Singular value decomposition for genome-wide expression data processing and modeling

We describe the use of singular value decomposition in transforming genome-wide expression data from genes × arrays space to reduced diagonalized “eigengenes” × “eigenarrays” space, where the eigengenes (or eigenarrays) are unique orthonormal superpositions of the genes (or arrays). Normalizing the data by filtering out the eigengenes (and eigenarrays) that are inferred to represent noise or experimental artifacts enables meaningful comparison of the expression of different genes across different arrays in different experiments. Sorting the data according to the eigengenes and eigenarrays gives a global picture of the dynamics of gene expression, in which individual genes and arrays appear to be classified into groups of similar regulation and function, or similar cellular state and biological phenotype, respectively. After normalization and sorting, the significant eigengenes and eigenarrays can be associated with observed genome-wide effects of regulators, or with measured samples, in which these regulators are overactive or underactive, respectively.

Characterization of residual structure in the thermally denatured state of barnase by simulation and experiment: Description of the folding pathway

Residual structure in the denatured state of a protein may contain clues about the early events in folding. We have simulated by molecular dynamics the denatured state of barnase, which has been studied by NMR spectroscopy. An ensemble of 104 structures was generated after 2 ns of unfolding and following for a further 2 ns. The ensemble was heterogeneous, but there was nonrandom, residual structure with persistent interactions. Helical structure in the C-terminal portion of helix α1 (residues 13–17) and in helix α2 as well as a turn and nonnative hydrophobic clustering between β3 and β4 were observed, consistent with NMR data. In addition, there were tertiary contacts between residues in α1 and the C-terminal portion of the β-sheet. The simulated structures allow the rudimentary NMR data to be fleshed out. The consistency between simulation and experiment inspires confidence in the methods. A description of the folding pathway of barnase from the denatured to the native state can be constructed by combining the simulation with experimental data from φ value analysis and NMR.

A combined kinetic and modeling study of the catalytic center subsites of human angiogenin.

Kinetic analysis and molecular modeling have been used to map the ribonucleolytic center of angiogenin (Ang). Pyrimidine nucleotides were found to interact very weakly with Ang, consistent with the inaccessible B1 pyrimidine binding site revealed by x-ray crystallography. Ang also lacks an effective phosphate binding site on the 5' side of B1. Although the B2 site that preferentially binds purines on the 3' side of B1 is also weak, its associated phosphate subsites make substantial contributions: both 3',5'-ADP and 5'-ADP have Ki values 6-fold lower than for 5'-AMP, and adding a 3'-phosphate to the substrate CpA increases Kcat/Km by 9-fold. Thus Ang has a functional P2 site on the 3' side of B2 and a site for a second phosphate on the 5' side of B2. Modeling of an Ang-d(ApTpApA) complex suggested that Arg-5 forms part of the P2 site and that a 2'-phosphate might bind more tightly than a 3'-phosphate. Both predictions were confirmed kinetically. The subsite map obtained by this combined approach indicated that 5'-diphosphoadenosine 2'-phosphate might be a more potent inhibitor than any of the nucleotides tested thus far. Indeed, its Ki value of 150 microM is 50-fold lower than that for the best nucleotide previously reported and 400-fold lower than the Km for the best dinucleotide substrate. This compound may serve as a suitable starting point for the eventual design of tight-binding inhibitors of Ang as antiangiogenic agents for human therapy.

Brownian dynamics simulations of protein folding: Access to milliseconds time scale and beyond

Protein folding occurs on a time scale ranging from milliseconds to minutes for a majority of proteins. Computer simulation of protein folding, from a random configuration to the native structure, is nontrivial owing to the large disparity between the simulation and folding time scales. As an effort to overcome this limitation, simple models with idealized protein subdomains, e.g., the diffusion–collision model of Karplus and Weaver, have gained some popularity. We present here new results for the folding of a four-helix bundle within the framework of the diffusion–collision model. Even with such simplifying assumptions, a direct application of standard Brownian dynamics methods would consume 10,000 processor-years on current supercomputers. We circumvent this difficulty by invoking a special Brownian dynamics simulation. The method features the calculation of the mean passage time of an event from the flux overpopulation method and the sampling of events that lead to productive collisions even if their probability is extremely small (because of large free-energy barriers that separate them from the higher probability events). Using these developments, we demonstrate that a coarse-grained model of the four-helix bundle can be simulated in several days on current supercomputers. Furthermore, such simulations yield folding times that are in the range of time scales observed in experiments.

