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Capstan-like mechanism in hyaluronan–phospholipid systems
Accepted Manuscript Title: Capstan-like mechanism in hyaluronan-phospholipid systems Author: P. Beldowski N. Kruszewska S. Yuvan Z. Dendzik T. Goudoulas A. Gadomski PII: DOI: Reference:
S0009-3084(18)30139-7 https://doi.org/doi:10.1016/j.chemphyslip.2018.08.002 CPL 4675
To appear in:
Chemistry and Physics of Lipids
Received date: Accepted date:
13-7-2018 13-8-2018
Please cite this article as: P. Beldowski, N. Kruszewska, S. Yuvan, Z. Dendzik, T. Goudoulas, A. Gadomski, Capstan-like mechanism in hyaluronanphospholipid systems, (2018), https://doi.org/10.1016/j.chemphyslip.2018.08.002 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Capstan-like mechanism in hyaluronan-phospholipid systems
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P. Beldowskia , N. Kruszewskaa , S. Yuvanb , Z. Dendzikc , T. Goudoulasd , A. Gadomskia a
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UTP University of Science and Technology, Institute of Mathematics and Physics, Kaliskiego 7, PL–85796 Bydgoszcz, Poland b Department of Physics, East Carolina University, Greenville, NC 27858, USA c Institute of Physics, University of Silesia, 75 Pulku Piechoty 1, 41-500 Chorzow, Poland and Silesian Center for Education and Interdisciplinary Research, University of Silesia, 75 Pulku Piechoty 1A, 41-500 Chorzow, Poland d Technical University of Munich, School of Life Sciences Weihenstephan, Maximus-von-Imhof-Forum 2, 85354 Freising, Germany
Abstract
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Functionality of articular cartilage results from complex interactions between its molecular components. Among many biomolecules, two are of prime importance for lubrication: hyaluronic acid (HA) and phospholipids (PL). The purpose of this study is to discuss a mechanism of interaction between these two components and how their synergies contribute to nanobiolubrication of articular cartilage. Preliminary molecular dynamics simulations have been performed to investigate these interactions by adopting a capstan-like mechanism of action. By applying a constant pulling force to both ends of a HA molecule, wrapped around a PL micelle, we viewed the rotation of the PL micelle. The simulations were performed upon two physicochemical constraints: force- and solvent-dependency. The results show the efficiency of rotation from intermolecular bond creation and annihilation. We found a direct relation between the available surface of the micelle and the magnitude of the force, which varies significantly through the unwinding. The movement of the attached molecules are characterized by a slide-to-roll relation, which is affected by the viscosity of the surrounding medium. As a
Email addresses: [email protected] (P. Beldowski), [email protected] (N. Kruszewska), [email protected] (Z. Dendzik), [email protected] (T. Goudoulas)
Preprint submitted to Chemistry and Physics of Lipids
July 13, 2018
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consequence, two solvents were studied for specific force conditions and the molecular dynamics simulation exhibited double the slide-to-roll coefficient for the viscous solvent as compared to its low-viscosity limit.
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Keywords: Hyaluronic acid, Lubrication, Phospholipids, Articular Cartilage
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1. Introduction
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Synovial joints are natural systems that provide low friction as well as a long period of functionality. The articular cartilage (AC) surfacing these joints is lubricated by a complex liquid called synovial fluid (SF). Regardless of the long debate over the mechanism of joint lubrication during the last decades [1, 2, 3], it has not been fully understood due to its complicated nature [2, 4]. Recently, an increasing number of studies suggest that the overall lubrication mechanism is of a multiscale, synergistic nature [4, 5, 6, 7]. Thus, to understand the nature of joint lubrication, an analysis based on that synergy is required. Hyaluronic acid (HA) and common phospholipids (PL) are the two important components in AC systems that provide modulation of fluid viscosity and surface lubrication [8]. Biopolymer-lipid systems spontaneously form a variety of nanostructures and it is very important to understand the interactions between them [9]. This work focuses on the tribological role of HA-PL interactions and their synergistic effects in synovial joint lubrication. Fig. 1 presents a depiction of a joint system as a complex interactive system with the SF, where the functionality is obtained due to multiscale phenomena. As an efficient lubricant, SF must function in all regimes of lubrication, namely: boundary, mixed and hydrodynamic [5, 12, 13, 14, 15]. The situation presented in Fig. 1 shows a mixed/hydrodynamic regime. Both AC surfaces are separated by synovial fluid consisting mainly of HA molecules, with PL bilayes present at the AC surface. However, after applying a normal load, PLs can be released into SF milieu and form vesicles within or on HA networks [16]. Due to the complexity of interactions of HA and PL molecules [17, 18] several scenarios need consideration. Dense HA networks can repel PL vesicles from their interior but may also be penetrated with free lipids which create vesicles inside the HA network [18]. PLs in the form of bilayers/vesicles can also interact with HA networks [19], which can also lead to facilitated lubrication at nanoscale level as governed by proton 2
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Figure 1: Artistic simplified depiction of AC system. Top and lower orange rectangles represent AC surfaces, green lines represent HA chains. Lipids are depicted as blue (hydrophilic) ”head” and red (hydrophobic) tails. The system undergoes several lubrication regimes [10]. Rolling friction is achieved due to presence of vesicles (created by phospholipids) and HA in regime of mixed lubrication [11].
