1
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Zhang H, Pan F, Li S. Self-Assembly of Lipid Molecules under Shear Flows: A Dissipative Particle Dynamics Simulation Study. Biomolecules 2023; 13:1359. [PMID: 37759759 PMCID: PMC10526246 DOI: 10.3390/biom13091359] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2023] [Revised: 08/28/2023] [Accepted: 09/04/2023] [Indexed: 09/29/2023] Open
Abstract
The self-assembly of lipid molecules in aqueous solution under shear flows was investigated using the dissipative particle dynamics simulation method. Three cases were considered: zero shear flow, weak shear flow and strong shear flow. Various self-assembled structures, such as double layers, perforated double layers, hierarchical discs, micelles, and vesicles, were observed. The self-assembly behavior was investigated in equilibrium by constructing phase diagrams based on chain lengths. Results showed the remarkable influence of chain length, shear flow and solution concentration on the self-assembly process. Furthermore, the self-assembly behavior of lipid molecules was analyzed using the system energy, particle number and shape factor during the dynamic processes, where the self-assembly pathways were observed and analyzed for the typical structures. The results enhance our understanding of biomacromolecule self-assembly in a solution and hold the potential for applications in biomedicine.
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Affiliation(s)
- Huan Zhang
- Department of Physics, Wenzhou University, Wenzhou 325035, China
| | - Fan Pan
- School of Data Science and Artificial Intelligence, Wenzhou University of Technology, Wenzhou 325035, China
| | - Shiben Li
- Department of Physics, Wenzhou University, Wenzhou 325035, China
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2
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Wang Y, Mou X, Ji Y, Pan F, Li S. Interaction of Macromolecular Chain with Phospholipid Membranes in Solutions: A Dissipative Particle Dynamics Simulation Study. Molecules 2023; 28:5790. [PMID: 37570760 PMCID: PMC10420874 DOI: 10.3390/molecules28155790] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2023] [Revised: 07/24/2023] [Accepted: 07/27/2023] [Indexed: 08/13/2023] Open
Abstract
The interaction between macromolecular chains and phospholipid membranes in aqueous solution was investigated using dissipative particle dynamics simulations. Two cases were considered, one in which the macromolecular chains were pulled along parallel to the membrane surfaces and another in which they were pulled vertical to the membrane surfaces. Several parameters, including the radius of gyration, shape factor, particle number, and order parameter, were used to investigate the interaction mechanisms during the dynamics processes by adjusting the pulling force strength of the chains. In both cases, the results showed that the macromolecular chains undergo conformational transitions from a coiled to a rod-like structure. Furthermore, the simulations revealed that the membranes can be damaged and repaired during the dynamic processes. The role of the pulling forces and the adsorption interactions between the chains and membranes differed in the parallel and perpendicular pulling cases. These findings contribute to our understanding of the interaction mechanisms between macromolecules and membranes, and they may have potential applications in biology and medicine.
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Affiliation(s)
- Yuane Wang
- Department of Physics, Wenzhou University, Wenzhou 325035, China; (Y.W.); (X.M.); (Y.J.)
| | - Xuankang Mou
- Department of Physics, Wenzhou University, Wenzhou 325035, China; (Y.W.); (X.M.); (Y.J.)
| | - Yongyun Ji
- Department of Physics, Wenzhou University, Wenzhou 325035, China; (Y.W.); (X.M.); (Y.J.)
| | - Fan Pan
- School of Data Science and Artificial Intelligence, Wenzhou University of Technology, Wenzhou 325035, China
| | - Shiben Li
- Department of Physics, Wenzhou University, Wenzhou 325035, China; (Y.W.); (X.M.); (Y.J.)
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3
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Tazawa K, Yamazaki M. Effect of monolayer spontaneous curvature on constant tension-induced pore formation in lipid bilayers. J Chem Phys 2023; 158:081101. [PMID: 36859073 DOI: 10.1063/5.0135561] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Abstract
The methodology of constant tension-induced rupture of giant unilamellar vesicles (GUVs) has provided information on tension-induced pore formation. This method was used to investigate the effect of spontaneous curvature (H0) for a lipid monolayer on the rate constant (kr) for constant tension (σ)-induced rupture, which originates from pore formation in lipid bilayers. Lipids were incorporated with different H0 values into GUV membranes to change the overall H0 value for the GUV monolayer. The dioleoylphosphatidylglycerol (DOPG)/dioleoylphosphatidylethanolamine (DOPE) (4/6, molar ratio, here and elsewhere) monolayer has a negative H0, whereas the DOPG/dioleoylphosphatidylcholine (DOPC) (4/6) monolayer has an essentially zero H0. A higher tension was required to induce the rupture of DOPG/DOPE (4/6)-GUVs compared with DOPG/DOPC (4/6)-GUVs. The line tension (Γ) for a pre-pore in DOPG/DOPE (4/6)-GUVs, determined by the analysis of the tension dependence of kr, was 1.5 times larger than that in DOPG/DOPC (4/6)-GUVs. The kr values for GUVs comprising DOPG/DOPC/18:1 lysophosphatidylcholine (LPC) (40/55/10), which has a positive H0, were larger than those for DOPG/DOPC (4/6)-GUVs under the same tension. The Γ value for DOPG/DOPC/LPC (40/55/10)-GUVs was almost half that for DOPG/DOPC (4/6)-GUVs. These results indicate that Γ decreases with increasing H0, which results in an increase in kr. Based on these results, the effect of H0 on kr and Γ is discussed.
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Affiliation(s)
- Kanta Tazawa
- Physics Course, Department of Science, Graduate School of Integrated Science and Technology, Shizuoka University, Shizuoka 422-8529, Japan
| | - Masahito Yamazaki
- Physics Course, Department of Science, Graduate School of Integrated Science and Technology, Shizuoka University, Shizuoka 422-8529, Japan
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4
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Lolicato F, Saleppico R, Griffo A, Meyer A, Scollo F, Pokrandt B, Müller HM, Ewers H, Hähl H, Fleury JB, Seemann R, Hof M, Brügger B, Jacobs K, Vattulainen I, Nickel W. Cholesterol promotes clustering of PI(4,5)P2 driving unconventional secretion of FGF2. J Biophys Biochem Cytol 2022; 221:213511. [PMID: 36173379 PMCID: PMC9526255 DOI: 10.1083/jcb.202106123] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2021] [Revised: 07/22/2022] [Accepted: 08/30/2022] [Indexed: 11/22/2022] Open
Abstract
FGF2 is a cell survival factor involved in tumor-induced angiogenesis that is secreted through an unconventional secretory pathway based upon direct protein translocation across the plasma membrane. Here, we demonstrate that both PI(4,5)P2-dependent FGF2 recruitment at the inner plasma membrane leaflet and FGF2 membrane translocation into the extracellular space are positively modulated by cholesterol in living cells. We further revealed cholesterol to enhance FGF2 binding to PI(4,5)P2-containing lipid bilayers. Based on extensive atomistic molecular dynamics (MD) simulations and membrane tension experiments, we proposed cholesterol to modulate FGF2 binding to PI(4,5)P2 by (i) increasing head group visibility of PI(4,5)P2 on the membrane surface, (ii) increasing avidity by cholesterol-induced clustering of PI(4,5)P2 molecules triggering FGF2 oligomerization, and (iii) increasing membrane tension facilitating the formation of lipidic membrane pores. Our findings have general implications for phosphoinositide-dependent protein recruitment to membranes and explain the highly selective targeting of FGF2 toward the plasma membrane, the subcellular site of FGF2 membrane translocation during unconventional secretion of FGF2.
