Thermodynamic parameters for the helix-coil transition of oligopeptides: molecular dynamics simulation with the peptide growth method.

The helix-coil transition equilibrium of polypeptides in aqueous solution was studied by molecular dynamics simulation. The peptide growth simulation method was introduced to generate dynamic models of polypeptide chains in a statistical (random) coil or an alpha-helical conformation. The key element of this method is to build up a polypeptide chain during the course of a molecular transformation simulation, successively adding whole amino acid residues to the chain in a predefined conformation state (e.g., alpha-helical or statistical coil). Thus, oligopeptides of the same length and composition, but having different conformations, can be incrementally grown from a common precursor, and their relative conformational free energies can be calculated as the difference between the free energies for growing the individual peptides. This affords a straightforward calculation of the Zimm-Bragg sigma and s parameters for helix initiation and helix growth. The calculated sigma and s parameters for the polyalanine alpha-helix are in reasonable agreement with the experimental measurements. The peptide growth simulation method is an effective way to study quantitatively the thermodynamics of local protein folding.

Optimal prediction of underresolved dynamics

A method is presented for computing the average solution of problems that are too complicated for adequate resolution, but where information about the statistics of the solution is available. The method involves computing average derivatives by interpolation based on linear regression, and an updating of a measure constrained by the available crude information. Examples are given.

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.

Estimating sequestered parasite population dynamics in cerebral malaria

Clinical investigation of malaria is hampered by the lack of a method for estimating the number of parasites that are sequestered in the tissues, for it is these parasites that are thought to be crucial to the pathogenesis of life-threatening complications such as cerebral malaria. We present a method of estimating this hidden population by using clinical observations of peripheral parasitemia combined with an age-structured mathematical model of the parasite erythrocyte cycle. Applying the model to data from 217 Gambian children undergoing treatment for cerebral malaria we conclude that although artemether clears parasitemia more rapidly than quinine, the clearance of sequestered parasites is similar for the two drugs. The estimated sequestered mass was found to be a more direct predictor of fatal outcome than clinically observed parasitemia. This method allows a sequential analysis of sequestered parasite population dynamics in children suffering from cerebral malaria, and the results offer a possible explanation for why artemether provides less advantage than might have been expected over quinine in reducing mortality despite its rapid effect on circulating parasites.

The use of site-directed fluorophore labeling and donor–donor energy migration to investigate solution structure and dynamics in proteins

The use of molecular genetics for introducing fluorescent molecules enables the use of donor–donor energy migration to determine intramolecular distances in a variety of proteins. This approach can be applied to examine the overall molecular dimensions of proteins and to investigate structural changes upon interactions with specific target molecules. In this report, the donor–donor energy migration method is demonstrated by experiments with the latent form of plasminogen activator inhibitor type 1. Based on the known x-ray structure of plasminogen activator inhibitor type 1, three positions forming the corners of a triangle were chosen. Double Cys substitution mutants (V106C-H185C, H185C-M266C, and M266C-V106C) and corresponding single substitution mutants (V106C, H185C, and M266C) were created and labeled with a sulfhydryl specific derivative of BODIPY (=the D molecule). The side lengths of this triangle were obtained from analyses of the experimental data. The analyses account for the local anisotropic order and rotational motions of the D molecules, as well as for the influence of a partial DD-labeling. The distances, as determined from x-ray diffraction, between the Cα-atoms of the positions V106C–H185C, H185C–M266C, and M266C–V106C were 60.9, 30.8, and 55.1 Å, respectively. These are in good agreement with the distances of 54 ± 4, 38 ± 3, and 55 ± 3 Å, as determined between the BODIPY groups attached via linkers to the same residues. Although the positions of the D-molecules and the Cα-atoms physically cannot coincide, there is a reasonable agreement between the methods.

Stability and dynamics in a hyperthermophilic protein with melting temperature close to 200°C

The rubredoxin protein from the hyperthermophilic archaebacterium Pyrococcus furiosus was examined by a hydrogen exchange method. Even though the protein does not exhibit reversible thermal unfolding, one can determine its stability parameters—free energy, enthalpy, entropy, and melting temperature—and also the distribution of stability throughout the protein, by using hydrogen exchange to measure the reversible cycling of the protein between native and unfolded states that occurs even under native conditions.

