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Introducing Structural Symmetry and Asymmetry Implications in Development of Recent Pharmacy and Medicine

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Lorentz Jäntschi

Symmetry 2022, 14(8), 1674; https://doi.org/10.3390/sym14081674 - 12 Aug 2022

Cited by 7 | Viewed by 1035

Abstract

Structural symmetry, anti-symmetry, or asymmetry represent a foundational property that, for chemical compounds, often determines their chemical and biological activity [...] Full article

(This article belongs to the Special Issue Structural Symmetry and Asymmetry Implications in Development of Recent Pharmacy and Medicine)

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Open AccessArticle

Numerical Solution of Nonlinear Problems with Multiple Roots Using Derivative-Free Algorithms

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Symmetry 2023, 15(6), 1249; https://doi.org/10.3390/sym15061249 - 12 Jun 2023

Viewed by 1077

Abstract

In the study of systems’ dynamics the presence of symmetry dramatically reduces the complexity, while in chemistry, symmetry plays a central role in the analysis of the structure, bonding, and spectroscopy of molecules. In a more general context, the principle of equivalence, a [...] Read more.

In the study of systems’ dynamics the presence of symmetry dramatically reduces the complexity, while in chemistry, symmetry plays a central role in the analysis of the structure, bonding, and spectroscopy of molecules. In a more general context, the principle of equivalence, a principle of local symmetry, dictated the dynamics of gravity, of space-time itself. In certain instances, especially in the presence of symmetry, we end up having to deal with an equation with multiple roots. A variety of optimal methods have been proposed in the literature for multiple roots with known multiplicity, all of which need derivative evaluations in the formulations. However, in the literature, optimal methods without derivatives are few. Motivated by this feature, here we present a novel optimal family of fourth-order methods for multiple roots with known multiplicity, which do not use any derivative. The scheme of the new iterative family consists of two steps, namely Traub-Steffensen and Traub-Steffensen-like iterations with weight factor. According to the Kung-Traub hypothesis, the new algorithms satisfy the optimality criterion. Taylor’s series expansion is used to examine order of convergence. We also demonstrate the application of new algorithms to real-life problems, i.e., Van der Waals problem, Manning problem, Planck law radiation problem, and Kepler’s problem. Furthermore, the performance comparisons have shown that the given derivative-free algorithms are competitive with existing optimal fourth-order algorithms that require derivative information. Full article

(This article belongs to the Special Issue Structural Symmetry and Asymmetry Implications in Development of Recent Pharmacy and Medicine)

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Open AccessFeature PaperArticle

Making and Breaking—Insight into the Symmetry of Salen Analogues

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Symmetry 2023, 15(2), 424; https://doi.org/10.3390/sym15020424 - 05 Feb 2023

Cited by 1 | Viewed by 1299

Abstract

This study focuses on selected members of the general salen-analogues family possessing two O-H⋯N hydrogen bonds, namely three isomers of N,N’-bis(salicylidene)-X-phenylenediamine, denoted as ortho, meta and para. Two of the isomers are not planar in the published crystal [...] Read more.

This study focuses on selected members of the general salen-analogues family possessing two O-H⋯N hydrogen bonds, namely three isomers of N,N’-bis(salicylidene)-X-phenylenediamine, denoted as ortho, meta and para. Two of the isomers are not planar in the published crystal structures. The current study tackles the problem of symmetry and interactions within the molecules, as well as in the crystal lattice. The aromaticity of the phenyl rings is evaluated using the Harmonic Oscillator Model of Aromaticity (HOMA) index. Intra- and inter-molecular non-covalent interactions are studied via Hirshfeld surface analysis, Independent Gradient Model (IGM), Quantum Theory of Atoms in Molecules (QTAIM), Non-Covalent Interaction (NCI) index, Electron Localisation Function (ELF), Core-Valence Bifurcation (CVB) index and Symmetry-Adapted Perturbation Theory (SAPT). Density Functional Theory (DFT) simulations were carried out in vacuo and with solvent reaction field based on Polarisable Continuum Model (IEF-PCM formulation) at the

