Vesicles+and+the+information+threshold

Prev: Stochastic corrector model Next: Micro and macrolevel dynamics: intricate implicit mutual interactions


 * TODO List**
 * What are implications of coupled timescales?

=Vesicles and the information threshold=

At this stage the role of vesicles in the information threshold is therefore still questionable: //Can vesicles increase the information threshold when mutation is included?// //Can group selection play a role with respect to the information threshold and overrule the negative effects of stochasticity due to vesicles?//

This issue was tackled by Hogeweg and Takeuchi ([|2003]) in a model in which they studied simple replicator dynamics and the effect of compartmentalization on the information threshold. For this they assumed the **mast****er-mutant equation model** in which both are identical except for a faster replication rate in the master equation. The model was a 2-layer CA, where in one layer the replicator dynamics and diffusion were modeled, and in the other layer the vesicles were modeled in terms of the Cellular-Potts model. The vesicle dynamics were dependent on the number of replicators inside a vesicle. The parameter DIVPOP was used as the number of replicators when vesicles can start to divide. Note that the two dynamics (replicators and vesicles) are hence explicitly coupled (as compared to the stochastic corrector model?).

The main result of this study is that it is very difficult to increase the information threshold (compare the results in the figure with the dotted line, which represents the case without vesicles). For small cells (low DIVPOP) below the information threshold the stochastic corrector does have some effect: the frequency of the master sequence increases. However, due to the reduced population size and increased stochasticity, the information threshold is still lower than in the case without vesicles. As DIVPOP increases, the growth of vesicles decreases and the system becomes more sensitive to the death rates (DR). However with DR=0 there is no growth, and no selection. Therefore DR needs to be high in order to get selection between vesicles and therefore group-level selection. However when DR is high the vesicles die out!

Therefore, one the results that emerge from this study is that DR determines the time-scale of the dynamics. As DR increases, group-selectivity increases. With low DR stochasticity becomes a problem, while with extreme DR vesicles die out. However, this model cannot reach DRs that lead to sufficient vesicle growth rates, i.e. group selection doesn't come for free and one needs a fine-tuning between replicator and vesicle death rates.

If an additional assumption is made that the division of vesicles depends on the number of master sequences in stead of the total number of molecules (differential division model), then the information threshold //does// increase for certain parameter settings, especially if DRs are low. This, however, is kind of cheating: we have now added a specific assumption that the molecules that replicate fastest also provide a growth advantage to the vesicle at the higher (vesicle) level.

In summary, the information threshold problem in this model is only eleviated by the vesicles under very specific (cheating) assumptions and when the parameters are fine-tuned to "work". The information threshold only goes up when group selection is outweighed by stochasticity, however due to limited diffusibility on a vesicle level, the information threshold is inhibited. Hence, we should conclude that this model does __not__ provide the answer for the information threshold problem.

In the hypercycle analysis, group dynamics are derived from hypercycle dynamics (i.e. intertwined time-scales). In the vesicle model there is an explicit implementation of group-level dynamics and therefore parameters need to be added to define these dynamics. Nonetheless, the timescales are coupled, in contrast to the stochastic corrector model, where timescales do not interact. (Q: WHAT IMPLICATIONS DOES THIS HAVE?).

Next: Micro and macrolevel dynamics: intricate implicit mutual interactions


 * References**
 * Hogeweg P and Takeuchi N** (2003) Multilevel selection in models of prebiotic evolution: compartments and spatial self-organization OLEB special issue on theoretical models of prebiotic evolution, ed. E Szathmary (in press) [|pdf]

(CHANGELOG 2014-2015) - Added explanation of why due to limited diffusibility info threshold is limited (was a TODO point) to prev page (stochastic corrector).