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Affiliation(s)
- Fabio Lolicato
- Heidelberg University Biochemistry Center, Heidelberg, Germany.,Department of Physics, University of Helsinki, Helsinki, Finland
| | | | - Alessandra Griffo
- Department of Experimental Physics, Saarland University, Saarbrücken, Germany.,Biophysical Engineering Group, Max Planck Institute for Medical Research, Heidelberg, Germany
| | - Annalena Meyer
- Heidelberg University Biochemistry Center, Heidelberg, Germany
| | - Federica Scollo
- Department of Biophysical Chemistry, J. Heyrovský Institute of Physical Chemistry, Czech Academy of Sciences, Prague, Czech Republic
| | - Bianca Pokrandt
- Heidelberg University Biochemistry Center, Heidelberg, Germany
| | | | - Helge Ewers
- Institute for Chemistry and Biochemistry, Freie Universität Berlin, Berlin, Germany
| | - Hendrik Hähl
- Department of Experimental Physics, Saarland University, Saarbrücken, Germany
| | | | - Ralf Seemann
- Department of Experimental Physics, Saarland University, Saarbrücken, Germany
| | - Martin Hof
- Department of Biophysical Chemistry, J. Heyrovský Institute of Physical Chemistry, Czech Academy of Sciences, Prague, Czech Republic
| | - Britta Brügger
- Heidelberg University Biochemistry Center, Heidelberg, Germany
| | - Karin Jacobs
- Department of Experimental Physics, Saarland University, Saarbrücken, Germany.,Max Planck School Matter to Life, Heidelberg, Germany
| | - Ilpo Vattulainen
- Department of Physics, University of Helsinki, Helsinki, Finland
| | - Walter Nickel
- Heidelberg University Biochemistry Center, Heidelberg, Germany
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5
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Sun L, Pan F, Li S. Self-Assembly of Lipid Mixtures in Solutions: Structures, Dynamics Processes and Mechanical Properties. MEMBRANES 2022; 12:membranes12080730. [PMID: 35893448 PMCID: PMC9394357 DOI: 10.3390/membranes12080730] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/07/2022] [Revised: 07/19/2022] [Accepted: 07/20/2022] [Indexed: 02/01/2023]
Abstract
The self-assembly of lipid mixtures in aqueous solution was investigated by dissipative particle dynamics simulation. Two types of lipid molecules were modelled, where three mixed structures, i.e., the membrane, perforated membrane and vesicle, were determined in the self-assembly processes. Phase behaviour was investigated by using the phase diagrams based on the tail chain lengths for the two types of lipids. Several parameters, such as chain number and average radius of gyration, were employed to explore the structural formations of the membrane and perforated membrane in the dynamic processes. Interface tension was used to demonstrate the mechanical properties of the membrane and perforated membrane in the equilibrium state and dynamics processes. Results help us to understand the self-assembly mechanism of the biomolecule mixtures, which has a potential application for designing the lipid molecule-based bio-membranes in solutions.
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Affiliation(s)
| | - Fan Pan
- Correspondence: (F.P.); (S.L.)
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6
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Stroh KS, Risselada HJ. Quantifying Membrane Curvature Sensing of Peripheral Proteins by Simulated Buckling and Umbrella Sampling. J Chem Theory Comput 2021; 17:5276-5286. [PMID: 34261315 DOI: 10.1021/acs.jctc.1c00021] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Membrane curvature plays an essential role in the organization and trafficking of membrane associated proteins. Comparison or prediction of the experimentally resolved protein concentrations adopted at different membrane curvatures requires direct quantification of the relative partitioning free energy. Here, we present a highly efficient and simple to implement a free-energy calculation method which is able to directly resolve the relative partitioning free energy of proteins as a direct function of membrane curvature, i.e., a curvature sensing profile, within (coarse-grained) molecular dynamics simulations. We demonstrate its utility by resolving these profiles for two known curvature sensing peptides, namely ALPS and α-synuclein, for a membrane curvature ranging from -1/6.5 to +1/6.5 nm-1. We illustrate that the difference in relative partitioning (binding) free energy between these two extrema is only about 13 kBT for both peptides, illustrating that the driving force of curvature sensing is subtle. Furthermore, we illustrate that ALPS and α-synuclein sense curvature via a contrasting mechanism, which is differentially affected by membrane composition. In addition, we demonstrate that the intrinsic spontaneous curvature of both of these peptides lies beyond the range of membrane curvature accessible in micropipette aspiration experiments, being about 1/7 nm -1. Our approach offers an efficient and simple to implement in silico tool for exploring and screening the membrane curvature sensing mechanisms of proteins.
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Affiliation(s)
- Kai Steffen Stroh
- Institute for Theoretical Physics, Georg-August University Göttingen, Göttingen, Germany
| | - Herre Jelger Risselada
- Institute for Theoretical Physics, Georg-August University Göttingen, Göttingen, Germany.,Leiden Institute of Chemistry, Leiden University, Leiden, The Netherlands.,Leibniz Institute for Surface Engineering, Leipzig, Germany
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7
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Nikfar M, Razizadeh M, Paul R, Zhou Y, Liu Y. Numerical simulation of intracellular drug delivery via rapid squeezing. BIOMICROFLUIDICS 2021; 15:044102. [PMID: 34367404 PMCID: PMC8331209 DOI: 10.1063/5.0059165] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2021] [Accepted: 07/19/2021] [Indexed: 05/06/2023]
Abstract
Intracellular drug delivery by rapid squeezing is one of the most recent and simple cell membrane disruption-mediated drug encapsulation approaches. In this method, cell membranes are perforated in a microfluidic setup due to rapid cell deformation during squeezing through constricted channels. While squeezing-based drug loading has been successful in loading drug molecules into various cell types, such as immune cells, cancer cells, and other primary cells, there is so far no comprehensive understanding of the pore opening mechanism on the cell membrane and the systematic analysis on how different channel geometries and squeezing speed influence drug loading. This article aims to develop a three-dimensional computational model to study the intracellular delivery for compound cells squeezing through microfluidic channels. The Lattice Boltzmann method, as the flow solver, integrated with a spring-connected network via frictional coupling, is employed to capture compound capsule dynamics over fast squeezing. The pore size is proportional to the local areal strain of triangular patches on the compound cell through mathematical correlations derived from molecular dynamics and coarse-grained molecular dynamics simulations. We quantify the drug concentration inside the cell cytoplasm by introducing a new mathematical model for passive diffusion after squeezing. Compared to the existing models, the proposed model does not have any empirical parameters that depend on operating conditions and device geometry. Since the compound cell model is new, it is validated by simulating a nucleated cell under a simple shear flow at different capillary numbers and comparing the results with other numerical models reported in literature. The cell deformation during squeezing is also compared with the pattern found from our compound cell squeezing experiment. Afterward, compound cell squeezing is modeled for different cell squeezing velocities, constriction lengths, and constriction widths. We reported the instantaneous cell center velocity, variations of axial and vertical cell dimensions, cell porosity, and normalized drug concentration to shed light on the underlying physics in fast squeezing-based drug delivery. Consistent with experimental findings in the literature, the numerical results confirm that constriction width reduction, constriction length enlargement, and average cell velocity promote intracellular drug delivery. The results show that the existence of the nucleus increases cell porosity and loaded drug concentration after squeezing. Given geometrical parameters and cell average velocity, the maximum porosity is achieved at three different locations: constriction entrance, constriction middle part, and outside the constriction. Our numerical results provide reasonable justifications for experimental findings on the influences of constriction geometry and cell velocity on the performance of cell-squeezing delivery. We expect this model can help design and optimize squeezing-based cargo delivery.
