1
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Paul A, Chakrabarti J. Dynamics of an aqueous suspension of short hyaluronic acid chains near a DPPC bilayer. Phys Chem Chem Phys 2024. [PMID: 39021115 DOI: 10.1039/d4cp01088d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/20/2024]
Abstract
The synergy between hyaluronic acid (HA) and lipid molecules plays a crucial role in synovial fluids, cell coatings, etc. Diseased cells in cancer and arthritis show changes in HA concentration and chain size, impacting the viscoelastic and mechanical properties of the cells. Although the solution behavior of HA is known in experiments, a molecular-level understanding of the role of HA in the dynamics at the interface of HA-water and the cellular boundary is lacking. Here, we perform atomistic molecular dynamics simulation of short HA chains in an explicit water solvent in the presence of a DPPC bilayer, relevant in pathological cases. We identify a stable interface between HA-water and the bilayer where the water molecules are in contact with the bilayer and the HA chains are located away without any direct contact. Both translation and rotation of the interfacial waters in contact with the lipid bilayer and translation of the HA chains exhibit subdiffusive behavior. The diffusive behavior sets in slightly away from the bilayer, where the diffusion coefficients of water and HA decrease monotonically with increase in HA concentration. On the contrary, the dependence on HA chain size is only marginal due to enhanced chain flexibility as their size increases.
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Affiliation(s)
- Anirban Paul
- Department of Physics of Complex Systems, S. N. Bose National Centre for Basic Sciences, Block JD, Sector - III, Salt Lake, Kolkata 700106, India.
| | - Jaydeb Chakrabarti
- Department of Physics of Complex Systems, S. N. Bose National Centre for Basic Sciences, Block JD, Sector - III, Salt Lake, Kolkata 700106, India.
- Department of Chemical and Biological Sciences and the Technical Research Centre, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India.
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2
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Linney JA, Routledge SJ, Connell SD, Larson TR, Pitt AR, Jenkinson ER, Goddard AD. Identification of membrane engineering targets for increased butanol tolerance in Clostridium saccharoperbutylacetonicum. BIOCHIMICA ET BIOPHYSICA ACTA. BIOMEMBRANES 2023; 1865:184217. [PMID: 37648011 DOI: 10.1016/j.bbamem.2023.184217] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2023] [Revised: 07/17/2023] [Accepted: 08/17/2023] [Indexed: 09/01/2023]
Abstract
There is a growing interest in the use of microbial cell factories to produce butanol, an industrial solvent and platform chemical. Biobutanol can also be used as a biofuel and represents a cleaner and more sustainable alternative to the use of conventional fossil fuels. Solventogenic Clostridia are the most popular microorganisms used due to the native expression of butanol synthesis pathways. A major drawback to the wide scale implementation and development of these technologies is the toxicity of butanol. Various membrane properties and related functions are perturbed by the interaction of butanol with the cell membrane, causing lower yields and higher purification costs. This is ultimately why the technology remains underemployed. This study aimed to develop a deeper understanding of butanol toxicity at the membrane to determine future targets for membrane engineering. Changes to the lipidome in Clostridium saccharoperbutylacetonicum N1-4 (HMT) throughout butanol fermentation were investigated with thin layer chromatography and mass spectrometry. By the end of fermentation, levels of phosphatidylglycerol lipids had increased significantly, suggesting an important role of these lipid species in tolerance to butanol. Using membrane models and in vitro assays to investigate characteristics such as permeability, fluidity, and swelling, it was found that altering the composition of membrane models can convey tolerance to butanol, and that modulating membrane fluidity appears to be a key factor. Data presented here will ultimately help to inform rational strain engineering efforts to produce more robust strains capable of producing higher butanol titres.
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Affiliation(s)
- John A Linney
- School of Health and Life Sciences, Aston University, Aston Triangle, Birmingham B4 7ET, UK
| | - Sarah J Routledge
- School of Health and Life Sciences, Aston University, Aston Triangle, Birmingham B4 7ET, UK
| | - Simon D Connell
- School of Physics and Astronomy and The Astbury Centre for Structural Molecular Biology, University of Leeds, Leeds LS2 9JT, UK
| | - Tony R Larson
- Department of Biology, University of York, York YO10 5DD, UK
| | - Andrew R Pitt
- Manchester Institute of Biotechnology, University of Manchester, Manchester M1 7DN, UK
| | | | - Alan D Goddard
- School of Health and Life Sciences, Aston University, Aston Triangle, Birmingham B4 7ET, UK.
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3
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Valdés Gómez A, Sevilla FJ. Fractional and scaled Brownian motion on the sphere: The effects of long-time correlations on navigation strategies. Phys Rev E 2023; 108:054117. [PMID: 38115432 DOI: 10.1103/physreve.108.054117] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2022] [Accepted: 10/04/2023] [Indexed: 12/21/2023]
Abstract
We analyze fractional Brownian motion and scaled Brownian motion on the two-dimensional sphere S^{2}. We find that the intrinsic long-time correlations that characterize fractional Brownian motion collude with the specific dynamics (navigation strategies) carried out on the surface giving rise to rich transport properties. We focus our study on two classes of navigation strategies: one induced by a specific set of coordinates chosen for S^{2} (we have chosen the spherical ones in the present analysis), for which we find that contrary to what occurs in the absence of such long-time correlations, nonequilibrium stationary distributions are attained. These results resemble those reported in confined flat spaces in one and two dimensions [Guggenberger et al. New J. Phys. 21, 022002 (2019)1367-263010.1088/1367-2630/ab075f; Vojta et al. Phys. Rev. E 102, 032108 (2020)2470-004510.1103/PhysRevE.102.032108]; however, in the case analyzed here, there are no boundaries that affect the motion on the sphere. In contrast, when the navigation strategy chosen corresponds to a frame of reference moving with the particle (a Frenet-Serret reference system), then the equilibrium distribution on the sphere is recovered in the long-time limit. For both navigation strategies, the relaxation times toward the stationary distribution depend on the particular value of the Hurst parameter. We also show that on S^{2}, scaled Brownian motion, distinguished by a time-dependent diffusion coefficient with a power-scaling, is independent of the navigation strategy finding a good agreement between the analytical calculations obtained from the solution of a time-dependent diffusion equation on S^{2}, and the numerical results obtained from our numerical method to generate ensemble of trajectories.
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Affiliation(s)
- Adriano Valdés Gómez
- Facultad de Ciencias, Universidad Nacional Autónoma de México, Alcaldía Coyoacán, C.P. 04510 Ciudad Universitaria, Ciudad de México, México
- BBVA AI Factory México
| | - Francisco J Sevilla
- Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, 01000, Ciudad de México, México
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4
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Campo MG, Corral GM. Structural, dynamic, and hydration properties of quercetin and its aggregates in solution. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:294001. [PMID: 35472688 DOI: 10.1088/1361-648x/ac6a99] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/05/2022] [Accepted: 04/26/2022] [Indexed: 06/14/2023]
Abstract
Quercetin is a flavonoid present in the human diet with multiple health benefits. Quercetin solutions are inhomogeneous even at very low concentrations due to quercetin's tendency to aggregate. We simulate, using molecular dynamics, three systems of quercetin solutions: infinite dilution, 0.22 M, and 0.46 M. The systems at the two highest concentrations represent regions of the quercetin aggregates, in which the concentration of this molecule is unusually high. We study the behavior of this molecule, its aggregates, and the modifications in the surrounding water. In the first three successive layers of quercetin hydration, the density of water and the hydrogen bonds formations between water molecules are smaller than that of bulk. Quercetin has a hydrophilic surface region that preferentially establishes donor hydrogen bonds with water molecules with relative frequencies from 0.12 to 0.46 at infinite dilution. Also, it has two hydrophobic regions above and below the planes of its rings, whose first hydration layers are further out from quercetin (≈0.3 Å) and their water molecules do not establish hydrogen bonds with it. Water density around the hydrophobic regions is smaller than that of the hydrophilic. Quercetin molecules aggregate inπ-stacking configurations, with a distance of ≈0.37 nm between the planes of their rings, and form bonds between their hydroxyl groups. The formation of quercetin aggregates decreases the hydrogen bonds between quercetin and the surrounding water and produces a subdiffusive behavior in water molecules. Quercetin has a subdiffusive behavior even at infinite dilution, which increases with the number of molecules within the aggregates and the time they remain within them.
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Affiliation(s)
- M G Campo
- Facultad de Ciencias Exactas y Naturales, Universidad Nacional de La Pampa, Uruguay 151, (6300) Santa Rosa, Argentina
| | - G M Corral
- Facultad de Ciencias Exactas y Naturales, Universidad Nacional de La Pampa, Uruguay 151, (6300) Santa Rosa, Argentina
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5
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Zhang Z, Han Y, Chen WR, Do C. Diffusion characteristics of water molecules in a lamellar structure formed by triblock copolymers. Phys Chem Chem Phys 2022; 24:8015-8021. [PMID: 35315475 DOI: 10.1039/d2cp00207h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The distribution and diffusion of water molecules are playing important roles in determining self-assembly and transport properties of polymeric systems. Small-angle neutron scattering (SANS) experiments and molecular dynamics (MD) simulation have been applied to understand the distribution of water molecules and their dynamics in the lamellar membrane formed by Pluronic L62 block copolymers. Penetration of water molecules into the polyethylene oxide (PEO) layers of the membranes has been estimated using scattering length density (SLD) profiles obtained from SANS measurements, which agree well with the molecular distribution observed from MD simulations. The water diffusion coefficient at different regions of the lamellar membrane was further investigated using MD simulation. The diffusion characteristic shows a transition from normal to anomalous diffusion as the position of the water molecule changes from the bulk to PEO and to the polypropylene oxide (PPO) layer. We find that water molecules within the PEO or PPO layers follow subdiffusive dynamics, which can be interpreted by the model of fractional Brownian motion.
