A Necessary Condition for Coexistence of Autocatalytic Replicators in a Prebiotic Environment
Abstract
:1. Introduction
2. Background
2.1. Mathematical Model of a Fed-Batch Bioreactor
2.2. A Mathematical Condition for Sustained Diversity
3. Analysis
Variable | Description | Units | Value |
---|---|---|---|
x0,1 | Initial concentration, x1 | mol/m3 | 0.1 |
x0,2 | Initial concentration, x2 | mol/m3 | 0.1 |
m0,a | Initial concentration, ma | mol/m3 | 0.5 |
m0,b | Initial concentration, mb | mol/m3 | 0.5 |
min,a | Inlet concentration, ma | mol/m3 | 0.5 |
min,b | Inlet concentration, mb | mol/m3 | 0.5 |
F | Inlet flow rate | m3/s | 1 |
V | Reactor volume | m3 | 1 |
tf | Simulation time | s | 1 × 107 |
Lia + Lib | Total replicator size | monomers | 20 |
4. Results
4.1. Growth of Replicators under a Constant Monomer Supply
4.2. Condition of Coexistence for Autocatalytic Replicators
Observed | Screening | Total | ||
---|---|---|---|---|
c1 < 0 c2 < 0 | c1 > 0, c2 < 0 c1 < 0, c2 > 0 | c1 > 0 c2 > 0 | ||
Extinction | 1.87% | 34.89% | 0.00% | 36.76% |
Single Winner | 0.00% | 53.96% | 0.83% | 54.79% |
Coexistence | 0.00% | 0.00% | 0.90% | 0.90% |
Extinction | Single Winner | Coexistence | Total |
---|---|---|---|
2.18% | 3.19% | 0.00 | 5.27% |
kr,1 = 4.3692 | kr,2 = 1.6605 |
kd,1 = 4.16 × 10−4 | kd,2 = 4.83 × 10−4 |
α1a = 0.2914 | α2a = 0.3585 |
α1b = 2.6602 | α2b = 0.7387 |
5. Discussion
6. Conclusions
Acknowledgments
Conflict of Interest
References
- Eigen, M.; Schuster, P. The hypercycle, a principle of natural self-organization. Part A: Emergence of the hypercycle. Naturwissenschaften 1977, 64, 541–565. [Google Scholar]
- Chen, I.A.; Nowak, M.A. From prelife to life: How chemical kinetics become evolutionary dynamics. Acc. Chem. Res. 2012, 45, 2088–2096. [Google Scholar] [CrossRef] [PubMed]
- Pross, A.; Khodorkovsky, V. Extending the concept of kinetic stability: Toward a paradigm for life. J. Phys. Org. Chem. 2004, 17, 312–316. [Google Scholar] [CrossRef]
- Lifson, S.; Lifson, H. A model of prebiotic replication: Survival of the fittest versus extinction of the unfittest. J. Theor. Biol. 1999, 199, 425–433. [Google Scholar] [CrossRef] [PubMed]
- Walker, S.I.; Grover, M.A.; Hud, N.V. Universal sequence replication,reversible polymerization and early functional biopolymers: A model for the initiation of prebiotic sequence evolution. PLoS One 2012, 7, e34166. [Google Scholar] [CrossRef] [PubMed]
- Yarus, M. Darwinian behavior in a cold,sporadically fed pool of ribonucleotides. Astrobiology 2012, 12, 870–883. [Google Scholar] [CrossRef] [PubMed]
- King, G. Was there a prebiotic soup? J. Theor. Biol. 1986, 123, 493–498. [Google Scholar] [CrossRef]
- Chacon, P.; Nuno, J. Spatial dynamics of a model for prebiotic evolution. Phys. D 1995, 81, 398–410. [Google Scholar] [CrossRef]
- Li, X.; Zhan, Z.Y.J.; Knipe, R.; Lynn, D.G. DNA-catalyzed polymerization. J. Am. Chem. Soc. 2002, 124, 746–747. [Google Scholar] [CrossRef] [PubMed]
- Ura, Y.; Beierle, J.; Leman, L.; Orgel, L.; Ghadiri, M. Self-assembling sequence-adaptive peptide nucleic acids. Science 2009, 325, 73–77. [Google Scholar] [CrossRef] [PubMed]
- Bean, H.; Anet, F.; Gould, I.; Hud, N. Glyoxylate as a backbone linkage for a prebiotic ancestor of RNA. Orig. Life Evol. B 2006, 36, 39–63. [Google Scholar] [CrossRef]
- Carnall, J.M.A.; Waudby, C.A.; Belenguer, A.M.; Stuart, M.C.A.; Peyralans, J.J.P.; Otto, S. Mechanosensitive self-replication driven by self-organization. Science 2010, 327, 1502–1506. [Google Scholar] [CrossRef] [PubMed]
- Hong, L.; Qi, X.; Zhang, Y. Dissecting the kinetic process of amyloid fiber formation through asymptotic analysis. J. Phys. Chem. B 2012, 116, 6611–6617. [Google Scholar] [CrossRef] [PubMed]
- Pedersen, J.T.; Østergaard, J.; Rozlosnlk, N.; Gammelgaard, B.; Heegaard, N.H. Cu (II) mediates kinetically distinct, non-amyloidogenic aggregation of amyloid-β peptides. J. Biol. Chem. 2011, 286, 26952–26963. [Google Scholar]
