Papers by Piotr Bełdowski
Materials, 2019
Synovial fluid is a lubricant of the synovial joint that shows remarkable tribological properties... more Synovial fluid is a lubricant of the synovial joint that shows remarkable tribological properties. These properties originate in the synergy between its components, with two of its major components, glycosaminoglycans (GAGs) and phospholipids (PLs), playing a major role in boundary and mixed lubrication regimes. All-atom molecular dynamic simulations were performed to investigate the way these components bond. Hyaluronic acid (HA) and chondroitin sulphate (CS) bonding with three types of lipids was tested. The results show that both glycosaminoglycans bind lipids at a similar rate, except for 1,2-d-ipalmitoyl-sn-glycero-3-phosphoethanolamine lipids, which bind to chondroitin at a much higher rate than to hyaluronan. The results suggest that different synovial fluid lipids may play a different role when binding to both hyaluronan and chondroitin sulphate. The presented results may help in understanding a process of lubrication of articular cartilage at a nanoscale level.
Molecules, Dec 24, 2022
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
arXiv (Cornell University), Nov 21, 2019
Many different processes take place to facilitate lubrication of the joints functioning in human ... more Many different processes take place to facilitate lubrication of the joints functioning in human locomotion system. The main purpose of this is to avoid destroying the articular cartilage. Viscoelastic properties of the joints system are very sensitive on both temperature and concentration changes because of the change in conformation presented in the system proteins and protein network formation. We are searching for an answer to the question on how changes in temperature and concentration influence the conformational entropy of mucin protein which is a part of one of the key components, lubricin, which is believed to be responsible for gel formation inside synovial fluid. We are using molecular dynamic technique to obtain the information about dihedral () angles of the mucin during protein self-assembly by means of the computer simulation with a time duration up to 50 ns, parameterized by six temperatures ranged between 300-315 K, and six concentrations 10.68-267.1 g/L. The results show that between c3 and c4 (160 g/L and 214 g/L) a transition exists where crowding begins affecting the dynamics of protein network formation. In such a concentration ranges mucin has a chance to change the frictional properties of the system. Simultaneously there were no significant changes in conformations of the mucin's molecules even after they created networks. The temperature changes also did not affect much of mucin's conformations but it introduced slightly modifications in dihedral angles and after some critical value T=306 K it changed conformational entropy trend from decreasing to raising.
Molecules
In this work, the interactions between hyaluronic acid and bovine serum albumin were investigated... more In this work, the interactions between hyaluronic acid and bovine serum albumin were investigated. The film-forming properties of the mixture were proven, and the mechanical and surface properties of the films were measured. The results showed the interactions between hyaluronic acid and albumin, mainly by hydrogen bonds. Molecular docking was used for the visualization of the interactions. The films obtained from the mixture of hyaluronic acid possessed different properties to films obtained from the single component. The addition of bovine serum albumin to hyaluronic acid led to a decrease in the mechanical properties, and to an increase in the surface roughness of the film. The new materials that have been obtained by blending can form a new group of materials for biomedicine and cosmetology.
Colloids and Interfaces
Phospholipids and hyaluronan are two key biomolecules that contribute to the excellent lubricatio... more Phospholipids and hyaluronan are two key biomolecules that contribute to the excellent lubrication of articular joints. Phospholipids alone and in combination with hyaluronan have also displayed low friction forces on smooth surfaces in micro- and nanosized tribological contacts. In an effort to develop aqueous-based lubrication systems, it is highly relevant to explore if these types of molecules also are able to provide efficient lubrication of macroscopic tribological contacts involving surfaces with roughness larger than the thickness of the lubricating layer. To this end, we investigated the lubrication performance of hyaluronan, the phospholipid 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), and mixtures of these two components using glass surfaces in a mini-traction machine. We compared our data with those obtained using flat silica surfaces in previous atomic force microscopy studies, and we also highlighted insights on hyaluronan–phospholipid interactions gained from r...
Materials, 2022
The ability to form strong intermolecular interactions by linear glucosamine polysaccharides with... more The ability to form strong intermolecular interactions by linear glucosamine polysaccharides with collagen is strictly related to their nonlinear dynamic behavior and hence bio-lubricating features. Type III collagen plays a crucial role in tissue regeneration, and its presence in the articular cartilage affects its bio-technical features. In this study, the molecular dynamics methodology was applied to evaluate the effect of deacetylation degree on the chitosan affinity to type III collagen. The computational procedure employed docking and geometry optimizations of different chitosan structures characterized by randomly distributed deacetylated groups. The eight different degrees of deacetylation from 12.5% to 100% were taken into account. We found an increasing linear trend (R2 = 0.97) between deacetylation degree and the collagen–chitosan interaction energy. This can be explained by replacing weak hydrophobic contacts with more stable hydrogen bonds involving amino groups in N-de...
