Computer-modeling origin of a simple genetic apparatus

Abstract

This computer simulation is based on a model of the origin of life proposed by H. Kuhn and J. Waser, where the evolution of short molecular strands is assumed to take place in a distinct spatiotemporal structured environment. In their model, the prebiotic situation is strongly simplified to grasp essential features of the evolution of the genetic apparatus without attempts to trace the historic path. With the tool of computer implementation confining to principle aspects and focused on critical features of the model, a deeper understanding of the model's premises is achieved. Each generation consists of three steps: (i) construction of devices (entities exposed to selection) presently available; (ii) selection; and (iii) multiplication of the isolated strands (R oligomers) by complementary copying with occasional variation by copying mismatch. In the beginning, the devices are single strands with random sequences; later, increasingly complex aggregates of strands form devices such as a hairpin-assembler device which develop in favorable cases. A monomers interlink by binding to the hairpin-assembler device, and a translation machinery, called the hairpin-assembler-enzyme device, emerges, which translates the sequence of R₁ and R₂ monomers in the assembler strand to the sequence of A₁ and A₂ monomers in the A oligomer, working as an enzyme.

Modern theories of the origin of life are related to M. Eigen's idea that life could have emerged, in principle, by self-organization of matter in a homogeneous phase in a stationary state by intrinsic necessity. The process is bound to the condition of Prigogine and Glansdorff (1–4). These ideas have strongly influenced developments in artificial life and complex systems formation (5). Eigen considers his general theory of molecular Darwinian processes to close the gap between physics and biology.

In contrast, in the view of H. Kuhn (6, 7), understanding the origin of life is not a general but a particular problem: to find a gapless sequence of physicochemical processes, beginning with prebiotically reasonable conditions and leading to systems equipped with a life-like genetic apparatus. Each step must be realistic, detailed, and as simple as possible to emphasize the basic mechanism. The search for such a pathway needs continuous improvement; it is important to have in mind always the entire task and the final goal. The following crucial questions have been addressed (6):

(i) What are the boundary conditions that drive a Darwinian process toward increasing complexity, beginning with short molecular strands that (a) are reproduced by replication (with occasional variation by copying mismatch) and (b) later coagulate into aggregates that are then exposed to selection? How to allow the alternation between these two processes? This task requires an alternation between radically different environmental conditions.

(ii) How to avoid the escape of functionally cooperating components and protect against competitors? This aim requires microcompartments that are slightly transparent to allow for occasional escape and results in an occupation of the whole favorable microstructure by the replicating species.

(iii) How to drive an evolution to higher complexity? This aim is reached by a diversified environment: populating a new region again and again with slightly less favorable microstructure requires increasing sophistication (bound to increasing genetic information, decreasing replication-error-rate, increasing intricacy of the genetic machinery).

The model pathway of a continuous sequence of steps determined by logical and chemical restrictions is quite narrow: the “blind” trial-and-error process leads by chance, sooner or later, to distinct functional properties allowing a distinct crucial step (e.g., populating a new region where an individual of the new form finds a situation allowing, all of a sudden, fast multiplication: the new form has strong selectional advantage, and further evolution is not suppressed by the old forms, which are now exploitative parasites).

In this view, the emergence of life and self-organization in a homogeneous medium by intrinsic necessity are two totally different processes. Appropriate temporal (cycle of day and night) and spatial (compartmentation as furnished by microporous rocks) environmental conditions (at some very particular location on the prebiotic earth) are of fundamental importance to the emergence of life.

The model (6) was later refined and extended (8–12). Important features of the model are the emergence of hairpins that fold back onto themselves in an antiparallel direction by complementary binding and the subsequent development of aggregates consisting of hairpins linked with their loop to an assembler. These aggregates later lead to a translation device, the Hairpin Assembler Enzyme device (HAE device) (Fig. 1). The compact arrangement of hairpins and their binding to the assembler by triplets are reasonable assumptions, as demonstrated by molecular modeling (9, 10), force-field calculations (13), and experiments (14, 15). Basic assumptions of the model are supported by experiments (16–19) and computer models (20, 21).

Figure 1.

