“Living” Under the Challenge of Information Decay: The Stochastic Corrector Model vs. Hypercycles

doi:10.1006/jtbi.2002.3026

Journal of Theoretical Biology

Volume 217, Issue 2, 21 July 2002, Pages 167-181

https://doi.org/10.1006/jtbi.2002.3026 Get rights and content

Abstract

The combined problem of having a large genome size when the accuracy of replication was a limiting factor is probably the most difficult transition to explain at the late stages of RNA world. One solution has been to suggest the existence of a cyclically coupled system of autocatalytic and cross-catalytic molecular mutualists, where each member helps the following member and receives help from the preceding one (i.e., a “hypercycle”). However, such a system is evolutionarily unstable when mutations are taken into account because it lacks individuality. In time, the cooperating networks of genes should have been encapsulated in a cell-like structure. But once the cell was invented, it closely aligned genes' common interests and helped to reduce gene selfishness, so there was no need for hypercycles. A simple package of competing genes, described by the “stochastic corrector model” (SCM), could have provided the solution. Until now, there is no clear demonstration that the proposed mechanisms (compartmentalized hypercycles and the stochastic corrector model) do in fact solve the error threshold problem. Here, we present a Monte Carlo model to test the viability of protocell populations that enclose a hypercyclic (HPC) or a non-hypercyclic (SCM) system when faced with realistic mutation rates before the evolution of efficient enzymic machinery for replication. The numerical results indicate that both systems are efficient information integrators and are able to overcome the danger of information decay in the absence of accurate replication. However, a population of SCM protocells can tolerate higher deleterious mutation rates and reaches an equilibrium mutational load lower than that in a population of HPC protocells.

References (35)

D.P. BARTEL et al.
Constructing an RNA world
Trends Genet.
(1999)
C. BRESCH et al.
Hypercycles, parasites and packages
J. theor. Biol.
(1980)
T. GÁNTI
Organisation of chemical reactions into dividing and metabolizing units: the chemotons
Biosystems
(1975)
E. SZATHMÁRY
The integration of the earliest genetic information
Trends Ecol. Evol.
(1989)
E. SZATHMÁRY et al.
Group selection of early replicators and the origin of life
J. theor. Biol.
(1987)
E. SZATHMÁRY et al.
From replicators to reproducers: the first major transitions leading to life
J. theor Biol.
(1997)
P.R.A. CAMPOS et al.
Finite- size scaling in a quasispecies model
Phys. Rev. E
(1998)
P.R.A. CAMPOS et al.
Error propagation in the hypercycle
Phys. Rev. E
(2000)
J.F. CROW
Genetic loads and the cost of natural selection
M. EIGEN
Self-organization of matter and the evolution of biological macromolecules
Naturwissenschaften
(1971)

M. EIGEN

Steps towards Life: a Prospective on Evolution

(1992)

M. EIGEN et al.

The Hypercycle: a Principle of Natural Self-organization

(1979)

M. EIGEN et al.

Stages of emerging life—five principles of early organization

J. Mol. Evol.

(1982)

M. EIGEN et al.

The origin of genetic information

Sci. Am.

(1981)

E.C. FRIEDBERG et al.

DNA Repair and Mutagenesis

(1995)

FTN77, 1997, Salford software...

T. GÁNTI

The Principle of Life

(1987)

Cited by (56)

