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Schirripa Spagnolo C, Luin S. Trajectory Analysis in Single-Particle Tracking: From Mean Squared Displacement to Machine Learning Approaches. Int J Mol Sci 2024; 25:8660. [PMID: 39201346 PMCID: PMC11354962 DOI: 10.3390/ijms25168660] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2024] [Revised: 08/01/2024] [Accepted: 08/07/2024] [Indexed: 09/02/2024] Open
Abstract
Single-particle tracking is a powerful technique to investigate the motion of molecules or particles. Here, we review the methods for analyzing the reconstructed trajectories, a fundamental step for deciphering the underlying mechanisms driving the motion. First, we review the traditional analysis based on the mean squared displacement (MSD), highlighting the sometimes-neglected factors potentially affecting the accuracy of the results. We then report methods that exploit the distribution of parameters other than displacements, e.g., angles, velocities, and times and probabilities of reaching a target, discussing how they are more sensitive in characterizing heterogeneities and transient behaviors masked in the MSD analysis. Hidden Markov Models are also used for this purpose, and these allow for the identification of different states, their populations and the switching kinetics. Finally, we discuss a rapidly expanding field-trajectory analysis based on machine learning. Various approaches, from random forest to deep learning, are used to classify trajectory motions, which can be identified by motion models or by model-free sets of trajectory features, either previously defined or automatically identified by the algorithms. We also review free software available for some of the analysis methods. We emphasize that approaches based on a combination of the different methods, including classical statistics and machine learning, may be the way to obtain the most informative and accurate results.
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Affiliation(s)
| | - Stefano Luin
- NEST Laboratory, Scuola Normale Superiore, Piazza San Silvestro 12, I-56127 Pisa, Italy
- NEST Laboratory, Istituto Nanoscienze-CNR, Piazza San Silvestro 12, I-56127 Pisa, Italy
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2
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Bibeau JP, Galotto G, Wu M, Tüzel E, Vidali L. Quantitative cell biology of tip growth in moss. PLANT MOLECULAR BIOLOGY 2021; 107:227-244. [PMID: 33825083 PMCID: PMC8492783 DOI: 10.1007/s11103-021-01147-7] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2020] [Accepted: 03/25/2021] [Indexed: 05/16/2023]
Abstract
KEY MESSAGE Here we review, from a quantitative point of view, the cell biology of protonemal tip growth in the model moss Physcomitrium patens. We focus on the role of the cytoskeleton, vesicle trafficking, and cell wall mechanics, including reviewing some of the existing mathematical models of tip growth. We provide a primer for existing cell biological tools that can be applied to the future study of tip growth in moss. Polarized cell growth is a ubiquitous process throughout the plant kingdom in which the cell elongates in a self-similar manner. This process is important for nutrient uptake by root hairs, fertilization by pollen, and gametophyte development by the protonemata of bryophytes and ferns. In this review, we will focus on the tip growth of moss cells, emphasizing the role of cytoskeletal organization, cytoplasmic zonation, vesicle trafficking, cell wall composition, and dynamics. We compare some of the existing knowledge on tip growth in protonemata against what is known in pollen tubes and root hairs, which are better-studied tip growing cells. To fully understand how plant cells grow requires that we deepen our knowledge in a variety of forms of plant cell growth. We focus this review on the model plant Physcomitrium patens, which uses tip growth as the dominant form of growth at its protonemal stage. Because mosses and vascular plants shared a common ancestor more than 450 million years ago, we anticipate that both similarities and differences between tip growing plant cells will provide mechanistic information of tip growth as well as of plant cell growth in general. Towards this mechanistic understanding, we will also review some of the existing mathematical models of plant tip growth and their applicability to investigate protonemal morphogenesis. We attempt to integrate the conclusions and data across cell biology and physical modeling to our current state of knowledge of polarized cell growth in P. patens and highlight future directions in the field.
