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1.
ACS Pharmacol Transl Sci ; 7(4): 1169-1177, 2024 Apr 12.
Artículo en Inglés | MEDLINE | ID: mdl-38633595

RESUMEN

The interaction between nanoparticles (NPs) and biological environments is profoundly influenced by a stable, strongly adsorbed "hard" protein corona. This corona significantly determines the NPs' pharmacokinetics and biological destiny. Our study delves into the mechanisms by which colloidal Au nanocrystals that are synthesized electrochemically without surface-capping organic ligands, known as CNM-Au8, traverse the blood-brain barrier (BBB) and target human brain tissue for treating neurodegenerative disorders. We discovered that upon interaction with human plasma, CNM-Au8 gold nanocrystals (AuNCs) effectively attract a variety of crucial apolipoproteins, notably apolipoproteins E, to their surfaces. This interaction likely facilitates their passage through the BBB. Furthermore, the coronas of these AuNCs exhibit a substantial presence of albumin and a notable absence of opsonin-based proteins, contributing to prolonged blood circulation. These characteristics align well with the clinical performance observed for the CNM-Au8 NCs. This study highlights that AuNCs with intentionally engineered structures and surfactant-free surfaces can create a distinct protein corona composition. This finding holds significant promise for the development of advanced therapeutic agents aimed at combating neurodegenerative diseases.

2.
J Mech Behav Biomed Mater ; 148: 106216, 2023 12.
Artículo en Inglés | MEDLINE | ID: mdl-37924665

RESUMEN

A human aorta from a female donor affected by Klippel-Trenaunay syndrome was retrieved during a surgery for organ donation for transplant. The aorta was preserved in refrigerated Belzer UW organ preservation solution and tested within a few hours for mechanical characterization with and without vascular smooth muscle activation. KCl and Noradrenaline were used as vasoactive agents in bubbled Krebs-Henseleit buffer solution at 37 °C. A quasi-static and a dynamic mechanical characterization of the full wall and the three individual layers were carried out for strips taken in longitudinal and circumferential directions. The full wall in the descending portion of the aorta underwent mechanical tests with and without smooth muscle activation. Results were compared to data obtained from healthy aortas and show a reduced stiffness of the full wall in circumferential direction. Also, a significant reduction of the response to vasoactive agents in circumferential direction was observed, while the longitudinal response was similar to healthy cases.


Asunto(s)
Aorta Torácica , Síndrome de Klippel-Trenaunay-Weber , Humanos , Femenino , Aorta Torácica/fisiología , Aorta , Norepinefrina , Músculo Liso Vascular
3.
Acta Biomater ; 160: 59-72, 2023 04 01.
Artículo en Inglés | MEDLINE | ID: mdl-36792047

RESUMEN

Decellularized porcine aortas are proposed as scaffolds for revolutionary active aortic grafts. A change in the static and dynamic mechanical properties, associated with the microstructure of elastin and collagen fibers, corresponds to alteration in the cyclic expansion and perfusion, in addition to possible graft damage. Therefore, the present study thoroughly investigates the mechanical response of the decellularized scaffolds of human and porcine origin to static and dynamic mechanical loads. The responses of the native human and porcine aortas are also compared; this is unavailable in the literature. Because the aorta is subjected to pulsatile blood pressure, dynamical responses to cyclic loads and their associated viscoelastic properties are particularly relevant for advanced graft design. In parallel, this study examines the microstructure of the decellularized aorta. The resulting data are compared to the analogous data obtained for the native human and porcine tissues. The results indicate that by using an optimized decellularization protocol - based on sodium dodecyl sulfate (SDS) and DNase - that minimizes mechanical and structural changes of the tissue, layered scaffolds with static and dynamic properties very similar to natural human aortas are obtained. In particular, a decellularized porcine aorta is non-inferior to a decellularized human aorta. STATEMENT OF SIGNIFICANCE: About 55,000 patients undergo abdominal aortic aneurysm repair annually in the USA. The currently implanted grafts present a large mechanical mismatch with the native tissue. This increases the pulsatile nature of the blood flow with negative consequences to the organ perfusion. For this reason, biomimetic and mechanically compatible grafts for aortic repair are urgently needed and they can be obtained through tissue engineering. In this study, scaffolds from porcine and human aortas are obtained from an optimized decellularization protocol. They are accurately compared to the native tissue and present the ideal static and dynamic mechanical properties for developing innovative aortic grafts.


