Stochastic Yield Catastrophes and Robustness in Self-Assembly
Authors:
Florian M. Gartner,
Isabella R. Graf,
Patrick Wilke,
Philipp M. Geiger,
Erwin Frey
Abstract:
A guiding principle in self-assembly is that, for high production yield, nucleation of structures must be significantly slower than their growth. However, details of the mechanism that impedes nucleation are broadly considered irrelevant. Here, we analyze self-assembly into finite-sized target structures employing mathematical modeling. We investigate two key scenarios to delay nucleation: (i) by…
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A guiding principle in self-assembly is that, for high production yield, nucleation of structures must be significantly slower than their growth. However, details of the mechanism that impedes nucleation are broadly considered irrelevant. Here, we analyze self-assembly into finite-sized target structures employing mathematical modeling. We investigate two key scenarios to delay nucleation: (i) by introducing a slow activation step for the assembling constituents and, (ii) by decreasing the dimerization rate. These scenarios have widely different characteristics. While the dimerization scenario exhibits robust behavior, the activation scenario is highly sensitive to demographic fluctuations. These demographic fluctuations ultimately disfavor growth compared to nucleation and can suppress yield completely. The occurrence of this stochastic yield catastrophe does not depend on model details but is generic as soon as number fluctuations between constituents are taken into account. On a broader perspective, our results reveal that stochasticity is an important limiting factor for self-assembly and that the specific implementation of the nucleation process plays a significant role in determining the yield.
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Submitted 18 March, 2020; v1 submitted 23 May, 2019;
originally announced May 2019.
Two-species active transport along cylindrical biofilaments is limited by emergent topological hindrance
Authors:
Patrick Wilke,
Emanuel Reithmann,
Erwin Frey
Abstract:
Active motion of molecules along filamentous structures is a crucial feature of cell biology and is often modeled with the paradigmatic asymmetric simple exclusion process. Motivated by recent experimental studies that have addressed the stepping behavior of kinesins on microtubules, we investigate a lattice gas model for simultaneous transport of two species of active particles on a cylinder. The…
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Active motion of molecules along filamentous structures is a crucial feature of cell biology and is often modeled with the paradigmatic asymmetric simple exclusion process. Motivated by recent experimental studies that have addressed the stepping behavior of kinesins on microtubules, we investigate a lattice gas model for simultaneous transport of two species of active particles on a cylinder. The species are distinguished by their different gaits: While the first species moves straight ahead, the second follows a helical path. We show that the collective properties of such systems critically differ from those of one-species transport in a way that cannot be accounted for by standard models. This is most evident in a jamming transition far below full occupation, as well as in non-equilibrium pattern formation. The altered behavior arises because - unlike the case in single-species transport - any given position may be targeted by two particles from different directions at the same time. However, a particle can leave a given position only in one direction. This simple change in connectivity significantly amplifies the impact of steric interactions and thus becomes a key determinant of mixed species transport. We computationally characterize this type of hindrance and develop a comprehensive theory for collective two-species transport along a cylinder. Our observations show high robustness against model extensions that account for additional biomolecular features and demonstrate that even small fractions of a second species can significantly alter transport. This suggests that our analysis is also relevant in a biological context.
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Submitted 6 July, 2018;
originally announced July 2018.