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Phougat M, Sahni NS, Choudhury D. Understanding the relationship between preferential interactions of peptides in water-acetonitrile mixtures with protein-solvent contact surface area. J Comput Aided Mol Des 2024; 38:38. [PMID: 39537830 DOI: 10.1007/s10822-024-00579-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2024] [Accepted: 10/29/2024] [Indexed: 11/16/2024]
Abstract
The influence of polar, water-miscible organic solvents (POS) on protein structure, stability, and functional activity is a subject of significant interest and complexity. This study examines the effects of acetonitrile (ACN), a semipolar, aprotic solvent, on the solvation properties of blocked Ace-Gly-X-Gly-Nme tripeptides (where Ace and Nme stands for acetyl and N-methyl amide groups respectively and X is any amino acid) through extensive molecular dynamics simulations. Individual simulations were conducted for each peptide, encompassing five different ACN concentrations within the range of χACN = 0.1-0.9. The preferential solvation parameter (Γ) calculated using the Kirkwood-Buff integral method was used for the assessment of peptide interactions with water/ACN. Additionally, weighted Voronoi tessellation was applied to obtain a three-way data set containing four time-averaged contact surface area types between peptide atoms and water/ACN atoms. A mathematical technique known as N-way Partial Least Squares (NPLS) was utilized to anticipate the preferential interactions between peptides and water/ACN from the contact surface areas. Furthermore, the temperature dependency of peptide-solvent interactions was investigated using a subset of 10 amino acids representing a range of hydrophobicities. MD simulations were conducted at five temperatures, spanning from 283 to 343 K, with subsequent analysis of data focusing on both preferential solvation and peptide-solvent contact surface areas. The results demonstrate the efficacy of utilizing contact surface areas between the peptide and solvent constituents for successfully predicting preferential interactions in water/ACN mixtures across various ACN concentrations and temperatures.
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Roshal DS, Fedorenko KK, Martin M, Baghdiguian S, Rochal SB. Topological balance of cell distributions in plane monolayers. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:265101. [PMID: 38537291 DOI: 10.1088/1361-648x/ad387a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2024] [Accepted: 03/27/2024] [Indexed: 04/06/2024]
Abstract
Most of normal proliferative epithelia of plants and metazoans are topologically invariant and characterized by similar cell distributions according to the number of cell neighbors (DCNs). Here we study peculiarities of these distributions and explain why the DCN obtained from the location of intercellular boundaries and that based on the Voronoi tessellation with nodes located on cell nuclei may differ from each other. As we demonstrate, special microdomains where four or more intercellular boundaries converge are topologically charged. Using this fact, we deduce a new equation describing the topological balance of the DCNs. The developed theory is applied for a series of microphotographs of non-tumoral epithelial cells of the human cervix (HCerEpiC) to improve the image processing near the edges of microphotographs and reveal the topological invariance of the examined monolayers. Special contact microdomains may be present in epithelia of various natures, however, considering the well-known vertex model of epithelium, we show that such contacts are absent in the usual solid-like state of the model and appear only in the liquid-like cancer state. Also, we discuss a possible biological role of special contacts in context of proliferative epithelium dynamics and tissue morphogenesis.
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Zhou Y, Isaksson P, Persson C. An improved trabecular bone model based on Voronoi tessellation. J Mech Behav Biomed Mater 2023; 148:106172. [PMID: 37852087 DOI: 10.1016/j.jmbbm.2023.106172] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2023] [Revised: 09/17/2023] [Accepted: 10/09/2023] [Indexed: 10/20/2023]
Abstract
BACKGROUND AND OBJECTIVE Accurate numerical and physical models of trabecular bone, correctly representing its complexity and variability, could be highly advantageous in the development of e.g. new bone-anchored implants due to the limited availability of real bone. Several Voronoi tessellation-based porous models have been reported in the literature, attempting to mimic the trabecular bone. However, these models have been limited to lattice rod-like structures, which are only structurally representative of very high-porosity trabecular bone. The objective of this study was to provide an improved model, more representative of trabecular bone of different porosity. METHODS Boolean operations were utilized to merge scaled Voronoi cells, thereby introducing different structural patterns, controlling porosity and to some extent anisotropy. The mechanical properties of the structures were evaluated using analytical estimations, numerical simulations, and experimental compression tests of 3D-printed versions of the structures. The capacity of the developed models to represent trabecular bone was assessed by comparing some key geometric features with trabecular bone characterized in previous studies. RESULTS The models gave the possibility to provide pore interconnectivity at relatively low porosities as well as both plate- and rod-like structures. The mechanical properties of the generated models were predictable with numerical simulations as well as an analytical approach. The permeability was found to be better than Sawbones at the same porosity. The models also showed the capability of matching e.g. some vertebral structures for key geometric features. CONCLUSIONS An improved numerical model for mimicking trabecular bone structures was successfully developed using Voronoi tessellation and Boolean operations. This is expected to benefit both computational and experimental studies by providing a more diverse and representative structure of trabecular bone.