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Affiliation(s)
- Jeffrey P Bibeau
- Department of Biology and Biotechnology, Worcester Polytechnic Institute, Worcester, MA, USA
| | - Giulia Galotto
- Department of Biology and Biotechnology, Worcester Polytechnic Institute, Worcester, MA, USA
| | - Min Wu
- Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA, USA
- Bioinformatics and Computational Biology Program, Worcester Polytechnic Institute, Worcester, MA, USA
| | - Erkan Tüzel
- Bioengineering Department, Temple University, Philadelphia, PA, USA
| | - Luis Vidali
- Department of Biology and Biotechnology, Worcester Polytechnic Institute, Worcester, MA, USA.
- Bioinformatics and Computational Biology Program, Worcester Polytechnic Institute, Worcester, MA, USA.
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3
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Li Y, Tang W, Guo M. The Cell as Matter: Connecting Molecular Biology to Cellular Functions. MATTER 2021; 4:1863-1891. [PMID: 35495565 PMCID: PMC9053450 DOI: 10.1016/j.matt.2021.03.013] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
Viewing cell as matter to understand the intracellular biomolecular processes and multicellular tissue behavior represents an emerging research area at the interface of physics and biology. Cellular material displays various physical and mechanical properties, which can strongly affect both intracellular and multicellular biological events. This review provides a summary of how cells, as matter, connect molecular biology to cellular and multicellular scale functions. As an impact in molecular biology, we review recent progresses in utilizing cellular material properties to direct cell fate decisions in the communities of immune cells, neurons, stem cells, and cancer cells. Finally, we provide an outlook on how to integrate cellular material properties in developing biophysical methods for engineered living systems, regenerative medicine, and disease treatments.
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Affiliation(s)
- Yiwei Li
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Wenhui Tang
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Ming Guo
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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4
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Bibeau JP, Furt F, Mousavi SI, Kingsley JL, Levine MF, Tüzel E, Vidali L. In vivo interactions between myosin XI, vesicles and filamentous actin are fast and transient in Physcomitrella patens. J Cell Sci 2020; 133:jcs.234682. [PMID: 31964706 DOI: 10.1242/jcs.234682] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2019] [Accepted: 01/07/2020] [Indexed: 12/25/2022] Open
Abstract
The actin cytoskeleton and active membrane trafficking machinery are essential for polarized cell growth. To understand the interactions between myosin XI, vesicles and actin filaments in vivo, we performed fluorescence recovery after photobleaching and showed that the dynamics of myosin XIa at the tip of the spreading earthmoss Physcomitrella patens caulonemal cells are actin-dependent and that 50% of myosin XI is bound to vesicles. To obtain single-particle information, we used variable-angle epifluorescence microscopy in protoplasts to demonstrate that protein myosin XIa and VAMP72-labeled vesicles localize in time and space over periods lasting only a few seconds. By tracking data with Hidden Markov modeling, we showed that myosin XIa and VAMP72-labeled vesicles exhibit short runs of actin-dependent directed transport. We also found that the interaction of myosin XI with vesicles is short-lived. Together, this vesicle-bound fraction, fast off-rate and short average distance traveled seem be crucial for the dynamic oscillations observed at the tip, and might be vital for regulation and recycling of the exocytosis machinery, while simultaneously promoting vesicle focusing and vesicle secretion at the tip, necessary for cell wall expansion.
