Mechanism of topology simplification by type II DNA topoisomerases

Type II DNA topoisomerases actively reduce the fractions of knotted and catenated circular DNA below thermodynamic equilibrium values. To explain this surprising finding, we designed a model in which topoisomerases introduce a sharp bend in DNA. Because the enzymes have a specific orientation relative to the bend, they act like Maxwell's demon, providing unidirectional strand passage. Quantitative analysis of the model by computer simulations proved that it can explain much of the experimental data. The required sharp DNA bend was demonstrated by a greatly increased cyclization of short DNA fragments from topoisomerase binding and by direct visualization with electron microscopy.

Additional evidence for an eight-transmembrane-domain topology for Caenorhabditis elegans and human presenilins

Presenilins have been implicated in the genesis of Alzheimer’s disease and in facilitating LIN-12/Notch activity during development. All presenilins have multiple hydrophobic regions that could theoretically span a membrane, and a description of the membrane topology is a crucial step toward deducing the mechanism of presenilin function. Previously, we proposed an eight-transmembrane-domain model for presenilin, based on studies of the Caenorhabditis elegans SEL-12 presenilin. Here, we describe experiments that support the view that two of the hydrophobic regions of SEL-12 function as the seventh and eighth transmembrane domains. Furthermore, we have shown that human presenilin 1 behaves like SEL-12 presenilin when analyzed by our methods. Our results provide additional experimental support for the eight-transmembrane-domain model of presenilin topology.

Transmembrane topology of a CLC chloride channel

CLC chloride channels form a large and conserved gene family unrelated to other channel proteins. Knowledge of the transmembrane topology of these channels is important for understanding the effects of mutations found in human myotonia and inherited hypercalciuric kidney stone diseases and for the interpretation of structure–function studies. We now systematically study the topology of human ClC-1, a prototype CLC channel that is defective in human myotonia. Using a combination of in vitro glycosylation scanning and protease protection assays, we show that both N and C termini face the cytoplasm and demonstrate the presence of 10 (or less likely 12) transmembrane spans. Difficult regions were additionally tested by inserting cysteines and probing the effect of cysteine-modifying reagents on ClC-1 currents. The results show that D3 crosses the membrane and D4 does not, and that L549 between D11 and D12 is accessible from the outside. Further, since the modification of cysteines introduced between D11 and D12 and at the extracellular end of D3 strongly affect ClC-1 currents, these regions are suggested to be important for ion permeation.

Equilibrium distributions of topological states in circular DNA: Interplay of supercoiling and knotting

Two variables define the topological state of closed double-stranded DNA: the knot type, K, and ΔLk, the linking number difference from relaxed DNA. The equilibrium distribution of probabilities of these states, P(ΔLk, K), is related to two conditional distributions: P(ΔLk|K), the distribution of ΔLk for a particular K, and P(K|ΔLk) and also to two simple distributions: P(ΔLk), the distribution of ΔLk irrespective of K, and P(K). We explored the relationships between these distributions. P(ΔLk, K), P(ΔLk), and P(K|ΔLk) were calculated from the simulated distributions of P(ΔLk|K) and of P(K). The calculated distributions agreed with previous experimental and theoretical results and greatly advanced on them. Our major focus was on P(K|ΔLk), the distribution of knot types for a particular value of ΔLk, which had not been evaluated previously. We found that unknotted circular DNA is not the most probable state beyond small values of ΔLk. Highly chiral knotted DNA has a lower free energy because it has less torsional deformation. Surprisingly, even at |ΔLk| > 12, only one or two knot types dominate the P(K|ΔLk) distribution despite the huge number of knots of comparable complexity. A large fraction of the knots found belong to the small family of torus knots. The relationship between supercoiling and knotting in vivo is discussed.

