Linking topography of its potential surface with the dynamics of folding of a protein model

The “3-color, 46-bead” model of a folding polypeptide is the vehicle for adapting to proteins a mode of analysis used heretofore for atomic clusters, to relate the topography of the potential surface to the dynamics that lead to formation of selected structures. The analysis is based on sequences of stationary points—successive minima, joined by saddles—that rise monotonically in energy from basin bottoms. Like structure-seeking clusters, the potential surface of the model studied here is staircase-like, rather than sawtooth-like, with highly collective motions required for passage from one minimum to the next. The surface has several deep basins whose minima correspond to very similar structures, but which are separated by high energy barriers.

On the role of the weather in the deaths of R. F. Scott and his companions

Robert Falcon Scott and his companions reached the South Pole in January of 1912, only to die on their return journey at a remote site on the Ross Ice Shelf, about 170 miles from their base camp on the coast. Numerous contributing causes for their deaths have been proposed, but it has been assumed that the cold temperatures they reported encountering on the Ross Ice Shelf, near 82–80°S during their northward trek toward safety, were not unusual. The weather in the region where they perished on their unassisted trek by foot from the Pole remained undocumented for more than half a century, but it has now been monitored by multiple automated weather stations for more than a decade. The data recorded by Scott and his men from late February to March 19, 1912, display daily temperature minima that were on average 10 to 20°F below those obtained in the same region and season since routine modern observations began in 1985. Only 1 year in the available 15 years of measurements from the location where Scott and his men perished displays persistent cold temperatures at this time of year close to those reported in 1912. These remarkably cold temperatures likely contributed substantially to the exhaustion and frostbite Scott and his companions endured, and their deaths were therefore due, at least in part, to the unusual weather conditions they endured during their cold march across the Ross Ice Shelf of Antarctica.

Cross-validated maximum likelihood enhances crystallographic simulated annealing refinement

Recently, the target function for crystallographic refinement has been improved through a maximum likelihood analysis, which makes proper allowance for the effects of data quality, model errors, and incompleteness. The maximum likelihood target reduces the significance of false local minima during the refinement process, but it does not completely eliminate them, necessitating the use of stochastic optimization methods such as simulated annealing for poor initial models. It is shown that the combination of maximum likelihood with cross-validation, which reduces overfitting, and simulated annealing by torsion angle molecular dynamics, which simplifies the conformational search problem, results in a major improvement of the radius of convergence of refinement and the accuracy of the refined structure. Torsion angle molecular dynamics and the maximum likelihood target function interact synergistically, the combination of both methods being significantly more powerful than each method individually. This is demonstrated in realistic test cases at two typical minimum Bragg spacings (dmin = 2.0 and 2.8 Å, respectively), illustrating the broad applicability of the combined method. In an application to the refinement of a new crystal structure, the combined method automatically corrected a mistraced loop in a poor initial model, moving the backbone by 4 Å.

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.

Folding simulations of a three-stranded antiparallel β-sheet peptide

Protein folding is a grand challenge of the postgenomic era. In this paper, 58 folding events sampled during 47 molecular dynamics trajectories for a total simulation time of more than 4 μs provide an atomic detail picture of the folding of a 20-residue synthetic peptide with a stable three-stranded antiparallel β-sheet fold. The simulations successfully reproduce the NMR solution conformation, irrespective of the starting structure. The sampling of the conformational space is sufficient to determine the free energy surface and localize the minima and transition states. The statistically predominant folding pathway involves the formation of contacts between strands 2 and 3, starting with the side chains close to the turn, followed by association of the N-terminal strand onto the preformed 2–3 β-hairpin. The folding mechanism presented here, formation of a β-hairpin followed by consolidation, is in agreement with a computational study of the free energy surface of another synthetic three-stranded antiparallel β-sheet by Bursulaya and Brooks [(1999) J. Am. Chem. Soc. 121, 9947–9951]. Hence, it might hold in general for antiparallel β-sheets with short turns.