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Olechnovič K, Venclovas Č. VoroIF-GNN: Voronoi tessellation-derived protein-protein interface assessment using a graph neural network. Proteins 2023; 91:1879-1888. [PMID: 37482904 DOI: 10.1002/prot.26554] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/21/2023] [Revised: 06/19/2023] [Accepted: 07/01/2023] [Indexed: 07/25/2023]
Abstract
We present VoroIF-GNN (Voronoi InterFace Graph Neural Network), a novel method for assessing inter-subunit interfaces in a structural model of a protein-protein complex, relying solely on the input structure without any additional information. Given a multimeric protein structural model, we derive interface contacts from the Voronoi tessellation of atomic balls, construct a graph of those contacts, and predict the accuracy of every contact using an attention-based GNN. The contact-level predictions are then summarized to produce whole interface-level scores. VoroIF-GNN was blindly tested for its ability to estimate the accuracy of protein complexes during CASP15 and showed strong performance in selecting the best multimeric model out of many. The method implementation is freely available at https://kliment-olechnovic.github.io/voronota/expansion_js/.
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Báez-Yáñez MG, Siero JCW, Petridou N. A mechanistic computational framework to investigate the hemodynamic fingerprint of the blood oxygenation level-dependent signal. NMR IN BIOMEDICINE 2023; 36:e5026. [PMID: 37643645 DOI: 10.1002/nbm.5026] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/06/2023] [Revised: 07/18/2023] [Accepted: 07/28/2023] [Indexed: 08/31/2023]
Abstract
Blood oxygenation level-dependent (BOLD) functional magnetic resonance imaging (fMRI) is one of the most used imaging techniques to map brain activity or to obtain clinical information about human cortical vasculature, in both healthy and disease conditions. Nevertheless, BOLD fMRI is an indirect measurement of brain functioning triggered by neurovascular coupling. The origin of the BOLD signal is quite complex, and the signal formation thus depends, among other factors, on the topology of the cortical vasculature and the associated hemodynamic changes. To understand the hemodynamic evolution of the BOLD signal response in humans, it is beneficial to have a computational framework available that virtually resembles the human cortical vasculature, and simulates hemodynamic changes and corresponding MRI signal changes via interactions of intrinsic biophysical and magnetic properties of the tissues. To this end, we have developed a mechanistic computational framework that simulates the hemodynamic fingerprint of the BOLD signal based on a statistically defined, three-dimensional, vascular model that approaches the human cortical vascular architecture. The microvasculature is approximated through a Voronoi tessellation method and the macrovasculature is adapted from two-photon microscopy mice data. Using this computational framework, we simulated hemodynamic changes-cerebral blood flow, cerebral blood volume, and blood oxygen saturation-induced by virtual arterial dilation. Then we computed local magnetic field disturbances generated by the vascular topology and the corresponding blood oxygen saturation changes. This mechanistic computational framework also considers the intrinsic biophysical and magnetic properties of nearby tissue, such as water diffusion and relaxation properties, resulting in a dynamic BOLD signal response. The proposed mechanistic computational framework provides an integrated biophysical model that can offer better insights regarding the spatial and temporal properties of the BOLD signal changes.
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Frenkel M, Shoval S, Bormashenko E. Shannon Entropy of Ramsey Graphs with up to Six Vertices. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1427. [PMID: 37895548 PMCID: PMC10606126 DOI: 10.3390/e25101427] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2023] [Revised: 10/03/2023] [Accepted: 10/07/2023] [Indexed: 10/29/2023]
Abstract
Shannon entropy quantifying bi-colored Ramsey complete graphs is introduced and calculated for complete graphs containing up to six vertices. Complete graphs in which vertices are connected with two types of links, labeled as α-links and β-links, are considered. Shannon entropy is introduced according to the classical Shannon formula considering the fractions of monochromatic convex α-colored polygons with n α-sides or edges, and the fraction of monochromatic β-colored convex polygons with m β-sides in the given complete graph. The introduced Shannon entropy is insensitive to the exact shape of the polygons, but it is sensitive to the distribution of monochromatic polygons in a given complete graph. The introduced Shannon entropies Sα and Sβ are interpreted as follows: Sα is interpreted as an average uncertainty to find the green α-polygon in the given graph; Sβ is, in turn, an average uncertainty to find the red β-polygon in the same graph. The re-shaping of the Ramsey theorem in terms of the Shannon entropy is suggested. Generalization for multi-colored complete graphs is proposed. Various measures quantifying the Shannon entropy of the entire complete bi-colored graphs are suggested. Physical interpretations of the suggested Shannon entropies are discussed.
