TY - CONF AB - Common geometric models for proteins and other molecules are the space filling diagram, the solvent accessible surface, and the molecular surface. We describe software that computes metric properties of these models, including volume and surface area. It also measures voids or empty space enclosed by the protein, and it keeps track of surface area contributions of individual atoms. The software is based on 3-dimensional alpha complexes and on inclusion-exclusion formulas with terms derived from the simplices in this complex. AU - Edelsbrunner, Herbert AU - Facello, Michael AU - Fu, Ping AU - Liang, Jie ID - 3551 SN - 0-8186-6930-6 T2 - Proceedings of the 28th Annual Hawaii International Conference on System Sciences TI - Measuring proteins and voids in proteins ER - TY - CONF AB - The concept of an α-shape of a finite set of points in R^d, with weights, is defined and illustrated. An α-shape is a polytope which is not necessarily convex nor connected and can be derived from the (weighted) Delaunay triangulation of the point set, with a parameter controlling the desired level of detail. The set of all α values leads to a descrete family of shapes capturing the intuitive notion of ``crude'' versus ``fine'' shapes of a point set. Software that computes such shapes in R^2 and R^3 is available via anonymous ftp from: ftp://ftp.ncsa.uiuc.edu/Visualization/Alpha-shape/ AU - Akkiraju, Nataraj AU - Edelsbrunner, Herbert AU - Facello, Michael AU - Fu, Ping AU - Mücke, Ernst AU - Varela, Carlos ID - 3552 TI - Alpha shapes: definition and software ER - TY - JOUR AB - Observations on the means, variances, and covariances of quantitative traits across hybrid zones can give information similar to that from Mendelian markers. In addition, they can identify particular traits through which the cline is maintained. We describe a survey of six traits across the hybrid zone between Bombina bombina and Bombina variegata (Amphibia: Discoglossidae) near Pescenica in Croatia. We obtained laboratory measuments of the belly pattern, skin thickness, mating call, skeletal form, egg size, and the developmental time of tadpoles. Although offspring from hybrid populations showed no evidence of reduced viability, a third of the F1 families failed completely, irrespective of the direction of the cross. All traits differed significantly between the taxa. Clines in belly pattern, skin thickness, mating call, and skeletal form were closely concordant with clines in four diagnostic enzyme loci. However, the cline in developmental time was displaced towards bombina, and the cline in egg size was displaced towards variegata. This discordance could be because the traits are not inherited additively or because they are subject to different selection pressures. We favor the latter explanation in the case of developmental time. We show that moderate selection acting directly on a trait suffices to shift its position; rather stronger selection is needed to change its width appreciably. Within hybrid populations, there are significant associations among quantitative traits, and between traits and enzymes. Phenotypic variances also increase in hybrid populations. These observations can be explained by linkage disequilibria among the underlying loci. However, the average magnitude of the covariance between traits is about half that expected from the linkage disequilibria between enzyme loci. The discrepancy is not readily explained by nonadditive gene action. This puzzle is now unresolved and calls for further investigation. AU - Nürnberger, Beate AU - Barton, Nicholas H AU - Maccallum, Catriona AU - Gilchrist, Jason AU - Appleby, Michael ID - 3636 IS - 6 JF - Evolution SN - 0014-3820 TI - Natural selection on quantitative traits in the Bombina hybrid zone VL - 49 ER - TY - JOUR AB - Hybridizing taxa remain distinct for two main reasons. Natural selection acts against hybrids either because of their incompatible genome, or because of differential adaptation of the pure types across an environmental gradient. Here, we provide experimental evidence that the location of the Bombina (Anura: Discoglossidae) hybrid zone in Croatia is, at least in part, determined by differential adaptation. B. bombina typically breeds in permanent water in the lowland, whereas B. variegata reproduces in puddles at higher elevations. In a reciprocal translocation, pure bombina and variegata tadpoles were introduced in equal proportions into lowland pond enclosures