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transport in so-called ”micellar channels” [20] or at the surface of bilayer [21]. Ultimately, the source of nanoscale friction in the system is the reorganization of molecules in response to external mechanical stress. HA on its own does not lower friction in the system - it has nano-shock absorbing properties - but may allow PLs in aggregated forms to reduce the friction coefficient by qualitatively altering the relative motion of molecules from sliding to vesicle facilitated rolling [16, 19, 22]. As described in [4], one can envision this reorganization as network strands being pulled through the environment by their heavily entangled ends or the presence of sheering flow. Such molecules entangled in the network may either slip past one another, encountering resistance from the destruction of bonds between adjacent (HA) strands, or prospectively, interact with interspersed spherical PL structures which allow HA molecules to ’roll’ past each other, instead forming relatively weaker bonds with PL heads. The present study implements a simplified model of such a structure in
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order to understand the general functionality of the system. This is based on the assumption that a simple cylindrical or rod-like micelle can mimic behavior of the larger, naturally occurring, PL vesicles. This assumption would seem defensible as the nanoscale friction effects under investigation are due to the chemical interaction of the surfaces rather than gross mechanical properties as in a typical capstan-like mechanism [23, 24]. In the model, this PL micelle is tangled with the HA chain (cf. Fig. 2). The HA chain, acting as a rope, wraps around the PL micelle, which serves as a pulley in the capstan mechanism. The wrapped angle of the HA molecule around the micelle has been denoted as θ in the Fig. 2. At each point of contact between the rope (HA) and pulley (PL) there is a normal force, which results in a frictional force acting tangentially to the pulley. The frictional force acts in the opposite direction to the rotation. In this way, the tension on the opposing side of the pulley is reduced. To simulate the tensile forces, two pulling forces, T1 and T2 (T1 > T2 ), have been added on both ends of the HA chain, mimicking the stress inside long-chain networks present in AC system (cf. Fig. 2). In a real capstan, one could then compute a coefficient of friction, µ, by finding the largest T1 possible without slipping, and using the standard formula T1 = T2 exp(µθ). This formula is not used, however, because there are critical differences between our system and actual capstans. Influenced by the pulling forces, the HA micelle can not only rotate, but slide (undergo an unbounded motion) inside the fluid in which it is immersed. In real capstan mechanisms the pulley can only rotate around a fixed axis (in the powered version of the mechanism) or not revolve at all (holding capstan). Additionally, the studied HA-PL system can be deformed. Thus applied forces to the HA chain cannot be too large, i.e. large enough to cause slipping (breaking all inter-molecular bonds simultaneously), because the micelle would start to break up. Rotation of the micelle causes an unwrapping of the chain instead of slipping. Due to the unwinding, the number of contact points between HA and PL decreases in time and the angle θ lowers. Thus, in the study, the capstan analogy is only used for visualizing the HA-PL system rather than to compute µ from the equation presented above. The rotation and slide of the micelle are conceptualized to be responses to the HA network motion. Efficient motion of the micelle is the result of hydrophobic interactions between those two structures as well as hydrogen bond creation and annihilation. Hydrophobic properties arise because the HA chain as well as micelle consist of both hydrophilic viz. polar (P) and 4
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Figure 2: Snapshots of the simulation box of HA-PL system. HA is colored green. PL building micelle are composed of carbon colored blue, hydrogen - white, oxygen - red, nitrogen - yellow. a) A snapshot of a beginning stage of simulation. b) A snapshot of a final stage of simulation with pulling forces presented as black arrows. The figure presents capstan-like mechanism of the soft matter HA-PL system.
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hydrophobic viz. nonpolar (NP) groups of molecules [25]. The NP molecules are water repellent; preferring proximity to other NP molecules. Therefore, an interaction appears that is similar to attraction. The P molecules, by contrast, are prone to contact with water. This is clearly demonstrated by PL micelles, (cf. Fig. 1) where P heads of lipids arrange to contact with water and NP tails stick together to avoid contacts with water. As a result, a double-layered spherical micelle is formed. This study provides cogitations, supported by preliminary computer simulation, on whether the aforementioned interactions between HA-PL may provide a plausible scheme to support lowered friction in the facilitated lubrication of the AC system. Our Derjaguin type [26] motivated results are a first-step attempt towards calculating the friction coefficient based on the statistics of the interactions. 2. Methods 2.1. Simulation details Investigating biomolecular systems usually focuses on identifying the physical mechanisms establishing their functions. Widely used in this regard are 5
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Molecular Dynamics (MD) simulations. Because the computational time required to simulate the majority of bioprocesses is usually prohibitively large, simulation using the Steered Molecular Dynamics (SMD) method permits competent investigation of molecular processes. A direct simulation can be too slow, because of the energy barriers. Therefore, by focusing on selected degrees of freedom and by applying external steering to accelerate processes, the SMD provides meaningful simulation results. Technically, SMD is based on the concept of applying an external force to one or more atoms (referred to as SMD atoms). This may be accomplished using either constant pulling force or constant pulling velocity. The former refers to a constant force directly applied to the SMD atom. In the case of a constant pulling velocity, the SMD atom is coupled to a virtual atom (moving with constant velocity), usually with a harmonic potential. In addition to this, positions of another group of atoms may be kept fixed. To avoid local heating, caused by applied external forces, all heavy atoms may be coupled to a heat bath. SMD has proven to be particularly useful in many applications, ranging from calculating the basic physical characteristic of the systems, such as the potential of mean force (PMF) [27], to study the molecular mechanisms of processes, such as transition of ions and organic compounds through biomembrane channels [28, 29, 30, 31]. Also, mechanical functions of proteins and other biomolecules have been investigated using SMD [32, 33, 34]. The simulations were performed by adopting AMBER03 force field [35]. Every case was repeated 30 times to obtain statistically more reliable information. HA and PL structures have been downloaded from PubChem (Open Chemistry DataBase). The DPPC (dipalmitylephosphatidocholine) lipid has been used (being the most common in SF systems [36]) to build cylindrical micelle composed of 73 lipids. DPPC in such small numbers does not normally create micelle or rod-like structures, however due to the computational cost of natural structures (of more than 800 PL) we used MSHAKE algorithm [37] to keep lipid tails in place during simulations. The HA molecule was modified to obtain longer chains by using YASARA Structure software. The final length of the HA was 25 nm and had a molecular mass of 10 kDa. These values are realistic if we consider that the HA persistence length is around 4 nm [38] allowing a fully covered PL, as it presented in Fig. 2. However, for similar computational rationale, the HA molecular mass used is much lower than can be found in real SF (around 2 MDa). Such a simplification is assumed to be acceptable as long as we are concerned only with 6
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HA-PL interactions’ of the micelle’s surface, for which the overall size of the structure is irrelevant. Our next studies will focus on creating more realistic representations, here we give a general impression of system functionality. The initial structure of the system is presented in Fig. 2a. As one can see, the micelle has been surrounded by HA. SMD has been performed by applying constant force (with constant direction) to each end of HA chain (composed of one HA bead) causing micelle to rotate (see, Fig. 3). All
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Figure 3: Sequential snapshots of the simulation box. HA is colored green, while atoms of the PL micelle are: C - blue, H - white, O - red, N - yellow. Time instances following the application of the force: a) 0 ps, b) 330 ps, c) 660 ps, d) 1000 ps, e) 1330 ps, f) 1660 ps.