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Affiliation(s)
- Jeffrey P Bibeau
- Department of Biology and Biotechnology, Worcester Polytechnic Institute, Worcester, MA 01609, USA
| | - Fabienne Furt
- Department of Biology and Biotechnology, Worcester Polytechnic Institute, Worcester, MA 01609, USA
| | - S Iman Mousavi
- Department of Physics, Worcester Polytechnic Institute, Worcester, MA 01609, USA
| | - James L Kingsley
- Department of Physics, Worcester Polytechnic Institute, Worcester, MA 01609, USA
| | - Max F Levine
- Bioinformatics and Computational Biology Program, Worcester Polytechnic Institute, Worcester, MA 01609, USA
| | - Erkan Tüzel
- Department of Physics, Worcester Polytechnic Institute, Worcester, MA 01609, USA.,Bioinformatics and Computational Biology Program, Worcester Polytechnic Institute, Worcester, MA 01609, USA.,Bioengineering Department, College of Engineering, Temple University, Philadelphia, PA 19122, USA
| | - Luis Vidali
- Department of Biology and Biotechnology, Worcester Polytechnic Institute, Worcester, MA 01609, USA .,Bioinformatics and Computational Biology Program, Worcester Polytechnic Institute, Worcester, MA 01609, USA
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5
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Young DC, Scrimgeour J. Optimizing likelihood models for particle trajectory segmentation in multi-state systems. Phys Biol 2018; 15:066003. [DOI: 10.1088/1478-3975/aacd5a] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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6
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Lee S, Kim H, Higuchi H. Numerical method for vesicle movement analysis in a complex cytoskeleton network. OPTICS EXPRESS 2018; 26:16236-16249. [PMID: 30119458 DOI: 10.1364/oe.26.016236] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2018] [Accepted: 05/28/2018] [Indexed: 06/08/2023]
Abstract
The detection of the precise movement of a vesicle during transport in a live cell provides key information for the intracellular delivery process. Here we report a novel numerical method for analyzing three-dimensional vesicle movement. Since the vesicle moves along a linear cytoskeleton during the active transport, our method first detects the orientation and position of the cytoskeleton as a linear section based on angle correlation and linear regression, after noise reduction. Then, the precise vesicle movement is calculated using vector analysis, in terms of rotation angle and translational displacement. Using this method, various vesicle trajectories obtained via high spatiotemporal resolution microscopy can be understood..
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7
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Zagato E, Vermeulen L, Dewitte H, Van Imschoot G, Vandenbroucke RE, Demeester J, De Smedt SC, Neyts K, Remaut K, Braeckmans K. Quantifying the Average Number of Nucleic Acid Therapeutics per Nanocarrier by Single Particle Tracking Microscopy. Mol Pharm 2018; 15:1142-1149. [DOI: 10.1021/acs.molpharmaceut.7b00999] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Affiliation(s)
- Elisa Zagato
- Laboratory of General Biochemistry and Physical Pharmacy, Ghent University Ottergemsesteenweg 460, 9000 Ghent, Belgium
| | - Lotte Vermeulen
- Laboratory of General Biochemistry and Physical Pharmacy, Ghent University Ottergemsesteenweg 460, 9000 Ghent, Belgium
| | - Heleen Dewitte
- Laboratory of General Biochemistry and Physical Pharmacy, Ghent University Ottergemsesteenweg 460, 9000 Ghent, Belgium
| | - Griet Van Imschoot
- Laboratory of General Biochemistry and Physical Pharmacy, Ghent University Ottergemsesteenweg 460, 9000 Ghent, Belgium
| | - Roosmarijn E. Vandenbroucke
- Laboratory of General Biochemistry and Physical Pharmacy, Ghent University Ottergemsesteenweg 460, 9000 Ghent, Belgium
| | - Jo Demeester
- Laboratory of General Biochemistry and Physical Pharmacy, Ghent University Ottergemsesteenweg 460, 9000 Ghent, Belgium
| | - Stefaan C. De Smedt
- Laboratory of General Biochemistry and Physical Pharmacy, Ghent University Ottergemsesteenweg 460, 9000 Ghent, Belgium
| | - Kristiaan Neyts
- Laboratory of General Biochemistry and Physical Pharmacy, Ghent University Ottergemsesteenweg 460, 9000 Ghent, Belgium
| | - Katrien Remaut
- Laboratory of General Biochemistry and Physical Pharmacy, Ghent University Ottergemsesteenweg 460, 9000 Ghent, Belgium
| | - Kevin Braeckmans
- Laboratory of General Biochemistry and Physical Pharmacy, Ghent University Ottergemsesteenweg 460, 9000 Ghent, Belgium
