We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Bose-Einstein condensation in a gas of sodium atoms

IA Basic Concepts.- 1 The Importance of Hydrogen Bonds.- 1.1 Historical Perspective.- 1.2 The Importance of Hydrogen Bonds in Biological Structure and Function.- 1.3 The Role of the Water Molecules.- 1.4 Significance of Small Molecule Crystal Structural Studies.- 1.5 The Structural Approach.- 2 Definitions and Concepts.- 2.1 Definition of the Hydrogen Bond - Strong and Weak Bonds.- 2.2 Hydrogen-Bond Configurations: Two- and Three-Center Hydrogen Bonds Bifurcated and Tandem Bonds.- 2.3 Hydrogen Bonds Are Very Different from Covalent Bonds.- 2.4 The van der Waals Radii Cut-Off Criterion Is Not Useful.- 2.5 The Concept of the Hydrogen-Bond Structure.- 2.6 The Importance of ? and ? Cooperativity.- 2.7 Homo-, Anti- and Heterodromic Patterns.- 2.8 Hydrogen Bond Flip-Flop Disorder: Conformational and Configurational.- 2.9 Proton-Deficient Hydrogen Bonds.- 2.10 The Excluded Region.- 2.11 The Hydrophobic Effect.- 3 Experimental Studies of Hydrogen Bonding.- 3.1 Infrared Spectroscopy and Gas Electron Diffraction.- 3.2 X-Ray and Neutron Crystal Structure Analysis.- 3.3 Treatment of Hydrogen Atoms in Neutron Diffraction Studies.- 3.4 Charge Density and Hydrogen-Bond Energies.- 3.5 Neutron Powder Diffraction.- 3.6 Solid State NMR Spectroscopy.- 4 Theoretical Calculations of Hydrogen-Bond Geometries.- 4.1 Calculating Hydrogen-Bond Geometries.- 4.2 Ab-Initio Molecular Orbital Methods.- 4.3 Application to Hydrogen-Bonded Complexes.- 4.4 Semi-Empirical Molecular Orbital Methods.- 4.5 Empirical Force Field or Molecular Mechanics Methods.- 5 Effect of Hydrogen Bonding on Molecular Structure.- IB Hydrogen-Bond Geometry.- 6 The Importance of Small Molecule Structural Studies.- 6.1 Problems Associated with the Hydrogen-Bond Geometry.- 6.2 The Hydrogen Bond Can Be Described Statistically.- 6.3 The Problems of Measuring Hydrogen-Bond Lengths and Angles in Small Molecule Crystal Structures.- 7 Metrical Aspects of Two-Center Hydrogen Bonds.- 7.1 The Metrical Properties of O-H *** O Hydrogen Bonds.- 7.1.1 Very Strong and Strong OH *** O Hydrogen Bonds Occur with Oxyanions, Acid Salts, Acid Hydrates, and Carboxylic Acids.- 7.1.2 OH *** O Hydrogen Bonds in the Ices and High Hydrates.- 7.1.3 Carbohydrates Provide the Best Data for OH ... O Hydrogen Bonds: Evidence for the Cooperative Effect.- 7.2 N-H *** O Hydrogen Bonds.- 7.3 N-H *** N Hydrogen Bonds.- 7.4 O-H *** N Hydrogen Bonds.- 7.5 Sequences in Lengths of Two-Center Hydrogen Bonds.- 7.6 H/D Isotope Effect.- 8 Metrical Aspects of Three- and Four-Center Hydrogen Bonds.- 8.1 Three-Center Hydrogen Bonds.- 8.2 Four-Center Hydrogen Bonds.- 9 Intramolecular Hydrogen Bonds.- 10 Weak Hydrogen-Bonding Interactions Formed by C-H Groups as Donors and Aromatic Rings as Acceptors.