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Merighi A, Lossi L. Co-cultures of cerebellar slices from mice with different reelin genetic backgrounds as a model to study cortical lamination. F1000Res 2023; 11:1183. [PMID: 37881513 PMCID: PMC10594056 DOI: 10.12688/f1000research.126787.1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Accepted: 09/07/2023] [Indexed: 10/27/2023] Open
Abstract
Background: Reelin has fundamental functions in the developing and mature brain. Its absence gives rise to the Reeler phenotype in mice, the first described cerebellar mutation. In homozygous mutants missing the Reelin gene ( reln -/-), neurons are incapable of correctly positioning themselves in layered brain areas such as the cerebral and cerebellar cortices. We here demonstrate that by employing ex vivo cultured cerebellar slices one can reduce the number of animals and use a non-recovery procedure to analyze the effects of Reelin on the migration of Purkinje neurons (PNs). Methods: We generated mouse hybrids (L7-GFP relnF1/) with green fluorescent protein (GFP)-tagged PNs, directly visible under fluorescence microscopy. We then cultured the slices obtained from mice with different reln genotypes and demonstrated that when the slices from reln -/- mutants were co-cultured with those from reln +/- mice, the Reelin produced by the latter induced migration of the PNs to partially rescue the normal layered cortical histology. We have confirmed this observation with Voronoi tessellation to analyze PN dispersion. Results: In images of the co-cultured slices from reln -/- mice, Voronoi polygons were larger than in single-cultured slices of the same genetic background but smaller than those generated from slices of reln +/- animals. The mean roundness factor, area disorder, and roundness factor homogeneity were different when slices from reln -/- mice were cultivated singularly or co-cultivated, supporting mathematically the transition from the clustered organization of the PNs in the absence of Reelin to a layered structure when the protein is supplied ex vivo. Conclusions: Neurobiologists are the primary target users of this 3Rs approach. They should adopt it for the possibility to study and manipulate ex vivo the activity of a brain-secreted or genetically engineered protein (scientific perspective), the potential reduction (up to 20%) of the animals used, and the total avoidance of severe surgery (3Rs perspective).
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Merighi A, Lossi L. Co-cultures of cerebellar slices from mice with different reelin genetic backgrounds as a model to study cortical lamination. F1000Res 2023; 11:1183. [PMID: 37881513 PMCID: PMC10594056 DOI: 10.12688/f1000research.126787.2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Accepted: 09/07/2023] [Indexed: 10/27/2023] Open
Abstract
Background: Reelin has fundamental functions in the developing and mature brain. Its absence gives rise to the Reeler phenotype in mice, the first described cerebellar mutation. In homozygous mutants missing the Reelin gene ( reln -/-), neurons are incapable of correctly positioning themselves in layered brain areas such as the cerebral and cerebellar cortices. We here demonstrate that by employing ex vivo cultured cerebellar slices one can reduce the number of animals and use a non-recovery procedure to analyze the effects of Reelin on the migration of Purkinje neurons (PNs). Methods: We generated mouse hybrids (L7-GFP relnF1/) with green fluorescent protein (GFP)-tagged PNs, directly visible under fluorescence microscopy. We then cultured the slices obtained from mice with different reln genotypes and demonstrated that when the slices from reln -/- mutants were co-cultured with those from reln +/- mice, the Reelin produced by the latter induced migration of the PNs to partially rescue the normal layered cortical histology. We have confirmed this observation with Voronoi tessellation to analyze PN dispersion. Results: In images of the co-cultured slices from reln -/- mice, Voronoi polygons were larger than in single-cultured slices of the same genetic background but smaller than those generated from slices of reln +/- animals. The mean roundness factor, area disorder, and roundness factor homogeneity were different when slices from reln -/- mice were cultivated singularly or co-cultivated, supporting mathematically the transition from the clustered organization of the PNs in the absence of Reelin to a layered structure when the protein is supplied ex vivo. Conclusions: Neurobiologists are the primary target users of this 3Rs approach. They should adopt it for the possibility to study and manipulate ex vivo the activity of a brain-secreted or genetically engineered protein (scientific perspective), the potential reduction (up to 20%) of the animals used, and the total avoidance of severe surgery (3Rs perspective).
