TY - CHAP AU - Herbert Edelsbrunner ID - 3574 T2 - Handbook of Discrete and Computational Geometry TI - Biological applications of computational topology ER - TY - GEN AB - Genome sizes vary enormously. This variation in DNA content correlates with effective population size, suggesting that deleterious additions to the genome can accumulate in small populations. On this view, the increased complexity of biological functions associated with large genomes partly reflects evolutionary degeneration. AU - Charlesworth, Brian AU - Nicholas Barton ID - 3595 IS - 6 T2 - Current Biology TI - Genome size: Does bigger mean worse? VL - 14 ER - TY - JOUR AB - We analyze the changes in the mean and variance components of a quantitative trait caused by changes in allele frequencies, concentrating on the effects of genetic drift. We use a general representation of epistasis and dominance that allows an arbitrary relation between genotype and phenotype for any number of diallelic loci. We assume initial and final Hardy-Weinberg and linkage equilibrium in our analyses of drift-induced changes. Random drift generates transient linkage disequilibria that cause correlations between allele frequency fluctuations at different loci. However, we show that these have negligible effects, at least for interactions among small numbers of loci. Our analyses are based on diffusion approximations that summarize the effects of drift in terms of F, the inbreeding coefficient, interpreted as the expected proportional decrease in heterozygosity at each locus. For haploids, the variance of the trait mean after a population bottleneck is var(Δz̄) =inline imagewhere n is the number of loci contributing to the trait variance, VA(1)=VA is the additive genetic variance, and VA(k) is the kth-order additive epistatic variance. The expected additive genetic variance after the bottleneck, denoted (V*A), is closely related to var(Δz̄); (V*A) (1 –F)inline imageThus, epistasis inflates the expected additive variance above VA(1 –F), the expectation under additivity. For haploids (and diploids without dominance), the expected value of every variance component is inflated by the existence of higher order interactions (e.g., third-order epistasis inflates (V*AA)). This is not true in general with diploidy, because dominance alone can reduce (V*A) below VA(1 –F) (e.g., when dominant alleles are rare). Without dominance, diploidy produces simple expressions: var(Δz̄)=inline image=1 (2F) kVA(k) and (V*A) = (1 –F)inline imagek(2F)k-1VA(k) With dominance (and even without epistasis), var(Δz̄)and (V*A) no longer depend solely on the variance components in the base population. For small F, the expected additive variance simplifies to (V*A)(1 –F) VA+ 4FVAA+2FVD+2FCAD, where CAD is a sum of two terms describing covariances between additive effects and dominance and additive × dominance interactions. Whether population bottlenecks lead to expected increases in additive variance depends primarily on the ratio of nonadditive to additive genetic variance in the base population, but dominance precludes simple predictions based solely on variance components. We illustrate these results using a model in which genotypic values are drawn at random, allowing extreme and erratic epistatic interactions. Although our analyses clarify the conditions under which drift is expected to increase VA, we question the evolutionary importance of such increases. AU - Nicholas Barton AU - Turelli, Michael ID - 3614 IS - 10 JF - Evolution; International Journal of Organic Evolution TI - Effects of allele frequency changes on variance components under a general model of epistasis VL - 58 ER - TY - JOUR AB - We investigate three alternative selection-based scenarios proposed to maintain polygenic variation: pleiotropic balancing selection, G x E interactions (with spatial or temporal variation in allelic effects), and sex-dependent allelic effects. Each analysis assumes an additive polygenic trait with n diallelic loci under stabilizing selection. We allow loci to have different effects and consider equilibria at which the population mean departs from the stabilizing-selection optimum. Under weak selection, each model produces essentially identical, approximate allele-frequency dynamics. Variation is maintained under pleiotropic balancing selection only at loci for which the strength of balancing selection exceeds the effective strength of stabilizing selection. In addition, for all models, polymorphism requires that the population mean be close enough to