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Nishizawa K, Bremerich M, Ayade H, Schmidt CF, Ariga T, Mizuno D. Feedback-tracking microrheology in living cells. SCIENCE ADVANCES 2017; 3:e1700318. [PMID: 28975148 PMCID: PMC5621978 DOI: 10.1126/sciadv.1700318] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2017] [Accepted: 09/07/2017] [Indexed: 05/12/2023]
Abstract
Living cells are composed of active materials, in which forces are generated by the energy derived from metabolism. Forces and structures self-organize to shape the cell and drive its dynamic functions. Understanding the out-of-equilibrium mechanics is challenging because constituent materials, the cytoskeleton and the cytosol, are extraordinarily heterogeneous, and their physical properties are strongly affected by the internally generated forces. We have analyzed dynamics inside two types of eukaryotic cells, fibroblasts and epithelial-like HeLa cells, with simultaneous active and passive microrheology using laser interferometry and optical trapping technology. We developed a method to track microscopic probes stably in cells in the presence of vigorous cytoplasmic fluctuations, by using smooth three-dimensional (3D) feedback of a piezo-actuated sample stage. To interpret the data, we present a theory that adapts the fluctuation-dissipation theorem (FDT) to out-of-equilibrium systems that are subjected to positional feedback, which introduces an additional nonequilibrium effect. We discuss the interplay between material properties and nonthermal force fluctuations in the living cells that we quantify through the violations of the FDT. In adherent fibroblasts, we observed a well-known polymer network viscoelastic response where the complex shear modulus scales as G* ∝ (-iω)3/4. In the more 3D confluent epithelial cells, we found glassy mechanics with G* ∝ (-iω)1/2 that we attribute to glassy dynamics in the cytosol. The glassy state in living cells shows characteristics that appear distinct from classical glasses and unique to nonequilibrium materials that are activated by molecular motors.
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Affiliation(s)
- Kenji Nishizawa
- Department of Physics, Graduate School of Sciences, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan
| | - Marcel Bremerich
- Department of Physics, Graduate School of Sciences, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan
| | - Heev Ayade
- Department of Physics, Graduate School of Sciences, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan
| | - Christoph F. Schmidt
- Third Institute of Physics, Faculty of Physics, University of Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | - Takayuki Ariga
- Department of Physics, Graduate School of Sciences, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan
| | - Daisuke Mizuno
- Department of Physics, Graduate School of Sciences, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan
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9
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Norregaard K, Metzler R, Ritter CM, Berg-Sørensen K, Oddershede LB. Manipulation and Motion of Organelles and Single Molecules in Living Cells. Chem Rev 2017; 117:4342-4375. [PMID: 28156096 DOI: 10.1021/acs.chemrev.6b00638] [Citation(s) in RCA: 114] [Impact Index Per Article: 16.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The biomolecule is among the most important building blocks of biological systems, and a full understanding of its function forms the scaffold for describing the mechanisms of higher order structures as organelles and cells. Force is a fundamental regulatory mechanism of biomolecular interactions driving many cellular processes. The forces on a molecular scale are exactly in the range that can be manipulated and probed with single molecule force spectroscopy. The natural environment of a biomolecule is inside a living cell, hence, this is the most relevant environment for probing their function. In vivo studies are, however, challenged by the complexity of the cell. In this review, we start with presenting relevant theoretical tools for analyzing single molecule data obtained in intracellular environments followed by a description of state-of-the art visualization techniques. The most commonly used force spectroscopy techniques, namely optical tweezers, magnetic tweezers, and atomic force microscopy, are described in detail, and their strength and limitations related to in vivo experiments are discussed. Finally, recent exciting discoveries within the field of in vivo manipulation and dynamics of single molecule and organelles are reviewed.
