Potentials of Mean Force for Protein Structure Prediction Vindicated, Formalized and Generalized

Understanding protein structure is of crucial importance in science, medicine and biotechnology. For about two decades, knowledge based potentials based on pairwise distances -- so-called "potentials of mean force" (PMFs) -- have been center stage in the prediction and design of protein structure and the simulation of protein folding. However, the validity, scope and limitations of these potentials are still vigorously debated and disputed, and the optimal choice of the reference state -- a necessary component of these potentials -- is an unsolved problem. PMFs are loosely justified by analogy to the reversible work theorem in statistical physics, or by a statistical argument based on a likelihood function. Both justifications are insightful but leave many questions unanswered. Here, we show for the first time that PMFs can be seen as approximations to quantities that do have a rigorous probabilistic justification: they naturally arise when probability distributions over different features of proteins need to be combined. We call these quantities reference ratio distributions deriving from the application of the reference ratio method. This new view is not only of theoretical relevance, but leads to many insights that are of direct practical use: the reference state is uniquely defined and does not require external physical insights; the approach can be generalized beyond pairwise distances to arbitrary features of protein structure; and it becomes clear for which purposes the use of these quantities is justified. We illustrate these insights with two applications, involving the radius of gyration and hydrogen bonding. In the latter case, we also show how the reference ratio method can be iteratively applied to sculpt an energy funnel. Our results considerably increase the understanding and scope of energy functions derived from known biomolecular structures

Lower objectively measured physical activity is linked with perceived risk of hypoglycemia in type 1 diabetes

Aims Compare physical activity (PA) levels in adults with and without type 1 diabetes and identify diabetes-specific barriers to PA. Methods Forty-four individuals with type 1 diabetes and 77 non-diabetic controls in the Coronary Artery Calcification in Type 1 Diabetes study wore an accelerometer for 2 weeks. Moderate-to-vigorous physical activity (MVPA) was compared by diabetes status using multiple linear regression. The Barriers to Physical Activity in Type 1 Diabetes questionnaire measured diabetes-specific barriers to PA, and the Clarke hypoglycemia awareness questionnaire measured hypoglycemia frequency. Results Individuals with type 1 diabetes engaged in less MVPA, fewer bouts of MVPA, and spent less time in MVPA bouts per week than individuals without diabetes (all p  0.05). The most common diabetes-specific barrier to PA was risk of hypoglycemia. Individuals with diabetes reporting barriers spent less time in MVPA bouts per week than those not reporting barriers (p = 0.047). Conclusions Individuals with type 1 diabetes engage in less MVPA than those without diabetes despite similar self-reported levels, with the main barrier being perceived risk of hypoglycemia. Adults with type 1 diabetes require guidance to meet current PA guidelines and reduce cardiovascular risk

The crust in the pamir: Insights from receiver functions

The Cenozoic convergence between India and Asia has created Earth's thickest crust in the Pamir‐Tibet Plateau by extreme crustal shortening. Here we study the crustal structure of the Pamir and western Tian Shan, the adjacent margins of the Tajik, Tarim, and Ferghana Basins, and the Hindu Kush, using data collected by temporary seismic experiments. We derive, compare, and combine independent observations from P and S receiver functions. The obtained Moho depth varies from ~40 km below the basins to a double‐normal thickness of 65–75 km underneath the Pamir and Hindu Kush. A Moho doublet—with the deeper interface down to a depth of ~90 km—coincides with the arc of intermediate‐depth seismicity underneath the Pamir, where Asian continental lower crust delaminates and rolls back. The crust beneath most of the Central and South Pamir has a low Vp/Vs ratio (<1.70), suggesting a dominantly felsic composition, probably a result of delamination/foundering of the mafic rocks of the lower crust. Beneath the Cenozoic gneiss domes of the Central and South Pamir, which represent extensional core complexes, the Vp/Vs ratios are moderate to high (~1.75), consistent with the previously observed, midcrustal low‐velocity zones, implying the presence of crustal partial melts. Even higher crustal average Vp/Vs ratios up to 1.90 are found in the sedimentary basins and along the Main Pamir Thrust. The ratios along the latter—the active thrust front of the Pamir—may reflect fluid accumulations within a strongly fractured fault system

