Super-helical filaments at surfaces: dynamics and elastic responses

Kinetic and structural roles for the surface in guiding SAS-6 self-assembly to direct centriole architecture

Discovering mechanisms governing organelle assembly is a fundamental pursuit in biology. The centriole is an evolutionarily conserved organelle with a signature 9-fold symmetrical chiral arrangement of microtubules imparted onto the cilium it templates. The first structure in nascent centrioles is a cartwheel, which comprises stacked 9-fold symmetrical SAS-6 ring polymers emerging orthogonal to a surface surrounding each resident centriole. The mechanisms through which SAS-6 polymerization ensures centriole organelle architecture remain elusive. We deploy photothermally-actuated off-resonance tapping high-speed atomic force microscopy to decipher surface SAS-6 self-assembly mechanisms. We show that the surface shifts the reaction equilibrium by ~10⁴ compared to solution. Moreover, coarse-grained molecular dynamics and atomic force microscopy reveal that the surface converts the inherent helical propensity of SAS-6 polymers into 9-fold rings with residual asymmetry, which may guide ring stacking and impart chiral features to centrioles and cilia. Overall, our work reveals fundamental design principles governing centriole assembly.

The centriole exhibits an evolutionarily conserved 9-fold radial symmetry that stems from a cartwheel containing vertically stacked ring polymers that harbor 9 homodimers of the protein SAS-6. Here the authors show how dual properties inherent to surface-guided SAS-6 self-assembly possess spatial information that dictates correct scaffolding of centriole architecture.

Free energy measurements by the generalized fluctuation theorems: Theory and numerical study of a model filament

We measure the free energy of a model filament, which undergoes deformations and structural transitions, as a function of its extension, in silico. We perform Brownian Dynamics (BD) simulations of pulling experiments at various speeds, following a protocol close to experimental ones. The results from the fluctuation theorems are compared with the estimates from Monte Carlo (MC) simulation, where the rugged free energy landscape is produced by the density of states method. The fluctuation theorems (FT) give accurate estimates of the free energy up to moderate pulling speeds. At higher pulling speeds, the work distributions do not efficiently sample the domain of small work and FT slightly overestimates free energy. In order to comprehend the differences, we analyze the work distributions from the BD simulations in the framework of trajectory thermodynamics and propose the generalized fluctuation theorems that take into account the information (relative entropy) evaluated in the expanded phase space. The measured work - free energy relation is consistent with the results obtained from the generalized fluctuation theorems. We discuss operational methods to improve the estimates at high pulling speed.

Adsorption of a Helical Filament Subject to Thermal Fluctuations

We consider semiflexible chains governed by preferred curvature and twist and their flexural and twist moduli. These filaments possess a helical rather than straight three-dimensional (3D) ground state and we call them helical filaments (H-filament). Depending on the moduli, the helical shape may be smeared by thermal fluctuations. Secondary superhelical structures are expected to form on top of the specific local structure of biofilaments, as is documented for vimentin. We study confinement and adsorption of helical filaments utilizing both a combination of numerical simulations and analytical theory. We investigate overall chain shapes, transverse chain fluctuations, loop and tail distributions, and energy distributions along the chain together with the mean square average height of the monomers 〈 z 2 〉 . The number fraction of adsorbed monomers serves as an order parameter for adsorption. Signatures of adsorbed helical polymers are the occurrence of 3D helical loops/tails and spiral or wavy quasi-flat shapes. None of these arise for the Worm-Like-Chain, whose straight ground state can be embedded in a plane.