Sturdier DNA nanotubes via ligation

DNA nanotubes are crystalline self-assemblies of DNA tiles ~10 nm in diameter that readily grow tens of micrometers in length. Easy assembly, programmability, and stiffness make them interesting for many applications, but DNA nanotubes begin to melt at temperatures below 40 °C, break open when deposited on mica or scanned by AFM, and disintegrate in deionized water. These weaknesses can be traced to the presence of discontinuities in the phosphate backbone, called nicks. The nanotubes studied here have five nicks, one in the core of a tile and one at each corner. We report the successful ligation of all four corner nicks by T4 DNA ligase. Although ligation does not change the nanotubes’ stiffness, ligated nanotubes withstand temperatures over 70 °C, resist breaking during AFM, and are stable in pure water for over a month. Ligated DNA nanotubes are thus physically and chemically sturdy enough to withstand the manipulations necessary for many technological applications

Islands of conformational stability for Filopodia

Filopodia are long, thin protrusions formed when bundles of fibers grow outwardly from a cell surface while remaining closed in a membrane tube. We study the subtle issue of the mechanical stability of such filopodia and how this depends on the deformation of the membrane that arises when the fiber bundle adopts a helical configuration. We calculate the ground state conformation of such filopodia, taking into account the steric interaction between the membrane and the enclosed semiflexible fiber bundle. For typical filopodia we find that a minimum number of fibers is required for filopodium stability. Our calculation elucidates how experimentally observed filopodia can obviate the classical Euler buckling condition and remain stable up to several tens of . We briefly discuss how experimental observation of the results obtained in this work for the helical-like deformations of enclosing membrane tubes in filopodia could possibly be observed in the acrosomal reactions of the sea cucumber Thyone, and the horseshoe crab Limulus. Any realistic future theories for filopodium stability are likely to rely on an accurate treatment of such steric effects, as analysed in this work

Morphology of axisymmetric vesicles with encapsulated filaments and impurities

The shape deformation of a three-dimensional axisymmetric vesicle with encapsulated filaments or impurities is analyzed by integrating a dissipation dynamics. This method can incorporate systematically the constraint of a fixed surface area and/or a fixed volume. The filament encapsulated in a vesicle is assumed to take a form of a rod or a ring so as to imitate cytoskeletons. In both cases, results of the shape transition of the vesicle are summarized in phase diagrams in the phase space of the vesicular volume and a rod length or a ring radius. We also study the dynamics of a vesicle with impurities coupled to the membrane curvature. The phase separation and the associated shape deformation in the early stage of the dynamical evolution can well be explained by the linear stability analysis. Long runs of simulation demonstrate the nonlinear coarsening of the wavy deformation of the vesicle in the late stage.Comment: 9 pages, 9 figure

Collective and single cell behavior in epithelial contact inhibition

Control of cell proliferation is a fundamental aspect of tissue physiology central to morphogenesis, wound healing and cancer. Although many of the molecular genetic factors are now known, the system level regulation of growth is still poorly understood. A simple form of inhibition of cell proliferation is encountered in vitro in normally differentiating epithelial cell cultures and is known as "contact inhibition". The study presented here provides a quantitative characterization of contact inhibition dynamics on tissue-wide and single cell levels. Using long-term tracking of cultured MDCK cells we demonstrate that inhibition of cell division in a confluent monolayer follows inhibition of cell motility and sets in when mechanical constraint on local expansion causes divisions to reduce cell area. We quantify cell motility and cell cycle statistics in the low density confluent regime and their change across the transition to epithelial morphology which occurs with increasing cell density. We then study the dynamics of cell area distribution arising through reductive division, determine the average mitotic rate as a function of cell size and demonstrate that complete arrest of mitosis occurs when cell area falls below a critical value. We also present a simple computational model of growth mechanics which captures all aspects of the observed behavior. Our measurements and analysis show that contact inhibition is a consequence of mechanical interaction and constraint rather than interfacial contact alone, and define quantitative phenotypes that can guide future studies of molecular mechanisms underlying contact inhibition

Thermal Fluctuations of Elastic Filaments with Spontaneous Curvature and Torsion

We study the effects of thermal flucutations on thin elastic filaments with spontaneous curvature and torsion. We derive analytical expressions for the orientational correlation functions and for the persistence length of helices, and find that this length varies non-monotonically with the strength of thermal fluctuations. In the weak fluctuation regime, the persistence length of a spontaneously twisted helix has three resonance peaks as a function of the twist rate. In the limit of strong fluctuations, all memory of the helical shape is lost.Comment: 1 figur

Functional significance may underlie the taxonomic utility of single amino acid substitutions in conserved proteins

