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.

Residual delay maps unveil global patterns of atmospheric nonlinearity and produce improved local forecasts

We use residual-delay maps of observational field data for barometric pressure to demonstrate the structure of latitudinal gradients in nonlinearity in the atmosphere. Nonlinearity is weak and largely lacking in tropical and subtropical sites and increases rapidly into the temperate regions where the time series also appear to be much noisier. The degree of nonlinearity closely follows the meridional variation of midlatitude storm track frequency. We extract the specific functional form of this nonlinearity, a V shape in the lagged residuals that appears to be a basic feature of midlatitude synoptic weather systems associated with frontal passages. We present evidence that this form arises from the relative time scales of high-pressure versus low-pressure events. Finally, we show that this nonlinear feature is weaker in a well regarded numerical forecast model (European Centre for Medium-Range Forecasts) because small-scale temporal and spatial variation is smoothed out in the grided inputs. This is significant, in that it allows us to demonstrate how application of statistical corrections based on the residual-delay map may provide marked increases in local forecast accuracy, especially for severe weather systems.

Multiple-complete-digest restriction fragment mapping: Generating sequence-ready maps for large-scale DNA sequencing

Multiple-complete-digest mapping is a DNA mapping technique based on complete-restriction-digest fingerprints of a set of clones that provides highly redundant coverage of the mapping target. The maps assembled from these fingerprints order both the clones and the restriction fragments. Maps are coordinated across three enzymes in the examples presented. Starting with yeast artificial chromosome contigs from the 7q31.3 and 7p14 regions of the human genome, we have produced cosmid-based maps spanning more than one million base pairs. Each yeast artificial chromosome is first subcloned into cosmids at a redundancy of ×15–30. Complete-digest fragments are electrophoresed on agarose gels, poststained, and imaged on a fluorescent scanner. Aberrant clones that are not representative of the underlying genome are rejected in the map construction process. Almost every restriction fragment is ordered, allowing selection of minimal tiling paths with clone-to-clone overlaps of only a few thousand base pairs. These maps demonstrate the practicality of applying the experimental and software-based steps in multiple-complete-digest mapping to a target of significant size and complexity. We present evidence that the maps are sufficiently accurate to validate both the clones selected for sequencing and the sequence assemblies obtained once these clones have been sequenced by a “shotgun” method.

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.

Congruent Docking of Dimeric Kinesin and ncd into Three-dimensional Electron Cryomicroscopy Maps of Microtubule–Motor ADP Complexes

We present a new map showing dimeric kinesin bound to microtubules in the presence of ADP that was obtained by electron cryomicroscopy and image reconstruction. The directly bound monomer (first head) shows a different conformation from one in the more tightly bound empty state. This change in the first head is amplified as a movement of the second (tethered) head, which tilts upward. The atomic coordinates of kinesin·ADP dock into our map so that the tethered head associates with the bound head as in the kinesin dimer structure seen by x-ray crystallography. The new docking orientation avoids problems associated with previous predictions; it puts residues implicated by proteolysis-protection and mutagenesis studies near the microtubule but does not lead to steric interference between the coiled-coil tail and the microtubule surface. The observed conformational changes in the tightly bound states would probably bring some important residues closer to tubulin. As expected from the homology with kinesin, the atomic coordinates of nonclaret disjunctional protein (ncd)·ADP dock in the same orientation into the attached head in a map of microtubules decorated with dimeric ncd·ADP. Our results support the idea that the observed direct interaction between the two heads is important at some stages of the mechanism by which kinesin moves processively along microtubules.

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.