ω

B97XD/6-311+G(2d,2p) level. Crystal structure analyses were performed for the data reported previously in the literature. The obtained results demonstrate that the three isomers differ greatly in their structural properties (molecular symmetry is broken for the ortho and meta isomers in the solid state) and ability to form intermolecular interactions, while retaining overall similar physico-chemical characteristics, e.g., aromaticity of the phenyl rings. It was found that the presence of the polar solvent does not significantly affect the structure of the studied compounds. An application of the Hirshfeld surface analysis revealed the nature of the non-covalent interactions present in the investigated crystals. The SAPT results showed that the stability of the dimers extracted from the crystals of the Schiff base derivatives arises from electrostatics and dispersion. Full article

(This article belongs to the Special Issue Structural Symmetry and Asymmetry Implications in Development of Recent Pharmacy and Medicine)

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Open AccessFeature PaperArticle

Synthesis and Spectroscopic Properties of Selected Acrylic and Methacrylic Derivatives of 2-Mercaptobenzothiazole

by

Janina Kabatc-Borcz

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Przemysław Czeleń

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Agnieszka Skotnicka

Symmetry 2023, 15(2), 370; https://doi.org/10.3390/sym15020370 - 30 Jan 2023

Viewed by 697

Abstract

One of the most basic properties of chemical compounds is structural symmetry or asymmetry. This property can be considered at different levels of structural organization. The physical, chemical, biological, and technological properties of organic compounds depend on their chemical structure and are systematically [...] Read more.

One of the most basic properties of chemical compounds is structural symmetry or asymmetry. This property can be considered at different levels of structural organization. The physical, chemical, biological, and technological properties of organic compounds depend on their chemical structure and are systematically related to it. The presented paper is focused on the synthesis and study of the spectroscopic properties of selected photoinitiators from the acrylate and methacrylate derivatives of 2-(benzothiazolylthio)ethyl. The indicated compounds can find potential application in medicine. The 2-(benzothiazolylthio)ethyl acrylate and methacrylate derivatives were characterized using infrared spectroscopy (IR) and nuclear magnetic resonance (NMR) spectroscopy. Their spectroscopic properties were determined on the basis of UV–Vis spectra. The calculated DFT energies and Frontier Molecular Orbitals calculations of the studied compounds were proved to be consistent with the experimental observations. The results have showed that the introduction of the ethoxy substituent increases the reactivity of the compounds and results in the slight bathochromic shift (~19 nm) of the absorption spectra maxima. Full article

(This article belongs to the Special Issue Structural Symmetry and Asymmetry Implications in Development of Recent Pharmacy and Medicine)

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Open AccessArticle

A Computational Study of the Immobilization of New 5-Nitroisatine Derivatives with the Use of C60-Based Functionalized Nanocarriers

by

Przemysław Czeleń

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Beata Szefler

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Agnieszka Skotnicka

Symmetry 2023, 15(1), 226; https://doi.org/10.3390/sym15010226 - 13 Jan 2023

Viewed by 909

Abstract

Isatin-based compounds are a large group of drugs used as competitive inhibitors of ATP. The 5-nitroisatin derivatives studied in this work are inhibitors of the CDK2 enzyme, which can be used in the development of new anti-cancer therapies. One of the basic activities [...] Read more.