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Gelléri M, Chen SY, Hübner B, Neumann J, Kröger O, Sadlo F, Imhoff J, Hendzel MJ, Cremer M, Cremer T, Strickfaden H, Cremer C. True-to-scale DNA-density maps correlate with major accessibility differences between active and inactive chromatin. Cell Rep 2023; 42:112567. [PMID: 37243597 DOI: 10.1016/j.celrep.2023.112567] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2022] [Revised: 03/02/2023] [Accepted: 05/10/2023] [Indexed: 05/29/2023] Open
Abstract
Chromatin compaction differences may have a strong impact on accessibility of individual macromolecules and macromolecular assemblies to their DNA target sites. Estimates based on fluorescence microscopy with conventional resolution, however, suggest only modest compaction differences (∼2-10×) between the active nuclear compartment (ANC) and inactive nuclear compartment (INC). Here, we present maps of nuclear landscapes with true-to-scale DNA densities, ranging from <5 to >300 Mbp/μm3. Maps are generated from individual human and mouse cell nuclei with single-molecule localization microscopy at ∼20 nm lateral and ∼100 nm axial optical resolution and are supplemented by electron spectroscopic imaging. Microinjection of fluorescent nanobeads with sizes corresponding to macromolecular assemblies for transcription into nuclei of living cells demonstrates their localization and movements within the ANC and exclusion from the INC.
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Bormashenko E, Legchenkova I, Frenkel M, Shvalb N, Shoval S. Voronoi Tessellations and the Shannon Entropy of the Pentagonal Tilings. ENTROPY (BASEL, SWITZERLAND) 2023; 25:92. [PMID: 36673233 PMCID: PMC9857938 DOI: 10.3390/e25010092] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/30/2022] [Revised: 12/28/2022] [Accepted: 12/29/2022] [Indexed: 06/17/2023]
Abstract
We used the complete set of convex pentagons to enable filing the plane without any overlaps or gaps (including the Marjorie Rice tiles) as generators of Voronoi tessellations. Shannon entropy of the tessellations was calculated. Some of the basic mosaics are flexible and give rise to a diversity of Voronoi tessellations. The Shannon entropy of these tessellations varied in a broad range. Voronoi tessellation, emerging from the basic pentagonal tiling built from hexagons only, was revealed (the Shannon entropy of this tiling is zero). Decagons and hendecagon did not appear in the studied Voronoi diagrams. The most abundant Voronoi tessellations are built from three different kinds of polygons. The most widespread is the combination of pentagons, hexagons, and heptagons. The most abundant polygons are pentagons and hexagons. No Voronoi tiling built only of pentagons was registered. Flexible basic pentagonal mosaics give rise to a diversity of Voronoi tessellations, which are characterized by the same symmetry group. However, the coordination number of the vertices is variable. These Voronoi tessellations may be useful for the interpretation of the iso-symmetrical phase transitions.
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Simulation of Diffusion-Controlled Growth of Interdependent Nuclei under Potentiostatic Conditions. MATERIALS 2022; 15:ma15103603. [PMID: 35629634 PMCID: PMC9147730 DOI: 10.3390/ma15103603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/23/2022] [Revised: 05/11/2022] [Accepted: 05/16/2022] [Indexed: 12/10/2022]
Abstract
The problem of diffusion-controlled growth following an instantaneous nucleation event was studied within the framework of a new numerical model, considering the spatial distribution of hemispherical nuclei on the electrode surface and the mutual influence of growing nuclei via the collision of 3D diffusion fields. The simulation of the diffusion-controlled growth of hexagonal and random ensembles was performed at the overpotential-dependent number density of nuclei. The diffusion flow to each nucleus within a random ensemble was simulated by the finite difference method using the derived analytical expressions for the surface areas and the volumes formed at the intersection of 3D diffusion fields with the side faces of a virtual right prism with a Voronoi polygon base. The implementation of this approach provides an accurate calculation of concentration profiles, time dependences of the size of nuclei, and current transients. The results, including total current density transients, growth exponents, and nucleus size distribution, were compared with models developed within the concept of planar diffusion zones, the mean-field approximation and the Brownian dynamics simulation method, as well as with experimental data from the literature. The prospects of the model for studying the initial stages of electrocrystallization were discussed.
