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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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Advantage of producing (-) strands. The value of  = (1 - e-(Δ+2a)τ)a/(Δ + 2a) (black solid line), that of  = (1 - e-(Δ+a)τ)a/(Δ + a) (red dashed line) and the difference thereof (blue dotted line) are plotted as a function of Δ (τ is set to Δ-1), with a = 0.5 [a is the rate of replication for single stranded templates – either (+) or (-) strands]. For those plotted values to be applicable to the CA model, a should lie between 0.1kS and kS where kS = kSP = kSM. This is because in the CA model the number of neighbors are 8 (rather than 2), and these 8 neighbors are not necesarily all P. Thus, to calculate values corresponding to  and  in the CA model, one must also factor in the probability that a molecule (P or M) interacts with P given that they are in the neighborhood of the molecule (see Methods for the details of how interactions are implemented in the CA model).
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Figure 4: Advantage of producing (-) strands. The value of = (1 - e-(Δ+2a)τ)a/(Δ + 2a) (black solid line), that of = (1 - e-(Δ+a)τ)a/(Δ + a) (red dashed line) and the difference thereof (blue dotted line) are plotted as a function of Δ (τ is set to Δ-1), with a = 0.5 [a is the rate of replication for single stranded templates – either (+) or (-) strands]. For those plotted values to be applicable to the CA model, a should lie between 0.1kS and kS where kS = kSP = kSM. This is because in the CA model the number of neighbors are 8 (rather than 2), and these 8 neighbors are not necesarily all P. Thus, to calculate values corresponding to and in the CA model, one must also factor in the probability that a molecule (P or M) interacts with P given that they are in the neighborhood of the molecule (see Methods for the details of how interactions are implemented in the CA model).

Mentions: Moreover, as Δ increases from 0 to infinity in Eqs. (10) and (11), a transition is expected to happen from Eq. (13) to Eq. (12) when the order of magnitude of Δ becomes equal to that of a (i.e. the rate of second strand synthesis) as shown in Fig. 4 (where a is set to 0.5). Indeed, a similar transition is also observed with respect to the evolved value of as shown in Fig. 3 (e.g. for d = 0.001), in that suddenly increases when Δ increases from 0.1 to 1 (see also the explanation in Fig. 3).


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)

Advantage of producing (-) strands. The value of  = (1 - e-(Δ+2a)τ)a/(Δ + 2a) (black solid line), that of  = (1 - e-(Δ+a)τ)a/(Δ + a) (red dashed line) and the difference thereof (blue dotted line) are plotted as a function of Δ (τ is set to Δ-1), with a = 0.5 [a is the rate of replication for single stranded templates – either (+) or (-) strands]. For those plotted values to be applicable to the CA model, a should lie between 0.1kS and kS where kS = kSP = kSM. This is because in the CA model the number of neighbors are 8 (rather than 2), and these 8 neighbors are not necesarily all P. Thus, to calculate values corresponding to  and  in the CA model, one must also factor in the probability that a molecule (P or M) interacts with P given that they are in the neighborhood of the molecule (see Methods for the details of how interactions are implemented in the CA model).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 4: Advantage of producing (-) strands. The value of = (1 - e-(Δ+2a)τ)a/(Δ + 2a) (black solid line), that of = (1 - e-(Δ+a)τ)a/(Δ + a) (red dashed line) and the difference thereof (blue dotted line) are plotted as a function of Δ (τ is set to Δ-1), with a = 0.5 [a is the rate of replication for single stranded templates – either (+) or (-) strands]. For those plotted values to be applicable to the CA model, a should lie between 0.1kS and kS where kS = kSP = kSM. This is because in the CA model the number of neighbors are 8 (rather than 2), and these 8 neighbors are not necesarily all P. Thus, to calculate values corresponding to and in the CA model, one must also factor in the probability that a molecule (P or M) interacts with P given that they are in the neighborhood of the molecule (see Methods for the details of how interactions are implemented in the CA model).
Mentions: Moreover, as Δ increases from 0 to infinity in Eqs. (10) and (11), a transition is expected to happen from Eq. (13) to Eq. (12) when the order of magnitude of Δ becomes equal to that of a (i.e. the rate of second strand synthesis) as shown in Fig. 4 (where a is set to 0.5). Indeed, a similar transition is also observed with respect to the evolved value of as shown in Fig. 3 (e.g. for d = 0.001), in that suddenly increases when Δ increases from 0.1 to 1 (see also the explanation in Fig. 3).

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