The HAE device. Postulated ancient precursor of a translation apparatus from a nucleotide sequence into an amino acid sequence. On top is the (+)-assembler (only the initial part shown) with five hairpins attached (dotted rounded rectangles; the hairpin on the right is somewhat detached to show its loop), which serve as adapters for A monomers (A reflecting amino acids in biosystems). Hairpins and assembler are strands of R monomers R₁ (white element) and R₂ (black element) binding complementarily (R reflecting ribonucleotide). The direction of the template, (+)-strand and its replica, (−)-strand, are antiparallel (indicated by > and <). The (+)-hairpin and (−)-hairpin differ only in the anticodon (second monomer in loop) and the open end. The (+)-hairpin with anticodon R₂, loop <R₁R₂R₂<, and open ends {R₁, R₁} is charged with A₁ (square). The (−)-hairpin with anticodon R₁, loop <R₁R₁R₂<, and open ends {R₂, R₂} is charged with A₂ (circle). The first and third monomer of all adjacent triplets >R₂R_αR₁> along the assembler fixed to R₂ and R₁ constitute a reading frame. The second monomers R_α are codons and by their specific sequence constitute a recipe: the HAE₁ device assists in the synthesis of enzyme E₁, an A oligomer of specific sequence, by translating the recipe on the (+)-assembler with the binary code R₁ for A₁ and R₂ for A₂. Its replicate, the (−)-assembler, leads to an A oligomer E₀ (the terminal part shown at bottom) of unspecific sequence with no catalytic activity, but which helps compartmentation by agglutination. The assembler is the precursor of the messenger RNA, the hairpins the precursors of the transfer RNA's equating R₁ and R₂ with cytidine and guanosine base-paired by triple hydrogen bonds (and equating R₃ and R₄ with adenosine and uridine base-paired by double hydrogen bonds, to appear later). The A oligomers are the precursors of proteins equating A₁ and A₂ with the simplest and most available amino acids glycine and alanine (and equating A₃ and A₄ with aspartate and valine, to appear later).

The computer simulation presented here is significant in facilitating a deeper analysis of the following critical steps, which are not obvious but were intuitively assumed in the theoretical model: (i) Can a reading frame develop? (ii) Can a binary code develop? (iii) Can the binary code be extended to a quaternary code? (iv) Can the translation device avoid exploitation by contaminants from earlier stages that are always produced as an undesirable byproduct? (v) Can the risk of moving away from the favorable path into harmful side channels be judged?

The Computer Implementation.

The theoretical model of H. Kuhn and J. Waser (11) is strongly simplified in the present computer simulation to focus on the significant features. The continuously changing environment requires many parameters (Table 1). The necessary restriction of options (i.e., initial sequences of strands, number of enzymes and their sequences) and the choice of parameter values (i.e., number of compartments, transparency of their walls, length of strands, fitness parameters of devices) are obviously rather artificial; however, it is not my purpose to simulate a realistic prebiotic situation.

Table 1.

Library of devices C_k of kind k

The devices C_k of kind k composed of I_k strands are listed in order of increasing complexity together with assigned values of fitness parameters (the probabilities S of the device to be selected, F of a mismatched replication, M of a strand to be replicated, and the number of trials ν, above which the construction is terminated). Beginning: initial equipment for modeling molecular Darwinian evolution. Interpositions Ip1 and Ip2: accessories appended to initial equipment. Arrows: properties needed to trigger entrance into the stages after the bold line.  

Each successive generation of the cyclic process of a molecular Darwinian evolution consists of three phases (Fig. 2): (i) construction of devices presently available simulating formation by diffusion and interlocking; (ii) selection; (iii) multiplication of isolated strands with occasional variation by copying mismatch. Two R monomers, R₁ and R₂, are covalently linked, forming R oligomers with m monomers. The population of a total of N strands is given as well as the K compartments lined up in a circle. The computer tries to construct devices with strands from the pool of strands in each compartment. The devices obtained are selected by chance. Each device has its specific a priori probability S to be selected. The chance of retention increases with increasing sophistication of the device. The selected devices dissociate into approximately N/2 single strands. Each strand has its specific a priori probability M to be replicated. If the strand is selected to replicate, random errors violating complementarity occur in the copying process with a probability F per R monomer. At the end of the cycle, the population of N strands has recovered.

Figure 2.

Implementing the model of molecular Darwinian evolution. Each generation consists of (i) construction phase; (ii) selection phase; and (iii) multiplication phase. The drawings are given as illustration. Random numbers are used throughout (specified in italics). Each seed to the random number generator produces a deterministic but statistically uncorrelated sequence of pseudorandom numbers.

