Symmetry

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5 pages, 454 KiB

Open AccessEditorial

Postface for Applied Designs in Chemical Structures with High Symmetry

by Lorentz Jäntschi

Symmetry 2022, 14(10), 2044; https://doi.org/10.3390/sym14102044 - 30 Sep 2022

Cited by 1 | Viewed by 1436

Abstract

Probably the best example to start with with regard to structures with high symmetry (SHS) is

C_{60}

fullerene (buckminsterfullerene) [...] Full article

(This article belongs to the Special Issue Applied Designs in Chemical Structures with High Symmetry)

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Research

Jump to: Editorial

7 pages, 1875 KiB

Open AccessArticle

Computational Exploration of Functionalized Rhombellanes: Building Blocks and Double-Shell Structures

by Katalin Nagy, Beata Szefler and Csaba L. Nagy

Symmetry 2020, 12(3), 343; https://doi.org/10.3390/sym12030343 - 1 Mar 2020

Cited by 3 | Viewed by 2485

Abstract

Double-shell covalent assemblies with the framework of the cube–rhombellane were recently proposed as potential drug delivery systems. Their potential to encapsulate guest molecules combined with appropriate surface modifications show great promise to meet the prerequisites of a drug carrier. This work reports the [...] Read more.

Double-shell covalent assemblies with the framework of the cube–rhombellane were recently proposed as potential drug delivery systems. Their potential to encapsulate guest molecules combined with appropriate surface modifications show great promise to meet the prerequisites of a drug carrier. This work reports the molecular design of such clusters with high molecular symmetry, as well as the evaluation of the geometric and electronic properties using density functional theory. The computational studies of the double-shell assemblies and their corresponding building blocks were conducted using the B3LYP/6-31G(d,p) method as implemented in Gaussian 09. The results show that the assembly of the building blocks is energetically favorable, leading to clusters with higher stability than the corresponding shell fragments, with large HOMO–LUMO gap values. In case of aromatic systems, interlayer stacking interactions between benzene rings contribute to the molecular geometry and stability. During geometry optimization the clusters preserve the high molecular symmetry of the building blocks. Full article

(This article belongs to the Special Issue Applied Designs in Chemical Structures with High Symmetry)

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11 pages, 10717 KiB

Open AccessArticle

Riemann-Symmetric-Space-Based Models in Screening for Gene Transfer Polymers

by Claudiu N. Lungu and Ireneusz P. Grudzinski

Symmetry 2019, 11(12), 1466; https://doi.org/10.3390/sym11121466 - 1 Dec 2019

Cited by 1 | Viewed by 2824

Abstract

Today, gene transfer using polymers as transfer vectors is hardly studied. Some polymers have an excellent gene-carrying ability, but their cytotoxic and biocompatibility properties are not suitable for use. Thus, increased insight into the drug space of such structures is needed in the [...] Read more.

Today, gene transfer using polymers as transfer vectors is hardly studied. Some polymers have an excellent gene-carrying ability, but their cytotoxic and biocompatibility properties are not suitable for use. Thus, increased insight into the drug space of such structures is needed in the screening for suitable molecules. This study aimed to introduce a mathematical model of polymers suitable for genes transfer. In this regard, Riemann surfaces were used. The concerned polymers were taken from secondary published experimental data. The results show that symmetric Reimann spaces are suitable for further drug screening. The branch point values of Riemann surfaces are especially increased for the polymers suitable in gene transfer. Full article

(This article belongs to the Special Issue Applied Designs in Chemical Structures with High Symmetry)

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14 pages, 3613 KiB

Open AccessArticle

Docking of Polyethylenimines Derivatives on Cube Rhombellane Functionalized Homeomorphs

by Beata Szefler and Przemysław Czeleń

Symmetry 2019, 11(8), 1048; https://doi.org/10.3390/sym11081048 - 14 Aug 2019

Cited by 4 | Viewed by 2536

Abstract

Nowadays, in the world of science, an important goal is to create new nanostructures that may act as potential drug carriers. Among different, real or hypothetical, polymeric networks, rhombellanes are very promising and, therefore, attempts were made to deposit polyethylenimines as possible nano-drug [...] Read more.

