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Nithianantham S, Iwanski MK, Gaska I, Pandey H, Bodrug T, Inagaki S, Major J, Brouhard GJ, Gheber L, Rosenfeld SS, Forth S, Hendricks AG, Al-Bassam J. The kinesin-5 tail and bipolar minifilament domains are the origin of its microtubule crosslinking and sliding activity. Mol Biol Cell 2023; 34:ar111. [PMID: 37610838 PMCID: PMC10559304 DOI: 10.1091/mbc.e23-07-0287] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2023] [Revised: 08/07/2023] [Accepted: 08/15/2023] [Indexed: 08/25/2023] Open
Abstract
Kinesin-5 crosslinks and slides apart microtubules to assemble, elongate, and maintain the mitotic spindle. Kinesin-5 is a tetramer, where two N-terminal motor domains are positioned at each end of the motor, and the coiled-coil stalk domains are organized into a tetrameric bundle through the bipolar assembly (BASS) domain. To dissect the function of the individual structural elements of the motor, we constructed a minimal kinesin-5 tetramer (mini-tetramer). We determined the x-ray structure of the extended, 34-nm BASS domain. Guided by these structural studies, we generated active bipolar kinesin-5 mini-tetramer motors from Drosophila melanogastor and human orthologues which are half the length of native kinesin-5. We then used these kinesin-5 mini-tetramers to examine the role of two unique structural adaptations of kinesin-5: 1) the length and flexibility of the tetramer, and 2) the C-terminal tails which interact with the motor domains to coordinate their ATPase activity. The C-terminal domain causes frequent pausing and clustering of kinesin-5. By comparing microtubule crosslinking and sliding by mini-tetramer and full-length kinesin-5, we find that both the length and flexibility of kinesin-5 and the C-terminal tails govern its ability to crosslink microtubules. Once crosslinked, stiffer mini-tetramers slide antiparallel microtubules more efficiently than full-length motors.
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Affiliation(s)
- Stanley Nithianantham
- Department of Molecular and Cellular Biology, University of California, Davis, CA 95616
| | - Malina K. Iwanski
- Departments of Biology and Bioengineering, McGill University, Montreal, Quebec Canada H3A 1B1
| | - Ignas Gaska
- Department of Biological Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180
| | - Himanshu Pandey
- Department of Molecular and Cellular Biology, University of California, Davis, CA 95616
| | - Tatyana Bodrug
- Department of Molecular and Cellular Biology, University of California, Davis, CA 95616
| | - Sayaka Inagaki
- Department of Pharmacology, Mayo Clinic, Jacksonville, FL 32224
| | - Jennifer Major
- Department of Pharmacology, Mayo Clinic, Jacksonville, FL 32224
| | - Gary J. Brouhard
- Departments of Biology and Bioengineering, McGill University, Montreal, Quebec Canada H3A 1B1
| | - Larissa Gheber
- Department of Chemistry, The Ben Gurion University, Ber Sheva, Israel
| | | | - Scott Forth
- Department of Biological Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180
| | - Adam G. Hendricks
- Departments of Biology and Bioengineering, McGill University, Montreal, Quebec Canada H3A 1B1
| | - Jawdat Al-Bassam
- Department of Molecular and Cellular Biology, University of California, Davis, CA 95616
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2
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Sadjadi Z, Vesperini D, Laurent AM, Barnefske L, Terriac E, Lautenschläger F, Rieger H. Ameboid cell migration through regular arrays of micropillars under confinement. Biophys J 2022; 121:4615-4623. [PMID: 36303426 PMCID: PMC9748361 DOI: 10.1016/j.bpj.2022.10.030] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2022] [Revised: 08/09/2022] [Accepted: 10/19/2022] [Indexed: 12/15/2022] Open
Abstract
Migrating cells often encounter a wide variety of topographic features-including the presence of obstacles-when navigating through crowded biological environments. Unraveling the impact of topography and crowding on the dynamics of cells is key to better understand many essential physiological processes such as the immune response. We study the impact of geometrical cues on ameboid migration of HL-60 cells differentiated into neutrophils. A microfluidic device is designed to track the cells in confining geometries between two parallel plates with distance h, in which identical micropillars are arranged in regular pillar forests with pillar spacing e. We observe that the cells are temporarily captured near pillars, with a mean contact time that is independent of h and e. By decreasing the vertical confinement h, we find that the cell velocity is not affected, while the persistence reduces; thus, cells are able to preserve their velocity when highly squeezed but lose the ability to control their direction of motion. At a given h, we show that by decreasing the pillar spacing e in the weak lateral confinement regime, the mean escape time of cells from effective local traps between neighboring pillars grows. This effect, together with the increase of cell-pillar contact frequency, leads to the reduction of diffusion constant D. By disentangling the contributions of these two effects on D in numerical simulations, we verify that the impact of cell-pillar contacts on cell diffusivity is more pronounced at smaller pillar spacing.