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Affiliation(s)
- Zhe Zhang
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA. .,Forschungszentrum Jülich, Jülich Center for Neutron Science, Outstation at the Spallation Neutron Source (SNS), Oak Ridge National Laboratory, Oak Ridge Tennessee, 37831, USA
| | - Youngkyu Han
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA.
| | - Wei-Ren Chen
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA.
| | - Changwoo Do
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA.
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6
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Esteki MH, Malandrino A, Alemrajabi AA, Sheridan GK, Charras G, Moeendarbary E. Poroelastic osmoregulation of living cell volume. iScience 2021; 24:103482. [PMID: 34927026 PMCID: PMC8649806 DOI: 10.1016/j.isci.2021.103482] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2021] [Revised: 08/19/2021] [Accepted: 11/19/2021] [Indexed: 11/22/2022] Open
Abstract
Cells maintain their volume through fine intracellular osmolarity regulation. Osmotic challenges drive fluid into or out of cells causing swelling or shrinkage, respectively. The dynamics of cell volume changes depending on the rheology of the cellular constituents and on how fast the fluid permeates through the membrane and cytoplasm. We investigated whether and how poroelasticity can describe volume dynamics in response to osmotic shocks. We exposed cells to osmotic perturbations and used defocusing epifluorescence microscopy on membrane-attached fluorescent nanospheres to track volume dynamics with high spatiotemporal resolution. We found that a poroelastic model that considers both geometrical and pressurization rates captures fluid-cytoskeleton interactions, which are rate-limiting factors in controlling volume changes at short timescales. Linking cellular responses to osmotic shocks and cell mechanics through poroelasticity can predict the cell state in health, disease, or in response to novel therapeutics. Cell height changes can be finely captured by defocusing microscopy Water permeation and cellular deformability regulate dynamics of cell volume changes Poroelasticity describes the dynamics of cell volume changes The response of cell to hypo or hyperosmotic shocks are modeled by poroelasticity
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Affiliation(s)
- Mohammad Hadi Esteki
- Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran.,Department of Mechanical Engineering, University College London, London, UK
| | - Andrea Malandrino
- Biomaterials, Biomechanics and Tissue Engineering Group, Department of Materials Science and Engineering, Universitat Politècnica de Catalunya, Barcelona, Spain
| | - Ali Akbar Alemrajabi
- Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran
| | - Graham K Sheridan
- School of Life Sciences, Queens Medical Centre, University of Nottingham, Nottingham, UK
| | - Guillaume Charras
- London Centre for Nanotechnology, University College London, London, UK.,Department of Cell and Developmental Biology, University College London, London, UK.,Institute for the Physics of Living Systems, University College London, London, UK
| | - Emad Moeendarbary
- Department of Mechanical Engineering, University College London, London, UK.,Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
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7
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Gonzalez MA, Zaragoza A, Lynch CI, Sansom MSP, Valeriani C. Influence of water models on water movement through AQP1. J Chem Phys 2021; 155:154502. [PMID: 34686053 DOI: 10.1063/5.0063986] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
Abstract
Water diffusion through membrane proteins is a key aspect of cellular function. Essential processes of cellular metabolism are driven by osmotic pressure, which depends on water channels. Membrane proteins such as aquaporins (AQPs) are responsible for enabling water permeation through the cell membrane. AQPs are highly selective, allowing only water and relatively small polar molecules to cross the membrane. Experimentally, estimation of water flux through membrane proteins is still a challenge, and hence, accurate simulations of water permeation are of particular importance. We present a numerical study of water diffusion through AQP1 comparing three water models: TIP3P, OPC, and TIP4P/2005. Bulk diffusion, diffusion permeability, and osmotic permeability are computed and compared among all models. The results show that there are significant differences between TIP3P (a particularly widespread model for simulations of biological systems) and the more recently developed TIP4P/2005 and OPC models. We demonstrate that OPC and TIP4P/2005 reproduce protein-water interactions and dynamics in very good agreement with experimental data. From this study, we find that the choice of the water model has a significant effect on the computed water dynamics as well as its molecular behavior within a biological nanopore.
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Affiliation(s)
| | - Alberto Zaragoza
- Department of Chemistry, The University of Utah, Salt Lake City, Utah 84112-0850, USA
| | - Charlotte I Lynch
- Department of Biochemistry, University of Oxford, South Parks Road, OX1 3QU Oxford, United Kingdom
| | - Mark S P Sansom
- Department of Biochemistry, University of Oxford, South Parks Road, OX1 3QU Oxford, United Kingdom
| | - Chantal Valeriani
- Universidad Complutense de Madrid, Facultad de Ciencias Fícias, Departamento de Estructura de la Materia, Física Térmica y Electrónica, 28040 Madrid, Spain
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8
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Malik S, Debnath A. Dehydration induced dynamical heterogeneity and ordering mechanism of lipid bilayers. J Chem Phys 2021; 154:174904. [PMID: 34241050 DOI: 10.1063/5.0044614] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Abstract
Understanding the influence of dehydration on the membrane structure is crucial to control membrane functionality related to domain formation and cell fusion under anhydrobiosis conditions. To this end, we perform all-atom molecular dynamic simulations of 1,2-dimyristoyl-sn-glycero-3-phosphocholine dimyristoylphosphatidylcholine lipid membranes at different hydration levels at 308 K. As dehydration increases, the lipid area per head group decreases with an increase in bilayer thickness and lipid order parameters indicating bilayer ordering. Concurrently, translational and rotational dynamics of interfacial water (IW) molecules near membranes slow down. On the onset of bilayer ordering, the IW molecules exhibit prominent features of dynamical heterogeneity evident from non-Gaussian parameters and one-dimensional van Hove correlation functions. At a fully hydrated state, diffusion constants (D) of the IW follow a scaling relation, D∼τα -1, where the α relaxation time (τα) is obtained from self-intermediate scattering functions. However, upon dehydration, the relation breaks and the D of the IW follows a power law behavior as D∼τα -0.57, showing the signature of glass dynamics. τα and hydrogen bond lifetime calculated from intermittent hydrogen bond auto-correlation functions undergo a similar crossover in association with bilayer ordering on dehydration. The bilayer ordering is accompanied with an increase in fraction of caged lipids spanned over the bilayer surface and a decrease in fraction of mobile lipids due to the non-diffusive dynamics. Our analyses reveal that the microscopic mechanism of lipid ordering by dehydration is governed by dynamical heterogeneity. The fundamental understanding from this study can be applied to complex bio-membranes to trap functionally relevant gel-like domains at room temperature.
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Affiliation(s)
- Sheeba Malik
- Department of Chemistry, Indian Institute of Technology Jodhpur, Karwad, Rajasthan, India
| | - Ananya Debnath
- Department of Chemistry, Indian Institute of Technology Jodhpur, Karwad, Rajasthan, India
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9
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Levin M, Bel G, Roichman Y. Measurements and characterization of the dynamics of tracer particles in an actin network. J Chem Phys 2021; 154:144901. [PMID: 33858166 DOI: 10.1063/5.0045278] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
Abstract
The underlying physics governing the diffusion of a tracer particle in a viscoelastic material is a topic of some dispute. The long-term memory in the mechanical response of such materials should induce diffusive motion with a memory kernel, such as fractional Brownian motion (fBM). This is the reason that microrheology is able to provide the shear modulus of polymer networks. Surprisingly, the diffusion of a tracer particle in a network of a purified protein, actin, was found to conform to the continuous time random walk type (CTRW). We set out to resolve this discrepancy by studying the tracer particle diffusion using two different tracer particle sizes, in actin networks of different mesh sizes. We find that the ratio of tracer particle size to the characteristic length scale of a bio-polymer network plays a crucial role in determining the type of diffusion it performs. We find that the diffusion of the tracer particles has features of fBm when the particle is large compared to the mesh size, of normal diffusion when the particle is much smaller than the mesh size, and of the CTRW in between these two limits. Based on our findings, we propose and verify numerically a new model for the motion of the tracer in all regimes. Our model suggests that diffusion in actin networks consists of fBm of the tracer particle coupled with caging events with power-law distributed escape times.