Nowadays, in the world of science, an important goal is to create new nanostructures that may act as potential drug carriers. Among different, real or hypothetical, polymeric networks, rhombellanes are very promising and, therefore, attempts were made to deposit polyethylenimines as possible nano-drug complexes on the cube rhombellane homeomorphs surface. For the search of ligand–fullerene interactions, was used AutoDockVina software. As a reference structure, the fullerene C₆₀ was used. After the docking procedure, the ligands–fullerenes interactions were tested. The important factor determining the mutual affinity of the tested ligands and nanocarriers is the symmetry of the analyzed nanostructures. Here, this feature has the influence on the distribution of such groups like donors and acceptors of hydrogen bonds on the surface of nanoparticles. We calculated the best binding affinities of ligands, values of binding constants and differences relative to C₆₀ molecules. The best binding efficiency was found for linear ligands. It was also found that the shorter the molecule, the better the binding performance, the more the particle grows and the lower the yield. Small structures of ligands react easily with small structures of nanoparticles. The highest positive percentage deviations were obtained for ligand–fullerene complexes showing the highest binding energy values. Detailed analysis of structural properties after docking showed that the values of affinity of the studied indolizine ligands to the rhombellanes surface are correlated with the strength/length of hydrogen bonds formed between them. Full article

(This article belongs to the Special Issue Applied Designs in Chemical Structures with High Symmetry)

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8 pages, 549 KiB

Open AccessEditor’s ChoiceCommunication

The Eigenproblem Translated for Alignment of Molecules

by Lorentz Jäntschi

Symmetry 2019, 11(8), 1027; https://doi.org/10.3390/sym11081027 - 9 Aug 2019

Cited by 44 | Viewed by 3373

Abstract

Molecular conformation as a subproblem of the geometrical shaping of the molecules is essential for the expression of biological activity. It is well known that from the series of all possible sugars, those that are most naturally occurring and usable by living organisms [...] Read more.

Molecular conformation as a subproblem of the geometrical shaping of the molecules is essential for the expression of biological activity. It is well known that from the series of all possible sugars, those that are most naturally occurring and usable by living organisms as a source of energy—because they can be phosphorylated by hexokinase, the first enzyme in the glycolysis pathway—are D-sugars (from the Latin dextro). Furthermore, the most naturally occurring amino acids in living cells are L-sugars (from the Latin laevo). However, a problem arises in dealing with the comparison of their conformers. One alternative way to compare sugars is via their molecular alignment. Here, a solution to the eigenproblem of molecular alignment is communicated. The Cartesian system is rotated, and eventually translated and reflected until the molecule arrives in a position characterized by the highest absolute values of the eigenvalues observed on the Cartesian coordinates. The rotation alone can provide eight alternate positions relative to the reflexes of each coordinate. Full article

(This article belongs to the Special Issue Applied Designs in Chemical Structures with High Symmetry)

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13 pages, 3744 KiB

Open AccessArticle

The Immobilization of ChEMBL474807 Molecules Using Different Classes of Nanostructures

by Przemysław Czeleń and Beata Szefler

Symmetry 2019, 11(8), 980; https://doi.org/10.3390/sym11080980 - 2 Aug 2019

Cited by 7 | Viewed by 2188

Abstract

Indirubin derivatives and analogues are a large group of compounds which are widely and successfully used in treatment of many cancer diseases. In particular, the ChEMBL474807 molecule, which has confirmed inhibiting abilities against CDK2 and GSK3B enzymes, can be included in this group. [...] Read more.

Indirubin derivatives and analogues are a large group of compounds which are widely and successfully used in treatment of many cancer diseases. In particular, the ChEMBL474807 molecule, which has confirmed inhibiting abilities against CDK2 and GSK3B enzymes, can be included in this group. The immobilization of inhibitors with the use of nanocarriers is an often used strategy in creation of targeted therapies. Evaluations were made of the possibility of immobilizing ligand molecules on different types of nanocarrier, such as carbon nanotubes (CNT), functionalized fullerene C₆₀ derivatives (FF_X), and functionalized cube rhombellanes, via the use of docking methods. All results were compared with a reference system, namely C₆₀ fullerene. The realized calculations allowed indication of a group of compounds that exhibited significant binding affinity relative to the ligand molecule. Obtained data shows that structural modifications, such as those related to the addition of functional groups or changes of structure symmetry, realized in particular types of considered nanostructures, can contribute to increases of their binding capabilities. The analysis of all obtained nano complexes clearly shows that the dominant role in stabilization of such systems is played by stacking and hydrophobic interactions. The realized research allowed identification of potential nanostructures that, together with the ChEMBL474807 molecule, enable the creation of targeted therapy. Full article