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Affiliation(s)
- Zeinab Sadjadi
- Department of Theoretical Physics, Saarland University, Saarbrücken, Germany; Centre for Biophysics, Saarland University, Saarbrücken, Germany.
| | - Doriane Vesperini
- Department of Experimental Physics, Saarland University, Saarbrücken, Germany
| | - Annalena M Laurent
- Department of Experimental Physics, Saarland University, Saarbrücken, Germany
| | - Lena Barnefske
- Leibniz-Institute for New Materials, Saarbrücken, Germany
| | - Emmanuel Terriac
- Department of Experimental Physics, Saarland University, Saarbrücken, Germany
| | - Franziska Lautenschläger
- Centre for Biophysics, Saarland University, Saarbrücken, Germany; Department of Experimental Physics, Saarland University, Saarbrücken, Germany
| | - Heiko Rieger
- Department of Theoretical Physics, Saarland University, Saarbrücken, Germany; Centre for Biophysics, Saarland University, Saarbrücken, Germany; Leibniz-Institute for New Materials, Saarbrücken, Germany
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3
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Shaebani MR, Piel M, Lautenschläger F. Distinct speed and direction memories of migrating dendritic cells diversify their search strategies. Biophys J 2022; 121:4099-4108. [PMID: 36181271 PMCID: PMC9675022 DOI: 10.1016/j.bpj.2022.09.033] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2022] [Revised: 08/10/2022] [Accepted: 09/26/2022] [Indexed: 11/19/2022] Open
Abstract
Migrating cells exhibit various motility patterns, resulting from different migration mechanisms, cell properties, or cell-environment interactions. The complexity of cell dynamics is reflected, e.g., in the diversity of the observed forms of velocity autocorrelation function-which has been widely served as a measure of diffusivity and spreading. By analyzing the dynamics of migrating dendritic cells in vitro, we disentangle the contributions of direction θ and speed v to the velocity autocorrelation. We find that the ability of cells to maintain their speed or direction of motion is unequal, reflected in different temporal decays of speed and direction autocorrelation functions, ACv(t)∼t-1.2 and ACθ(t)∼t-0.5, respectively. The larger power-law exponent of ACv(t) indicates that the cells lose their speed memory considerably faster than the direction memory. Using numerical simulations, we investigate the influence of ACθ and ACv as well as the direction-speed cross correlation Cθ-v on the search time of a persistent random walker to find a randomly located target in confinement. Although ACθ and Cθ-v play the major roles, we find that the speed autocorrelation ACv can be also tuned to minimize the search time. Adopting an optimal ACv can reduce the search time even up to 10% compared with uncorrelated spontaneous speeds. Our results suggest that migrating cells can improve their search efficiency, especially in crowded environments, through the directional or speed persistence or the speed-direction correlation.