We hypothesized that some amino acid substitutions in conserved proteins that are strongly fixed by critical functional roles would show lineage-specific distributions. As an example of an archetypal conserved eukaryotic protein we considered the active site of ß-tubulin. Our analysis identified one amino acid substitution—ß-tubulin F224—which was highly lineage specific. Investigation of ß-tubulin for other phylogenetically restricted amino acids identified several with apparent specificity for well-defined phylogenetic groups. Intriguingly, none showed specificity for “supergroups” other than the unikonts. To understand why, we analysed the ß-tubulin Neighbor-Net and demonstrated a fundamental division between core ß-tubulins (plant-like) and divergent ß-tubulins (animal and fungal). F224 was almost completely restricted to the core ß-tubulins, while divergent ß-tubulins possessed Y224. Thus, our specific example offers insight into the restrictions associated with the co-evolution of ß-tubulin during the radiation of eukaryotes, underlining a fundamental dichotomy between F-type, core ß-tubulins and Y-type, divergent ß-tubulins. More broadly our study provides proof of principle for the taxonomic utility of critical amino acids in the active sites of conserved proteins

Modeling oscillatory Microtubule--Polymerization

Polymerization of microtubules is ubiquitous in biological cells and under certain conditions it becomes oscillatory in time. Here simple reaction models are analyzed that capture such oscillations as well as the length distribution of microtubules. We assume reaction conditions that are stationary over many oscillation periods, and it is a Hopf bifurcation that leads to a persistent oscillatory microtubule polymerization in these models. Analytical expressions are derived for the threshold of the bifurcation and the oscillation frequency in terms of reaction rates as well as typical trends of their parameter dependence are presented. Both, a catastrophe rate that depends on the density of {\it guanosine triphosphate} (GTP) liganded tubulin dimers and a delay reaction, such as the depolymerization of shrinking microtubules or the decay of oligomers, support oscillations. For a tubulin dimer concentration below the threshold oscillatory microtubule polymerization occurs transiently on the route to a stationary state, as shown by numerical solutions of the model equations. Close to threshold a so--called amplitude equation is derived and it is shown that the bifurcation to microtubule oscillations is supercritical.Comment: 21 pages and 12 figure

Fluctuating Filaments I: Statistical Mechanics of Helices

We examine the effects of thermal fluctuations on thin elastic filaments with non-circular cross-section and arbitrary spontaneous curvature and torsion. Analytical expressions for orientational correlation functions and for the persistence length of helices are derived, and it is found that this length varies non-monotonically with the strength of thermal fluctuations. In the weak fluctuation regime, the local helical structure is preserved and the statistical properties are dominated by long wavelength bending and torsion modes. As the amplitude of fluctuations is increased, the helix ``melts'' and all memory of intrinsic helical structure is lost. Spontaneous twist of the cross--section leads to resonant dependence of the persistence length on the twist rate.Comment: 5 figure

Vesicle-Like Biomechanics Governs Important Aspects of Nuclear Geometry in Fission Yeast

It has long been known that during the closed mitosis of many unicellular eukaryotes, including the fission yeast (Schizosaccharomyces pombe), the nuclear envelope remains intact while the nucleus undergoes a remarkable sequence of shape transformations driven by elongation of an intranuclear mitotic spindle whose ends are capped by spindle pole bodies embedded in the nuclear envelope. However, the mechanical basis of these normal cell cycle transformations, and abnormal nuclear shapes caused by intranuclear elongation of microtubules lacking spindle pole bodies, remain unknown. Although there are models describing the shapes of lipid vesicles deformed by elongation of microtubule bundles, there are no models describing normal or abnormal shape changes in the nucleus. We describe here a novel biophysical model of interphase nuclear geometry in fission yeast that accounts for critical aspects of the mechanics of the fission yeast nucleus, including the biophysical properties of lipid bilayers, forces exerted on the nuclear envelope by elongating microtubules, and access to a lipid reservoir, essential for the large increase in nuclear surface area during the cell cycle. We present experimental confirmation of the novel and non-trivial geometries predicted by our model, which has no free parameters. We also use the model to provide insight into the mechanical basis of previously described defects in nuclear division, including abnormal nuclear shapes and loss of nuclear envelope integrity. The model predicts that (i) despite differences in structure and composition, fission yeast nuclei and vesicles with fluid lipid bilayers have common mechanical properties; (ii) the S. pombe nucleus is not lined with any structure with shear resistance, comparable to the nuclear lamina of higher eukaryotes. We validate the model and its predictions by analyzing wild type cells in which ned1 gene overexpression causes elongation of an intranuclear microtubule bundle that deforms the nucleus of interphase cells