- 11 Halides and Halogen Atoms as Hydrogen-Bond Acceptors.- 12 Hydrogen-Bond Acceptor Geometries.- II Hydrogen Bonding in Small Biological Molecules.- 13 Hydrogen Bonding in Carbohydrates.- 13.1 Sugar Alcohols (Alditols) as Model Cooperative Hydrogen-Bonded Structures.- 13.2 Influence of Hydrogen Bonding on Configuration and Conformation in Cyclic Monosaccharides.- 13.3 Rules to Describe Hydrogen-Bonding Patterns in Monosaccharides.- 13.4 The Water Molecules Link Hydrogen-Bond Chains into Nets in the Hydrated Monosaccharide Crystal Structures.- 13.5 The Disaccharide Crystal Structures Provide an Important Source of Data About Hydrogen-Bonding Patterns in Polysaccharides.- 13.6 Hydrogen Bonding in the Tri- and Tetrasaccharides Is More Complex and Less Well Defined.- 13.7 The Hydrogen Bonding in Polysaccharide Fiber Structures Is Poorly Defined.- 14 Hydrogen Bonding in Amino Acids and Peptides: Predominance of Zwitterions.- 15 Purines and Pyrimidines.- 15.1 Bases Are Planar and Each Contains Several Different Hydrogen-Bonding Donor and Acceptor Groups.- 15.2 Many Tautomeric Forms Are Feasible But Not Observed.- 15.3 ?-Bond Cooperativity Enhances Hydrogen-Bonding Forces.- 15.4 General, Non-Base-Pairing Hydrogen Bonds.- 16 Base Pairing in the Purine and Pyrimidine Crystal Structures.- 16.1 Base-Pair Configurations with Purine and Pyrimidine Homo-Association.- 16.2 Base-Pair Configurations with Purine-Pyrimidine Hetero-Association: the Watson-Crick Base-Pairs.- 16.3 Base Pairs Can Combine to Form Triplets and Quadruplets.- 17 Hydrogen Bonding in the Crystal Structures of the Nucleosides and Nucleotides.- 17.1 Conformational and Hydrogen-Bonding Characteristics of the Nucleosides and Nucleotides.- 17.2 A Selection of Cyclic Hydrogen-Bonding Patterns Formed in Nucleoside and Nucleotide Crystal Structures.- 17.3 General Hydrogen-Bonding Patterns in Nucleoside and Nucleotide Crystal Structures.- III Hydrogen Bonding in Biological Macromolecules.- 18 O-H *** O Hydrogen Bonding in Crystal Structures of Cyclic and Linear Oligoamyloses: Cyclodextrins, Maltotriose, and Maltohexaose.- 18.1 The Cyclodextrins and Their Inclusion Complexes.- 18.2 Crystal Packing Patterns of Cyclodextrins Are Determined by Hydrogen Bonding.- 18.3 Cyclodextrins as Model Compounds to Study Hydrogen-Bonding Networks.- 18.4 Cooperative, Homodromic, and Antidromic Hydrogen-Bonding Patterns in the ?-Cyclodextrin Hydrates.- 18.5 Homodromic and Antidromic O-H *** O Hydrogen-Bonding Systems Analyzed Theoretically.- 18.6 Intramolecular Hydrogen Bonds in the ?-Cyclodextrin Molecule are Variable - the Induced-Fit Hypothesis.- 18.7 Flip-Flop Hydrogen Bonds in ?-Cyclodextrin * 11 H2O.- 18.8 From Flip-Flop Disorder to Ordered Homodromic Arrangements at Low lbmperature: The Importance of the Cooperative Effect.