Foldamer hypothesis for the growth and sequence differentiation of prebiotic polymers

Abstract

It is not known how life originated. It is thought that prebiotic processes were able to synthesize short random polymers. However, then, how do short-chain molecules spontaneously grow longer? Also, how would random chains grow more informational and become autocatalytic (i.e., increasing their own concentrations)? We study the folding and binding of random sequences of hydrophobic ([Formula: see text]) and polar ([Formula: see text]) monomers in a computational model. We find that even short hydrophobic polar (HP) chains can collapse into relatively compact structures, exposing hydrophobic surfaces. In this way, they act as primitive versions of today's protein catalysts, elongating other such HP polymers as ribosomes would now do. Such foldamer catalysts are shown to form an autocatalytic set, through which short chains grow into longer chains that have particular sequences. An attractive feature of this model is that it does not overconverge to a single solution; it gives ensembles that could further evolve under selection. This mechanism describes how specific sequences and conformations could contribute to the chemistry-to-biology (CTB) transition.

Keywords: HP model; autocatalytic sets; biopolymers; origin of life.

Fig. 1.

Polymerization processes lead to mostly short chains. (A) Spontaneous polymerization processes typically lead to a Flory distribution of chain lengths. Green line gives $⟨l⟩=6$, and blue line corresponds to $⟨l⟩=2$ (B) Fitted distributions from experiments on prebiotic polymerization: red, Kanavarioti et al. (36); cyan, Ding et al. (46); magenta, Ferris (47).

Fig. 2.

Examples of HP sequences that fold to unique native structures in the HP lattice model. Red (or pink if in the beginning of the sequence) corresponds to $H$ monomers, and blue corresponds to $P$.

Fig. 3.

Some HP foldamers have hydrophobic patches, which serve as landing pads that can catalyze the elongation of other HP chains. Chain $A$ folds and exposes a hydrophobic sticky spot, or landing pad, where another $HP$ molecule $B$ as well as a hydrophobic monomer $C$ can bind. This localization reduces the barrier for adding monomer $C$ to the hydrophobic end of the growing chain $B$.

Fig. 4.

Chains become elongated by foldamer catalyst HP sequences. Case 1 (gray): a soup of chains has a Flory-like length distribution in the absence of folding and catalysis. Case 2 (blue): a soup of chains still has a Flory-like length distribution in the absence of catalysis (but allowing now for folding). Case 3 (red): a soup of chains contains considerable populations of longer chains when the soup contains HP chains that can fold and catalyze. We run 30 simulations for every case. To produce each line, we took a time average over ${10}^6$ time points in the steady-state interval, then counted molecules for each length, and divided it by the total molecular count.

Fig. 5.

The distributions over individual sequences are highly heterogeneous. We show the populations (molecule counts of individual sequences) for the three cases. In case 1, we do not allow folding or catalysis. In case 2, we allow folding but not catalysis, and in case 3, both folding and catalysis are allowed. For all of the cases, gray dots represent populations of the sequences that cannot fold, blue dots represent sequences that fold but cannot catalyze, and red dots represent sequences which act as catalysts and for which at least one elongation reaction has been catalyzed. For cases 1 and 2, populations of the sequences of the given length are distributed exponentially. Thus, we can take mean or median population for the given length as a faithful representation of the behavior of average sequence of that length. Case 3 is drastically different: the populations of the sequences of the given lengths are distributed polynomially. While most of the sequences have very low population for the longer chains, several sequences (mostly autocatalytic ones) have very high ones and constitute most of the biomass. For case 3, neither mean nor median is a good representation of the behavior of the chains; as we can see from the figure, all of the chains basically separate into two groups with different distributions, and this information cannot be shown in the mean or median. Every point is a time average over ${10}^6$ time points in the steady-state interval. Lower limit of ${10}^{-6}$ is because of computational precision.

Fig. 6.

(A) HP lattice chains that fold and are autocatalytic. They fold into unique structures and have landing pads that can catalyze the elongation of each other. (B) HP chains that fold but are not catalytic. Most chains are not catalysts, but the size of the autocatalytic set is nonnegligible (Fig. 8).

Fig. 7.

(Upper) Cross-catalysis of two different sequences. (Lower) Autocatalysis of two copies of an identical sequence. Dashed arrows represent multiple reactions of chain growth. Among them, there are both $\cdots HH+H\to \cdots HHH$ catalyzed reactions and spontaneous chain elongations. Catalysis is represented by red solid arrows. Solid black lines are folding reactions. Chains, which we call “autocatalytic,” experience catalysis during one (or more often, several) of the steps of elongation. Then, when they reach the length at which they can fold ($A_u\text{,}{B}_u\text{,}{C}_u$), they fold and serve as catalysts themselves ($A_f\text{,}{B}_f\text{,}{C}_f$). Mutual catalysis can happen between different sequences (here, A and B) and between different instances of the same sequence (here, C).

Fig. 8.

Different sequence spaces grow exponentially with chain length: gray, the space of all HP sequences; blue, the space of foldamers; red, the space of foldamer catalysts.

Fig. 9.

The longer the chains, the bigger the contribution of the autocatalysts. Each red line shows how the contribution of autocatalytic chains to the biomass of the given length grows with chain length. Different red lines correspond to different simulation runs. The black line shows the median over 30 simulations.

Fig. 10.

Sequences can evolve to different autocatalytic sets. (A) $HP$ catalytic system has at least two attractors. The lines are length distributions from case 3. Again, each line represents distribution of length in the steady state for one simulation run. It is clear that there are two kinds of distribution which get realized during the simulations. The system bifurcates either to a state represented by a green line or to one represented by a red one. These are the same lines as in Fig. 5A but separated in two sets by the clustering algorithm k-means. (B) Structure of the sequences which most often are main contributors into the total population of the polymers of their length. Upper corresponds to the macrostate shown in red in A, and Lower corresponds to the one shown in green.