A new replicator: a theoretical framework for analysing replication

Abstract

Background: Replicators are the crucial entities in evolution. The notion of a replicator, however, is far less exact than the weight of its importance. Without identifying and classifying multiplying entities exactly, their dynamics cannot be determined appropriately. Therefore, it is importance to decide the nature and characteristics of any multiplying entity, in a detailed and formal way.

Results: Replication is basically an autocatalytic process which enables us to rest on the notions of formal chemistry. This statement has major implications. Simple autocatalytic cycle intermediates are considered as non-informational replicators. A consequence of which is that any autocatalytically multiplying entity is a replicator, be it simple or overly complex (even nests). A stricter definition refers to entities which can inherit acquired changes (informational replicators). Simple autocatalytic molecules (and nests) are excluded from this group. However, in turn, any entity possessing copiable information is to be named a replicator, even multicellular organisms. In order to deal with the situation, an abstract, formal framework is presented, which allows the proper identification of various types of replicators. This sheds light on the old problem of the units and levels of selection and evolution. A hierarchical classification for the partition of the replicator-continuum is provided where specific replicators are nested within more general ones. The classification should be able to be successfully applied to known replicators and also to future candidates.

Conclusion: This paper redefines the concept of the replicator from a bottom-up theoretical approach. The formal definition and the abstract models presented can distinguish between among all possible replicator types, based on their quantity of variable and heritable information. This allows for the exact identification of various replicator types and their underlying dynamics. The most important claim is that replication, in general, is basically autocatalysis, with a specific defined environment and selective force. A replicator is not valid unless its working environment, and the selective force to which it is subject, is specified.

Figure 1

An autocatalytic cycle of the form Σx_i + A —①→ Σy_j + 2A (following Gánti's notation [68]). x_i and y_j denote all the necessary input and waste molecules respectively, of one turn of the cycle.

Figure 2

A truly autocatalytic cycle: the autocatalytic core of the formose cycle [18]. The framed molecule is glycolaldehyde.

Figure 3

(a) A simple cycle, that can be autocatalytic if B₁ ~ A and/or B₂ ~ A; or non-autocatalytic if B₁ !~ A !~ B₂, where ~ is the equivalency relation. (b) A valid autocatalytic cycle.

Figure 4

Domains of the S N space. S is the number of possible states of a replicator, N is the number of individuals present in a population of such replicators.

Figure 5

The reductive citric acid cycle. Note the asymmetric branches leading to the two molecules of oxaloacetate.

Figure 6

The Calvin cycle. It is clear that it is autocatalytic, but it is also clear that one molecule of 3-phosphoglycerate is not enough to ignite the system. The minimum number of molecules is two (for example, one molecule of Se7P and one DHAP), provided that all the obligate enzymes are present. (Se7p = sedulose-7-phosphate; DHAP = dihydroxi-acetone-phosphate). From Szathmáry [16].

Figure 7

Autocatalytic nucleic acid systems. (a) RNA as a true replicator. (b) proteins (P) appear as side-products of RNA replication, which facultatively catalyze the formation of the new RNA molecule (dashed arrow). (c) The present (simplified) relationship between genes (DNA) and enzymes (E), which are both obligatory for the other to be autocatalytic. x_i denotes all input materials while y_j and z_k denote waste materials.

Figure 8

Autocatalytic system of birds and nests. (a) Birds as simple catalysts of nests. No nest is needed to produce new birds. (b) The nesting bird phase can only continue if there is a nest present (possibly one that was built by the bird, as it is pictured here). Small circle indicates point where a nest is obligatory. (c) Formal version of (b), with A₁ as the bird, A₂ the nesting bird and B the nest. Note: Figure 7(b) is equivalent to (b) and (c) if E is an obligatory catalyst of RNA.

Figure 9

The same autocatalytic cycle of Figure 8c from the viewpoint of A₂.

Figure 10

Ordered informational scheme of a multiplying entity. I is the complete information set of the entity, V is the subset of I that can change, H is the subset of V that can pass on changes to offspring.

Figure 11

Semantic domains of the V H space. V: variable part size; H: heritable part size. By definition: H ≤ V.

Figure 12

Contour plots representing similarity values between parent and offspring entities (both being modular) as a function of V and H. Parameters υ, and μ are mutation rate during lifetime and mutation rate during replication, respectively. The chance of backmutation is taken to be negligible (ε = 0). By definition H ≤ V.

Figure 13

Hierarchy and classification of multiplying entities. Each downward arrow introduces a new feature. Inset diagrams show a vague concept of the parts of the given entity regarding the V H model. Obviously, the replicator continuum can be categorized based on various aspects, for example variable/exact, modular/non-modular or informational/non-informational, unlimited-/limited-/non-hereditary, and so on.