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Affiliation(s)
- M Reza Shaebani
- Department of Theoretical Physics, Saarland University, Saarbrücken, Germany; Centre for Biophysics, Saarland University, Saarbrücken, Germany.
| | - Matthieu Piel
- Institut Curie and Institut Pierre Gilles de Gennes, PSL Research University, CNRS, UMR 144, Paris, France
| | - Franziska Lautenschläger
- Centre for Biophysics, Saarland University, Saarbrücken, Germany; Department of Experimental Physics, Saarland University, Saarbrücken, Germany
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4
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Shaebani MR, Stankevicins L, Vesperini D, Urbanska M, Flormann DAD, Terriac E, Gad AKB, Cheng F, Eriksson JE, Lautenschläger F. Effects of vimentin on the migration, search efficiency, and mechanical resilience of dendritic cells. Biophys J 2022; 121:3950-3961. [PMID: 36056556 PMCID: PMC9675030 DOI: 10.1016/j.bpj.2022.08.033] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2022] [Revised: 06/20/2022] [Accepted: 08/24/2022] [Indexed: 11/24/2022] Open
Abstract
Dendritic cells use amoeboid migration to pass through narrow passages in the extracellular matrix and confined tissue in search for pathogens and to reach the lymph nodes and alert the immune system. Amoeboid migration is a migration mode that, instead of relying on cell adhesion, is based on mechanical resilience and friction. To better understand the role of intermediate filaments in ameboid migration, we studied the effects of vimentin on the migration of dendritic cells. We show that the lymph node homing of vimentin-deficient cells is reduced in our in vivo experiments in mice. Lack of vimentin also reduces the cell stiffness, the number of migrating cells, and the migration speed in vitro in both 1D and 2D confined environments. Moreover, we find that lack of vimentin weakens the correlation between directional persistence and migration speed. Thus, vimentin-expressing dendritic cells move faster in straighter lines. Our numerical simulations of persistent random search in confined geometries verify that the reduced migration speed and the weaker correlation between the speed and direction of motion result in longer search times to find regularly located targets. Together, these observations show that vimentin enhances the ameboid migration of dendritic cells, which is relevant for the efficiency of their random search for pathogens.
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Affiliation(s)
- M Reza Shaebani
- Department of Theoretical Physics, Saarland University, Saarbrücken, Germany; Centre for Biophysics, Saarland University, Saarbrücken, Germany
| | - Luiza Stankevicins
- Department of Experimental Physics, Saarland University, Saarbrücken, Germany
| | - Doriane Vesperini
- Department of Experimental Physics, Saarland University, Saarbrücken, Germany
| | - Marta Urbanska
- Biotechnology Centre, Centre for Molecular and Cellular Bioengineering, Technische Universität Dresden, Dresden, Germany
| | - Daniel A D Flormann
- Department of Experimental Physics, Saarland University, Saarbrücken, Germany
| | - Emmanuel Terriac
- Department of Experimental Physics, Saarland University, Saarbrücken, Germany
| | - Annica K B Gad
- Department of Oncology and Metabolism, University of Sheffield, Sheffield, United Kingdom; Centro de Química da Madeira, Universidade da Madeira, Funchal, Portugal
| | - Fang Cheng
- Cell Biology, Faculty of Science and Engineering, Åbo Akademi University, Turku, Finland; Turku Bioscience Centre, University of Turku and Åbo Akademi University, Turku, Finland; School of Pharmaceutical Sciences (Shenzhen), Sun Yat-sen University, Guangzhou, China
| | - John E Eriksson
- Cell Biology, Faculty of Science and Engineering, Åbo Akademi University, Turku, Finland; Turku Bioscience Centre, University of Turku and Åbo Akademi University, Turku, Finland
| | - Franziska Lautenschläger
- Centre for Biophysics, Saarland University, Saarbrücken, Germany; Department of Experimental Physics, Saarland University, Saarbrücken, Germany.
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5
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Shaebani MR, Rieger H, Sadjadi Z. Kinematics of persistent random walkers with two distinct modes of motion. Phys Rev E 2022; 106:034105. [PMID: 36266824 DOI: 10.1103/physreve.106.034105] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2021] [Accepted: 08/25/2022] [Indexed: 06/16/2023]
Abstract
We study the stochastic motion of active particles that undergo spontaneous transitions between two distinct modes of motion. Each mode is characterized by a velocity distribution and an arbitrary (anti)persistence. We present an analytical formalism to provide a quantitative link between these two microscopic statistical properties of the trajectory and macroscopically observable transport quantities of interest. For exponentially distributed residence times in each state, we derive analytical expressions for the initial anomalous exponent, the characteristic crossover time to the asymptotic diffusive dynamics, and the long-term diffusion constant. We also obtain an exact expression for the time evolution of the mean square displacement over all timescales and provide a recipe to obtain higher displacement moments. Our approach enables us to disentangle the combined effects of velocity, persistence, and switching probabilities between the two states on the kinematics of particles in a wide range of stochastic active or passive processes and to optimize the transport quantities of interest with respect to any of the particle dynamics properties.
