Noise and Robustness in Phyllotaxis

A striking feature of vascular plants is the regular arrangement of lateral organs on the stem, known as phyllotaxis. The most common phyllotactic patterns can be described using spirals, numbers from the Fibonacci sequence and the golden angle. This rich mathematical structure, along with the experimental reproduction of phyllotactic spirals in physical systems, has led to a view of phyllotaxis focusing on regularity. However all organisms are affected by natural stochastic variability, raising questions about the effect of this variability on phyllotaxis and the achievement of such regular patterns. Here we address these questions theoretically using a dynamical system of interacting sources of inhibitory field. Previous work has shown that phyllotaxis can emerge deterministically from the self-organization of such sources and that inhibition is primarily mediated by the depletion of the plant hormone auxin through polarized transport. We incorporated stochasticity in the model and found three main classes of defects in spiral phyllotaxis – the reversal of the handedness of spirals, the concomitant initiation of organs and the occurrence of distichous angles – and we investigated whether a secondary inhibitory field filters out defects. Our results are consistent with available experimental data and yield a prediction of the main source of stochasticity during organogenesis. Our model can be related to cellular parameters and thus provides a framework for the analysis of phyllotactic mutants at both cellular and tissular levels. We propose that secondary fields associated with organogenesis, such as other biochemical signals or mechanical forces, are important for the robustness of phyllotaxis. More generally, our work sheds light on how a target pattern can be achieved within a noisy background

Effects of DNA supercoiling on chromatin architecture

Disruptions in chromatin structure are necessary for the regulation of eukaryotic genomes, from remodelling of nucleosomes at the base pair level through to large-scale chromatin domains that are hundreds of kilobases in size. RNA polymerase is a powerful motor which, prevented from turning with the tight helical pitch of the DNA, generates over-wound DNA ahead of itself and under-wound DNA behind. Mounting evidence supports a central role for transcription-dependent DNA supercoiling in disrupting chromatin structure at all scales. This supercoiling changes the properties of the DNA helix in a manner that substantially alters the binding specificity of DNA binding proteins and complexes, including nucleosomes, polymerases, topoisomerases and transcription factors. For example, transient over-wound DNA destabilises nucleosome core particles ahead of a transcribing polymerase, whereas under-wound DNA facilitates pre-initiation complex formation, transcription factor binding and nucleosome core particle association behind the transcribing polymerase. Importantly, DNA supercoiling can also dissipate through DNA, even in a chromatinised context, to influence both local elements and large chromatin domains. We propose a model in which changes in unconstrained DNA supercoiling influences higher levels of chromatin organisation through the additive effects of DNA supercoiling on both DNA-protein and DNA-nucleosome interactions. This model links small-scale changes in DNA and chromatin to the higher-order fibre and large-scale chromatin structures, providing a mechanism relating gene regulation to chromatin architecture in vivo

On Argumentation Logic and Propositional Logic

This paper studies the relationship between Argumentation Logic (AL), a recently defined logic based on the study of argumentation in AI, and classical Propositional Logic (PL). In particular, it shows that AL and PL are logically equivalent in that they have the same entailment relation from any given classically consistent theory. This equivalence follows from a correspondence between the non-acceptability of (arguments for) sentences in AL and Natural Deduction (ND) proofs of the complement of these sentences. The proof of this equivalence uses a restricted form of ND proofs, where hypotheses in the application of the Reductio of Absurdum inference rule are required to be “relevant” to the absurdity derived in the rule. The paper also discusses how the argumentative re-interpretation of PL could help control the application of ex-falso quodlibet in the presence of inconsistencies