97 research outputs found
The stable set polytope of claw-free graphs with stability number at least four. I. Fuzzy antihat graphs are W-perfect
Abstract Fuzzy antihat graphs are graphs obtained as 2-clique-bond compositions of fuzzy line graphs with three different types of three-cliqued graphs. By the decomposition theorem of Chudnovsky and Seymour [2] , fuzzy antihat graphs form a large subclass of claw-free, not quasi-line graphs with stability number at least four and with no 1-joins. A graph is W -perfect if its stable set polytope is described by: nonnegativity, rank, and lifted 5-wheel inequalities. By exploiting the polyhedral properties of the 2-clique-bond composition, we prove that fuzzy antihat graphs are W -perfect and we move a crucial step towards the solution of the longstanding open question of finding an explicit linear description of the stable set polytope of claw-free graphs
Euclidean distance geometry and applications
Euclidean distance geometry is the study of Euclidean geometry based on the
concept of distance. This is useful in several applications where the input
data consists of an incomplete set of distances, and the output is a set of
points in Euclidean space that realizes the given distances. We survey some of
the theory of Euclidean distance geometry and some of the most important
applications: molecular conformation, localization of sensor networks and
statics.Comment: 64 pages, 21 figure
Two essays in computational optimization: computing the clar number in fullerene graphs and distributing the errors in iterative interior point methods
Fullerene are cage-like hollow carbon molecules graph of pseudospherical sym-
metry consisting of only pentagons and hexagons faces. It has been the object
of interest for chemists and mathematicians due to its widespread application
in various fields, namely including electronic and optic engineering, medical sci-
ence and biotechnology. A Fullerene molecular, Γ n of n atoms has a multiplicity
of isomers which increases as N iso ∼ O(n 9 ). For instance, Γ 180 has 79,538,751
isomers. The Fries and Clar numbers are stability predictors of a Fullerene
molecule. These number can be computed by solving a (possibly N P -hard)
combinatorial optimization problem. We propose several ILP formulation of
such a problem each yielding a solution algorithm that provides the exact value
of the Fries and Clar numbers. We compare the performances of the algorithm
derived from the proposed ILP formulations. One of this algorithm is used to
find the Clar isomers, i.e., those for which the Clar number is maximum among
all isomers having a given size. We repeated this computational experiment for
all sizes up to 204 atoms. In the course of the study a total of 2 649 413 774
isomers were analyzed.The second essay concerns developing an iterative primal dual infeasible path
following (PDIPF) interior point (IP) algorithm for separable convex quadratic
minimum cost flow network problem. In each iteration of PDIPF algorithm, the
main computational effort is solving the underlying Newton search direction
system. We concentrated on finding the solution of the corresponding linear
system iteratively and inexactly. We assumed that all the involved inequalities
can be solved inexactly and to this purpose, we focused on different approaches
for distributing the error generated by iterative linear solvers such that the
convergences of the PDIPF algorithm are guaranteed. As a result, we achieved
theoretical bases that open the path to further interesting practical investiga-
tion
Investigating the Specificity of Coiled-Coil Recognition
The bZIP transcription factors make up a family of long α-helical proteins that dimerize based on a pattern of hydrophobic residues and bind to DNA through a region of basic residues. Because binding specificity is a particular topic of interest, the dimerization interaction is attractive as a possible candidate to better understand protein quaternary structure. Use of the Knob-Socket (KS) model for determination of packing structure provides a novel approach to analyze protein-protein interactions. A KS analysis of the protein-protein interface provides unique insight into the specificity of the classical leucine zipper pseudo-7mer repeat. From an analysis of the KS packing maps, this research provides evidence of a general framework for defining the specificity between coiled-coils. The KS maps show how hydrophobic specificity is defined in the coiled-coil interface, where knobs are centralized in the middle of the socket packing, while the peripheral socket residues are hydrophilic. Based on this KS analysis, the KS model will be used to design proteins that mimic the leucine zipper region of bZIP proteins. The proteins will be purified into E. coli and its 2º structure will be confirmed through circular dichroism. Binding specificity will be studied through mutations of the designed proteins and compared using the BACTH (bacterial adenylate cyclase two-hybrid) system
