37 research outputs found
Transcendental obstructions to weak approximation on general K3 surfaces
We construct an explicit K3 surface over the field of rational numbers that
has geometric Picard rank one, and for which there is a transcendental
Brauer-Manin obstruction to weak approximation. To do so, we exploit the
relationship between polarized K3 surfaces endowed with particular kinds of
Brauer classes and cubic fourfolds.Comment: 24 pages, 3 figures, Magma scripts included at the end of the source
file
Mobile linkers on DNA-coated colloids: valency without patches.
Colloids coated with single-stranded DNA (ssDNA) can bind selectively to other colloids coated with complementary ssDNA. The fact that DNA-coated colloids (DNACCs) can bind to specific partners opens the prospect of making colloidal "molecules." However, in order to design DNACC-based molecules, we must be able to control the valency of the colloids, i.e., the number of partners to which a given DNACC can bind. One obvious, but not very simple approach is to decorate the colloidal surface with patches of single-stranded DNA that selectively bind those on other colloids. Here we propose a design principle that exploits many-body effects to control the valency of otherwise isotropic colloids. Using a combination of theory and simulation, we show that we can tune the valency of colloids coated with mobile ssDNA, simply by tuning the nonspecific repulsion between the particles. Our simulations show that the resulting effective interactions lead to low-valency colloids self-assembling in peculiar open structures, very different from those observed in DNACCs with immobile DNA linkers.This is the author's accepted manuscript. The final version is published by APS in Physical Review Letters (http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.128303)
A general theory of DNA-mediated and other valence-limited interactions
We present a general theory for predicting the interaction potentials between
DNA-coated colloids, and more broadly, any particles that interact via
valence-limited ligand-receptor binding. Our theory correctly incorporates the
configurational and combinatorial entropic factors that play a key role in
valence-limited interactions. By rigorously enforcing self-consistency, it
achieves near-quantitative accuracy with respect to detailed Monte Carlo
calculations. With suitable approximations and in particular geometries, our
theory reduces to previous successful treatments, which are now united in a
common and extensible framework. We expect our tools to be useful to other
researchers investigating ligand-mediated interactions. A complete and
well-documented Python implementation is freely available at
http://github.com/patvarilly/DNACC .Comment: 18 pages, 10 figure
Consistent treatment of hydrophobicity in protein lattice models accounts for cold denaturation
The hydrophobic effect stabilizes the native structure of proteins by
minimizing the unfavourable interactions between hydrophobic residues and water
through the formation of a hydrophobic core. Here we include the entropic and
enthalpic contributions of the hydrophobic effect explicitly in an implicit
solvent model. This allows us to capture two important effects: a length-scale
dependence and a temperature dependence for the solvation of a hydrophobic
particle. This consistent treatment of the hydrophobic effect explains cold
denaturation and heat capacity measurements of solvated proteins.Comment: Added and corrected references for design procedure in main text (p.
2) and in Supplemental Information (p. 8
Designing stimulus-sensitive colloidal walkers.
Colloidal particles with DNA "legs" that can bind reversibly to receptors on a surface can be made to 'walk' if there is a gradient in receptor concentration. We use a combination of theory and Monte Carlo simulations to explore how controllable parameters, e.g. coating density and binding strength, affect the dynamics of such colloids. We find that competition between thermodynamic and kinetic trends imply that there is an optimal value for both the binding strength and the number of "legs" for which transport is the fastest. Using available thermodynamic data on DNA binding, we indicate how directionally reversible, temperature-controlled transport of colloidal walkers can be achieved. In particular, the present results should make it possible to design a chromatographic technique that can be used to separate colloids with different DNA functionalizations