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The evolution of strand preference in simulated RNA replicators with strand displacement: implications for the origin of transcription.

Takeuchi N, Salazar L, Poole AM, Hogeweg P - Biol. Direct (2008)

Bottom Line: Our results indicated that if the system is well-mixed, there is no selective force acting upon strand preference per se.Interestingly, the results showed that selective forces "emerge" because of finite diffusion.For the full reviews, please go to the Reviewers' comments section.

View Article: PubMed Central - HTML - PubMed

Affiliation: Theoretical Biology and Bioinformatics Group, Utrecht University, Utrecht, The Netherlands. takeuchi.nobuto@gmail.com

ABSTRACT

Background: The simplest conceivable example of evolving systems is RNA molecules that can replicate themselves. Since replication produces a new RNA strand complementary to a template, all templates would eventually become double-stranded and, hence, become unavailable for replication. Thus the problem of how to separate the two strands is considered a major issue for the early evolution of self-replicating RNA. One biologically plausible way to copy a double-stranded RNA is to displace a preexisting strand by a newly synthesized strand. Such copying can in principle be initiated from either the (+) or (-) strand of a double-stranded RNA. Assuming that only one of them, say (+), can act as replicase when single-stranded, strand displacement produces a new replicase if the (-) strand is the template. If, however, the (+) strand is the template, it produces a new template (but no replicase). Modern transcription exhibits extreme strand preference wherein anti-sense strands are always the template. Likewise, replication by strand displacement seems optimal if it also exhibits extreme strand preference wherein (-) strands are always the template, favoring replicase production. Here we investigate whether such strand preference can evolve in a simple RNA replicator system with strand displacement.

Results: We first studied a simple mathematical model of the replicator dynamics. Our results indicated that if the system is well-mixed, there is no selective force acting upon strand preference per se. Next, we studied an individual-based simulation model to investigate the evolution of strand preference under finite diffusion. Interestingly, the results showed that selective forces "emerge" because of finite diffusion. Strikingly, the direction of the strand preference that evolves [i.e. (+) or (-) strand excess] is a complex non-monotonic function of the diffusion intensity. The mechanism underlying this behavior is elucidated. Furthermore, a speciation-like phenomenon is observed under certain conditions: two extreme replication strategies, namely replicase producers and template producers, emerge and coexist among competing replicators.

Conclusion: Finite diffusion enables the evolution of strand preference, the direction of which is a non-monotonic function of the diffusion intensity. By identifying the conditions under which strand preference evolves, this study provides an insight into how a rudimentary transcription-like pattern might have emerged in an RNA-based replicator system.

Reviewers: This article was reviewed by Eugene V Koonin, Rob Kinght and István Scheuring (nominated by David H Ardell). For the full reviews, please go to the Reviewers' comments section.

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The evolution of strand preference (r) as a function of the diffusion intensity (Δ) in the system with complex formation. Solid lines represent the evolved value of  as a function of the diffusion intensity (Δ) for various decay rates (d). Dashed lines represent the minimum value of r necessary to ensure system survival (rmin). Colors (and simbols) represent the value of d: d = 0.0025 (black circles); d = 0.0125 (red squares); d = 0.025 (blue triangles). The other parameters are as follows: kSP = kSM = kDP + kDM = 1; b = 1; κ = 1; μ = 0.01; δr = 0.1.
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Figure 10: The evolution of strand preference (r) as a function of the diffusion intensity (Δ) in the system with complex formation. Solid lines represent the evolved value of as a function of the diffusion intensity (Δ) for various decay rates (d). Dashed lines represent the minimum value of r necessary to ensure system survival (rmin). Colors (and simbols) represent the value of d: d = 0.0025 (black circles); d = 0.0125 (red squares); d = 0.025 (blue triangles). The other parameters are as follows: kSP = kSM = kDP + kDM = 1; b = 1; κ = 1; μ = 0.01; δr = 0.1.

Mentions: The results show the following (Fig. 10). When the value of Δ is sufficiently great, the system goes extinct, as in the ODE model. This is because the evolved value of decreases as Δ increases, and at a certain point becomes smaller than the minimum value of r (rmin) necessary to ensure system survival (note that rmin increases as Δ increases; Fig. 10 dashed lines). When, however, the value of Δ is sufficiently small, the system can survive. This is because the advantage of producing P due to local aggregation keeps the evolved value of greater than rmin. Moreover, the non-monotonic behavior of with respect to Δ is lost, which can be explained as follows. In the current system, the advantage of producing M does not diminish at Δ = a (i.e. when the diffusion intensity is equal to the rate of replication for double strand formation from a single-stranded template), because the advantage of producing M due to complex formation is not affected by the value of Δ. The advantage of producing P, however, does diminish as Δ increases for the same reason as we saw in the earlier sections (the degree of local aggregation diminishes as Δ increases). Therefore, the behavior of is monotonic with respect to Δ.