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Affiliation(s)
- Mehdi Nikfar
- Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, Pennsylvania 18015, USA
| | - Meghdad Razizadeh
- Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, Pennsylvania 18015, USA
| | - Ratul Paul
- Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, Pennsylvania 18015, USA
| | - Yuyuan Zhou
- Department of Bioengineering, Lehigh University, Bethlehem, Pennsylvania 18015, USA
| | - Yaling Liu
- Author to whom correspondence should be addressed:
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8
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Dixit M, Lazaridis T. Free energy of hydrophilic and hydrophobic pores in lipid bilayers by free energy perturbation of a restraint. J Chem Phys 2021; 153:054101. [PMID: 32770888 DOI: 10.1063/5.0016682] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The free energy of pore formation in lipid bilayers has been previously calculated using a variety of reaction coordinates. Here, we use free energy perturbation of a cylindrical lipid exclusion restraint to compute the free energy profile as a function of pore radius in dimyristoylphosphatidylcholine (DMPC) and dioleoylphosphatidylcholine (DOPC) bilayers. Additionally restraining the headgroups to lie on the membrane surface allows us to also calculate the free energy profile of hydrophobic pores, i.e., cylindrical pores lined by acyl chains. For certain pore radii, the free energy of wetting of hydrophobic pores is calculated using the density bias method. It is found that wetting of hydrophobic pores becomes thermodynamically favorable at 5.0 Å for DMPC and 6.5 Å for DOPC, although significant barriers prevent spontaneous wetting of the latter on a nanosecond time scale. The free energy of transformation of hydrophilic pores to hydrophobic ones is also calculated using free energy perturbation of headgroup restraints along the bilayer normal. This quantity, along with wetting and pore growth free energies, provides complete free energy profiles as a function of radius. Pore line tension values for the hydrophilic pores obtained from the slope of the free energy profiles are 37.6 pN for DMPC and 53.7 pN for DOPC. The free energy profiles for the hydrophobic pores are analyzed in terms of elementary interfacial tensions. It is found that a positive three-phase line tension is required to explain the results. The estimated value for this three-phase line tension (51.2 pN) lies within the expected range.
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Affiliation(s)
- Mayank Dixit
- Department of Chemistry, City College of New York, 160 Convent Ave., New York, New York 10031, USA
| | - Themis Lazaridis
- Department of Chemistry, City College of New York, 160 Convent Ave., New York, New York 10031, USA
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9
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Dai X, Ji Y, Wang Z, He L, Wang X, Li S. Interaction between Bottlebrush Polymers and Phospholipid Membranes in Solutions. Polymers (Basel) 2020; 12:E3033. [PMID: 33348889 PMCID: PMC7766109 DOI: 10.3390/polym12123033] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2020] [Revised: 12/04/2020] [Accepted: 12/15/2020] [Indexed: 11/23/2022] Open
Abstract
In this work, the interactions between bottlebrush polymers and phospholipid membranes were investigated using dissipative particle dynamics simulations. The weak and strong adsorption phenomena between the polymers and membranes were examined by calculating the system parameters. A spring model was introduced to explain the variances in the shape factors and the radius of gyration of the bottlebrush polymers, as well as the order parameters of the phospholipid membrane in the pulling processes. This work provides further understanding for the application of bottlebrush polymers in biological processes.
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Affiliation(s)
| | | | - Zhenguo Wang
- Department of Physics, Wenzhou University, Wenzhou 325035, China; (X.D.); (Y.J.); (L.H.); (X.W.)
| | | | | | - Shiben Li
- Department of Physics, Wenzhou University, Wenzhou 325035, China; (X.D.); (Y.J.); (L.H.); (X.W.)
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10
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Endter LJ, Smirnova Y, Risselada HJ. Density Field Thermodynamic Integration (DFTI): A "Soft" Approach to Calculate the Free Energy of Surfactant Self-Assemblies. J Phys Chem B 2020; 124:6775-6785. [PMID: 32631061 DOI: 10.1021/acs.jpcb.0c03982] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Thermodynamic integration is one of the most established methods to quantify excess free energies between different metastable states. Excess intermolecular interactions in surfactant assemblies are on the scale of the energy of thermal fluctuations. Therefore, these materials can be deformed and topologically altered via relatively small mechanical stresses. It is thus intuitive to design reaction paths and associated order parameters that exploit the "soft" nature of these materials to mechanically rather than alchemically morph surfactant assemblies from state to state. Here, we propose a novel method coined "density field thermodynamic integration" (DFTI) that adopts the universality and transferability of alchemical methods while simultaneously exploiting the soft excess interactions between surfactant molecules. DFTI was designed for a rapid quantification of the free energy differences between different metastable structures in soft fluid materials. The DFTI method uses an external field coupled to the local density to mechanically morph the system between metastable states of interest. Here, we explored the capability of the DFTI method to swiftly and accurately calculate free energy differences between states. To this aim, we studied two different coarse-grained lipidic surfactant systems: (i) a fusion stalk and (ii) a worm-like micelle. Our results illustrate that DFTI can provide an efficient, versatile, and rather reliable method to calculate the free energy differences between surfactant assemblies.
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Affiliation(s)
- Laura Josefine Endter
- Institute for Theoretical Physics, Georg-August University, 37077 Göttingen, Germany
| | - Yuliya Smirnova
- Institute for Theoretical Physics, Georg-August University, 37077 Göttingen, Germany
| | - Herre Jelger Risselada
- Institute for Theoretical Physics, Georg-August University, 37077 Göttingen, Germany.,Leiden Institute of Chemistry (LIC), University of Leiden, 2311 Leiden,The Netherlands.,Chemical Deptartment, Leibniz Institute of Surface Modifications, 04318 Leipzig, Germany
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11
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Nikfar M, Razizadeh M, Paul R, Liu Y. Multiscale modeling of hemolysis during microfiltration. MICROFLUIDICS AND NANOFLUIDICS 2020; 24:33. [PMID: 33235552 PMCID: PMC7682248 DOI: 10.1007/s10404-020-02337-3] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2019] [Accepted: 03/28/2020] [Indexed: 05/22/2023]
Abstract
In this paper, we propose a multiscale numerical algorithm to simulate the hemolytic release of hemoglobin (Hb) from red blood cells (RBCs) flowing through sieves containing micropores with mean diameters smaller than RBCs. Analyzing the RBC damage in microfiltration is important in the sense that it can quantify the sensitivity of human erythrocytes to mechanical hemolysis while they undergo high shear rate and high deformation. Here, the numerical simulations are carried out via lattice Boltzmann method and spring connected network (SN) coupled by an immersed boundary method. To predict the RBC sublytic damage, a sub-cellular damage model derived from molecular dynamic simulations is incorporated in the cellular solver. In the proposed algorithm, the local RBC strain distribution calculated by the cellular solver is used to obtain the pore radius on the RBC membrane. Index of hemolysis (IH) is calculated by resorting to the resulting pore radius and solving a diffusion equation considering the effects of steric hinderance and increased hydrodynamic drag due to the size of the hemoglobin molecule. It should be mentioned that current computational hemolysis models usually utilize empirical fitting of the released free hemoglobin (Hb) in plasma from damaged RBCs. These empirical correlations contain ad hoc parameters that depend on specific device and operating conditions, thus cannot be used to predict hemolysis under different conditions. In contrast to the available hemolysis model, the proposed algorithm does not have any empirical parameters. Therefore, it can predict the IH in microfilter with different sieve pore sizes and filtration pressures. Also, in contrast to empirical correlations in which the Hb release is related to shear stress and exposure time without considering the physical processes, the proposed model links flow-induced deformation of the RBC membrane to membrane permeabilization and hemoglobin release. In this paper, the cellular solver is validated by simulating optical tweezers experiment, shear flow experiment as well as an experiment to measure RBC deformability in a very narrow microchannel. Moreover, the shape of a single RBC at the rupture moment is compared with corresponding experimental data. Finally, to validate the damage model, the results obtained from our parametric study on the role of filtration pressure and sieve pore size in Hb release are compared with experimental data. Numerical results are in good agreement with experimental data. Similar to the corresponding experiment, the numerical results confirm that hemolysis increases with increasing the filtration pressure and reduction in pore size on the sieve. While in experiment, the RBC pore size cannot be measured, the numerical results can quantify the RBC pore size. The numerical results show that at the sieve pore size of 2.2 μm above 25 cm Hg, RBC pore size is above 75 nm and RBCs experience rupture. More importantly, the results demonstrate that the proposed approach is independent from the operating conditions and it can estimate the hemolysis in a wide range of filtration pressure and sieve pore size with reasonable accuracy.