Asunto(s)
Aorta , Ingeniería de Tejidos , Porcinos , Humanos , Animales , Ingeniería de Tejidos/métodos , Dodecil Sulfato de Sodio/química , Andamios del Tejido , Matriz Extracelular/química
4.
Acta Biomater ; 155: 182-198, 2023 01 01.
Artículo en Inglés | MEDLINE | ID: mdl-36435437

RESUMEN

The structural and functional properties of collagen are modulated by the presence of intramolecular and intermolecular crosslinks. Advanced Glycation End-products (AGEs) can produce intermolecular crosslinks by bonding the free amino groups of neighbouring proteins. In this research, the following hypothesis is explored: The accumulation of AGEs in collagen decreases its proteolytic degradation rates while increasing its stiffness. Fluorescence Lifetime Imaging (FLIM) and Fourier-transform infrared spectroscopy (FTIR) detect biochemical changes in collagen scaffolds during the glycation process. The accumulation of AGEs increases exponentially in the collagen scaffolds as a function of Methylglyoxal (MGO) concentration by performing autofluorescence measurement and competitive ELISA. Glycated scaffolds absorb water at a much higher rate confirming the direct affinity between AGEs and interstitial water within collagen fibrils. In addition, the topology of collagen fibrils as observed by Atomic Force Microscopy (AFM) is a lot more defined following glycation. The elastic modulus of collagen fibrils decreases as a function of glycation, whereas the elastic modulus of collagen scaffolds increases. Finally, the enzymatic degradation of collagen by bacterial collagenase shows a sigmoidal pattern with a much slower degradation rate in the glycated scaffolds. This study identifies unique variations in the properties of collagen following the accumulation of AGEs. STATEMENT OF SIGNIFICANCE: In humans, Advanced Glycation End-products (AGEs) are naturally produced as a result of aging process. There is an evident lack of knowledge in the basic science literature explaining the biomechanical impact of AGE-mediated crosslinks on the functional and structural properties of collagen at both the nanoscale (single fibrils) and mesoscale (bundles of fibrils). This research, demonstrates how it is possible to harness this natural phenomenon in vitro to enhance the properties of engineered collagen fibrils and scaffolds. This study identifies unique variations in the properties of collagen at nanoscale and mesoscale following accumulation of AGEs. In their approach, they investigate the unique properties conferred to collagen, namely enhanced water sorption, differential elastic modulus, and finally sigmoidal proteolytic degradation behavior.


Asunto(s)
Reacción de Maillard , Ingeniería de Tejidos , Humanos , Productos Finales de Glicación Avanzada/metabolismo , Colágeno/química , Matriz Extracelular/metabolismo
5.
JBMR Plus ; 6(5): e10622, 2022 May.
Artículo en Inglés | MEDLINE | ID: mdl-35509630

RESUMEN

Loss-of-function mutations in the MEN1 tumor-suppressor gene cause the multiple endocrine neoplasia type 1 syndrome. Menin, the MEN1 gene product, is expressed in many tissues, including bone, where its function remains elusive. We conditionally inactivated menin in mesenchymal stem cells (MSCs) using paired-related homeobox 1 (Prx1)-Cre and compared resultant skeletal phenotypes of Prx1-Cre;Men1 f/f menin-knockout mice (KO) and wild-type controls using in vivo and in vitro experimental approaches and mechanics simulation. Dual-energy X-ray absorptiometry demonstrated significantly reduced bone mineral density, and 3-dimensional micro-CT imaging revealed a decrease in trabecular bone volume, altered trabecular structure, and an increase in trabecular separation in KO mice at 6 and 9 months of age. Numbers of osteoblasts were unaltered, and dynamic histomorphometry demonstrated unaltered bone formation; however, osteoclast number and activity and receptor activator of NF-κB ligand/osteoprotegerin (RANKL/OPG) mRNA profiles were increased, supporting increased osteoclastogenesis and bone resorption. In vitro, proliferative capabilities of bone marrow stem cells and differentiation of osteoblasts and mineralization were unaltered; however, osteoclast generation was increased. Gross femur geometrical alterations observed included significant reductions in length and in mid-metaphyseal cross-sectional area. Atomic force microscopy demonstrated significant decreases in elasticity of both cortical and trabecular bone at the nanoscale, whereas three-point bending tests demonstrated a 30% reduction in bone stiffness; finite element analysis showed morphological changes of the femur microgeometry and a significantly diminished femur flexural rigidity. The biomechanical results demonstrated the detrimental outcome of the accelerated osteoclastic bone resorption. Our studies have a twofold implication; first, MEN1 deletion from MSCs can negatively regulate bone mass and bone biomechanics, and second, the experimental and computational biomechanical analyses employed in the present study should be applicable for improved phenotypic characterization of murine bone. Furthermore, our findings of critical menin function in bone may underpin the more severe skeletal phenotype found in hyperparathyroidism associated with loss-of-function of the MEN1 gene. © 2022 The Authors. JBMR Plus published by Wiley Periodicals LLC on behalf of American Society for Bone and Mineral Research.