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Zou S, Gong H, Gao J. Additively Manufactured Multilevel Voronoi-Lattice Scaffolds with Bonelike Mechanical Properties. ACS Biomater Sci Eng 2022; 8:3022-3037. [PMID: 35537212 DOI: 10.1021/acsbiomaterials.1c01482] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Irregular porous scaffold through Voronoi tessellation based on global modeling demonstrated randomness to a certain degree and susceptibility to producing large processing deviations. A modeling method for new types of scaffolds based on periodic arrays of Voronoi unit cell was proposed in this study. These porous scaffolds presented controllable local cells and satisfactory mechanical properties. The topological structure of the Voronoi unit cell was controlled using three independent cell design factors (Voronoi polyhedron volume V, face-centered scaled factor F1, and body-centered scaled factor F2), and multilevel Voronoi-lattice scaffolds were constructed on the basis of periodic arrays of the Voronoi unit cell. Compressive test and simulation were combined to quantify the mechanical properties of scaffolds. The regression equations were established using the response surface method (RSM) to determine relationships between Voronoi unit cell design factors and structural characteristic parameters and mechanical properties. The same trends were observed in stress-strain curves of the compressive test and simulation. The mechanical properties of scaffolds can be appropriately quantified via simulation. Regression equations based on RSM can properly predict the structural characteristic parameters and mechanical properties of the scaffold. Compared with V, F1 and F2 exerted a stronger influence on the structural characteristic parameters and mechanical properties of the scaffold. The modeling method of the multilevel Voronoi-lattice scaffold based on the Voronoi unit cell was proposed in this study to design the porous scaffold and meet the requirements of human bone morphology, mechanical properties, and actual manufacturing by adjusting factors V, F1, and F2. The proposed method can provide a feasible strategy for designing implants with suitable and similar morphologies and mechanical properties to cancellous bone.
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Boribayeva A, Iniyatova G, Uringaliyeva A, Golman B. Porous Structure of Cylindrical Particle Compacts. MICROMACHINES 2021; 12:mi12121498. [PMID: 34945346 PMCID: PMC8706371 DOI: 10.3390/mi12121498] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/16/2021] [Revised: 11/18/2021] [Accepted: 11/22/2021] [Indexed: 11/16/2022]
Abstract
The porous compacts of non-spherical particles are frequently used in energy storage devices and other advanced applications. In the present work, the microstructures of compacts of monodisperse cylindrical particles are investigated. The cylindrical particles with various aspect ratios are generated using superquadrics, and the discrete element method was adopted to simulate the compacts formed under gravity deposition of randomly oriented particles. The Voronoi tessellation is then used to quantify the porous microstructure of compacts. With one exception, the median reduced free volume of Voronoi cells increases, and the median local packing density decreases for compacts composed of cylinders with a high aspect ratio, indicating a loose packing of long cylinders due to their mechanical interlocking during compaction. The obtained data are needed for further optimization of compact porous microstructure to improve the transport properties of compacts of non-spherical particles.
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Cooperative success in epithelial public goods games. J Theor Biol 2021; 528:110838. [PMID: 34303702 DOI: 10.1016/j.jtbi.2021.110838] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2021] [Revised: 07/06/2021] [Accepted: 07/19/2021] [Indexed: 11/23/2022]
Abstract
Cancer cells obtain mutations which rely on the production of diffusible growth factors to confer a fitness benefit. These mutations can be considered cooperative, and studied as public goods games within the framework of evolutionary game theory. The population structure, benefit function and update rule all influence the evolutionary success of cooperators. We model the evolution of cooperation in epithelial cells using the Voronoi tessellation model. Unlike traditional evolutionary graph theory, this allows us to implement global updating, for which birth and death events are spatially decoupled. We compare, for a sigmoid benefit function, the conditions for cooperation to be favoured and/or beneficial for well-mixed and structured populations. We find that when population structure is combined with global updating, cooperation is more successful than if there were local updating or the population were well-mixed. Interestingly, the qualitative behaviour for the well-mixed population and the Voronoi tessellation model is remarkably similar, but the latter case requires significantly lower incentives to ensure cooperation.