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Affiliation(s)
- Mehdi Nikfar
- Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA
| | - Meghdad Razizadeh
- Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA
| | - Ratul Paul
- Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA
| | - Yaling Liu
- Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA
- Department of Bioengineering, Lehigh University, Bethlehem, PA 18015, USA
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12
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Nikfar M, Razizadeh M, Zhang J, Paul R, Wu ZJ, Liu Y. Prediction of mechanical hemolysis in medical devices via a Lagrangian strain-based multiscale model. Artif Organs 2020; 44:E348-E368. [PMID: 32017130 DOI: 10.1111/aor.13663] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2019] [Revised: 12/22/2019] [Accepted: 01/31/2020] [Indexed: 01/25/2023]
Abstract
This work introduces a new Lagrangian strain-based model to predict the shear-induced hemolysis in biomedical devices. Current computational models for device-induced hemolysis usually utilize empirical fitting of the released free hemoglobin (Hb) in plasma from damaged red blood cells (RBCs). These empirical correlations contain parameters that depend on specific device and operating conditions, thus cannot be used to predict hemolysis in a general device. The proposed algorithm does not have any empirical parameters, thus can presumably be used for hemolysis prediction in various blood-wetting medical devices. In contrast to empirical correlations in which the Hb release is related to the shear stress and exposure time without considering the physical processes, the proposed model links flow-induced deformation of the RBC membrane to membrane permeabilization and Hb release. In this approach, once the steady-state numerical solution of blood flow in the device is obtained under a prescribed operating condition, sample path lines are traced from the inlet of the device to the outlet to calculate the history of the shear stress tensor. In solving the fluid flow, it is assumed that RBCs do not have any influence on the flow pattern. Along each path line, shear stress tensor will be input into a coarse-grained (CG) RBC model to calculate the RBC deformation. Then the correlations obtained from molecular dynamics (MD) simulations are applied to relate the local areal RBC deformation to the perforated area on the RBC membrane. Finally, Hb released out of transient pores is calculated over each path line via a diffusion equation considering the effects of the steric hindrance and increased hydrodynamic drag due to the size of the Hb molecule. The total index of hemolysis (IH) is calculated by integration of released Hb over all the path lines in the computational domain. Hemolysis generated in the Food and Drug Administration (FDA) nozzle and two blood pumps, that is, a CentriMag blood pump (a centrifugal pump) and HeartMate II (an axial pump), for different flow regimes including the laminar and turbulent flows are calculated via the proposed algorithm. In all the simulations, the numerical predicted IH is close to the range of experimental data. The results promisingly indicate that this multiscale approach can be used as a tool for predicting hemolysis and optimizing the hematologic design of other types of blood-wetting devices.
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Affiliation(s)
- Mehdi Nikfar
- Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA, USA
| | - Meghdad Razizadeh
- Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA, USA
| | - Jiafeng Zhang
- Department of Surgery, University of Maryland, School of Medicine, Baltimore, MD, USA
| | - Ratul Paul
- Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA, USA
| | - Zhongjun J Wu
- Department of Surgery, University of Maryland, School of Medicine, Baltimore, MD, USA
| | - Yaling Liu
- Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA, USA.,Department of Bioengineering, Lehigh University, Bethlehem, PA, USA
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13
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Ramírez PG, Del Pópolo MG, Vila JA, Szleifer I, Longo GS. Adsorption and insertion of polyarginine peptides into membrane pores: The trade-off between electrostatics, acid-base chemistry and pore formation energy. J Colloid Interface Sci 2019; 552:701-711. [PMID: 31176053 DOI: 10.1016/j.jcis.2019.05.087] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2019] [Revised: 05/24/2019] [Accepted: 05/25/2019] [Indexed: 12/21/2022]
Abstract
The mechanism that arginine-rich cell penetrating peptides (ARCPPs) use to translocate lipid membranes is not entirely understood. In the present work, we develop a molecular theory that allows to investigate the adsorption and insertion of ARCPPs on membranes bearing hydrophilic pores. This method accounts for size, shape, conformation, protonation state and charge distribution of the peptides; it also describes the state of protonation of acidic membrane lipids. We present a systematic investigation of the effect of pore size, peptide concentration and sequence length on the extent of peptide adsorption and insertion into the pores. We show that adsorption on the intact (non-porated) lipid membrane plays a key role on peptide translocation. For peptides shorter than nona-arginine, adsorption on the intact membrane increases significantly with chain length, but it saturates for longer peptides. However, this adsorption behavior only occurs at relatively low peptide concentrations; increasing peptide concentration favors adsorption of the shorter molecules. Adsorption of longer peptides increases the intact membrane negative charge as a result of further deprotonation of acidic lipids. Peptide insertion into the pores depends non-monotonically on pore radius, which reflects the short range nature of the effective membrane-peptide interactions. The size of the pore that promotes maximum adsorption depends on the peptide chain length. Peptide translocation is a thermally activated process, so we complement our thermodynamic approach with a simple kinetic model that allows to rationalize the ARCPPs translocation rate in terms of the free energy gain of adsorption, and the energy cost of creating a transmembrane pore with peptides in it. Our results indicate that strategies to improve translocation efficiency should focus on enhancing peptide adsorption.
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Affiliation(s)
- Pedro G Ramírez
- Instituto de Matemática Aplicada San Luis (IMASL), UNSL-CONICET, San Luis, Argentina
| | - Mario G Del Pópolo
- IICB-CONICET & Facultad de Ciencias Exactas y Naturales (FCEN), UNCuyo, Mendoza, Argentina
| | - Jorge A Vila
- Instituto de Matemática Aplicada San Luis (IMASL), UNSL-CONICET, San Luis, Argentina
| | - I Szleifer
- Department of Biomedical Engineering, Department of Chemistry and Chemistry of Life Processes Institute, Northwestern University, Evanston IL, USA
| | - Gabriel S Longo
- Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas (INIFTA), UNLP-CONICET, La Plata, Argentina.