Micelle Confined in Aqueous Environment: Lubrication at the Nanoscale and Its Nonlinear Characteristics
Springer Proceedings in Mathematics & Statistics, 2016
We present constant pressure molecular dynamics simulation results of a micelle in an aqueous env... more We present constant pressure molecular dynamics simulation results of a micelle in an aqueous environment confined between two surfaces. The lipid-water interactions are described in terms of the MARTINI force field, and the constant pressure simulation approach as described in Winkler and Hentschke (J Chem Phys 99:5405–5417 (1993), [1]) is applied. The fluid–surface interactions are taken into account by a static external potential field. Our results provide a molecular picture of the surface-induced structure of the fluid, the fluid dynamics, and the corresponding non-linear properties of the micelle as a mechanical system. Hence, the performed analyses provide insight into lubrication at the nanoscale of the articulating system; the lubrication effect becomes nonlinear in terms of the basic defect creation-annihilation mechanism. According to the model of facilitated lubrication Gadomski et al. (Tribol Lett 30:83–90 (2008), [2]), micellar interactions contribute to a lowering the friction coefficient of articular cartilage (AC).
Fractional Calculus Evaluation of Hyaluronic Acid Crosslinking in a Nanoscopic Part of Articular Cartilage Model System
This work presents a study of the mechanism of physical crosslinking of hyaluronic acid in the pr... more This work presents a study of the mechanism of physical crosslinking of hyaluronic acid in the presence of common phospholipids in synovial joint organ systems. Molecular dynamic simulations have been executed to understand the formation of hyaluronan networks at various phospholipid concentrations. The results of the simulations suggest that the mechanisms exhibit subdiffusion characteristics. Transportation quantities derive as a function of time during numerical calculations of mean square displacement, and observations of sublinear growth were noted. Coarse-grained models are deployed to obtain a mathematical description where a random walker and several subdiffusion schemes of its motion describe the models. The findings of this study may establish mechanisms of biopolymer network formations in normal and pathologic synovial fluid and help elucidate the mechanism of facilitated AC biolubrication.
Analysis of Protein Intramolecular and Solvent Bonding on Example of Major Sonovital Fluid Component
Biologically-Inspired Systems, 2021
Molecular interactions within proteins are fundamental to maintain their conformation and role in... more Molecular interactions within proteins are fundamental to maintain their conformation and role in biological systems. Understanding the nature and dynamics of the interactions is crucial as it can help understand phenomena occurring during physiological processes, drug design, and delivery, etc. This chapter presents the analysis of the dynamics of molecular interactions inside proteins on an example of albumin. We have performed computer simulations of albumin protein at its native/equilibrium state to understand the dynamics of bonding/interactions inside the protein and with water: hydrogen bonds and hydrophobic interactions. Furthermore, we extracted the data to look into interactions between particular amino acids (AA). As expected, charged AA, such as the glutamic acid (GLU) and lysine (LYS) one, form most intermolecular hydrogen bonds and bind most water.
International Journal of Molecular Sciences, 2021
The lubrication mechanism in synovial fluid and joints is not yet fully understood. Nevertheless,... more The lubrication mechanism in synovial fluid and joints is not yet fully understood. Nevertheless, intermolecular interactions between various neutral and ionic species including large macromolecular systems and simple inorganic ions are the key to understanding the excellent lubrication performance. An important tool for characterizing the intermolecular forces and their structural consequences is molecular dynamics. Albumin is one of the major components in synovial fluid. Its electrostatic properties, including the ability to form molecular complexes, are closely related to pH, solvation, and the presence of ions. In the context of synovial fluid, it is relevant to describe the possible interactions between albumin and hyaluronate, taking into account solution composition effects. In this study, the influence of Na+, Mg2+, and Ca2+ ions on human serum albumin–hyaluronan interactions were examined using molecular dynamics tools. It was established that the presence of divalent cati...
Sensors, 2021
Due to the semi-liquid nature and uneven morphologies of biological membranes, indentation may oc... more Due to the semi-liquid nature and uneven morphologies of biological membranes, indentation may occur in a range of non-ideal conditions. These conditions are relatively unstudied and may alter the physical characteristics of the process. One of the basic challenges in the construction of nanoindenters is to appropriately align the nanotube tip and approach the membrane at a perpendicular angle. To investigate the impact of deviations from this ideal, we performed non-equilibrium steered molecular dynamics simulations of the indentation of phospholipid membranes by homogeneous CNT and non-homogeneous SiCNT indenters. We used various angles, rates, and modes of indentation, and the withdrawal of the relative indenter out of the membrane in corresponding conditions was simulated.