6.
Acta Biomater ; 134: 401-421, 2021 10 15.
Artículo en Inglés | MEDLINE | ID: mdl-34303867

RESUMEN

The mechanical properties of human aortas are linked to the layered tissue and its microstructure at different length scales. Each layer has specific mechanical and structural properties. While the ground substance and the elastin play an important role in tissue stiffness at small strain, collagen fibers carry most of the load at larger strains, which corresponds to the physiological conditions of the aorta at maximum pulsatile blood pressure. In fact, collagen fibers are crimped in the unloaded state. Collagen fibers show different orientation distributions when they are observed in a plane that is tangent to the aortic wall (in-plane section) or along a direction orthogonal to it (out-of-plane section). This was systematically investigated using large images (2500 × 2500 µm) with high resolution obtained by second harmonic generation (SHG) in order to homogenize tissue heterogeneity after a convergence analysis, which is a main goal of the study. In addition, collagen fibers show lateral interactions due to entanglements and the presence of transverse elastin fibers, observed on varying length scales using atomic force microscopy and a three-dimensional rendering obtained by stacking a sequence of SHG and two-photon fluorescence images; this is another important contribution. Human descending thoracic aortas from 13 heartbeat donors aged 28 to 66 years were examined. Uniaxial tensile tests were carried out on the longitudinal and circumferential strips of the aortic wall and the three separated layers (intima, media and adventitia). A structurally-motivated material model with (i) a term to describe the combined response of ground substance and elastin and (ii) terms to consider four families of collagen fibers with different directions was applied. The exclusion of compressed fibers was implemented in the fitting process of the experimental data, which was optimized by a genetic algorithm. The results show that a single fiber family with directional and dispersion parameters measured from SHG images can describe the mechanical response of all 39 layers (3 layers for each of the 13 aortas) with very good accuracy when a second (auxiliary) family of aligned fibers is introduced in the orthogonal direction to account for lateral fiber interaction. Indeed, all observed distributions of collagen directions can be accurately fitted by a single bivariate von Mises distribution. Statistical analysis of in-plane and out-of-plane dispersion of fiber orientations reveals structural differences between the three layers and a change of collagen dispersion parameters with age. STATEMENT OF SIGNIFICANCE: The stiffness of healthy young aortas is adjusted so that a diameter expansion of about 10 % is possible during the heartbeat. This creates the Windkessel effect, which smooths out the pulsating nature of blood flow and benefits organ perfusion. The specific elastic properties of the aorta that are required to achieve this effect are related to the microstructure of the aortic tissue at different length scales. An increase in the aortic stiffness, in addition to reducing cyclic expansion and worsening perfusion, is a risk factor for clinical hypertension. The present study relates the microstructure of healthy human aortas to the mechanical response and examines the changes in microstructural parameters with age, which is a key factor in increasing stiffness.


Asunto(s)
Aorta Torácica , Elastina , Adventicia , Aorta , Fenómenos Biomecánicos , Humanos , Estrés Mecánico
7.
Acta Biomater ; 122: 236-248, 2021 03 01.
Artículo en Inglés | MEDLINE | ID: mdl-33359296