Isatin-based compounds are a large group of drugs used as competitive inhibitors of ATP. The 5-nitroisatin derivatives studied in this work are inhibitors of the CDK2 enzyme, which can be used in the development of new anti-cancer therapies. One of the basic activities that often allows for an increase in biological activity while reducing the undesirable effects associated with the toxicity of medicinal substances is immobilization based on carriers. In this work, fifty nanocarriers derived from C60 fullerene, containing a bound phenyl ring on their surfaces, were used in the process of the immobilization of isatin derivatives. Based on flexible docking methods, the binding capacities of the drugs under consideration were determined using a wide range of nanocarriers containing symmetric and asymmetric modifications of the phenyl ring, providing various types of interactions. Based on the data collected for each of the tested drugs, including the binding affinity and the structure and stability of complexes, the best candidates were selected in terms of the type of substituent that modified the nanoparticle and its location. Among the systems with the highest affinity are the dominant complexes created by functionalized fullerenes containing substituents with a symmetrical location, such as R₂-R₆ and R₃-R₅. Based on the collected data, nanocarriers with a high potential for immobilization and use in the development of targeted therapies were selected for each of the tested drugs. Full article

(This article belongs to the Special Issue Structural Symmetry and Asymmetry Implications in Development of Recent Pharmacy and Medicine)

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Open AccessCommunication

Binomial Distributed Data Confidence Interval Calculation: Formulas, Algorithms and Examples

by

Lorentz Jäntschi

Symmetry 2022, 14(6), 1104; https://doi.org/10.3390/sym14061104 - 27 May 2022

Cited by 7 | Viewed by 1266

Abstract

When collecting experimental data, the observable may be dichotomous. Sampling (eventually with replacement) thus emulates a Bernoulli trial leading to a binomial proportion. Because the binomial distribution is discrete, the analytical evaluation of the exact confidence interval of the sampled outcome is a [...] Read more.

When collecting experimental data, the observable may be dichotomous. Sampling (eventually with replacement) thus emulates a Bernoulli trial leading to a binomial proportion. Because the binomial distribution is discrete, the analytical evaluation of the exact confidence interval of the sampled outcome is a mathematical challenge. This paper proposes three alternative confidence interval calculation methods that are characterized and exemplified. Full article

(This article belongs to the Special Issue Structural Symmetry and Asymmetry Implications in Development of Recent Pharmacy and Medicine)

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Open AccessArticle

Microsolvation of Histidine—A Theoretical Study of Intermolecular Interactions Based on AIM and SAPT Approaches

by

Beata Kizior

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Jarosław J. Panek

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Aneta Jezierska

Symmetry 2020, 12(7), 1153; https://doi.org/10.3390/sym12071153 - 10 Jul 2020

Cited by 3 | Viewed by 2429

Abstract

Histidine is unique among amino acids because of its rich tautomeric properties. It participates in essential enzymatic centers, such as catalytic triads. The main aim of the study is the modeling of the change of molecular properties between the gas phase and solution [...] Read more.

Histidine is unique among amino acids because of its rich tautomeric properties. It participates in essential enzymatic centers, such as catalytic triads. The main aim of the study is the modeling of the change of molecular properties between the gas phase and solution using microsolvation models. We investigate histidine in its three protonation states, microsolvated with 1:6 water molecules. These clusters are studied computationally, in the gas phase and with water as a solvent (Polarizable Continuum Model, PCM) within the Density Functional Theory (DFT) framework. The structural analysis reveals the presence of intra- and intermolecular hydrogen bonds. The Atoms-in-Molecules (AIM) theory is employed to determine the impact of solvation on the charge flow within the histidine, with emphasis on the similarity of the two imidazole nitrogen atoms—topologically not equivalent, they are revealed as electronically similar due to the heterocyclic ring aromaticity. Finally, the Symmetry-Adapted Perturbation Theory (SAPT) is used to examine the stability of the microsolvation clusters. While electrostatic and exchange terms dominate in magnitude over polarization and dispersion, the sum of electrostatic and exchange term is close to zero. This makes polarization the factor governing the actual interaction energy. The most important finding of this study is that even with microsolvation, the polarization induced by the presence of implicit solvent is still significant. Therefore, we recommend combined approaches, mixing explicit water molecules with implicit models. Full article

(This article belongs to the Special Issue Structural Symmetry and Asymmetry Implications in Development of Recent Pharmacy and Medicine)

