Emili Besalú

A general survey of molecular quantum similarity

Abstract A comprehensive survey of the theoretical foundations and definitions associated with quantum similarity is given. In this task care has been taken to determine the primary mathematical structure which can be associated with quantum similarity measures. Due to this, the concept of a tagged set is defined to demonstrate how molecular sets can be described systematically. The definition of quantum object, a notion introduced by our laboratory and employed for a long time in quantum similarity studies, is clarified by means of a blend involving quantum theory and the tagged set structure formalism, and used afterwards as the cornerstone of the subsequent development of the theory. In the definition of quantum objects, density functions play a fundamental role. To formally construct the quantum similarity measure, it is very interesting to study the main algorithmic ideas, which may serve to compute approximate density forms, accurate enough to be employed in the practical calculation of nuclear, atomic and molecular quantum similarity measures. Thus, the atomic shell approximation is defined accompanied by all the implied computational constraints and the consequences they have in the whole theory development as well as to the physical interpretation of the results. A wide and complex field appears from all these ideas, where convex sets play a fundamental role, and a new definition emerges: one associated with vector semispaces, where the main numerical formalism of quantum similarity seems perfectly adapted. Applications of this development embrace quantum taxonomy, visual representation of molecular sets, QSAR and QSPR, topological indices, molecular alignment, etc., and among this range of procedures and fields, there appears with distinct importance the discrete representation of molecular structures.

A library of linear undecapeptides with bactericidal activity against phytopathogenic bacteria

A 125-member library of synthetic linear undecapeptides was prepared based on a previously described peptide H-K(1)KLFKKILKF(10)L-NH(2) (BP76) that inhibited in vitro growth of the plant pathogenic bacteria Erwinia amylovora, Xanthomonas axonopodis pv. vesicatoria, and Pseudomonas syringae pv. syringae at low micromolar concentrations. Peptides were designed using a combinatorial chemistry approach by incorporating amino acids possessing various degrees of hydrophobicity and hydrophilicity at positions 1 and 10 and by varying the N-terminus. Library screening for in vitro growth inhibition identified 27, 40 and 113 sequences with MIC values below 7.5 microM against E. amylovora, P. syringae and X. axonopodis, respectively. Cytotoxicity, bactericidal activity and stability towards protease degradation of the most active peptides were also determined. Seven peptides with a good balance between antibacterial and hemolytic activities were identified. Several analogues displayed a bactericidal effect and low susceptibility to protease degradation. The most promising peptides were tested in vivo by evaluating their preventive effect of inhibition of E. amylovora infection in detached apple and pear flowers. The peptide H-KKLFKKILKYL-NH(2) (BP100) showed efficacies in flowers of 63-76% at 100 microM, being more potent than BP76 and only less effective than streptomycin, currently used for fire blight control.

Molecular Quantum Similarity: theoretical Framework, Ordering Principles, and Visualization Techniques12

Publisher Summary This chapter focuses on the practical results of Quantum Similarity Measures (QSM). It defines and interprets a QSM according to quantum mechanical principles and this is accompanied by a construction of a QSM theoretical framework. The set of QSM can be transformed or combined to obtain a new kind of auxiliary terms that can be named “Similarity Indices.” There is a great deal of possible QSM manipulations leading to a variety of Quantum Similarity Index (QSI) definitions. Some of them are cosine-like similarity index, distance similarity index, and the Hodgkin-Richards or Tanimoto indices. The matrix representation of a molecular set can be associated to a set of finite dimensional vectors representing the molecules. This leads to the concept of “point-molecules” collected as a “Molecular Point Cloud.” To construct a solid theoretical body concerning QSM, a set of rules referred to as the Mendeleev Postulates are described in the chapter.

Foundations and recent developments on molecular quantum similarity

A general definition of the Quantum Molecular Similarity Measure is reported. Particular cases of this definition are discussed, drawing special attention to the new definition of Gravitational-like Quantum Molecular Similarity Measures. Applications to the study of fluoromethanes and chloromethanes, the Carbonic Anhydrase enzyme, and the Hammond postulate are presented. Our calculations fully support the use of Quantum Molecular Similarity Measures as an efficient molecular engineering tool in order to predict physical properties, biological and pharmacological activities, as well as to interpret complex chemical problems.

Quantum molecular similarity measures (QMSM) as a natural way leading towards a theoretical foundation of quantitative structure-properties relationships (QSPR)

Quantum molecular similarity measures (QMSM) are succinctly described and justified as a tool to obtain ordered patterns within a given set of molecular electronic structures. The nature of QMSM appears also to establish the way leading towards a discrete representation of a given electronic structure, when using a quantum mechanical framework, in the form of somen-dimensional column vector. As a consequence, quantitative structure-properties relationships (QSPR) can be considered, in general, to be coincident with a procedure to obtain the discrete approximate representation vector elements of some unknown operator whose expectation values can be associated with a chosen observed experimental property value.

