The document discusses computational studies related to pKa calculations of proteins and nucleic acids, focusing on the structural aspects that improve sequence alignments. It highlights the complexity of ribozymes, particularly in the context of the hepatitis delta virus (HDV), which relies on specific catalytic mechanisms. The findings emphasize the importance of structural geometry in understanding pKa shifts and the role of electrostatics in determining nucleotide interactions within RNA.

1. Computational Studies of Proteins and Nucleic AcidsOn pKa Calculations in RNA and the Use of Structure to Improve Sequence AlignmentsMay 13, 2008 – Christopher L. Tang, ICRC 816, Columbia University

2. Electrostatics and RNAMetal ion binding sites in23S ribosomal RNAMisra & Draper, 2002

3. Ribozyme Function is Highly Varied(b)(d)(c)(a)(h)(g)(f)(e)Ribozymes use only nucleic acid groups to perform catalysisRibozymes. (a) 50S ribosome (b) Ribonuclease P, (c) Group I intron, (d) glms, (e) Diels-Alderase, (f) Hepatitis delta virus, (g) Hairpin, (h) Hammerhead

4. ribozymedelta antigenThe Hepatitis Delta VirusReplication of HDV genome employs catalysis by two related ribozymesHDV genomic RNAcomplement ribozymeI. HDV genome (G) replicatesGcomplement strand cleavedreligationCIII. complement (C) replicatesgenome strand cleavedMM Lai, 1995

5. HDVR function involves hydrolysis of an internal phosphodiester bondPRODUCTREACTANT:+H2’:5’+CCHShih & Been, Ann Rev. Bioch., 2002

6. Cleavage site of HDVRwithin 10 ÅKeet al., 2004

7. 2.8 ÅHDVR ACTIVE SITEPRODUCT5’OH(Nakano & Bevilacqua, 2000)

8. HDVR active site structure is suggestive of catalytic mechanismPRODUCTPRODUCTREACTANTU-1U-1Not observedC+75C75 G 1 G 1+CCHShih & Been, Ann Rev. Bioch., 2002

9. PRODUCT2’5’— O – H :O –—BASE CATALYZEDACID CATALYZEDSummary of mechanism_H+2’5’— O: –:H – O —+CCH(Nakano & Bevilacqua, 2000)

10. 2’5’OHO–— O – H :O –—BASE CATALYZEDACID CATALYZEDH+2’5’— O: –:C75H – O —+CCHpH

11. Not observed !~6~7kobs+ free OHO–pHObserved reaction rate dependence on pH(Perrottaet al., 2007)???C75

12. Solution pKas of nucleotides Ade and Cyt nucleotides are poor basesAde  Ade (+)(3.8)Cyt Cyt(+)(4.3)+H(pKaref)Izattet al., 1970pH1478910111213654321+CCH% ionized

13. Framework for calculating pKa shift I: Reference and Structure pKas IsolatednucleotideH+H+––pKaref++–++–––++++DpKaStructure++++–––––––++++––pKastruct––++––++++++++–++

14. Framework for calculating pKa shift II: Effects due to Salt–––H+H+––

15. Potentials can be solved using classical equations of continuum electrostaticsPoisson-Boltzmann equationpairwise interactionsmobile ion interactionswater interactions (solvation)eext

16. Framework for calculating pKa shift III: Free energyBADpKa = (DG AB (struct) – DG AB (ref)) / 2.3kBT

17. +H+CCH

18. pKa calculations using MCCE (Alexov & Gunner)Calculating pKas in RNA with Multiple Titratable groups0002N states001B010011…100AC+1=111+1+1The potential at any single site (A) depends on the protonation state of all other sites, (B and C) This problem is solved using the Multiple Conformation Continuum Electrostatics (MCCE) method to identify and sample low energy states

19. Origin of the Error using the Linear Approximation for Highly Charged SystemsLINEAR PBENONLINEAR PBE++++LINEAR CASENONLINEAR CASE0102

20. Correction of the Error due to Nonlinearity is a Function that Depends on Protonation StateDG ABNL (struct) = DG ABLPB (struct) + DG AB (corr APPROX)Tang, Alexov, Pyle & Honig 2007

21. Partial charges were derived for A+ & C+Tang, Alexov, Pyle & Honig 2007

22. RESULTSTang, Alexov, Pyle & Honig 2007

23. Calculated and experimental pKas are consistentBranch Point Helix(12 conf)A135.5A76.1pKaA7A8A13A16A17A18A25BPHSmith & Niconowicz, 1998Tang, Alexov, Pyle & Honig 2007

24. Calculated and experimental pKas are consistentA16Lead-Dependent Ribozyme (25 conf)3.8A173.83.5A18pKaA84.3A256.5A7A8A13A16A17A18A25Salt dependence of A25 pKain leadzymeLeadzymeBPHTang, Alexov, Pyle & Honig 2007Legault & Pardi, 1997