In the beginning of the construction phase, each strand is assigned to one of two forms according to its sequence: hairpin (maximal folded strand) or potential assembler (unfolded strand). Then an assembler and a hairpin are chosen randomly from the pool of strands in the compartment singled out. If a triplet at any location along the assembler is found where the hairpin loop is complementary, the hairpin is linked to the assembler, and it acts as a seed for further hairpins to link by complementary binding to the adjacent triplets on the assembler either to the right or to the left, thus without gaps in between. If the hairpin thus fits onto the device, the procedure is continued until the maximum possible number of hairpins link to the assembler eventually forming a Hairpin Assembler-device (complete HA device). But, at the present stage of the construction and at later time, a hairpin that does not fit onto the device is put back into the pool of strands, and another hairpin is chosen randomly from the pool of strands. This is repeated at most ν times (allowing simulation of the repeated transient binding and dissociation in case of missing complementarity). If no fit is achieved within this limited number of trials, the construction is terminated, and an incomplete HA device forms. The procedure is repeated for the next assembler, singled out randomly from the pool of strands, and is continued until all strands within the compartment are used up. This is done for each compartment. The fitness parameters for each device thus obtained are taken from the library (Table 1).

Setting the Parameter Values.

In the library of all possible devices, each device is defined by its functionality, which is given by appropriate values of fitness parameters. Each device is classified into one of the groups indicated by devices C_k of kind k (Table 1).

The Hairpin.

A hairpin conformation is highly favored, because the interior is protected against hydrolytic or other attack from the outside. Although copying errors are needed to provide a pool of variations from which selection can take place, errors that prevent hairpin folding are disadvantageous. The length m of R oligomers must be shorter than 1/w, where w is the bare error probability per monomer, to allow for a sufficient amount of error-free copies, but not too much shorter, to allow sufficient variation (w < 1/m, e.g., m = 29 and w = 1/80).

The HA Device and the Reading Frame.

An assembler, to which hairpins can attach by complementary bonding, greatly speeds up the formation of interlocking picket-fence-like aggregates of hairpins without gaps in between (Fig. 1). These picket-fence-like aggregates offer additional protection against hydrolysis or other attacks on the sides of hairpins, that are adjacent and thereby provide a strong selective advantage. Furthermore, the HA devices are hindered by their size to leave the compartment through pore openings, whereas single hairpins easily disappear by diffusion. This fact justifies assuming a strong selection pressure from hairpin to complete HA device (by factor 12; see Table 1; Figs. 3 and 4), but a weak selection pressure (by factor 2.44; see Fig. 5) would be sufficient to allow the evolution of a genetic apparatus. The four possible kinds of triplets (Table 2a) along an assembler of random sequence become mutually exclusive for complete HA devices: only assemblers with a single kind of adjacent triplets and a population of hairpins with corresponding loops constitute a reading frame, ensuring firm and precise incorporation of hairpins into the complete HA device.

Figure 3.

Computer simulation with a particular seed given to the random number generator. Number H_k (g) of devices C_k at the end of the selection phase versus number of generations g. (a) Total number of hairpins shown. At g ≈ 350, hairpins with all possible loops (Table 2a) emerged. At g ≈ 1,100, hairpins with loop <R₁R_αR₂< (belonging to a significant reading frame) dominated. (b) Number of HA devices shown. As soon as hairpins developed, they formed incomplete HA devices. Occasionally, complete HA devices with nine adjacent hairpins attached but without occurrence of a reading frame. At g ≈ 1,165, complete HA devices with a significant reading frame >R₂R_βR₁> were selected (by regions of nucleation). This reading frame exactly was almost the loser shortly before it turned out to be the winner (Fig. 3a). (c) Interposition Ip1 at g = 1,300. By chance, the first HAE₀ device appeared at g ≈ 1,360, but only a small fraction of hairpins carried A monomers. At g ≈ 1,440, nearly all hairpins carried A monomers, and the HAE₀ devices took over. At g ≈ 1,630, the HAE₁–HAE₂ cooperative built up with enzymes E₁ and E₁, numbered 4 and 7 (Table 2c), simultaneously binary code 1 (Table 2d) was selected (by regions of nucleation). (d) Interposition Ip2 at g = 1,700. At g ≈ 3,185, the HAE₁–HAE₄ cooperative producing enzyme E₄ numbered 52 emerged, and quaternary code 1d was selected (Table 2d). At g ≈ 3,405, the HAE₃–HAE₄ cooperative producing enzyme E₃ numbered 33 emerged. Enzyme E₃ is a transcriptase (= improved replicase E₁), which assists in the separation of replication and translation by D monomers (“D” reflecting desoxy-ribonucleotide) (6, 11). The nonsensical (−)-assemblers disappear, avoiding accumulation of agglutinate. (e) Fraction of coding adapters to total adapters shown. After interposition Ip1, the two pairs of hairpins (Table 2b) are of comparable amounts. At g ≈ 1,630, the binary code 1 comes into being and, after interposition Ip2, the quaternary code 1d took over at g ≈ 3,185.