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Affiliation(s)
- M Reza Shaebani
- Department of Theoretical Physics and Center for Biophysics, Saarland University, 66123 Saarbrücken, Germany
| | - Heiko Rieger
- Department of Theoretical Physics and Center for Biophysics, Saarland University, 66123 Saarbrücken, Germany
| | - Zeinab Sadjadi
- Department of Theoretical Physics and Center for Biophysics, Saarland University, 66123 Saarbrücken, Germany
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6
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Sadjadi Z, Shaebani MR. Orientational memory of active particles in multistate non-Markovian processes. Phys Rev E 2021; 104:054613. [PMID: 34942759 DOI: 10.1103/physreve.104.054613] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2021] [Accepted: 11/17/2021] [Indexed: 01/10/2023]
Abstract
The orientational memory of particles can serve as an effective measure of diffusivity, spreading, and search efficiency in complex stochastic processes. We develop a theoretical framework to describe the decay of directional correlations in a generic class of stochastic active processes consisting of distinct states of motion characterized by their persistence and switching probabilities between the states. For exponentially distributed sojourn times, the orientation autocorrelation is analytically derived and the characteristic times of its crossovers are obtained in terms of the persistence of each state and the switching probabilities. We show how nonexponential sojourn-time distributions of interest, such as Gaussian and power-law distributions, can result from history-dependent transitions between the states. The relaxation behavior of the correlation function in such non-Markovian processes is governed by the history dependence of the switching probabilities and cannot be solely determined by the mean sojourn times of the states.
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Affiliation(s)
- Zeinab Sadjadi
- Department of Theoretical Physics, Center for Biophysics, Saarland University, D-66123 Saarbrücken, Germany
| | - M Reza Shaebani
- Department of Theoretical Physics, Center for Biophysics, Saarland University, D-66123 Saarbrücken, Germany
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7
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Man YH, Warmbrunn I, Zhang L, Zhang ZB. The roles of intraflagellar transport (IFT) protein 25 in mammalian signaling transduction and flagellogenesis. Asian J Androl 2021; 24:238-242. [PMID: 34747727 PMCID: PMC9226691 DOI: 10.4103/aja202179] [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] [Indexed: 11/04/2022] Open
Abstract
Cilium, an organelle with a unique proteome and organization, protruding from the cell surface, generally serves as a force generator and signaling compartment. During ciliogenesis, ciliary proteins are synthesized in cytoplasm and transported into cilia by intraflagellar transport (IFT) particles, where the inner counterparts undergo reverse trafficking. The homeostasis of IFT plays a key role in cilial structure assembly and signaling transduction. Much progress has been made on the mechanisms and functions of IFT; however, recent studies have revealed the involvement of IFT particle subunits in organogenesis and spermatogenesis. In this review, we discuss new concepts concerning the molecular functions of IFT protein IFT25 and how its interactions with other IFT particle subunits are involved in mammalian development and fertility.