Modeling the origin of cells
2023, Trends in Genetics
The comparative analysis of prebiological evolution models
2020, Chinese Journal of Physics
Several models of prebiological systems are described and analyzed. The following models are characterized: a quasispecies model, a hypercycle model, a syser model (the term "syser" is an abbreviation of SYstem of SElf-Reproduction), a stochastic corrector model, a model of the origin of a primordial genome through spontaneous symmetry breaking. The quasispecies model analyzes the Darwinian evolution of information chains; this evolution is similar to the evolution of RNA molecules. Rather general estimates of the speed and efficiency of evolutionary processes can be obtained in the framework of the quasispecies model. We briefly describe the method for obtaining these estimates and the corresponding results. The hypercycle model considers the interaction of RNA chains and enzymes. The syser model characterizes a rather general scheme of the self-reproducing system, which is similar to the self-reproducing systems of biological cells. Syser includes a polynucleotide sequence, a replication enzyme, a translation enzyme, and other enzymes; these macromolecules are located inside the protocell. The stochastic corrector model describes the process of using a relatively small number of molecules of competing and cooperating replicators in protocells. The model of the origin of a primordial genome through spontaneous symmetry breaking characterizes an interesting and important process of the appearance of genotypes in protocells. This model was proposed and investigated by Takeuchi, Hogeweg, and Kaneko in 2017; we call it further “the THK model.” The current article characterizes and compares all these models.
Moderate sex between protocells can balance between a decrease in assortment load and an increase in parasite spread
2019, Journal of Theoretical Biology
Citation Excerpt :
Differences to the usual modelling practices for SCM dynamics included: (i) Metabolic templates were growing at approximately the same rate., (ii) lack of dosage effect by the metabolic genes (i.e. cells having at least one metabolic gene of both types had maximal fitness, and (iii) no intragenomic conflict between the two metabolic genes. In the case of deleterious recurrent mutations of the metabolic templates the fitness function used by Santos et al. (2003) was the same as in Zintzaras et al. (2002): multiplicative for the different ribozymes (note that, unlike in the present paper, there was no resulting dosage effect). Santos et al. (2003) found that without recurrent deleterious mutations, the spread of selfish replicases through occasional protocell fusion was harmful, but also that mutations of metabolic genes under high mutation rates accumulated more slowly in the presence of selfish replicases and could lead to increased average protocell fitness (due to fewer replication rounds of the metabolic genes).
Sexual reproduction is widespread in nature despite the different kinds of cost that it entails. We do not know exactly when the first sexual process took place and especially why it was beneficial at first. It is clearer why sex is advantageous for the prokaryotes and eukaryotes but the benefit of sex for protocells with individually replicating ribozymes is not yet fully understood. In this context sex is the simple horizontal gene transfer among two protocells that undergo transient fusion. Many authors argue that horizontal gene transfer (HGT) was very common in the early stage of evolution. However, HGT is a risky mechanism considering both the disruption of optimal compositions and the spread of parasites among protocells. In order to test the effects of HGT on the fitness of a protocell population, we explored by numerical simulations those conditions under which fusion might have been beneficial. We investigated multiple conceivable types of fusion in the stochastic corrector model framework and we considered the spread of parasites in every case. Protocells contain up to five species of unlinked, essential ribozymes; if a protocell has the same amount of each, it reaches maximum fitness. Fusion is dangerous not only due to the spread of parasites but also because it can ruin the cells with balanced ribozyme composition. We show that fusion can restore the ribozyme composition of the protocells under certain circumstances (high gene count, intermediate split size and low rate of fusion) and thus it can decrease the effect of the genetic load. Fusion could have been a useful early mechanism in contributing to the reliable coexistence of the different ribozymes before the spread of the chromosomes.
Maximal gene number maintainable by stochastic correction – The second error threshold
2016, Journal of Theoretical Biology
Citation Excerpt :
