The protein folding problem must ultimately be solved on all length scales from the atomic up through a hierarchy of complicated structures. By analyzing the stability of the folding process using physics and mathematics, this paper shows that featur
es without length scales, i.e. topological features, are potentially of central importance. Topology is a natural mathematical tool for the study of shape and we avail ourselves of that tool to examine the relationship between the amino acid sequence and the shapes of protein molecules. We apply what we learn to conjectures about their biological evolution.
We present new evidence for a problem with cooling rates predicted by substellar evolutionary models that implies model-derived masses in the literature for brown dwarfs and directly imaged planets may be too high. Based on our dynamical mass for Gl
417BC (L4.5+L6) and a gyrochronology system age from its young, solar-type host star, commonly used models predict luminosities 0.2$-$0.4 dex lower than we observe. This corroborates a similar luminosity$-$age discrepancy identified in our previous work on the L4+L4 binary HD 130948BC, which coincidentally has nearly identical component masses ($approx$50$-$55 $M_{rm Jup}$) and age ($approx$800 Myr) as Gl 417BC. Such a luminosity offset would cause systematic errors of 15%$-$25% in model-derived masses at this age. After comparing different models, including cloudless models that should not be appropriate for mid-L dwarfs like Gl 417BC and HD 130948BC but actually match their luminosities better, we speculate the observed over-luminosity could be caused by opacity holes (i.e., patchy clouds) in these objects. Moreover, from hybrid substellar evolutionary models that account for cloud disappearance we infer the corresponding phase of over-luminosity may extend from a few hundred Myr up to a few Gyr and cause masses to to be over-estimated by up to 25%, even well after clouds disappear from view entirely. Thus, the range of of ages and spectral types affected by this potential systematic shift in luminosity evolution would encompass most known directly imaged gas-giants and field brown dwarfs.
Processes that proceed reliably from a variety of initial conditions to a unique final form, regardless of moderately changing conditions, are of obvious importance in biophysics. Protein folding is a case in point. We show that the action principle
can be applied directly to study the stability of biological processes. The action principle in classical physics starts with the first variation of the action and leads immediately to the equations of motion. The second variation of the action leads in a natural way to powerful theorems that provide quantitative treatment of stability and focusing and also explain how some very complex processes can behave as though some seemingly important forces drop out. We first apply these ideas to the non-equilibrium states involved in two-state folding. We treat torsional waves and use the action principle to talk about critical points in the dynamics. For some proteins the theory resembles TST. We reach several quantitative and qualitative conclusions. Besides giving an explanation of why TST often works in folding, we find that the apparent smoothness of the energy funnel is a natural consequence of the putative critical points in the dynamics. These ideas also explain why biological proteins fold to unique states and random polymers do not. The insensitivity to perturbations which follows from the presence of critical points explains how folding to a unique shape occurs in the presence of dilute denaturing agents in spite of the fact that those agents disrupt the folded structure of the native state. This paper contributes to the theoretical armamentarium by directing attention to the logical progression from first physical principles to the stability theorems related to catastrophe theory as applied to folding. This can potentially have the same success in biophysics as it has enjoyed in optics.
We have measured high-precision parallaxes for a large sample of candidate young (~10-100 Myr) and intermediate-age (~100-600 Myr) ultracool dwarfs, with spectral types ranging from M8 to T2.5. These objects are compelling benchmarks for substellar e
volution and ultracool atmospheres at lower surface gravities (i.e., masses) than most of the field population. We find that the absolute magnitudes of our young sample can be systematically offset from ordinary (older) field dwarfs, with the young late-M objects being brighter and the young/dusty mid-L (L3-L6.5) objects being fainter, especially at J band. Thus, we conclude the underluminosity of the young planetary-mass companions HR 8799b and 2MASS J1207-39b compared to field dwarfs is also manifested in young free-floating brown dwarfs, though the effect is not as extreme. At the same time, some young objects over the full spectral type range of our sample are similar to field objects, and thus a simple correspondence between youth and magnitude offset relative to the field population appears to be lacking. Comparing the kinematics of our sample to nearby stellar associations and moving groups, we identify several new moving group members, including the first free-floating L dwarf in the AB Dor moving group, 2MASS J0355+11. Altogether, the effects of surface gravity (age) and dust content on the magnitudes and colors of substellar objects appear to be degenerate.
We have tested the effect of spatial gradients in stellar mass-to-light ratio (Y) on measurements of black hole masses (MBH) derived from stellar orbit superposition models. Such models construct a static gravitational potential for a galaxy and its
central black hole, but typically assume spatially uniform Y. We have modeled three giant elliptical galaxies with gradients alpha = d(log Y)/d(log r) from -0.2 to +0.1. Color and line strength gradients suggest mildly negative alpha in these galaxies. Introducing a negative (positive) gradient in Y increases (decreases) the enclosed stellar mass near the center of the galaxy and leads to systematically smaller (larger) MBH measurements. For models with alpha = -0.2, the best-fit values of MBH are 28%, 27%, and 17% lower than the constant-Y case, in NGC 3842, NGC 6086, and NGC 7768, respectively. For alpha = +0.1, MBH are 14%, 22%, and 17% higher than the constant-Y case for the three respective galaxies. For NGC 3842 and NGC 6086, this bias is comparable to the statistical errors from individual modeling trials. At larger radii, negative (positive) gradients in Y cause the total stellar mass to decrease (increase) and the dark matter fraction within one effective radius to increase (decrease).