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Affiliation(s)
- Maayan Levin
- Raymond and Beverly Sackler School of Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Golan Bel
- Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus 8499000, Israel
| | - Yael Roichman
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 6997801, Israel
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10
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Yamamoto E, Akimoto T, Mitsutake A, Metzler R. Universal Relation between Instantaneous Diffusivity and Radius of Gyration of Proteins in Aqueous Solution. PHYSICAL REVIEW LETTERS 2021; 126:128101. [PMID: 33834804 DOI: 10.1103/physrevlett.126.128101] [Citation(s) in RCA: 49] [Impact Index Per Article: 16.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2020] [Accepted: 02/09/2021] [Indexed: 06/12/2023]
Abstract
Protein conformational fluctuations are highly complex and exhibit long-term correlations. Here, molecular dynamics simulations of small proteins demonstrate that these conformational fluctuations directly affect the protein's instantaneous diffusivity D_{I}. We find that the radius of gyration R_{g} of the proteins exhibits 1/f fluctuations that are synchronous with the fluctuations of D_{I}. Our analysis demonstrates the validity of the local Stokes-Einstein-type relation D_{I}∝1/(R_{g}+R_{0}), where R_{0}∼0.3 nm is assumed to be a hydration layer around the protein. From the analysis of different protein types with both strong and weak conformational fluctuations, the validity of the Stokes-Einstein-type relation appears to be a general property.
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Affiliation(s)
- Eiji Yamamoto
- Department of System Design Engineering, Keio University, Yokohama, Kanagawa 223-8522, Japan
| | - Takuma Akimoto
- Department of Physics, Tokyo University of Science, Noda, Chiba 278-8510, Japan
| | - Ayori Mitsutake
- Department of Physics, Meiji University, Kawasaki, Kanagawa 214-8571, Japan
| | - Ralf Metzler
- Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
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11
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Balcerek M, Burnecki K. Testing of Multifractional Brownian Motion. ENTROPY 2020; 22:e22121403. [PMID: 33322676 PMCID: PMC7764075 DOI: 10.3390/e22121403] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/18/2020] [Revised: 12/09/2020] [Accepted: 12/10/2020] [Indexed: 12/12/2022]
Abstract
Fractional Brownian motion (FBM) is a generalization of the classical Brownian motion. Most of its statistical properties are characterized by the self-similarity (Hurst) index 0<H<1. In nature one often observes changes in the dynamics of a system over time. For example, this is true in single-particle tracking experiments where a transient behavior is revealed. The stationarity of increments of FBM restricts substantially its applicability to model such phenomena. Several generalizations of FBM have been proposed in the literature. One of these is called multifractional Brownian motion (MFBM) where the Hurst index becomes a function of time. In this paper, we introduce a rigorous statistical test on MFBM based on its covariance function. We consider three examples of the functions of the Hurst parameter: linear, logistic, and periodic. We study the power of the test for alternatives being MFBMs with different linear, logistic, and periodic Hurst exponent functions by utilizing Monte Carlo simulations. We also analyze mean-squared displacement (MSD) for the three cases of MFBM by comparing the ensemble average MSD and ensemble average time average MSD, which is related to the notion of ergodicity breaking. We believe that the presented results will be helpful in the analysis of various anomalous diffusion phenomena.
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12
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Akimoto T, Sera T, Yamato K, Yano K. Aging arcsine law in Brownian motion and its generalization. Phys Rev E 2020; 102:032103. [PMID: 33075938 DOI: 10.1103/physreve.102.032103] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2020] [Accepted: 08/12/2020] [Indexed: 06/11/2023]
Abstract
Classical arcsine law states that the fraction of occupation time on the positive or the negative side in Brownian motion does not converge to a constant but converges in distribution to the arcsine distribution. Here we consider how a preparation of the system affects the arcsine law, i.e., aging of the arcsine law. We derive an aging distributional theorem for occupation time statistics in Brownian motion, where the ratio of time when measurements start to the measurement time plays an important role in determining the shape of the distribution. Furthermore, we show that this result can be generalized as an aging distributional limit theorem in renewal processes.
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Affiliation(s)
- Takuma Akimoto
- Department of Physics, Tokyo University of Science, Noda, Chiba 278-8510, Japan
| | - Toru Sera
- Department of Mathematics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan
| | - Kosuke Yamato
- Department of Mathematics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan
| | - Kouji Yano
- Department of Mathematics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan
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13
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Arai N, Kobayashi Y, Yasuoka K. A biointerface effect on the self-assembly of ribonucleic acids: a possible mechanism of RNA polymerisation in the self-replication cycle. NANOSCALE 2020; 12:6691-6698. [PMID: 32163058 DOI: 10.1039/c9nr09537c] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Despite decades of intensive research, many questions remain on the formation and growth of the first cells on Earth. Here, we used computer simulation to compare the self-assembly process of ribonucleic acids in two environments: enclosed in a vesicle-cell membrane and in the bulk. The self-assembly was found to be more favoured in the former environment, and the origin of such a biointerface effect was identified. These results will contribute to a better understanding of the origin of life on the primitive Earth.
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Affiliation(s)
- Noriyoshi Arai
- Department of Engineering, Keio University, Yokohama 223-8522, Japan.
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14
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Bhattacharjee T, Datta SS. Confinement and activity regulate bacterial motion in porous media. SOFT MATTER 2019; 15:9920-9930. [PMID: 31750508 DOI: 10.1039/c9sm01735f] [Citation(s) in RCA: 44] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Understanding how bacteria move in porous media is critical to applications in healthcare, agriculture, environmental remediation, and chemical sensing. Recent work has demonstrated that E. coli, which moves by run-and-tumble dynamics in a homogeneous medium, exhibits a new form of motility when confined in a disordered porous medium: hopping-and-trapping motility, in which cells perform rapid, directed hops punctuated by intervals of slow, undirected trapping. Here, we use direct visualization to shed light on how these processes depend on pore-scale confinement and cellular activity. We find that hopping is determined by pore-scale confinement, and is independent of cellular activity; by contrast, trapping is determined by the competition between pore-scale confinement and cellular activity, as predicted by an entropic trapping model. These results thus help to elucidate the factors that regulate bacterial motion in porous media, and could help aid the development of new models of motility in heterogeneous environments.
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Affiliation(s)
- Tapomoy Bhattacharjee
- The Andlinger Center for Energy and the Environment, Princeton University, 86 Olden Street, Princeton, NJ 08544, USA
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15
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Grebenkov DS. Reversible reactions controlled by surface diffusion on a sphere. J Chem Phys 2019; 151:154103. [PMID: 31640367 DOI: 10.1063/1.5119969] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Denis S. Grebenkov
- Laboratoire de Physique de la Matière Condensée (UMR 7643), CNRS – Ecole Polytechnique, IP Paris, 91128 Palaiseau, France
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16
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Miyaguchi T, Uneyama T, Akimoto T. Brownian motion with alternately fluctuating diffusivity: Stretched-exponential and power-law relaxation. Phys Rev E 2019; 100:012116. [PMID: 31499895 DOI: 10.1103/physreve.100.012116] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2019] [Indexed: 11/07/2022]
Abstract
We investigate Brownian motion with diffusivity alternately fluctuating between fast and slow states. We assume that sojourn-time distributions of these two states are given by exponential or power-law distributions. We develop a theory of alternating renewal processes to study a relaxation function which is expressed with an integral of the diffusivity over time. This relaxation function can be related to a position correlation function if the particle is in a harmonic potential and to the self-intermediate scattering function if the potential force is absent. It is theoretically shown that, at short times, the exponential relaxation or the stretched-exponential relaxation are observed depending on the power-law index of the sojourn-time distributions. In contrast, at long times, a power-law decay with an exponential cutoff is observed. The dependencies on the initial ensembles (i.e., equilibrium or nonequilibrium initial ensembles) are also elucidated. These theoretical results are consistent with numerical simulations.
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Affiliation(s)
- Tomoshige Miyaguchi
- Department of Mathematics, Naruto University of Education, Naruto, Tokushima 772-8502, Japan
| | - Takashi Uneyama
- Center for Computational Science, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa, Nagoya 464-8603, Japan
| | - Takuma Akimoto
- Department of Physics, Tokyo University of Science, Noda, Chiba 278-8510, Japan
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17
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Goiko M, de Bruyn JR, Heit B. Membrane Diffusion Occurs by Continuous-Time Random Walk Sustained by Vesicular Trafficking. Biophys J 2019; 114:2887-2899. [PMID: 29925025 DOI: 10.1016/j.bpj.2018.04.024] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2018] [Revised: 03/06/2018] [Accepted: 04/16/2018] [Indexed: 10/28/2022] Open
Abstract
Diffusion in cellular membranes is regulated by processes that occur over a range of spatial and temporal scales. These processes include membrane fluidity, interprotein and interlipid interactions, interactions with membrane microdomains, interactions with the underlying cytoskeleton, and cellular processes that result in net membrane movement. The complex, non-Brownian diffusion that results from these processes has been difficult to characterize, and moreover, the impact of factors such as membrane recycling on membrane diffusion remains largely unexplored. We have used a careful statistical analysis of single-particle tracking data of the single-pass plasma membrane protein CD93 to show that the diffusion of this protein is well described by a continuous-time random walk in parallel with an aging process mediated by membrane corrals. The overall result is an evolution in the diffusion of CD93: proteins initially diffuse freely on the cell surface but over time become increasingly trapped within diffusion-limiting membrane corrals. Stable populations of freely diffusing and corralled CD93 are maintained by an endocytic/exocytic process in which corralled CD93 is selectively endocytosed, whereas freely diffusing CD93 is replenished by exocytosis of newly synthesized and recycled CD93. This trafficking not only maintained CD93 diffusivity but also maintained the heterogeneous distribution of CD93 in the plasma membrane. These results provide insight into the nature of the biological and biophysical processes that can lead to significantly non-Brownian diffusion of membrane proteins and demonstrate that ongoing membrane recycling is critical to maintaining steady-state diffusion and distribution of proteins in the plasma membrane.
