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Evidence for Phase Transitions in Replication Fidelity and Survival Probability at the Origin of Life

Sy Garte
Sy Garte
   | 05 dic 2021
BioCosmos: New perspectives on the origin and evolution of life's Cover Image
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Article Category: Original Study
Pubblicato online: 05 dic 2021
Pagine: 2 - 10
DOI: https://doi.org/10.2478/biocosmos-2021-0002
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© 2021 Sy Garte, published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1

Illustration of various model phase transitions from nonlife to life. Regions of the nonliving phase (no possible growth or evolution) are indicated in all figures by solid patterns, whereas the phase of life contains arrows suggesting continuous evolution to improvements in both survival and replication fidelity. A. Evolution without any phase transitions. This is the default assumption for many origin-of-life theorists. Arrows indicate that any starting values of P and F can lead to further growth and evolution. B. Phase transition at F = 0.5. Below that threshold, no growth or further evolution is possible, independent of P. C. Phase transition at F=0.5, P = 0.5. The threshold for life is a function of both P and F, at a fixed value.
Illustration of various model phase transitions from nonlife to life. Regions of the nonliving phase (no possible growth or evolution) are indicated in all figures by solid patterns, whereas the phase of life contains arrows suggesting continuous evolution to improvements in both survival and replication fidelity. A. Evolution without any phase transitions. This is the default assumption for many origin-of-life theorists. Arrows indicate that any starting values of P and F can lead to further growth and evolution. B. Phase transition at F = 0.5. Below that threshold, no growth or further evolution is possible, independent of P. C. Phase transition at F=0.5, P = 0.5. The threshold for life is a function of both P and F, at a fixed value.

Figure 2

Phase transition as a function of P and F from simulation data. This is a replot of Figure 1 from ref. 32 showing that the actual phase transition follows a specific trajectory dependent on both P and F.
Phase transition as a function of P and F from simulation data. This is a replot of Figure 1 from ref. 32 showing that the actual phase transition follows a specific trajectory dependent on both P and F.

Figure 3

An illustration of the general strategy used in the simulation model described in ref. 32 and in this text. Numbers in cells are the values for P. A. Perfect replication fidelity (F = 1.0) and survival probability (P = 1.0) results in each A and B cell having the exact value of P =1 as its parent. The growth rate of this cell population is the maximum value of 2.0 or a doubling of cell numbers with every generation. B. Changing the starting values of P and F to 0.9 and 0.7, respectively, the parental P value is inherited by some of the descendants of the original cell. Cell death (about 10% of parental cells) or a changed value of P in daughter B cells (due to mutations in 30% of B cells) are found in individual cells as cell divisions occur (see the Methods section for details on how mutations modify the value of P, as functions of the two parameters M and D). In this example the growth constant is reduced to 1.7.
An illustration of the general strategy used in the simulation model described in ref. 32 and in this text. Numbers in cells are the values for P. A. Perfect replication fidelity (F = 1.0) and survival probability (P = 1.0) results in each A and B cell having the exact value of P =1 as its parent. The growth rate of this cell population is the maximum value of 2.0 or a doubling of cell numbers with every generation. B. Changing the starting values of P and F to 0.9 and 0.7, respectively, the parental P value is inherited by some of the descendants of the original cell. Cell death (about 10% of parental cells) or a changed value of P in daughter B cells (due to mutations in 30% of B cells) are found in individual cells as cell divisions occur (see the Methods section for details on how mutations modify the value of P, as functions of the two parameters M and D). In this example the growth constant is reduced to 1.7.

Figure 4

Results from theoretical calculations as described in the text. A. Phase transitions as a function of P, F, and D > 5.0. B. Phase transitions for D < 1.0.
Results from theoretical calculations as described in the text. A. Phase transitions as a function of P, F, and D > 5.0. B. Phase transitions for D < 1.0.

Definitions of Symbols

P Probability of cell survival between replication events
Pm Value of P after a mutation
F Replication fidelity as a probability of perfect replication
M Magnitude of the effect of a mutation on P
D Ratio of deleterious to beneficial mutations
K Growth constant of a cell population starting with a single cell
C Cell number
Ct Cell number at t generations
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