- 18.9 Maltohexaose Polyiodide and Maltotriose - Double and Single Left-Handed Helices With and Without Intramolecular O(2) *** O(3?) Hydrogen Bonds.- 19 Hydrogen Bonding in Proteins.- 19.1 Geometry of Secondary-Structure Elements: Helix, Pleated Sheet, and Turn.- 19.2 Hydrogen-Bond Analysis in Protein Crystal Structures.- 19.3 Hydrogen-Bonding Patterns in the Secondary Structure Elements.- 19.4 Hydrogen-Bonding Patterns Involving Side-Chains.- 19.5 Internal Water Molecules as Integral Part of Protein Structures.- 19.6 Metrical Analysis of Hydrogen Bonds in Proteins.- 19.7 Nonsecondary-Structure Hydrogen-Bond Geometry Between Main-Chains, Side-Chains and Water Molecules.- 19.8 Three-Center (Bifurcated) Bonds in Proteins.- 19.9 Neutron Diffraction Studies on Proteins Give Insight into Local Hydrogen-Bonding Flexibility.- 19.10 Site-Directed Mutagenesis Gives New Insight into Protein Thermal Stability and Strength of Hydrogen Bonds.- 20 The Role of Hydrogen Bonding in the Structure and Function of the Nucleic Acids.- 20.1 Hydrogen Bonding in Nucleic Acids is Essential for Life.- 20.2 The Structure of DNA and RNA Double Helices is Determined by Watson-Crick Base-Pair Geometry.- 20.3 Systematic and Accidental Base-Pair Mismatches: "Wobbling" and Mutations.- 20.4 Noncomplementary Base Pairs Have a Structural Role in tRNA.- 20.5 Homopolynucleotide Complexes Are Stabilized by a Variety of Base-Base Hydrogen Bonds - Three-Center (Bifurcated) Hydrogen Bonds in A-Tracts.- 20.6 Specific Protein-Nucleic Acid Recognition Involves Hydrogen Bonding.- IV Hydrogen Bonding by the Water Molecule.- 21 Hydrogen-Bonding Patterns in Water, Ices, the Hydrate Inclusion Compounds, and the Hydrate Layer Structures.- 21.1 Liquid Water and the Ices.- 21.2 The Hydrate Inclusion Compounds.- 21.3 Hydrate Layer Structures.- 22 Hydrates of Small Biological Molecules: Carbohydrates, Amino Acids, Peptides, Purines, Pyrimidines, Nucleosides and Nucleotides.- 23 Hydration of Proteins.- 23.1 Characterization of "Bound Water" at Protein Surfaces - the First Hydration Shell.- 23.2 Sites of Hydration in Proteins.- 23.3 Metrics of Water Hydrogen Bonding to Proteins.- 23.4 Ordered Water Molecules at Protein Surfaces - Clusters and Pentagons.- 24 Hydration of Nucleic Acids.- 24.1 Two Water Layers Around the DNA Double Helix.- 24.2 Crystallographically Determined Hydration Sites in A-, B-, Z-DNA. A Statistical Analysis.- 24.3 Hydration Motifs in Double Helical Nucleic Acids.- 24.3.1 Sequence-Independent Motifs.- 24.3.2 Sequence-Dependent Motifs.- 24.4 DNA Hydration and Structural Transitions Are Correlated: Some Hypotheses.- 25 The Role of Three-Center Hydrogen Bonds in the Dynamics of Hydration and of Structure Transition.- References.- Refcodes.

