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.

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.

Dissection of De Novo Membrane Insertion Activities of Internal Transmembrane Segments of ATP-Binding-Cassette Transporters: Toward Understanding Topological Rules for Membrane Assembly of Polytopic Membrane Proteins

The membrane assembly of polytopic membrane proteins is a complicated process. Using Chinese hamster P-glycoprotein (Pgp) as a model protein, we investigated this process previously and found that Pgp expresses more than one topology. One of the variations occurs at the transmembrane (TM) domain including TM3 and TM4: TM4 inserts into membranes in an Nin-Cout rather than the predicted Nout-Cin orientation, and TM3 is in cytoplasm rather than the predicted Nin-Cout orientation in the membrane. It is possible that TM4 has a strong activity to initiate the Nin-Cout membrane insertion, leaving TM3 out of the membrane. Here, we tested this hypothesis by expressing TM3 and TM4 in isolated conditions. Our results show that TM3 of Pgp does not have de novo Nin-Cout membrane insertion activity whereas TM4 initiates the Nin-Cout membrane insertion regardless of the presence of TM3. In contrast, TM3 and TM4 of another polytopic membrane protein, cystic fibrosis transmembrane conductance regulator (CFTR), have a similar level of de novo Nin-Cout membrane insertion activity and TM4 of CFTR functions only as a stop-transfer sequence in the presence of TM3. Based on these findings, we propose that 1) the membrane insertion of TM3 and TM4 of Pgp does not follow the sequential model, which predicts that TM3 initiates Nin-Cout membrane insertion whereas TM4 stops the insertion event; and 2) “leaving one TM segment out of the membrane” may be an important folding mechanism for polytopic membrane proteins, and it is regulated by the Nin-Cout membrane insertion activities of the TM segments.

Coupled Translocation Events Generate Topological Heterogeneity at the Endoplasmic Reticulum Membrane

Topogenic determinants that direct protein topology at the endoplasmic reticulum membrane usually function with high fidelity to establish a uniform topological orientation for any given polypeptide. Here we show, however, that through the coupling of sequential translocation events, native topogenic determinants are capable of generating two alternate transmembrane structures at the endoplasmic reticulum membrane. Using defined chimeric and epitope-tagged full-length proteins, we found that topogenic activities of two C-trans (type II) signal anchor sequences, encoded within the seventh and eighth transmembrane (TM) segments of human P-glycoprotein were directly coupled by an inefficient stop transfer (ST) sequence (TM7b) contained within the C-terminus half of TM7. Remarkably, these activities enabled TM7 to achieve both a single- and a double-spanning TM topology with nearly equal efficiency. In addition, ST and C-trans signal anchor activities encoded by TM8 were tightly linked to the weak ST activity, and hence topological fate, of TM7b. This interaction enabled TM8 to span the membrane in either a type I or a type II orientation. Pleiotropic structural features contributing to this unusual topogenic behavior included 1) a short, flexible peptide loop connecting TM7a and TM7b, 2) hydrophobic residues within TM7b, and 3) hydrophilic residues between TM7b and TM8.

Nonatomic games on Loeb spaces

In the setting of noncooperative game theory, strategic negligibility of individual agents, or diffuseness of information, has been modeled as a nonatomic measure space, typically the unit interval endowed with Lebesgue measure. However, recent work has shown that with uncountable action sets, for example the unit interval, there do not exist pure-strategy Nash equilibria in such nonatomic games. In this brief announcement, we show that there is a perfectly satisfactory existence theory for nonatomic games provided this nonatomicity is formulated on the basis of a particular class of measure spaces, hyperfinite Loeb spaces. We also emphasize other desirable properties of games on hyperfinite Loeb spaces, and present a synthetic treatment, embracing both large games as well as those with incomplete information.