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simulations were performed at identical conditions, that is, a temperature equal to 310 K, and a pH of 7.0. Time steps were set to 2.5 fs and simulations allowed to run until the pulled chain reached a wall of simulation box (the total number of simulation steps was on the magnitude of 106 for all cases). Two solvents have been used in this study: (a) a water solution of 0.9% NaCl to closely mimic the physiological solution, and (b) 30% glycerol in the previous solution. Simulations in some narrow ranges of pulling forces have been prepared in order to decrease or eliminate the probability of the micelle breaking, which can result from application of an external (quasi)normal load [39]. The range of forces we used is in range of ones used for other SMD simulations of biological systems [40]. However it is hard to estimate an actual forces occurring in our system due to HA network shock absorbing properties, where load applied to actual vesicles may differ depending on their position. In the case of a water solution we analyzed characteristics of HA and PL micelles for three different pulling force: T1 = 16, 32 and 64 pN 7
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to one end of HA. For the glycerol solution, we used one pulling force T1 = 64 pN. For all cases, the other end of the HA molecule was pulled with the same force of T2 = 4 pN in opposite direction. In this way the soft-matter capstanlike mechanism, mimicking a micelle wrapped by HA chain under stress in network, has been simulated (cf. Fig. 2).
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1 1 µ v = ∆T + ζ, m m m
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2.2. Calculated parameters of the system The effective pulling force ∆T = T1 − T2 , driving the rotation and slide of the micelle, was resisted by the viscosity of the solvent leading to an overdamped system. The Langevin equation, describing a velocity, v, of the mass element of the HA chain, m, can be written as (1)
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where µ stands for a friction coefficient as above, ζ is a stochastic-force (typically Gaussian correlated) variable representing the effect of background noise from fluctuations in density and temperature. The velocity is an important parameter due to its connection to slide and roll speeds of PL micelle. The HA chain stays in connection with PL micelle mediated by lubricant (solvent). Thus, the pulling force of the HA chain as well as fluctuations inside the chain both influence micelle rotation and translation. The system mimics a mini traction machine comprised of a ball and disc in contact, submerged in a reservoir full of lubricant (see Fig. 2 in [41]). For such systems a slide to roll ratio (SRR) parameter is usually calculated. The SRR is defined as the ratio of the mean sliding speed to the mean rolling speed between two bodies: SRR =| uD − uB | /US
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where uD and uB are the speeds of two (nano)surfaces of the disc (in our case HA surface) and the ball (uB is a sum of micelle rotational and sliding speeds), respectively. US is the entrainment or two-point arithmetic mean speed, (uB + uD )/2. When the ball and the disc rotate at the same surface speed in the same direction, contact conditions are ’pure rolling’, SRR is equal 0, whereas for SRR = 2 there is ’pure sliding’ [42]. The number of hydrophobic interactions (between hydrophobic atoms) and hydrogen bond energy is calculated by the algorithm described previously [43]. 8
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The solvent accessible surface as evaluated in this study, consists of all the points that the center of the water probe (i.e. the nucleus of the oxygen atom in the water molecule) can reach while rolling over the solute. The procedure of calculating this variable has been presented in [44, 45].
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3. Results
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To describe the nanoscale HA-PL interactions and their influence on facilitated lubrication of AC, we focused on the rotation of the micelle and the effect of HA-PL dynamical contact creation and annihilation. To better understand the efficiency of the proposed mechanism here, we performed SMD calculations for two conditions: (i) force dependent and (ii) solvent dependent.
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3.1. Dependence on force Rotation angles of the micelle, φ, and rotation velocities, U , upon three different pulling forces, are presented in Fig. 4. Varying the pulling force
Figure 4: (a) Rotation angle φ and (b) rotation velocity U of a micelle as a function of time divided by total time t∗ of simulation of each case. Simulation results are presented for three cases of applied pulling forces whose values are given in the insert.
naturally has a direct impact on the time required to reach the end of the simulation box. In order to compare all three cases, time values, t, have been 9
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normalized using t∗ , representing the total time required for the particular simulation in question. In all cases, the rotation velocities behave similarly. The pulling force T1 − T2 takes effect immediately and dominates at the start of simulation, but this velocity is quickly damped as the system begins to behave according to the Langevin equation in Eq. (1) resulting in constant velocity throughout much of simulation. Then near the end of simulation the rotational velocity falls further as the HA chain is almost entirely unwrapped from the PL micelle. There are two major effects influencing efficient rotation of the micelle. First is hydrogen bond creation and annihilation, presented in Fig. 5. Second are the creation of hydrophobic contacts between molecules presented in Fig. 6. Both parameters decrease as the total contact area becomes smaller. However, the plateau of the third case in Fig. 6 is due to closer contact between HA and PL as a result of the HA chain cutting into the PL micelle.
Figure 5: Number and total energy of hydrogen bonds between the PL micelle and HA as a function of time. Simulation results are presented for three cases of applied pulling forces whose values are given in the insert.
This means that for higher pulling forces than T1 = 64 pN, the micelle collapses. This was confirmed by the SMD simulation results (data not shown 10
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Figure 6: Number of hydrophobic interactions between the PL micelle and HA as a function of time. Simulation results are presented for three cases of applied pulling forces whose values are given in the insert.
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here). One can see that for the smallest force applied (T1 = 16 pN) all data show much higher fluctuations throughout the simulations than for the remaining cases. Even higher effects of fluctuations have been noticed for applied forces smaller than 16 pN (not presented in this study). The number of hydrophobic and hydrogen interactions also depends on the solvent type. Additionally, looking on Eq. (1), the solvent viscosity is an important factor in the presented mechanism. Solvent accessible surfaces presented in Fig. 7 show that, for the largest force, solvent can penetrate the micelle more easily than for the other cases, obstructing its lubricating properties. Thus, this variable is important for describing the stability of the micelle: the higher force results in poorer integrity. SRR as a function of time, presented in Fig. 8, shows relative sliding versus rotation of the micelle for all cases in water solvent, with domination of rotation when SRR < 1 throughout almost all time of simulation. However for the smallest force (T1 = 16 pN), near the end of simulation, the motion is ’pure sliding’. This is caused by some stable hydrogen bonds keeping two molecules in contact despite the near complete unwrapping of the HA chain from the micelle. The same hydrogen bonds, in the case of larger pulling forces, break more easily. On the other hand, in that case, the atoms of both 11
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Figure 7: Solvent accessible surface of the PL micelle as a function of time. Simulation results are presented for three cases of applied pulling forces whose values are given in the insert.
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molecules are closer to each other and create more contacts. This observation can not be presented quantitatively in this study due to software constraints, however, future study could present more atomic details.
