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 – 600036. Email: sakthi@cs.iitm.ernet.in kamala@iitm.ernet.in TCS Lab, IITM

Organization DNA Computing Peptide Computing Proposed Model Addition Algorithm Subtraction Algorithm Discussion TCS Lab, IITM

DNA Computing Uses DNA strands and Watson-Crick Complementarity as operation Highly non-deterministic Massive parallelism Solves NP-Complete Problems quite efficiently TCS Lab, IITM

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 TCS Lab, IITM

Peptide Computing Contd.. Peptides – sequence of amino acids Twenty amino acids. Example – Glycine, Valine Connected by covalent bonds TCS Lab, IITM

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 TCS Lab, IITM

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 TCS Lab, IITM

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. TCS Lab, IITM

Peptide Sequence for a 5-bit number y4 x4 z4 y0 x0 z0 Peptide Sequence for a 5-bit number TCS Lab, IITM

Antibodies A = {A0, A1, …, An-1} B = {B0, B1, …, Bn-1} TAB = {TAB0, TAB1, …, TAB(n-1)} TBA = {TBA0, TBA1, …, TBA(n-1)} TCS Lab, IITM

Binding Sites xizi yixi For Bi For Ai xi xi xizi > xi yixi > xi TABi Zi TBAi yi TCS Lab, IITM

Affinity aff(TABi) > aff(Ai) aff(TBAi) > aff(Bi) aff(TABi) = aff(TBAi) TCS Lab, IITM

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 TCS Lab, IITM

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 TCS Lab, IITM

Example B4 A3 B2 A1 B0 10101 TCS Lab, IITM

Addition of Two Binary Numbers A = an-1an-2 …a0 B = bn-1bn-2 …b0 C = cn cn-1cn-2 …c0 TCS Lab, IITM

XOR ai bi ci 1 2 3 4 TCS Lab, IITM

Addition (Contd..) First step – guessing equivalent to XOR gate. The bit cn is initialized to zero. Carry propagation. TCS Lab, IITM

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) TCS Lab, IITM

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. TCS Lab, IITM

Example 10110 10011 + 000101 A5 A4 A3 B2 A1 B0 TCS Lab, IITM

Example (Contd..) 101101 B5 A4 B3 B2 A1 B0 TCS Lab, IITM

Example (Contd..) 101001 B5 A4 B3 A2 A1 B0 TCS Lab, IITM

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. TCS Lab, IITM

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 TCS Lab, IITM

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) TCS Lab, IITM

Algorithm – Inverttozero Inverttozero(C,i) Same(C) Add antibody TABi Add antibody Ai TCS Lab, IITM

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 ? TCS Lab, IITM

Acknowledgments Authors thank Saravanakumar Narayanan, TU-Munchen, Germany for helpful discussions TCS Lab, IITM

“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 TCS Lab, IITM