Structure and function in rhodopsin: Topology of the C-terminal polypeptide chain in relation to the cytoplasmic loops*

Cysteine mutagenesis and site-directed spin labeling in the C-terminal region of rhodopsin have been used to probe the local structure and proximity of that region to the cytoplasmic loops. Each of the native amino acids in the sequence T335–T340 was replaced with Cys, one at a time. The sulfhydryl groups of all mutants reacted rapidly with the sulfhydryl reagent 4,4′-dithiodipyridine, which indicated a high degree of solvent accessibility. Furthermore, to probe the proximity relationships, a series of double Cys mutants was constructed. One Cys in all sets was at position 338 and the other was at a position in the sequence S240–V250 in the EF interhelical loop, at position 65 in the AB interhelical loop, or at position 140 in the CD interhelical loop. In the dark state, no significant disulfide formation was observed between C338 and C65 or C140 under the conditions used, whereas a relatively rapid disulfide formation was observed between C338 and C242 or C245. Spin labels in the double Cys mutants showed the strongest magnetic interactions between the nitroxides attached to C338 and C245 or C246. Light activation of the double mutant T242C/S338C resulted in slower disulfide formation, whereas interactions between nitroxides at C338 and C245 or C246 decreased. These results suggest the proximity of the C-terminal residue C338 to residues located on the outer face of a cytoplasmic helical extension of the F helix with an apparent increase of distance upon photoactivation.

Equilibrium constants and free energies in unfolding of proteins in urea solutions

A novel thermodynamic approach to the reversible unfolding of proteins in aqueous urea solutions has been developed based on the premise that urea ligands are bound cooperatively to the macromolecule. When successive stoichiometric binding constants have values larger than expected from statistical effects, an equation for moles of bound urea can be derived that contains imaginary terms. For a very steep unfolding curve, one can then show that the fraction of protein unfolded, B̄, depends on the square of the urea concentration, U, and is given by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}\bar {B}=\frac{{\mathit{A}}^{{\mathit{2}}}_{{\mathit{1}}}{\mathit{e}}^{{\mathrm{{\lambda}}}n\bar {B}}{\mathit{U}}^{{\mathit{2}}}}{{\mathrm{1\hspace{.167em}+\hspace{.167em}}}{\mathit{A}}^{{\mathrm{2}}}_{{\mathrm{1}}}{\mathit{e}}^{{\mathrm{{\lambda}}}\bar {B}}{\mathit{U}}^{{\mathrm{2}}}}{\mathrm{.}}\end{equation*}\end{document} A12 is the binding constant as B̄→ 0, and λ is a parameter that reflects the augmentation in affinities of protein for urea as the moles bound increases to the saturation number, n. This equation provides an analytic expression that reproduces the unfolding curve with good precision, suggests a simple linear graphical procedure for evaluating A12 and λ, and leads to the appropriate standard free energy changes. The calculated ΔG° values reflect the coupling of urea binding with unfolding of the protein. Some possible implications of this analysis to protein folding in vivo are described.

Transition-state structure as a unifying basis in protein-folding mechanisms: Contact order, chain topology, stability, and the extended nucleus mechanism

I attempt to reconcile apparently conflicting factors and mechanisms that have been proposed to determine the rate constant for two-state folding of small proteins, on the basis of general features of the structures of transition states. Φ-Value analysis implies a transition state for folding that resembles an expanded and distorted native structure, which is built around an extended nucleus. The nucleus is composed predominantly of elements of partly or well-formed native secondary structure that are stabilized by local and long-range tertiary interactions. These long-range interactions give rise to connecting loops, frequently containing the native loops that are poorly structured. I derive an equation that relates differences in the contact order of a protein to changes in the length of linking loops, which, in turn, is directly related to the unfavorable free energy of the loops in the transition state. Kinetic data on loop extension mutants of CI2 and α-spectrin SH3 domain fit the equation qualitatively. The rate of folding depends primarily on the interactions that directly stabilize the nucleus, especially those in native-like secondary structure and those resulting from the entropy loss from the connecting loops, which vary with contact order. This partitioning of energy accounts for the success of some algorithms that predict folding rates, because they use these principles either explicitly or implicitly. The extended nucleus model thus unifies the observations of rate depending on both stability and topology.

