Stochastic Yield Catastrophes and Robustness in Self-Assembly

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

How can cells count? Robustness in self-assembly pathways

Cells are characterised by different kinds of structures, organelles, each of them with a specific function. In some cases, in order to perform its task, an organelle needs to have some precise features, lika a location, or shape, size and requires to be present in an exact number. Some of these features can't be directly encoded in DNA itself and they are controlled by other means. The present work addresses the poorly understood problem of how cells can count. More precisely, what mechanisms are used by the cell in order to control and constrain the number of structures it needs. In order to do so, this thesis starts by considering the flagellum, a structure that allows the cell to move in its environment, and analyses its self-assembly pathway traying to figure out what the purpose of each step of the process is in making the "counting mechanism" robust to initial resources number variations and stochastic fluctuations.ope

Negative differential response in chemical reactions

Reaction currents in chemical networks usually increase when increasing their driving affinities. But far from equilibrium the opposite can also happen. We find that such negative differential response (NDR) occurs in reaction schemes of major biological relevance, namely, substrate inhibition and autocatalysis. We do so by deriving the full counting statistics of two minimal representative models using large deviation methods. We argue that NDR implies the existence of optimal affinities that maximize the robustness against environmental and intrinsic noise at intermediate values of dissipation. An analogous behavior is found in dissipative self-assembly, for which we identify the optimal working conditions set by NDR.Comment: Main text and S

Gene duplication and subsequent diversification strongly affect phenotypic evolvability and robustness.

We study the effects of non-determinism and gene duplication on the structure of genotype-phenotype (GP) maps by introducing a non-deterministic version of the Polyomino self-assembly model. This model has previously been used in a variety of contexts to model the assembly and evolution of protein quaternary structure. Firstly, we show the limit of the current deterministic paradigm which leads to built-in anti-correlation between evolvability and robustness at the genotypic level. We develop a set of metrics to measure structural properties of GP maps in a non-deterministic setting and use them to evaluate the effects of gene duplication and subsequent diversification. Our generalized versions of evolvability and robustness exhibit positive correlation for a subset of genotypes. This positive correlation is only possible because non-deterministic phenotypes can contribute to both robustness and evolvability. Secondly, we show that duplication increases robustness and reduces evolvability initially, but that the subsequent diversification that duplication enables has a stronger, inverse effect, greatly increasing evolvability and reducing robustness relative to their original values

A tractable genotype-phenotype map for the self-assembly of protein quaternary structure

The mapping between biological genotypes and phenotypes is central to the study of biological evolution. Here we introduce a rich, intuitive, and biologically realistic genotype-phenotype (GP) map, that serves as a model of self-assembling biological structures, such as protein complexes, and remains computationally and analytically tractable. Our GP map arises naturally from the self-assembly of polyomino structures on a 2D lattice and exhibits a number of properties: $\textit{redundancy}$ (genotypes vastly outnumber phenotypes), $\textit{phenotype bias}$ (genotypic redundancy varies greatly between phenotypes), $\textit{genotype component disconnectivity}$ (phenotypes consist of disconnected mutational networks) and $\textit{shape space covering}$ (most phenotypes can be reached in a small number of mutations). We also show that the mutational robustness of phenotypes scales very roughly logarithmically with phenotype redundancy and is positively correlated with phenotypic evolvability. Although our GP map describes the assembly of disconnected objects, it shares many properties with other popular GP maps for connected units, such as models for RNA secondary structure or the HP lattice model for protein tertiary structure. The remarkable fact that these important properties similarly emerge from such different models suggests the possibility that universal features underlie a much wider class of biologically realistic GP maps.Comment: 12 pages, 6 figure

Hardware Architecture Review of Swarm Robotics System: Self-Reconfigurability, Self-Reassembly, and Self-Replication

Swarm robotics is one of the most fascinating and new research areas of recent decades, and one of the grand challenges of robotics is the design of swarm robots that are self-sufficient. This can be crucial for robots exposed to environments that are unstructured or not easily accessible for a human operator, such as the inside of a blood vessel, a collapsed building, the deep sea, or the surface of another planet. In this paper, we present a comprehensive study on hardware architecture and several other important aspects of modular swarm robots, such as self-reconfigurability, self-replication, and self-assembly. The key factors in designing and building a group of swarm robots are cost and miniaturization with robustness, flexibility, and scalability. In robotics intelligence, self-assembly and self-reconfigurability are among the most important characteristics as they can add additional capabilities and functionality to swarm robots. Simulation and model design for swarm robotics is highly complex and expensive, especially when attempting to model the behavior of large swarm robot groups.http://dx.doi.org/10.5402/2013/84960