Case study of the effects of atmospheric aerosols and regional haze on agriculture: An opportunity to enhance crop yields in China through emission controls?

The effect of atmospheric aerosols and regional haze from air pollution on the yields of rice and winter wheat grown in China is assessed. The assessment is based on estimates of aerosol optical depths over China, the effect of these optical depths on the solar irradiance reaching the earth’s surface, and the response of rice and winter wheat grown in Nanjing to the change in solar irradiance. Two sets of aerosol optical depths are presented: one based on a coupled, regional climate/air quality model simulation and the other inferred from solar radiation measurements made over a 12-year period at meteorological stations in China. The model-estimated optical depths are significantly smaller than those derived from observations, perhaps because of errors in one or both sets of optical depths or because the data from the meteorological stations has been affected by local pollution. Radiative transfer calculations using the smaller, model-estimated aerosol optical depths indicate that the so-called “direct effect” of regional haze results in an ≈5–30% reduction in the solar irradiance reaching some of China’s most productive agricultural regions. Crop-response model simulations suggest an ≈1:1 relationship between a percentage increase (decrease) in total surface solar irradiance and a percentage increase (decrease) in the yields of rice and wheat. Collectively, these calculations suggest that regional haze in China is currently depressing optimal yields of ≈70% of the crops grown in China by at least 5–30%. Reducing the severity of regional haze in China through air pollution control could potentially result in a significant increase in crop yields and help the nation meet its growing food demands in the coming decades.

Vibrational population relaxation of carbon monoxide in the heme pocket of photolyzed carbonmonoxy myoglobin: Comparison of time-resolved mid-IR absorbance experiments and molecular dynamics simulations

The vibrational energy relaxation of carbon monoxide in the heme pocket of sperm whale myoglobin was studied by using molecular dynamics simulation and normal mode analysis methods. Molecular dynamics trajectories of solvated myoglobin were run at 300 K for both the δ- and ɛ-tautomers of the distal His-64. Vibrational population relaxation times of 335 ± 115 ps for the δ-tautomer and 640 ± 185 ps for the ɛ-tautomer were estimated by using the Landau–Teller model. Normal mode analysis was used to identify those protein residues that act as the primary “doorway” modes in the vibrational relaxation of the oscillator. Although the CO relaxation rates in both the ɛ- and δ-tautomers are similar in magnitude, the simulations predict that the vibrational relaxation of the CO is faster in the δ-tautomer with the distal His playing an important role in the energy relaxation mechanism. Time-resolved mid-IR absorbance measurements were performed on photolyzed carbonmonoxy hemoglobin (Hb13CO). From these measurements, a T1 time of 600 ± 150 ps was determined. The simulation and experimental estimates are compared and discussed.

Dynamic weighting in Monte Carlo and optimization

Dynamic importance weighting is proposed as a Monte Carlo method that has the capability to sample relevant parts of the configuration space even in the presence of many steep energy minima. The method relies on an additional dynamic variable (the importance weight) to help the system overcome steep barriers. A non-Metropolis theory is developed for the construction of such weighted samplers. Algorithms based on this method are designed for simulation and global optimization tasks arising from multimodal sampling, neural network training, and the traveling salesman problem. Numerical tests on these problems confirm the effectiveness of the method.

Gamma rhythms and beta rhythms have different synchronization properties

Experimental and modeling efforts suggest that rhythms in the CA1 region of the hippocampus that are in the beta range (12–29 Hz) have a different dynamical structure than that of gamma (30–70 Hz). We use a simplified model to show that the different rhythms employ different dynamical mechanisms to synchronize, based on different ionic currents. The beta frequency is able to synchronize over long conduction delays (corresponding to signals traveling a significant distance in the brain) that apparently cannot be tolerated by gamma rhythms. The synchronization properties are consistent with data suggesting that gamma rhythms are used for relatively local computations whereas beta rhythms are used for higher level interactions involving more distant structures.

Architecture and mechanism of the light-harvesting apparatus of purple bacteria

Photosynthetic organisms fuel their metabolism with light energy and have developed for this purpose an efficient apparatus for harvesting sunlight. The atomic structure of the apparatus, as it evolved in purple bacteria, has been constructed through a combination of x-ray crystallography, electron microscopy, and modeling. The detailed structure and overall architecture reveals a hierarchical aggregate of pigments that utilizes, as shown through femtosecond spectroscopy and quantum physics, elegant and efficient mechanisms for primary light absorption and transfer of electronic excitation toward the photosynthetic reaction center.