Szathmáry and Demeter (1987) have shown that given a low number of replicators inside a cell having a far from optimal copy number distribution (the goal distribution can be arbitrary), stochastic separation of the genes into the daughter cells can ameliorate the copy number distribution of the parent cells. Previous works on the SCM have focused on cells with only two (Grey et al., 1995; Zintzaras et al., 2010) or three genes (Zintzaras et al., 2002). A few enzymes can coexist without a problem even without full compartmentalisation, i.e. on surfaces (Boerlijst, 2000; Czárán and Szathmáry, 2000; Hogeweg and Takeuchi, 2003; Könnyű and Czárán, 2013; Takeuchi and Hogeweg, 2009).
There is still no general solution to Eigen׳s Paradox, the chicken-or-egg problem of the origin of life: neither accurate copying, nor long genomes could have evolved without one another being established beforehand. But an array of small, individually replicating genes might offer a workaround, provided that multilevel selection assists the survival of the ensemble. There are two key difficulties that such a system has to overcome: the non-synchronous replication of genes, and their random assortment into daughter cells (the units of higher-level selection) upon fission. Here we find, using the Stochastic Corrector Model framework, that a large number (τ≥90) of genes can coexist. Furthermore, the system can tolerate about 10% replication rate asymmetry (competition) among the genes. On this basis, we put forward a plausible (and testable!) scenario for how novel genes could have been incorporated into early living systems: a route to complex metabolism.
The RNA world as a model system to study the origin of life
2015, Current Biology
Understanding how life arose is a fundamental problem of biology. Much progress has been made by adopting a synthetic and mechanistic perspective on originating life. We present a current view of the biochemistry of the origin of life, focusing on issues surrounding the emergence of an RNA World in which RNA dominated informational and functional roles. There is cause for optimism on this difficult problem: the prebiotic chemical inventory may not have been as nightmarishly complex as previously thought; the catalytic repertoire of ribozymes continues to expand, approaching the goal of self-replicating RNA; encapsulation in protocells provides evolutionary and biophysical advantages. Nevertheless, major issues remain unsolved, such as the origin of a genetic code. Attention to this field is particularly timely given the accelerating discovery and characterization of exoplanets.
Evolution before life
2012, Developments in Environmental Modelling
Citation Excerpt :
Much the same as a deleterious mutation in current DNA in one individual has no effect on others, parasitic branches must be isolated and removed from the population by the death of the compartment. The compartmentalized hypercycle model, as expected, is now evolutionary stable (Zintharas et al., 2002); but then again, once compartments are available and link the destinies of replicating polynucleotides together, there is no need for linking them via a hypercycle. According to the stochastic corrector model (Grey et al., 1995; Szathmáry and Demeter, 1987), a simple package of competing replicators can be reliably maintained, given that each replicator is needed for the survival of the protocell.
All life, as we know it, springs from already existing life. But how did it all begin? We argue that evolution preceded life, and we must understand the origin of evolvable chemical systems as their gradual increase of complexity lead to the appearance of the first living entity. In this chapter, we discuss various theoretical models that have been proposed to explain the origin of evolvable systems (including template replicators, autocatalytic cycles, polymer autocatalytic sets, and the GARD model) and translate the critical properties of evolution to features of chemical networks.

View all citing articles on Scopus

¹: Corresponding author. Collegium Budapest, Institute for Advanced Study, Szentháromság u. 2, H-1014, Budapest, Hungary. Tel.: +36-1-224-83-31; fax: +36-1-224-83-10. E-mail addresses: [email protected] (E. Zintzaras), [email protected] (M. Santos), [email protected] (E. Szathmáry)

View full text

Regular Article“Living” Under the Challenge of Information Decay: The Stochastic Corrector Model vs. Hypercycles

Abstract

Trends Genet.

J. theor. Biol.

Biosystems

Trends Ecol. Evol.

J. theor. Biol.

J. theor Biol.

Finite- size scaling in a quasispecies model

Phys. Rev. E

Error propagation in the hypercycle

Phys. Rev. E

Genetic loads and the cost of natural selection

Self-organization of matter and the evolution of biological macromolecules

Naturwissenschaften

Steps towards Life: a Prospective on Evolution

The Hypercycle: a Principle of Natural Self-organization

Stages of emerging life—five principles of early organization

J. Mol. Evol.

The origin of genetic information

Sci. Am.

DNA Repair and Mutagenesis

The Principle of Life

Regular Article
“Living” Under the Challenge of Information Decay: The Stochastic Corrector Model vs. Hypercycles