(This article belongs to the Special Issue Applied Designs in Chemical Structures with High Symmetry)

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20 pages, 3368 KiB

Open AccessArticle

Investigation of the Inhibition Potential of New Oxindole Derivatives and Assessment of Their Usefulness for Targeted Therapy

by Przemysław Czeleń

Symmetry 2019, 11(8), 974; https://doi.org/10.3390/sym11080974 - 1 Aug 2019

Cited by 7 | Viewed by 2282

Abstract

Oxindole derivatives are a large group of compounds that can play the role of Adenosine triphosphate (ATP) competitive inhibitors. The possibility of modification of such compounds by addition of active groups to both cyclic systems of oxindole allows the obtaining of derivatives showing [...] Read more.

Oxindole derivatives are a large group of compounds that can play the role of Adenosine triphosphate (ATP) competitive inhibitors. The possibility of modification of such compounds by addition of active groups to both cyclic systems of oxindole allows the obtaining of derivatives showing significant affinity toward cyclin-dependent kinase (CDK) proteins. Overexpression of that enzyme is observed in the case of most cancers. The discovery of new efficient inhibitors, which could be used in the development of targeted therapies, is one of the current goals setting trends in recent research. In this research, an oxindole molecular core was used, which was modified by the addition of different substituents to both side chains. The realized procedure allowed the creation of a set of oxindole derivatives characterized by binding affinity values and molecular descriptors evaluated during docking procedures and QSAR calculations. The most promising structures characterized by best sets of parameters were used during the molecular dynamics stage. The analysis of structural and energetic properties of systems obtained during this stage of computation gives an indication of inhibitors creating the most stable complexes, characterized by the highest affinity. During this stage, two structures were selected, where affinity towards potential nanocarriers was evaluated. Realized calculations confirmed a significant role of stacking interactions in the stabilization of ligand complexes with fullerene molecules. Obtained data indicates that complexes of oxindole derivatives and considered nanocarriers exhibit significant potential in the creation of immobilized drugs, and can be used in the development of targeted therapies. Full article

(This article belongs to the Special Issue Applied Designs in Chemical Structures with High Symmetry)

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12 pages, 4954 KiB

Open AccessArticle

DFT Calculations of the Structural, Mechanical, and Electronic Properties of TiV Alloy Under High Pressure

by Fang Yu and Yu Liu

Symmetry 2019, 11(8), 972; https://doi.org/10.3390/sym11080972 - 1 Aug 2019

Cited by 9 | Viewed by 4346

Abstract

A calculation program based on the density functional theory (DFT) is applied to study the structural, mechanical, and electronic properties of TiV alloys with symmetric structure under high pressure. We calculate the dimensionless ratio, elastic constants, shear modulus, Young’s modulus, bulk modulus, ductile-brittle [...] Read more.

A calculation program based on the density functional theory (DFT) is applied to study the structural, mechanical, and electronic properties of TiV alloys with symmetric structure under high pressure. We calculate the dimensionless ratio, elastic constants, shear modulus, Young’s modulus, bulk modulus, ductile-brittle transition, material anisotropy, and Poisson’s ratio as functions of applied pressure. Results suggest that the critical pressure of structural phase transition is 42.05 GPa for the TiV alloy, and structural phase transition occurs when the applied pressure exceeds 42.05 GPa. High pressure can improve resistance to volume change, as well as the ductility and atomic bonding, but the strongest resistances to elastic and shear deformation occur at

P = 5 GPa

for TiV alloy. Furthermore, the results of the density of states (DOS) indicate that the TiV alloy presents metallicity. High pressure disrupts the structural stability of the TiV alloy with symmetry, thereby inducing structural phase transition. Full article

(This article belongs to the Special Issue Applied Designs in Chemical Structures with High Symmetry)

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11 pages, 654 KiB

Open AccessArticle

Predicting Value of Binding Constants of Organic Ligands to Beta-Cyclodextrin: Application of MARSplines and Descriptors Encoded in SMILES String

by Piotr Cysewski and Maciej Przybyłek

Symmetry 2019, 11(7), 922; https://doi.org/10.3390/sym11070922 - 15 Jul 2019

Cited by 7 | Viewed by 4197

Abstract

The quantitative structure–activity relationship (QSPR) model was formulated to quantify values of the binding constant (lnK) of a series of ligands to beta–cyclodextrin (β-CD). For this purpose, the multivariate adaptive regression splines (MARSplines) methodology was adopted with molecular descriptors derived from the simplified [...] Read more.