the optimum that directional selection does not overwhelm balancing selection. This balance allows many simultaneously stable equilibria, and we explore their properties numerically. Both spatial and temporal G x E can maintain variation at loci for which the coefficient of variation (across environments) of the effect of a substitution exceeds a critical value greater than one. The critical value depends on the correlation between substitution effects at different loci. For large positive correlations (e.g., ρ2ij > 3/4), even extreme fluctuations in allelic effects cannot maintain variation. Surprisingly, this constraint on correlations implies that sex-dependent allelic effects cannot maintain polygenic variation. We present numerical results that support our analytical approximations and discuss our results in connection to relevant data and alternative variance-maintaining mechanisms. AU - Turelli, Michael AU - Nicholas Barton ID - 3615 IS - 2 JF - Genetics TI - Polygenic variation maintained by balancing selection: pleiotropy, sex-dependent allelic effects and GxE interactions VL - 166 ER - TY - JOUR AB - The time course of Mg(2+) block and unblock of NMDA receptors (NMDARs) determines the extent they are activated by depolarization. Here, we directly measure the rate of NMDAR channel opening in response to depolarizations at different times after brief (1 ms) and sustained (4.6 s) applications of glutamate to nucleated patches from neocortical pyramidal neurons. The kinetics of Mg(2+) unblock were found to be non-instantaneous and complex, consisting of a prominent fast component (time constant approximately 100 micros) and slower components (time constants 4 and approximately 300 ms), the relative amplitudes of which depended on the timing of the depolarizing pulse. Fitting a kinetic model to these data indicated that Mg(2+) not only blocks the NMDAR channel, but reduces both the open probability and affinity for glutamate, while enhancing desensitization. These effects slow the rate of NMDAR channel opening in response to depolarization in a time-dependent manner such that the slower components of Mg(2+) unblock are enhanced during depolarizations at later times after glutamate application. One physiological consequence of this is that brief depolarizations occurring earlier in time after glutamate application are better able to open NMDAR channels. This finding has important implications for spike-timing-dependent synaptic plasticity (STDP), where the precise (millisecond) timing of action potentials relative to synaptic inputs determines the magnitude and sign of changes in synaptic strength. Indeed, we find that STDP timing curves of NMDAR channel activation elicited by realistic dendritic action potential waveforms are narrower than expected assuming instantaneous Mg(2+) unblock, indicating that slow Mg(2+) unblock of NMDAR channels makes the STDP timing window more precise. AU - Kampa, Bjorn M AU - Clements, John AU - Peter Jonas AU - Stuart, Greg J ID - 3807 IS - Pt 2 JF - Journal of Physiology TI - Kinetics of Mg(2+) unblock of NMDA receptors: implications for spike-timing dependent synaptic plasticity VL - 556 ER - TY - JOUR AB - Neural stem cells in various regions of the vertebrate brain continuously generate neurons throughout life. In the mammalian hippocampus, a region important for spatial and episodic memory, thousands of new granule cells are produced per day, with the exact number depending on environmental conditions and physical exercise. The survival of these neurons is improved by learning and conversely learning may be promoted by neurogenesis. Although it has been suggested that newly generated neurons may have specific properties to facilitate learning, the cellular and synaptic mechanisms of plasticity in these neurons are largely unknown. Here we show that young granule cells in the adult hippocampus differ substantially from mature granule cells in both active and passive membrane properties. In young neurons, T-type Ca2+ channels can generate isolated Ca2+ spikes and boost fast Na+ action potentials, contributing to the induction of synaptic plasticity. Associative long-term potentiation can be induced more easily in young neurons than in mature neurons under identical conditions. Thus, newly generated neurons express unique mechanisms to facilitate synaptic plasticity, which may be important for the formation of new memories. AU - Schmidt-Hieber, Christoph AU - Peter Jonas AU - Bischofberger, Josef ID - 3809 IS - 6988 JF - Nature