1. Parallel Computation of Simple Arithmetic using Peptide-Antibody Interactions
M. Sakthi Balan Kamala Krithivasan
Theoretical Computer Science Lab
Department of Computer Science and
Engineering
Indian Institute of Technology Madras
Chennai –
TCS Lab, IITM

2. Organization DNA Computing Peptide Computing Proposed Model
Addition Algorithm
Subtraction Algorithm
Discussion
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3. DNA Computing
Uses DNA strands and Watson-Crick Complementarity as operation
Highly non-deterministic
Massive parallelism
Solves NP-Complete Problems quite efficiently
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4. Peptide Computing Uses peptides and antibodies
Operation – binding of antibodies to epitopes in peptides
Epitope – The site in peptide recognized by antibody
Highly non-deterministic
Massive parallelism
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5. Peptide Computing Contd..
Peptides – sequence of amino acids
Twenty amino acids.
Example – Glycine, Valine
Connected by covalent bonds
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6. Peptide Computing Contd..
Antibodies recognizes epitopes by binding to it
Binding of antibodies to epitopes has associated power called affinity
Higher priority to the antibody with larger affinity power
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7. Computing DNA Vs Peptide
Twenty building blocks (20 amino acids)
Example: Glycine, Valine
Different antibodies can recognize different epitopes
Binding affinity of antibodies can be different
Four building blocks
Adenine (A), Guanine(G), Cytosine (C), Thiamine (T)
Only one reverse complement – Watson-Crick Complement
Complement (A) = T and Complement (G) = C
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8. Proposed Model Consists of a peptide and set of antibodies
Peptide sequence has n position specific epitopes
Epitopes epi = yi xi zi, yi and zi are switching epitopes for the ith bit.
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9. Peptide Sequence for a 5-bit numbery4 x4 z4 y0 x0 z0
Peptide Sequence for a 5-bit number
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10. Antibodies A = {A0, A1, …, An-1} B = {B0, B1, …, Bn-1}
TAB = {TAB0, TAB1, …, TAB(n-1)}
TBA = {TBA0, TBA1, …, TBA(n-1)}
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11. Binding Sites xizi yixi For Bi For Ai xi xi xizi > xi yixi > xi
TABi Zi
TBAi yi
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12. Affinity aff(TABi) > aff(Ai) aff(TBAi) > aff(Bi)
aff(TABi) = aff(TBAi)
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13. What it denotes? Ai – denotes ith bit is zero
Bi – denotes ith bit is one
TABi – used to switch ith bit from zero to one
TBAi – used to switch ith bit from one to zero
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14. Representation of Binary Numbers
If the ith bit is 0 then the antibody Ai is bounded to the epitope yixi
If the ith bit is 1 then the antibody Bi is bounded to the epitope xizi
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15. Example B4 A3 B2 A1 B0
10101
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16. Addition of Two Binary Numbers
A = an-1an-2 …a0
B = bn-1bn-2 …b0
C = cn cn-1cn-2 …c0
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17. XOR ai bi ci 1 2 3 4
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18. Addition (Contd..) First step – guessing equivalent to XOR gate.
The bit cn is initialized to zero.
Carry propagation.
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19. Addition (Contd..)
Carry occurs only when both the bits ai and bi are 1.
Carry is propagated to the left until both the bits aj and bj(j > i) are 0.
If no such j exists then propagation stops making nth bit 1.
j.j-1….i+1 is called the carry block.
For each carry block j.j-1….i+1 invert the digits ck (i+1  k  j)
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20. Algorithm
Add antibodies Ai where ai = 0 and bi = 0 or ai = 1 and bi = 1.
Add antibodies Bi where ai = 0 and bi = 1 or ai = 1 and bi = 0.
For all carry block jkjk-1…ik+1 do the following in parallel. For ik +1  s  jk
Add antibodies TABs,
Add antibodies Bs,
Add antibodies TBAs, and
Add antibodies As.
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21. Example
10110
10011 +
000101 A5 A4 A3 B2 A1 B0
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22. Example (Contd..)
101101 B5 A4 B3 B2 A1 B0
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23. Example (Contd..)
101001 B5 A4 B3 A2 A1 B0
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24. Algorithm ADD(A,B,C) XOR(A,B,C)
BlockInversion(I1,I2,…Ik,C) where Ij are carry blocks and k is the number of carry blocks.
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25. Algorithm - Same(C) Add excess of epitopes yi Add antibodies Ai
To get the peptide sequence with antibodies in workable form
Add excess of epitopes yi
Add antibodies Ai
Add excess of eptiopes zi
Add antibodies Bi
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26. Algorithm - Subtraction
SUB(A,B,C)
BlockInversion(I1,, B, B’) where I1 =
n-1…0
ADD(B’, ONE, B’’) where
ONE = an-1an-2…a11, ai = 0
ADD(A, B’’, C)
Inverttozero(C,n)
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27. Algorithm – Inverttozero
Inverttozero(C,i)
Same(C)
Add antibody TABi
Add antibody Ai
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28. Discussion To extract numbers from this system Limitations
NMR can be used or
X-ray crystallography
Limitations
Obtaining monoclonal antibodies
Manual process
Implementation ?
Universal operations ?
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29. Acknowledgments Authors thank Saravanakumar Narayanan,
TU-Munchen, Germany
for helpful discussions
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30. “They were built by 3 billion years of evolution, and we’re just beginning to tap their potential to serve non-biological purposes. Nature has given us an incredible toolbox, and we’re starting to explore what we might build”
Leonard Adleman
Thank You
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