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Affiliation(s)
- Yong-Hong Man
- Department of Occupational and Environmental Medicine, School of Public Health, Wuhan University of Science and Technology, Wuhan 430065, China.,Center of Scientific Research and Experiment, Nanyang Medical College, Nanyang 473006, China
| | - Isabella Warmbrunn
- Department of Physiology, Wayne State University School of Medicine, Detroit, MI 48201, USA
| | - Ling Zhang
- Department of Occupational and Environmental Medicine, School of Public Health, Wuhan University of Science and Technology, Wuhan 430065, China
| | - Zhi-Bing Zhang
- Department of Physiology, Wayne State University School of Medicine, Detroit, MI 48201, USA.,Department of Obstetrics and Gynecology, Wayne State University School of Medicine, Detroit, MI 48201, USA
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8
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Sadjadi Z, Zhao R, Hoth M, Qu B, Rieger H. Migration of Cytotoxic T Lymphocytes in 3D Collagen Matrices. Biophys J 2020; 119:2141-2152. [PMID: 33264597 PMCID: PMC7732778 DOI: 10.1016/j.bpj.2020.10.020] [Citation(s) in RCA: 35] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2020] [Revised: 10/15/2020] [Accepted: 10/19/2020] [Indexed: 12/27/2022] Open
Abstract
CD8+ cytotoxic T lymphocytes (CTL) and natural killer cells are the main cytotoxic killer cells of the human body to eliminate pathogen-infected or tumorigenic cells (also known as target cells). To find their targets, they have to navigate and migrate through complex biological microenvironments, a key component of which is the extracellular matrix (ECM). The mechanisms underlying killer cell's navigation are not well understood. To mimic an ECM, we use a matrix formed by different collagen concentrations and analyze migration trajectories of primary human CTLs. Different migration patterns are observed and can be grouped into three motility types: slow, fast, and mixed. The dynamics are well described by a two-state persistent random walk model, which allows cells to switch between slow motion with low persistence and fast motion with high persistence. We hypothesize that the slow motility mode describes CTLs creating channels through the collagen matrix by deforming and tearing apart collagen fibers and that the fast motility mode describes CTLs moving within these channels. Experimental evidence supporting this scenario is presented by visualizing migrating T cells following each other on exactly the same track and showing cells moving quickly in channel-like cavities within the surrounding collagen matrix. Consequently, the efficiency of the stochastic search process of CTLs in the ECM should strongly be influenced by a dynamically changing channel network produced by the killer cells themselves.
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Affiliation(s)
- Zeinab Sadjadi
- Department of Theoretical Physics and Center for Biophysics, Universität des Saarlandes, Saarbrücken, Saarland, Germany.
| | - Renping Zhao
- Department of Biophysics, Center for Integrative Physiology and Molecular Medicine, School of Medicine, Universität des Saarlandes, Homburg, Saarland, Germany
| | - Markus Hoth
- Department of Biophysics, Center for Integrative Physiology and Molecular Medicine, School of Medicine, Universität des Saarlandes, Homburg, Saarland, Germany
| | - Bin Qu
- Department of Biophysics, Center for Integrative Physiology and Molecular Medicine, School of Medicine, Universität des Saarlandes, Homburg, Saarland, Germany; Leibniz Institute for New Materials, Saarbrücken, Germany
| | - Heiko Rieger
- Department of Theoretical Physics and Center for Biophysics, Universität des Saarlandes, Saarbrücken, Saarland, Germany
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9
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Kucera J, Terentjev EM. FliI 6-FliJ molecular motor assists with unfolding in the type III secretion export apparatus. Sci Rep 2020; 10:7127. [PMID: 32346005 PMCID: PMC7189227 DOI: 10.1038/s41598-020-63330-y] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2019] [Accepted: 03/27/2020] [Indexed: 01/05/2023] Open
Abstract
The role of rotational molecular motors of the ATP synthase class is integral to the metabolism of cells. Yet the function of FliI6-FliJ complex, a homolog of the F1 ATPase motor, within the flagellar export apparatus remains unclear. We use a simple two-state model adapted from studies of linear molecular motors to identify key features of this motor. The two states are the 'locked' ground state where the FliJ coiled coil filament experiences angular fluctuations in an asymmetric torsional potential, and a 'free' excited state in which FliJ undergoes rotational diffusion. Michaelis-Menten kinetics was used to treat transitions between these two states, and obtain the average angular velocity of the unloaded FliJ filament within the FliI6 stator: ωmax ≈ 9.0 rps. The motor was then studied under external counter torque conditions in order to ascertain its maximal power output: Pmax ≈ 42 kBT/s (or 102 kW/mol), and the stall torque: Gstall ≈ 3 kBT/rad (or 0.01 nN·nm/rad). Two modes of action within the flagellar export apparatus are proposed, in which the motor performs useful work either by continuously 'grinding' through the resistive environment of the export gate, or by exerting equal and opposite stall force on it. In both cases, the resistance is provided by flagellin subunits entering the flagellar export channel prior to their unfolding. We therefore propose that the function of the FliI6-FliJ complex is to lower the energy barrier, and therefore assist in unfolding of the flagellar proteins before feeding them into the transport channel.
