TY - JOUR
AB - We present a method for prediction of functional sites in a set of aligned protein sequences. The method selects sites which are both well conserved and clustered together in space, as inferred from the 3D structures of proteins included in the alignment. We tested the method using 86 alignments from the NCBI CDD database, where the sites of experimentally determined ligand and/or macromolecular interactions are annotated. In agreement with earlier investigations, we found that functional site predictions are most successful when overall background sequence conservation is low, such that sites under evolutionary constraint become apparent. In addition, we found that averaging of conservation values across spatially clustered sites improves predictions under certain conditions: that is, when overall conservation is relatively high and when the site in question involves a large macromolecular binding interface. Under these conditions it is better to look for clusters of conserved sites than to look for particular conserved sites.
AU - Panchenko, Anna R
AU - Fyodor Kondrashov
AU - Bryant, Stephen H
ID - 864
IS - 4
JF - Protein Science
TI - Prediction of functional sites by analysis of sequence and structure conservation
VL - 13
ER -
TY - JOUR
AB - Only a fraction of eukaryotic genes affect the phenotype drastically. We compared 18 parameters in 1273 human morbid genes, known to cause diseases, and in the remaining 16 580 unambiguous human genes. Morbid genes evolve more slowly, have wider phylogenetic distributions, are more similar to essential genes of Drosophila melanogaster, code for longer proteins containing more alanine and glycine and less histidine, lysine and methionine, possess larger numbers of longer introns with more accurate splicing signals and have higher and broader expressions. These differences make it possible to classify as non-morbid 34% of human genes with unknown morbidity, when only 5% of known morbid genes are incorrectly classified as non-morbid. This classification can help to identify disease-causing genes among multiple candidates.
AU - Fyodor Kondrashov
AU - Ogurtsov, Aleksey Yu
AU - Kondrashov, Alexey S
ID - 870
IS - 5
JF - Nucleic Acids Research
TI - Bioinformatical assay of human gene morbidity
VL - 32
ER -
TY - JOUR
AB - The dominance of wild-type alleles and the concomitant recessivity of deleterious mutant alleles might have evolved by natural selection or could be a by-product of the molecular and physiological mechanisms of gene action. We compared the properties of human haplosufficient genes, whose wild-type alleles are dominant over loss-of-function alleles, with haploinsufficient (recessive wild-type) genes, which produce an abnormal phenotype when heterozygous for a loss-of-function allele. The fraction of haplosufficient genes is the highest among the genes that encode enzymes, which is best compatible with the physiological theory. Haploinsufficient genes, on average, have more paralogs than haplosufficient genes, supporting the idea that gene dosage could be important for the initial fixation of duplications. Thus, haplo(in)sufficiency of a gene and its propensity for duplication might have a common evolutionary basis.
AU - Fyodor Kondrashov
AU - Koonin, Eugene V
ID - 875
IS - 7
JF - Trends in Genetics
TI - A common framework for understanding the origin of genetic dominance and evolutionary fates of gene duplications
VL - 20
ER -
TY - JOUR
AB - The function of protein and RNA molecules depends on complex epistatic interactions between sites. Therefore, the deleterious effect of a mutation can be suppressed by a compensatory second-site substitution. In relating a list of 86 pathogenic mutations in human IRNAs encoded by mitochondrial genes to the sequences of their mammalian orthologs, we noted that 52 pathogenic mutations were present in normal tRNAs of one or several nonhuman mammals. We found at least five mechanisms of compensation for 32 pathogenic mutations that destroyed a Watson-Crick pair in one of the four tRNA stems: restoration of the affected Watson-Crick interaction (25 cases), strengthening of another pair (4 cases), creation of a new pair (8 cases), changes of multiple interactions in the affected stem (11 cases) and changes involving the interaction between the loop and stem structures (3 cases). A pathogenic mutation and its compensating substitution are fixed in a lineage in rapid succession, and often a compensatory interaction evolves convergently in different clades. At least 10%, and perhaps as many as 50%, of all nucleotide substitutions in evolving mammalian (RNAs participate in such interactions, indicating that the evolution of tRNAs proceeds along highly epistatic fitness ridges.