Top-down free-energy minimization on protein potential energy landscapes

The hierarchical properties of potential energy landscapes have been used to gain insight into thermodynamic and kinetic properties of protein ensembles. It also may be possible to use them to direct computational searches for thermodynamically stable macroscopic states, i.e., computational protein folding. To this end, we have developed a top-down search procedure in which conformation space is recursively dissected according to the intrinsic hierarchical structure of a landscape's effective-energy barriers. This procedure generates an inverted tree similar to the disconnectivity graphs generated by local minima-clustering methods, but it fundamentally differs in the manner in which the portion of the tree that is to be computationally explored is selected. A key ingredient is a branch-selection algorithm that takes advantage of statistically predictive properties of the landscape to guide searches down the tree branches that are most likely to lead to the physically relevant macroscopic states. Using the computational folding of a β-hairpin-forming peptide as an example, we show that such predictive properties indeed exist and can be used for structure prediction by free-energy global minimization.

Lifetimes of intermediates in the β-sheet to α-helix transition of β-lactoglobulin by using a diffusional IR mixer

The extremely slow α-helix/β-sheet transition of proteins is a crucial step in amylogenic diseases and represents an internal rearrangement of local contacts in an already folded protein. These internal structural rearrangements within an already folded protein are a critical aspect of biological action and are a product of conformational flow along unknown metastable local minima of the energy landscape of the compact protein. We use a diffusional IR mixer with time-resolved Fourier transform IR spectroscopy capable of 400-μs time resolution to show that the trifluoroethanol driven β-sheet to α-helix transition of β-lactoglobulin proceeds via a compact β-sheet intermediate with a lifetime of 7 ms, small compared with the overall folding time of β-lactoglobulin.

Circadian-Regulated Transcription of the psbD Light-Responsive Promoter in Wheat Chloroplasts1

The level of mRNAs derived from the plastid-encoded psbD light-responsive promoter (LRP) is controlled by a circadian clock(s) in wheat (Triticum aestivum). The circadian oscillations in the psbD LRP mRNA level persisted for at least three cycles in continuous light and for one cycle in continuous dark, with maxima in subjective morning and minima in subjective early night. In vitro transcription in chloroplast extracts revealed that the circadian cycles in the psbD LRP mRNA level were dominantly attributed to the circadian-regulated transcription of the psbD LRP. The effects of various mutations introduced into the promoter region on the psbD LRP activity in vitro suggest the existence of two positive elements located between −54 and −36, which generally enhance the transcription activity, and an anomalous core promoter structure lacking the functional “−35” element, which plays a crucial role in the circadian fluctuation and light dependency of psbD LRP transcription activity.

Accumulation of a Clock-Regulated Transcript during Flower-Inductive Darkness in Pharbitis nil1

To clarify the molecular basis of the photoperiodic induction of flowering in the short-day plant Pharbitis nil cv Violet, we examined changes in the level of mRNA in cotyledons during the flower-inductive photoperiod using the technique of differential display by the polymerase chain reaction. A transcript that accumulated during the inductive dark period was identified and a cDNA corresponding to the transcript, designated PnC401 (P. nil C401), was isolated. RNA-blot hybridization verified that levels of PnC401 mRNA fluctuated with a circadian rhythm, with maxima between 12 and 16 h after the beginning of the dark period) and minima of approximately 0. This oscillation continued even during an extended dark period but was damped under continuous light. Accumulation of PnC401 mRNA was reduced by a brief exposure to red light at the 8th h of the dark period (night-break treatment) or by exposure to far-red light at the end of the light period (end-of-day far-red treatment). These results suggest that fluctuations in levels of PnC401 mRNA are regulated by phytochrome(s) and a circadian clock and that they are associated with photoperiodic events that include induction of flowering.

Temperature dependence of the isotope chemistry of the heavy elements.

The temperature coefficient of equilibrium isotope fractionation in the heavy elements is shown to be larger at high temperatures than that expected from the well-studied vibrational isotope effects. The difference in the isotopic behavior of the heavy elements as compared with the light elements is due to the large nuclear isotope field shifts in the heavy elements. The field shifts introduce new mechanisms for maxima, minima, crossovers, and large mass-independent isotope effects in the isotope chemistry of the heavy elements. The generalizations are illustrated by the temperature dependence of the isotopic fractionation in the redox reaction between U(VI) and U(IV) ions.

Betidamino acids: versatile and constrained scaffolds for drug discovery.