The evolution of strand preference in simulated RNA replicators with strand displacement: implications for the origin of transcription.

Takeuchi N, Salazar L, Poole AM, Hogeweg P - Biol. Direct (2008)

The evolution of strand preference (r) as a function of the diffusion intensity (Δ) in the system with complex formation. Solid lines represent the evolved value of  as a function of the diffusion intensity (Δ) for various decay rates (d). Dashed lines represent the minimum value of r necessary to ensure system survival (rmin). Colors (and simbols) represent the value of d: d = 0.0025 (black circles); d = 0.0125 (red squares); d = 0.025 (blue triangles). The other parameters are as follows: kSP = kSM = kDP + kDM = 1; b = 1; κ = 1; μ = 0.01; δr = 0.1.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2648946&req=5

Figure 10: The evolution of strand preference (r) as a function of the diffusion intensity (Δ) in the system with complex formation. Solid lines represent the evolved value of as a function of the diffusion intensity (Δ) for various decay rates (d). Dashed lines represent the minimum value of r necessary to ensure system survival (rmin). Colors (and simbols) represent the value of d: d = 0.0025 (black circles); d = 0.0125 (red squares); d = 0.025 (blue triangles). The other parameters are as follows: kSP = kSM = kDP + kDM = 1; b = 1; κ = 1; μ = 0.01; δr = 0.1.
Mentions: The results show the following (Fig. 10). When the value of Δ is sufficiently great, the system goes extinct, as in the ODE model. This is because the evolved value of decreases as Δ increases, and at a certain point becomes smaller than the minimum value of r (rmin) necessary to ensure system survival (note that rmin increases as Δ increases; Fig. 10 dashed lines). When, however, the value of Δ is sufficiently small, the system can survive. This is because the advantage of producing P due to local aggregation keeps the evolved value of greater than rmin. Moreover, the non-monotonic behavior of with respect to Δ is lost, which can be explained as follows. In the current system, the advantage of producing M does not diminish at Δ = a (i.e. when the diffusion intensity is equal to the rate of replication for double strand formation from a single-stranded template), because the advantage of producing M due to complex formation is not affected by the value of Δ. The advantage of producing P, however, does diminish as Δ increases for the same reason as we saw in the earlier sections (the degree of local aggregation diminishes as Δ increases). Therefore, the behavior of is monotonic with respect to Δ.

Bottom Line: Our results indicated that if the system is well-mixed, there is no selective force acting upon strand preference per se.Interestingly, the results showed that selective forces "emerge" because of finite diffusion.For the full reviews, please go to the Reviewers' comments section.

View Article: PubMed Central - HTML - PubMed

Affiliation: Theoretical Biology and Bioinformatics Group, Utrecht University, Utrecht, The Netherlands. takeuchi.nobuto@gmail.com

ABSTRACT

Background: The simplest conceivable example of evolving systems is RNA molecules that can replicate themselves. Since replication produces a new RNA strand complementary to a template, all templates would eventually become double-stranded and, hence, become unavailable for replication. Thus the problem of how to separate the two strands is considered a major issue for the early evolution of self-replicating RNA. One biologically plausible way to copy a double-stranded RNA is to displace a preexisting strand by a newly synthesized strand. Such copying can in principle be initiated from either the (+) or (-) strand of a double-stranded RNA. Assuming that only one of them, say (+), can act as replicase when single-stranded, strand displacement produces a new replicase if the (-) strand is the template. If, however, the (+) strand is the template, it produces a new template (but no replicase). Modern transcription exhibits extreme strand preference wherein anti-sense strands are always the template. Likewise, replication by strand displacement seems optimal if it also exhibits extreme strand preference wherein (-) strands are always the template, favoring replicase production. Here we investigate whether such strand preference can evolve in a simple RNA replicator system with strand displacement.

Results: We first studied a simple mathematical model of the replicator dynamics. Our results indicated that if the system is well-mixed, there is no selective force acting upon strand preference per se. Next, we studied an individual-based simulation model to investigate the evolution of strand preference under finite diffusion. Interestingly, the results showed that selective forces "emerge" because of finite diffusion. Strikingly, the direction of the strand preference that evolves [i.e. (+) or (-) strand excess] is a complex non-monotonic function of the diffusion intensity. The mechanism underlying this behavior is elucidated. Furthermore, a speciation-like phenomenon is observed under certain conditions: two extreme replication strategies, namely replicase producers and template producers, emerge and coexist among competing replicators.

Conclusion: Finite diffusion enables the evolution of strand preference, the direction of which is a non-monotonic function of the diffusion intensity. By identifying the conditions under which strand preference evolves, this study provides an insight into how a rudimentary transcription-like pattern might have emerged in an RNA-based replicator system.

Reviewers: This article was reviewed by Eugene V Koonin, Rob Kinght and István Scheuring (nominated by David H Ardell). For the full reviews, please go to the Reviewers' comments section.

Show MeSH
Related in: MedlinePlus