Multi-Overlap Simulations for Transitions between Reference Configurations

We introduce a new procedure to construct weight factors, which flatten the probability density of the overlap with respect to some pre-defined reference configuration. This allows one to overcome free energy barriers in the overlap variable. Subsequently, we generalize the approach to deal with the overlaps with respect to two reference configurations so that transitions between them are induced. We illustrate our approach by simulations of the brainpeptide Met-enkephalin with the ECEPP/2 energy function using the global-energy-minimum and the second lowest-energy states as reference configurations. The free energy is obtained as functions of the dihedral and the root-mean-square distances from these two configurations. The latter allows one to identify the transition state and to estimate its associated free energy barrier.Comment: 12 pages, (RevTeX), 14 figures, Phys. Rev. E, submitte

Metropolis simulations of Met-Enkephalin with solvent-accessible area parameterizations

We investigate the solvent-accessible area method by means of Metropolis simulations of the brain peptide Met-Enkephalin at 300$K$. For the energy function ECEPP/2 nine atomic solvation parameter (ASP) sets are studied. The simulations are compared with one another, with simulations with a distance dependent electrostatic permittivity $\epsilon (r)$, and with vacuum simulations ($\epsilon =2$). Parallel tempering and the biased Metropolis techniques RM$_1$ are employed and their performance is evaluated. The measured observables include energy and dihedral probability densities (pds), integrated autocorrelation times, and acceptance rates. Two of the ASP sets turn out to be unsuitable for these simulations. For all other systems selected configurations are minimized in search of the global energy minima, which are found for the vacuum and the $\epsilon(r)$ system, but for none of the ASP models. Other observables show a remarkable dependence on the ASPs. In particular, we find three ASP sets for which the autocorrelations at 300$$K are considerably smaller than for vacuum simulations.Comment: 10 pages and 8 figure

Knowledge-based energy functions for computational studies of proteins

This chapter discusses theoretical framework and methods for developing knowledge-based potential functions essential for protein structure prediction, protein-protein interaction, and protein sequence design. We discuss in some details about the Miyazawa-Jernigan contact statistical potential, distance-dependent statistical potentials, as well as geometric statistical potentials. We also describe a geometric model for developing both linear and non-linear potential functions by optimization. Applications of knowledge-based potential functions in protein-decoy discrimination, in protein-protein interactions, and in protein design are then described. Several issues of knowledge-based potential functions are finally discussed.Comment: 57 pages, 6 figures. To be published in a book by Springe

Partition Function Zeros and Finite Size Scaling of Helix-Coil Transitions in a Polypeptide

We report on multicanonical simulations of the helix-coil transition of a polypeptide. The nature of this transition was studied by calculating partition function zeros and the finite-size scaling of various quantities. Estimates for critical exponents are presented.Comment: RevTex, 4 eps-files; to appear in Phys. Rev. Le

A combinatorial TIR1/AFB–Aux/IAA co-receptor system for differential sensing of auxin

The plant hormone auxin regulates virtually every aspect of plant growth and development. Auxin acts by binding the F-box protein transport inhibitor response 1 (TIR1) and promotes the degradation of the AUXIN/INDOLE-3-ACETIC ACID (Aux/IAA) transcriptional repressors. Here we show that efficient auxin binding requires assembly of an auxin co-receptor complex consisting of TIR1 and an Aux/IAA protein. Heterologous experiments in yeast and quantitative IAA binding assays using purified proteins showed that different combinations of TIR1 and Aux/IAA proteins form co-receptor complexes with a wide range of auxin-binding affinities. Auxin affinity seems to be largely determined by the Aux/IAA. As there are 6 TIR1/AUXIN SIGNALING F-BOX proteins (AFBs) and 29 Aux/IAA proteins in Arabidopsis thaliana, combinatorial interactions may result in many co-receptors with distinct auxin-sensing properties. We also demonstrate that the AFB5–Aux/IAA co-receptor selectively binds the auxinic herbicide picloram. This co-receptor system broadens the effective concentration range of the hormone and may contribute to the complexity of auxin response