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Affiliation(s)
- Maria Goiko
- Department of Microbiology and Immunology, The University of Western Ontario, London, Ontario, Canada; Department of Physics and Astronomy, The University of Western Ontario, London, Ontario, Canada
| | - John R de Bruyn
- Department of Physics and Astronomy, The University of Western Ontario, London, Ontario, Canada
| | - Bryan Heit
- Department of Microbiology and Immunology, The University of Western Ontario, London, Ontario, Canada; Centre for Human Immunology, The University of Western Ontario, London, Ontario, Canada.
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18
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Iorio A, Camisasca G, Rovere M, Gallo P. Characterization of hydration water in supercooled water-trehalose solutions: The role of the hydrogen bonds network. J Chem Phys 2019; 151:044507. [PMID: 31370561 DOI: 10.1063/1.5108579] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The structural and dynamical properties of hydration water in aqueous solutions of trehalose are studied with molecular dynamics simulation. We simulate the systems in the supercooled region to investigate how the interaction with the trehalose molecules modifies the hydrogen bond network, the structural relaxation, and the diffusion properties of hydration water. The analysis is performed by considering the radial distribution functions, the residence time of water molecules in the hydration shell, the two body excess entropy, and the hydrogen bond water-water and water-trehalose correlations of the hydration water. The study of the two body excess entropy shows the presence of a fragile to strong crossover in supercooled hydration water also found in the relaxation time of the water-water hydrogen bond correlation function, and this is in agreement with predictions of the mode coupling theory and of previous studies of the oxygen-oxygen density correlators [A. Iorio et al., J. Mol. Liq. 282, 617 (2019); Sci. China: Phys., Mech. Astron. 62, 107011 (2019)]. The water-trehalose hydrogen bond correlation function instead evidences a strong to strong crossover in the relaxation time, and this crossover is related to a trehalose dynamical transition. This signals the role that the strong interplay between the soluted molecules and the surrounding solvent has in determining the dynamical transition common to both components of the system that happens upon cooling and that is similar to the well known protein dynamical transition. We connect our results with the cryoprotecting role of trehalose molecules.
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Affiliation(s)
- A Iorio
- Dipartimento di Matematica e Fisica, Università Roma Tre, Via della Vasca Navale 84, 00146 Rome, Italy
| | - G Camisasca
- Department of Physics, AlbaNova University Center, Stockholm University, S-106 91 Stockholm, Sweden
| | - M Rovere
- Dipartimento di Matematica e Fisica, Università Roma Tre, Via della Vasca Navale 84, 00146 Rome, Italy
| | - P Gallo
- Dipartimento di Matematica e Fisica, Università Roma Tre, Via della Vasca Navale 84, 00146 Rome, Italy
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19
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Hachiya Y, Uneyama T, Kaneko T, Akimoto T. Unveiling diffusive states from center-of-mass trajectories in glassy dynamics. J Chem Phys 2019; 151:034502. [DOI: 10.1063/1.5100640] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yuto Hachiya
- Department of Physics, Tokyo University of Science, Noda, Chiba 278-8510, Japan
| | - Takashi Uneyama
- Center for Computational Science, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa, Nagoya 464-8603, Japan
| | - Toshihiro Kaneko
- Department of Mechanical Engineering, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Takuma Akimoto
- Department of Physics, Tokyo University of Science, Noda, Chiba 278-8510, Japan
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20
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Dos Santos MAF, Habitzreuter MA, Schwade MH, Borrasca R, Antonacci M, Gonzatti GK, Netz PA, Barbosa MC. Dynamical aspects of supercooled TIP3P-water in the grooves of DNA. J Chem Phys 2019; 150:235101. [PMID: 31228916 DOI: 10.1063/1.5100601] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
We investigate by molecular dynamics simulations the mobility of the water located at the DNA minor and major grooves. We employ the TIP3P water model, and our system is analyzed for a range of temperatures 190-300 K. For high temperatures, the water at the grooves shows an Arrhenius behavior similar to that observed in the bulk water. At lower temperatures, a departure from the bulk behavior is observed. This slowing down in the dynamics is compared with the dynamics of the hydrogen of the DNA at the grooves and with the autocorrelation functions of the water hydrogen bonds. Our results indicate that the hydrogen bonds of the water at the minor grooves are highly correlated, which suggests that this is the mechanism for the slow dynamics at this high confinement.
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Affiliation(s)
- M A F Dos Santos
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970, Porto Alegre, RS, Brazil
| | - M A Habitzreuter
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970, Porto Alegre, RS, Brazil
| | - M H Schwade
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970, Porto Alegre, RS, Brazil
| | - R Borrasca
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970, Porto Alegre, RS, Brazil
| | - M Antonacci
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970, Porto Alegre, RS, Brazil
| | - G K Gonzatti
- Instituto de Química, Universidade Federal do Rio Grande do Sul, CEP 91501-970, Porto Alegre, RS, Brazil
| | - P A Netz
- Instituto de Química, Universidade Federal do Rio Grande do Sul, CEP 91501-970, Porto Alegre, RS, Brazil
| | - M C Barbosa
- Instituto de Física, Departamento de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970, Porto Alegre, RS, Brazil
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21
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Abstract
Diverse processes-e.g. bioremediation, biofertilization, and microbial drug delivery-rely on bacterial migration in disordered, three-dimensional (3D) porous media. However, how pore-scale confinement alters bacterial motility is unknown due to the opacity of typical 3D media. As a result, models of migration are limited and often employ ad hoc assumptions. Here we reveal that the paradigm of run-and-tumble motility is dramatically altered in a porous medium. By directly visualizing individual Escherichia coli, we find that the cells are intermittently and transiently trapped as they navigate the pore space, exhibiting diffusive behavior at long time scales. The trapping durations and the lengths of "hops" between traps are broadly distributed, reminiscent of transport in diverse other disordered systems; nevertheless, we show that these quantities can together predict the long-time bacterial translational diffusivity. Our work thus provides a revised picture of bacterial motility in complex media and yields principles for predicting cellular migration.
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Affiliation(s)
- Tapomoy Bhattacharjee
- The Andlinger Center for Energy and the Environment, Princeton University, 86 Olden Street, Princeton, NJ, 08544, USA
| | - Sujit S Datta
- Department of Chemical and Biological Engineering, Princeton University, 41 Olden Street, Princeton, NJ, 08544, USA.
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22
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Hou R, Cherstvy AG, Metzler R, Akimoto T. Biased continuous-time random walks for ordinary and equilibrium cases: facilitation of diffusion, ergodicity breaking and ageing. Phys Chem Chem Phys 2018; 20:20827-20848. [PMID: 30066003 DOI: 10.1039/c8cp01863d] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Abstract
We examine renewal processes with power-law waiting time distributions (WTDs) and non-zero drift via computing analytically and by computer simulations their ensemble and time averaged spreading characteristics. All possible values of the scaling exponent α are considered for the WTD ψ(t) ∼ 1/t1+α. We treat continuous-time random walks (CTRWs) with 0 < α < 1 for which the mean waiting time diverges, and investigate the behaviour of the process for both ordinary and equilibrium CTRWs for 1 < α < 2 and α > 2. We demonstrate that in the presence of a drift CTRWs with α < 1 are ageing and non-ergodic in the sense of the non-equivalence of their ensemble and time averaged displacement characteristics in the limit of lag times much shorter than the trajectory length. In the sense of the equivalence of ensemble and time averages, CTRW processes with 1 < α < 2 are ergodic for the equilibrium and non-ergodic for the ordinary situation. Lastly, CTRW renewal processes with α > 2-both for the equilibrium and ordinary situation-are always ergodic. For the situations 1 < α < 2 and α > 2 the variance of the diffusion process, however, depends on the initial ensemble. For biased CTRWs with α > 1 we also investigate the behaviour of the ergodicity breaking parameter. In addition, we demonstrate that for biased CTRWs the Einstein relation is valid on the level of the ensemble and time averaged displacements, in the entire range of the WTD exponent α.
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Affiliation(s)
- Ru Hou
- School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China.
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23
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Shweta H, Sen S. Dynamics of water and ions around DNA: What is so special about them? J Biosci 2018; 43:499-518. [PMID: 30002269] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Water around biomolecules is special for behaving strangely - both in terms of structure and dynamics, while ions are found to control various interactions in biomolecules such as DNA, proteins and lipids. The questions that how water and ions around these biomolecules behave in terms of their structure and dynamics, and how they affect the biomolecular functions have triggered tremendous research activities worldwide. Such activities not only unfolded important static and dynamic properties of water and ions around these biomolecules, but also provoked heated debate regarding their explanation and role in biological functions. DNA, being negatively charged, interacts strongly with the surrounding dipolar water and positively charged counterions, leading to complex electrostatic coupling of water and ions with the DNA. Recent timeresolved fluorescence Stokes shift experiments and related computer simulation studies from our and other laboratories have unfolded some unique dynamic characteristics of water and ions near different structures of DNA. These results are discussed here to showcase the specialty of water and ion dynamics around DNA.