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Affiliation(s)
- Jiri Kucera
- Cavendish Laboratory, University of Cambridge, Cambridge, CB3 0HE, UK
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10
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Witzel P, Götz M, Lanoiselée Y, Franosch T, Grebenkov DS, Heinrich D. Heterogeneities Shape Passive Intracellular Transport. Biophys J 2019; 117:203-213. [PMID: 31278001 PMCID: PMC6700759 DOI: 10.1016/j.bpj.2019.06.009] [Citation(s) in RCA: 28] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2019] [Revised: 05/22/2019] [Accepted: 06/11/2019] [Indexed: 01/06/2023] Open
Abstract
A living cell's interior is one of the most complex and intrinsically dynamic systems, providing an elaborate interplay between cytosolic crowding and ATP-driven motion that controls cellular functionality. Here, we investigated two distinct fundamental features of the merely passive, non-biomotor-shuttled material transport within the cytoplasm of Dictyostelium discoideum cells: the anomalous non-linear scaling of the mean-squared displacement of a 150-nm-diameter particle and non-Gaussian distribution of increments. Relying on single-particle tracking data of 320,000 data points, we performed a systematic analysis of four possible origins for non-Gaussian transport: 1) sample-based variability, 2) rarely occurring strong motion events, 3) ergodicity breaking/aging, and 4) spatiotemporal heterogeneities of the intracellular medium. After excluding the first three reasons, we investigated the remaining hypothesis of a heterogeneous cytoplasm as cause for non-Gaussian transport. A, to our knowledge, novel fit model with randomly distributed diffusivities implementing medium heterogeneities suits the experimental data. Strikingly, the non-Gaussian feature is independent of the cytoskeleton condition and lag time. This reveals that efficiency and consistency of passive intracellular transport and the related anomalous scaling of the mean-squared displacement are regulated by cytoskeleton components, whereas cytoplasmic heterogeneities are responsible for the generic, non-Gaussian distribution of increments.
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Affiliation(s)
- Patrick Witzel
- Faculty for Chemistry and Pharmacy, Julius-Maximilians-Universität Würzburg, Würzburg, Germany; Fraunhofer Institute for Silicate Research ISC, Würzburg, Germany
| | - Maria Götz
- Faculty for Chemistry and Pharmacy, Julius-Maximilians-Universität Würzburg, Würzburg, Germany; Fraunhofer Institute for Silicate Research ISC, Würzburg, Germany
| | - Yann Lanoiselée
- Laboratoire de Physique de la Matière Condensée, CNRS-Ecole Polytechnique, Palaiseau, France
| | - Thomas Franosch
- Institut für Theoretische Physik, Universität Innsbruck, Innsbruck, Austria
| | - Denis S Grebenkov
- Laboratoire de Physique de la Matière Condensée, CNRS-Ecole Polytechnique, Palaiseau, France
| | - Doris Heinrich
- Fraunhofer Institute for Silicate Research ISC, Würzburg, Germany; Leiden Institute of Physics, Huygens-Kamerlingh Onnes Laboratory, Leiden University, Leiden, the Netherlands.