TI - Enhanced synaptic plasticity in newly generated granule cells of the adult hippocampus VL - 429 ER - TY - JOUR AB - The operation of neuronal networks crucially depends on a fast time course of signaling in inhibitory interneurons. Synapses that excite interneurons generate fast currents, owing to the expression of glutamate receptors of specific subunit composition. Interneurons generate brief action potentials in response to transient synaptic activation and discharge repetitively at very high frequencies during sustained stimulation. The ability to generate short-duration action potentials at high frequencies depends on the expression of specific voltage-gated K+ channels. Factors facilitating fast action potential initiation following synaptic excitation include depolarized interneuron resting potential, subthreshold conductances and active dendrites. Finally, GABA release at interneuron output synapses is rapid and highly synchronized, leading to a faster inhibition in postsynaptic interneurons than in principal cells. Thus, the expression of distinct transmitter receptors and voltage-gated ion channels ensures that interneurons operate with high speed and temporal precision. AU - Peter Jonas AU - Bischofberger, Josef AU - Fricker, Desdemona AU - Miles, Richard ID - 3805 IS - 1 JF - Trends in Neurosciences TI - Interneuron Diversity series: Fast in, fast out--temporal and spatial signal processing in hippocampal interneurons VL - 27 ER - TY - JOUR AB - Wingless (ergatoid) males of the tramp ant Cardiocondyla minutior attack and kill their young ergatoid rivals and thus attempt to monopolize mating with female sexuals reared in the colony. Because of the different strength of local mate competition in colonies with one or several reproductive queens, we expected the production of new ergatoid males to vary with queen number. Sex ratios were mostly female-biased, but in contrast to the sympatric species C. obscurior (Cremer and Heinze, 2002) neither the percentage of ergatoid males nor of female sexuals among the first 20 sexuals produced varied considerably with queen number. As in C. obscurior, experimental colony fragmentation led to the production of winged males, whereas in unfragmented control colonies only ergatoid males eclosed. AU - Heinze, Jürgen AU - Böttcher, A. AU - Cremer, Sylvia ID - 3918 IS - 3 JF - Insectes Sociaux TI - Production of winged and wingless males in the ant, Cardiocondyla minutior VL - 51 ER - TY - CONF AB - We give an algorithm that locally improves the fit between two proteins modeled as space-filling diagrams. The algorithm defines the fit in purely geometric terms and improves by applying a rigid motion to one of the two proteins. Our implementation of the algorithm takes between three and ten seconds and converges with high likelihood to the correct docked configuration, provided it starts at a position away from the correct one by at most 18 degrees of rotation and at most 3.0Angstrom of translation. The speed and convergence radius make this an attractive algorithm to use in combination with a coarse sampling of the six-dimensional space of rigid motions. AU - Choi, Vicky AU - Agarwal, Pankaj K AU - Herbert Edelsbrunner AU - Rudolph, Johannes ID - 3988 TI - Local search heuristic for rigid protein docking VL - 3240 ER - TY - JOUR AB - The motion of a biomolecule greatly depends on the engulfing solution, which is mostly water. Instead of representing individual water molecules, it is desirable to develop implicit solvent models that nevertheless accurately represent the contribution of the solvent interaction to the motion. In such models, hydrophobicity is expressed as a weighted sum of atomic surface areas. The derivatives of these weighted areas contribute to the force that drives the motion. In this paper we give formulas for the weighted and unweighted area derivatives of a molecule modeled as a space-filling diagram made up of balls in motion. Other than the radii and the centers of the balls, the formulas are given in terms of the sizes of circular arcs of the boundary and edges of the power diagram. We also give inclusion-exclusion formulas for these sizes. AU - Bryant, Robert AU - Herbert Edelsbrunner AU - Koehl, Patrice AU - Levitt, Michael ID - 3986 IS - 3 JF - Discrete & Computational Geometry TI - The area derivative of a space-filling diagram VL - 32 ER - TY - JOUR AB - We combine topological and geometric methods to construct a multiresolution representation for a function over a two-dimensional domain. In a