Evolution requires mutation and selection in the replication process of genes. Where the former allows exploitation of the genotype space, the latter restricts actual gene instances to a set of qualified instances with respect to a fitness function.
We have studied the emergence of mutation and selection from molecular properties of the gene biopolymers in dissipative particle dynamics [1]. In the qualitative toy model of the Los Alamos bug, genes are represented as strands of nucleotide beads with one hydrophobic anchor bead attached to each. Interaction parameters have been set to model the amphiphilic properties of decorated peptide nucleic acid (PNA). For simplicity, only two complementary bases are employed. Watson-Crick binding is achieved by defining attractive bead interactions between complementary bead pairs. We have implemented and analyzed three different force fields for this interaction: a) undirected attraction, b) directed attraction parallel to the axis defined by a base bead and its hydrophobic anchor (see “radial attraction” in Fig. 1), c) directed attraction perpendicular to the anchor axis and the nucleic acid strand (“tangential attraction” in Fig. 1). The first definition is clearly unphysical, and serves only as null hypothesis in the context of DPD where commonly only undirected interactions are employed. Alternatives b) and c) are closer related to the behavior of real nucleic acids. However, unlike the H-bonds in real Watson-Crick binding, the attractive force in our model is not saturated, i.e. a single bead can attract two complementary bases.
Figure 1: Different force fields for complementary base
attraction. Bases are shown in black and white, whereas hydrophobic anchors are
rendered in gray.
Results
We have studied hybridization and ligation of short nucleic acid oligomers (dimers) on complementary templates (4 to 6-mers) [1]. Simulations were perform with the gene replication taking place a) at the oil-water interface of a two-phase system, or b) at the surface of a surfactant coated oil droplet. In both scenarios, the results coincided.
Fig. 2: Association
times of complementary dimers against different template base sequences
(4-mers). Each panel shows results for one of the three tested force fields,
six different sequences, three different strengthes of complemetary attraction
and values for 20 independent simulation runs. In the case of directed
“tangential” attraction, the stability of the hybridization complex differs
significantly with the sequence.
We find two cause for mutations to occur in the replication process: spontaneous background ligations in the absence of a template strand, and miss-pairings due to the hybridization of not fully complementary oligomers. Mutation due to background reactions can be controlled to some extend by the rate of the ligation reaction. However, possible rates are limited by the association time of oligomers at the template strand.
We find a strong variance in the stability of the hybridization complex prior to ligation: mean association times differ significantly with the composition and sequence of bases in the oligomers (see Fig. 2). In particular, we find that sequences consisting of equal bases are more likely to slide off the template, whereas oligomers with varying bases stick closer and longer to the template strands. The stability of hybridized oligomers determines the ability to successfully replicate genetic information, i.e. geometric properties of the base interactions define a molecular fitness function that selects for template sequences with stable hybridization complexes. Similar results are known experimentally [2,3].
Simulations that employ more than one template strand reveal that hybridization complexes of two full templates are significantly more stable than complexes of one template and short oligomers. Template agglomeration is particularly strong for base sequences that yield stable hybridization complexes with oligomers.
The geometric
aspects of the molecular fitness function concur with other aspects of the
fitness function such as the redox potential of electron donors (oxo-guanine)
and pi-stacking of bases to allow for electron transport in the mediation of
metabolic precursor turnover.
References
[1] H. Fellermann, S. Rasmussen, H.-J. Ziock, and R. Solé, Life-cycle of a minimal protocell - a dissipative particle dynamics (DPD) study. Artif. Life 13(4):319-345, 2007
[2] O. L. Acevedo and L. E. Orgel,
Non-enzymatic transcription of an oligodeoxynucleotice 14 residues long, J.
Mol. Biol. 197 (2), 187-193, 1987
[3] G. F. Joyce, Non-enzyme template-directed
synthesis of RNA copolymers, Orig. L. Evol. Biosph. 14, 613-620, 1984