Kinetic equilibrium of forces and molecular events in muscle contraction

In biomolecular systems, the mechanical transfer of free energy occurs with both high efficiency and high speed. It is shown here that such a transfer can be achieved only if the participating free-energy-storing elements exhibit opposing relationships between their content of free energy and the force they exert in the transfer direction. A kinetic equilibrium of forces (KEF) results, in which the transfer of free energy is mediated essentially by thermal molecular motion. On the basis of present evidence, KEF is used as a guiding principle in developing a mechanical model of the crossbridge cycle in muscle contraction. The model allows the basic features of molecular events to be visualized in terms of plausible structures. Real understanding of the process will require identification of the elements that perform the functions described here. Besides chemomechanical energy transduction, KEF may have a role in other biomolecular processes in which free energy is transferred mechanically over large distances.

An equilibrium statistical model for the spreading phase of open-ocean convection

A “most probable state” equilibrium statistical theory for random distributions of hetons in a closed basin is developed here in the context of two-layer quasigeostrophic models for the spreading phase of open-ocean convection. The theory depends only on bulk conserved quantities such as energy, circulation, and the range of values of potential vorticity in each layer. The simplest theory is formulated for a uniform cooling event over the entire basin that triggers a homogeneous random distribution of convective towers. For a small Rossby deformation radius typical for open-ocean convection sites, the most probable states that arise from this theory strongly resemble the saturated baroclinic states of the spreading phase of convection, with a stabilizing barotropic rim current and localized temperature anomaly.

NMR investigation of ferricytochrome c unfolding: Detection of an equilibrium unfolding intermediate and residual structure in the denatured state

Horse ferricytochrome c (cyt c) undergoes exchange of one of its axial heme ligands (Met-80) for one or more non-native ligands under denaturing conditions. We have used 1H NMR spectroscopy to detect two conformations of paramagnetic cyt c with non-native heme ligation through a range of urea concentrations. One non-native form is an equilibrium unfolding intermediate observed under partially denaturing conditions and is attributed to replacement of Met-80 with one or more Lys side chains. The second non-native form, in which the native Met ligand is replaced by a His, is observed under strongly denaturing conditions. Thermodynamic analysis of these data indicates a relatively small ΔG (17 kJ/mol) for the transition from native to the Lys-ligated intermediate and a significantly larger ΔG (47 kJ/mol) for the transition from native to the His-ligated species. Although CD and fluorescence data indicate that the equilibrium unfolding of cyt c is a two-state process, these NMR results implicate an intermediate with His-Lys ligation.

Temperature, ordering, and equilibrium with time-dependent confining forces

The concepts of temperature and equilibrium are not well defined in systems of particles with time-varying external forces. An example is a radio frequency ion trap, with the ions laser cooled into an ordered solid, characteristic of sub-mK temperatures, whereas the kinetic energies associated with the fast coherent motion in the trap are up to 7 orders of magnitude higher. Simulations with 1,000 ions reach equilibrium between the degrees of freedom when only aperiodic displacements (secular motion) are considered. The coupling of the periodic driven motion associated with the confinement to the nonperiodic random motion of the ions is very small at low temperatures and increases quadratically with temperature.

How does a β-hairpin fold/unfold? Competition between topology and heterogeneity in a solvable model

We study the competition between topological effects and sequence inhomogeneities in determining the thermodynamics and the un/folding kinetics of a β-hairpin. Our work utilizes a new exactly solvable model that allows for arbitrary configurations of native contacts. In general, the competition between heterogeneity and topology results in a crossover of the dominant transition state. Interestingly, near this crossover, the single reaction coordinate picture can be seriously misleading. Our results also suggest that inferring the folding pathway from unfolding simulations is not always justified.