and upland puddles. After three weeks, variegata exceeded bombina in survival and growth in both habitats. The effect was most pronounced in puddles, where the few surviving bombina tadpoles had hardly grown at all. In comparison to variegata, the smaller hatchlings of bombina grew relatively faster in ponds, but remained smaller in absolute terms. Nevertheless, B. bombina appears better adapted to ponds than to puddles. The mechanisms by which variegata is excluded from ponds remain to be demonstrated. These data show that habitat dependent selection prevents the invasion of bombina tadpole traits into the variegata gene pool. Given the strong linkage disequilibria in hybrid populations, differential selection on tadpoles may be sufficient to maintain the integrity of the two gene pools. AU - Maccallum, Catriona AU - Nürnberger, Beate AU - Barton, Nicholas H ID - 3637 IS - 1359 JF - Proceedings of the Royal Society of London Series B Biological Sciences SN - 0962-8452 TI - Experimental evidence for habitat dependent selection in a Bombina hybrid zone VL - 260 ER - TY - JOUR AB - A general representation of multilocus selection is extended to allow recombination to depend on genotype. The equations simplify if modifier alleles have small effects on recombination. The evolution of such modifiers only depends on how they alter recombination between the selected loci, and does not involve dominance in modifier effects. The net selection on modifiers can be found explicitly if epistasis is weak relative to recombination. This analysis shows that recombination can be favoured in two ways: because it impedes the response to epistasis which fluctuates in sign, or because it facilitates the response to directional selection. The first mechanism is implausible, because epistasis must change sign over periods of a few generations: faster or slower fluctuations favour reduced recombination. The second mechanism requires weak negative epistasis between favourable alleles, which may either be increasing, or held in check by mutation. The selection (si) on recombination modifiers depends on the reduction in additive variance of log (fitness) due to linkage disequilibria (υ1 < 0), and on non-additive variance in log (fitness) (V′2, V′3,.. epistasis between 2, 3.. loci). For unlinked loci and pairwise epistasis, si = − (υ1 + 4V2/3)δr, where δr is the average increase in recombination caused by the modifier. The approximations are checked against exact calculations for three loci, and against Charlesworth's analyses of mutation/selection balance (1990), and directional selection (1993). The analysis demonstrates a general relation between selection on recombination and observable components of fitness variation, which is open to experimental test. AU - Barton, Nicholas H ID - 3639 IS - 2 JF - Genetical Research SN - 0016-6723 TI - A general model for the evolution of recombination VL - 65 ER - TY - JOUR AB - Any sample of genes traces back to a single common ancestor. Each gene also has other properties: its sequence, its geographic location and the phenotype and fitness of the organism that carries it. With sexual reproduction, different genes have different genealogies, which gives us much more information, but also greatly complicates population genetic analysis. We review the close relation between the distribution of genealogies and the classic theory of identity by descent in spatially structured populations, and develop a simple diffusion approximation to the distribution of coalescence times in a homogeneous two-dimensional habitat. This shows that when neighbourhood size is large (as in most populations) only a small fraction of pairs of genes are closely related, and only this fraction gives information about current rates of gene flow. The increase of spatial dispersion with lineage age is thus a poor estimator of gene flow. The bulk of the genealogy depends on the long-term history of the population; we discuss ways of inferring this history from the concordance between genealogies across loci. AU - Barton, Nicholas H AU - Wilson, I ID - 3638 IS - 1327 JF - Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences SN - 0962-8436 TI - Genealogies and geography VL - 349 ER - TY - JOUR AB - Let S be a set of n points in ℝd . A set W is a weak ε-net for (convex ranges of)S if, for any T⊆S containing εn points, the convex hull of T intersects W. We show the existence of weak ε-nets of size {Mathematical