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11
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Korabel N, Waigh TA, Fedotov S, Allan VJ. Non-Markovian intracellular transport with sub-diffusion and run-length dependent detachment rate. PLoS One 2018; 13:e0207436. [PMID: 30475848 PMCID: PMC6261056 DOI: 10.1371/journal.pone.0207436] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2018] [Accepted: 10/31/2018] [Indexed: 11/19/2022] Open
Abstract
Intracellular transport of organelles is fundamental to cell function and health. The mounting evidence suggests that this transport is in fact anomalous. However, the reasons for the anomaly is still under debate. We examined experimental trajectories of organelles inside a living cell and propose a mathematical model that describes the previously reported transition from sub-diffusive to super-diffusive motion. In order to explain super-diffusive behaviour at long times, we introduce non-Markovian detachment kinetics of the cargo: the rate of detachment is inversely proportional to the time since the last attachment. Recently, we observed the non-Markovian detachment rate experimentally in eukaryotic cells. Here we further discuss different scenarios of how this effective non-Markovian detachment rate could arise. The non-Markovian model is successful in simultaneously describing the time averaged variance (the time averaged mean squared displacement corrected for directed motion), the mean first passage time of trajectories and the multiple peaks observed in the distributions of cargo velocities. We argue that non-Markovian kinetics could be biologically beneficial compared to the Markovian kinetics commonly used for modelling, by increasing the average distance the cargoes travel when a microtubule is blocked by other filaments. In turn, sub-diffusion allows cargoes to reach neighbouring filaments with higher probability, which promotes active motion along the microtubules.
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Affiliation(s)
- Nickolay Korabel
- School of Mathematics, University of Manchester, Manchester, United Kingdom
- * E-mail:
| | - Thomas A. Waigh
- Biological Physics, School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom
- The Photon Science Institute, University of Manchester, Manchester, United Kingdom
| | - Sergei Fedotov
- School of Mathematics, University of Manchester, Manchester, United Kingdom
| | - Viki J. Allan
- Faculty of Biology, Medicine and Health, School of Biological Sciences, University of Manchester, Manchester, United Kingdom
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12
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Jose R, Santen L, Shaebani MR. Trapping in and Escape from Branched Structures of Neuronal Dendrites. Biophys J 2018; 115:2014-2025. [PMID: 30366628 DOI: 10.1016/j.bpj.2018.09.029] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2017] [Revised: 09/20/2018] [Accepted: 09/26/2018] [Indexed: 10/28/2022] Open
Abstract
We present a coarse-grained model for stochastic transport of noninteracting chemical signals inside neuronal dendrites and show how first-passage properties depend on the key structural factors affected by neurodegenerative disorders or aging: the extent of the tree, the topological bias induced by segmental decrease of dendrite diameter, and the trapping probabilities in biochemical cages and growth cones. We derive an exact expression for the distribution of first-passage times, which follows a universal exponential decay in the long-time limit. The asymptotic mean first-passage time exhibits a crossover from power-law to exponential scaling upon reducing the topological bias. We calibrate the coarse-grained model parameters and obtain the variation range of the mean first-passage time when the geometrical characteristics of the dendritic structure evolve during the course of aging or neurodegenerative disease progression (a few disorders for which clear trends for the pathological changes of dendritic structure have been reported in the literature are chosen and studied). We prove the validity of our analytical approach under realistic fluctuations of structural parameters by comparison to the results of Monte Carlo simulations. Moreover, by constructing local structural irregularities, we analyze the resulting influence on transport of chemical signals and formation of heterogeneous density patterns. Because neural functions rely on chemical signal transmission to a large extent, our results open the possibility of establishing a direct link between the disease progression and neural functions.
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Affiliation(s)
- Robin Jose
- Department of Theoretical Physics and Center for Biophysics, Saarland University, Saarbrücken, Germany
| | - Ludger Santen
- Department of Theoretical Physics and Center for Biophysics, Saarland University, Saarbrücken, Germany
| | - M Reza Shaebani
- Department of Theoretical Physics and Center for Biophysics, Saarland University, Saarbrücken, Germany.