Figure 4.

Simulations with different seeds. Of 20 runs performed, 6 resulted in the emergence of a significant reading frame (50% expected in the average, Table 2a). (a) In all of these favorable six runs, a HAE₁–HAE₂ cooperative emerged with enzymes E₁ and E₂ from the list 1–6 and 7–12 and with binary code 1 or 2. Only in a fraction (three runs of the six) did the quaternary codes 1a–1d or 2a–2d become manifest within the given number of g = 5,000 generations. (b) Course of computer simulation starting with a random seed that resulted in an ambiguous reading frame contrasting Fig. 3a.

Figure 5.

Simulations with weak selectional pressure. The devices C_k of kind k as listed in Table 1 (k = 0:1:2 (i = 2, 3, 4, 5, 6, 7, 8):3:4:5:6:7) are assigned the following values for probabilities S to be selected (S = 1:1.25:(1.40, 1.56, 1.75, 1.95, 2.19, 2.44, 2.74):3.05:4.58:4.58:5.72:7.15). Incomplete HA devices are necessary links in the emergence of complete HA devices (300 < g < 2,800). Incomplete HA devices are diminished but still exceed (2,800 < g < 4,320). Contamination is considerable: at g = 3,500, only 34% of the 1,620 given strands are components of complete HA devices, 46% of the strands are involved in incomplete HA devices, and the residual are 4% free hairpins and 16% open strands. Incomplete HA devices fall off and are of no significant contamination as soon as HAE₀ devices are formed and selected (4,320 < g). The HAE₁–HAE₂ cooperative is stable against exploitation by a great surplus of impurities: at g = 6,000, only about 14% of the given strands are involved in the cooperative.

Table 2.

List of sequences

(a) The four possible reading frames (the two significant reading frames boxed, contrasting the two ambiguous reading frames, which are of no use later on). The triplets with the corresponding loops of hairpins listed (R_α = R₁ or R₂ and R_β = R₂ or R₁ complementary to R_α). (b) The four hairpins with anticodon R₁ or R₂ (second monomer in loops <R₁R₁R₂< and <R₁R₂R₂< with given significant reading frame) and A-monomer A₁ or A₂ (attached to open end {R₁, R₁} and {R₂, R₂}) make up the pair 1 and pair 2 of hairpins of mutual replica. (c) Among the 2⁹ = 512 possible sequences of A oligomers with length of 9 monomers, A₁ or A₂ are the specific sequences with assumed enzymatic activity of type E₁ (6 sequences, numbered 1–6, sequence 4 shown) and of type E₂ (6 sequences, numbered 7–12, sequence 7 shown). For a given A oligomer, there are 2⁹ = 512 descendants by randomly replacing A₁ with A₃ and A₂ with A₄. The specific sequences are assumed to have enzymatic activity of type E₃ (36 sequences, numbered 13–48, all descendants of E₁, e.g., 6 descendants of parent 4, numbered 31–36, sequence 33 shown) and of type E₄ (36 sequences, numbered 49–84, all descendants of E₂, e.g., 6 descendants of parent 7, numbered 49–54, sequence 52 shown). (d) Binary code 1 (or 2) extends to quaternary codes 1a–1d (or 2a–2d), respectively. R₁:A₁ denotes a hairpin that is charged with A₁ and that has the anticodon R₂, which binds complementarily to the assembler with the codon R₁.  

The HAE₀ Device and the Agglutinate E₀ Constituting New Boundary of Compartment.