25. HDVR exhibits a deep cleft proximal to C75 and the scissile bondP1P2P3C75P1.1P4U1A2.8 ÅNakano et al., 2001G1C75

26. pKa shifts of Adenosines and Cytidines in HDVR DpKaC75C412.8 ÅG1C75Tang, Alexov, Pyle & Honig 2007

27. The pKa of C75 is elevated above its solution pKaDesolvation opposes the shift but the potential acting on C75 due to phosphate charges is much stronger Interactions with Phos. only: – 9.2 kcal/molInteractions with solvent: + 1.5 kcal/mol– 7.7 kcal/mol

28. pKa shifts of Adenosines and Cytidines in HDVR C41DpKaC75C412.8 ÅG1C75Tang, Alexov, Pyle & Honig 2007

29. G73C44A43C+41Modifying the C41 nucleotide interaction can abrogate pH-dependent HDV activityA73U44C41A43Nakano et al., 2007

30. Bell-shaped pH curve: Revisitedbasekobs+ free C41 !C75pHkobs

31. G28G12C26C13A12A25C10C8C41 is part of a commonly found structural motifIn all cases where the motif is found, the folded RNA is stable at higher pH than expected given the solution pKa of CG73C44A43C41BWYVPEMV calc pKaHDVR 10.6BWYV 13.7PEMV 10.6Determined by NMR at pH = 6Crystallized at pH = 7, RTpH at Tm ½ = 7pH at Tm ½ = 7Tang et al. 2007*pH ½ (Su, Rich et al., 1998)(Nixon, Giedrocet al., 2000; 2002)

32. A1005+ : C963A45+ : U115How common are pKa-shifted nucleotides?Nucleotides probably protonated in H. marismortui 50S ribosomal subunit (pdb: 1ffk)identified using a hydrogen bond distance rule (acc-acc dist. < 3.0 Å):Results (3.0 Å cutoff)C1026+ : G940C1069+ : phos

33. ConclusionsEstablished a method for calculating pKas of nucleotides of RNAA version of MCCE 2.4 can now perform calculations on RNANucleotides with shifted pKasActive sitesConserved motifspKa shifts can be understood in terms of structureSome geometric rules can be established for finding pKa-shifted nucleotides50S ribosomal subunit, H. morismortui

34. Barry Honig

35. Acknowledgements Emil Alexov, Anna Marie Pyle, Lei Xie, BurkhardRost, Larry Shapiro, Diana Murray, An-Suei Yang, Marilyn Gunner Lucy Forrest, ShoshanaPosy, Markus Fischer, Remo Rohs, Donald Petrey, Jiang Zhu, Jeremie Vendome,KelyNorel, Brian Chen, Rachel Kolodny, Trevor Siggers, Cinque Soto, Andy Kuziemko, Sean West, Peng Liu, Andrew Kernytsky, AvnerSchlessinger, Henry Bigelow, Michael, Christine, Kaz, Dariusz, Claudia, Marco, Sven, Raj… and many other members of the Honig and Rost labs, andfriends of us, both past and present.Yifan Song and Junjun Mao for their help with MCCE 2.4 My roommates Chintan and Sean, for putting up with my lapses on the household chores Dr. Ron Liem, Katie Rosa, ZaiaSivo, Fred Loweff, and the Integrated and Biochemistry officesBarry Honig

37. John Tang1942-1988

39. P15’ O:<3.0 ÅC75G1P1.1C41

40. tRNAmRNAribosometRNA > 1958 (Hoagland, et. al)mRNA > 1961 (Brenner, Jacob, Meselson)

41. Framework for calculating pKa shift IV: Electrostatic potentialBut f in solution must involve:Pr+PPairwise interactionsSolvent interactionsMobile ions

42. Given the chemical reaction: Define: Ka = acid dissociation constantDefine: Then: from the Law of Mass Action: Then:Similarlyfor bases: and:

43. Derivation of DpKaGiven the reactions:BB+ (unfolded); andBB+ (folded);What is DpKa?DpKa=pKa(folded) – pKa(unfolded)DG BB+ (unfolded) = – 2.3 kT ( pKa (unfolded) – pH )DG BB+ (folded) = – 2.3 kT ( pKa (folded) – pH )DG BB+ (folded) – DG BB+ (unfolded) = – 2.3 kT ( pKa (folded) – pKa (unfolded) )DpKa = 1/(2.3 kT) DDG BB+ (folded – unfolded)1 DpK unit = 1.36 kcal/mol = 2.3kT.