expression}, where β2=0, β3=1, and βd ≈0.149·2d-1(d-1)!, improving a previous bound of Alon et al. Such a net can be computed effectively. We also consider two special cases: when S is a planar point set in convex position, we prove the existence of a net of size O((1/ε) log1.6(1/ε)). In the case where S consists of the vertices of a regular polygon, we use an argument from hyperbolic geometry to exhibit an optimal net of size O(1/ε), which improves a previous bound of Capoyleas. AU - Chazelle, Bernard AU - Edelsbrunner, Herbert AU - Grigni, Michelangelo AU - Guibas, Leonidas AU - Sharir, Micha AU - Welzl, Emo ID - 4035 IS - 1 JF - Discrete & Computational Geometry SN - 0179-5376 TI - Improved bounds on weak ε-nets for convex sets VL - 13 ER - TY - CONF AB - Any arbitrary polyhedron P contained as a subset within Rd can be written as algebraic sum of simple terms, each an integer multiple of the intersection of d or fewer half-spaces defined by facets of P. P can be non-convex and can have holes of any kind. Among the consequences of this result are a short boolean formula for P, a fast parallel algorithm for point classification, and a new proof of the Gram-Sommerville angle relation. AU - Edelsbrunner, Herbert ID - 4034 SN - 0272-5428 T2 - Proceedings of IEEE 36th Annual Foundations of Computer Science TI - Algebraic decomposition of non-convex polyhedra ER - TY - JOUR AU - Ransom, D. AU - Brownlie, Alison AU - Haffter, Pascal AU - Odenthal, Jörg AU - Kelsh, Robert AU - Brand, Michael AU - Furutani Seiki, Makoto AU - Granato, Michael AU - Hammerschmidt, Matthias AU - Heisenberg, Carl-Philipp J AU - Jiang, Yunjin AU - Kane, David AU - Mullins, Mary AU - Van Eden, Fredericus AU - Warga, Rachel AU - Nüsslein Volhard, Christiane AU - Zon, L. ID - 4153 IS - 10 JF - Blood SN - 0006-4971 TI - Hematopoietic mutants identified in a saturation screen of the zebrafish genome VL - 86 ER - TY - JOUR AB - 1. Glutamate receptor (GluR) channels were studied in basket cells in the dentate gyrus of rat hippocampal slices. Basket cells were identified by their location, dendritic morphology and high frequency of action potentials generated during sustained current injection. 2. Dual-component currents were activated by fast application of glutamate to outside-out membrane patches isolated from basket cell somata (10 μM glycine, no external Mg2+). The fast component was selectively blocked by 6-cyano-7-nitroquinoxaline-2,3-dione (CNQX), the slow component by D-2-amino-5-phosphonopentanoic acid (D-AP5). This suggests that the two components were mediated by α-amino-3-hydroxy-5-methyl-4-isoxazolepropionate receptor (AMPAR)/kainate receptor and N-methyl-D-aspartate receptor (NMDAR) channels, respectively. The mean ratio of the peak current of the NMDAR component to that of the AMPAR/kainate receptor component was 0.22 (1 ms pulses of 10 mM glutamate). 3. The AMPAR/kainate receptor component, which was studied in isolation in the presence of D-AP5, was identified as AMPAR mediated on the basis of the preferential activation by AMPA as compared with kainate, the weak desensitization of kainate-activated currents, the cross-desensitization between AMPA and kainate, and the reduction of desensitization by cyclothiazide. 4. Deactivation of basket cell AMPARs following 1 ms pulses of glutamate occurred with a time constant (τ) of 1.2 ± 0.1 ms (mean ± S.E.M.). During 100 ms glutamate pulses, AMPARs desensitized with a τ of 3.7 ± 0.2 ms. 5. The peak current-voltage (I-V) relation of AMPAR-mediated currents in Na+-rich extracellular solution showed a reversal potential of -4.0 ± 2.6 mV and was characterized by a doubly rectifying shape. The conductance of single AMPAR channels was estimated as 22.6 ± 1.6 pS using non-stationary fluctuation analysis. AMPARs expressed in hippocampal basket cells mere highly Ca2+ permeable (P(Ca)/P(K) = 1.79). 6. NMDARs in hippocampal basket cells were studied in isolation in the presence of CNQX. Deactivation of NMDARs activated by glutamate pulses occurred bi-exponentially with mean τ values of 266 ± 23 ms (76%) and 2620 ± 383 ms (24%). 7. The peak I-V relation of the NMDAR-mediated component in Na+-rich extracellular solution showed a reversal potential of 1.5 ± 0.6 mV and a region of negative slope at negative membrane potentials in the presence of external Mg2+, due to voltage-dependent block by these ions. The conductance of single NMDAR channels in the main open state was 50.2 ± 1.8 pS. NMDARs in hippocampal basket cells were highly permeable to Ca2+ (P(Ca)/P(K) = 6.68). 