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3.2. Solvent dependence As presented in Fig. 9 and 10 solvent is an important factor influencing micelle motion. The rotation angle φ increases more slowly in time for glycerine than for water solvent, thus, the rotation velocity is smaller, though still constant for much of the simulation, as previously described in Sec. 3.1. SRR values presented in Fig. 10 show that, for glycerine, the system behaves differently for water, there is much less rotation than sliding in the motion of micelle. This is like caused by the much higher viscosity of the glycerine. 4. Discussion
The nature of HA-PL interaction is very complex as both species take on several forms even within a single cell [8, 46]. Thus, the proposed mechanism for improved lubrication can be viewed as one well-substantiated possibility among many. PLs (in the form of bilayers or even multilayers) appear to play a key role in boundary lubrication via Derjaguin type hydration-repulsion 12
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Figure 8: SRR as a function of time. Simulation results are presented for three cases of applied pulling forces whose values are given in the insert.
Figure 9: Rotation angle φ, and rotation (angular) velocity of the PL micelle, U , as a function of time divided by total time t∗ of simulation. Simulation results are presented for two solvent as described in the insert (see, Sec. 2.1).
lubrication [47, 48, 26]. Synergistic effects of HA-PL interactions play an important role in the functioning of many biological systems [8]. 13
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Figure 10: SRR as a function of time for water and glycerol solutions for pulling force T1 = 64 pN applied. Simulation results are presented for two solvent as described in the insert.
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The concept of a closed-packing formation of layer-by-layer deposition close to the cartilage interface, as proposed by [4], is also assumed here. In these conditions, the motion of join surfaces can cause relative sliding of such layers resulting in the forces on HA chains studied here. The adopted scheme in Fig. 2, is an initial approach to the more complex condition inside a joint, where high-molecular-weight molecules of HA will interact with each other to form large-scale networks, with the DPPC-HA complexes trapped inside. Several factors govern these interactions, however, two are of major importance: HA molecular mass and concentration of both species. It has been shown that longer HA chains create cylindrical structures when surrounded by PLs [17]. On the other hand, shorter chains are absorbed into PL vesicles. There are additionally two ways in which resulting PL structures can be attached to HA chains. The first is hydrophilic in nature and results in hydrogen bond creation. PLs turn toward HA with their hydrophilic heads and water molecules fill the interspaces between HA and PL. The second form is between hydrophobic parts. This orientation can be found in low concentrations of PL, where nonpolar tails attach to hydrophobic sites on HA [43]. This is a probable scenario for pathological SF, where all components are diluted due to the increased amount of serum in the joint cavity. 14
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Our findings represent a model of rolling friction of the micelle as a result of lateral quasi-normal load coming from HA network. The modeled system mimics a capstan mechanism where both ends of rope, wrapped around a pulley, are pulled by some stress forces (see, Fig. 2). This model of HA-PL interactions has been applied to better understand the process of facilitated lubrication of AC system at the nanoscale level. Motion of the micelle depends on dynamics of contacts created between the molecules. This involves efficient hydrogen bond creation and annihilation as well as formation of hydrophobic ”bonds” between interacting groups. The implication is that those systems create energetically favorable conditions for the following two effects to act on micelles and improve lubrication: hydration repulsion and rolling friction. Rolling may result in a reduction of the friction coefficient due to how intermolecular bond breaking occurs. Namely, sliding/rolling is facilitated by an energetically favorable bond exchange between interacting molecules. Thus, a small pulling force T1 could result in efficient ”hopping” of hydrogen and hydrophobic bonds (cf. Fig. 5 and 6). Presented data show the molecular details of this fairly hypothetical mechanism of facilitated lubrication at the nanoscale, and the large spectrum of pulling forces over which it can operate. The reduction of friction force occurs when itermolecular interaction is of smaller magnitude than intramolecular interaction. Thus, in spaces where HA density is low enough to permit interactions with PLs, more efficient bond redistribution will result compared to a pure HA network. From this perspective PLs are necessary for system to decrease friction force, but HA networks simultaneously need to remain dense enough to provide shock absorption to the system. For small applied forces (smaller than 16 pN) a lot of environmental fluctuations are evident in simulation results. For the case of T1 = 64 pN (higher forces), one can see the plateau resulting from the HA chain cutting into the PL micelle and compromising its integrity. The plateau lasts about t/t∗ = 0.8, then decline resumes at the end of the simulation. Evidently as the chain is unwound from the micelle, the compressive force is no longer enough to cause deformation. For a better understanding of the proposed explanation of friction reduction, based on the intermolecular bond breaking, more studies must be conducted. Contrasting variations in the solvent exposed surface area have been observed in the course of the simulation for the applied forces. The higher 15
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force on the HA-micelle system uncovers more of its hydrophobic parts. As noted, for even higher forces a destruction of the micelle occurs. Moreover, the nature of the applied forces is still under consideration, but is likely attributable to the shear or elongation flow field, or even more, to a partial anchor of the HA molecule on the AC. Finally, the simulation results show that a micelle behaves differently in water than in glycerine. In water, rotation is much faster than in glycerine. But the most noticeable difference is seen in the SRR figure (cf. Fig. 10). There is a prominent peak in the first part of the motion (0.1-0.2 of simulation time) in the case of glycerine, but even beyond this peak sliding prevails over rolling. Lastly, the slight increase in the SRR value’s at the tail end of the simulation is not observed in for glycerol solution. This may be explained with a mixed mode motion as the water system passed through a greater overall rotation. It is worth noting that Lazarev and Derjaguin [26], in their macroscopic experiment, use wire that tightly embraces the round rubbing surfaces via an oil. Between the components only a few molecules of inter-layer lubricant is applied. We can see an analogy with HA-PL system, taking the PL micelle as the shaft and the HA chain, trapped in a network created by various components of the AC system, as the wire. Tensions in the network are then analogous to a load force applied at the end of the wire in [26]. Drawing such a parallel is a novel contribution of our study. The extension of such macroscopic tools to the nanoscale level is also thoroughly addressed in [48]. 5. Conclusions
The presented study aims at rationalizing the nanoscale friction contribution to facilitated lubrication of AC system. Collected simulation data show that a HA-PL system can contribute to lowering friction forces by altering its characteristic action from sliding to rolling. For more realistic results we would turn toward larger systems consisting of larger micelles (vesicles). This could be made feasible with the use of mixed coarse-grained and allatom simulations. There remains the question of which effect, hydrophobic interaction or hydrogen bond creation, is more significant for the mechanism. Another important avenue of investigation is the influence of temperature, pH and ionic concentration on the proposed mechanism. Also energy dissipation [49] could be very interesting problem to study as the association
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structure is changed and disentangled due to forces acting on the polymer chain. 6. Acknowledgements
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This work is supported by UTP BS39/14. The authors are grateful to Damian Ledzi´ nski for granting access to the computing infrastructure built in the projects No. POIG.02.03.00-00-028/08 ’PLATON - Science Services Platform’ and No. POIG.02.03.00-00-110/13 ’Deploying high-availability, critical services in Metropolitan Area Networks (MAN-HA)’.
