1. Function-Information Relationship in Nucleic Acids Andrej Luptak aluptak@uci.edueu U NIVERSITY oU NIVERSITY of C ALIFORNIA ‧ I RVINE Andrej Luptak aluptak@uci.edueu U NIVERSITY oU NIVERSITY of C ALIFORNIA ‧ I RVINE

2. Information flow in biological systems

3. In vitro selection

4. How many solutions are there to a biochemical problem?

5. In vitro selected RNAs AptamersOrganic dyes, amino acids, nucleotides, metabolites Aminoglycosides, peptides, proteins, liposomes Cells, tissues, single-walled nanotubes Transition state analogs RibozymesPhosphoryl (incl. polymerase), acyl and alkyl transfer Isomerisation, Diels-Alder, nucleotide synthesis, Michael Metal insertion into mesoporphyrin Metal-metal bond formation (palladium nanoparticles)

6. How many solutions are there to a biochemical problem? How does one measure complexity? How does one measure structural complexity? And what does this have to do with evolution, biosensors and the origin of life? Informational complexity and functional activity Hazen et al. PNAS 2007 104

7. How many solutions are there to a biochemical problem?

8. Isolation of high-affinity GTP aptamers from partially structured RNA libraries Jonathan H. Davis* and Jack W. Szostak† PNAS 2002 vol. 99 no. 18

9. How many solutions are there to a biochemical problem? J.AM.CHEM.SOC. 2004,126, 5130 Informational Complexity and Functional Activity of RNA Structures James M. Carothers, Stephanie C. Oestreich,‡ Jonathan H. Davis,† and Jack W. Szostak

10. How does one measure structural complexity? J.AM.CHEM.SOC. 2004,126, 5130 Informational Complexity and Functional Activity of RNA Structures James M. Carothers, Stephanie C. Oestreich,‡ Jonathan H. Davis,† and Jack W. Szostak

11. How does one measure informational complexity? J.AM.CHEM.SOC. 2004,126, 5130 Informational Complexity and Functional Activity of RNA Structures James M. Carothers, Stephanie C. Oestreich,‡ Jonathan H. Davis,† and Jack W. Szostak

12. How does one measure informational complexity? J.AM.CHEM.SOC. 2004,126, 5130 & RNA 2006 12, 4 Informational Complexity and Functional Activity of RNA Structures James M. Carothers, Stephanie C. Oestreich,‡ Jonathan H. Davis,† and Jack W. Szostak

13. How does one measure informational complexity? J.AM.CHEM.SOC. 2004,126, 5130 & RNA 2006 12, 4 Shannon Uncertainty Information Content= Max Information - Shannon Uncertainty Max Information using 4 bases=2 bit Informational Complexity and Functional Activity of RNA Structures James M. Carothers, Stephanie C. Oestreich,‡ Jonathan H. Davis,† and Jack W. Szostak

14. How does one measure informational complexity? J.AM.CHEM.SOC. 2004,126, 5130 Informational Complexity and Functional Activity of RNA Structures James M. Carothers, Stephanie C. Oestreich,‡ Jonathan H. Davis,† and Jack W. Szostak

15. Shannon Uncertainty Information Content = Max Information - Shannon Uncertainty Max information using 4 bases=2 bits Invariant A: P(A)=0.997 P(C)=0.001 P(G)=0.001 P(U)=0.001 H= -(-0.997*0.00433 - 3*0.001*9.966) = 0.00432+0.0299 = 0.0342 IC= 2 - 0.0342 = 1.9658 One position in a base-pair: IC=1 bit (a base-pair is 2 bits) Informational complexity and functional activity Invariant A or G: P(A)=0.498 P(C)=0.002 P(G)=0.498 P(U)=0.002 H= -(-2*0.498*1.006 - 2*0.002*8.965) = 1.002+0.036 = 1.038 IC= 2 - 1.038 = 0.9622 One position in a regular or wobble pair: IC=0.5 (1 bit per loose base-pair)

16. Another RNA aptamer example: adenosine aptamer

18. Class II ligase ribozyme Pitt & Ferré-D’Amaré, J. Am. Chem. Soc., 2009, 131 (10), pp 3532–3540

19. Class II ligase ribozyme Rapid Construction of Empirical RNA Fitness Landscapes Jason N. PittJason N. Pitt and Adrian R. Ferré-D’Amaré* Science 2010: Vol. 330 no. 6002 pp. 376-379ré-D’Amaré* Science 201. Evolution is an adaptive walk through a hypothetical fitness landscape Fitness landscape shows the relationship between genotypes and the fitness of each corresponding phenotype Empirical fitness landscape is determined for a catalytic RNA by combining next-generation sequencing, computational analysis, and “serial depletion,” an in vitro selection protocol Abundance in serially depleted pools correlates with biochemical activity MS = a4-11 master sequence of the ligase ribozyme

20. Class II ligase ribozyme Rapid Construction of Empirical RNA Fitness Landscapes Jason N. PittJason N. Pitt and Adrian R. Ferré-D’Amaré* Science 2010: Vol. 330 no. 6002 pp. 376-379ré-D’Amaré* Science 201. Changes in population structure during serial depletion (in vitro selection)