8. AMPARs in hippocampal basket cells are characterized by about threefold faster kinetics and twentyfold higher Ca2+ permeability than AMPARs in hippocampal granule or pyramidal cells. Simulations show that the Ca2+ influx through basket cell AMPARs is comparable to that through NMDARs at negative membrane potentials with physiological concentrations of Ca2+ and Mg2+. This suggests a dual pathway of synaptically mediated Ca2+ entry into interneurones. AU - Koh, Duk AU - Geiger, Jörg AU - Jonas, Peter M AU - Sakmann, Bert ID - 3479 IS - Pt 2 JF - Journal of Physiology SN - 0022-3751 TI - Ca(2+)-permeable AMPA and NMDA receptor channels in basket cells of rat hippocampal dentate gyrus VL - 485 ER - TY - JOUR AB - 1. The influence of intracellular factors on current rectification of different subtypes of native α-amino-3-hydroxy-5-methyl-4-isoxazolepropionate receptors (AMPARs) was studied in rat brain slices by combining fast application of glutamate with patch pipette perfusion. 2. The peak current-voltage (I-V) relation of the AMPARs expressed in Bergmann glial cells of cerebellum and dentate gyrus (DG) basket cells of hippocampus was weakly rectifying in outside-out patches and nystatin-perforated vesicles, but showed a doubly rectifying shape with a region of reduced slope between 0 and +40 mV in nucleated patches. The I-V relation of AMPARs expressed in hippocampal CA3 pyramidal neurones was linear in all recording configurations. 3. Intracellular application of 2.5 μM spermine, a naturally occurring polyamine, blocked outward currents in outside-oat patches from Bergmann glial cells and DG basket cells in a voltage-dependent manner, generating I-V relations with a doubly rectifying shape which were similar to those recorded in nucleated patches. AMPARs in CA3 pyramidal cell patches were unaffected by 25 μM spermine. 4. The half-maximal blocking concentration of spermine at +40 mV was 0.3 μM in Bergmann glial cell patches and 1.5 μM in DG basket cell patches, whereas it was much higher (≥ 100 μM) for CA3 pyramidal. cell patches. Spermidine also affected current rectification, but with lower affinity. The block of outward current by polyamines following voltage jumps developed within < 0.5 ms. 5. We conclude that current rectification, rather than being an intrinsic property of the Ca2+ permeable AMPAR channel, is generated by polyamine block. AU - Koh, Duk AU - Burnashev, Nail AU - Jonas, Peter M ID - 3481 IS - Pt 2 JF - Journal of Physiology SN - 0022-3751 TI - Block of native Ca(2+)-permeable AMPA receptors in rat brain by intracellular polyamines generates double rectification VL - 486 ER - TY - JOUR AB - Recording of glutamate-activated currents in membrane patches was combine with RT-PCR-mediated AMPA receptor (AMPAR) subunit mRNA analysis in single identified cells of rat brain slices. Analysis of AMPARs in principal neurons end interneurons of hippocampus and neocortex and in auditory relay neurons and Bergmann glial cells indicates that the GluR-B subunit in its flip version determines formation of receptors with relatively slow gating, whereas the GluR-D subunit promotes assembly of more rapidly gated receptors. The relation between Ca 2+ permeability of AMPAR channels and the relative GluR-B mRNA abundance is consistent with the dominance of this subunit in determining the Ca 2+ permeability of native receptors. The results suggest that differential expression of GluR-B and GluR-D subunit genes, as well as splicing end editing of their mRNAs, account for the differences in gating and Ca 2+ permeability of native AMPAR channels. AU - Geiger, Jörg AU - Melcher, Thorsten AU - Koh, Duk AU - Sakmann, Bert AU - Seeburg, Peter AU - Jonas, Peter M AU - Monyer, Hannah ID - 3480 IS - 1 JF - Neuron SN - 0896-6273 TI - Relative abundance of subunit mRNAs determines gating and Ca(2+) permeability of AMPA receptors in principal neurons and interneurons in rat CNS VL - 15 ER - TY - GEN AU - Kirkpatrick, Mark AU - Barton, Nicholas H ID - 3597 SN - 0028-0836 T2 - Nature TI - Déjà vu all over again VL - 377 ER - TY - JOUR AB - The probability of fixation of a favorable mutation is reduced if selection at other loci causes inherited variation in fitness. A general method for calculating the fixation probability of an allele that can find itself in a variety of genetic backgrounds is applied to find the effect of substitutions, fluctuating