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S0009-3084(18)30139-7 https://doi.org/doi:10.1016/j.chemphyslip.2018.08.002 CPL 4675
To appear in:
Chemistry and Physics of Lipids
Received date: Accepted date:
13-7-2018 13-8-2018
Please cite this article as: P. Beldowski, N. Kruszewska, S. Yuvan, Z. Dendzik, T. Goudoulas, A. Gadomski, Capstan-like mechanism in hyaluronanphospholipid systems, (2018), https://doi.org/10.1016/j.chemphyslip.2018.08.002 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Capstan-like mechanism in hyaluronan-phospholipid systems
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P. Beldowskia , N. Kruszewskaa , S. Yuvanb , Z. Dendzikc , T. Goudoulasd , A. Gadomskia a
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UTP University of Science and Technology, Institute of Mathematics and Physics, Kaliskiego 7, PL–85796 Bydgoszcz, Poland b Department of Physics, East Carolina University, Greenville, NC 27858, USA c Institute of Physics, University of Silesia, 75 Pulku Piechoty 1, 41-500 Chorzow, Poland and Silesian Center for Education and Interdisciplinary Research, University of Silesia, 75 Pulku Piechoty 1A, 41-500 Chorzow, Poland d Technical University of Munich, School of Life Sciences Weihenstephan, Maximus-von-Imhof-Forum 2, 85354 Freising, Germany
Abstract
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Functionality of articular cartilage results from complex interactions between its molecular components. Among many biomolecules, two are of prime importance for lubrication: hyaluronic acid (HA) and phospholipids (PL). The purpose of this study is to discuss a mechanism of interaction between these two components and how their synergies contribute to nanobiolubrication of articular cartilage. Preliminary molecular dynamics simulations have been performed to investigate these interactions by adopting a capstan-like mechanism of action. By applying a constant pulling force to both ends of a HA molecule, wrapped around a PL micelle, we viewed the rotation of the PL micelle. The simulations were performed upon two physicochemical constraints: force- and solvent-dependency. The results show the efficiency of rotation from intermolecular bond creation and annihilation. We found a direct relation between the available surface of the micelle and the magnitude of the force, which varies significantly through the unwinding. The movement of the attached molecules are characterized by a slide-to-roll relation, which is affected by the viscosity of the surrounding medium. As a
Email addresses: [email protected] (P. Beldowski), [email protected] (N. Kruszewska), [email protected] (Z. Dendzik), [email protected] (T. Goudoulas)
Preprint submitted to Chemistry and Physics of Lipids
July 13, 2018
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consequence, two solvents were studied for specific force conditions and the molecular dynamics simulation exhibited double the slide-to-roll coefficient for the viscous solvent as compared to its low-viscosity limit.
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Keywords: Hyaluronic acid, Lubrication, Phospholipids, Articular Cartilage
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1. Introduction
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Synovial joints are natural systems that provide low friction as well as a long period of functionality. The articular cartilage (AC) surfacing these joints is lubricated by a complex liquid called synovial fluid (SF). Regardless of the long debate over the mechanism of joint lubrication during the last decades [1, 2, 3], it has not been fully understood due to its complicated nature [2, 4]. Recently, an increasing number of studies suggest that the overall lubrication mechanism is of a multiscale, synergistic nature [4, 5, 6, 7]. Thus, to understand the nature of joint lubrication, an analysis based on that synergy is required. Hyaluronic acid (HA) and common phospholipids (PL) are the two important components in AC systems that provide modulation of fluid viscosity and surface lubrication [8]. Biopolymer-lipid systems spontaneously form a variety of nanostructures and it is very important to understand the interactions between them [9]. This work focuses on the tribological role of HA-PL interactions and their synergistic effects in synovial joint lubrication. Fig. 1 presents a depiction of a joint system as a complex interactive system with the SF, where the functionality is obtained due to multiscale phenomena. As an efficient lubricant, SF must function in all regimes of lubrication, namely: boundary, mixed and hydrodynamic [5, 12, 13, 14, 15]. The situation presented in Fig. 1 shows a mixed/hydrodynamic regime. Both AC surfaces are separated by synovial fluid consisting mainly of HA molecules, with PL bilayes present at the AC surface. However, after applying a normal load, PLs can be released into SF milieu and form vesicles within or on HA networks [16]. Due to the complexity of interactions of HA and PL molecules [17, 18] several scenarios need consideration. Dense HA networks can repel PL vesicles from their interior but may also be penetrated with free lipids which create vesicles inside the HA network [18]. PLs in the form of bilayers/vesicles can also interact with HA networks [19], which can also lead to facilitated lubrication at nanoscale level as governed by proton 2
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Figure 1: Artistic simplified depiction of AC system. Top and lower orange rectangles represent AC surfaces, green lines represent HA chains. Lipids are depicted as blue (hydrophilic) ”head” and red (hydrophobic) tails. The system undergoes several lubrication regimes [10]. Rolling friction is achieved due to presence of vesicles (created by phospholipids) and HA in regime of mixed lubrication [11].