46. Calculated and experimental pKas are consistentpKaA8A7A13A16A17A18A25Salt dependence of A25 pKain leadzyme1Lead-dependent2ribozymeBPH1Smith & Niconowicz, 1998Legault & Pardi, 1997

48. A+CA+- C pair, leadzyme pH 5.5C+CC+- C pair, DNA pH 6Protonated nucleotides in RNA structuresUC

49. Branch Point Helix(12 conf)A13A10C14A7C15A6A17C3C20C21

50. +H+CH?

52. Poisson-Boltzmann equationTwo forms for Function F (j):Linear: suitable for low charge systems like proteins, low saltNonlinear: necessary for high charge systems that require salt

53. Mutagenesis and rescue experimentsNakano et al., 2007 and Perrottaet al., 2007baseC75baseC41+ free C75

54. 320K 347K

55. G73C44*A43C41Nucleotides in analogous structures have similar pKas BWYV Y-knotHDV ribozymeHDVRBWYVNixon & GiedrocNixon et al.

56. G28G12C13C26G73C44A12A25C10C8A43C41C14G74G123.8 ÅG733.9 ÅC8C41U72C11C10C9G59Analogous structures are stabilized by conserved interactions13.7(9.3-10.3)10.2 (9.9)10.6BWYV-yPEMV-yHDVRU29G28C10A27U9A262.9 Å

57. Biology of HDV and function of HDV ribozymeHepatitis delta virus

58. Obligate satellite virus of Hepatitis B virus

59. Circular ss-RNA genome, unique in animal viruses & reminiscent of plant satellite viruses.

60. Genome replicates by rolling circle mechanism

61. HDV ribozyme

62. Two forms, present on genomic and anti-genomic genome

63. Self-cleaving activity is essential for HDV replication cycle – trims multimeric strands into monomeric unitsGenome structure of HDVMMC Lai, The molecular biology of the Hepatitis Delta Virus, 1995

65. Rosenstein & Been, 1991genomic strandHepatitis Delta Virus (HDV)and its Ribozymes688compliment strand (antigenomic)904I. genomic strand (G) replicatesGribozyme (gen) cleaves & compliment circularizesAGIII. compliment (AG) replicatesribozyme (anti) cleaves & genome circularizes…

66. HDVRApplication in a system where pKas have not been directly measuredHepatitis Delta Virus ribozymeCritical for the replication of delta virus RNA genomeStructure12 crystal structures of the precursor & product exist – Ferre-D’Amare & Doudna; Ke et al.2.3-3.5 Å resolutionNested, double Y-knot topology5 major helical sectionsBiochemistryA77, A78, C75 (J4/2)C41 (J1.1/4 – P4)pH-dependent reaction kineticsSalt-dependent reaction kinetics

67. Structural roles for ionized nucleotides in RNAExample: BWYV H-type Y-knotFirst crystallized by Su et al., 1999 to 1.6 ÅResponsible for a -1 frame-shifting event that controls expression of alternative gene products in various virusesTertiary structure is well-stabilized, beyond typical H-type knotsMeasured stability exceeds that expected by considering only 2° structureFormation of 3° structure contributes more H-bonds than the formation 2° structureFolding of the Y-knot studied by Nixon & GiedrocpH-dependent (transition at pH 6.8)Attributed to C8-G12-C26-A25 interactionSubstitution of C8 with U reduces stabilityNixon & Giedroc, 2000

68. Why is this RNA substructure conserved?GC+CThree properties of this substructure:Rotation per turn deviates from 25° to almost 90°Base stacking is preserved through both sides of C+GC plane6 hydrogen-bonds, probably most stabile isostere with this structure

69. O5’C75G1U20O3’,O1PC22O2PC21pKa calculations identify active site residues**A78A77C75G1(C21,C22)

70. Mechanism Proposed: Ke et al., Nature 2004

71. Independent tests confirm partial charges derived for nucleotides are consistent w/ exp.New charges for A and C are similar to those in standard FFsCalculated hydration free energy yielded good agreement w/ exp.Hydration free energy depends on cavitation + solvationExperimental hydration free energies: (rms error depends on r-scaling)DGtr(vw)(9-methyladenine), DGtr(vcf)(9-methyladenine), DGtr(vcf)(1-methyluracil)(v=vacuum e=1, w=water e=80, cf=chloroform e=4.8) – Wolfenden & colleagues, 1998Used for pKa calculationsSitkoff, Sharp & Honig

72. Nonlinear contribution is mostly dependent on total charge of the RNAn = # of protonsCorrection for nonlinearity: E(Coulomb) + E(Solvation) + E(Ions) + ENL(n) = Etotal

75. Structural elements in RNAUCBase pair structureDouble HelixHairpin TurnSecondary structure

76. 622 RNA-only structures in the RCSB1132 ribozyme structuresUUCC1PDB statistics page:http://www.rcsb.org

