Exponential self-replication enabled through a fibre elongation/breakage mechanism

Abstract

Self-replicating molecules are likely to have played a central role in the origin of life. Most scenarios of Darwinian evolution at the molecular level require self-replicators capable of exponential growth, yet only very few exponential replicators have been reported to date and general design criteria for exponential replication are lacking. Here we show that a peptide-functionalized macrocyclic self-replicator exhibits exponential growth when subjected to mild agitation. The replicator self-assembles into elongated fibres of which the ends promote replication and fibre growth. Agitation results in breakage of the growing fibres, generating more fibre ends. Our data suggest a mechanism in which mechanical energy promotes the liberation of the replicator from the inactive self-assembled state, thereby overcoming self-inhibition that prevents the majority of self-replicating molecules developed to date from attaining exponential growth.

Figure 1. Replication mechanisms.

(a) Traditional mechanism based on template-directed ligation of two replicator precursors. (b) Oxidation of building block 1 containing two thiol functionalities leads to a mixture of interconverting macrocycles. (c) Self-assembly of hexamers 1₆ results in the formation of fibres. Fibre fragmentation results in doubling of the number of fibre ends. (d) Species distribution as a function of time of a non-seeded dynamic combinatorial library made from 3.8 mM 1 in 50 mM borate buffer pH 8.1 stirred at 1,500 r.p.m.

Figure 2. Experimental determination of the order in replicator.

Initial replication rates against initial replicator concentration. Data points correspond to seed concentrations (expressed as concentration of 1₆) of 31, 63, 95 and 127 μM, respectively. The error bars on the data points correspond to one standard deviation for each seed concentration and the error on the slope is the standard deviation based on the complete set of measurements.

Figure 3. Influence of the stirring rate on fibre length and replication kinetics.

(a) Average fibre length for different stirring rates. (b) Kinetics of replicator growth at various stirring rates (lighter to darker blue: 200, 400, 800, 1,000 and 1,500 r.p.m.). (c) Time needed for the replicator to represent 50% of the library material (t₅₀), as a function of the average fibre length; the line represents a linear fit of the data.

Figure 4. Change in replicator concentration and average fibre length during replication.

(a) Change in product distribution with time of a library made from building block 1 (3.8 mM) stirred at 1,200 r.p.m. composed of 1 and cyclic trimer and tetramer seeded at t=0 min with 20% pre-formed hexamer fibres (monomer concentration as black squares, trimers as green triangles, tetramers as red circles, hexamers as blue triangles). (b) Average fibre length (blue squares) and associated standard deviation of the fibre length distribution (green circles) of this seeded library as a function of time (determined by TEM).

Figure 5. Computational model of the replicating system.

Fibre elongation and fibre breakage could be toggled on or off in order to study their role in replication.

Figure 6. Computational studies on the growth/breakage mechanism.

The numerical simulations show distinct kinetics in the presence of the breakage mechanism and in the absence thereof. (a) Typical kinetics observed in the numerical simulations of the growth/breakage mechanism (monomers in black, trimers in green, tetramers in red and hexamers in blue). (b) Computational determination of the order in replicator r in the case of a growth/breakage mechanism. (c) Computational determination of the replication order in the case of an elongation-only (breakage-free) mechanism. (d) Fibre length distribution as a function of time. After an initial transient regime, replication occurs at a steady-state length distribution.