The A monomers A₁ and A₂ are attributed with the capability of becoming linked to hairpins: monomers A₁ are attached to hairpins with the open end {R₁, R₁}, whereas monomers A₂ are attached to hairpins with the open end {R₂, R₂}. A monomers do not bind to closed-end {R₁, R₂}. HA devices incompletely charged with A monomers are considered to have the same survival chances as HA devices. A HAE₀ device is present if each hairpin of the complete HA device is charged with an A monomer: the A monomers are then side by side, and their proximity to each other greatly facilitates their becoming linked by covalent bonds (Fig. 1). These A oligomers of random sequence form an agglutinate E₀, replacing the original compartment exemplified by porous rock, thus promoting independence from the environment and providing a strong selective advantage. The compartment is now considered nontransparent but capable of dividing (stage b, Fig. 2 and Table 1), then the devices are arbitrarily distributed over the two daughter compartments, whereas, in keeping the number of compartments K constant, the compartment with the least content is assumed to vanish. This procedure simulates the occasional division of the agglutinate into separate entities.

The HAE₁-HAE₂ Cooperative and the Binary Code.

An A oligomer of specific sequence with enzymatic activity as of a replicase or synthetase provides a strong selective advantage. There is no premium on the development of a relationship between the R monomer in the middle of a hairpin loop and the A monomer attached to its open end: all four combinations (making up pairs 1 and 2 of hairpins; Table 2b) are equally present in HAE₀ devices. But the two pairs are mutually exclusive in a HAE_i device with a recipe for enzyme E_i (a specific sequence of second monomers in consecutive triplets along the assembler): only hairpins of one pair that translate this recipe constitute a code. Let us assume that, by chance, only hairpins of pair 1 are present in a given compartment and, again by chance, an assembler has the appropriate sequence that allows the production of an A oligomer of a specific sequence of A₁ and A₂ (Table 2c; one of the possible sequences attributed to act as enzyme E₁). Enzyme E₁ functions as a replication catalyst that reduces the copying error probability to w/3 = 1/240. Then the recipe for producing enzyme E₁ is kept over a number of generations but disappears because of the missing selectional advantage of the HAE₁ device. This selection advantage is provided by an A oligomer of another specific sequence of A₁ and A₂ (Table 2c; one of the sequences assumed for enzyme E₂). But the synthetase E₂ alone also disappears, because the very copying errors that led to its creation will eventually also destroy it. Then, if in addition to enzyme E₁ an assembler occurs in the considered compartment with a sequence that allows the production of E₂, the HAE₁–HAE₂ cooperative comes into being, which has the power to keep the recipes for E₁ and E₂ and their translation by the pair 1 of hairpins specified by binary code 1 (Table 2d).

Extension to the Quaternary Code.

R oligomers, with R-monomers R₃ and R₄ incorporated, are assumed to multiply better (by the better-adjusted double- to single-strand transition temperature crucial for maintaining the cycle between the multiplication phase and the selection phase in the given environment). A-monomer A₃ can replace A₁ and A-monomer A₄ can replace A₂ anywhere in the sequence of A oligomers. Then agglutinate E₀ is considered to have an improved function as an envelope. For the enzymes E₁ and E₂, the new A monomers are incorporated without loss of their beneficial properties. Among the pool of possible sequences for equivalents of enzymes E₁ and E₂, it is assumed that for each enzyme there are six descendants with specific sequences forming enzymes E₃ and E₄ each that have the improved enzymatic activity (Table 2c). Only a subset of possible quaternary codes is available, e.g., binary code 1 extends to quaternary codes 1a–1d (Table 2d).

Results and Conclusion.

With a particular seed given to the random number generator, the computer simulation presents devices entering the scene in order of increasing complexity (Fig. 3). With different seeds given to the random number generator for each run, it is shown (Fig. 4) that evolution frequently became stuck at an early stage because of the emergence of an ambiguous reading frame (e.g., Fig. 4b) or at the later stage of a binary code because of an incomplete incorporation of the additional monomers R₃ and R₄, A₃ and A₄ within the 5,000 generations given (Fig. 4a). This fact supports the idea that many starts of an evolution process were needed until the breakthrough occurred leading to the explosion of life. Fig. 5 demonstrates that even for a small selection pressure, evolution takes place, and the translation device can survive considerable contamination by impurities: proceeding to the next evolutionary stage guarantees protection against exploitation.

The presented computer modeling and the theory on which it is based should be helpful in understanding the evolution of today's genetic code (22, 23). The theory should also be useful in the search for ways to create novel devices by self-organization (24–26).

Abbreviation

HAE

Hairpin Assembler Enzyme