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14
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López Martí JM, English NJ, Del Pópolo MG. Elucidating mysteries of phase-segregated membranes: mobile-lipid recruitment facilitates pores' passage to the fluid phase. Phys Chem Chem Phys 2018; 20:19234-19239. [PMID: 29989117 DOI: 10.1039/c8cp00958a] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
Abstract
Phase segregation of multicomponent lipid bilayers leads to, under phase-coexistence conditions, domain formation, featuring delimitation by essentially one-dimensional borders. (Micro-)phase segregation of bilayers is proposed to influence the physiological behaviour of cell membranes and provides the driving force for lipid-raft formation. Experiments show a maximum in the electrical-conductivity of membranes at the phase-transition point, which has been conjectured to arise from border-nucleated transmembrane-conducting defects or pores. However, recent electroporation experiments on phase-segregated bilayers demonstrate electro-pore detection in the liquid disordered phase (Ld), wherein they diffuse over macroscopic periods without absorption into the liquid ordered phase (Lo). Here, we scrutinise transmembrane-pore formation via molecular dynamics simulations on a multicomponent phase-segregated bilayer. We find that pores created in Lo domains always migrate spontaneously to the Ld phase, via 'recruitment' of unsaturated lipids to the pore's rim to transport the pore to the fluid phase under a large stress-field driving force. Once in Ld domains, pores migrate towards their centre, never returning or pinning to Lo. These findings are explained by thermodynamics. By comparing the free-energy cost for creating pores in the bulk of Ld and Lo membranes, and in the phase-segregated system, we show that it is always more energetically tractable to create pores in Ld domains, independent of the pore size.
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Affiliation(s)
- Jesús M López Martí
- CONICET & Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Cuyo, Padre Jorge Contreras 1300, CP5500, Mendoza, Argentina.
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15
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Ting CL, Awasthi N, Müller M, Hub JS. Metastable Prepores in Tension-Free Lipid Bilayers. PHYSICAL REVIEW LETTERS 2018; 120:128103. [PMID: 29694074 DOI: 10.1103/physrevlett.120.128103] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2017] [Indexed: 06/08/2023]
Abstract
The formation and closure of aqueous pores in lipid bilayers is a key step in various biophysical processes. Large pores are well described by classical nucleation theory, but the free-energy landscape of small, biologically relevant pores has remained largely unexplored. The existence of small and metastable "prepores" was hypothesized decades ago from electroporation experiments, but resolving metastable prepores from theoretical models remained challenging. Using two complementary methods-atomistic simulations and self-consistent field theory of a minimal lipid model-we determine the parameters for which metastable prepores occur in lipid membranes. Both methods consistently suggest that pore metastability depends on the relative volume ratio between the lipid head group and lipid tails: lipids with a larger head-group volume fraction (or shorter saturated tails) form metastable prepores, whereas lipids with a smaller head-group volume fraction (or longer unsaturated tails) form unstable prepores.
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Affiliation(s)
- Christina L Ting
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - Neha Awasthi
- University of Goettingen, Institute for Microbiology and Genetics, 37077 Göttingen, Germany
- Göttingen Center for Molecular Biosciences, 37077 Göttingen, Germany
| | - Marcus Müller
- University of Goettingen, Institute for Theoretical Physics, 37077 Göttingen, Germany
| | - Jochen S Hub
- University of Goettingen, Institute for Microbiology and Genetics, 37077 Göttingen, Germany
- Göttingen Center for Molecular Biosciences, 37077 Göttingen, Germany
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16
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Qiang X, Wang X, Ji Y, Li S, He L. Liquid-crystal self-assembly of lipid membranes on solutions: A dissipative particle dynamic simulation study. POLYMER 2017. [DOI: 10.1016/j.polymer.2017.03.021] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
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17
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Sohrabi S, Liu Y. A Cellular Model of Shear-Induced Hemolysis. Artif Organs 2017; 41:E80-E91. [PMID: 28044355 DOI: 10.1111/aor.12832] [Citation(s) in RCA: 31] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2016] [Revised: 06/12/2016] [Accepted: 07/19/2016] [Indexed: 12/13/2022]
Abstract
A novel model is presented to study red blood cell (RBC) hemolysis at cellular level. Under high shear rates, pores form on RBC membranes through which hemoglobin (Hb) leaks out and increases free Hb content of plasma leading to hemolysis. By coupling lattice Boltzmann and spring connected network models through immersed boundary method, we estimate hemolysis of a single RBC under various shear rates. First, we use adaptive meshing to find local strain distribution and critical sites on RBC membranes, and then we apply underlying molecular dynamics simulations to evaluate damage. Our approach comprises three sub-models: defining criteria of pore formation, calculating pore size, and measuring Hb diffusive flux out of pores. Our damage model uses information of different scales to predict cellular level hemolysis. Results are compared with experimental studies and other models in literature. The developed cellular damage model can be used as a predictive tool for hydrodynamic and hematologic design optimization of blood-wetting medical devices.
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Affiliation(s)
| | - Yaling Liu
- Department of Mechanical Engineering & Mechanics.,Bioengineering Program, Lehigh University, Bethlehem, PA, USA
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18
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Bubnis G, Risselada HJ, Grubmüller H. Exploiting Lipid Permutation Symmetry to Compute Membrane Remodeling Free Energies. PHYSICAL REVIEW LETTERS 2016; 117:188102. [PMID: 27834997 DOI: 10.1103/physrevlett.117.188102] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2016] [Indexed: 05/26/2023]
Abstract
A complete physical description of membrane remodeling processes, such as fusion or fission, requires knowledge of the underlying free energy landscapes, particularly in barrier regions involving collective shape changes, topological transitions, and high curvature, where Canham-Helfrich (CH) continuum descriptions may fail. To calculate these free energies using atomistic simulations, one must address not only the sampling problem due to high free energy barriers, but also an orthogonal sampling problem of combinatorial complexity stemming from the permutation symmetry of identical lipids. Here, we solve the combinatorial problem with a permutation reduction scheme to map a structural ensemble into a compact, nondegenerate subregion of configuration space, thereby permitting straightforward free energy calculations via umbrella sampling. We applied this approach, using a coarse-grained lipid model, to test the CH description of bending and found sharp increases in the bending modulus for curvature radii below 10 nm. These deviations suggest that an anharmonic bending term may be required for CH models to give quantitative energetics of highly curved states.
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Affiliation(s)
- Greg Bubnis
- Department of Theoretical and Computational Biophysics, Max-Planck-Institute for Biophysical Chemistry, Göttingen 37077, Germany
| | - Herre Jelger Risselada
- Department of Theoretical and Computational Biophysics, Max-Planck-Institute for Biophysical Chemistry, Göttingen 37077, Germany
- Chemistry Department, Leibniz Institute of Surface Modification, Leipzig 04318, Germany
- Deptartment of Theoretical Physics, Georg-August University Göttingen, Göttingen 37077, Germany
| | - Helmut Grubmüller
- Department of Theoretical and Computational Biophysics, Max-Planck-Institute for Biophysical Chemistry, Göttingen 37077, Germany
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19
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Lyubartsev AP, Rabinovich AL. Force Field Development for Lipid Membrane Simulations. BIOCHIMICA ET BIOPHYSICA ACTA-BIOMEMBRANES 2016; 1858:2483-2497. [PMID: 26766518 DOI: 10.1016/j.bbamem.2015.12.033] [Citation(s) in RCA: 72] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/11/2015] [Revised: 12/21/2015] [Accepted: 12/23/2015] [Indexed: 02/04/2023]
Abstract
With the rapid development of computer power and wide availability of modelling software computer simulations of realistic models of lipid membranes, including their interactions with various molecular species, polypeptides and membrane proteins have become feasible for many research groups. The crucial issue of the reliability of such simulations is the quality of the force field, and many efforts, especially in the latest several years, have been devoted to parametrization and optimization of the force fields for biomembrane modelling. In this review, we give account of the recent development in this area, covering different classes of force fields, principles of the force field parametrization, comparison of the force fields, and their experimental validation. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.