Betidamino acids (a contraction of "beta" position and "amide") are N'-monoacylated (optionally, N'-monoacylated and N-mono- or N,N'-dialkylated) aminoglycine derivatives in which each N'acyl/alkyl group may mimic naturally occurring amino acid side chains or introduce novel functionalities. Betidamino acids are most conveniently generated on solid supports used for the synthesis of peptides by selective acylation of one of the two amino functions of orthogonally protected aminoglycine(s) to generate the side chain either prior to or after the elongation of the main chain. We have used unresolved Nalpha-tert-butyloxycarbonyl-N'alpha-fluorenylmethoxycarbonyl++ + aminoglycine, and Nalpha-(Nalpha-methyl)-tert-butyloxycarbonyl-N'alpha-fluo renylmethoxycarbonyl aminoglycine as the templates for the introduction of betidamino acids in Acyline [Ac-D2Nal-D4Cpa-D3Pal-Ser-4Aph(Ac)-D4Aph(A c)-Leu-Ilys-Pro-DAla-NH2, where 2Nal is 2-naphthylalanine, 4Cpa is 4-chlorophenylalanine, 3Pal is 3-pyridylalanine, Aph is 4-aminophenylalanine, and Ilys is Nepsilon-isopropyllysine], a potent gonadotropin-releasing hormone antagonist, in order to test biocompatibility of these derivatives. Diasteremneric peptides could be separated in most cases by reverse-phase HPLC. Biological results indicated small differences in relative potencies (<5-fold) between the D and L nonalkylated betidamino acid-containing Acyline derivatives. Importantly, most betide diastereomers were equipotent with Acyline. In an attempt to correlate structure and observed potency, Ramachandran-type plots were calculated for a series of betidamino acids and their methylated homologs. According to these calculations, betidamino acids have access to a more limited and distinct number of conformational states (including those associated with alpha-helices, beta-sheets, or turn structures), with deeper minima than those observed for natural amino acids.

Unusual dynamics of extinction in a simple ecological model.

Studies on natural populations and harvesting biological resources have led to the view, commonly held, that (i) populations exhibiting chaotic oscillations run a high risk of extinction; and (ii) a decrease in emigration/exploitation may reduce the risk of extinction. Here we describe a simple ecological model with emigration/depletion that shows behavior in contrast to this. This model displays unusual dynamics of extinction and survival, where populations growing beyond a critical rate can persist within a band of high depletion rates, whereas extinction occurs for lower depletion rates. Though prior to extinction at lower depletion rates the population exhibits chaotic dynamics with large amplitudes of variation and very low minima, at higher depletion rates the population persists at chaos but with reduced variation and increased minima. For still higher values, within the band of persistence, the dynamics show period reversal leading to stability. These results illustrate that chaos does not necessarily lead to population extinction. In addition, the persistence of populations at high depletion rates has important implications in the considerations of strategies for the management of biological resources.

The old problems of glass and the glass transition, and the many new twists.

In this paper I review the ways in which the glassy state is obtained both in nature and in materials science and highlight a "new twist"--the recent recognition of polymorphism within the glassy state. The formation of glass by continuous cooling (viscous slowdown) is then examined, the strong/fragile liquids classification is reviewed, and a new twist-the possibility that the slowdown is a result of an avoided critical point-is noted. The three canonical characteristics of relaxing liquids are correlated through the fragility. As a further new twist, the conversion of strong liquids to fragile liquids by pressure-induced coordination number increases is demonstrated. It is then shown that, for comparable systems, it is possible to have the same conversion accomplished via a first-order transition within the liquid state during quenching. This occurs in the systems in which "polyamorphism" (polymorphism in the glassy state) is observed, and the whole phenomenology is accounted for by Poole's bond-modified van der Waals model. The sudden loss of some liquid degrees of freedom through such weak first-order transitions is then related to the polyamorphic transition between native and denatured hydrated proteins, since the latter are also glass-forming systems--water-plasticized, hydrogen bond-cross-linked chain polymers (and single molecule glass formers). The circle is closed with a final new twist by noting that a short time scale phenomenon much studied by protein physicists-namely, the onset of a sharp change in d/dT ( is the Debye-Waller factor)--is general for glass-forming liquids, including computer-simulated strong and fragile ionic liquids, and is closely correlated with the experimental glass transition temperature. The latter thus originates in strong anharmonicity in certain components of the vibrational density of states, which permits the system to access the multiple minima of its configuration space. The connection between the anharmonicity in these modes, vibrational localization, the Kauzmann temperature, and the fragility of the liquid is proposed as the key problem in glass science.