AU - Kern, Andrew D
AU - Fyodor Kondrashov
ID - 889
IS - 11
JF - Nature Genetics
TI - Mechanisms and convergence of compensatory evolution in mammalian mitochondrial tRNAs
VL - 36
ER -
TY - JOUR
AB - New alleles become fixed owing to random drift of nearly neutral mutations or to positive selection of substantially advantageous mutations. After decades of debate, the fraction of fixations driven by selection remains uncertain. Within 9,390 genes, we analysed 28,196 codons at which rat and mouse differ from each other at two nucleotide sites and 1,982 codons with three differences. At codons where rat-mouse divergence involved two non-synonymous substitutions, both of them occurred in the same lineage, either rat or mouse, in 64% of cases; however, independent substitutions would occur in the same lineage with a probability of only 50%. All three non-synonymous substitutions occurred in the same lineage for 46% of codons, instead of the 25% expected. Furthermore, comparison of 12 pairs of prokaryotic genomes also shows clumping of multiple non-synonymous substitutions in the same lineage. This pattern cannot be explained by correlated mutation or episodes of relaxed negative selection, but instead indicates that positive selection acts at many sites of rapid, successive amino acid replacement.
AU - Bazykin, Georgii A
AU - Fyodor Kondrashov
AU - Ogurtsov, Aleksey Yu
AU - Sunyaev, Shamil R
AU - Kondrashov, Alexey S
ID - 898
IS - 6991
JF - Nature
TI - Positive selection at sites of multiple amino acid replacements since rat-mouse divergence
VL - 429
ER -
TY - JOUR
AB - We compare the functional spectrum of protein evolution in two separate animal lineages with respect to two hypotheses: (1) rates of divergence are distributed similarly among functional classes within both lineages, indicating that selective pressure on the proteome is largely independent of organismic-level biological requirements; and (2) rates of divergence are distributed differently among functional classes within each lineage, indicating species-specific selective regimes impact genome-wide substitutional patterns. Integrating comparative genome sequence with data from tissue-specific expressed-sequence-tag (EST) libraries and detailed database annotations, we find a functional genomic signature of rapid evolution and selective constraint shared between mammalian and nematode lineages despite their extensive morphological and ecological differences and distant common ancestry. In both phyla, we find evidence of accelerated evolution among components of molecular systems involved in coevolutionary change. In mammals, lineage-specific fast evolving genes include those involved in reproduction, immunity, and possibly, maternal-fetal conflict. Likelihood ratio tests provide evidence for positive selection in these rapidly evolving functional categories in mammals. In contrast, slowly evolving genes, in terms of amino acid or insertion/deletion (indel) change, in both phyla are involved in core molecular processes such as transcription, translation, and protein transport. Thus, strong purifying selection appears to act on the same core cellular processes in both mammalian and nematode lineages, whereas positive and/or relaxed selection acts on different biological processes in each lineage.
AU - Castillo-Davis, Cristian I
AU - Fyodor Kondrashov
AU - Hartl, Daniel L
AU - Kulathinal, Rob J
ID - 902
IS - 5
JF - Genome Research
TI - The functional genomic distribution of protein divergence in two animal phyla: Coevolution, genomic conflict, and constraint
VL - 14
ER -
TY - JOUR
AB - We study the space of L2 harmonic forms on complete manifolds with metrics of fibred boundary or fibred cusp type. These metrics generalize the geometric structures at infinity of several different well-known classes of metrics, including asymptotically locally Euclidean manifolds, the (known types of) gravitational instantons, and also Poincaré metrics on ℚ-rank 1 ends of locally symmetric spaces and on the complements of smooth divisors in Kähler manifolds. The answer in all cases is given in terms of intersection cohomology of a stratified compactification of the manifold. The L2 signature formula implied by our result is closely related to the one proved by Dai and more generally by Vaillant and identifies Dai's τ-invariant directly in terms of intersection cohomology of differing perversities. This work is also closely related to a recent paper of Carron and the forthcoming paper of Cheeger and Dai. We apply our results to a number of examples, gravitational instantons among them, arising in predictions about L2 harmonic forms in duality theories in string theory.