RESUMEN

Nature's masterfully synthesized biological materials take on greater relevance when viewed through the perspective of evolutionary abundance. The fact that beetles (order Coleoptera) account for a quarter of all extant lifeforms on Earth, makes them prime exponents of evolutionary success. In fact, their forewings are acknowledged as key traits to their radiative-adaptive success, which makes the beetle elytra a model structure for next-generation bioinspired synthetic materials. In this work, the multiscale morphological and mechanical characteristics of a variety of beetle species from the Cetoniinae subfamily are investigated with the aim of unraveling the underlying principles behind Nature's adaptation of the elytral bauplan to differences in body weight spanning three orders of magnitude. Commensurate with the integral implications of size variation in organisms, a combined material, morphological, and mechanical characterization framework, across spatial scales, was pursued. The investigation revealed the simultaneous presence of size-invariant strategies (chemical compositions, layered-fibrous architectures, graded motifs) as well as size-dependent features (scaling of elytral layers and characteristic dimensions of building blocks), synergistically combined to achieve similar levels of biomechanical functionality (stiffness, energy absorption, strength, deformation and toughening mechanisms) in response to developmental and selection constraints. The integral approach here presented seeks to shed light on Nature's solution to the problem of size variation, which underpins the diversity of beetles and the living world.


Asunto(s)
Escarabajos , Animales , Evolución Biológica
8.
Sci Rep ; 10(1): 506, 2020 01 16.
Artículo en Inglés | MEDLINE | ID: mdl-31949232

RESUMEN

As a physical response to water loss during drought, inner Selaginella lepidophylla stems curl into a spiral shape to prevent photoirradiation damage to their photosynthetic surfaces. Curling is reversible and involves hierarchical deformation, making S. lepidophylla an attractive model with which to study water-responsive actuation. Investigation at the organ and tissue level has led to the understanding that the direction and extent of stem curling can be partially attributed to stiffness gradients between adaxial and abaxial stem sides at the nanoscale. Here, we examine cell wall elasticity to understand how it contributes to the overall stem curling. We compare the measured elastic moduli along the stem length and between adaxial and abaxial stem sides using atomic force microscopy nano-indentation testing. We show that changes in cortex secondary cell wall development lead to cell wall stiffness gradients from stem tip to base, and also between adaxial and abaxial stem sides. Changes in cortical cell wall morphology and secondary cell wall composition are suggested to contribute to the observed stiffness gradients.


Asunto(s)
Pared Celular/ultraestructura , Selaginellaceae/fisiología , Sequías , Microscopía de Fuerza Atómica , Tallos de la Planta/fisiología , Selaginellaceae/ultraestructura , Imagen de Lapso de Tiempo
9.
J R Soc Interface ; 16(159): 20190454, 2019 10 31.
Artículo en Inglés | MEDLINE | ID: mdl-31662070

RESUMEN

Upon hydration and dehydration, the vegetative tissue of Selaginella lepidophylla can reversibly swell and shrink to generate complex morphological transformations. Here, we investigate how structural and compositional properties at tissue and cell wall levels in S. lepidophylla lead to different stem curling profiles between inner and outer stems. Our results show that directional bending in both stem types is associated with cross-sectional gradients of tissue density, cell orientation and secondary cell wall composition between adaxial and abaxial stem sides. In inner stems, longitudinal gradients of cell wall thickness and composition affect tip-to-base tissue swelling and shrinking, allowing for more complex curling as compared to outer stems. Together, these features yield three-dimensional functional gradients that allow the plant to reproducibly deform in predetermined patterns that vary depending on the stem type. This study is the first to demonstrate functional gradients at different hierarchical levels combining to operate in a three-dimensional context.


Asunto(s)
Pared Celular/metabolismo , Modelos Biológicos , Tallos de la Planta/crecimiento & desarrollo , Selaginellaceae/crecimiento & desarrollo , Tallos de la Planta/citología , Selaginellaceae/citología
10.
J Mech Behav Biomed Mater ; 93: 81-92, 2019 05.
Artículo en Inglés | MEDLINE | ID: mdl-30776678