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Simulation of Leather Visco-Elastic Behavior Based on Collagen Fiber-Bundle Properties and a Meso-Structure Network Model. MATERIALS 2021; 14:ma14081894. [PMID: 33920286 PMCID: PMC8070376 DOI: 10.3390/ma14081894] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/11/2021] [Revised: 04/02/2021] [Accepted: 04/06/2021] [Indexed: 11/17/2022]
Abstract
Simulation-based prediction of mechanical properties is highly desirable for optimal choice and treatment of leather. Nowadays, this is state-of-the-art for many man-made materials. For the natural material leather, this task is however much more demanding due to the leather's high variability and its extremely intricate structure. Here, essential geometric features of the leather's meso-scale are derived from 3D images obtained by micro-computed tomography and subsumed in a parameterizable structural model. That is, the fiber-bundle structure is modeled. The structure model is combined with bundle properties derived from tensile tests. Then the effective leather visco-elastic properties are simulated numerically in the finite element representation of the bundle structure model with sliding contacts between bundles. The simulation results are validated experimentally for two animal types, several tanning procedures, and varying sample positions within the hide. Finally, a complete workflow for assessing leather quality by multi-scale simulation of elastic and visco-elastic properties is established and validated.
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Brehm M, Thomas M. Optimized Atomic Partial Charges and Radii Defined by Radical Voronoi Tessellation of Bulk Phase Simulations. Molecules 2021; 26:1875. [PMID: 33810337 PMCID: PMC8036805 DOI: 10.3390/molecules26071875] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2021] [Revised: 03/22/2021] [Accepted: 03/24/2021] [Indexed: 12/05/2022] Open
Abstract
We present a novel method for the computation of well-defined optimized atomic partial charges and radii from the total electron density. Our method is based on a two-step radical Voronoi tessellation of the (possibly periodic) system and subsequent integration of the total electron density within each Voronoi cell. First, the total electron density is partitioned into the contributions of each molecule, and subsequently the electron density within each molecule is assigned to the individual atoms using a second set of atomic radii for the radical Voronoi tessellation. The radii are optimized on-the-fly to minimize the fluctuation (variance) of molecular and atomic charges. Therefore, our method is completely free of empirical parameters. As a by-product, two sets of optimized atomic radii are produced in each run, which take into account many specific properties of the system investigated. The application of an on-the-fly interpolation scheme reduces discretization noise in the Voronoi integration. The approach is particularly well suited for the calculation of partial charges in periodic bulk phase systems. We apply the method to five exemplary liquid phase simulations and show how the optimized charges can help to understand the interactions in the systems. Well-known effects such as reduced ion charges below unity in ionic liquid systems are correctly predicted without any tuning, empiricism, or rescaling. We show that the basis set dependence of our method is very small. Only the total electron density is evaluated, and thus, the approach can be combined with any electronic structure method that provides volumetric total electron densities-it is not limited to Hartree-Fock or density functional theory (DFT). We have implemented the method into our open-source software tool TRAVIS.
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Zhang M, Shang J, Guo S, Hur B, Yue X. Numerical Investigation of Effective Thermal Conductivity of Strut-Based Cellular Structures Designed by Spatial Voronoi Tessellation. MATERIALS 2020; 14:ma14010138. [PMID: 33396900 PMCID: PMC7795474 DOI: 10.3390/ma14010138] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/23/2020] [Revised: 12/18/2020] [Accepted: 12/28/2020] [Indexed: 02/04/2023]
Abstract
Porous materials possess light weight and excellent thermal insulation performance. For disordered porous structures, the number of seed points is an important design parameter which is closely related to the morphology and mean pore size of the structure. Based on the arrangement of points in three-dimensional space, seven kinds of structures were designed by spatial Voronoi tessellation in this paper. The effect of the number of seed points on effective thermal conductivity for Voronoi was studied. Numerical simulation was conducted to research the effects of structural porosity, filling material and structural orientation on the effective thermal conductivity and heat transfer characteristics. The results showed that the effective thermal conductivity is closely related to the porosity and the matrix material. Different number and arrangement of seed points make the structure have different anisotropic performance due to different thermal paths. In addition, required the least number of seed points was obtained for the designation of isotropic random Voronoi.
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Abstract
Cooperation is prevalent in nature, not only in the context of social interactions within the animal kingdom but also on the cellular level. In cancer, for example, tumour cells can cooperate by producing growth factors. The evolution of cooperation has traditionally been studied for well-mixed populations under the framework of evolutionary game theory, and more recently for structured populations using evolutionary graph theory (EGT). The population structures arising due to cellular arrangement in tissues, however, are dynamic and thus cannot be accurately represented by either of these frameworks. In this work, we compare the conditions for cooperative success in an epithelium modelled using EGT, to those in a mechanical model of an epithelium—the Voronoi tessellation (VT) model. Crucially, in this latter model, cells are able to move, and birth and death are not spatially coupled. We calculate fixation probabilities in the VT model through simulation and an approximate analytic technique and show that this leads to stronger promotion of cooperation in comparison with the EGT model.