21. Class II ligase ribozyme Rapid Construction of Empirical RNA Fitness Landscapes Jason N. PittJason N. Pitt and Adrian R. Ferré-D’Amaré* Science 2010: Vol. 330 no. 6002 pp. 376-379ré-D’Amaré* Science 201. Histogram of correlation coefficients of k obs (n = 135 point mutants) with randomly reassorted mutation frequencies Correlation of genotype frequency and experimental rate constants

22. Class II ligase ribozyme Rapid Construction of Empirical RNA Fitness Landscapes Jason N. PittJason N. Pitt and Adrian R. Ferré-D’Amaré* Science 2010: Vol. 330 no. 6002 pp. 376-379ré-D’Amaré* Science 201. Information content per position of the class II ligase ribozyme

23. In vitro selection of ribozymes Optimized for single-turnover enzymes

24. In vitro selected RNAs AptamersOrganic dyes, amino acids, nucleotides, metabolites Aminoglycosides, peptides, proteins, liposomes Cells, tissues, single-walled nanotubes Transition state analogs RibozymesPhosphoryl (incl. polymerase), acyl and alkyl transfer Isomerisation, Diels-Alder, nucleotide synthesis, Michael Metal insertion into mesoporphyrin Metal-metal bond formation (palladium nanoparticles)

25. In vitro selected ribozymes Ligase (Bartel & Szostak, Science, 1993) RNA polymerase (Johnston & Bartel, Science 2001) Polynucleotide kinase (Lorsch & Szostak, Nature 1994) Diels-Alderase (Agresti & Griffiths, PNAS 2005) All of these multiple-turnover ribozymes were converted from single-turnover isolates ribozymeprotein enzyme Serganov et. al. Nature Structural & Molecular Biology 2005, V 12, pp 218 - 224 Diels-Alderase

26. Shannon UncertaintyInformation Content = Max Information - Shannon Uncertainty Max information using 20 amino acids=4.3219 bits or 1.301 dits (base 10) Informational complexity and functional activity: Peptides

27. Shannon UncertaintyInformation Content = Max Information - Shannon Uncertainty Max information using 20 amino acids=4.3219 bits or 1.301 dits (base 10) Almost Invariant Glycine: P(Gly)=0.9981 P(Ala)=P(Arg)=P(Asn)=...=P(Val)=0.0001 H= -(-0.9981*0.002744 - 19*0.0001*13.28) = 0.002739+0.02523 = 0.05262 IC= 4.3219 - 0.0526 = 4.2693 Informational complexity and functional activity: Peptides

28. Informational complexity and functional activity: Peptides # possible AAs Shannon Uncertainty Information Content 10.00004.3219 21.00003.3219 31.58502.7369 42.00002.3219 5 2.0000 62.58501.7369 72.80741.5145 83.00001.3219 93.16991.1520 103.32191.0000 113.45940.8625 123.58500.7369 133.70040.6215 143.80740.5145 153.90690.4150 164.00000.3219 174.08750.2344 184.16990.1520 194.24790.0740 204.32190.0000 Peptide functions to consider: What’s the information content of a His-tag? What’s the information content of an HPQ streptavidin tag? What about two HPQ tags? A cystine bridge? What’s the information content of a hydrophobic position? And charged? What about a salt bridge? Small domains: zinc finger

29. Structure of the model peptide and of the residues incorporated at the guest position Richardson J. M. et.al. PNAS 2005;102:1413-1418 Copyright © 2005, The National Academy of Sciences Comparison of the enthalpy of helix formation Δhα obtained from different peptides

30. Richardson J. M. et.al. PNAS 2005;102:1413-1418 Copyright © 2005, The National Academy of Sciences # possible AAs Shannon Uncertainty Information Content 10.00004.3219 21.00003.3219 31.58502.7369 42.00002.3219 5 2.0000 62.58501.7369 72.80741.5145 83.00001.3219 93.16991.1520 103.32191.0000 113.45940.8625 123.58500.7369 133.70040.6215 143.80740.5145 153.90690.4150 164.00000.3219 174.08750.2344 184.16990.1520 194.24790.0740 204.32190.0000 Informational complexity and functional activity: Peptide secondary structure

31. # possible AAs Shannon Uncertainty Information Content 10.00004.3219 21.00003.3219 31.58502.7369 42.00002.3219 5 2.0000 62.58501.7369 72.80741.5145 83.00001.3219 93.16991.1520 103.32191.0000 113.45940.8625 123.58500.7369 133.70040.6215 143.80740.5145 153.90690.4150 164.00000.3219 174.08750.2344 184.16990.1520 194.24790.0740 204.32190.0000 Informational complexity and functional activity: Peptide secondary structure Beta-sheet formation propensity (from Minor&Kim Nature 1994) High Thr, Ile, Tyr, Phe, Val, Met, Ser Medium Trp, Cys, Leu, Arg Low Lys, Gln Negative propensity (sheet breakers) Gly, Pro