Rational Design of Peptide Ligands Based on Knob−Socket Protein Packing Model Using CD13 as a Prototype Receptor
Structure-based computational peptide design methods have gained significant interest in recent years owing to the availability of structural insights into protein–protein interactions obtained from the crystal structures. The majority of these approaches design new peptide ligands by connecting the crucial amino acid residues from the protein interface and are generally not based on any predicted receptor–ligand interaction. In this work, a peptide design method based on the Knob–Socket model was used to identify the specific ligand residues packed into the receptor interface. This method enables peptide ligands to be designed rationally by predicting amino acid residues that will fit best at the binding site of the receptor protein. In this, specific peptide ligands were designed for the model receptor CD13, overexpression of which has been observed in several cancer types. From the initial library of designed peptides, three potential candidates were selected based on simulated energies in the CD13 binding site using the programs molecular operating environment and AutoDock Vina. In the CD13 enzymatic activity inhibition assay, the three identified peptides exhibited 2.7–7.4 times lower IC50 values (GYPAY, 227 μM; GFPAY, 463 μM; GYPAVYLF, 170 μM) as compared to the known peptide ligand CNGRC (C1–C5) (1260 μM). The apparent binding affinities of the peptides (GYPAY, Ki = 54.0 μM; GFPAY, Ki = 74.3 μM; GYPAVYLF, Ki = 38.8 μM) were 10–20 times higher than that of CNGRC (C1–C5) (Ki = 773 μM). The double reciprocal plots from the steady-state enzyme kinetic assays confirmed the binding of the peptides to the intended active site of CD13. The cell binding and confocal microscopy assays showed that the designed peptides selectively bind to the CD13 on the cell surface. Our study demonstrates the feasibility of a Knob–Socket-based rational design of novel peptide ligands in improving the identification of specific binding versus current more labor-intensive methods
Efficient Algorithms for Graph Optimization Problems
A doktori értekezés hatékony algoritmusokat mutat be gráfokon értelmezett nehéz kombinatorikus optimalizálási feladatok megoldására. A kutatás legfontosabb eredményét különböző megoldási módszerekhez kidolgozott javítások jelentik, amelyek magukban foglalnak új heurisztikákat, valamint gráfok és fák speciális reprezentációit is. Az elvégzett elemzések igazolták, hogy a szerző által adott leghatékonyabb algoritmusok az esetek többségében gyorsabbak, illetve jobb eredményeket adnak, mint más elérhető implementációk. A dolgozat első fele hét különböző algoritmust és számos hasznos javítást mutat be a minimális költségű folyam feladatra, amely a legtöbbet vizsgált és alkalmazott gráfoptimalizálási problémák egyike. Az implementációinkat egy átfogó tapasztalati elemzés keretében összehasonlítottuk nyolc másik megoldóprogrammal, köztük a leggyakrabban használt és legelismertebb implementációkkal. A hálózati szimplex algoritmusunk lényegesen hatékonyabbnak és robusztusabbnak bizonyult, mint a módszer más implementációi, továbbá a legtöbb tesztadaton ez az algoritmus a leggyorsabb. A bemutatott költségskálázó algoritmus szintén rendkívül hatékony; nagy méretű ritka gráfokon felülmúlja a hálózati szimplex implementációkat. Az értekezésben tárgyalt másik optimalizálási feladat a legnagyobb közös részgráf probléma. Ezt a feladatot kémiai alkalmazások szempontjából vizsgáltuk. Hatékony heurisztikákat dolgoztunk ki, amelyek jelentősen javítják két megoldási módszer pontosságát és sebességét, valamint kémiailag relevánsabb módon rendelik egymáshoz molekulagráfok atomjait és kötéseit. Az algoritmusainkat összehasonlítottuk két ismert megoldóprogrammal, amelyeknél lényegesen jobb eredményeket sikerült elérnünk. A kifejlesztett implementációk bekerültek a ChemAxon Kft. több szoftvertermékébe, melyek vezető nemzetközi gyógyszercégek használatában állnak. Ezen kívül az értekezés röviden bemutatja a LEMON nevű nyílt forrású C++ gráfoptimalizációs programkönyvtárat, amely magában foglalja a minimális költségű folyam feladatra adott algoritmusokat. Ezek az implementációk nagy mértékben hozzájárultak a programcsomag népszerűségének növekedéséhez
Supersymmetry on the lattice: Geometry, Topology, and Spin Liquids
In quantum mechanics, supersymmetry (SUSY) posits an equivalence between two
elementary degrees of freedom, bosons and fermions. Here we show how this
fundamental concept can be applied to connect bosonic and fermionic lattice
models in the realm of condensed matter physics, e.g., to identify a variety of
(bosonic) phonon and magnon lattice models which admit topologically nontrivial
free fermion models as superpartners. At the single-particle level, the bosonic