The quantitative structure–activity relationship (QSPR) model was formulated to quantify values of the binding constant (lnK) of a series of ligands to beta–cyclodextrin (β-CD). For this purpose, the multivariate adaptive regression splines (MARSplines) methodology was adopted with molecular descriptors derived from the simplified molecular input line entry specification (SMILES) strings. This approach allows discovery of regression equations consisting of new non-linear components (basis functions) being combinations of molecular descriptors. The model was subjected to the standard internal and external validation procedures, which indicated its high predictive power. The appearance of polarity-related descriptors, such as XlogP, confirms the hydrophobic nature of the cyclodextrin cavity. The model can be used for predicting the affinity of new ligands to β-CD. However, a non-standard application was also proposed for classification into Biopharmaceutical Classification System (BCS) drug types. It was found that a single parameter, which is the estimated value of lnK, is sufficient to distinguish highly permeable drugs (BCS class I and II) from low permeable ones (BCS class II and IV). In general, it was found that drugs of the former group exhibit higher affinity to β-CD then the latter group (class III and IV). Full article

(This article belongs to the Special Issue Applied Designs in Chemical Structures with High Symmetry)

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9 pages, 4846 KiB

Open AccessArticle

Docking Linear Ligands to Glucose Oxidase

by Beata Szefler

Symmetry 2019, 11(7), 901; https://doi.org/10.3390/sym11070901 - 10 Jul 2019

Cited by 5 | Viewed by 2486

Abstract

GOX (3QVR), glucose oxidase, is an oxidoreductase enzyme, which has found many applications in biotechnology and modern diagnostics with typical assays including biosensors useful in the determination of free glucose in body fluids. PEI (polyethylenimines) are polymer molecules made up of amine groups [...] Read more.

GOX (3QVR), glucose oxidase, is an oxidoreductase enzyme, which has found many applications in biotechnology and modern diagnostics with typical assays including biosensors useful in the determination of free glucose in body fluids. PEI (polyethylenimines) are polymer molecules made up of amine groups and two aliphatic carbons, which are cyclically repeated. PEI are transfection reagents which, using positively charged units, bind well to anionic DNA residues. During the studies on GOX, PEI were used both in their linear and branched structures. Rhombellanes, RBL, are structures decorated with rhombs/squares. The aim of the paper is to study the interactions of two kinds of linear ligands: PEIs (Polyethylenimines) and CHRs (ethers of Hexahydroxy-cyclohexane) with the glucose oxidase enzyme, GOX (3QVR). To understand the structure-activity relationship between the GOX enzyme and the linear ligands PEI and CHR, two steps of docking simulation were performed; mapping the whole area of the 3QVR enzyme and docking on the first and second surface of the enzyme, separately. The studied ligands interacted with amino acids of GOX inside the protein and on its surface, with stronger and shorter bonds inside of the protein. However, long chain ligands can only interact with amino acids on the external protein surface. After the study, two domains of the enzyme were clearly evidenced; the external surface domain more easily creates interactions with ligands, particularly with CHR ligands. Full article

(This article belongs to the Special Issue Applied Designs in Chemical Structures with High Symmetry)

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11 pages, 4143 KiB

Open AccessEditor’s ChoiceArticle

The Immobilization of Oxindole Derivatives with Use of Cube Rhombellane Homeomorphs

by Przemysław Czeleń and Beata Szefler

Symmetry 2019, 11(7), 900; https://doi.org/10.3390/sym11070900 - 10 Jul 2019

Cited by 9 | Viewed by 2725

Abstract

A key aspect of modern drug research is the development of delivery methods that ensure the possibility of implementing targeted therapy for a specific biological target. The use of nanocarriers enables to achieve this objective, also allowing to reduce the toxicity of used [...] Read more.