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transport in so-called ”micellar channels” [20] or at the surface of bilayer [21]. Ultimately, the source of nanoscale friction in the system is the reorganization of molecules in response to external mechanical stress. HA on its own does not lower friction in the system - it has nano-shock absorbing properties - but may allow PLs in aggregated forms to reduce the friction coefficient by qualitatively altering the relative motion of molecules from sliding to vesicle facilitated rolling [16, 19, 22]. As described in [4], one can envision this reorganization as network strands being pulled through the environment by their heavily entangled ends or the presence of sheering flow. Such molecules entangled in the network may either slip past one another, encountering resistance from the destruction of bonds between adjacent (HA) strands, or prospectively, interact with interspersed spherical PL structures which allow HA molecules to ’roll’ past each other, instead forming relatively weaker bonds with PL heads. The present study implements a simplified model of such a structure in
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order to understand the general functionality of the system. This is based on the assumption that a simple cylindrical or rod-like micelle can mimic behavior of the larger, naturally occurring, PL vesicles. This assumption would seem defensible as the nanoscale friction effects under investigation are due to the chemical interaction of the surfaces rather than gross mechanical properties as in a typical capstan-like mechanism [23, 24]. In the model, this PL micelle is tangled with the HA chain (cf. Fig. 2). The HA chain, acting as a rope, wraps around the PL micelle, which serves as a pulley in the capstan mechanism. The wrapped angle of the HA molecule around the micelle has been denoted as θ in the Fig. 2. At each point of contact between the rope (HA) and pulley (PL) there is a normal force, which results in a frictional force acting tangentially to the pulley. The frictional force acts in the opposite direction to the rotation. In this way, the tension on the opposing side of the pulley is reduced. To simulate the tensile forces, two pulling forces, T1 and T2 (T1 > T2 ), have been added on both ends of the HA chain, mimicking the stress inside long-chain networks present in AC system (cf. Fig. 2). In a real capstan, one could then compute a coefficient of friction, µ, by finding the largest T1 possible without slipping, and using the standard formula T1 = T2 exp(µθ). This formula is not used, however, because there are critical differences between our system and actual capstans. Influenced by the pulling forces, the HA micelle can not only rotate, but slide (undergo an unbounded motion) inside the fluid in which it is immersed. In real capstan mechanisms the pulley can only rotate around a fixed axis (in the powered version of the mechanism) or not revolve at all (holding capstan). Additionally, the studied HA-PL system can be deformed. Thus applied forces to the HA chain cannot be too large, i.e. large enough to cause slipping (breaking all inter-molecular bonds simultaneously), because the micelle would start to break up. Rotation of the micelle causes an unwrapping of the chain instead of slipping. Due to the unwinding, the number of contact points between HA and PL decreases in time and the angle θ lowers. Thus, in the study, the capstan analogy is only used for visualizing the HA-PL system rather than to compute µ from the equation presented above. The rotation and slide of the micelle are conceptualized to be responses to the HA network motion. Efficient motion of the micelle is the result of hydrophobic interactions between those two structures as well as hydrogen bond creation and annihilation. Hydrophobic properties arise because the HA chain as well as micelle consist of both hydrophilic viz. polar (P) and 4
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Figure 2: Snapshots of the simulation box of HA-PL system. HA is colored green. PL building micelle are composed of carbon colored blue, hydrogen - white, oxygen - red, nitrogen - yellow. a) A snapshot of a beginning stage of simulation. b) A snapshot of a final stage of simulation with pulling forces presented as black arrows. The figure presents capstan-like mechanism of the soft matter HA-PL system.
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hydrophobic viz. nonpolar (NP) groups of molecules [25]. The NP molecules are water repellent; preferring proximity to other NP molecules. Therefore, an interaction appears that is similar to attraction. The P molecules, by contrast, are prone to contact with water. This is clearly demonstrated by PL micelles, (cf. Fig. 1) where P heads of lipids arrange to contact with water and NP tails stick together to avoid contacts with water. As a result, a double-layered spherical micelle is formed. This study provides cogitations, supported by preliminary computer simulation, on whether the aforementioned interactions between HA-PL may provide a plausible scheme to support lowered friction in the facilitated lubrication of the AC system. Our Derjaguin type [26] motivated results are a first-step attempt towards calculating the friction coefficient based on the statistics of the interactions. 2. Methods 2.1. Simulation details Investigating biomolecular systems usually focuses on identifying the physical mechanisms establishing their functions. Widely used in this regard are 5
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Molecular Dynamics (MD) simulations. Because the computational time required to simulate the majority of bioprocesses is usually prohibitively large, simulation using the Steered Molecular Dynamics (SMD) method permits competent investigation of molecular processes. A direct simulation can be too slow, because of the energy barriers. Therefore, by focusing on selected degrees of freedom and by applying external steering to accelerate processes, the SMD provides meaningful simulation results. Technically, SMD is based on the concept of applying an external force to one or more atoms (referred to as SMD atoms). This may be accomplished using either constant pulling force or constant pulling velocity. The former refers to a constant force directly applied to the SMD atom. In the case of a constant pulling velocity, the SMD atom is coupled to a virtual atom (moving with constant velocity), usually with a harmonic potential. In addition to this, positions of another group of atoms may be kept fixed. To avoid local heating, caused by applied external forces, all heavy atoms may be coupled to a heat bath. SMD has proven to be particularly useful in many applications, ranging from calculating the basic physical characteristic of the systems, such as the potential of mean force (PMF) [27], to study the molecular mechanisms of processes, such as transition of ions and organic compounds through biomembrane channels [28, 29, 30, 31]. Also, mechanical functions of proteins and other biomolecules have been investigated using SMD [32, 33, 34]. The simulations were performed by adopting AMBER03 force field [35]. Every case was repeated 30 times to obtain statistically more reliable information. HA and PL structures have been downloaded from PubChem (Open Chemistry DataBase). The DPPC (dipalmitylephosphatidocholine) lipid has been used (being the most common in SF systems [36]) to build cylindrical micelle composed of 73 lipids. DPPC in such small numbers does not normally create micelle or rod-like structures, however due to the computational cost of natural structures (of more than 800 PL) we used MSHAKE algorithm [37] to keep lipid tails in place during simulations. The HA molecule was modified to obtain longer chains by using YASARA Structure software. The final length of the HA was 25 nm and had a molecular mass of 10 kDa. These values are realistic if we consider that the HA persistence length is around 4 nm [38] allowing a fully covered PL, as it presented in Fig. 2. However, for similar computational rationale, the HA molecular mass used is much lower than can be found in real SF (around 2 MDa). Such a simplification is assumed to be acceptable as long as we are concerned only with 6
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HA-PL interactions’ of the micelle’s surface, for which the overall size of the structure is irrelevant. Our next studies will focus on creating more realistic representations, here we give a general impression of system functionality. The initial structure of the system is presented in Fig. 2a. As one can see, the micelle has been surrounded by HA. SMD has been performed by applying constant force (with constant direction) to each end of HA chain (composed of one HA bead) causing micelle to rotate (see, Fig. 3). All
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Figure 3: Sequential snapshots of the simulation box. HA is colored green, while atoms of the PL micelle are: C - blue, H - white, O - red, N - yellow. Time instances following the application of the force: a) 0 ps, b) 330 ps, c) 660 ps, d) 1000 ps, e) 1330 ps, f) 1660 ps.
