TY - JOUR
T1 - An extended model for the evolution of prebiotic homochirality
T2 - A bottom-up approach to the origin of life
AU - Gleiser, Marcelo
AU - Walker, Sara Imari
N1 - Funding Information:
The authors were partially supported by a National Science Foundation grant PHY-0653341. We had access to the NCSA Teragrid cluster under grant number PHY-070021. We acknowledge extensive use of the FermiQCD parallelization program for solving the coupled systems of PDES.
PY - 2008/8
Y1 - 2008/8
N2 - A generalized autocatalytic model for chiral polymerization is investigated in detail. Apart from enantiomeric cross-inhibition, the model allows for the autogenic (non-catalytic) formation of left and right-handed monomers from a substrate with reaction rates ε L and ε R , respectively. The spatiotemporal evolution of the net chiral asymmetry is studied for models with several values of the maximum polymer length, N. For N = 2, we study the validity of the adiabatic approximation often cited in the literature. We show that the approximation obtains the correct equilibrium values of the net chirality, but fails to reproduce the short time behavior. We show also that the autogenic term in the full N = 2 model behaves as a control parameter in a chiral symmetry-breaking phase transition leading to full homochirality from racemic initial conditions. We study the dynamics of the N→ ∞ model with symmetric (ε L = ε R ) autogenic formation, showing that it only achieves homochirality for ε > ε c , where ε c is an N-dependent critical value. For ε ≤ ε c we investigate the behavior of models with several values of N, showing that the net chiral asymmetry grows as tanh(N). We show that for a given symmetric autogenic reaction rate, the net chirality and the concentrations of chirally pure polymers increase with the maximum polymer length in the model. We briefly discuss the consequences of our results for the development of homochirality in prebiotic Earth and possible experimental verification of our findings.
AB - A generalized autocatalytic model for chiral polymerization is investigated in detail. Apart from enantiomeric cross-inhibition, the model allows for the autogenic (non-catalytic) formation of left and right-handed monomers from a substrate with reaction rates ε L and ε R , respectively. The spatiotemporal evolution of the net chiral asymmetry is studied for models with several values of the maximum polymer length, N. For N = 2, we study the validity of the adiabatic approximation often cited in the literature. We show that the approximation obtains the correct equilibrium values of the net chirality, but fails to reproduce the short time behavior. We show also that the autogenic term in the full N = 2 model behaves as a control parameter in a chiral symmetry-breaking phase transition leading to full homochirality from racemic initial conditions. We study the dynamics of the N→ ∞ model with symmetric (ε L = ε R ) autogenic formation, showing that it only achieves homochirality for ε > ε c , where ε c is an N-dependent critical value. For ε ≤ ε c we investigate the behavior of models with several values of N, showing that the net chiral asymmetry grows as tanh(N). We show that for a given symmetric autogenic reaction rate, the net chirality and the concentrations of chirally pure polymers increase with the maximum polymer length in the model. We briefly discuss the consequences of our results for the development of homochirality in prebiotic Earth and possible experimental verification of our findings.
KW - Early planetary environments
KW - Homochirality
KW - Origin of life
KW - Prebiotic chemistry
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U2 - 10.1007/s11084-008-9134-5
DO - 10.1007/s11084-008-9134-5
M3 - Article
C2 - 18465201
AN - SCOPUS:46749146457
SN - 0169-6149
VL - 38
SP - 293
EP - 315
JO - Origins of Life and Evolution of Biospheres
JF - Origins of Life and Evolution of Biospheres
IS - 4
ER -