- Morris, A.M.; Watzky, M.A.; Agar, J.N.; Finke, R.G. Fitting neurological protein aggregation kinetic data via a 2-Step,minimal/Ockhams razor model: The Finke-Watzky mechanism of nucleation followed by autocatalytic surface growth. Biochemistry 2008, 47, 2413–2427. [Google Scholar] [CrossRef] [PubMed]
- Martin, O.; Horvath, J.E. Biological evolution of replicator systems: Towards a quantitative approach. Orig. Life Evol. B 2013, 43, 151–160. [Google Scholar] [CrossRef]
- Szathmary, E.; Smith, J.M. From replicators to reproducers: The first major transitions leading to life. J. Theor. Biol. 1997, 187, 555–571. [Google Scholar] [CrossRef] [PubMed]
- Wu, M.; Higgs, P.G. Origin of self-replicating biopolymers: Autocatalytic feedback can jump-start the RNA world. J. Mol. Evol. 2009, 69, 541–554. [Google Scholar] [CrossRef] [PubMed]
- Scheuring, I.; Szathmary, E. Survival of replicators with parabolic growth tendency and exponential decay. J. Theor. Biol. 2001, 212, 99–105. [Google Scholar] [CrossRef] [PubMed]
- Bailey, J.E.; Ollis, D.F. Biochemical Engineering Fundamentals, 2nd ed.; McGraw-Hill Company: New York, NY, USA, 1986; Chapter 9; p. 533. [Google Scholar]
- Nauman, E.B. Chemical Reactor Design,Optimization and Scaleup, 2nd ed.; John Wiley & Sons: Hoboken, NJ, USA, 2008; Chapter 12; p. 445. [Google Scholar]
- Wright, D.H. A simple,stable model of mutualism incorporating handling time. Am. Nat. 1989, 134, 664–667. [Google Scholar] [CrossRef]
- Hsu, S.B.; Hwang, T.W.; Kuang, Y. Rich dynamics of a ratio-dependent one-prey two-predators model. J. Math. Biol. 2001, 43, 377–396. [Google Scholar] [CrossRef] [PubMed]
- Xie, C.; Fan, M.; Zhao, W. Dynamics of a discrete stoichiometric two predators one prey model. J. Biol. Syst. 2010, 18, 649–667. [Google Scholar] [CrossRef]
- Ko, W.; Ahn, I. A diffusive one-prey and two-competing-predator system with a ratio-dependent functional response: I,long time behavior and stability of equilibria. J. Math. Anal. Appl. 2013, 397, 9–28. [Google Scholar] [CrossRef]
- Deck, C.; Jauker, M.; Richert, C. Efficient enzyme-free copying of all four nucleobases templated by immobilized RNA. Nat. Chem. 2011, 3, 603–608. [Google Scholar] [CrossRef] [PubMed]
- Luther, A.; Brandsch, R.; von Kiedrowski, G. Surface-promoted replication and exponential amplification of DNA analogues. Nature 1998, 396, 245–248. [Google Scholar] [CrossRef] [PubMed]
- Fogler, H.S. Elements of Chemical Reaction Engineering, 4th ed.; Prentice Hall: Englewood Cliffs, NJ, USA, 2005; Chapter 12; pp. 833–834. [Google Scholar]
- Von Kiedrowski, G. Minimal replocator theory I: Parabolic versus exponential growth. Bioorg. Chem. Front. 1993, 3, 113–146. [Google Scholar]
- Szathmary, E.; Gladkih, I. Sub-exponential growth and coexistence of non-enzymatically replicating templates. J. Theor. Biol. 1989, 138, 55–58. [Google Scholar] [CrossRef] [PubMed]
- Takeuchi, N.; Hogeweg, P. Evolutionary dynamics of RNA-like replicator systems: A bioinformatic approach to the origin of life. J. Mol. Evol. 2012, 9, 219–263. [Google Scholar]
- Takeuchi, N.; Hogeweg, P. Multilevel selection in models of prebiotic evolution II: A direct comparison of compartamentalization and spatial self-organization. PLoS Comp. Biol. 2009, 5, e1000542. [Google Scholar] [CrossRef]
- McKay, M.; Beckman, R.; Conover, W. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 1979, 21, 239–245. [Google Scholar]
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Hernandez, A.F.; Grover, M.A. A Necessary Condition for Coexistence of Autocatalytic Replicators in a Prebiotic Environment. Life 2013, 3, 403-420. https://doi.org/10.3390/life3030403
Hernandez AF, Grover MA. A Necessary Condition for Coexistence of Autocatalytic Replicators in a Prebiotic Environment. Life. 2013; 3(3):403-420. https://doi.org/10.3390/life3030403
Chicago/Turabian StyleHernandez, Andres F., and Martha A. Grover. 2013. "A Necessary Condition for Coexistence of Autocatalytic Replicators in a Prebiotic Environment" Life 3, no. 3: 403-420. https://doi.org/10.3390/life3030403