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simulations were performed at identical conditions, that is, a temperature equal to 310 K, and a pH of 7.0. Time steps were set to 2.5 fs and simulations allowed to run until the pulled chain reached a wall of simulation box (the total number of simulation steps was on the magnitude of 106 for all cases). Two solvents have been used in this study: (a) a water solution of 0.9% NaCl to closely mimic the physiological solution, and (b) 30% glycerol in the previous solution. Simulations in some narrow ranges of pulling forces have been prepared in order to decrease or eliminate the probability of the micelle breaking, which can result from application of an external (quasi)normal load [39]. The range of forces we used is in range of ones used for other SMD simulations of biological systems [40]. However it is hard to estimate an actual forces occurring in our system due to HA network shock absorbing properties, where load applied to actual vesicles may differ depending on their position. In the case of a water solution we analyzed characteristics of HA and PL micelles for three different pulling force: T1 = 16, 32 and 64 pN 7
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to one end of HA. For the glycerol solution, we used one pulling force T1 = 64 pN. For all cases, the other end of the HA molecule was pulled with the same force of T2 = 4 pN in opposite direction. In this way the soft-matter capstanlike mechanism, mimicking a micelle wrapped by HA chain under stress in network, has been simulated (cf. Fig. 2).
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1 1 µ v = ∆T + ζ, m m m
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2.2. Calculated parameters of the system The effective pulling force ∆T = T1 − T2 , driving the rotation and slide of the micelle, was resisted by the viscosity of the solvent leading to an overdamped system. The Langevin equation, describing a velocity, v, of the mass element of the HA chain, m, can be written as (1)
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where µ stands for a friction coefficient as above, ζ is a stochastic-force (typically Gaussian correlated) variable representing the effect of background noise from fluctuations in density and temperature. The velocity is an important parameter due to its connection to slide and roll speeds of PL micelle. The HA chain stays in connection with PL micelle mediated by lubricant (solvent). Thus, the pulling force of the HA chain as well as fluctuations inside the chain both influence micelle rotation and translation. The system mimics a mini traction machine comprised of a ball and disc in contact, submerged in a reservoir full of lubricant (see Fig. 2 in [41]). For such systems a slide to roll ratio (SRR) parameter is usually calculated. The SRR is defined as the ratio of the mean sliding speed to the mean rolling speed between two bodies: SRR =| uD − uB | /US
(2)
where uD and uB are the speeds of two (nano)surfaces of the disc (in our case HA surface) and the ball (uB is a sum of micelle rotational and sliding speeds), respectively. US is the entrainment or two-point arithmetic mean speed, (uB + uD )/2. When the ball and the disc rotate at the same surface speed in the same direction, contact conditions are ’pure rolling’, SRR is equal 0, whereas for SRR = 2 there is ’pure sliding’ [42]. The number of hydrophobic interactions (between hydrophobic atoms) and hydrogen bond energy is calculated by the algorithm described previously [43]. 8
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The solvent accessible surface as evaluated in this study, consists of all the points that the center of the water probe (i.e. the nucleus of the oxygen atom in the water molecule) can reach while rolling over the solute. The procedure of calculating this variable has been presented in [44, 45].
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3. Results
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To describe the nanoscale HA-PL interactions and their influence on facilitated lubrication of AC, we focused on the rotation of the micelle and the effect of HA-PL dynamical contact creation and annihilation. To better understand the efficiency of the proposed mechanism here, we performed SMD calculations for two conditions: (i) force dependent and (ii) solvent dependent.
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3.1. Dependence on force Rotation angles of the micelle, φ, and rotation velocities, U , upon three different pulling forces, are presented in Fig. 4. Varying the pulling force
Figure 4: (a) Rotation angle φ and (b) rotation velocity U of a micelle as a function of time divided by total time t∗ of simulation of each case. Simulation results are presented for three cases of applied pulling forces whose values are given in the insert.
naturally has a direct impact on the time required to reach the end of the simulation box. In order to compare all three cases, time values, t, have been 9
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normalized using t∗ , representing the total time required for the particular simulation in question. In all cases, the rotation velocities behave similarly. The pulling force T1 − T2 takes effect immediately and dominates at the start of simulation, but this velocity is quickly damped as the system begins to behave according to the Langevin equation in Eq. (1) resulting in constant velocity throughout much of simulation. Then near the end of simulation the rotational velocity falls further as the HA chain is almost entirely unwrapped from the PL micelle. There are two major effects influencing efficient rotation of the micelle. First is hydrogen bond creation and annihilation, presented in Fig. 5. Second are the creation of hydrophobic contacts between molecules presented in Fig. 6. Both parameters decrease as the total contact area becomes smaller. However, the plateau of the third case in Fig. 6 is due to closer contact between HA and PL as a result of the HA chain cutting into the PL micelle.
Figure 5: Number and total energy of hydrogen bonds between the PL micelle and HA as a function of time. Simulation results are presented for three cases of applied pulling forces whose values are given in the insert.
This means that for higher pulling forces than T1 = 64 pN, the micelle collapses. This was confirmed by the SMD simulation results (data not shown 10
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Figure 6: Number of hydrophobic interactions between the PL micelle and HA as a function of time. Simulation results are presented for three cases of applied pulling forces whose values are given in the insert.
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here). One can see that for the smallest force applied (T1 = 16 pN) all data show much higher fluctuations throughout the simulations than for the remaining cases. Even higher effects of fluctuations have been noticed for applied forces smaller than 16 pN (not presented in this study). The number of hydrophobic and hydrogen interactions also depends on the solvent type. Additionally, looking on Eq. (1), the solvent viscosity is an important factor in the presented mechanism. Solvent accessible surfaces presented in Fig. 7 show that, for the largest force, solvent can penetrate the micelle more easily than for the other cases, obstructing its lubricating properties. Thus, this variable is important for describing the stability of the micelle: the higher force results in poorer integrity. SRR as a function of time, presented in Fig. 8, shows relative sliding versus rotation of the micelle for all cases in water solvent, with domination of rotation when SRR < 1 throughout almost all time of simulation. However for the smallest force (T1 = 16 pN), near the end of simulation, the motion is ’pure sliding’. This is caused by some stable hydrogen bonds keeping two molecules in contact despite the near complete unwrapping of the HA chain from the micelle. The same hydrogen bonds, in the case of larger pulling forces, break more easily. On the other hand, in that case, the atoms of both 11
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Figure 7: Solvent accessible surface of the PL micelle as a function of time. Simulation results are presented for three cases of applied pulling forces whose values are given in the insert.
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molecules are closer to each other and create more contacts. This observation can not be presented quantitatively in this study due to software constraints, however, future study could present more atomic details.
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3.2. Solvent dependence As presented in Fig. 9 and 10 solvent is an important factor influencing micelle motion. The rotation angle φ increases more slowly in time for glycerine than for water solvent, thus, the rotation velocity is smaller, though still constant for much of the simulation, as previously described in Sec. 3.1. SRR values presented in Fig. 10 show that, for glycerine, the system behaves differently for water, there is much less rotation than sliding in the motion of micelle. This is like caused by the much higher viscosity of the glycerine. 4. Discussion
The nature of HA-PL interaction is very complex as both species take on several forms even within a single cell [8, 46]. Thus, the proposed mechanism for improved lubrication can be viewed as one well-substantiated possibility among many. PLs (in the form of bilayers or even multilayers) appear to play a key role in boundary lubrication via Derjaguin type hydration-repulsion 12
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Figure 8: SRR as a function of time. Simulation results are presented for three cases of applied pulling forces whose values are given in the insert.