polymorphisms, and deleterious mutations in a large population. With loose linkage, r, the effects depend on the additive genetic variance in relative fitness, var(W), and act by reducing effective population size by (N/Ne) = 1 + var(W)/2r2. However, tightly linked loci can have a substantial effect not predictable from Ne. Linked deleterious mutations reduce the fixation probability of weakly favored alleles by exp (-2U/R), where U is the total mutation rate and R is the map length in Morgans. Substitutions can cause a greater reduction: an allele with advantage s < scrit = (pi 2/6) loge (S/s) [var(W)/R] is very unlikely to be fixed. (S is the advantage of the substitution impeding fixation.) Fluctuating polymorphisms at many (n) linked loci can also have a substantial effect, reducing fixation probability by exp [square root of 2Kn var(W)/R] [K = -1/E((u-u)2/uv) depending on the frequencies (u,v) at the selected polymorphisms]. Hitchhiking due to all three kinds of selection may substantially impede adaptation that depends on weakly favored alleles. AU - Barton, Nicholas H ID - 3640 IS - 2 JF - Genetics SN - 0016-6731 TI - Linkage and the limits to natural selection VL - 140 ER - TY - JOUR AB - Efficient algorithms are described for computing topological, combinatorial, and metric properties of the union of finitely many spherical balls in R(d) These algorithms are based on a simplicial complex dual to a decomposition of the union of balls using Voronoi cells, and on short inclusion-exclusion formulas derived from this complex. The algorithms are most relevant in R(3) where unions of finitely many balls are commonly used as models of molecules. AU - Edelsbrunner, Herbert ID - 4028 IS - 1 JF - Discrete & Computational Geometry SN - 0179-5376 TI - The union of balls and its dual shape VL - 13 ER - TY - JOUR AB - A general and direct method for computing the Betti numbers of a finite simplicial complex in Bd is given. This method is complete for d less than or equal to 3, where versions of this method run in time O(n alpha(n)) and O(n), n the number of simplices. An implementation of the algorithm is applied to alpha shapes, which is a novel geometric modeling tool. AU - Delfinado, Cecil AU - Edelsbrunner, Herbert ID - 4029 IS - 7 JF - Computer Aided Geometric Design SN - 0167-8396 TI - An incremental algorithm for Betti numbers of simplicial complexes on the 3-sphere VL - 12 ER - TY - JOUR AB - The F5 (2n = 34) and FM2 (2n = 44-46) chromosome races of the Sceloporus grammicus complex form a parapatric hybrid zone in the Mexican state of Hidalgo, characterized by steep concordant clines among three diagnostic chromosome markers across a straight-line distance of about 2 km. Here, we show that this zone is actually structured into local patches in which hybridization extends over an extremely irregular front. The distribution of hybrid-index (HI) scores across the transect reveals some hybridization at almost all localities mapped in a central 7 km x 3 km area. Pooling the central samples produces both a strong heterozygote deficit for all diagnostic markers and strong linkage disequilibria between all pairwise combinations of these (unlinked) markers. Moreover, a highly significant association exists between the habitat on which each individual was caught and its karyotype (F5 chromosomes are more likely to be found on oak). Analysis of genotype frequencies over a range of spatial scales shows that there is no significant heterozygote deficit or habitat association within local areas of less than about 200 m; however, there is significant linkage disequilibrium over the smallest scales (R = D (pquv)1/2 = 0.29, support limits, 0.18-0.36) over 100 m. These patterns suggest that lizards mate and choose habitats randomly within local patches. This conclusion is supported by mark-recapture estimates of dispersal (≈ 80 m in a generation) and by inference of matings from embryo and maternal karyotypes. Closer examination of the two-dimensional pattern reveals a convoluted cline for all three markers, with a width of 830 m (support limits 770 m-930 m). This cline width, combined with the strength of local linkage disequilibrium, implies a dispersal rate of σ = 160 m in a generation and an effective selection pressure of 30% on each chromosome marker. The proportion of inviable embryos is greater in females from the center of the hybrid zone; this is caused by effects associated with both karyotype and location. The