Coexistence of linear zones and pinwheels within orientation maps in cat visual cortex

Revealing the layout of cortical maps is important both for understanding the processes involved in their development and for uncovering the mechanisms underlying neural computation. The typical organization of orientation maps in the cat visual cortex is radial; complete orientation cycles are mapped around orientation singularities. In contrast, long linear zones of orientation representation have been detected in the primary visual cortex of the tree shrew. In this study, we searched for the existence of long linear sequences and wide linear zones within orientation preference maps of the cat visual cortex. Optical imaging based on intrinsic signals was used. Long linear sequences and wide linear zones of preferred orientation were occasionally detected along the border between areas 17 and 18, as well as within area 18. Adjacent zones of distinct radial and linear organizations were observed across area 18 of a single hemisphere. However, radial and linear organizations were not necessarily segregated; long (7.5 mm) linear sequences of preferred orientation were found embedded within a typical pinwheel-like organization of orientation. We conclude that, although the radial organization is dominant, perfectly linear organization may develop and perform the processing related to orientation in the cat visual cortex.

A novel modifier gene for plasma von Willebrand factor level maps to distal mouse chromosome 11

Type 1 von Willebrand disease (VWD), characterized by reduced levels of plasma von Willebrand factor (VWF), is the most common inherited bleeding disorder in humans. Penetrance of VWD is incomplete, and expression of the bleeding phenotype is highly variable. In addition, plasma VWF levels vary widely among normal individuals. To identify genes that influence VWF level, we analyzed a genetic cross between RIIIS/J and CASA/Rk, two strains of mice that exhibit a 20-fold difference in plasma VWF level. DNA samples from F2 progeny demonstrating either extremely high or extremely low plasma VWF levels were pooled and genotyped for 41 markers spanning the autosomal genome. A novel locus accounting for 63% of the total variance in VWF level was mapped to distal mouse chromosome 11, which is distinct from the murine Vwf locus on chromosome 6. We designated this locus Mvwf for “modifier of VWF.” Additional genotyping of as many as 2407 meioses established a high resolution genetic map with gene order Cola1-Itg3a-Ngfr-Mvwf/Gip-Hoxb9-Hoxb1-Cbx·rs2-Cox5a-Gfap. The Mvwf candidate interval between Ngfr and Hoxb9 is ≈0.5 centimorgan (cM). These results demonstrate that a single dominant gene accounts for the low VWF phenotype of RIIIS/J mice in crosses with several other strains. The pattern of inheritance suggests a gain-of-function mutation in a unique component of VWF biosynthesis or processing. Characterization of the human homologue for Mvwf may have relevance for a subset of type 1 VWD cases and may define an important genetic factor modifying penetrance and expression of mutations at the VWF locus.

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.

Formation of temporal-feature maps by axonal propagation of synaptic learning

Computational maps are of central importance to a neuronal representation of the outside world. In a map, neighboring neurons respond to similar sensory features. A well studied example is the computational map of interaural time differences (ITDs), which is essential to sound localization in a variety of species and allows resolution of ITDs of the order of 10 μs. Nevertheless, it is unclear how such an orderly representation of temporal features arises. We address this problem by modeling the ontogenetic development of an ITD map in the laminar nucleus of the barn owl. We show how the owl's ITD map can emerge from a combined action of homosynaptic spike-based Hebbian learning and its propagation along the presynaptic axon. In spike-based Hebbian learning, synaptic strengths are modified according to the timing of pre- and postsynaptic action potentials. In unspecific axonal learning, a synapse's modification gives rise to a factor that propagates along the presynaptic axon and affects the properties of synapses at neighboring neurons. Our results indicate that both Hebbian learning and its presynaptic propagation are necessary for map formation in the laminar nucleus, but the latter can be orders of magnitude weaker than the former. We argue that the algorithm is important for the formation of computational maps, when, in particular, time plays a key role.

Imaging neuroscience: Principles or maps?

This article reviews some recent trends in imaging neuroscience. A distinction is made between making maps of functional responses in the brain and discerning the rules or principles that underlie their organization. After considering developments in the characterization of brain imaging data, several examples are presented that highlight the context-sensitive nature of neuronal responses that we measure. These contexts can be endogenous and physiological, reflecting the fact that each cortical area, or neuronal population, expresses its dynamics in the context of interactions with other areas. Conversely, these contexts can be experimental or psychological and can have a profound effect on the regional effects elicited. In this review we consider experimental designs and analytic strategies that go beyond cognitive subtraction and speculate on how functional imaging can be used to address both the details and principles underlying functional integration and specialization in the brain.

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.