and the fermionic models that are generated by the SUSY are isospectral except
for zero modes, such as flat bands, whose existence is undergirded by the
Witten index of the SUSY theory. We develop a unifying framework to formulate
these SUSY connections in terms of general lattice graph correspondences and
discuss further ramifications such as the definition of supersymmetric
topological invariants for generic bosonic systems. Notably, a Hermitian form
of the supercharge operator, the generator of the SUSY, can itself be
interpreted as a hopping Hamiltonian on a bipartite lattice. This allows us to
identify a wide class of interconnected lattices whose tight-binding
Hamiltonians are superpartners of one another or can be derived via squaring or
square-rooting their energy spectra all the while preserving band topology
features. We introduce a five-fold way symmetry classification scheme of these
SUSY lattice correspondences, including cases with a non-zero Witten index,
based on a topological classification of the underlying Hermitian supercharge
operator. These concepts are illustrated for various explicit examples
including frustrated magnets, Kitaev spin liquids, and topological
superconductors.Comment: 37 pages, 27 figure
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Predicting multibody assembly of proteins
textThis thesis addresses the multi-body assembly (MBA) problem in the context of protein assemblies. [...] In this thesis, we chose the protein assembly domain because accurate and reliable computational modeling, simulation and prediction of such assemblies would clearly accelerate discoveries in understanding of the complexities of metabolic pathways, identifying the molecular basis for normal health and diseases, and in the designing of new drugs and other therapeutics. [...] [We developed] F²Dock (Fast Fourier Docking) which includes a multi-term function which includes both a statistical thermodynamic approximation of molecular free energy as well as several of knowledge-based terms. Parameters of the scoring model were learned based on a large set of positive/negative examples, and when tested on 176 protein complexes of various types, showed excellent accuracy in ranking correct configurations higher (F² Dock ranks the correcti solution as the top ranked one in 22/176 cases, which is better than other unsupervised prediction software on the same benchmark). Most of the protein-protein interaction scoring terms can be expressed as integrals over the occupied volume, boundary, or a set of discrete points (atom locations), of distance dependent decaying kernels. We developed a dynamic adaptive grid (DAG) data structure which computes smooth surface and volumetric representations of a protein complex in O(m log m) time, where m is the number of atoms assuming that the smallest feature size h is [theta](r[subscript max]) where r[subscript max] is the radius of the largest atom; updates in O(log m) time; and uses O(m)memory. We also developed the dynamic packing grids (DPG) data structure which supports quasi-constant time updates (O(log w)) and spherical neighborhood queries (O(log log w)), where w is the word-size in the RAM. DPG and DAG together results in O(k) time approximation of scoring terms where k << m is the size of the contact region between proteins. [...] [W]e consider the symmetric spherical shell assembly case, where multiple copies of identical proteins tile the surface of a sphere. Though this is a restricted subclass of MBA, it is an important one since it would accelerate development of drugs and antibodies to prevent viruses from forming capsids, which have such spherical symmetry in nature. We proved that it is possible to characterize the space of possible symmetric spherical layouts using a small number of representative local arrangements (called tiles), and their global configurations (tiling). We further show that the tilings, and the mapping of proteins to tilings on arbitrary sized shells is parameterized by 3 discrete parameters and 6 continuous degrees of freedom; and the 3 discrete DOF can be restricted to a constant number of cases if the size of the shell is known (in terms of the number of protein n). We also consider the case where a coarse model of the whole complex of proteins are available. We show that even when such coarse models do not show atomic positions, they can be sufficient to identify a general location for each protein and its neighbors, and thereby restricts the configurational space. We developed an iterative refinement search protocol that leverages such multi-resolution structural data to predict accurate high resolution model of protein complexes, and successfully applied the protocol to model gp120, a protein on the spike of HIV and currently the most feasible target for anti-HIV drug design.Computer Science
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