AU - Tamas Hausel
AU - Hunsicker, Eugénie
AU - Mazzeo, Rafe R
ID - 1456
IS - 3
JF - Duke Mathematical Journal
TI - Hodge cohomology of gravitational instantons
VL - 122
ER -
TY - JOUR
AB - The moduli space of stable vector bundles on a Riemann surface is smooth when the rank and degree are coprime, and is diffeomorphic to the space of unitary connections of central constant curvature. A classic result of Newstead and Atiyah and Bott asserts that its rational cohomology ring is generated by the universal classes, that is, by the Kunneth components of the Chern classes of the universal bundle.
This paper studies the larger, non-compact moduli space of Higgs bundles, as introduced by Hitchin and Simpson, with values in the canonical bundle K. This is diffeomorphic to the space of all connections of central constant curvature, whether unitary or not. The main result of the paper is that, in the rank 2 case, the rational cohomology ring of this space is again generated by universal classes.
The spaces of Higgs bundles with values in K(n) for n > 0 turn out to be essential to the story. Indeed, we show that their direct limit has the homotopy type of the classifying space of the gauge group, and hence has cohomology generated by universal classes. 2000 Mathematics Subject Classification 14H60 (primary), 14D20, 14H81, 32Q55, 58D27 (secondary).
AU - Tamas Hausel
AU - Thaddeus, Michael
ID - 1464
IS - 3
JF - Proceedings of the London Mathematical Society
TI - Generators for the cohomology ring of the moduli space of rank 2 higgs bundles
VL - 88
ER -
TY - JOUR
AB - The simultaneous multiple volume (SMV) approach in navigator-gated MRI allows the use of the whole motion range or the entire scan time for the reconstruction of final images by simultaneously acquiring different image volumes at different motion states. The motion tolerance range for each volume is kept small, thus SMV substantially increases the scan efficiency of navigator methods while maintaining the effectiveness of motion suppression. This article reports a general implementation of the SMV approach using a multiprocessor scheduling algorithm. Each motion state is regarded as a processor and each volume is regarded as a job. An efficient scheduling that completes all jobs in minimal time is maintained even when the motion pattern changes. Initial experiments demonstrated that SMV significantly increased the scan efficiency of navigatorgated MRI.
AU - Vladimir Kolmogorov
AU - Nguyen, Thành D
AU - Nuval, Anthony
AU - Spincemaille, Pascal
AU - Prince, Martin R
AU - Zabih, Ramin
AU - Wang, Yusu
ID - 3172
IS - 2
JF - Magnetic Resonance in Medicine
TI - Multiprocessor scheduling implementation of the simultaneous multiple volume SMV navigator method
VL - 52
ER -
TY - JOUR
AB - In the last few years, several new algorithms based on graph cuts have been developed to solve energy minimization problems in computer vision. Each of these techniques constructs a graph such that the minimum cut on the graph also minimizes the energy. Yet, because these graph constructions are complex and highly specific to a particular energy function, graph cuts have seen limited application to date. In this paper, we give a characterization of the energy functions that can be minimized by graph cuts. Our results are restricted to functions of binary variables. However, our work generalizes many previous constructions and is easily applicable to vision problems that involve large numbers of labels, such as stereo, motion, image restoration, and scene reconstruction. We give a precise characterization of what energy functions can be minimized using graph cuts, among the energy functions that can be written as a sum of terms containing three or fewer binary variables. We also provide a general-purpose construction to minimize such an energy function. Finally, we give a necessary condition for any energy function of binary variables to be minimized by graph cuts. Researchers who are considering the use of graph cuts to optimize a particular energy function can use our results to determine if this is possible and then follow our construction to create the appropriate graph. A software implementation is freely available.
AU - Vladimir Kolmogorov
AU - Zabih, Ramin
ID - 3173
IS - 2
JF - IEEE Transactions on Pattern Analysis and Machine Intelligence
TI - What energy functions can be minimized via graph cuts?