78. P2A78U-1A77C75J4/2G1C22C21P1.1G39G38C75 is located in the active site of HDVR

79. A cluster of phosphates surrounds the catalytic C75

80. In biology…perturbed pKas are observed in distinct & diverse biological processes

81. Splice site recognition: branch-point helix motif(RNA binding of viral matrix proteins)

82. Bulged DNA duplexes and triple helices

83. Structural: tRNA(Lys)

84. Functional: Frameshifting pseudoknots

85. Shifts codon reading frames: BWYV, PEMV, PLRVtRNA(Lys)(Durant & Davis, 1999)Beet Western Yellows Viruspseudoknot (Su et al., 1999)

86. How much versatility in just 4 bases?UUAetc…UUHoogsteenWatson CrickCOther Pairs ObservedCC

87. Functional rolesStructural roles2.8 ÅC75↑Hypothetical mechanism for catalysis & product state of HDVR ↑BWYV pseudoknot &HDV ribozyme RNA with same local structure↓Vanadate-stabilized transition/product states of HR obs. at 2.4 Å↓G73C44*A43C41

88. SolvationPairwise interactionsMobile IonspKa shifts depend on electrostatic properties we can calculate~ water ~

89. ++LINEAR: fsalt = k1 * (2q/r) = k1 * 2 * (q/r)NONLINEAR: fsalt = k2 * sinh (2q/r) ≠ k2 * 2 * sinh (q/r)

91. 3’3’3’5’5’

92. ~32°+HUU+CCCH

93. RNApolymeraseribosome

94. 1 “specializedribosome”1 protein1 DNA< 1961

95. optionalRNApolymeraseribosome> 1986 (Zaug, Cech)

96. RNA catalysispolymerase> 1986 (Zaug, Cech)Group I intron(Stahley & Strobel, 2005)

97. Group I/II intronsmiRNArRNAsiRNASpliceosomeTelomerasetmRNAtRNARibozymesRNA genespolymeraseToday

98. NH’C = OOg1CbH”CaCgNOg2H”’O = COb’CaCbNOb”Standard MCCE (protein-based calculation)Multiple Conformation Continuum ElectrostaticsEach polar or charged residue is treated as a set of rotamersCharges on the backbone & nonpolar aa. are treated as fixedMany possible conformations due to the choice of rotamers at each position (‘microstate’)A microstate energy is defined for each possible conformationComponents of microstate energy solved using linear PB equationTakes advantage of linearity to compute microstate energy1 Alexov & Gunner, 1997

99. O3’PO1PO2PO5’O1’A or AH+O3’H–O2’PO1PO2PO5’O1’C or CH+O3’H–O2’New MCCE (RNA-based calculation)Instead of amino acids, nucleotidesSimple modelAdenosine (A) and cytidine (C) each can have two rotamers, ionized (AH+,CH+) or neutral (A,C)Adenosine: pKaref = 3.8Cytidine: pKaref = 4.3Deal with nonlinearityUse a nonlinear correction to microstate energy (NL-MCCE)Need to estimate partial charges for AH+ and CH+Use an AMBER-like approach

100. log [C+75]log [2’O-]

101. Enzymatic activity depends on the structural organization of the active siteHis 57Ser 195Asp 102Structural conservation of the active sites in trypsin, chymotrypsin & elastaseCatalytic chemistry depends on the arrangement of the active site residuesArrangement of His 57, Asp 102 & Ser 195 in the active site of serine proteases

102. Why might pKa calculations be interesting to the casual biologist?An example using the protein transferrinDifferences between the open and closed forms of transferrin result in dramatic changes to their theoretical titration curvesTheoretical titration curves predicted by THEMATICS(Murga, Ondrechen & Ringe 2008)

103. pKas calculations for catalytic residues are generally accurate in proteinsE.g. for LysozymeExperimental (expt) pKas :Glu 35 : 6.2Asp 52 : 3.7 Calculated (range) pKas :Glu 35 : 5.6 (4.3-7.3)Asp 52 : 3.8 (1.8-6.6) Nielsen et al., 2003

104. tRNA ~100ntribosome 30S subunit ~3500nt

105. Honig LabProtein structure predictionMarc Fasnacht, Lucy Forrest, Andy Kuziemko, Rachel Kolodny, Peng Liu, Donald Petrey, Cinque Soto, Chris Tang, KelyNorel, Sean West, Li Xie, Jiang Zhu Remo Rohs & others in the Honig & Pyle labsProtein-DNA recognitionRemo Rohs, Tonia Silkov, Alona SosinskyShana Posy & Jeremie Vendome (cadherins), Mickey Kosloff (GPCRs)Columbia, Integrated / Biochemistry & BiophysicsZaia Sivo, Katie Rosa, Ron Liem, Stacey Warren, Rachel Hernandez, Ed Johnson