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Najafi J, Shaebani MR, John T, Altegoer F, Bange G, Wagner C. Flagellar number governs bacterial spreading and transport efficiency. SCIENCE ADVANCES 2018; 4:eaar6425. [PMID: 30263953 PMCID: PMC6157962 DOI: 10.1126/sciadv.aar6425] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2017] [Accepted: 08/22/2018] [Indexed: 05/31/2023]
Abstract
Peritrichous bacteria synchronize and bundle their flagella to actively swim, while disruption of the bundle leads to a slow motility phase with a weak propulsion. It is still not known whether the number of flagella represents an evolutionary adaptation toward optimizing bacterial navigation. We study the swimming dynamics of differentially flagellated Bacillus subtilis strains in a quasi-two-dimensional system. We find that decreasing the number of flagella N f reduces the average turning angle between two successive run phases and enhances the run time and the directional persistence of the run phase. As a result, having fewer flagella is beneficial for long-distance transport and fast spreading, while having a lot of flagella is advantageous for the processes that require a slower spreading, such as biofilm formation. We develop a two-state random walk model that incorporates spontaneous switchings between the states and yields exact analytical expressions for transport properties, in remarkable agreement with experiments. The results of numerical simulations based on our two-state model suggest that the efficiency of searching and exploring the environment is optimized at intermediate values of N f. The optimal choice of N f, for which the search time is minimized, decreases with increasing the size of the environment in which the bacteria swim.
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Affiliation(s)
- Javad Najafi
- Center for Biophysics, Saarland University, 66041 Saarbrücken, Germany
| | | | - Thomas John
- Center for Biophysics, Saarland University, 66041 Saarbrücken, Germany
| | - Florian Altegoer
- Department of Chemistry and LOEWE Center for Synthetic Microbiology, Philipps University Marburg, 35043 Marburg, Germany
| | - Gert Bange
- Department of Chemistry and LOEWE Center for Synthetic Microbiology, Philipps University Marburg, 35043 Marburg, Germany
| | - Christian Wagner
- Center for Biophysics, Saarland University, 66041 Saarbrücken, Germany
- Physics and Materials Science Research Unit, University of Luxembourg, 1511 Luxembourg, Luxembourg
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Spatial Cytoskeleton Organization Supports Targeted Intracellular Transport. Biophys J 2018; 114:1420-1432. [PMID: 29590599 DOI: 10.1016/j.bpj.2018.01.042] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2017] [Revised: 01/05/2018] [Accepted: 01/30/2018] [Indexed: 01/28/2023] Open
Abstract
The efficiency of intracellular cargo transport from specific sources to target locations is strongly dependent upon molecular motor-assisted motion along the cytoskeleton. Radial transport along microtubules and lateral transport along the filaments of the actin cortex underneath the cell membrane are characteristic for cells with a centrosome. The interplay between the specific cytoskeleton organization and the motor performance results in a spatially inhomogeneous intermittent search strategy. To analyze the efficiency of such intracellular search strategies, we formulate a random velocity model with intermittent arrest states. We evaluate efficiency in terms of mean first passage times for three different, frequently encountered intracellular transport tasks: 1) the narrow escape problem, which emerges during cargo transport to a synapse or other specific region of the cell membrane; 2) the reaction problem, which considers the binding time of two particles within the cell; and 3) the reaction-escape problem, which arises when cargo must be released at a synapse only after pairing with another particle. Our results indicate that cells are able to realize efficient search strategies for various intracellular transport tasks economically through a spatial cytoskeleton organization that involves only a narrow actin cortex rather than a cell body filled with randomly oriented actin filaments.
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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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Abstract
Swimming bacteria exhibit a repertoire of motility patterns, in which persistent motion is interrupted by turning events. What are the statistical properties of such random walks? If some particular instances have long been studied, the general case where turning times do not follow a Poisson process has remained unsolved. We present a generic extension of the continuous time random walks formalism relying on operators and noncommutative calculus. The approach is first applied to a unimodal model of bacterial motion. We examine the existence of a minimum in velocity correlation function and discuss the maximum of diffusivity at an optimal value of rotational diffusion. The model is then extended to bimodal patterns and includes as particular cases all swimming strategies: run-and-tumble, run-stop, run-reverse and run-reverse-flick. We characterize their velocity correlation functions and investigate how bimodality affects diffusivity. Finally, the wider applicability of the method is illustrated by considering curved trajectories and Lévy walks. Our results are relevant for intermittent motion of living beings, be they swimming micro-organisms or crawling cells.
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Affiliation(s)
- François Detcheverry
- Univ Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, F-69622 Villeurbanne, France
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