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Affiliation(s)
- Him Shweta
- Spectroscopy Laboratory, School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
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24
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25
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26
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Ren KX, Jia XM, Jiao GS, Chen T, Qian HJ, Lu ZY. Interfacial Properties and Hopping Diffusion of Small Nanoparticle in Polymer/Nanoparticle Composite with Attractive Interaction on Side Group. Polymers (Basel) 2018; 10:E598. [PMID: 30966632 PMCID: PMC6403981 DOI: 10.3390/polym10060598] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2018] [Revised: 05/21/2018] [Accepted: 05/25/2018] [Indexed: 12/03/2022] Open
Abstract
The diffusion dynamics of fullerene (C 60 ) in unentangled linear atactic polystyrene (PS) and polypropylene (PP) melts and the structure and dynamic properties of polymers in interface area are investigated by performing all-atom molecular dynamics simulations. The comparison of the results in two systems emphasises the influence of local interactions exerted by polymer side group on the diffusion dynamics of the nanoparticle. In the normal diffusive regime at long time scales, the displacement distribution function (DDF) follows a Gaussian distribution in PP system, indicating a normal diffusion of C 60 . However, we observe multiple peaks in the DDF curve for C 60 diffusing in PS melt, which indicates a diffusion mechanism of hopping of C 60 . The attractive interaction between C 60 and phenyl ring side groups are found to be responsible for the observed hopping diffusion. In addition, we find that the C 60 is dynamically coupled with a subsection of a tetramer on PS chain, which has a similar size with C 60 . The phenyl ring on PS chain backbone tends to have a parallel configuration in the vicinity of C 60 surface, therefore neighbouring phenyl rings can form chelation effect on the C 60 surface. Consequently, the rotational dynamics of phenyl ring and the translational diffusion of styrene monomers are found to be slowed down in this interface area. We hope our results can be helpful for understanding of the influence of the local interactions on the nanoparticle diffusion dynamics and interfacial properties in polymer/nanoparticle composites.
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Affiliation(s)
- Kai-Xin Ren
- State Key Laboratory of Supramolecular Structure and Materials, and Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun 130023, China.
| | - Xiang-Meng Jia
- State Key Laboratory of Supramolecular Structure and Materials, and Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun 130023, China.
| | - Gui-Sheng Jiao
- State Key Laboratory of Supramolecular Structure and Materials, and Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun 130023, China.
| | - Tao Chen
- State Key Laboratory of Supramolecular Structure and Materials, and Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun 130023, China.
| | - Hu-Jun Qian
- State Key Laboratory of Supramolecular Structure and Materials, and Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun 130023, China.
| | - Zhong-Yuan Lu
- State Key Laboratory of Supramolecular Structure and Materials, and Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun 130023, China.
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27
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Sikora G, Kepten E, Weron A, Balcerek M, Burnecki K. An efficient algorithm for extracting the magnitude of the measurement error for fractional dynamics. Phys Chem Chem Phys 2018; 19:26566-26581. [PMID: 28920611 DOI: 10.1039/c7cp04464j] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
Modern live-imaging fluorescent microscopy techniques following the stochastic motion of labeled tracer particles, i.e. single particle tracking (SPT) experiments, have uncovered significant deviations from the laws of Brownian motion in a variety of biological systems. Accurately characterizing the anomalous diffusion for SPT experiments has become a central issue in biophysics. However, measurement errors raise difficulty in the analysis of single trajectories. In this paper, we introduce a novel surface calibration method based on a fractionally integrated moving average (FIMA) process as an effective tool for extracting both the magnitude of the measurement error and the anomalous exponent for autocorrelated processes of various origins. This method is developed using a toy model - fractional Brownian motion disturbed by independent Gaussian white noise - and is illustrated on both simulated and experimental biological data. We also compare this new method with the mean-squared displacement (MSD) technique, extended to capture the measurement noise in the toy model, which shows inferior results. The introduced procedure is expected to allow for more accurate analysis of fractional anomalous diffusion trajectories with measurement errors across different experimental fields and without the need for any calibration measurements.
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Affiliation(s)
- G Sikora
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wroclaw University of Science and Technology, Wyspianskiego 27, 50-370 Wroclaw, Poland.
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28
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Cherstvy AG, Nagel O, Beta C, Metzler R. Non-Gaussianity, population heterogeneity, and transient superdiffusion in the spreading dynamics of amoeboid cells. Phys Chem Chem Phys 2018; 20:23034-23054. [DOI: 10.1039/c8cp04254c] [Citation(s) in RCA: 51] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
What is the underlying diffusion process governing the spreading dynamics and search strategies employed by amoeboid cells?
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Affiliation(s)
- Andrey G. Cherstvy
- Institute for Physics & Astronomy
- University of Potsdam
- 14476 Potsdam-Golm
- Germany
| | - Oliver Nagel
- Institute for Physics & Astronomy
- University of Potsdam
- 14476 Potsdam-Golm
- Germany
| | - Carsten Beta
- Institute for Physics & Astronomy
- University of Potsdam
- 14476 Potsdam-Golm
- Germany
| | - Ralf Metzler
- Institute for Physics & Astronomy
- University of Potsdam
- 14476 Potsdam-Golm
- Germany
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29
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Yamamoto E. Computational and theoretical approaches for studies of a lipid recognition protein on biological membranes. Biophys Physicobiol 2017; 14:153-160. [PMID: 29159013 PMCID: PMC5689545 DOI: 10.2142/biophysico.14.0_153] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2017] [Accepted: 09/26/2017] [Indexed: 01/13/2023] Open
Abstract
Many cellular functions, including cell signaling and related events, are regulated by the association of peripheral membrane proteins (PMPs) with biological membranes containing anionic lipids, e.g., phosphatidylinositol phosphate (PIP). This association is often mediated by lipid recognition modules present in many PMPs. Here, I summarize computational and theoretical approaches to investigate the molecular details of the interactions and dynamics of a lipid recognition module, the pleckstrin homology (PH) domain, on biological membranes. Multiscale molecular dynamics simulations using combinations of atomistic and coarse-grained models yielded results comparable to those of actual experiments and could be used to elucidate the molecular mechanisms of the formation of protein/lipid complexes on membrane surfaces, which are often difficult to obtain using experimental techniques. Simulations revealed some modes of membrane localization and interactions of PH domains with membranes in addition to the canonical binding mode. In the last part of this review, I address the dynamics of PH domains on the membrane surface. Local PIP clusters formed around the proteins exhibit anomalous fluctuations. This dynamic change in protein-lipid interactions cause temporally fluctuating diffusivity of proteins, i.e., the short-term diffusivity of the bound protein changes substantially with time, and may in turn contribute to the formation/dissolution of protein complexes in membranes.
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Affiliation(s)
- Eiji Yamamoto
- Graduate School of Science and Technology, Keio University, Yokohama, Kanagawa 223-8522, Japan
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30
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Ergodicity breaking on the neuronal surface emerges from random switching between diffusive states. Sci Rep 2017; 7:5404. [PMID: 28710444 PMCID: PMC5511290 DOI: 10.1038/s41598-017-05911-y] [Citation(s) in RCA: 58] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2017] [Accepted: 06/05/2017] [Indexed: 12/27/2022] Open
Abstract
Stochastic motion on the surface of living cells is critical to promote molecular encounters that are necessary for multiple cellular processes. Often the complexity of the cell membranes leads to anomalous diffusion, which under certain conditions it is accompanied by non-ergodic dynamics. Here, we unravel two manifestations of ergodicity breaking in the dynamics of membrane proteins in the somatic surface of hippocampal neurons. Three different tagged molecules are studied on the surface of the soma: the voltage-gated potassium and sodium channels Kv1.4 and Nav1.6 and the glycoprotein CD4. In these three molecules ergodicity breaking is unveiled by the confidence interval of the mean square displacement and by the dynamical functional estimator. Ergodicity breaking is found to take place due to transient confinement effects since the molecules alternate between free diffusion and confined motion.
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31
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Abstract
Anomalous diffusion is being discovered in a fast growing number of systems. The exact nature of this anomalous diffusion provides important information on the physical laws governing the studied system. One of the central properties analysed for finite particle motion time series is the intrinsic variability of the apparent diffusivity, typically quantified by the ergodicity breaking parameter EB. Here we demonstrate that frequently EB is insufficient to provide a meaningful measure for the observed variability of the data. Instead, important additional information is provided by the higher order moments entering by the skewness and kurtosis. We analyse these quantities for three popular anomalous diffusion models. In particular, we find that even for the Gaussian fractional Brownian motion a significant skewness in the results of physical measurements occurs and needs to be taken into account. Interestingly, the kurtosis and skewness may also provide sensitive estimates of the anomalous diffusion exponent underlying the data. We also derive a new result for the EB parameter of fractional Brownian motion valid for the whole range of the anomalous diffusion parameter. Our results are important for the analysis of anomalous diffusion but also provide new insights into the theory of anomalous stochastic processes.