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Affiliation(s)
- Alexander P Lyubartsev
- Department of Materials and Environmental Chemistry, Stockholm University, SE 106 91, Stockholm, Sweden.
| | - Alexander L Rabinovich
- Institute of Biology, Karelian Research Center, Russian Academy of Sciences, Pushkinskaya 11, Petrozavodsk, 185910, Russian Federation.
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20
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Kirsch SA, Böckmann RA. Membrane pore formation in atomistic and coarse-grained simulations. BIOCHIMICA ET BIOPHYSICA ACTA-BIOMEMBRANES 2015; 1858:2266-2277. [PMID: 26748016 DOI: 10.1016/j.bbamem.2015.12.031] [Citation(s) in RCA: 47] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2015] [Revised: 12/23/2015] [Accepted: 12/24/2015] [Indexed: 12/26/2022]
Abstract
Biological cells and their organelles are protected by ultra thin membranes. These membranes accomplish a broad variety of important tasks like separating the cell content from the outer environment, they are the site for cell-cell interactions and many enzymatic reactions, and control the in- and efflux of metabolites. For certain physiological functions e.g. in the fusion of membranes and also in a number of biotechnological applications like gene transfection the membrane integrity needs to be compromised to allow for instance for the exchange of polar molecules across the membrane barrier. Mechanisms enabling the transport of molecules across the membrane involve membrane proteins that form specific pores or act as transporters, but also so-called lipid pores induced by external fields, stress, or peptides. Recent progress in the simulation field enabled to closely mimic pore formation as supposed to occur in vivo or in vitro. Here, we review different simulation-based approaches in the study of membrane pores with a focus on lipid pore properties such as their size and energetics, poration mechanisms based on the application of external fields, charge imbalances, or surface tension, and on pores that are induced by small molecules, peptides, and lipids. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.
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Affiliation(s)
- Sonja A Kirsch
- Computational Biology, Department of Biology, Friedrich-Alexander Universität Erlangen-Nürnberg, Erlangen, Germany
| | - Rainer A Böckmann
- Computational Biology, Department of Biology, Friedrich-Alexander Universität Erlangen-Nürnberg, Erlangen, Germany.
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21
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Pera H, Kleijn JM, Leermakers FAM. On the edge energy of lipid membranes and the thermodynamic stability of pores. J Chem Phys 2015; 142:034101. [PMID: 25612683 DOI: 10.1063/1.4905260] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
To perform its barrier function, the lipid bilayer membrane requires a robust resistance against pore formation. Using a self-consistent field (SCF) theory and a molecularly detailed model for membranes composed of charged or zwitterionic lipids, it is possible to predict structural, mechanical, and thermodynamical parameters for relevant lipid bilayer membranes. We argue that the edge energy in membranes is a function of the spontaneous lipid monolayer curvature, the mean bending modulus, and the membrane thickness. An analytical Helfrich-like model suggests that most bilayers should have a positive edge energy. This means that there is a natural resistance against pore formation. Edge energies evaluated explicitly in a two-gradient SCF model are consistent with this. Remarkably, the edge energy can become negative for phosphatidylglycerol (e.g., dioleoylphosphoglycerol) bilayers at a sufficiently low ionic strength. Such bilayers become unstable against the formation of pores or the formation of lipid disks. In the weakly curved limit, we study the curvature dependence of the edge energy and evaluate the preferred edge curvature and the edge bending modulus. The latter is always positive, and the former increases with increasing ionic strength. These results point to a small window of ionic strengths for which stable pores can form as too low ionic strengths give rise to lipid disks. Higher order curvature terms are necessary to accurately predict relevant pore sizes in bilayers. The electric double layer overlap across a small pore widens the window of ionic strengths for which pores are stable.
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Affiliation(s)
- H Pera
- Laboratory of Physical Chemistry and Colloid Science, W ageningen University, Dreijenplein 6, 6307 HB Wageningen, The Netherlands
| | - J M Kleijn
- Laboratory of Physical Chemistry and Colloid Science, W ageningen University, Dreijenplein 6, 6307 HB Wageningen, The Netherlands
| | - F A M Leermakers
- Laboratory of Physical Chemistry and Colloid Science, W ageningen University, Dreijenplein 6, 6307 HB Wageningen, The Netherlands
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22
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Astafyeva K, Urbach W, Garroum N, Taulier N, Thiam AR. Stability of C(12)E(j) Bilayers Probed with Adhesive Droplets. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2015; 31:6791-6796. [PMID: 26035626 DOI: 10.1021/acs.langmuir.5b00749] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
The stability of model surfactant bilayers from the poly(ethylene glycol) mono-n-dodecyl ether (C12Ej) family was probed. The surfactant bilayers were formed by the adhesion of emulsion droplets. We generated C12Ej bilayers by forming water-in-oil (w/o) emulsions with saline water droplets, covered by the surfactant, in a silicone and octane oil mixture. Using microfluidics, we studied the stability of those bilayers. C12E1 allowed only short-lived bilayers whereas C12E2 bilayers were stable over a wide range of oil mixtures. At high C12E2 concentration, a two-phase region was displayed in the phase diagram: bilayers formed by the adhesion of two water droplets and Janus-like particles consisting of adhering aqueous and amphiphilic droplets. C12E8 and C12E25 did not mediate bilayer formation and caused phase inversion leading to o/w emulsion. With intermediate C12E4 and C12E5 surfactants, both w/o and o/w emulsions were unstable. We provided the titration of the C12E2 bilayer with C12E4 and C12E5 to study and predict their stability behavior.
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Affiliation(s)
- Ksenia Astafyeva
- †Laboratoire de Physique Statistique, Ecole Normale Supérieure, Sorbonne Universités, UPMC Université, and Université Paris Diderot, CNRS, 24 rue Lhomond, F-75005 Paris, France
| | - Wladimir Urbach
- †Laboratoire de Physique Statistique, Ecole Normale Supérieure, Sorbonne Universités, UPMC Université, and Université Paris Diderot, CNRS, 24 rue Lhomond, F-75005 Paris, France
- ‡Université René Descartes, Paris, France
| | - Nabil Garroum
- †Laboratoire de Physique Statistique, Ecole Normale Supérieure, Sorbonne Universités, UPMC Université, and Université Paris Diderot, CNRS, 24 rue Lhomond, F-75005 Paris, France
| | - Nicolas Taulier
- §Sorbonne Universités, UPMC Univ. Paris 06, CNRS, Laboratoire d'Imagerie Biomédicale, INSERM, F-75006 Paris, France
| | - Abdou R Thiam
- †Laboratoire de Physique Statistique, Ecole Normale Supérieure, Sorbonne Universités, UPMC Université, and Université Paris Diderot, CNRS, 24 rue Lhomond, F-75005 Paris, France
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23
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Dehghan A, Pastor KA, Shi AC. Line tension of multicomponent bilayer membranes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:022713. [PMID: 25768537 DOI: 10.1103/physreve.91.022713] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2014] [Indexed: 06/04/2023]
Abstract
The line tension or edge energy of bilayer membranes self-assembled from binary amphiphilic molecules is studied using self-consistent-field theory (SCFT). Specifically, solutions of the SCFT equations corresponding to an infinite membrane with a circular pore, or an open membrane, are obtained for a coarse-grained model in which the amphiphilic species and hydrophilic solvents are represented by ABandED diblock copolymers and C homopolymers, respectively. The edge energy of the membrane is extracted from the free energy of the open membranes. Results for membranes composed of mixtures of symmetric and cone- or inverse cone-shaped amphiphilic molecules with neutral and/or repulsive interactions are obtained and analyzed. It is observed that an increase in the concentration of the cone-shaped species leads to a decrease of the line tension. In contrast, adding inverse cone-shaped copolymers results in an increase of the line tension. Furthermore, the density profile of the copolymers reveals that the line tension is regulated by the distribution of the amphiphiles at the bilayer edge.