Figure 9: Rotation angle φ, and rotation (angular) velocity of the PL micelle, U , as a function of time divided by total time t∗ of simulation. Simulation results are presented for two solvent as described in the insert (see, Sec. 2.1).
lubrication [47, 48, 26]. Synergistic effects of HA-PL interactions play an important role in the functioning of many biological systems [8]. 13
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Figure 10: SRR as a function of time for water and glycerol solutions for pulling force T1 = 64 pN applied. Simulation results are presented for two solvent as described in the insert.
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The concept of a closed-packing formation of layer-by-layer deposition close to the cartilage interface, as proposed by [4], is also assumed here. In these conditions, the motion of join surfaces can cause relative sliding of such layers resulting in the forces on HA chains studied here. The adopted scheme in Fig. 2, is an initial approach to the more complex condition inside a joint, where high-molecular-weight molecules of HA will interact with each other to form large-scale networks, with the DPPC-HA complexes trapped inside. Several factors govern these interactions, however, two are of major importance: HA molecular mass and concentration of both species. It has been shown that longer HA chains create cylindrical structures when surrounded by PLs [17]. On the other hand, shorter chains are absorbed into PL vesicles. There are additionally two ways in which resulting PL structures can be attached to HA chains. The first is hydrophilic in nature and results in hydrogen bond creation. PLs turn toward HA with their hydrophilic heads and water molecules fill the interspaces between HA and PL. The second form is between hydrophobic parts. This orientation can be found in low concentrations of PL, where nonpolar tails attach to hydrophobic sites on HA [43]. This is a probable scenario for pathological SF, where all components are diluted due to the increased amount of serum in the joint cavity. 14
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Our findings represent a model of rolling friction of the micelle as a result of lateral quasi-normal load coming from HA network. The modeled system mimics a capstan mechanism where both ends of rope, wrapped around a pulley, are pulled by some stress forces (see, Fig. 2). This model of HA-PL interactions has been applied to better understand the process of facilitated lubrication of AC system at the nanoscale level. Motion of the micelle depends on dynamics of contacts created between the molecules. This involves efficient hydrogen bond creation and annihilation as well as formation of hydrophobic ”bonds” between interacting groups. The implication is that those systems create energetically favorable conditions for the following two effects to act on micelles and improve lubrication: hydration repulsion and rolling friction. Rolling may result in a reduction of the friction coefficient due to how intermolecular bond breaking occurs. Namely, sliding/rolling is facilitated by an energetically favorable bond exchange between interacting molecules. Thus, a small pulling force T1 could result in efficient ”hopping” of hydrogen and hydrophobic bonds (cf. Fig. 5 and 6). Presented data show the molecular details of this fairly hypothetical mechanism of facilitated lubrication at the nanoscale, and the large spectrum of pulling forces over which it can operate. The reduction of friction force occurs when itermolecular interaction is of smaller magnitude than intramolecular interaction. Thus, in spaces where HA density is low enough to permit interactions with PLs, more efficient bond redistribution will result compared to a pure HA network. From this perspective PLs are necessary for system to decrease friction force, but HA networks simultaneously need to remain dense enough to provide shock absorption to the system. For small applied forces (smaller than 16 pN) a lot of environmental fluctuations are evident in simulation results. For the case of T1 = 64 pN (higher forces), one can see the plateau resulting from the HA chain cutting into the PL micelle and compromising its integrity. The plateau lasts about t/t∗ = 0.8, then decline resumes at the end of the simulation. Evidently as the chain is unwound from the micelle, the compressive force is no longer enough to cause deformation. For a better understanding of the proposed explanation of friction reduction, based on the intermolecular bond breaking, more studies must be conducted. Contrasting variations in the solvent exposed surface area have been observed in the course of the simulation for the applied forces. The higher 15
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force on the HA-micelle system uncovers more of its hydrophobic parts. As noted, for even higher forces a destruction of the micelle occurs. Moreover, the nature of the applied forces is still under consideration, but is likely attributable to the shear or elongation flow field, or even more, to a partial anchor of the HA molecule on the AC. Finally, the simulation results show that a micelle behaves differently in water than in glycerine. In water, rotation is much faster than in glycerine. But the most noticeable difference is seen in the SRR figure (cf. Fig. 10). There is a prominent peak in the first part of the motion (0.1-0.2 of simulation time) in the case of glycerine, but even beyond this peak sliding prevails over rolling. Lastly, the slight increase in the SRR value’s at the tail end of the simulation is not observed in for glycerol solution. This may be explained with a mixed mode motion as the water system passed through a greater overall rotation. It is worth noting that Lazarev and Derjaguin [26], in their macroscopic experiment, use wire that tightly embraces the round rubbing surfaces via an oil. Between the components only a few molecules of inter-layer lubricant is applied. We can see an analogy with HA-PL system, taking the PL micelle as the shaft and the HA chain, trapped in a network created by various components of the AC system, as the wire. Tensions in the network are then analogous to a load force applied at the end of the wire in [26]. Drawing such a parallel is a novel contribution of our study. The extension of such macroscopic tools to the nanoscale level is also thoroughly addressed in [48]. 5. Conclusions
The presented study aims at rationalizing the nanoscale friction contribution to facilitated lubrication of AC system. Collected simulation data show that a HA-PL system can contribute to lowering friction forces by altering its characteristic action from sliding to rolling. For more realistic results we would turn toward larger systems consisting of larger micelles (vesicles). This could be made feasible with the use of mixed coarse-grained and allatom simulations. There remains the question of which effect, hydrophobic interaction or hydrogen bond creation, is more significant for the mechanism. Another important avenue of investigation is the influence of temperature, pH and ionic concentration on the proposed mechanism. Also energy dissipation [49] could be very interesting problem to study as the association
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structure is changed and disentangled due to forces acting on the polymer chain. 6. Acknowledgements
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This work is supported by UTP BS39/14. The authors are grateful to Damian Ledzi´ nski for granting access to the computing infrastructure built in the projects No. POIG.02.03.00-00-028/08 ’PLATON - Science Services Platform’ and No. POIG.02.03.00-00-110/13 ’Deploying high-availability, critical services in Metropolitan Area Networks (MAN-HA)’.
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