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32
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Sabbar EH, Amar JG. Island nucleation and growth with anomalous diffusion in one-dimension. J Chem Phys 2017; 146:074702. [PMID: 28228016 DOI: 10.1063/1.4976137] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Recently a general rate-equation (RE) theory of submonolayer island nucleation and growth was developed [J. G. Amar and M. Semaan, Phys. Rev. E 93, 062805 (2016)] which takes into account the critical island-size i, island fractal dimension df, substrate dimension d, and diffusion exponent μ, and good agreement with simulations was found for the case of irreversible growth corresponding to a critical island-size i=1 with d = 2. Here we present the results of simulations carried out in 1D (corresponding to d = 1) of island nucleation and growth with anomalous diffusion which were carried out for both the case of superdiffusion (μ>1) and subdiffusion (μ<1). Excellent agreement is found with the general RE theory for both irreversible growth (i=1) and reversible growth with i=2 for all 0≤μ≤2.
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Affiliation(s)
- Ehsan H Sabbar
- Department of Physics and Astronomy, University of Toledo, Toledo, Ohio 43606, USA
| | - Jacques G Amar
- Department of Physics and Astronomy, University of Toledo, Toledo, Ohio 43606, USA
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33
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Taheriyoun AR, Moghimbeygi M. Visual information and expert's idea in Hurst index estimation of the fractional Brownian motion using a diffusion type approximation. Sci Rep 2017; 7:42482. [PMID: 28195153 PMCID: PMC5307349 DOI: 10.1038/srep42482] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2016] [Accepted: 01/11/2017] [Indexed: 12/02/2022] Open
Abstract
An approximation of the fractional Brownian motion based on the Ornstein-Uhlenbeck process is used to obtain an asymptotic likelihood function. Two estimators of the Hurst index are then presented in the likelihood approach. The first estimator is produced according to the observed values of the sample path; while the second one employs the likelihood function of the incremental process. We also employ visual roughness of realization to restrict the parameter space and to obtain prior information in Bayesian approach. The methods are then compared with three contemporary estimators and an experimental data set is studied.
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Affiliation(s)
- Ali R Taheriyoun
- Shahid Beheshti University, G.C., Department of Statistics, Tehran, 1983969411, Iran
| | - Meisam Moghimbeygi
- Shahid Beheshti University, G.C., Department of Statistics, Tehran, 1983969411, Iran
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34
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Yamamoto E, Akimoto T, Kalli AC, Yasuoka K, Sansom MSP. Dynamic interactions between a membrane binding protein and lipids induce fluctuating diffusivity. SCIENCE ADVANCES 2017; 3:e1601871. [PMID: 28116358 PMCID: PMC5249258 DOI: 10.1126/sciadv.1601871] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2016] [Accepted: 12/07/2016] [Indexed: 05/08/2023]
Abstract
Pleckstrin homology (PH) domains are membrane-binding lipid recognition proteins that interact with phosphatidylinositol phosphate (PIP) molecules in eukaryotic cell membranes. Diffusion of PH domains plays a critical role in biological reactions on membrane surfaces. Although diffusivity can be estimated by long-time measurements, it lacks information on the short-time diffusive nature. We reveal two diffusive properties of a PH domain bound to the surface of a PIP-containing membrane using molecular dynamics simulations. One is fractional Brownian motion, attributed to the motion of the lipids with which the PH domain interacts. The other is temporally fluctuating diffusivity; that is, the short-time diffusivity of the bound protein changes substantially with time. Moreover, the diffusivity for short-time measurements is intrinsically different from that for long-time measurements. This fluctuating diffusivity results from dynamic changes in interactions between the PH domain and PIP molecules. Our results provide evidence that the complexity of protein-lipid interactions plays a crucial role in the diffusion of proteins on biological membrane surfaces. Changes in the diffusivity of PH domains and related membrane-bound proteins may in turn contribute to the formation/dissolution of protein complexes in membranes.
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Affiliation(s)
- Eiji Yamamoto
- Graduate School of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan
| | - Takuma Akimoto
- Graduate School of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan
| | - Antreas C. Kalli
- Department of Biochemistry, University of Oxford, South Parks Road, Oxford OX1 3QU, UK
- Leeds Institute of Cancer and Pathology, School of Medicine, St. James’s University Hospital, University of Leeds, Leeds LS9 7TF, UK
| | - Kenji Yasuoka
- Department of Mechanical Engineering, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan
| | - Mark S. P. Sansom
- Department of Biochemistry, University of Oxford, South Parks Road, Oxford OX1 3QU, UK
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35
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Safdari H, Cherstvy AG, Chechkin AV, Bodrova A, Metzler R. Aging underdamped scaled Brownian motion: Ensemble- and time-averaged particle displacements, nonergodicity, and the failure of the overdamping approximation. Phys Rev E 2017; 95:012120. [PMID: 28208482 DOI: 10.1103/physreve.95.012120] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2016] [Indexed: 06/06/2023]
Abstract
We investigate both analytically and by computer simulations the ensemble- and time-averaged, nonergodic, and aging properties of massive particles diffusing in a medium with a time dependent diffusivity. We call this stochastic diffusion process the (aging) underdamped scaled Brownian motion (UDSBM). We demonstrate how the mean squared displacement (MSD) and the time-averaged MSD of UDSBM are affected by the inertial term in the Langevin equation, both at short, intermediate, and even long diffusion times. In particular, we quantify the ballistic regime for the MSD and the time-averaged MSD as well as the spread of individual time-averaged MSD trajectories. One of the main effects we observe is that, both for the MSD and the time-averaged MSD, for superdiffusive UDSBM the ballistic regime is much shorter than for ordinary Brownian motion. In contrast, for subdiffusive UDSBM, the ballistic region extends to much longer diffusion times. Therefore, particular care needs to be taken under what conditions the overdamped limit indeed provides a correct description, even in the long time limit. We also analyze to what extent ergodicity in the Boltzmann-Khinchin sense in this nonstationary system is broken, both for subdiffusive and superdiffusive UDSBM. Finally, the limiting case of ultraslow UDSBM is considered, with a mixed logarithmic and power-law dependence of the ensemble- and time-averaged MSDs of the particles. In the limit of strong aging, remarkably, the ordinary UDSBM and the ultraslow UDSBM behave similarly in the short time ballistic limit. The approaches developed here open ways for considering other stochastic processes under physically important conditions when a finite particle mass and aging in the system cannot be neglected.
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Affiliation(s)
- Hadiseh Safdari
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
- Department of Physics, Shahid Beheshti University, 19839 Tehran, Iran
| | - Andrey G Cherstvy
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
| | - Aleksei V Chechkin
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
- Institute for Theoretical Physics, Kharkov Institute of Physics and Technology, 61108 Kharkov, Ukraine
- Department of Physics & Astronomy, University of Padova, "Galileo Galilei" - DFA, 35131 Padova, Italy
| | - Anna Bodrova
- Institute of Physics, Humboldt University Berlin, 12489 Berlin, Germany
- Faculty of Physics, M. V. Lomonosov Moscow State University, 119991 Moscow, Russia
| | - Ralf Metzler
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
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36
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Hoiles W, Gupta R, Cornell B, Cranfield C, Krishnamurthy V. The Effect of Tethers on Artificial Cell Membranes: A Coarse-Grained Molecular Dynamics Study. PLoS One 2016; 11:e0162790. [PMID: 27736860 PMCID: PMC5063460 DOI: 10.1371/journal.pone.0162790] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2015] [Accepted: 08/29/2016] [Indexed: 11/18/2022] Open
Abstract
Tethered bilayer lipid membranes (tBLMs) provide a stable platform for modeling the dynamics and order of biological membranes where the tethers mimic the cytoskeletal supports present in biological cell membranes. In this paper coarse-grained molecular dynamics (CGMD) is applied to study the effects of tethers on lipid membrane properties. Using results from the CGMD model and the overdamped Fokker-Planck equation, we show that the diffusion tensor and particle density of water in the tBLM is spatially dependent. Further, it is shown that the membrane thickness, lipid diffusion, defect density, free energy of lipid flip-flop, and membrane dielectric permittivity are all dependent on the tether density. The numerically computed results from the CGMD model are in agreement with the experimentally measured results from tBLMs containing different tether densities and lipids derived from Archaebacteria. Additionally, using experimental measurements from Escherichia coli bacteria and Saccharomyces Cerevisiae yeast tethered membranes, we illustrate how previous molecular dynamics results can be combined with the proposed model to estimate the dielectric permittivity and defect density of these membranes as a function of tether density.
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Affiliation(s)
- William Hoiles
- Department of Electrical and Computer Engineering, The University of British Columbia, Vancouver, British Columbia, Canada
| | - Rini Gupta
- Department of Electrical and Computer Engineering, The University of British Columbia, Vancouver, British Columbia, Canada
| | - Bruce Cornell
- Director of Science and Technology, Surgical Diagnostics Pty Ltd., Unit 6 30-32 Barcoo Street, Roseville, New South Wales, 2069, Australia
| | - Charles Cranfield
- School of Life Sciences, University of Technology Sydney, Broadway, New South Wales, Australia
| | - Vikram Krishnamurthy
- Electrical and Computer Engineering, Cornell University, New York, New York, United States of America
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37
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Madsen JJ, Fristrup P, Peters GH. Theoretical Assessment of Fluorinated Phospholipids in the Design of Liposomal Drug-Delivery Systems. J Phys Chem B 2016; 120:9661-71. [DOI: 10.1021/acs.jpcb.6b07206] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Affiliation(s)
- Jesper J. Madsen
- Department of Chemistry, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
| | - Peter Fristrup
- Department of Chemistry, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
| | - Günther H. Peters
- Department of Chemistry, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
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38
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Javierre E. Impact of anomalous transport kinetics on the progress of wound healing. Med Eng Phys 2016; 38:885-94. [PMID: 27461569 DOI: 10.1016/j.medengphy.2016.04.015] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2015] [Revised: 02/12/2016] [Accepted: 04/03/2016] [Indexed: 11/15/2022]
Abstract
This work focuses on the transport kinetics of chemical and cellular species during wound healing. Anomalous transport kinetics, coupling sub- and superdiffusion with chemotaxis, and fractional viscoelasticity of soft tissues are analyzed from a modeling point of view. The paper presents a generalization of well stablished mechano-chemical models of wound contraction (Murphy et al., 2012; Valero et al., 2014) to include the previously mentioned anomalous effects by means of partial differential equations of fractional order. Results show the effect that anomalous dynamics have on the contraction rate and extension and on the distribution of biological species, and indicators of fibroproliferative disorders are identified.