A key aspect of modern drug research is the development of delivery methods that ensure the possibility of implementing targeted therapy for a specific biological target. The use of nanocarriers enables to achieve this objective, also allowing to reduce the toxicity of used substances and often extending their bioavailability. Through the application of docking methods, the possibility of using cube rhombellanes as potential carriers for two oxindole derivatives was analyzed. In the studies, compounds identified as inhibitors of the CDK2 enzyme and a set of nanostructures proposed by the Topo Cluj Group were used. The popular fullerene molecule C₆₀ was used as the reference system. The estimated binding affinities and structures of obtained complexes show that use of functionalized cube rhombellanes containing hydrogen bond donors and acceptors in their external molecular shell significantly increases ligand affinity toward considered nanocariers, compared to classic fullerenes. The presented values also allow to state that an important factor determining the mutual affinity of the tested ligands and nanostructures is the symmetry of the analyzed nanocarriers and its influence on the distribution of binding groups (aromatic systems, donors and acceptors of hydrogen bonds) on the surface of nanoparticles. Full article

(This article belongs to the Special Issue Applied Designs in Chemical Structures with High Symmetry)

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11 pages, 3127 KiB

Open AccessEditor’s ChoiceArticle

Docking of Cisplatin on Fullerene Derivatives and Some Cube Rhombellane Functionalized Homeomorphs

by Beata Szefler and Przemysław Czeleń

Symmetry 2019, 11(7), 874; https://doi.org/10.3390/sym11070874 - 3 Jul 2019

Cited by 10 | Viewed by 3402

Abstract

Cisplatin (cisPt) is one of the strongest anticancer agents with proven clinical activity against a wide range of solid tumors. Its mode of action has been linked to its ability to crosslink with the canonical purine bases, primarily with guanine. Theoretical studies performed [...] Read more.

Cisplatin (cisPt) is one of the strongest anticancer agents with proven clinical activity against a wide range of solid tumors. Its mode of action has been linked to its ability to crosslink with the canonical purine bases, primarily with guanine. Theoretical studies performed at the molecular level suggest that such nonspecific interactions can also take place with many competitive compounds, such as vitamins of the B group, containing aromatic rings with lone-pair orbitals. This might be an indicator of reduction of the anticancer therapeutic effects of the Cisplatin drug in the presence of vitamins of the B group inside the cell nucleus. That is why it seems to be important to connect CisPt with nanostructures and in this way prevent the drug from combining with the B vitamins. As a proposal for a new nanodrug, an attempt was made to implement Cispaltin (CisPt) ligand on functionalized C₆₀ fullerenes and on a cube rhombellane homeomorphic surface. The symmetry of the analyzed nanostructures is an important factor determining the mutual affinity of the tested ligand and nanocarriers. The behavior of Cisplatin with respect to rhombellane homeomorphs and functionalized fullerenes C₆₀, in terms of their (interacting) energy, geometry and topology was studied and a detailed analysis of structural properties after docking showed many interesting features. Full article

(This article belongs to the Special Issue Applied Designs in Chemical Structures with High Symmetry)

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20 pages, 1840 KiB

Open AccessArticle

Application of the Consonance Solvent Concept for Accurate Prediction of Buckminster Solubility in 180 Net Solvents using COSMO-RS Approach

by Piotr Cysewski

Symmetry 2019, 11(6), 828; https://doi.org/10.3390/sym11060828 - 22 Jun 2019

Cited by 7 | Viewed by 2889

Abstract

The default COSMO-RS (Conductor like Screening Model for Real Solvents) approach is incapable of accurate computation of C60 solubility in net solvents. Additionally, there is no adequate selection of single or multiple reference solvent, which can be applied to the whole population of [...] Read more.

The default COSMO-RS (Conductor like Screening Model for Real Solvents) approach is incapable of accurate computation of C60 solubility in net solvents. Additionally, there is no adequate selection of single or multiple reference solvent, which can be applied to the whole population of 180 solvents for improving prediction of mole fraction at saturated conditions. This failure cannot be addressed to inaccurate data of the Buckminster fusion, although they pose a challenge for experimental measurement due to intense sublimation of C60 at elevated temperatures and the possibility of solvates precipitation. However, taking advantage of the richness of experimental data of fullerene solubility, it is possible to identify the source of errors expressed in terms of fluidization affinity. Classification of solvents according to the value of this fluidization term allowed for formulation of a consonance solvents approach, which enables accurate prediction of C60 solubility using the single reference solvent method. Full article

(This article belongs to the Special Issue Applied Designs in Chemical Structures with High Symmetry)

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