Stretching single-domain proteins: Phase diagram and kinetics of force-induced unfolding

Single-molecule force spectroscopy reveals unfolding of domains in titin on stretching. We provide a theoretical framework for these experiments by computing the phase diagrams for force-induced unfolding of single-domain proteins using lattice models. The results show that two-state folders (at zero force) unravel cooperatively, whereas stretching of non-two-state folders occurs through intermediates. The stretching rates of individual molecules show great variations reflecting the heterogeneity of force-induced unfolding pathways. The approach to the stretched state occurs in a stepwise “quantized” manner. Unfolding dynamics and forces required to stretch proteins depend sensitively on topology. The unfolding rates increase exponentially with force f till an optimum value, which is determined by the barrier to unfolding when f = 0. A mapping of these results to proteins shows qualitative agreement with force-induced unfolding of Ig-like domains in titin. We show that single-molecule force spectroscopy can be used to map the folding free energy landscape of proteins in the absence of denaturants.

Explanation by the double-metal-ion mechanism of catalysis for the differential metal ion effects on the cleavage rates of 5′-oxy and 5′-thio substrates by a hammerhead ribozyme

In a previous examination using natural all-RNA substrates that contained either a 5′-oxy or 5′-thio leaving group at the cleavage site, we demonstrated that (i) the attack by the 2′-oxygen at C17 on the phosphorus atom is the rate-limiting step only for the substrate that contains a 5′-thio group (R11S) and (ii) the departure of the 5′ leaving group is the rate-limiting step for the natural all-RNA substrate (R11O) in both nonenzymatic and hammerhead ribozyme-catalyzed reactions; the energy diagrams for these reactions were provided in our previous publication. In this report we found that the rate of cleavage of R11O by a hammerhead ribozyme was enhanced 14-fold when Mg2+ ions were replaced by Mn2+ ions, whereas the rate of cleavage of R11S was enhanced only 2.2-fold when Mg2+ ions were replaced by Mn2+ ions. This result appears to be exactly the opposite of that predicted from the direct coordination of the metal ion with the leaving 5′-oxygen, because a switch in metal ion specificity was not observed with the 5′-thio substrate. However, our quantitative analyses based on the previously provided energy diagram indicate that this result is in accord with the double-metal-ion mechanism of catalysis.

Molecular Interaction Map of the Mammalian Cell Cycle Control and DNA Repair Systems

Eventually to understand the integrated function of the cell cycle regulatory network, we must organize the known interactions in the form of a diagram, map, and/or database. A diagram convention was designed capable of unambiguous representation of networks containing multiprotein complexes, protein modifications, and enzymes that are substrates of other enzymes. To facilitate linkage to a database, each molecular species is symbolically represented only once in each diagram. Molecular species can be located on the map by means of indexed grid coordinates. Each interaction is referenced to an annotation list where pertinent information and references can be found. Parts of the network are grouped into functional subsystems. The map shows how multiprotein complexes could assemble and function at gene promoter sites and at sites of DNA damage. It also portrays the richness of connections between the p53-Mdm2 subsystem and other parts of the network.

Multiple DNA and protein sequence alignment based on segment-to-segment comparison.

In this paper, a new way to think about, and to construct, pairwise as well as multiple alignments of DNA and protein sequences is proposed. Rather than forcing alignments to either align single residues or to introduce gaps by defining an alignment as a path running right from the source up to the sink in the associated dot-matrix diagram, we propose to consider alignments as consistent equivalence relations defined on the set of all positions occurring in all sequences under consideration. We also propose constructing alignments from whole segments exhibiting highly significant overall similarity rather than by aligning individual residues. Consequently, we present an alignment algorithm that (i) is based on segment-to-segment comparison instead of the commonly used residue-to-residue comparison and which (ii) avoids the well-known difficulties concerning the choice of appropriate gap penalties: gaps are not treated explicity, but remain as those parts of the sequences that do not belong to any of the aligned segments. Finally, we discuss the application of our algorithm to two test examples and compare it with commonly used alignment methods. As a first example, we aligned a set of 11 DNA sequences coding for functional helix-loop-helix proteins. Though the sequences show only low overall similarity, our program correctly aligned all of the 11 functional sites, which was a unique result among the methods tested. As a by-product, the reading frames of the sequences were identified. Next, we aligned a set of ribonuclease H proteins and compared our results with alignments produced by other programs as reported by McClure et al. [McClure, M. A., Vasi, T. K. & Fitch, W. M. (1994) Mol. Biol. Evol. 11, 571-592]. Our program was one of the best scoring programs. However, in contrast to other methods, our protein alignments are independent of user-defined parameters.

Bond orientational order, molecular motion, and free energy of high-density DNA mesophases.

By equilibrating condensed DNA arrays against reservoirs of known osmotic stress and examining them with several structural probes, it has been possible to achieve a detailed thermodynamic and structural characterization of the change between two distinct regions on the liquid-crystalline phase diagram: (i) a higher density hexagonally packed region with long-range bond orientational order in the plane perpendicular to the average molecular direction and (ii) a lower density cholesteric region with fluid-like positional order. X-ray scattering on highly ordered DNA arrays at high density and with the helical axis oriented parallel to the incoming beam showed a sixfold azimuthal modulation of the first-order diffraction peak that reflects the macroscopic bond-orientational order. Transition to the less-dense cholesteric phase through osmotically controlled swelling shows the loss of this bond orientational order, which had been expected from the change in optical birefringence patterns and which is consistent with a rapid onset of molecular positional disorder. This change in order was previously inferred from intermolecular force measurements and is now confirmed by 31P NMR. Controlled reversible swelling and compaction under osmotic stress, spanning a range of densities between approximately 120 mg/ml to approximately 600 mg/ml, allow measurement of the free-energy changes throughout each phase and at the phase transition, essential information for theories of liquid-crystalline states.