preprocessing stage, we create the Morse-Smale complex of the function and progressively simplify its topology by cancelling pairs of critical points. Based on a simple notion of dependency among these cancellations, we construct a hierarchical data structure supporting traversal and reconstruction operations similarly to traditional geometry-based representations. We use this data structure to extract topologically valid approximations that satisfy error bounds provided at runtime. AU - Bremer, Peer-Timo AU - Herbert Edelsbrunner AU - Hamann, Bernd AU - Pascucci, Valerio ID - 3984 IS - 4 JF - IEEE Transactions on Visualization and Computer Graphics TI - A topological hierarchy for functions on triangulated surfaces VL - 10 ER - TY - JOUR AB - We consider scientific data sets that describe density functions over three-dimensional geometric domains. Such data sets are often large and coarsened representations are needed for visualization and analysis. Assuming a tetrahedral mesh representation, we construct such representations with a simplification algorithm that combines three goals: the approximation of the function, the preservation of the mesh topology, and the improvement of the mesh quality. The third goal is achieved with a novel extension of the well-known quadric error metric. We perform a number of computational experiments to understand the effect of mesh quality improvement on the density map approximation. In addition, we study the effect of geometric simplification on the topological features of the function by monitoring its critical points. AU - Natarajan, Vijay AU - Herbert Edelsbrunner ID - 3987 IS - 5 JF - IEEE Transactions on Visualization and Computer Graphics TI - Simplification of three-dimensional density maps VL - 10 ER - TY - JOUR AB - Given a Morse function f over a 2-manifold with or without boundary, the Reeb graph is obtained by contracting the connected components of the level sets to points. We prove tight upper and lower bounds on the number of loops in the Reeb graph that depend on the genus, the number of boundary components, and whether or not the 2-manifold is orientable. We also give an algorithm that constructs the Reeb graph in time O(n log n), where n is the number of edges in the triangulation used to represent the 2-manifold and the Morse function. AU - Cole-McLaughlin, Kree AU - Herbert Edelsbrunner AU - Harer, John AU - Natarajan, Vijay AU - Pascucci, Valerio ID - 3985 IS - 2 JF - Discrete & Computational Geometry TI - Loops in Reeb graphs of 2-manifolds VL - 32 ER - TY - CONF AB - We introduce local and global comparison measures for a collection of k less than or equal to d real-valued smooth functions on a common d-dimensional Riemannian manifold. For k = d = 2 we relate the measures to the set of critical points of one function restricted to the level sets of the other. The definition of the measures extends to piecewise linear functions for which they ace easy to compute. The computation of the measures forms the centerpiece of a software tool which we use to study scientific datasets. AU - Herbert Edelsbrunner AU - Harer, John AU - Natarajan, Vijay AU - Pascucci, Valerio ID - 3989 TI - Local and global comparison of continuous functions ER - TY - JOUR AB - During vertebrate gastrulation, a relatively limited number of blastodermal cells undergoes a stereotypical set of cellular movements that leads to formation of the three germ layers: ectoderm, mesoderm and endoderm. Gastrulation, therefore, provides a unique developmental system in which to study cell movements in vivo in a fairly simple cellular context. Recent advances have been made in elucidating the cellular and molecular mechanisms that underlie cell movements during zebrafish gastrulation. These findings can be compared with observations made in other model systems to identify potential general mechanisms of cell migration during development. AU - Montero, Juan AU - Heisenberg, Carl-Philipp J ID - 4172 IS - 11 JF - Trends in Cell Biology TI - Gastrulation dynamics: cells move into focus VL - 14 ER - TY - JOUR AB - The dynamical basis of tumoral growth has been controversial. Many models have been proposed to explain cancer development. The descriptions employ exponential, potential, logistic or Gompertzian growth laws. Some of these models are concerned with the interaction between cancer and the immunological, system. Among other properties, these models are concerned with the microscopic behavior of tumors and the emergence of cancer. We propose a modification