Symmetry and designability for lattice protein models

Native protein folds often have a high degree of symmetry. We study the relationship between the symmetries of native proteins, and their designabilities -- how many different sequences encode a given native structure. Using a two-dimensional lattice protein model based on hydrophobicity, we find that those native structures that are encoded by the largest number of different sequences have high symmetry. However only certain symmetries are enhanced, e.g. x/y-mirror symmetry and $180^o$ rotation, while others are suppressed. If it takes a large number of mutations to destabilize the native state of a protein, then, by definition, the state is highly designable. Hence, our findings imply that insensitivity to mutation implies high symmetry. It appears that the relationship between designability and symmetry results because protein substructures are also designable. Native protein folds may therefore be symmetric because they are composed of repeated designable substructures.Comment: 13 pages, 10 figure

Structure Space of Model Proteins --A Principle Component Analysis

We study the space of all compact structures on a two-dimensional square lattice of size $N=6\times6$. Each structure is mapped onto a vector in $N$-dimensions according to a hydrophobic model. Previous work has shown that the designabilities of structures are closely related to the distribution of the structure vectors in the $N$-dimensional space, with highly designable structures predominantly found in low density regions. We use principal component analysis to probe and characterize the distribution of structure vectors, and find a non-uniform density with a single peak. Interestingly, the principal axes of this peak are almost aligned with Fourier eigenvectors, and the corresponding Fourier eigenvalues go to zero continuously at the wave-number for alternating patterns ($q=\pi$). These observations provide a stepping stone for an analytic description of the distribution of structural points, and open the possibility of estimating designabilities of realistic structures by simply Fourier transforming the hydrophobicities of the corresponding sequences.Comment: 14 pages, 12 figures, Conclusion has been modifie

An Analytical Approach to the Protein Designability Problem

We present an analytical method for determining the designability of protein structures. We apply our method to the case of two-dimensional lattice structures, and give a systematic solution for the spectrum of any structure. Using this spectrum, the designability of a structure can be estimated. We outline a heirarchy of structures, from most to least designable, and show that this heirarchy depends on the potential that is used.Comment: 16 pages 4 figure

Role of Secondary Motifs in Fast Folding Polymers: A Dynamical Variational Principle

A fascinating and open question challenging biochemistry, physics and even geometry is the presence of highly regular motifs such as alpha-helices in the folded state of biopolymers and proteins. Stimulating explanations ranging from chemical propensity to simple geometrical reasoning have been invoked to rationalize the existence of such secondary structures. We formulate a dynamical variational principle for selection in conformation space based on the requirement that the backbone of the native state of biologically viable polymers be rapidly accessible from the denatured state. The variational principle is shown to result in the emergence of helical order in compact structures.Comment: 4 pages, RevTex, 4 eps figure

Nuclei beyond the drip line

In a Thomas-Fermi model, calculations are presented for nuclei beyond the nuclear drip line at zero temperature. These nuclei are in equilibrium by the presence of an external gas, as may be envisaged in the astrophysical scenario. We find that there is a limiting asymmetry beyond which these nuclei can no longer be made stable.Comment: Physical Review C (in press), 1 ReVteX file for text, 4 PS-files for figure

Geometric and Statistical Properties of the Mean-Field HP Model, the LS Model and Real Protein Sequences

Lattice models, for their coarse-grained nature, are best suited for the study of the ``designability problem'', the phenomenon in which most of the about 16,000 proteins of known structure have their native conformations concentrated in a relatively small number of about 500 topological classes of conformations. Here it is shown that on a lattice the most highly designable simulated protein structures are those that have the largest number of surface-core switchbacks. A combination of physical, mathematical and biological reasons that causes the phenomenon is given. By comparing the most foldable model peptides with protein sequences in the Protein Data Bank, it is shown that whereas different models may yield similar designabilities, predicted foldable peptides will simulate natural proteins only when the model incorporates the correct physics and biology, in this case if the main folding force arises from the differing hydrophobicity of the residues, but does not originate, say, from the steric hindrance effect caused by the differing sizes of the residues.Comment: 12 pages, 10 figure

Isospin-rich nuclei in neutron star matter

Stability of nuclei beyond the drip lines in the presence of an enveloping gas of nucleons and electrons, as prevailing in the inner crust of a neutron star, is studied in the temperature-dependent Thomas-Fermi framework. A limiting asymmetry in the isospin space beyond which nuclei cannot exist emerges from the calculations. The ambient conditions like temperature, baryon density and neutrino concentration under which these exotic nuclear systems can be formed are studied in some detail.Comment: Submitted to Phy. Rev. C: Revtex version of manuscript 22 pages and 10 PS-files for figure

Soliton back-action evading measurement using spectral filtering

We report on a back-action evading (BAE) measurement of the photon number of fiber optical solitons operating in the quantum regime. We employ a novel detection scheme based on spectral filtering of colliding optical solitons. The measurements of the BAE criteria demonstrate significant quantum state preparation and transfer of the input signal to the signal and probe outputs exiting the apparatus, displaying the quantum-nondemolition (QND) behavior of the experiment.Comment: 5 pages, 5 figure

Isospin-rich nuclei in neutron star matter

Stability of nuclei beyond the drip lines in the presence of an enveloping gas of nucleons and electrons, as prevailing in the inner crust of a neutron star, is studied in the temperature-dependent Thomas-Fermi framework. A limiting asymmetry in the isospin space beyond which nuclei cannot exist emerges from the calculations. The ambient conditions like temperature, baryon density and neutrino concentration under which these exotic nuclear systems can be formed are studied in some detail.Comment: Submitted to Phy. Rev. C: Revtex version of manuscript 22 pages and 10 PS-files for figure

A robust, scanning quantum system for nanoscale sensing and imaging

Controllable atomic-scale quantum systems hold great potential as sensitive tools for nanoscale imaging and metrology. Possible applications range from nanoscale electric and magnetic field sensing to single photon microscopy, quantum information processing, and bioimaging. At the heart of such schemes is the ability to scan and accurately position a robust sensor within a few nanometers of a sample of interest, while preserving the sensor's quantum coherence and readout fidelity. These combined requirements remain a challenge for all existing approaches that rely on direct grafting of individual solid state quantum systems or single molecules onto scanning-probe tips. Here, we demonstrate the fabrication and room temperature operation of a robust and isolated atomic-scale quantum sensor for scanning probe microscopy. Specifically, we employ a high-purity, single-crystalline diamond nanopillar probe containing a single Nitrogen-Vacancy (NV) color center. We illustrate the versatility and performance of our scanning NV sensor by conducting quantitative nanoscale magnetic field imaging and near-field single-photon fluorescence quenching microscopy. In both cases, we obtain imaging resolution in the range of 20 nm and sensitivity unprecedented in scanning quantum probe microscopy