Coding Theory and Protein Coding Theory and Protein SynthesisSynthesis
Avogadro-Scale Engineering: Form and FunctionAvogadro-Scale Engineering: Form and FunctionNovember 18, 19 2003November 18, 19 2003
Elebeoba E. MayElebeoba E. May
Computational Biology DepartmentComputational Biology DepartmentSandia National LaboratoriesSandia National Laboratories
*[email protected]*[email protected]
Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company,for the United States Department of Energy under contract DE-AC04-94AL85000.
AgendaAgenda It is the glory of God to conceal a matter; to search out a matter is the glory of kings. Proverbs 25:2 (NIV)
• Error Control at Diverse Molecular Scales
• Coding Theory Models of Protein Synthesis– Gatlin– Yockey– May et al.
• Applications of Coding Theory to– Genetic Classification– Molecular Computation– Construction and Control in Protein Synthesis
Nucleotides: Did nature select a parity check code?
D. A. Mac Dónaill : “ Numerical Interpretation of nucleotides depicted as positions on a B^4 hypercube: (a) even-parity nucleotides; (b) odd-parity nucleotides. The natural alphabet is structured as an error-checking code.”
*D.A. Mac Dónaill, “A parity code interpretation of nucleotide alphabet composition,” Chem. Comm. (2002) 2062-2063 and http://www.tcd.ie/Chemistry/People/macdonaill/
Protein: Degeneracy of the genetic code
B. Hayes : “how quickly a biochemical puzzle … was reduced to an abstract problem in symbol manipulation.” B. Hayes, “The Invention of the Genetic Code,” Sc. Am. 1998 (Physicist George Gamow and coding-theorist Solomon W. Golomb. Experimental evidence from Marshall W. Nirenberg and J. Heinrich Matthaei, NIH)
http://ww
w.people.virginia.edu/~rjh9u/code.htm
l
Protein: Information theory and binding sites
T. D. Schneider : “Strong minor groove base conservation in sequence logos implies DNA distortion or base flipping during replication and transcription initiation,” Nucleic Acids Research, 2001, Vol. 29, No. 23 4881-4891
Comparison of microbial genome base mutation rate to genome size: exhibits power law behavior; inverse relation between genome size and base mutation rate.
Mutation RatesMutation Rates• RNA viruses: 1 - 0.1• DNA microbes: 1/300• Higher eukaryotes: 1/300 EfGn
Genome: Increased length, increased fidelity
Comparison of higher eukaryotic genome base mutation rate to genome size: inverse relation between genome size and base mutation rate.
G. Battail: “… increasing the codeword length results in a decreasing probability of error…”
Evidence: Is there evidence of error control in protein synthesis process?
Liebovitch et al. 1996, Rosen and Moore 2003 computational experiments did not find evidence for linear block codesApproach not comprehensive, did not consider convolutional coding or noiseMay et al. Looked for optimal generator for translation initiation sitesHighly probable for encoding model not to conform to known error control codes.
AgendaAgenda It is the glory of God to conceal a matter; to search out a matter is the glory of kings. Proverbs 25:2 (NIV)
• Error Control at Diverse Molecular Scales
• Coding Theory Models of Protein Synthesis– Gatlin– Yockey– May et al.
• Applications of Coding Theory to– Genetic Classification– Molecular Computation– Construction and Control in Protein Synthesis
(eukaryotes)
Central Dogma of Genetics = Genetic Information Central Dogma of Genetics = Genetic Information TransmissionTransmission
(http://www-stat.stanford.edu/~susan/courses/s166/central.gif)
Encode
Channel
B
Decode
A
Coding Theory Models of Protein Synthesis Gatlin, LL., Information theory and the Living System. 1972.