Hydrogen Bonding in Biological Structures

Hypoxia is a feature of most tumours, albeit with variable incidence and severity within a given patient population. It is a negative prognostic and predictive factor owing to its multiple contributions to chemoresistance, radioresistance, angiogenesis, vasculogenesis, invasiveness, metastasis, resistance to cell death, altered metabolism and genomic instability. Given its central role in tumour progression and resistance to therapy, tumour hypoxia might well be considered the best validated target that has yet to be exploited in oncology. However, despite an explosion of information on hypoxia, there are still major questions to be addressed if the long-standing goal of exploiting tumour hypoxia is to be realized. Here, we review the two main approaches, namely bioreductive prodrugs and inhibitors of molecular targets upon which hypoxic cell survival depends. We address the particular challenges and opportunities these overlapping strategies present, and discuss the central importance of emerging diagnostic tools for patient stratification in targeting hypoxia.

Targeting hypoxia in cancer therapy

Hepatocyte growth factor/scatter factor and its receptor, the tyrosine kinase Met, arose late in evolution and are unique to vertebrates In spite of this, Met uses molecules such as Gab1 — homologues of which are present in Caenorhabditis elegans and Drosophila melanogaster — for downstream signalling Pivotal roles for Met in development and cancer have been established: Met controls cell migration and growth in embryogenesis; it also controls growth, invasion and metastasis in cancer cells; and activating Met mutations predispose to human cancer

Met, metastasis, motility and more

A Generalized Born (GB) model, describing the mean-field electrostatic energy of a molecular system in a continuous, polarizable solvent environment, is compared with Kirkwood and Poisson-Boltzmann (PB) standard approaches. GB energy data for amino acids, a dodecapeptide, and three protein molecules are validated against the corresponding PB numerical results. A new approximation for the Born radii, dependent on the geometry of the system, as well as on the ratio of the solute and solvent dielectric constants, is proposed. The refined GB approach also takes into account the ionic strength. The most important discrepancies between the GB and PB results for proteins are identified and interpreted. A more precise procedure for computing the GB energy is proposed.

Generalized Born model: Analysis, refinement, and applications to proteins

Purpose: Since 2-deoxy-D-glucose (2-DG) is currently in phase I clinical trials to selectively target slow-growing hypoxic tumor cells, 2-halogenated D-glucose analogs were synthesized for improved activity. Given the fact that 2-DG competes with D-glucose for binding to hexokinase, in silico modeling of molecular interactions between hexokinase I and these new analogs was used to determine whether binding energies correlate with biological effects, i.e. inhibition of glycolysis and subsequent toxicity in hypoxic tumor cells. Methods and Results: Using a QSAR-like approach along with a flexible docking strategy, it was determined that the binding affinities of the analogs to hexokinase I decrease as a function of increasing halogen size as follows: 2-fluoro-2-deoxy-D-glucose (2-FG) > 2-chloro-2-deoxy-D-glucose (2-CG) > 2-bromo-2-deoxy-D-glucose (2-BG). Furthermore, D-glucose was found to have the highest affinity followed by 2-FG and 2-DG, respectively. Similarly, flow cytometry and trypan blue exclusion assays showed that the efficacy of the halogenated analogs in preferentially inhibiting growth and killing hypoxic vs. aerobic cells increases as a function of their relative binding affinities. These results correlate with the inhibition of glycolysis as measured by lactate inhibition, i.e. ID50 1 mM for 2-FG, 6 mM for 2-CG and > 6 mM for 2-BG. Moreover, 2-FG was found to be more potent than 2-DG for both glycolytic inhibition and cytotoxicity. Conclusions: Overall, our in vitro results suggest that 2-FG is more potent than 2-DG in killing hypoxic tumor cells, and therefore may be more clinically effective when combined with standard chemotherapeutic protocols.

Efficacy of 2-halogen substituted d-glucose analogs in blocking glycolysis and killing “hypoxic tumor cells”

Dipole moments of 2,4-diketopyrimidines. II. Uracil, thymine and their derivatives.

We present a detailed comparison of the efficiency and accuracy of the second‐ and third‐order split operator methods, a time dependent modified Cayley method, and the Chebychev polynomial expansion method for solving the time dependent Schrodinger equation in the one‐dimensional double well potential energy function. We also examine the efficiency and accuracy of the split operator and modified Cayley methods for the imaginary time propagation.

/pdf/a-comparative-study-of-time-dependent-quantum-mechanical-32whb6sdqh.pdf

Bogdan Lesyng

Papers

Generalized Born model: Analysis, refinement, and applications to proteins

Efficacy of 2-halogen substituted d-glucose analogs in blocking glycolysis and killing “hypoxic tumor cells”

Dipole moments of 2,4-diketopyrimidines. II. Uracil, thymine and their derivatives.

A comparative study of time dependent quantum mechanical wave packet evolution methods

Ab initio study of proton transfer in [H3N−H−NH3]+ and [H3N−H−OH2]+