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Olechnovič K, Venclovas Č. Contact Area-Based Structural Analysis of Proteins and Their Complexes Using CAD-Score. Methods Mol Biol 2020; 2112:75-90. [PMID: 32006279 DOI: 10.1007/978-1-0716-0270-6_6] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Quantifying discrepancies between computationally derived and native (reference) structures is an essential step in the development and comparison of protein modeling and protein-protein docking methods. Measuring conformational differences of proteins or protein complexes is also important in other areas of structural biology such as molecular dynamics and crystallography. There are multiple scores to do that. However, nearly all of them, whether superposition-based (e.g., RMSD) or superposition-free, use distances to measure similarity. CAD-score is conceptually different as it uses physical contacts represented as contact areas. Such representation makes it possible to quantify differences of both structures and surfaces (e.g., protein-protein interfaces and binding sites) using the same framework. A number of studies have found CAD-score to be among the most robust scores. The method is implemented both as a web server and as standalone software available at http://bioinformatics.lt/software/cad-score . Here, we describe how to use the standalone CAD-score software for comparison and analysis of protein structures, interfaces, and binding sites.
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Jenner AL, Frascoli F, Coster ACF, Kim PS. Enhancing oncolytic virotherapy: Observations from a Voronoi Cell-Based model. J Theor Biol 2019; 485:110052. [PMID: 31626813 DOI: 10.1016/j.jtbi.2019.110052] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2018] [Revised: 09/13/2019] [Accepted: 10/14/2019] [Indexed: 02/07/2023]
Abstract
Oncolytic virotherapy is a promising cancer treatment using genetically modified viruses. Unfortunately, virus particles rapidly decay inside the body, significantly hindering their efficacy. In this article, treatment perturbations that could overcome obstacles to oncolytic virotherapy are investigated through the development of a Voronoi Cell-Based model (VCBM). The VCBM derived captures the interaction between an oncolytic virus and cancer cells in a 2-dimensional setting by using an agent-based model, where cell edges are designated by a Voronoi tessellation. Here, we investigate the sensitivity of treatment efficacy to the configuration of the treatment injections for different tumour shapes: circular, rectangular and irregular. The model predicts that multiple off-centre injections improve treatment efficacy irrespective of tumour shape. Additionally, we investigate delaying the infection of cancer cells by modifying viral particles with a substance such as alginate (a hydrogel polymer used in a range of cancer treatments). Simulations of the VCBM show that delaying the infection of cancer cells, and thus allowing more time for virus dissemination, can improve the efficacy of oncolytic virotherapy. The simulated treatment noticeably decreases the tumour size with no increase in toxicity. Improving oncolytic virotherapy in this way allows for a more effective treatment without changing its fundamental essence.
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Validation and Investigation on the Mechanical Behavior of Concrete Using a Novel 3D Mesoscale Method. MATERIALS 2019; 12:ma12162647. [PMID: 31434332 PMCID: PMC6721098 DOI: 10.3390/ma12162647] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/21/2019] [Revised: 08/13/2019] [Accepted: 08/14/2019] [Indexed: 11/30/2022]
Abstract
The mechanical performance of concrete is strongly influenced by the geometry and properties of its components (namely aggregate, mortar, and Interfacial Transitional Zone (ITZ)) from the mesoscale viewpoint, and analyzing the material at that level should be a powerful tool for understanding macroscopic behavior. In this paper, a simple and highly efficient method is proposed for constructing realistic mesostructures of concrete. A shrinking process based on 3D Voronoi tessellation was employed to generate aggregates with random polyhedron and grading size, and reversely, an extending procedure was applied for ITZ generation. 3D mesoscale numerical simulation was conducted under a quasi-static load using an implicit solver which demonstrated the good robustness and feasibility of the presented model. The simulated results resembled favorably the corresponding experiments both in stress–strain curves and failure modes. Damage evolution analysis showed that the ITZ phase has profound influence on the damage behavior of concrete as damage initially develops from here and propagates to mortar. In addition, it was found that tensile damage is the principal factor of mortar failure while compressive damage is the principal factor of ITZ failure under compression.