Yockey, Hubert, Information Theory and Molecular Biology. 1992
Genetic Encoder
Coding Theory View of Protein Synthesis, May et al., JFI 2004
Genetic Information
Errors
Genetic Channel
3’AUG UAA
mRNA
Genetic Decoder
Principal Hypothesis:Principal Hypothesis: If mRNA is viewed If mRNA is viewed as a noisy encoded signal, it is feasible to use as a noisy encoded signal, it is feasible to use principles of error control coding theory to principles of error control coding theory to interpret the genetic translation initiation interpret the genetic translation initiation mechanismmechanism
111-000-000-111
111-001-000-110
1-0-0-1
k-bitInformation
Errors!111-001-000-110
n-bitInformation
Noise+n-bitInformation
A B
~ k-bitInformation
Channel
Encoder
Decoder
1-0-0-1
1-0-0-1
Engineering Communication System
Error Control
111-000-000-111
111-001-000-110
1-0-0-1
k-bitInformation
Errors!111-001-000-110
n-bitInformation
Noise+n-bitInformation
A B
~ k-bitInformation
Channel
Encoder
Decoder
1-0-0-1
1-0-0-1
Engineering Communication System
Error Control
????????
AgendaAgenda It is the glory of God to conceal a matter; to search out a matter is the glory of kings. Proverbs 25:2 (NIV)
• Error Control at Diverse Molecular Scales
• Coding Theory Models of Protein Synthesis– Gatlin– Yockey– May et al.
• Applications of Coding Theory to– Genetic Classification– Molecular Computation– Construction and Control in Protein Synthesis
• Efficient Coding for the Desoxyribonucleic Channel (S. W. Golomb 1962)– Applied Biorthogonal codes to genetic
coding problem (the codon to amino acid mapping challenge)
• Andrzej K. Konopka (1984)• Gerard Battail • Table-Based Convolutional Code for E. coli
Promoter (P. Bermel) – Based on the informational content of E.
coli promoter, approximates the coding rate for promoter region as 1/9.
– Developed a possible 1/5 binary code for E. coli promoter region.
Biological Coding TheoryBiological Coding Theory David Loewenstern, et. al
• Compression for DNA sequence classification
Leonard Adleman, et al.; Lila Kari, et al.• Molecular computation• Encoding for DNA computing• Error-control coding
Thomas Schneider, et al.• Biological information theory• Error-control via sphere packing
TransmissionTransmission
StorageStorage
Error-Control Coding Based MethodsError-Control Coding Based Methods
Horizontal axis is position relative to the first base of the initiation codon.Vertical axis is the mean of the aligned minimum Hamming distance values by position, for the 3 sequence groups (Hamming distance = # of positions where two vectors differ)
Coding Theory in RBS ClassificationCoding Theory in RBS Classification
AUGSD
NRD DB
May et al., BioSystems 2004
b-15, b-14, …, b-11, … , b-1, A U G
b-15 b-14 b-13 b-12 b-11 b-10 b-9 b-8 b-7
Davg-15 Davg-14 ………. Davg-
11
s
59.065
40.935
73.81
26.19
62.105
37.895
50 50
0
10
20
30
40
50
60
70
80
Correct Classification Incorrect Classification
PDF PDF (p=0.5) CDF CDF (p=0.5)
Coding Theory in RBS ClassificationCoding Theory in RBS Classification
v1
v2
v1
v2v1
v2
ligase
Coding Theory and Molecular ComputationCoding Theory and Molecular ComputationLeonard M. Adleman, et al.; Lila Kari, et al.
•Molecular computation•Encoding for DNA computing•Error-control coding
http://www.scs.uiuc.edu/~scott/index_files/ligation.gif
M. Stojanovic and D. Stefanovic, “A deoxyribozyme-based molecular automaton.” Nature Biotech. 2003
•Can achieve computational robustness using coding theory
Construction and control: Quantify and Optimize Protein Translation
InitiationFactors
3’AUG UAA
50s sub-unit
30s sub-unit
Polypeptide Protein
AUGGUGUUG
UAAUAGUGA
3’Leader* Coding Region*Ribosome binding site contained in leader region
Messenger RNA (mRNA)
5’
5’
•Phases of translation: initiation, elongation, termination•Initiation is most time consuming, affects overall gene expression level•Qualitative outline for initiation process exists: 1) 30S + Ifs bind to mRNA and fMet-tRNA; 2) Ternary complex binds 50S subunit; 3) IFs released prior to elongation.
mRNA is the only variable aspect of translation initiation.Information encoded in mRNA determines specificity and efficiency
Construction and control : Quantify and Optimize Protein Translation
AUGGUGUUG5’ 3’
mRNA Leader Region (UTR)
3’..AUUCCUCCACUAG….
Ribosome Binding Site
5’
Downstream box
Non-randomdomain
Modify E.coli Intergenic