VL - 26
ER -
TY - CONF
AB - Feature space clustering is a popular approach to image segmentation, in which a feature vector of local properties (such as intensity, texture or motion) is computed at each pixel. The feature space is then clustered, and each pixel is labeled with the cluster that contains its feature vector. A major limitation of this approach is that feature space clusters generally lack spatial coherence (i.e., they do not correspond to a compact grouping of pixels). In this paper, we propose a segmentation algorithm that operates simultaneously in feature space and in image space. We define an energy function over both a set of clusters and a labeling of pixels with clusters. In our framework, a pixel is labeled with a single cluster (rather than, for example, a distribution over clusters). Our energy function penalizes clusters that are a poor fit to the data in feature space, and also penalizes clusters whose pixels lack spatial coherence. The energy function can be efficiently minimized using graph cuts. Our algorithm can incorporate both parametric and non-parametric clustering methods. It can be applied to many optimization-based clustering methods, including k-means and k-medians, and can handle models which are very close in feature space. Preliminary results are presented on segmenting real and synthetic images, using both parametric and non-parametric clustering.
AU - Zabih, Ramin
AU - Vladimir Kolmogorov
ID - 3177
TI - Spatially coherent clustering using graph cuts
VL - 2
ER -
TY - JOUR
AB - Minimum cut/maximum flow algorithms on graphs have emerged as an increasingly useful tool for exactor approximate energy minimization in low-level vision. The combinatorial optimization literature provides many min-cut/max-flow algorithms with different polynomial time complexity. Their practical efficiency, however, has to date been studied mainly outside the scope of computer vision. The goal of this paper is to provide an experimental comparison of the efficiency of min-cut/max flow algorithms for applications in vision. We compare the running times of several standard algorithms, as well as a new algorithm that we have recently developed. The algorithms we study include both Goldberg-Tarjan style "push -relabel" methods and algorithms based on Ford-Fulkerson style "augmenting paths." We benchmark these algorithms on a number of typical graphs in the contexts of image restoration, stereo, and segmentation. In many cases, our new algorithm works several times faster than any of the other methods, making near real-time performance possible. An implementation of our max-flow/min-cut algorithm is available upon request for research purposes.
AU - Boykov, Yuri
AU - Vladimir Kolmogorov
ID - 3178
IS - 9
JF - IEEE Transactions on Pattern Analysis and Machine Intelligence
TI - An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision
VL - 26
ER -
TY - CONF
AB - The problem of efficient, interactive foreground/background segmentation in still images is of great practical importance in image editing. Classical image segmentation tools use either texture (colour) information, e.g. Magic Wand, or edge (contrast) information, e.g. Intelligent Scissors. Recently, an approach based on optimization by graph-cut has been developed which successfully combines both types of information. In this paper we extend the graph-cut approach in three respects. First, we have developed a more powerful, iterative version of the optimisation. Secondly, the power of the iterative algorithm is used to simplify substantially the user interaction needed for a given quality of result. Thirdly, a robust algorithm for "border matting" has been developed to estimate simultaneously the alpha-matte around an object boundary and the colours of foreground pixels. We show that for moderately difficult examples the proposed method outperforms competitive tools.
AU - Rother, Carsten
AU - Vladimir Kolmogorov
AU - Blake, Andrew
ID - 3179
IS - 3
TI - "GrabCut" - Interactive foreground extraction using iterated graph cuts
VL - 23
ER -
TY - CONF
AB - A new technique for proving the adaptive indistinguishability of two systems, each composed of some component systems, is presented, using only the fact that corresponding component systems are non-adaptively indistinguishable. The main tool is the definition of a special monotone condition for a random system F, relative to another random system G, whose probability of occurring for a given distinguisher D is closely related to the distinguishing advantage ε of D for F and G, namely it is lower and upper bounded by ε and (1+ln1), respectively.