The Journal of Physical Chemistry B, 2020
Synthesis of graphene (GN) in 2004 stimulated wide interest in potential applications of 2D mater... more Synthesis of graphene (GN) in 2004 stimulated wide interest in potential applications of 2D materials in catalysis, optoelectronics, biotechnology, and construction of sensing devices. In the presented study, interactions between GN sheets and phospholipid bilayers are examined using steered molecular dynamics simulations. GN sheets of different sizes were inserted into a bilayer and subsequently withdrawn from it at two different rates (1 and 2 m/s). In some cases, nanoindentation led to substantial damage of the phospholipid bilayer; however, an effective self-sealing process occurred even after significant degradation. The average force and work, deflection of the membrane during indentation, withdrawal processes, and structural changes caused by moving sheets are discussed. These quantities are utilized to estimate the suitability of GN sheets for targeted drug delivery or other nanomedicine tools. The results are compared with those obtained for other nanostructures such as homogeneous and heterogeneous nanotubes.
Acta Physica Polonica B, 2021
Articular cartilage is a natural tribochemical device just-designed by nature. Yet, a vivid debat... more Articular cartilage is a natural tribochemical device just-designed by nature. Yet, a vivid debate goes on toward the mechanisms by which its nanoscopic viscoelastic properties facilitate lubrication in terms of ultralow static and kinetic friction coefficients. In this concisely conducted conceptual discussion, we wish to point out that a nanoscale tribomechanistic description based upon certain "viscoelastic quanta", called fractons, expressing spectral-mechanical properties of viscoelastic nets under the influence of force/pressure factor(s), may contribute substantially to the elucidation of ultralow coefficients of friction in the articular cartilage of predictable relaxational response. Our example unveils a part of a mechanically responsive viscoelastic network, such as a tied piece of hyaluronan molecule, fit in an Edwards type tube, in which upon water-mediated interaction of lipids with the hyaluronan when subjected to loading at the nanoscale, a consecutive stress-field and ion diffusion action is going to occur simultaneously. It results in a natural-logarithmic formula that interrelates a number of hyaluronan's interactive residues, N , with certain molecular-elastic (an exponent γ) and surface-to-volume (nano-colloid type) characteristics of around 2/3 to emerge near thermodynamic equilibrium, that is to say after a frictional loading action performed. It enables to relate uniquely a value of the exponent 0 < γ < 1/2 with a virtual tribomicellization scenario of the nanoscale friction-lubrication event accompanied by inevitable tubularmilieu viscosity alterations when the quasi-static friction scenario shows up, preferably with γ → 1/3 from above for large enough N-s. A periodic vibrational super-biopolymer's mode is exploited, leading to a change in the nanoscale friction-lubrication period from which an opportunity to involve an essential contribution to the (nanoscale) coefficient of friction arises.
Molecules, 2020
Hyaluronan is an essential physiological bio macromolecule with different functions. One prominen... more Hyaluronan is an essential physiological bio macromolecule with different functions. One prominent area is the synovial fluid which exhibits remarkable lubrication properties. However, the synovial fluid is a multi-component system where different macromolecules interact in a synergetic fashion. Within this study we focus on the interaction of hyaluronan and phospholipids, which are thought to play a key role for lubrication. We investigate how the interactions and the association structures formed by hyaluronan (HA) and 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) are influenced by the molecular weight of the bio polymer and the ionic composition of the solution. We combine techniques allowing us to investigate the phase behavior of lipids (differential scanning calorimetry, zeta potential and electrophoretic mobility) with structural investigation (dynamic light scattering, small angle scattering) and theoretical simulations (molecular dynamics). The interaction of hyalurona...
Entropy, 2020
This work presents the analysis of the conformation of albumin in the temperature range of 300 K ... more This work presents the analysis of the conformation of albumin in the temperature range of 300 K – 312 K , i.e., in the physiological range. Using molecular dynamics simulations, we calculate values of the backbone and dihedral angles for this molecule. We analyze the global dynamic properties of albumin treated as a chain. In this range of temperature, we study parameters of the molecule and the conformational entropy derived from two angles that reflect global dynamics in the conformational space. A thorough rationalization, based on the scaling theory, for the subdiffusion Flory–De Gennes type exponent of 0 . 4 unfolds in conjunction with picking up the most appreciable fluctuations of the corresponding statistical-test parameter. These fluctuations coincide adequately with entropy fluctuations, namely the oscillations out of thermodynamic equilibrium. Using Fisher’s test, we investigate the conformational entropy over time and suggest its oscillatory properties in the correspond...
