modified from Katharina Mir and Steffen Schober enetic ode Optimality 3
8 Ulm University ORF Open reading frame Institute of ommunications Engineering Katharina Mir and Steffen Schober enetic ode Optimality 4
9 Ulm University ORF Open reading frame Institute of ommunications Engineering Katharina Mir and Steffen Schober enetic ode Optimality 4
10 Ulm University ORF Open reading frame Institute of ommunications Engineering Katharina Mir and Steffen Schober enetic ode Optimality 4
11 Overlapping ORFs Ulm University Institute of ommunications Engineering Position of annotated gene defines the coding reading frame +1. Other part of overlapping gene pair is called shadow ORF (sorf). Katharina Mir and Steffen Schober enetic ode Optimality 5
12 Scheme of ransitions Ulm University Institute of ommunications Engineering iven: odon transition matrix P +1 (e.g., of annotated genes) P +1 (c j c j 1 )P +1 (c j+1 c j ) c +1 j 1 c +1 j c +1 j+1 n (1) j 1 n(2) j 1 n(3) j 1 n(1) j n (2) j n (3) j n (1) j+1 n(2) j+1 n(3) j c +2 i 1 c +2 i c +3 i 1 c +3 i 5 n (1) j 1 n(2) j 1 n(3) j 1 n(1) j n (2) j n (3) j n (1) j+1 n(2) j+1 n(3) j+1 3 c 1 i c 1 i 1 P 1 (c i c i 1 ) = P +1 (c j 1 c j ) Determine: P f, f { 1, ±2, ±3} and codons distribution π f Katharina Mir and Steffen Schober enetic ode Optimality 6
13 Ulm University Institute of ommunications Engineering verage waiting time for stop codons (1) Mean recurrence time iven: stationary distribution of codons π f π f (i) average time spent by Markov chain in state i. verage waiting time to reach stop codon for the first time starting in a stop codons t (f) M = 1 S {,, } i S πf (i), Katharina Mir and Steffen Schober enetic ode Optimality 7
14 Ulm University Institute of ommunications Engineering verage waiting time for stop codons (2) bsorption time iven: transition matrices P f onstruct absorbing Markov chain P f abs ( P f Q abs = f R f 0 I r with t = 61 transient states and r = 3 stop codons as absorbing states, rewrite ), with Q f matrix of transient states, I r identity matrix and R f transition matrix from transient to absorbing states. he i-th entry of vector t f = (I t Q f ) 1 1, gives the expected number of steps before being absorbed when starting in transient state i average waiting time for a stop codon: bsorption time t (f) = 1 61 i t i Katharina Mir and Steffen Schober enetic ode Optimality 8
15 Ulm University lternative enetic odes Institute of ommunications Engineering [Itzkovitz/lon]: (4!) 3 = alternative genetic codes with same structure 6912 unique codes due to equal codes replacing in third position Second Base Phe Phe Leu Leu Ser Ser Ser Ser yr yr Stop Stop ys ys Stop rp First Base Leu Leu Leu Leu Ile Ile Ile Met Pro Pro Pro Pro hr hr hr hr His His ln ln sn sn Lys Lys rg rg rg rg Ser Ser rg rg hird Base Val Val Val Val la la la la sp sp lu lu ly ly ly ly Input matrix P +1 from amino acid distribution of EHE π +1 get codon distribution p assuming uniform distribution assume iid codon transitions P +1 (c j c j 1 ) = p(c j ) Katharina Mir and Steffen Schober enetic ode Optimality 9
16 Ulm University ranslational frame-shift errors Institute of ommunications Engineering If a translational frame-shift error occurs, what is the absorption time averaged over reading frames +2, +3? 400 Number of odes SD bsorption time t Results match empirical comparison of [Itzkovitz/lon] Only 210 of 6912 codes abort translation faster! Katharina Mir and Steffen Schober enetic ode Optimality 10
17 Ulm University Institute of ommunications Engineering Optimality regarding long sorfs (1) 1,200 Number of odes 1, SD Mean recurrence time t M verage waiting time to return to a stop codon in frame codes have t M 80 and 16 of the have t SD Katharina Mir and Steffen Schober enetic ode Optimality 11
18 Ulm University Institute of ommunications Engineering Optimality regarding long sorfs (2) 1,200 Number of odes 1, SD Mean recurrence time t M verage waiting time to return to a stop codon in frame codes have t M 39 and 22 of the have t SD Katharina Mir and Steffen Schober enetic ode Optimality 12
19 Ulm University Institute of ommunications Engineering Optimality regarding long sorfs (3) 1,200 Number of odes 1, SD Mean recurrence time t M verage waiting time to return to a stop codon in frame codes have t M 33 and 8 of the have t SD Katharina Mir and Steffen Schober enetic ode Optimality 13
20 Summary Ulm University Institute of ommunications Engineering Discrete-time Markov Process (DMP) models transitions between codons and all reading frames DMP predicts codon usage in all reading frames (paper) DMP can be applied to alternative genetic codes Optimality of standard genetic code regarding translational frame-shift errors No optimality of the standard genetic code regarding the existence of long ORFs in alternative reading frames lternative codes exist that optimize both aspects Katharina Mir and Steffen Schober enetic ode Optimality 14
21 Ulm University Institute of ommunications Engineering hank you for your attention! Katharina Mir and Steffen Schober enetic ode Optimality 15
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