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Open AccessArticle

Docking of Platinum Compounds on Cube Rhombellane Functionalized Homeomorphs

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Beata Szefler

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Przemysław Czeleń

Symmetry 2020, 12(5), 749; https://doi.org/10.3390/sym12050749 - 06 May 2020

Cited by 4 | Viewed by 1601

Abstract

Platinum compounds are anti-cancer drugs and can bind to canonical purine bases, mainly guanine, found within double helical DNA. Platinum compounds can be transferred directly to pathologically altered sites in a specific and site-oriented manner by nanocarriers as potential nanocarriers for carboplatin. Two [...] Read more.

Platinum compounds are anti-cancer drugs and can bind to canonical purine bases, mainly guanine, found within double helical DNA. Platinum compounds can be transferred directly to pathologically altered sites in a specific and site-oriented manner by nanocarriers as potential nanocarriers for carboplatin. Two types of nanostructures were used as potential nanocarriers for carboplatin, the first were functionalized C60 fullerene molecules and the second were rhombellanes. The analyzed nanostructures show considerable symmetry, which affects the affinity of the studied nanocarriers and ligands. Thus symmetry of nanostructures affects the distribution of binding groups on their surface. After the docking procedure, analysis of structural properties revealed many interesting features. In all described cases, binding affinities of complexes of platinum compounds with functionalized fullerene C60 are higher compared with affinities of complexes of platinum compounds with rhombellane structures. All platinum compounds easily create complexes with functionalized fullerene C60, CID_16156307, and at the same time show the highest binding affinity. The binding affinities of lobaplatin and heptaplatin are higher compared with oxaliplatin and nedaplatin. The high value of binding affinity and equilibrium constant K is correlated with creation of strong and medium hydrogen bonds or is correlated with forming a hydrogen bond network. The performed investigations enabled finding nanocarriers for lobaplatin, heptaplatin, oxaliplatin and nedaplatin molecules. Full article

(This article belongs to the Special Issue Structural Symmetry and Asymmetry Implications in Development of Recent Pharmacy and Medicine)

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Open AccessArticle

The Immobilization of Oxindole Derivatives Using New Designed Functionalized C60 Nanomolecules

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Przemysław Czeleń

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Beata Szefler

Symmetry 2020, 12(4), 636; https://doi.org/10.3390/sym12040636 - 17 Apr 2020

Cited by 3 | Viewed by 1498

Abstract

Indirubin and its analogs such as oxindole derivatives are well known as competitive inhibitors of cyclin-dependent kinase 2 (CDK2) and play an important role in the creation of therapies in many cancer diseases. Recent research, in order to increase efficiency, is aimed at [...] Read more.

Indirubin and its analogs such as oxindole derivatives are well known as competitive inhibitors of cyclin-dependent kinase 2 (CDK2) and play an important role in the creation of therapies in many cancer diseases. Recent research, in order to increase efficiency, is aimed at creating targeted therapy, which is often based on the immobilization of drugs on the surface of nanocarriers. In this work, two oxindole derivatives were used to test the binding capabilities of newly in silico designed C60 fullerene derivatives. Seventy functionalized nanostructures were created by the addition of amino acid substituents to the single phenyl ring attached to the fullerene surface. Realized calculations, based on flexible docking methods, allowed for obtaining energetic characteristics and structural aspects of complexes created by nanomolecules with considered ligands. Analysis of obtained complexes shows that symmetric substitution to position R3 and R5 allows obtaining fullerene derivatives exhibiting the highest binding capabilities, while the lowest ones are the effect of asymmetric substitution (R2; R4). Obtained values clearly allowed to select a group of substituents and substitution sites that provide the most stable complexes which can be used to create new nanocarriers for the group of drugs under consideration. Full article

(This article belongs to the Special Issue Structural Symmetry and Asymmetry Implications in Development of Recent Pharmacy and Medicine)

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