of a previous model by Stepanova, which describes the specific immunological response against cancer. The modification consists of the substitution of a Gompertian law for the exponential rate used for tumoral growth. This modification is motivated by the numerous works confirming that Gompertz's equation correctly describes solid tumor growth. The modified model predicts that near zero, tumors always tend to grow. Immunological contraposition never suffices to induce a complete regression of the tumor. Instead, a stable microscopic equilibrium between cancer and immunological activity can be attained. In other words, our model predicts that the theory of immune surveillance is plausible. A macroscopic equilibrium in which the system develops cancer is also possible. In this case, immunological activity is depleted. This is consistent with the phenomena of cancer tolerance. Both equilibrium points can coexist or can exist without the other. In all cases the fixed point at zero tumor size is unstable. Since immunity cannot induce a complete tumor regression, a therapy is required. We include constant-dose therapies and show that they are insufficient. Final levels of immunocompetent cells and tumoral cells are finite, thus post-treatment regrowth of the tumor is certain. We also evaluate late-intensification therapies which are successful. They induce an asymptotic regression to zero tumor size. Immune response is also suppressed by the therapy, and thus plays a negligible role in the remission. We conclude that treatment evaluation should be successful without taking into account immunological effects. (C) 2003 Elsevier Ltd. All rights reserved. AU - de Vladar, Harold AU - González, J. ID - 4238 IS - 3 JF - Journal of Theoretical Biology TI - Dynamic response of cancer under the influence of immunological activity and therapy VL - 227 ER - TY - CHAP AU - Harold Vladar AU - Cipriani, Roberto AU - Scharifker, Benjamin AU - Bubis, Jose ED - Hanslmeier,A. ED - Kempe,S. ED - Seckbach,J. ID - 4230 T2 - Life in the Universe From the Miller Experiment to the Search for Life on Other Worlds TI - A mechanism for the prebiotic emergence of proteins ER - TY - THES AU - de Vladar, Harold ID - 4236 TI - Métodos no lineales y sus aplicaciones en dinámicas aleatorias de poblaciones celulares ER - TY - CONF AU - Maler, Oded AU - Dejan Nickovic ID - 4372 TI - Monitoring Temporal Properties of Continuous Signals ER - TY - THES AB - The enormous cost and ubiquity of software errors necessitates the need for techniques and tools that can precisely analyze large systems and prove that they meet given specifications, or if they don't, return counterexample behaviors showing how the system fails. Recent advances in model checking, decision procedures, program analysis and type systems, and a shift of focus to partial specifications common to several systems (e.g., memory safety and race freedom) have resulted in several practical verification methods. However, these methods are either precise or they are scalable, depending on whether they track the values of variables or only a fixed small set of dataflow facts (e.g., types), and are usually insufficient for precisely verifying large programs. We describe a new technique called Lazy Abstraction (LA) which achieves both precision and scalability by localizing the use of precise information. LA automatically builds, explores and refines a single abstract model of the program in a way that different parts of the model exhibit different degrees of precision, namely just enough to verify the desired property. The algorithm automatically mines the information required by partitioning mechanical proofs of unsatisfiability of spurious counterexamples into Craig Interpolants. For multithreaded systems, we give a new technique based on analyzing the behavior of a single thread executing in a context which is an abstraction of the other (arbitrarily many) threads. We define novel context models and show how to automatically infer them and analyze the full system (thread + context) using LA. LA is implemented in BLAST. We have run BLAST on Windows and Linux Device Drivers to verify API conformance properties, and have used it to find (or guarantee the absence of) data races in multithreaded Networked Embedded Systems (NESC) applications. BLAST is able to prove the absence of races in several cases where earlier methods, which depend on lock-based synchronization, fail. AU - Jhala, Ranjit ID - 4424 TI - Program verification by lazy abstraction ER -