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Affiliation(s)
- Ashkan Dehghan
- Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, Canada L8S 4M1
| | - Kyle A Pastor
- Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, Canada L8S 4M1
| | - An-Chang Shi
- Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, Canada L8S 4M1
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24
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Deserno M. Fluid lipid membranes: From differential geometry to curvature stresses. Chem Phys Lipids 2015; 185:11-45. [DOI: 10.1016/j.chemphyslip.2014.05.001] [Citation(s) in RCA: 137] [Impact Index Per Article: 15.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2014] [Revised: 04/21/2014] [Accepted: 05/06/2014] [Indexed: 10/25/2022]
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25
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Tu ZC, Ou-Yang ZC. Recent theoretical advances in elasticity of membranes following Helfrich's spontaneous curvature model. Adv Colloid Interface Sci 2014; 208:66-75. [PMID: 24508501 DOI: 10.1016/j.cis.2014.01.008] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2013] [Revised: 01/16/2014] [Accepted: 01/17/2014] [Indexed: 11/19/2022]
Abstract
Recent theoretical advances in elasticity of membranes following Helfrich's famous spontaneous curvature model are summarized in this review. The governing equations describing equilibrium configurations of lipid vesicles, lipid membranes with free edges, and chiral lipid membranes are presented. Several analytic solutions to these equations and their corresponding configurations are demonstrated.
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Affiliation(s)
- Z C Tu
- Department of Physics, Beijing Normal University, Beijing 100875, China.
| | - Z C Ou-Yang
- Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100080, China.
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26
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Grafmüller A, Knecht V. The free energy of nanopores in tense membranes. Phys Chem Chem Phys 2014; 16:11270-8. [PMID: 24780914 DOI: 10.1039/c3cp54685c] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
Membrane nanopores are central players for a range of important cellular membrane remodeling processes as well as membrane rupture. Understanding pore formation in tense membranes requires comprehension of the molecular mechanism of pore formation and the associated free energy change as a function of the membrane tension. Here we propose a scheme to calculate the free energy change associated with the formation of a nanometer sized pore in molecular dynamics simulations as a function of membrane tension, which requires the calculation of only one computationally expensive potential of mean force. We show that membrane elastic theory can be used to estimate the pore formation free energy at different tension values from the free energy change in a relaxed membrane and the area expansion curves of the membranes. We have computed the pore formation free energy for a dipalmitoyl-phosphatidylcholine (DPPC) membrane at two different lateral pressure values, 1 bar and -40 bar, by calculating the potential of mean force acting on the head group of a single lipid molecule. Unrestrained simulations of the closing process confirm that the intermediate states along this reaction coordinate are reasonable and show that hydrophilic indentations spanning half the bilayer connected by a hydrophobic pore segment represent the corresponding high energy transition state. A comparison of the stability of simulated membranes to experiment at high loading rates show that, contrary to expectation, pores form too easily in small simulated membrane patches. This discrepancy originates from a combination of the absence of ions in the simulations and the small membrane size.
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Affiliation(s)
- Andrea Grafmüller
- Max Planck Institute for Colloids and Interfaces, 14424 Potsdam, Germany.
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27
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Affiliation(s)
- Xiaofei Xu
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125;
| | | | - Isamu Kusaka
- William G. Lowrie Department of Chemical and Biomolecular Engineering, The Koffolt Laboratories, The Ohio State University, Columbus, Ohio 43210
| | - Zhen-Gang Wang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125;
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28
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Rabinovich AL, Lyubartsev AP. Computer simulation of lipid membranes: Methodology and achievements. POLYMER SCIENCE SERIES C 2013. [DOI: 10.1134/s1811238213070060] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
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29
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Li J, Pastor KA, Shi AC, Schmid F, Zhou J. Elastic properties and line tension of self-assembled bilayer membranes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:012718. [PMID: 23944501 DOI: 10.1103/physreve.88.012718] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2013] [Indexed: 05/27/2023]
Abstract
The elastic properties of a self-assembled bilayer membrane are studied using the self-consistent field theory, applied to a model system composed of flexible amphiphilic chains dissolved in hydrophilic polymeric solvents. Examining the free energy of bilayer membranes with different geometries allows us to calculate their bending modulus, Gaussian modulus, two fourth-order membrane moduli, and the line tension. The dependence of these parameters on the microscopic characteristics of the amphiphilic chain, characterized by the volume fraction of the hydrophilic component, is systematically studied. The theoretical predictions are compared with the results from a simple monolayer model, which approximates a bilayer membrane by two monolayers. The region of validity of the linear elasticity theory is analyzed by examining the higher-order contributions.
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Affiliation(s)
- Jianfeng Li
- The State Key Laboratory of Molecular Engineering of Polymers, Department of Macromolecular Science, Fudan University, Shanghai 200433, China
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30
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DISSIPATIVE PARTICLE DYNAMICS SIMULATION ON THE EFFECT OF LINE TENSION ON BENDING RIGIDITY OF BILAYER MEMBRANES. ACTA POLYM SIN 2013. [DOI: 10.3724/sp.j.1105.2013.12341] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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31
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Wong KY, York DM. Exact Relation between Potential of Mean Force and Free-Energy Profile. J Chem Theory Comput 2012; 8:3998-4003. [PMID: 23185141 PMCID: PMC3505112 DOI: 10.1021/ct300392f] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
We apply concepts of covariant and contravariant vector space in differential geometry and general relativity to derive new, general, exact relations between potential of mean force and free-energy profile. These relations are immensely practical in free-energy simulations because a full Jacobian transformation (which is usually unknown) is not required; rather, only knowledge of the (constraint) coordinate of interest is needed. We reveal that in addition to the Jacobian determinant, the Jacobian scale factor and Leibnizian contributions must also be considered, as well a Fixman term with correct mass dependence. Our newly derived relations are verified with new non-trivial benchmark numerical examples for which exact results can be computed, and compared with relations available in the literature that turn out to exhibit significant deviations from the exact values.
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Affiliation(s)
- Kin-Yiu Wong
- Department of Physics, Hong Kong Baptist University, 224 Waterloo Road, Kowloon Tong, Hong Kong
- BioMaPS Institute for Quantitative Biology, Department of Chemistry & Chemical Biology Rutgers, The State University of New Jersey, 174 Frelinghuysen Road, Piscataway, NJ 08854, USA
| | - Darrin M. York
- BioMaPS Institute for Quantitative Biology, Department of Chemistry & Chemical Biology Rutgers, The State University of New Jersey, 174 Frelinghuysen Road, Piscataway, NJ 08854, USA
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32
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Determining the Gaussian curvature modulus of lipid membranes in simulations. Biophys J 2012; 102:1403-10. [PMID: 22455923 DOI: 10.1016/j.bpj.2012.02.013] [Citation(s) in RCA: 145] [Impact Index Per Article: 12.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2011] [Revised: 01/25/2012] [Accepted: 02/08/2012] [Indexed: 11/20/2022] Open
Abstract
The Gaussian curvature modulus κ¯ of lipid bilayers likely contributes more than 100 kcal/mol to every cellular fission or fusion event. This huge impact on membrane remodeling energetics might be a factor that codetermines the complex lipid composition of biomembranes through tuning of κ¯. Yet, its value has been measured only for a handful of simple lipids, and no simulation has so far determined it better than a factor of two, rendering a systematic investigation of such enticing speculations impossible. Here we propose a highly accurate method to determine κ¯ in computer simulations. It relies on the interplay between curvature stress and edge tension of partially curved axisymmetric membrane disks and requires determining their closing probability. For a simplified lipid model we obtain κ¯ and its relation to the normal bending modulus κ for membranes differing both in stiffness and spontaneous lipid curvature. The elastic ratio κ¯/κ can be determined with a few percent statistical accuracy. Its value agrees with the scarce experimental data, and its change with spontaneous lipid curvature is compatible with theoretical expectations, thereby granting additional information on monolayer properties. We also show that an alternative determination of these elastic parameters based on moments of the lateral stress profile gives markedly different and unphysical values.