A concrete instantiation of this result shows that the cascade of two random permutations (with the second one inverted) is indistinguishable from a uniform random permutation by adaptive distinguishers which may query the system from both sides, assuming the components’ security only against non-adaptive one-sided distinguishers.
As applications we provide some results in various fields as almost k-wise independent probability spaces, decorrelation theory and computational indistinguishability (i.e., pseudo-randomness).
AU - Maurer, Ueli M
AU - Krzysztof Pietrzak
ID - 3208
TI - Composition of random systems: When two weak make one strong
VL - 2951
ER -
TY - JOUR
AB - The folding and stability of transmembrane proteins is a fundamental and unsolved biological problem. Here, single bacteriorhodopsin molecules were mechanically unfolded from native purple membranes using atomic force microscopy and force spectroscopy. The energy landscape of individual transmembrane α helices and polypeptide loops was mapped by monitoring the pulling speed dependence of the unfolding forces and applying Monte Carlo simulations. Single helices formed independently stable units stabilized by a single potential barrier. Mechanical unfolding of the helices was triggered by 3.9–7.7 Å extension, while natural unfolding rates were of the order of 10−3 s−1. Besides acting as individually stable units, helices associated pairwise, establishing a collective potential barrier. The unfolding pathways of individual proteins reflect distinct pulling speed-dependent unfolding routes in their energy landscapes. These observations support the two-stage model of membrane protein folding in which α helices insert into the membrane as stable units and then assemble into the functional protein.
AU - Harald Janovjak
AU - Struckmeier, Jens
AU - Hubain, Maurice
AU - Kessler, Max
AU - Kedrov, Alexej
AU - Mueller, Daniel J
ID - 3419
IS - 5
JF - Structure
TI - Probing the energy landscape of the membrane protein bacteriorhodopsin
VL - 12
ER -
TY - JOUR
AB - Single-molecule force-spectroscopy was employed to unfold and refold single sodium-proton antiporters (NhaA) of Escherichia coli from membrane patches. Although transmembrane α-helices and extracellular polypeptide loops exhibited sufficient stability to individually establish potential barriers against unfolding, two helices predominantly unfolded pairwise, thereby acting as one structural unit. Many of the potential barriers were detected unfolding NhaA either from the C-terminal or the N-terminal end. It was found that some molecular interactions stabilizing secondary structural elements were directional, while others were not. Additionally, some interactions appeared to occur between the secondary structural elements. After unfolding ten of the 12 helices, the extracted polypeptide was allowed to refold back into the membrane. After five seconds, the refolded polypeptide established all secondary structure elements of the native protein. One helical pair showed a characteristic spring like “snap in” into its folded conformation, while the refolding process of other helices was not detected in particular. Additionally, individual helices required characteristic periods of time to fold. Correlating these results with the primary structure of NhaA allowed us to obtain the first insights into how potential barriers establish and determine the folding kinetics of the secondary structure elements.
AU - Kedrov, Alexej
AU - Ziegler, Christine
AU - Harald Janovjak
AU - Kühlbrandt, Werner
AU - Mueller, Daniel J
ID - 3420
IS - 5
JF - Journal of Molecular Biology
TI - Controlled unfolding and refolding of a single sodium/proton antiporter using atomic force microscopy
VL - 340
ER -
TY - CHAP
AU - Herbert Edelsbrunner
ID - 3574
T2 - Handbook of Discrete and Computational Geometry
TI - Biological applications of computational topology
ER -
TY - CHAP
AB - The Jacobi set of two Morse functions defined on a common - manifold is the set of critical points of the restrictions of one func- tion to the level sets of the other function. Equivalently, it is the set of points where the gradients of the functions are parallel. For a generic pair of Morse functions, the Jacobi set is a smoothly embed- ded 1-manifold. We give a polynomial-time algorithm that com- putes the piecewise linear analog of the Jacobi set for functions specified at the vertices of a triangulation, and we generalize all results to more than two but at most Morse functions.
AU - Herbert Edelsbrunner
AU - Harer, John
ID - 3575
T2 - Foundations of Computational Mathematics
TI - Jacobi sets of multiple Morse functions
VL - 312
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 -