Function-Information Relationship in
Nucleic Acids
Andrej Luptak
aluptak@uci.edu
UNIVERSITY of CALIFORNIA ‧ IRVINE
Information flow in biological systems
In vitro selection
How many solutions are there to a biochemical problem?
In vitro selected RNAs
Aptamers
Organic dyes, amino acids, nucleotides, metabolites
Aminoglycosides, peptides, proteins, liposomes
Cells, tissues, single-walled nanotubes
Transition state analogs
Ribozymes
Phosphoryl (incl. polymerase), acyl and alkyl transfer
Isomerisation, Diels-Alder, nucleotide synthesis, Michael
Metal insertion into mesoporphyrin
Metal-metal bond formation (palladium nanoparticles)
Informational complexity and functional activity
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?
Hazen et al. PNAS 2007 104
How many solutions are there to a biochemical problem?
How many solutions are there to a biochemical problem?
Isolation of high-affinity GTP aptamers from partially
structured RNA libraries
Jonathan H. Davis* and Jack W. Szostak†
PNAS 2002 vol. 99 no. 18
How many solutions are there to a biochemical problem?
Informational Complexity and Functional Activity of RNA Structures
James M. Carothers, Stephanie C. Oestreich,‡ Jonathan H. Davis,† and Jack W. Szostak
J.AM.CHEM.SOC. 2004,126, 5130
How does one measure structural complexity?
Informational Complexity and Functional Activity of RNA Structures
James M. Carothers, Stephanie C. Oestreich,‡ Jonathan H. Davis,† and Jack W. Szostak
J.AM.CHEM.SOC. 2004,126, 5130
How does one measure informational complexity?
Informational Complexity and Functional Activity of RNA Structures
James M. Carothers, Stephanie C. Oestreich,‡ Jonathan H. Davis,† and Jack W. Szostak
J.AM.CHEM.SOC. 2004,126, 5130
How does one measure informational complexity?
Informational Complexity and Functional Activity of RNA Structures
James M. Carothers, Stephanie C. Oestreich,‡ Jonathan H. Davis,† and Jack W. Szostak
J.AM.CHEM.SOC. 2004,126, 5130 & RNA 2006 12, 4
How does one measure informational complexity?
Informational Complexity and Functional Activity of RNA Structures
James M. Carothers, Stephanie C. Oestreich,‡ Jonathan H. Davis,† and Jack W. Szostak
Shannon Uncertainty
H   Pi log 2 Pi
i  A,U,G,C
Information Content=
Max Information
- Shannon Uncertainty
Max Information using 4 bases=2 bit
J.AM.CHEM.SOC. 2004,126, 5130 & RNA 2006 12, 4
How does one measure informational complexity?
Informational Complexity and Functional Activity of RNA Structures
James M. Carothers, Stephanie C. Oestreich,‡ Jonathan H. Davis,† and Jack W. Szostak
J.AM.CHEM.SOC. 2004,126, 5130
Informational complexity and functional activity
Information Content =
Max Information
- Shannon Uncertainty
Shannon Uncertainty
H   Pi log 2 Pi
i  A,U,G,C
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
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 - 0.0342 = 1.9658
IC= 2 - 1.038 = 0.9622
One position in a base-pair:
IC=1 bit (a base-pair is 2 bits)
One position in a regular or wobble pair:
IC=0.5 (1 bit per loose base-pair)
Another RNA aptamer example: adenosine aptamer
Class II ligase ribozyme
Pitt & Ferré-D’Amaré, J. Am. Chem.
