Homochirality through enantiomeric cross-inhibition Axel Brandenburg, Anja Andersen, Susanne Höfner, Martin Nilsson To appear in Orig. Life Evol. Biosph., q-bio.BM/

2 Aminoacids in protein: left-handed Sugars in DNA and RNA: right-handed Louis Pasteur ( ) animogroup carboxylgroup

3 PNA world prior to RNA world PE Nielsen (1993) Nielsen (1993) Nelson, Levi, Miller (2000) CH 2 NH 2 C00H CH 2 C0 Base NH N C0 NH 2 C0 CH 2 NH C00H glycine dipeptide NH 2 C00H carboxylgroup aminogroup CH C00H CH 3 Peptidenucleotide alanine achiral chiral

4 Chirality and origin of life Life: plausible with left/right handed nucleotides Origin of life: possibly achiral (e.g. PNA world) –chiral nucleotides preferred: structurally more stable Source of chirality: –Polarized light, electroweak interaction –auto-catalytic (enzymatic) reactions during polymerization  chirality as a consequence of life

5 Relevant experiments: nucleotides template-directed oligomerization poly (C D )  oligo (G D )  Mononucleotides with wrong chirality terminate chain growth cytosine guanine ok poisoned Joyce, et al. (1984) (using HPLC)  enantiomeric cross-inhibition

6 Relevant experiments: crystals Crystal growth with stirring: primary nucleation suppressed Crystal growth, many different nucleation sites: racemic mixture  autocatalytic self-amplification Frank (1953), Goldanskii & Kuzmin (1989), …  competition important Alkanol with 2% e.e. treated with carboxylaldehyde Kondepudi et al. (1990) Soai et al. (1995)

7 Model by Saito & Hyuga (2004) Can the right model be found by trial/error? non-autocatalytic linearly autocatalytic nonlinearlyautocatalytic nonlin+autocat. with backreaction Frank (1953)

8 Polymerization model of Sandars Reaction for left-handed monomers Loss term for each constituent Orig. Life Evol. Biosph. (Dec 2003)

9 Combined equations: traveling wave Loss term for each constituent (if Q L =0)

10 Including enantiomeric cross-inhibition Loss term for each constituent Racemic solution ~2 1-n Stability

11 Coupling to substrate S Q L comes from substrate acts as a sink of S S sustained by source Q Catalytic properties of substrate (depending on how much L and R one has)  Q L = Q R (L n,R n ) Source of L 1 monomers Q L

12 Self-catalytic effect Form of Q L = Q R (L n,R n ) Possible proposals for C L (similarly for C R ) fidelity

13 Birfurcation properties exponential growth  growth rate  growth rate Degree of homochirality Red line: source Q from fragmented polymers (“waste”)

14 Reduced equations Quantitatively close to full model Initial bias 

15 Conclusions Polymerization model: –Based on measurable processes –Predicts wavelike chromatograms (HPLC) Reduction to accurate simplified model –Homochirality in space (earth, interstellar, etc)