Topological testing of the mechanism of homology search promoted by RecA protein

To initiate homologous recombination, sequence similarity between two DNA molecules must be searched for and homology recognized. How the search for and recognition of homology occurs remains unproven. We have examined the influences of DNA topology and the polarity of RecA–single-stranded (ss)DNA filaments on the formation of synaptic complexes promoted by RecA. Using two complementary methods and various ssDNA and duplex DNA molecules as substrates, we demonstrate that topological constraints on a small circular RecA–ssDNA filament prevent it from interwinding with its duplex DNA target at the homologous region. We were unable to detect homologous pairing between a circular RecA–ssDNA filament and its relaxed or supercoiled circular duplex DNA targets. However, the formation of synaptic complexes between an invading linear RecA–ssDNA filament and covalently closed circular duplex DNAs is promoted by supercoiling of the duplex DNA. The results imply that a triplex structure formed by non-Watson–Crick hydrogen bonding is unlikely to be an intermediate in homology searching promoted by RecA. Rather, a model in which RecA-mediated homology searching requires unwinding of the duplex DNA coupled with local strand exchange is the likely mechanism. Furthermore, we show that polarity of the invading RecA–ssDNA does not affect its ability to pair and interwind with its circular target duplex DNA.

Capabilities of liposomes for topological transformation

Dynamic behaviors of liposomes caused by interactions between liposomal membranes and surfactant were studied by direct real-time observation by using high-intensity dark-field microscopy. Solubilization of liposomes by surfactants is thought to be a catastrophic event akin to the explosion of soap bubbles in the air; however, the actual process has not been clarified. We studied this process experimentally and found that liposomes exposed to various surfactants exhibited unusual behavior, namely continuous shrinkage accompanied by intermittent quakes, release of encapsulated liposomes, opening up, and inside–out topological inversion.

Distinct Biochemical and Topological Properties of the 31- and 27-Kilodalton Plasma Membrane Intrinsic Protein Subgroups from Red Beet1

Plasma membrane vesicles from red beet (Beta vulgaris L.) storage tissue contain two prominent major intrinsic protein species of 31 and 27 kD (X. Qi, C.Y Tai, B.P. Wasserman [1995] Plant Physiol 108: 387–392). In this study affinity-purified antibodies were used to investigate their localization and biochemical properties. Both plasma membrane intrinsic protein (PMIP) subgroups partitioned identically in sucrose gradients; however, each exhibited distinct properties when probed for multimer formation, and by limited proteolysis. The tendency of each PMIP species to form disulfide-linked aggregates was studied by inclusion of various sulfhydryl agents during tissue homogenization and vesicle isolation. In the absence of dithiothreitol and sulfhydryl reagents, PMIP27 yielded a mixture of monomeric and aggregated species. In contrast, generation of a monomeric species of PMIP31 required the addition of dithiothreitol, iodoacetic acid, or N-ethylmaleimide. Mixed disulfide-linked heterodimers between the PMIP31 and PMIP27 subgroups were not detected. Based on vectorial proteolysis of right-side-out vesicles with trypsin and hydropathy analysis of the predicted amino acid sequence derived from the gene encoding PMIP27, a topological model for a PMIP27 was established. Two exposed tryptic cleavage sites were identified from proteolysis of PMIP27, and each was distinct from the single exposed site previously identified in surface loop C of a PMIP31. Although the PMIP31 and PMIP27 species both contain integral proteins that appear to occur within a single vesicle population, these results demonstrate that each PMIP subgroup responds differently to perturbations of the membrane.

Topological challenges to DNA replication: Conformations at the fork

The unwinding of the parental DNA duplex during replication causes a positive linking number difference, or superhelical strain, to build up around the elongating replication fork. The branching at the fork and this strain bring about different conformations from that of (−) supercoiled DNA that is not being replicated. The replicating DNA can form (+) precatenanes, in which the daughter DNAs are intertwined, and (+) supercoils. Topoisomerases have the essential role of relieving the superhelical strain by removing these structures. Stalled replication forks of molecules with a (+) superhelical strain have the additional option of regressing, forming a four-way junction at the replication fork. This four-way junction can be acted on by recombination enzymes to restart replication. Replication and chromosome folding are made easier by topological domain barriers, which sequester the substrates for topoisomerases into defined and concentrated regions. Domain barriers also allow replicated DNA to be (−) supercoiled. We discuss the importance of replicating DNA conformations and the roles of topoisomerases, focusing on recent work from our laboratory.