RESUMEN

This paper investigates the elastic properties of bone tissue in the adult mouse femur through Atomic Force Microscopy (AFM) indentation with the goal of understanding its microstructure and underlying mechanics at the nano length scale. Both trabecular and cortical bone types are studied. In particular, we examined the elasticity of cortical bone and individual trabeculae in the longitudinal and transverse directions of the samples. For cortical bone, the elastic modulus in the longitudinal direction was found to be 10-15% higher than that in the transverse direction; for trabecular bone, this difference was 42%. For the trabeculae, this value was found to be in a lower range (0.92 ± 0.22 GPa). As per the transverse elastic modulus, an average of 1.58 ± 0.36 GPa was measured for cortical bone, and 0.55 ± 0.21 GPa for trabecular bone. The anisotropy ratio was within the range of 1.2-1.5 for cortical bone and 1.7-2 for trabecular bone. While the elastic modulus of cortical bone varied along the length of the femur with up to 30% variation, no significant differences were observed within each transverse section. The effect of indentation frequency (1-500 Hz) on the longitudinal elastic moduli was also investigated for cortical and trabecular bone, with results showing a correlation between indentation frequency and elastic modulus. Statement of significance: This study examines the adult mouse femur with a twofold aim: to investigate the anisotropy and inhomogeneity of cortical and trabecular bone tissues and to elucidate their elastic behavior at the nanometer length scale. The elastic moduli of cortical bone and individual trabecula are measured in the longitudinal and transverse cross-sections via AFM indentation at selected locations and in specific directions of the adult mouse femur. The results provide insights into the relationship between mechanical properties and structural morphology of cortical and trabecular bone tissue.


Asunto(s)
Hueso Esponjoso , Hueso Cortical , Elasticidad , Fémur , Ensayo de Materiales , Microscopía de Fuerza Atómica , Animales , Anisotropía , Masculino , Ratones
11.
Sci Rep ; 8(1): 1047, 2018 01 18.
Artículo en Inglés | MEDLINE | ID: mdl-29348423

RESUMEN

While collagen type I (Col-I) is commonly used as a structural component of biomaterials, collagen type III (Col-III), another fibril forming collagen ubiquitous in many soft tissues, has not previously been used. In the present study, the novel concept of an injectable hydrogel with semi-interpenetrating polymeric networks of heterotypic collagen fibrils, with tissue-specific Col-III to Col-I ratios, in a glycol-chitosan matrix was investigated. Col-III was introduced as a component of the novel hydrogel, inspired by its co-presence with Col-I in many soft tissues, its influence on the Col-I fibrillogenesis in terms of diameter and mechanics, and its established role in regulating scar formation. The hydrogel has a nano-fibrillar porous structure, and is mechanically stable under continuous dynamic stimulation. It was found to provide a longer half-life of about 35 days than similar hyaluronic acid-based hydrogels, and to support cell implantation in terms of viability, metabolic activity, adhesion and migration. The specific case of pure Col-III fibrils in a glycol-chitosan matrix was investigated. The proposed hydrogels meet many essential requirements for soft tissue engineering applications, particularly for mechanically challenged tissues such as vocal folds and heart valves.


Asunto(s)
Biomimética , Tejido Conectivo , Hidrogeles/química , Nanofibras/química , Ingeniería de Tejidos , Andamios del Tejido , Biomimética/métodos , Supervivencia Celular , Fenómenos Químicos , Quitosano/química , Colágeno/química , Colágeno/metabolismo , Matriz Extracelular/metabolismo , Fibroblastos , Humanos , Ensayo de Materiales , Fenómenos Mecánicos , Microscopía de Fuerza Atómica , Nanofibras/ultraestructura
12.
Soft Matter ; 13(39): 7112-7128, 2017 Oct 11.
Artículo en Inglés | MEDLINE | ID: mdl-28858368

RESUMEN

We present theoretical and experimental descriptions of the elasticity of cylindrical micellar filaments using micro-mechanical and continuum theories, and atomic force microscopy. Following our micro-mechanical elasticity model for micellar filaments [M. Asgari, Eur. Phys. J. E: Soft Matter Biol. Phys., 2015, 38(9), 1-16], the elastic bending energy of hemispherical end caps is found. The continuum description of the elastic bending energy of a cylindrical micellar filament is also derived using constrained Cosserat rod theory. While the continuum approach provides macroscopic description of the strain energy of the micellar filament, the micro-mechanical approach has a microscopic view of the filament, and provides expressions for kinetic variables based on a selected interaction potential between the molecules comprising the filament. Our model predicts the dependence of the elastic modulus of the micellar filaments on their diameter, which agrees with previous experimental observations. Atomic force microscopy is applied to estimate the elastic modulus of the filaments using force volume analysis. The obtained values of elastic modulus yield the persistence length of micellar filaments on the same order of the previously reported values. Consistent with previous studies, our results indicate that semi-flexible linear micelles have a relatively large local strain energy at their end points, which explains their tendency to fuse to minimize the number of end caps at relatively low total surfactant volume fractions. Also, the elastic modulus of micellar filaments was found to increase when the indentation frequency increases, a finding which agrees with previous rheological observations on the bulk shear modulus of micellar solutions.