Soc., 2009, 131 (10), pp 3532–3540
Class II ligase ribozyme
Rapid Construction of Empirical RNA Fitness Landscapes
Jason N. Pitt and Adrian R. Ferré-D’Amaré* Science 2010: Vol. 330 no. 6002 pp. 376-379
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
Class II ligase ribozyme
Rapid Construction of Empirical RNA Fitness Landscapes
Jason N. Pitt and Adrian R. Ferré-D’Amaré* Science 2010: Vol. 330 no. 6002 pp. 376-379
Changes in population structure during serial depletion (in vitro selection)
Class II ligase ribozyme
Rapid Construction of Empirical RNA Fitness Landscapes
Jason N. Pitt and Adrian R. Ferré-D’Amaré* Science 2010: Vol. 330 no. 6002 pp. 376-379
Correlation of genotype frequency and
experimental rate constants
Histogram of correlation coefficients of kobs (n = 135
point mutants) with randomly reassorted mutation
frequencies
Class II ligase ribozyme
Rapid Construction of Empirical RNA Fitness Landscapes
Jason N. Pitt and Adrian R. Ferré-D’Amaré* Science 2010: Vol. 330 no. 6002 pp. 376-379
Information content per position of the class II ligase ribozyme
In vitro selection of ribozymes
Optimized for single-turnover enzymes
In vitro selected RNAs
Aptamers
Organic dyes, amino acids, nucleotides, metabolites
Aminoglycosides, peptides, proteins, liposomes
Cells, tissues, single-walled nanotubes
Transition state analogs
Ribozymes
Phosphoryl (incl. polymerase), acyl and alkyl transfer
Isomerisation, Diels-Alder, nucleotide synthesis, Michael
Metal insertion into mesoporphyrin
Metal-metal bond formation (palladium nanoparticles)
In vitro selected ribozymes
ribozyme
Diels-Alderase
protein enzyme
Serganov et. al. Nature Structural & Molecular Biology 2005, V 12, pp 218 - 224
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
Informational complexity and functional activity:
Peptides
Information Content =
Max Information
- Shannon Uncertainty
Shannon Uncertainty
H   Pi log 2 Pi
Max information using 20 amino acids=4.3219 bits
or 1.301 dits (base 10)


i  A,U,G,C
i  Ala...Trp
Informational complexity and functional activity:
Peptides
Information Content =
Max Information
- Shannon Uncertainty
Shannon Uncertainty
H   Pi log 2 Pi
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


i  A,U,G,C
i  Ala...Trp
Informational complexity and functional activity:
Peptides
# possible AAs
Shannon
Uncertainty
Information Content
1
0.0000
4.3219
2
1.0000
3.3219
3
1.5850
2.7369
4
2.0000
2.3219
5
2.3219
2.0000
6
2.5850
1.7369
7
2.8074
1.5145
8
3.0000
1.3219
9
3.1699
1.1520
10
3.3219
1.0000
11
3.4594
0.8625
12
3.5850
0.7369
13
3.7004
0.6215
14
3.8074
0.5145
15
3.9069
0.4150
16
4.0000
0.3219
17
4.0875
0.2344
18
4.1699
0.1520
19
4.2479
0.0740
20
4.3219
0.0000
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
Structure of the model peptide and of the residues incorporated at the guest position
Comparison of the enthalpy of helix formation Δhα obtained from different peptides
Copyright © 2005, The National Academy of Sciences
Richardson J. M. et.al. PNAS 2005;102:1413-1418
Informational complexity and functional activity:
Peptide secondary structure
# possible AAs
Shannon
Uncertainty
Information Content
1
0.0000
4.3219
2
1.0000
3.3219
3
1.5850
2.7369
4
2.0000
2.3219
5
2.3219
2.0000
6
2.5850
1.7369
7
2.8074
1.5145
8
3.0000
1.3219
9
3.1699
1.1520
10
3.3219
1.0000
11
3.4594
0.8625
12
3.5850
0.7369
13
3.7004
0.6215
14
3.8074
0.5145
15
3.9069
0.4150
16
4.0000
0.3219
17
4.0875
0.2344
18
4.1699
0.1520
19
4.2479
0.0740
20
4.3219
0.0000
Copyright © 2005, The National Academy of Sciences
Richardson J. M. et.al. PNAS 2005;102:1413-1418
Informational complexity and functional activity:
Peptide secondary structure
# possible AAs
Shannon
Uncertainty
Information Content
1
0.0000
4.3219
2
1.0000
3.3219
3
1.5850
2.7369
4
2.0000
2.3219
5
2.3219
2.0000
6
2.5850
1.7369
7
2.8074
1.5145
8
3.0000
1.3219
9
3.1699
1.1520
10
3.3219
1.0000
11
3.4594
0.8625
12
3.5850
0.7369
13
3.7004
0.6215
14
3.8074
0.5145
15
3.9069
0.4150
16
4.0000
0.3219
17
4.0875
0.2344
18
4.1699
0.1520
19
4.2479
0.0740
20
4.3219
0.0000
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