On quantum molecular similarity measures (QMSM) and indices (QMSI)

Quantum molecular similarity measures (QMSM) and the possibility to construct a discreten-dimensional representation of any electronic structure is briefly described. The quantum molecular similarity indices (QMSI) are presented next. They constitute a possible transformation of the initial QMSM, intended to be useful in a great variety of applications. A set of diverse possibilities in QMSI definitions is given. A comparison of the indices obtained directly from electronic density distributions with those derived from the QMSM discrete representation of molecules leads to a handful of useful results, allowing a mathematical connection between the initial description of Carbó and the Hodgkin-Richards QMSIs. From the discussion of this kind of comparative reasoning a description of new index forms can be deduced. A brief numerical example is given.

Improvement of cyclic decapeptides against plant pathogenic bacteria using a combinatorial chemistry approach

Cyclic decapeptides were developed based on the previously reported peptide c(LysLeuLysLeuLysPheLysLeuLysGln). These compounds were active against the economically important plant pathogenic bacteria Erwinia amylovora, Pseudomonas syringae and Xanthomonas vesicatoria. A library of 56 cyclic decapeptides was prepared and screened for antibacterial activity and eukaryotic cytotoxicity, and led to the identification of peptides with improved minimum inhibitory concentration (MIC) against P. syringae (3.1-6.2 microM) and X. vesicatoria (1.6-3.1 microM). Notably, peptides active against E. amylovora (MIC of 12.5-25 microM) were found, constituting the first report of cyclic peptides with activity towards this bacteria. A second library based on the structure c(X(1)X(2)X(3)X(4)LysPheLysLysLeuGln) with X being Lys or Leu yielded peptides with optimized activity profiles. The activity against E. amylovora was further improved (MIC of 6.2-12.5 microM) and the best peptides displayed a low eukaryotic cytotoxicity at concentrations 30-120 times higher than the MIC values. A design of experiments permitted to define rules for high antibacterial activity and low cytotoxicity, being the main rule X(2) not equal X(3), and the secondary rule X(4)=Lys. The best analogs can be considered as good candidates for the development of effective antibacterial agents for use in plant protection.

MOLECULAR QUANTUM SIMILARITY MEASURES TUNED 3D QSAR : AN ANTITUMORAL FAMILY VALIDATION STUDY

In this work, a new methodology to construct a tuned QSAR model is presented, which is based on a convex set formalism. The present procedure continues previous 3D QSAR studies, performed using molecular quantum similarity measures (MQSM). With this new computational tool, the efficiency of MQSM applied to QSAR analysis is significantly improved. A reliable QSAR model is obtained using convex linear combinations of different kinds of MQSM, corresponding to different quantum-mechanical operators related to the quantum similarity integral. The active compounds studied here, as a case study, are a set of antitumor agents, the camptothecin molecule and analogues, and the property evaluated is the topoisomerase-I inhibition activity. Before performing a tuned QSAR analysis with this particular molecular set, a simple QSAR study for all the different possible types of MQSM is carried out. In addition, another application of MQSM is presented, to determine which method can be used to optimize molecular structures in order to reproduce experimental molecular geometries as well as possible.

Triple density molecular quantum similarity measures: A general connection between theoretical calculations and experimental results

A newquantum similarity measure is defined. It is proposed as a way to project density functions from infinite dimensional spaces, where density functions belong, to finite dimensional ones. The procedure allows the representation of a given molecule initially described in terms ofnth order density functions as a point in a finite dimensional Euclidean space: apoint-molecule. Further manipulation of the obtained information permits the representation of a molecular set as a cloud of points: amolecular point cloud, in a variety of graphical manners. A previous experience in the field is compared with this new approach.

Definition, mathematical examples and quantum chemical applications of nested summation symbols and logical Kronecker deltas

Abstract Two mathematical symbols are introduced and their applications to computational chemistry and to artificial intelligence are described. The first symbol is called a nested summation symbol (NSS). After a discussion of its properties, we insist on the significance of this symbol in developing sequential and parallel computational algorithms. Another group of symbols, related to logical expressions, are defined under the name logical Kronecker deltas (LKDs). Application examples of the NSS and LKD technique to several computational quantum chemistry topics are given. It is shown how some standard formulae become shorter and easier to write, generalize, program and evaluate. It is emphasized that both symbols constitute a powerful link between mathematical formalism and programming in high level languages.