Equilibrium distributions of microsatellite repeat length resulting from a balance between slippage events and point mutations

We describe and test a Markov chain model of microsatellite evolution that can explain the different distributions of microsatellite lengths across different organisms and repeat motifs. Two key features of this model are the dependence of mutation rates on microsatellite length and a mutation process that includes both strand slippage and point mutation events. We compute the stationary distribution of allele lengths under this model and use it to fit DNA data for di-, tri-, and tetranucleotide repeats in humans, mice, fruit flies, and yeast. The best fit results lead to slippage rate estimates that are highest in mice, followed by humans, then yeast, and then fruit flies. Within each organism, the estimates are highest in di-, then tri-, and then tetranucleotide repeats. Our estimates are consistent with experimentally determined mutation rates from other studies. The results suggest that the different length distributions among organisms and repeat motifs can be explained by a simple difference in slippage rates and that selective constraints on length need not be imposed.

Temperature, template topology, and factor requirements of archaeal transcription

Although Archaea are prokaryotic and resemble Bacteria morphologically, their transcription apparatus is remarkably similar to those of eukaryotic cell nuclei. Because some Archaea exist in environments with temperatures of around 100°C, they are likely to have evolved unique strategies for transcriptional control. Here, we investigate the effects of temperature and DNA template topology in a thermophilic archaeal transcription system. Significantly, and in marked contrast with characterized eucaryal systems, archaeal DNA template topology has negligible effect on transcription levels at physiological temperatures using highly purified polymerase and recombinant transcription factors. Furthermore, archaeal transcription does not require hydrolysis of the β-γ phosphoanhydride bond of ATP. However, at lower temperatures, negatively supercoiled templates are transcribed more highly than those that are positively supercoiled. Notably, the block to transcription on positively supercoiled templates at lowered temperatures is at the level of polymerase binding and promoter opening. These data imply that Archaea do not possess a functional homologue of transcription factor TFIIH, and that for the promoters studied, transcription is mediated by TATA box-binding protein, transcription factor TFB, and RNA polymerase alone. Furthermore, they suggest that the reduction of plasmid linking number by hyperthermophilic Archaea in vivo in response to cold shock is a mechanism to maintain gene expression under these adverse circumstances.

Topology of allosteric regulation of lactose permease

Sugar transport by some permeases in Escherichia coli is allosterically regulated by the phosphorylation state of the intracellular regulatory protein, enzyme IIAglc of the phosphoenolpyruvate:sugar phosphotransferase system. A sensitive radiochemical assay for the interaction of enzyme IIAglc with membrane-associated lactose permease was used to characterize the binding reaction. The binding is stimulated by transportable substrates such as lactose, melibiose, and raffinose, but not by sugars that are not transported (maltose and sucrose). Treatment of lactose permease with N-ethylmaleimide, which blocks ligand binding and transport by alkylating Cys-148, also blocks enzyme IIAglc binding. Preincubation with the substrate analog β-d-galactopyranosyl 1-thio-β-d-galactopyranoside protects both lactose transport and enzyme IIAglc binding against inhibition by N-ethylmaleimide. A collection of lactose permease replacement mutants at Cys-148 showed, with the exception of C148V, a good correlation of relative transport activity and enzyme IIAglc binding. The nature of the interaction of enzyme IIAglc with the cytoplasmic face of lactose permease was explored. The N- and C-termini, as well as five hydrophilic loops in the permease, are exposed on the cytoplasmic surface of the membrane and it has been proposed that the central cytoplasmic loop of lactose permease is the major determinant for interaction with enzyme IIAglc. Lactose permease mutants with polyhistidine insertions in cytoplasmic loops IV/V and VI/VII and periplasmic loop VII/VIII retain transport activity and therefore substrate binding, but do not bind enzyme IIAglc, indicating that these regions of lactose permease may be involved in recognition of enzyme IIAglc. Taken together, these results suggest that interaction of lactose permease with substrate promotes a conformational change that brings several cytoplasmic loops into an arrangement optimal for interaction with the regulatory protein, enzyme IIAglc. A topological map of the proposed interaction is presented.