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Koshiyama K, Wada S. Molecular dynamics simulations of pore formation dynamics during the rupture process of a phospholipid bilayer caused by high-speed equibiaxial stretching. J Biomech 2011; 44:2053-8. [DOI: 10.1016/j.jbiomech.2011.05.014] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2011] [Revised: 05/02/2011] [Accepted: 05/08/2011] [Indexed: 10/18/2022]
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Balleza D. Toward understanding protocell mechanosensation. ORIGINS LIFE EVOL B 2011; 41:281-304. [PMID: 21080073 DOI: 10.1007/s11084-010-9225-y] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2010] [Accepted: 10/20/2010] [Indexed: 01/11/2023]
Abstract
Mechanosensitive (MS) channels can prevent bacterial bursting during hypo-osmotic shocks by responding to increases in lateral tension at the membrane level through an integrated and coordinated opening mechanism. Mechanical regulation in protocells could have been one of the first mechanisms to evolve in order to preserve their integrity against changing environmental conditions. How has the rich functional diversity found in present cells been created throughout evolution, and what did the primordial MS channels look like? This review has been written with the aim of identifying which factors may have been important for the appearance of the first osmotic valve in a prebiotic context, and what this valve may have been like. It highlights the mechanical properties of lipid bilayers, the association of peptides as aggregates in membranes, and the conservation of sequence motifs as central aspects to understand the evolution of proteins that gate below the tension required for spontaneous pore formation and membrane rupture. The arguments developed here apply to both MscL and MscS homologs, but could be valid to mechano-susceptible proteins in general.
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Affiliation(s)
- Daniel Balleza
- Unidad de Biofísica, CSIC-UPV/EHU, Universidad del País Vasco, Barrio Sarriena s/n, Leioa, Spain.
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Ting CL, Appelö D, Wang ZG. Minimum energy path to membrane pore formation and rupture. PHYSICAL REVIEW LETTERS 2011; 106:168101. [PMID: 21599415 PMCID: PMC3225126 DOI: 10.1103/physrevlett.106.168101] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2011] [Indexed: 05/27/2023]
Abstract
We combine dynamic self-consistent field theory with the string method to calculate the minimum energy path to membrane pore formation and rupture. In the regime where nucleation can occur on experimentally relevant time scales, the structure of the critical nucleus is between a solvophilic stalk and a locally thinned membrane. Classical nucleation theory fails to capture these molecular details and significantly overestimates the free energy barrier. Our results suggest that thermally nucleated rupture may be an important factor for the low rupture strains observed in lipid membranes.
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Affiliation(s)
- Christina L. Ting
- Biochemistry and Molecular Biophysics, California Institute of Technology, Pasadena, California 91125, USA
| | - Daniel Appelö
- Mechanical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Zhen-Gang Wang
- Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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A lipocentric view of peptide-induced pores. EUROPEAN BIOPHYSICS JOURNAL: EBJ 2011; 40:399-415. [PMID: 21442255 PMCID: PMC3070086 DOI: 10.1007/s00249-011-0693-4] [Citation(s) in RCA: 88] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/08/2010] [Accepted: 03/03/2011] [Indexed: 01/26/2023]
Abstract
Although lipid membranes serve as effective sealing barriers for the passage of most polar solutes, nonmediated leakage is not completely improbable. A high activation energy normally keeps unassisted bilayer permeation at a very low frequency, but lipids are able to self-organize as pores even in peptide-free and protein-free membranes. The probability of leakage phenomena increases under conditions such as phase coexistence, external stress or perturbation associated to binding of nonlipidic molecules. Here, we argue that pore formation can be viewed as an intrinsic property of lipid bilayers, with strong similarities in the structure and mechanism between pores formed with participation of peptides, lipidic pores induced by different types of stress, and spontaneous transient bilayer defects driven by thermal fluctuations. Within such a lipocentric framework, amphipathic peptides are best described as pore-inducing rather than pore-forming elements. Active peptides bound to membranes can be understood as a source of internal surface tension which facilitates pore formation by diminishing the high activation energy barrier. This first or immediate action of the peptide has some resemblance to catalysis. However, the presence of membrane-active peptides has the additional effect of displacing the equilibrium towards the pore-open state, which is then maintained over long times, and reducing the size of initial individual pores. Thus, pore-inducing peptides, regardless of their sequence and oligomeric organization, can be assigned a double role of increasing the probability of pore formation in membranes to high levels as well as stabilizing these pores after they appear.
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Gurtovenko AA, Anwar J, Vattulainen I. Defect-Mediated Trafficking across Cell Membranes: Insights from in Silico Modeling. Chem Rev 2010; 110:6077-103. [DOI: 10.1021/cr1000783] [Citation(s) in RCA: 158] [Impact Index Per Article: 11.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Affiliation(s)
- Andrey A. Gurtovenko
- Institute of Macromolecular Compounds, Russian Academy of Sciences, Bolshoi Prospect 31, V.O., St. Petersburg, 199004 Russia, Computational Laboratory, Institute of Pharmaceutical Innovation, University of Bradford, Bradford, West Yorkshire BD7 1DP, U.K., Department of Physics, Tampere University of Technology, P.O. Box 692, FI-33101 Tampere, Finland, Aalto University, School of Science and Technology, Finland, and MEMPHYS—Center for Biomembrane Physics, University of Southern Denmark, Odense, Denmark
| | - Jamshed Anwar
- Institute of Macromolecular Compounds, Russian Academy of Sciences, Bolshoi Prospect 31, V.O., St. Petersburg, 199004 Russia, Computational Laboratory, Institute of Pharmaceutical Innovation, University of Bradford, Bradford, West Yorkshire BD7 1DP, U.K., Department of Physics, Tampere University of Technology, P.O. Box 692, FI-33101 Tampere, Finland, Aalto University, School of Science and Technology, Finland, and MEMPHYS—Center for Biomembrane Physics, University of Southern Denmark, Odense, Denmark
| | - Ilpo Vattulainen
- Institute of Macromolecular Compounds, Russian Academy of Sciences, Bolshoi Prospect 31, V.O., St. Petersburg, 199004 Russia, Computational Laboratory, Institute of Pharmaceutical Innovation, University of Bradford, Bradford, West Yorkshire BD7 1DP, U.K., Department of Physics, Tampere University of Technology, P.O. Box 692, FI-33101 Tampere, Finland, Aalto University, School of Science and Technology, Finland, and MEMPHYS—Center for Biomembrane Physics, University of Southern Denmark, Odense, Denmark
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