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Zufiria PJ, Hernández-Medina MÁ. A New Technique Based on Voronoi Tessellation to Assess the Space-Dependence of Categorical Variables. ENTROPY 2019; 21:e21080774. [PMID: 33267486 PMCID: PMC7515304 DOI: 10.3390/e21080774] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/02/2019] [Revised: 08/02/2019] [Accepted: 08/02/2019] [Indexed: 11/20/2022]
Abstract
Based on a sample of geolocated elements, each of them labeled with a (not necessarily ordered) categorical feature, several indexes for assessing the relationship between the geolocation variables (latitude and longitude) and the categorical variable are evaluated. Among these indexes, a new one based on a Voronoi tessellation presents several advantages since it does not require a variable transformation or a previous discretization; in addition, simulations show that this index is considerably robust when compared with the previously known ones. Finally, the use of the presented indexes is also illustrated by analyzing the geolocation of communities in some communication networks derived from Call Detail Records.
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Bormashenko E, Legchenkova I, Frenkel M. Symmetry and Shannon Measure of Ordering: Paradoxes of Voronoi Tessellation. ENTROPY 2019; 21:e21050452. [PMID: 33267166 PMCID: PMC7514941 DOI: 10.3390/e21050452] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/27/2019] [Revised: 04/28/2019] [Accepted: 04/29/2019] [Indexed: 11/17/2022]
Abstract
The Voronoi entropy for random patterns and patterns demonstrating various elements of symmetry was calculated. The symmetric patterns were characterized by the values of the Voronoi entropy being very close to those inherent to random ones. This contradicts the idea that the Voronoi entropy quantifies the ordering of the seed points constituting the pattern. Extension of the Shannon-like formula embracing symmetric patterns is suggested. Analysis of Voronoi diagrams enables the elements of symmetry of the patterns to be revealed.
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Influence of Porosity on the Mechanical Behavior during Uniaxial Compressive Testing on Voronoi-Based Open-Cell Aluminium Foam. MATERIALS 2019; 12:ma12071041. [PMID: 30934831 PMCID: PMC6480085 DOI: 10.3390/ma12071041] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/17/2018] [Revised: 03/18/2019] [Accepted: 03/25/2019] [Indexed: 11/17/2022]
Abstract
We have studied an application of the Voronoi tessellation method in the modeling of open-cell aluminium foam under uniaxial compressive loading. The Voronoi code was merged with computer-aided design (CAD) for converting the polyhedral model into an irregular open-cell cellular structure to create porous samples for compression testing simulations. Numerical simulations of the uniaxial compression uniformly over the upper surface of the sample in the z-axis direction at a constant 20 N load was realised. Samples with three different porosities (30%, 60% and 80%) were studied. A nonlinear elasto-plastic material model with perfect plasticity, without hardening, based on the von Mises yield criterion was applied below 10% strain. Corresponding stress–strain curves were observed and the influence of porosity on deformation mechanism was discussed. Samples with higher porosity exhibited significantly higher normal stress under the same load, and increased stress plateaus. An increase of porosity produced an increase of both compressive and tensile stresses and struts exhibited complex stress fields. Voronoi-based modeling was in accordance with experimental results in the literature in the case of the quasi-static condition and linear elastic region (below 1% strain). Further study is necessary to enable the simulation of real dynamic behaviour under all deformation regimes by using the Voronoi tessellation method.
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Hummel MH, Yu B, Simmerling C, Coutsias EA. LAGUERRE-INTERSECTION METHOD FOR IMPLICIT SOLVATION. ACTA ACUST UNITED AC 2019; 28:1-38. [PMID: 30853740 DOI: 10.1142/s0218195918500012] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Explicit solvent molecular dynamics simulations of a macromolecule are slow as the number of solvent atoms considered typically increases by order of magnitude. Implicit methods introduce surface-dependent corrections to the force field, gaining speed at the expense of accuracy. Properties such as molecular interface surfaces, volumes and cavities are captured by Laguerre tessellations of macromolecules. However, Laguerre cells of exterior atoms tend to be overly large or unbounded. Our method, the inclusion-exclusion based Laguerre-Intersection method, caps cells in a physically accurate manner by considering the intersection of the space-filling diagram with the Laguerre tessellation. We optimize an adjustable parameter, the weight, to ensure the areas and volumes of capped cells exposed to solvent are as close as possible, on average, to those computed from equilibrated explicit solvent simulations. The contact planes are radical planes, meaning that as the solvent weight is varied, interior cells remain constant. We test the consistency of our model using a high-quality trajectory of HIV-protease, a dimer with flexible loops and open-close transitions. We also compare our results with interval-arithmetic Gauss-Bonnet based method. Optimal solvent parameters quickly converge, which we use to illustrate the increased fidelity of the Laguerre-Intersection method over two recently proposed methods as compared to the explicit model.
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