Exploring the origins of topological frustration: Design of a minimally frustrated model of fragment B of protein A

Topological frustration in an energetically unfrustrated off-lattice model of the helical protein fragment B of protein A from Staphylococcus aureus was investigated. This Gō-type model exhibited thermodynamic and kinetic signatures of a well-designed two-state folder with concurrent collapse and folding transitions and single exponential kinetics at the transition temperature. Topological frustration is determined in the absence of energetic frustration by the distribution of Fersht φ values. Topologically unfrustrated systems present a unimodal distribution sharply peaked at intermediate φ, whereas highly frustrated systems display a bimodal distribution peaked at low and high φ values. The distribution of φ values in protein A was determined both thermodynamically and kinetically. Both methods yielded a unimodal distribution centered at φ = 0.3 with tails extending to low and high φ values, indicating the presence of a small amount of topological frustration. The contacts with high φ values were located in the turn regions between helices I and II and II and III, intimating that these hairpins are in large part required in the transition state. Our results are in good agreement with all-atom simulations of protein A, as well as lattice simulations of a three- letter code 27-mer (which can be compared with a 60-residue helical protein). The relatively broad unimodal distribution of φ values obtained from the all-atom simulations and that from the minimalist model for the same native fold suggest that the structure of the transition state ensemble is determined mostly by the protein topology and not energetic frustration.

Exploring the folding free energy surface of a three-helix bundle protein

The multidimensional free energy surface for a small fast folding helical protein is explored based on first-principle calculations. The model represents the 46-residue segment from fragment B of staphylococcal protein A. The relationship between collapse and tertiary structure formation, and the order of collapse and secondary structure formation, are investigated. We find that the initial collapse process gives rise to a transition state with about 30% of the native tertiary structure and 50–70% of the native helix content. We also observe two distinct distributions of native helix in this collapsed state (Rg ≈ 12 Å), one with about 20% of the native helical hydrogen bonds, the other with near 70%. The former corresponds to a local minimum. The barrier from this metastable state to the native state is about 2 kBT. In the latter case, folding is essentially a downhill process involving topological assembly. In addition, the order of formation of secondary structure among the three helices is examined. We observe cooperative formation of the secondary structure in helix I and helix II. Secondary structure in helix III starts to form following the formation of certain secondary structure in both helix I and helix II. Comparisons of our results with those from theory and experiment are made.

Magnesium-dependent folding of self-splicing RNA: Exploring the link between cooperativity, thermodynamics, and kinetics

Folding of the Tetrahymena self-splicing RNA into its active conformation involves a set of discrete intermediate states. The Mg2+-dependent equilibrium transition from the intermediates to the native structure is more cooperative than the formation of the intermediates from the unfolded states. We show that the degree of cooperativity is linked to the free energy of each transition and that the rate of the slow transition from the intermediates to the native state decreases exponentially with increasing Mg2+ concentration. Monovalent salts, which stabilize the folded RNA nonspecifically, induce states that fold in less than 30 s after Mg2+ is added to the RNA. A simple model is proposed that predicts the folding kinetics from the Mg2+-dependent change in the relative stabilities of the intermediate and native states.

Measuring the thickness of the human cerebral cortex from magnetic resonance images

Accurate and automated methods for measuring the thickness of human cerebral cortex could provide powerful tools for diagnosing and studying a variety of neurodegenerative and psychiatric disorders. Manual methods for estimating cortical thickness from neuroimaging data are labor intensive, requiring several days of effort by a trained anatomist. Furthermore, the highly folded nature of the cortex is problematic for manual techniques, frequently resulting in measurement errors in regions in which the cortical surface is not perpendicular to any of the cardinal axes. As a consequence, it has been impractical to obtain accurate thickness estimates for the entire cortex in individual subjects, or group statistics for patient or control populations. Here, we present an automated method for accurately measuring the thickness of the cerebral cortex across the entire brain and for generating cross-subject statistics in a coordinate system based on cortical anatomy. The intersubject standard deviation of the thickness measures is shown to be less than 0.5 mm, implying the ability to detect focal atrophy in small populations or even individual subjects. The reliability and accuracy of this new method are assessed by within-subject test–retest studies, as well as by comparison of cross-subject regional thickness measures with published values.

Exploring the DNA-binding specificities of zinc fingers with DNA microarrays

A key step in the regulation of networks that control gene expression is the sequence-specific binding of transcription factors to their DNA recognition sites. A more complete understanding of these DNA–protein interactions will permit a more comprehensive and quantitative mapping of the regulatory pathways within cells, as well as a deeper understanding of the potential functions of individual genes regulated by newly identified DNA-binding sites. Here we describe a DNA microarray-based method to characterize sequence-specific DNA recognition by zinc-finger proteins. A phage display library, prepared by randomizing critical amino acid residues in the second of three fingers of the mouse Zif268 domain, provided a rich source of zinc-finger proteins with variant DNA-binding specificities. Microarrays containing all possible 3-bp binding sites for the variable zinc fingers permitted the quantitation of the binding site preferences of the entire library, pools of zinc fingers corresponding to different rounds of selection from this library, as well as individual Zif268 variants that were isolated from the library by using specific DNA sequences. The results demonstrate the feasibility of using DNA microarrays for genome-wide identification of putative transcription factor-binding sites.

Exploring the active site of chorismate mutase by combinatorial mutagenesis and selection: the importance of electrostatic catalysis.

Chorismate mutase (EC 5.4.99.5) catalyzes the intramolecular rearrangement of chorismate to prephenate. Arg-90 in the active site of the enzyme from Bacillus subtilis is in close proximity to the substrate's ether oxygen and may contribute to efficient catalysis by stabilizing the presumed dipolar transition state that would result upon scission of the C--O bond. To test this idea, we have developed a novel complementation system for chorismate mutase activity in Escherichia coli by reengineering parts of the aromatic amino acid biosynthetic pathway. The codon for Arg-90 was randomized, alone and in combination with that for Cys-88, and active clones were selected. The results show that a positively charged residue either at position 88 (Lys) or 90 (Arg or Lys) is essential. Our data provide strong support for the hypothesis that the positive charge is required for stabilization of the transition state of the enzymatic chorismate rearrangement. The new selection system, in conjunction with combinatorial mutagenesis, renders the mechanism of the natural enzyme(s) accessible to further exploration and opens avenues for the improvement of first generation catalytic antibodies with chorismate mutase activity.