Protein folding free energy landscape along the committor - the optimal folding coordinate

Recent advances in simulation and experiment have led to dramatic increases in the quantity and complexity of produced data, which makes the development of automated analysis tools very important. A powerful approach to analyze dynamics contained in such data sets is to describe/approximate it by diffusion on a free energy landscape - free energy as a function of reaction coordinates (RC). For the description to be quantitatively accurate, RCs should be chosen in an optimal way. Recent theoretical results show that such an optimal RC exists; however, determining it for practical systems is a very difficult unsolved problem. Here we describe a solution to this problem. We describe an adaptive nonparametric approach to accurately determine the optimal RC (the committor) for an equilibrium trajectory of a realistic system. In contrast to alternative approaches, which require a functional form with many parameters to approximate an RC and thus extensive expertise with the system, the suggested approach is nonparametric and can approximate any RC with high accuracy without system specific information. To avoid overfitting for a realistically sampled system, the approach performs RC optimization in an adaptive manner by focusing optimization on less optimized spatiotemporal regions of the RC. The power of the approach is illustrated on a long equilibrium atomistic folding simulation of HP35 protein. We have determined the optimal folding RC - the committor, which was confirmed by passing a stringent committor validation test. It allowed us to determine a first quantitatively accurate protein folding free energy landscape. We have confirmed the recent theoretical results that diffusion on such a free energy profile can be used to compute exactly the equilibrium flux, the mean first passage times, and the mean transition path times between any two points on the profile. We have shown that the mean squared displacement along the optimal RC grows linear with time as for simple diffusion. The free energy profile allowed us to obtain a direct rigorous estimate of the pre-exponential factor for the folding dynamics

An improved model of the Edgeworth-Kuiper debris disk

(Abridged) We access the expected EKB dust disk properties by modeling. We treat the debiased population of the known transneptunian objects (TNOs) as parent bodies and generate the dust with our collisional code. The resulting dust distributions are modified to take into account the influence of gravitational scattering and resonance trapping by planets on migrating dust grains as well as the effect of sublimation. A difficulty is that the amount and distribution of dust are largely determined by sub-kilometer-sized bodies. These are directly unobservable, and their properties cannot be accessed by collisional modeling, because objects larger than 10...60m in the present-day EKB are not in a collisional equilibrium. To place additional constraints, we use in-situ measurements of the New Horizons spacecraft within 20AU. We show that the TNO population has to have a break in the size distribution at s<70km. However, even this still leaves us with several models that all correctly reproduce a nearly constant dust impact rates in the region of giant planet orbits and do not violate the constraints from the non-detection of the EKB dust thermal emission by the COBE spacecraft. The modeled EKB dust disks, which conform to the observational constraints, can either be transport-dominated or intermediate between the transport-dominated and collision-dominated regime. The in-plane optical depth of such disks is tau(r>10AU)~10^-6 and their fractional luminosity is f_d~10^-7. Planets and sublimation are found to have little effect on dust impact fluxes and dust thermal emission. The spectral energy distribution of an EKB analog, as would be seen from 10pc distance, peaks at wavelengths of 40...50\mum at F~0.5mJy, which is less than 1% of the photospheric flux at those wavelengths. Therefore, exact EKB analogs cannot be detected with present-day instruments such as Herschel/PACS.Comment: 10 pages, 8 figures, accepted for publication in Astronomy and Astophysic

Determination of the observation conditions of celestial bodies with the aid of the DISPO system

The interactive system for determining the observation conditions of celestial bodies is described. A system of programs was created containing a part of the DISPO Display Interative System of Orbit Planning. The system was used for calculating the observatiion characteristics of Halley's comet during its approach to Earth in 1985-86