Kinematic Self-Replicating Machines

© 2004 Robert A. Freitas Jr. and Ralph C. Merkle. All Rights Reserved.

Robert A. Freitas Jr., Ralph C. Merkle, Kinematic Self-Replicating Machines, Landes Bioscience, Georgetown, TX, 2004.


5.1.4 Szathmary Classification of Replicators (1995-2000)

Starting in 1995 originally in collaboration with John Maynard Smith [2415], and continuing through a succession of refinements over several years [2411-2417], Eors Szathmary has created an interesting classification of replicators which identifies five distinct bi-valued properties of replicators, as follows:

Potential: Limited Heredity or Unlimited Heredity
Mode: Holistic or Modular
Level: Phenotypic or Genotypic
Set: Solitary or Ensemble
Maintenance: Attractor-based or Storage-based

(1) Potential. Like Dawkins [275], Szathmary [2415] in 1995 originally distinguished replicators having limited heredity and potentially unlimited heredity. Replicators with potentially unlimited heredity can have many more types than the number of objects in any realistic system, whereas replicators with limited heredity have fewer or only about the same number of types than the number of objects in realistic systems – that is, they “exist only in a few alternate types,” or, possibly, only in a single type. “Systems with limited heredity have only a limited evolutionary potential because the number of available types is too low.”[2417] Pattee [2418] also recognized the importance of “hereditary process” in reproduction.

(2) Mode. Szathmary [2415] also originally distinguished replicators according to their mode of synthesis, of which there are two types. In the first mode of synthesis, originally termed processive [2415] and later holistic [2416, 2417], the information carried is of an analog character and the process passes through a continuum of closely-related states, most nearly resembling an autocatalytic chemical reaction or a cyclically processive reaction like the citric acid cycle, or the “replication” demonstrated by spreading fire or even by a series of falling dominoes. “Chemical cycles, such as the formose reaction [2419], are holistic replicators since replication is not based on the successive addition of modules.”[2417] In the second mode of synthesis, termed modular [2412, 2415-2417], the information carried is of a digital* character [2420] and the process passes through a series of discrete states, as exemplified by the complementary-shape interactions observed in DNA. For example, oligonucleotides are copied by the template effect of a sequence composed of digits (modules) belonging to a restricted alphabet [2412]. A large number of artificial oligonucleotide modular replicators are now known [1361-1367, 1373].

* In 2002, Ellington and Levy [2421] proposed a similar replicator nomenclature in which nucleic acid and peptide replicators are considered either “digital” (“composed of discrete units...that can alternate between stable states, [and] can be combined into an informational code”) or “continuous” (“capable of giving rise to a variety of products”). Note the authors: “The structural complementarity of discrete replicators is of necessity greater than that of other replicators. However, increased complementarity leads to product inhibition. These facts imply a fundamental conundrum: the less discrete a replicator is, the less information it can transfer; the more discrete a replicator is, the more its evolution is limited by parabolic growth.”

(3) Level. In 1999, Szathmary [2416] revised his classification of replicators to include a new functional dimension based on the level at which replication takes place – either phenotypic or genotypic. In phenotypic replicators, the phenotype (physical structure) of the replicator is transmitted without genotype (structure description) copying. Replication occurs without needing an onboard instruction tape (the genotype) to be copied along with the physical structure of the replicator. “Phenotypic replicators do not pass on their genotypes, only some aspects of the phenotype are transmitted. Phenotypic replicators with limited heredity include genetic membranes [2422], prions [2423-2425] and simple memetic systems.”[2417] Cortical inheritance in ciliates [2426] is another phenotypic inheritance system “whereby the orientation of kinetids (basal body plus associated cortical and fibrillar structures) is passed on from cell generation to generation.” [2416] Still another example of a phenotypic replicator, having unlimited heredity, would be Laing’s example (Section 2.3.5) of machine replication by inspection. By contrast, in genotypic replicators, phenotype duplication requires duplicating the genotype along with the replicator structure.

(4) Set. In 2000, Szathmary [2417] further distinguished replicators according to the set of entities capable of replication. In solitary replication, each member of a set of entities is individually capable of replication. In ensemble replication, no individual entity is individually capable of replication and only the set as a whole can replicate. “Replicator networks consisting of catalytic molecules (such as reflexively autocatalytic sets of proteins [1626, 1662, 2396-2398], or self-reproducing lipid vesicles [2427, 2428]) are hypothetical ensemble replicators. Ensemble replicators suffer from the paradox of specificity: while their abstract feasibility seems to require a high number of molecular types, the harmful effect of side reactions calls for a small system size.”[2417]

(5) Maintenance. Also in 2000, Szathmary [2417] added the concept of attractor-based heredity to his replicator classification scheme, in which goal maintenance of the replicating systems is achieved either by stochastic gravitation toward an “attractor” in the dynamic control space, or more directly by “storage” based control information. For example, the membrane vesicle can be considered a molecular replicator [1333] and this system is attractor-based [2429] “since it is the dynamical nature of the network of reactions that makes replication possible, and the identity of the network is preserved by its dynamical stability (the system’s basin of attraction)” [2417]. Attractor-based systems can have limited heredity only [2417].* In contrast, information carried by gene-like replicators is storage-based [2429]: “to a good approximation all possible gene sequences are equally stable and transmissible, using the same copying mechanism” [2417]. Storage-based systems (e.g., contemporary DNA-based organisms) can have unlimited hereditary potential [2417]. Szathmary [2417] also notes that “the typical path of evolution goes from limited to unlimited heredity, and from attractor-based [and holistic] to modular (digital) replicators.”

* C. Phoenix [572] observes that the set of attractors stabilizes the system but is also defined by the system. There is no requirement that offspring have the same attractor-configuration as their parents. If offspring can explore an attractor-space capable of containing several attractor-configurations, then heredity could be unlimited.


Last updated on 1 August 2005