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Affiliation(s)
- E Javierre
- Centro Universitario de la Defensa, Academia General Militar, Ctra. Huesca s/n. 50090 Zaragoza, Spain.
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39
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Amar JG, Semaan M. Island nucleation and growth with anomalous diffusion. Phys Rev E 2016; 93:062805. [PMID: 27415339 DOI: 10.1103/physreve.93.062805] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2016] [Indexed: 11/07/2022]
Abstract
While most studies of submonolayer island nucleation and growth have been based on the assumption of ordinary monomer diffusion corresponding to diffusion exponent μ=1, in some cases either subdiffusive (μ<1) or superdiffusive (μ>1) behavior may occur. Here we present general expressions for the exponents describing the flux dependence of the island and monomer densities as a function of the critical island size i, substrate dimension d, island fractal dimension d_{f}, and diffusion exponent μ, where 0≤μ≤2. Our results are compared with kinetic Monte Carlo simulations for the case of irreversible island growth (i=1) with 0≤μ≤2 and d=2 as well as simulation results for d=1, 3, and 4, and excellent agreement is found.
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Affiliation(s)
- Jacques G Amar
- Department of Physics & Astronomy, University of Toledo, Toledo, Ohio 43606, USA
| | - Mikhael Semaan
- Department of Physics & Astronomy, University of Toledo, Toledo, Ohio 43606, USA.,Department of Physics & Astronomy, California State University, Long Beach, Long Beach, California 90840, USA
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40
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Miyaguchi T, Akimoto T, Yamamoto E. Langevin equation with fluctuating diffusivity: A two-state model. Phys Rev E 2016; 94:012109. [PMID: 27575079 DOI: 10.1103/physreve.94.012109] [Citation(s) in RCA: 35] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2016] [Indexed: 11/07/2022]
Abstract
Recently, anomalous subdiffusion, aging, and scatter of the diffusion coefficient have been reported in many single-particle-tracking experiments, though the origins of these behaviors are still elusive. Here, as a model to describe such phenomena, we investigate a Langevin equation with diffusivity fluctuating between a fast and a slow state. Namely, the diffusivity follows a dichotomous stochastic process. We assume that the sojourn time distributions of these two states are given by power laws. It is shown that, for a nonequilibrium ensemble, the ensemble-averaged mean-square displacement (MSD) shows transient subdiffusion. In contrast, the time-averaged MSD shows normal diffusion, but an effective diffusion coefficient transiently shows aging behavior. The propagator is non-Gaussian for short time and converges to a Gaussian distribution in a long-time limit; this convergence to Gaussian is extremely slow for some parameter values. For equilibrium ensembles, both ensemble-averaged and time-averaged MSDs show only normal diffusion and thus we cannot detect any traces of the fluctuating diffusivity with these MSDs. Therefore, as an alternative approach to characterizing the fluctuating diffusivity, the relative standard deviation (RSD) of the time-averaged MSD is utilized and it is shown that the RSD exhibits slow relaxation as a signature of the long-time correlation in the fluctuating diffusivity. Furthermore, it is shown that the RSD is related to a non-Gaussian parameter of the propagator. To obtain these theoretical results, we develop a two-state renewal theory as an analytical tool.
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Affiliation(s)
- Tomoshige Miyaguchi
- Department of Mathematics Education, Naruto University of Education, Tokushima 772-8502, Japan
| | - Takuma Akimoto
- Department of Mechanical Engineering, Keio University, Yokohama 223-8522, Japan
| | - Eiji Yamamoto
- Department of Mechanical Engineering, Keio University, Yokohama 223-8522, Japan
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41
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Cherstvy AG, Metzler R. Ergodicity breaking and particle spreading in noisy heterogeneous diffusion processes. J Chem Phys 2016; 142:144105. [PMID: 25877560 DOI: 10.1063/1.4917077] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We study noisy heterogeneous diffusion processes with a position dependent diffusivity of the form D(x) ∼ D0|x|(α0) in the presence of annealed and quenched disorder of the environment, corresponding to an effective variation of the exponent α in time and space. In the case of annealed disorder, for which effectively α0 = α0(t), we show how the long time scaling of the ensemble mean squared displacement (MSD) and the amplitude variation of individual realizations of the time averaged MSD are affected by the disorder strength. For the case of quenched disorder, the long time behavior becomes effectively Brownian after a number of jumps between the domains of a stratified medium. In the latter situation, the averages are taken over both an ensemble of particles and different realizations of the disorder. As physical observables, we analyze in detail the ensemble and time averaged MSDs, the ergodicity breaking parameter, and higher order moments of the time averages.
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Affiliation(s)
- Andrey G Cherstvy
- Institute for Physics and Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
| | - Ralf Metzler
- Institute for Physics and Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
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42
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Hanot S, Lyonnard S, Mossa S. Sub-diffusion and population dynamics of water confined in soft environments. NANOSCALE 2016; 8:3314-3325. [PMID: 26690685 DOI: 10.1039/c5nr05853h] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We have studied by using molecular dynamics computer simulations the dynamics of water confined in ionic surfactant phases, ranging from well ordered lamellar structures to micelles at low and high water loading, respectively. We have analysed in depth the main dynamical features in terms of mean-squared displacements and intermediate scattering functions, and found clear evidence of sub-diffusive behaviour. We have identified water molecules lying at the charged interface with the hydrophobic confining matrix as the main factor responsible for this unusual feature, and given a comprehensive picture of dynamics based on a very precise analysis of lifetimes at the interface. We conclude by providing, for the first time to our knowledge, a unique framework for rationalizing the existence of important dynamical heterogeneities in fluids adsorbed in soft confining environments.
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Affiliation(s)
- Samuel Hanot
- Institut Laue-Langevin, 71 Avenue des Martyrs, CS 20156, 38042 Grenoble Cedex 9, France.
| | - Sandrine Lyonnard
- Univ. Grenoble Alpes, INAC-SPRAM, F-38000 Grenoble, France. and CNRS, INAC-SPRAM, F-38000 Grenoble, France and CEA, INAC-SPRAM, F-38000 Grenoble, France.
| | - Stefano Mossa
- Univ. Grenoble Alpes, INAC-SPRAM, F-38000 Grenoble, France. and CNRS, INAC-SPRAM, F-38000 Grenoble, France and CEA, INAC-SPRAM, F-38000 Grenoble, France.
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43
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Metzler R, Jeon JH, Cherstvy AG. Non-Brownian diffusion in lipid membranes: Experiments and simulations. BIOCHIMICA ET BIOPHYSICA ACTA-BIOMEMBRANES 2016; 1858:2451-2467. [PMID: 26826272 DOI: 10.1016/j.bbamem.2016.01.022] [Citation(s) in RCA: 127] [Impact Index Per Article: 15.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2015] [Revised: 01/21/2016] [Accepted: 01/23/2016] [Indexed: 12/14/2022]
Abstract
The dynamics of constituents and the surface response of cellular membranes-also in connection to the binding of various particles and macromolecules to the membrane-are still a matter of controversy in the membrane biophysics community, particularly with respect to crowded membranes of living biological cells. We here put into perspective recent single particle tracking experiments in the plasma membranes of living cells and supercomputing studies of lipid bilayer model membranes with and without protein crowding. Special emphasis is put on the observation of anomalous, non-Brownian diffusion of both lipid molecules and proteins embedded in the lipid bilayer. While single component, pure lipid bilayers in simulations exhibit only transient anomalous diffusion of lipid molecules on nanosecond time scales, the persistence of anomalous diffusion becomes significantly longer ranged on the addition of disorder-through the addition of cholesterol or proteins-and on passing of the membrane lipids to the gel phase. Concurrently, experiments demonstrate the anomalous diffusion of membrane embedded proteins up to macroscopic time scales in the minute time range. Particular emphasis will be put on the physical character of the anomalous diffusion, in particular, the occurrence of ageing observed in the experiments-the effective diffusivity of the measured particles is a decreasing function of time. Moreover, we present results for the time dependent local scaling exponent of the mean squared displacement of the monitored particles. Recent results finding deviations from the commonly assumed Gaussian diffusion patterns in protein crowded membranes are reported. The properties of the displacement autocorrelation function of the lipid molecules are discussed in the light of their appropriate physical anomalous diffusion models, both for non-crowded and crowded membranes. In the last part of this review we address the upcoming field of membrane distortion by elongated membrane-binding particles. We discuss how membrane compartmentalisation and the particle-membrane binding energy may impact the dynamics and response of lipid membranes. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.