hybrid zone is likely to be maintained by selection against chromosomal heterozygotes, by other kinds of selection against hybrids, and by selection adapting the chromosome races to different habitats. The structure of the contact may be caused by both random drift and by selection in relation to habitat. AU - Sites, Jack AU - Barton, Nicholas H AU - Reed, Kent ID - 4297 IS - 1 JF - Evolution SN - 0014-3820 TI - The genetic structure of a mosaic hybrid zone between two chromosome races of the Sceloporus grammicus complex (Sauria, Phrynosomatidae) in central Mexico VL - 49 ER - TY - JOUR AB - Three replicate lines of Drosophila melanogaster were cultured at each of two temperatures (16.5⚬C and 25⚬C) in population cages for 4 yr. The lifespans of both sexes and the fecundity and fertility of the females were then measured at both experimental temperatures. The characters showed evidence of adaptation; flies of both sexes from each selection regime showed higher longevity, and females showed higher fecundity and fertility, than flies from the other selection regime when they were tested at the experimental temperature at which they had evolved. Calculation of intrinsic rates of increase under different assumptions about the rate of population increase showed that the difference between the lines from the two selection regimes became less the higher the rate of population increase, because the lines were more similar in early adulthood than they were later. Despite the increased adaptation of the low-temperature lines to the low temperature, like the high temperature lines they produced progeny at a higher rate at the higher temperature. The lines may have independently evolved adaptations to their respective thermal regimes during the experiment, or there may have been a trade-off between adaptation to the two temperatures, or mutation pressure may have lowered adaptation to the temperature that the flies no longer encountered. AU - Partridge, Linda AU - Barrie, Brian AU - Barton, Nicholas H AU - Fowler, Kevin AU - French, Vernon ID - 4296 IS - 3 JF - Evolution SN - 0014-3820 TI - Rapid laboratory evolution of adult life history traits in Drosophila melanogaster in response to temperature VL - 49 ER - TY - JOUR AU - Barton, Nicholas H ID - 4298 IS - 6 JF - Evolution SN - 1558-5646 TI - Appendix to "A simulation study of multilocus clines" by S J E Baird VL - 49 ER - TY - THES AB - Hybrid systems are real-time systems that react to both discrete and continuous activities (such as analog signals, time, temperature, and speed). Typical examples of hybrid systems are embedded systems, timing-based communication protocols, and digital circuits at the transistor level. Due to the rapid development of microprocessor technology, hybrid systems directly control much of what we depend on in our daily lives. Consequently, the formal specification and verification of hybrid systems has become an active area of research. This dissertation presents the first general framework for the formal specification and verification of hybrid systems, as well as the first hybrid-system analysis tool--HyTech. The framework consists of a graphical finite-state-machine-like language for modeling hybrid systems, a temporal logic for modeling the requirements of hybrid systems, and a computer procedure that verifies modeled hybrid systems against modeled requirements. The tool HyTech is the implementation of the framework using C++ and Mathematica. More specifically, our hybrid-system modeling language, Hybrid Automata, is an extension of timed automata with discrete and continuous variables whose dynamics are governed by differential equations. Our requirement modeling language, ICTL, is a branching-time temporal logic, and is an extension of TCTL with stop-watch variables. Our verification procedure is a symbolic model-checking procedure that verifies linear hybrid automata against ICTL formulas. To make HyTech more efficient and effective, we use model-checking strategies and abstract operators that can expedite the verification process. To enable HyTech to verify nonlinear hybrid automata, we introduce two translations from nonlinear hybrid automata to linear hybrid automata. We have applied HyTech to analyze more than 30 hybrid-system benchmarks. In this dissertation, we present the application of HyTech to three nontrivial hybrid systems taken from the literature. AU - Ho, Pei ID - 4428 TI - Automatic analysis of hybrid systems ER -