We measure the average temperature decrement on the cosmic microwave background (CMB) produced by voids selected in the SDSS DR7 spectroscopic redshift galaxy catalog, spanning redshifts $0<z<0.44$. We find an imprint of amplitude between 2.6 and 2.9
$mu K$ as viewed through a compensated top-hat filter scaled to the radius of each void; we assess the statistical significance of the imprint at ~2$sigma$. We make crucial use of $N$-body simulations to calibrate our analysis. As expected, we find that large voids produce cold spots on the CMB through the Integrated Sachs-Wolfe (ISW) effect. However, we also find that small voids in the halo density field produce hot spots, because they reside in contracting, larger-scale overdense regions. This is an important effect to consider when stacking CMB imprints from voids of different radius. We have found that the same filter radius that gives the largest ISW signal in simulations also yields close to the largest detected signal in the observations. However, although it is low in significance, our measured signal is much higher-amplitude than expected from ISW in the concordance $Lambda$CDM universe. The discrepancy is also at the ~2$sigma$ level. We have demonstrated that our result is robust against the varying of thresholds over a wide range.
We present positions, kinematics, and the planetary nebula luminosity function (PNLF) for 35 planetary nebulae (PNe) in the nearest starburst galaxy IC10 extending out to 3kpc from the galaxys centre. We take advantage of the deep imaging and spectro
scopic capabilities provided by the spectrograph FOCAS on the 8.2m Subaru telescope. The PN velocities were measured through the slitless-spectroscopy technique, which allows us to explore the kinematics of IC10 with high precision. Using these velocities, we conclude that there is a kinematic connection between the HI envelope located around IC10 and the galaxys PN population. By assuming that the PNe in the central regions and in the outskirts have similar ages, our results put strong observational constraints on the past tidal interactions in the Local Group. This is so because by dating the PN central stars, we, therefore, infer the epoch of a major episode of star formation likely linked to the first encounter of the HI extended envelope with the galaxy. Our deep [OIII] images also allow us to use the PNLF to estimate a distance modulus of 24.1+/-0.25, which is in agreement with recent results in the literature based on other techniques.
The frequency and properties of multiple star systems offer powerful tests of star formation models. Multiplicity surveys over the past decade have shown that binary properties vary strongly with mass, but the functional forms and the interplay betwe
en frequency and semimajor axis remain largely unconstrained. We present the results of a large-scale survey of multiplicity at the bottom of the IMF in several nearby young associations, encompassing 78 very low mass members observed with Keck laser guide star adaptive optics. Our survey confirms the overall trend observed in the field for lower-mass binary systems to be less frequent and more compact, including a null detection for any substellar binary systems with separations wider than ~7 AU. Combined with a Bayesian re-analysis of existing surveys, our results demonstrate that the binary frequency and binary separations decline smoothly between masses of 0.5 Msun and 0.02 Msun, though we can not distinguish the functional form of this decline due to a degeneracy between the total binary frequency and the mean binary separation. We also show that the mass ratio distribution becomes progressively more concentrated at q~1 for declining masses, though a small number of systems appear to have unusually wide separations and low mass ratios for their mass. Finally, we compare our results to synthetic binary populations generated by smoothed particle hydrodynamic simulations, noting the similarities and discussing possible explanations for the differences.
We present the first results from our high-precision infrared (IR) astrometry program at the Canada-France-Hawaii Telescope. We measure parallaxes for 83 ultracool dwarfs (spectral types M6--T9) in 49 systems, with a median uncertainty of 1.1 mas (2.
3%) and as good as 0.7 mas (0.8%). We provide the first parallaxes for 48 objects in 29 systems, and for another 27 objects in 17 systems, we significantly improve upon published results, with a median (best) improvement of 1.7x (5x). Three systems show astrometric perturbations indicative of orbital motion; two are known binaries (2MASSJ0518-2828AB and 2MASSJ1404-3159AB) and one is spectrally peculiar (SDSSJ0805+4812). In addition, we present here a large set of Keck adaptive optics imaging that more than triples the number of binaries with L6--T5 components that have both multi-band photometry and distances. Our data enable an unprecedented look at the photometric properties of brown dwarfs as they cool through the L/T transition. Going from approxL8 to approxT4.5, flux in the Y and J bands increases by approx0.7 mag and approx0.5 mag, respectively (the Y- and J-band bumps), while flux in the H, K, and L bands declines monotonically. This wavelength dependence is consistent with cloud clearing over a narrow range of temperature, since condensate opacity is expected to dominate at 1.0--1.3 micron. Interestingly, despite more than doubling the near-IR census of L/T transition objects, we find a conspicuous paucity of objects on the color--magnitude diagram just blueward of the late-L/early-T sequence. This L/T gap occurs at MKO(J-H) = 0.1--0.3 mag, MKO(J-K) = 0.0--0.4 mag, and implies that the last phases of cloud evolution occur rapidly. Finally, we provide a comprehensive update to the absolute magnitudes of ultracool dwarfs as a function of spectral type using a combined sample of 314 objects.
We adopt the point of view that analysis of the stability of the protein folding process is central to understanding the underlying physics of folding. Stability of the folding process means that many perturbations do not disrupt the progress from th
e random coil to the native state. In this paper we explore the stability of folding using established methods from physics and mathematics. Our result is a preliminary theory of the physics of folding. We suggest some tests of these ideas using folding simulations. We begin by supposing that folding events are related in some way to mechanical waves on the molecule. We adopt an analytical approach to the physics which was pioneered by M.V. Berry, (in another context), based upon mathematics developed mainly by R. Thom and V.I. Arnold. We find that the stability of the folding process can be understood in terms of structures known as caustics, which occur in many kinds of wave phenomena. The picture that emerges is that natural selection has given us a set of protein molecules which have mechanical waves that propagate according to several mathematically specific restrictions. Successful simulations of folding can be used to test and constrain these wave motions. With some additional assumptions the theory explains or is consistent with a number of experimental facts about folding. We emphasize that this wave-based approach is fundamentally different from energy-based approaches.