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Affiliation(s)
- R Metzler
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany; Department of Physics, Tampere University of Technology, 33101 Tampere, Finland.
| | - J-H Jeon
- Korea Institute for Advanced Study (KIAS), Seoul, Republic of Korea
| | - A G Cherstvy
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
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44
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Anomalous Dynamics of a Lipid Recognition Protein on a Membrane Surface. Sci Rep 2015; 5:18245. [PMID: 26657413 PMCID: PMC4677404 DOI: 10.1038/srep18245] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2015] [Accepted: 11/11/2015] [Indexed: 12/12/2022] Open
Abstract
Pleckstrin homology (PH) domains are lipid-binding modules present in peripheral membrane proteins which interact with phosphatidyl-inositol phosphates (PIPs) in cell membranes. We use multiscale molecular dynamics simulations to characterize the localization and anomalous dynamics of the DAPP1 PH domain on the surface of a PIP-containing lipid bilayer. Both translational and rotational diffusion of the PH domain on the lipid membrane surface exhibit transient subdiffusion, with an exponent α ≈ 0.5 for times of less than 10 ns. In addition to a PIP3 molecule at the canonical binding site of the PH domain, we observe additional PIP molecules in contact with the protein. Fluctuations in the number of PIPs associated with the PH domain exhibit 1/f noise. We suggest that the anomalous diffusion and long-term correlated interaction of the PH domain with the membrane may contribute to an enhanced probability of encounter with target complexes on cell membrane surfaces.
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45
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Basu I, Manna M, Mukhopadhyay C. Insights into the behavioral difference of water in the presence of GM1. FEBS Lett 2015; 589:3887-92. [DOI: 10.1016/j.febslet.2015.11.014] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2015] [Revised: 11/16/2015] [Accepted: 11/16/2015] [Indexed: 11/26/2022]
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46
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Boţan A, Joly L, Fillot N, Loison C. Mixed Mechanism of Lubrication by Lipid Bilayer Stacks. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2015; 31:12197-12202. [PMID: 26381720 DOI: 10.1021/acs.langmuir.5b02786] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Although the key role of lipid bilayer stacks in biological lubrication is generally accepted, the mechanisms underlying their extreme efficiency remain elusive. In this article, we report molecular dynamics simulations of lipid bilayer stacks undergoing load and shear. When the hydration level is reduced, the velocity accommodation mechanism changes from viscous shear in hydration water to interlayer sliding in the bilayers. This enables stacks of hydrated lipid bilayers to act as efficient boundary lubricants for various hydration conditions, structures, and mechanical loads. We also propose an estimation for the friction coefficient; thanks to the strong hydration forces between lipid bilayers, the high local viscosity is not in contradiction with low friction coefficients.
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Affiliation(s)
- Alexandru Boţan
- Institut Lumière Matière, UMR5306 Université Lyon 1-CNRS, Université de Lyon , 69622 Villeurbanne, France
| | - Laurent Joly
- Institut Lumière Matière, UMR5306 Université Lyon 1-CNRS, Université de Lyon , 69622 Villeurbanne, France
| | - Nicolas Fillot
- LaMCoS, UMR5259 INSA-Lyon-CNRS, Université de Lyon , 69622 Villeurbanne, France
| | - Claire Loison
- Institut Lumière Matière, UMR5306 Université Lyon 1-CNRS, Université de Lyon , 69622 Villeurbanne, France
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47
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Sandev T, Chechkin AV, Korabel N, Kantz H, Sokolov IM, Metzler R. Distributed-order diffusion equations and multifractality: Models and solutions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:042117. [PMID: 26565178 DOI: 10.1103/physreve.92.042117] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2015] [Indexed: 06/05/2023]
Abstract
We study distributed-order time fractional diffusion equations characterized by multifractal memory kernels, in contrast to the simple power-law kernel of common time fractional diffusion equations. Based on the physical approach to anomalous diffusion provided by the seminal Scher-Montroll-Weiss continuous time random walk, we analyze both natural and modified-form distributed-order time fractional diffusion equations and compare the two approaches. The mean squared displacement is obtained and its limiting behavior analyzed. We derive the connection between the Wiener process, described by the conventional Langevin equation and the dynamics encoded by the distributed-order time fractional diffusion equation in terms of a generalized subordination of time. A detailed analysis of the multifractal properties of distributed-order diffusion equations is provided.
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Affiliation(s)
- Trifce Sandev
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
- Radiation Safety Directorate, Partizanski odredi 143, P.O. Box 22, 1020 Skopje, Macedonia
| | - Aleksei V Chechkin
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
- Akhiezer Institute for Theoretical Physics, Kharkov 61108, Ukraine
- Institute for Physics and Astronomy, University of Potsdam, D-14776 Potsdam-Golm, Germany
| | - Nickolay Korabel
- School of Mathematics, The University of Manchester, Manchester M60 1QD, United Kingdom
| | - Holger Kantz
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
| | - Igor M Sokolov
- Institute of Physics, Humboldt University Berlin, Newtonstrasse 15, D-12489 Berlin, Germany
| | - Ralf Metzler
- Institute for Physics and Astronomy, University of Potsdam, D-14776 Potsdam-Golm, Germany
- Department of Physics, Tampere University of Technology, FI-33101 Tampere, Finland
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48
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Wittmeier A, Holterhoff AL, Johnson J, Gibbs JG. Rotational Analysis of Spherical, Optically Anisotropic Janus Particles by Dynamic Microscopy. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2015; 31:10402-10. [PMID: 26352095 DOI: 10.1021/acs.langmuir.5b02864] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
We analyze the rotational dynamics of spherical colloidal Janus particles made from silica (SiO2) with a hemispherical gold/palladium (Au/Pd) cap. Since the refractive index difference between the surrounding fluid and a two-faced, optically anisotropic Janus microsphere is a function of the particle's orientation, it is possible to observe its rotational dynamics with bright-field optical microscopy. We investigate rotational diffusion and constant rotation of single Janus microspheres which are partially tethered to a solid surface so they are free to rotate but show little or no translational motion. Also, since the metal cap is a powerful catalyst in the breakdown of hydrogen peroxide, H2O2, the particles can be activated chemically. In this case, we analyze the motion of coupled Janus dimers which undergo a stable rotary motion about a mutual center. The analysis of both experimental and simulation data, which are microscopy and computer-generated videos, respectively, is based upon individual particle tracking and differential dynamic microscopy (DDM). DDM, which typically requires ensemble averages to extract meaningful information for colloidal dynamics, can be effective in certain situations for systems consisting of single entities. In particular, when translational motion is suppressed, both rotational diffusion and constant rotation can be probed.
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Affiliation(s)
- Andrew Wittmeier
- Department of Physics and Astronomy and ‡Center for Bioengineering Innovation, Northern Arizona University , S San Francisco St., Flagstaff, Arizona 86011, United States
| | - Andrew Leeth Holterhoff
- Department of Physics and Astronomy and ‡Center for Bioengineering Innovation, Northern Arizona University , S San Francisco St., Flagstaff, Arizona 86011, United States
| | - Joel Johnson
- Department of Physics and Astronomy and ‡Center for Bioengineering Innovation, Northern Arizona University , S San Francisco St., Flagstaff, Arizona 86011, United States
| | - John G Gibbs
- Department of Physics and Astronomy and ‡Center for Bioengineering Innovation, Northern Arizona University , S San Francisco St., Flagstaff, Arizona 86011, United States
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49
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Akimoto T, Seki K. Transition from distributional to ergodic behavior in an inhomogeneous diffusion process: Method revealing an unknown surface diffusivity. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:022114. [PMID: 26382351 DOI: 10.1103/physreve.92.022114] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2014] [Indexed: 06/05/2023]
Abstract
Diffusion of molecules in cells plays an important role in providing a biological reaction on the surface by finding a target on the membrane surface. The water retardation (slow diffusion) near the target assists the searching molecules to recognize the target. Here, we consider effects of the surface diffusivity on the effective diffusivity, where diffusion on the surface is slower than that in bulk. We show that the ensemble-averaged mean-square displacements increase linearly with time when the desorption rate from the surface is finite, which is valid even when the diffusion on the surface is anomalous (subdiffusion). Moreover, this slow diffusion on the surface affects the fluctuations of the time-averaged mean-square displacements (TAMSDs). We find that fluctuations of the TAMSDs remain large when the measurement time is smaller than a characteristic time, and decays according to an increase of the measurement time for a relatively large measurement time. Therefore, we find a transition from nonergodic (distributional) to ergodic diffusivity in a target search process. Moreover, this fluctuation analysis provides a method to estimate an unknown surface diffusivity.
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Affiliation(s)
- Takuma Akimoto
- Department of Mechanical Engineering, Keio University, Yokohama, 223-8522, Japan
| | - Kazuhiko Seki
- Nanosystem Research Institute, AIST, Tsukuba, 305-8565, Japan
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50
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Sändig N, Bakalis E, Zerbetto F. Stochastic analysis of movements on surfaces: The case of C60 on Au(111). Chem Phys Lett 2015. [DOI: 10.1016/j.cplett.2015.05.042] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
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