Dynamics of fluorescence fluctuations in green fluorescent protein observed by fluorescence correlation spectroscopy

We have investigated the pH dependence of the dynamics of conformational fluctuations of green fluorescent protein mutants EGFP (F64L/S65T) and GFP-S65T in small ensembles of molecules in solution by using fluorescence correlation spectroscopy (FCS). FCS utilizes time-resolved measurements of fluctuations in the molecular fluorescence emission for determination of the intrinsic dynamics and thermodynamics of all processes that affect the fluorescence. Fluorescence excitation of a bulk solution of EGFP decreases to zero at low pH (pKa = 5.8) paralleled by a decrease of the absorption at 488 nm and an increase at 400 nm. Protonation of the hydroxyl group of Tyr-66, which is part of the chromophore, induces these changes. When FCS is used the fluctuations in the protonation state of the chromophore are time resolved. The autocorrelation function of fluorescence emission shows contributions from two chemical relaxation processes as well as diffusional concentration fluctuations. The time constant of the fast, pH-dependent chemical process decreases with pH from 300 μs at pH 7 to 45 μs at pH 5, while the time-average fraction of molecules in a nonfluorescent state increases to 80% in the same range. A second, pH-independent, process with a time constant of 340 μs and an associated fraction of 13% nonfluorescent molecules is observed between pH 8 and 11, possibly representing an internal proton transfer process and associated conformational rearrangements. The FCS data provide direct measures of the dynamics and the equilibrium properties of the protonation processes. Thus FCS is a convenient, intrinsically calibrated method for pH measurements in subfemtoliter volumes with nanomolar concentrations of EGFP.

Dynamics of Gene Expression Revealed by Comparison of Serial Analysis of Gene Expression Transcript Profiles from Yeast Grown on Two Different Carbon SourcesD⃞

We describe a genome-wide characterization of mRNA transcript levels in yeast grown on the fatty acid oleate, determined using Serial Analysis of Gene Expression (SAGE). Comparison of this SAGE library with that reported for glucose grown cells revealed the dramatic adaptive response of yeast to a change in carbon source. A major fraction (>20%) of the 15,000 mRNA molecules in a yeast cell comprised differentially expressed transcripts, which were derived from only 2% of the total number of ∼6300 yeast genes. Most of the mRNAs that were differentially expressed code for enzymes or for other proteins participating in metabolism (e.g., metabolite transporters). In oleate-grown cells, this was exemplified by the huge increase of mRNAs encoding the peroxisomal β-oxidation enzymes required for degradation of fatty acids. The data provide evidence for the existence of redox shuttles across organellar membranes that involve peroxisomal, cytoplasmic, and mitochondrial enzymes. We also analyzed the mRNA profile of a mutant strain with deletions of the PIP2 and OAF1 genes, encoding transcription factors required for induction of genes encoding peroxisomal proteins. Induction of genes under the immediate control of these factors was abolished; other genes were up-regulated, indicating an adaptive response to the changed metabolism imposed by the genetic impairment. We describe a statistical method for analysis of data obtained by SAGE.

Ultrafast diffraction and structural dynamics: The nature of complex molecules far from equilibrium

Studies of molecular structures at or near their equilibrium configurations have long provided information on their geometry in terms of bond distances and angles. Far-from-equilibrium structures are relatively unknown—especially for complex systems—and generally, neither their dynamics nor their average geometries can be extrapolated from equilibrium values. For such nonequilibrium structures, vibrational amplitudes and bond distances play a central role in phenomena such as energy redistribution and chemical reactivity. Ultrafast electron diffraction, which was developed to study transient molecular structures, provides a direct method for probing the nature of complex molecules far from equilibrium. Here we present our ultrafast electron diffraction observations of transient structures for two cyclic hydrocarbons. At high internal energies of ≈4 eV, these molecules display markedly different behavior. For 1,3,5-cycloheptatriene, excitation results in the formation of hot ground-state structures with bond distances similar to those of the initial structure, but with nearly three times the average vibrational amplitude. Energy is redistributed within 5 ps, but with a negative temperature characterizing the nonequilibrium population. In contrast, the ring-opening reaction of 1,3-cyclohexadiene is shown to result in hot structures with a C—C bond distance of over 1.7 Å, which is 0.2 Å away from any expected equilibrium value. Even up to 400 ps, energy remains trapped in large-amplitude motions comprised of torsion and asymmetric stretching. These studies promise a new direction for studying structural dynamics in nonequilibrium complex systems.