13.
Sci Rep ; 7(1): 1392, 2017 05 03.
Artículo en Inglés | MEDLINE | ID: mdl-28469139

RESUMEN

Tropocollagen types I and III were simultaneously fibrilized in vitro, and the differences between the geometric and mechanical properties of the heterotypic fibrils with different mixing ratios of tropocollagen III to I were investigated. Transmission electron microscopy was used to confirm the simultaneous presence of both tropocollagen types within the heterotypic fibrils. The incorporation of collagen III in I caused the fibrils to be thinner with a shorter D-banding than pure collagen I. Hertzian contact model was used to obtain the elastic moduli from atomic force microscope indentation testing using a force volume analysis. The results indicated that an increase in the percentage of tropocollagen III reduced the mechanical stiffness of the obtained fibrils. The mechanical stiffness of the collagen fibrils was found to be greater at higher loading frequencies. This observation might explain the dominance of collagen III over I in soft distensible organs such as human vocal folds.


Asunto(s)
Colágeno Tipo III/química , Colágeno Tipo I/química , Tropocolágeno/química , Colágeno Tipo I/ultraestructura , Colágeno Tipo III/ultraestructura , Módulo de Elasticidad , Elasticidad , Técnicas In Vitro , Microscopía de Fuerza Atómica , Tropocolágeno/ultraestructura
14.
Eur Phys J E Soft Matter ; 38(9): 98, 2015 Sep.
Artículo en Inglés | MEDLINE | ID: mdl-26362658

RESUMEN

An expression for the elastic free-energy density of a wormlike micelle is derived taking into account interactions between its constituent molecules. The resulting expression is quadratic in the curvature and torsion of the centerline of micelle and thus resembles free-energy density functions for polymer chains and helical filaments such as DNA. The model is applied on a wormlike micelle in the shape of a circular arc, open or closed. Conditions under which linear chains in dilute systems transform into toroidal rings are analyzed. Two concrete anisotropic soft-core interaction potentials are used to calculate the elastic moduli present in the derived model, in terms of the density of the molecules and their dimensions. Expressions for the persistence length of the wormlike micelle are found based on the flexural rigidities so obtained. Similar to previous observations, our results indicate that the persistence length of a wormlike micelle increases as the aspect ratio of its constituent molecules increases. A detailed application of the model on wormlike micelles of toroidal geometry, along with employing statistical-thermodynamical concepts of self-assembly is performed, and the results are found to be well consistent with the literature. Steps to obtain the material parameters through possible experiments are discussed.


Asunto(s)
ADN/química , ADN/ultraestructura , Micelas , Modelos Químicos , Modelos Moleculares , Simulación por Computador , Módulo de Elasticidad , Transferencia de Energía , Conformación de Ácido Nucleico , Estrés Mecánico
15.
Int J Non Linear Mech ; 76: 135-143, 2015 Nov.
Artículo en Inglés | MEDLINE | ID: mdl-26213414

RESUMEN

Lipid-bilayers are the fundamental constituents of the walls of most living cells and lipid vesicles, giving them shape and compartment. The formation and growing of pores in a lipid bilayer have attracted considerable attention from an energetic point of view in recent years. Such pores permit targeted delivery of drugs and genes to the cell, and regulate the concentration of various molecules within the cell. The formation of such pores is caused by various reasons such as changes in cell environment, mechanical stress or thermal fluctuations. Understanding the energy and elastic behaviour of a lipid-bilayer edge is crucial for controlling the formation and growth of such pores. In the present work, the interactions in the molecular level are used to obtain the free energy of the edge of an open lipid bilayer. The resulted free-energy density includes terms associated with flexural and torsional energies of the edge, in addition to a line-tension contribution. The line tension, elastic moduli, and spontaneous normal and geodesic curvatures of the edge are obtained as functions of molecular distribution, molecular dimensions, cutoff distance, and the interaction strength. These parameters are further analyzed by implementing a soft-core interaction potential in the microphysical model. The dependence of the elastic free-energy of the edge to the size of the pore is reinvestigated through an illustrative example, and the results are found to be in agreement with the previous observations.

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