Advances in Colloid and Interface Science, 2019
The manner in which nature has solved lubrication issues has fascinated scientists for centuries,... more The manner in which nature has solved lubrication issues has fascinated scientists for centuries, in particular when considering that lubrication is achieved in aqueous media. The most outstanding system in this respect is likely the synovial joint, where close to frictionless motion is realized under different loads and shear rates. This review article focuses on two components present in the synovial area, hyaluronan and phospholipids. We recapitulate what has been learned about their interactions at interfaces from recent experiments, with focus on results obtained using reflectivity techniques at large scale facilities. In parallel, modelling experiments have been carried out and from these efforts new detailed knowledge about how hyaluronan and phospholipids interact has been gained. In this review we combine findings from modelling and experiments to gain deeper insight. Finally, we summarize what has been learned of the lubrication performance of mixtures of phospholipids and hyaluronan.
Energies, 2019
Molecular dynamics simulations have been performed for a model aqueous solution of mucin. As muci... more Molecular dynamics simulations have been performed for a model aqueous solution of mucin. As mucin is a central part of lubricin, a key component of synovial fluid, we investigate its ability to form cross-linked networks. Such network formation could be of major importance for the viscoelastic properties of the soft-matter system and crucial for understanding the lubrication mechanism in articular cartilage. Thus, the inter- and intra-molecular interaction energies between the residues of mucin are analyzed. The results indicate that the mucin concentration significantly impacts its cross-linking behavior. Between 160 g/L and 214 g/L, there seems to be a critical concentration above which crowding begins to alter intermolecular interactions and their energies. This transition is further supported by the mean squared displacement of the molecules. At a high concentration, the system starts to behave subdiffusively due to network development. We also calculate a sample mean squared d...
Polymers, 2018
Glycosaminoglycans are a wide class of biopolymers showing great lubricating properties due to th... more Glycosaminoglycans are a wide class of biopolymers showing great lubricating properties due to their structure and high affinity to water. Two of them, hyaluronic acid and chondroitin sulfate, play an important role in articular cartilage lubrication. In this work, we present results of the all-atom molecular dynamics simulations of both molecules placed in water-based solution. To mimic changes of the physiological conditions, especially temperature, of the synovial fluid in joints under successive load (e.g., walking, jogging, jumping), simulations have been performed at different physiological temperatures in the range of 300 to 320 Kelvin (normal intra-articular temperature is 305 K). The stability of the biopolymeric network at equilibrium (isothermal and isobaric) conditions has been studied. To understand the process of physical crosslinking, the dynamics of intra-and intermolecular hydrogen bonds forming and breaking have been studied. The results show that following addition of chondroitin sulfate, hyaluronan creates more intermolecular hydrogen bonds than when in homogeneous solution. The presence of chondroitin in a hyaluronan network is beneficial as it may increase its stability. Presented data show hyaluronic acid and chondroitin sulfate as viscosity modifiers related to their crosslinking properties in different physicochemical conditions.
Fluctuation and Noise Letters, 2019
This work presents the process of physical crosslinking of hyaluronic acid (HA) in the presence o... more This work presents the process of physical crosslinking of hyaluronic acid (HA) in the presence of phospholipids (PL) as applied to the lubrication in articular cartilage system. Three time scales of the process have been studied using Molecular Dynamics simulation: 2[Formula: see text]ps, 200[Formula: see text]ps and 20[Formula: see text]ns. The simulations were carried out for long and short chains of HA in the presence and in the absence of PL. We show that in contrast to the macroscopic thermal (white) noise, the short-time noise on the molecular scale has the properties of color noise with the power spectrum distribution proportional to the inverse of frequency, [Formula: see text]. The long-time simulations are characterized by a power spectrum similar to that of white noise.
The European Physical Journal B, 2018
We propose to adopt a non-isothermal and colloid type cluster-cluster aggregation stochastic mode... more We propose to adopt a non-isothermal and colloid type cluster-cluster aggregation stochastic model aimed at comprehending the temperature driven and polymer swelling accompanying volume expansion encountered in microgels. The nonequilibrium nature of the process is captured by describing expansion characteristics with simplified power laws, indicating the scalability of properties with time and temperature. Additionally, molecular dynamics simulations of the presented mechanism for a chosen biopolymer have been performed. This can be of interest for experimenters working in the field of nonequilibrium phase transitions, and fairly prospectively, within the area of thermal phonon-involving technology. In these areas, scanning the system's temperature, or sometimes tuning similar dissipation-addressing physical factors, such as pH, appears to be a fairly pivotal examination case.
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Papers by Piotr Bełdowski