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Affiliation(s)
- Kamilla Norregaard
- Cluster for Molecular Imaging, Department of Biomedical Science and Department of Clinical Physiology, Nuclear Medicine and PET, Rigshospitalet, University of Copenhagen , 2200 Copenhagen, Denmark
| | - Ralf Metzler
- Institute for Physics & Astronomy, University of Potsdam , 14476 Potsdam-Golm, Germany
| | - Christine M Ritter
- Niels Bohr Institute, University of Copenhagen , 2100 Copenhagen, Denmark
| | | | - Lene B Oddershede
- Niels Bohr Institute, University of Copenhagen , 2100 Copenhagen, Denmark
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Bodnar M, Okińczyc N, Vela-Pérez M. Mathematical model for path selection by ants between nest and food source. Math Biosci 2016; 285:14-24. [PMID: 27979678 DOI: 10.1016/j.mbs.2016.12.002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2016] [Revised: 11/28/2016] [Accepted: 12/10/2016] [Indexed: 11/24/2022]
Abstract
Several models have been proposed to describe the behavior of ants when moving from nest to food sources. Most of these studies where based on numerical simulations with no mathematical justification. In this paper, we propose a mechanism for the formation of paths of minimal length between two points by a collection of individuals undergoing reinforced random walks taking into account not only the lengths of the paths but also the angles (connected to the preference of ants to move along straight lines). Our model involves reinforcement (pheromone accumulation), persistence (tendency to preferably follow straight directions in absence of any external effect) and takes into account the bifurcation angles of each edge (represented by a probability of willingness of choosing the path with the smallest angle). We describe analytically the results for 2 ants and different path lengths and numerical simulations for several ants.
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Affiliation(s)
- Marek Bodnar
- Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland.
| | - Natalia Okińczyc
- Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland.
| | - M Vela-Pérez
- Universidad Europea de Madrid, C/ Tajo, Villaviciosa de Odón, Madrid 28670, Spain; Service de Physique de l'Etat Condensé, CEA-Saclay, 91191 Gif-sur-Yvette, France; Instituto de Ciencias Matemáticas, (CSIC), C/ Nicolás Cabrera 15, 28049 Madrid, Spain.
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11
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An Intermittent Model for Intracellular Motions of Gold Nanostars by k-Space Scattering Image Correlation. Biophys J 2016; 109:2246-58. [PMID: 26636936 DOI: 10.1016/j.bpj.2015.10.025] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2015] [Revised: 10/09/2015] [Accepted: 10/21/2015] [Indexed: 11/20/2022] Open
Abstract
Anisotropic metallic nanoparticles have been devised as powerful potential tools for in vivo imaging, photothermal therapy, and drug delivery thanks to plasmon-enhanced absorption and scattering cross sections, ease in synthesis and functionalization, and controlled cytotoxicity. The rational design of all these applications requires the characterization of the nanoparticles intracellular trafficking pathways. In this work, we exploit live-cell time-lapse confocal reflectance microscopy and image correlation in both direct and reciprocal space to investigate the intracellular transport of branched gold nanostars (GNSs). Different transport mechanisms, spanning from pure Brownian diffusion to (sub-)ballistic superdiffusion, are revealed by temporal and spatio-temporal image correlation spectroscopy on the tens-of-seconds timescale. According to these findings, combined with numerical simulations and with a Bayesian (hidden Markov model-based) analysis of single particle tracking data, we ascribe the superdiffusive, subballistic behavior characterizing the GNSs dynamics to a two-state switching between Brownian diffusion in the cytoplasm and molecular motor-mediated active transport. For the investigation of intermittent-type transport phenomena, we derive an analytical theoretical framework for Fourier-space image correlation spectroscopy (kICS). At first, we evaluate the influence of all the dynamic and kinetic parameters (the diffusion coefficient, the drift velocity, and the transition rates between the diffusive and the active transport regimes) on simulated kICS correlation functions. Then we outline a protocol for data analysis and employ it to derive whole-cell maps for each parameter underlying the GNSs intracellular dynamics. Capable of identifying even simpler transport phenomena, whether purely diffusive or ballistic, our intermittent kICS approach allows an exhaustive investigation of the dynamics of GNSs and biological macromolecules.
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12
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Martin MJ, Smelser AM, Holzwarth G. Dividing organelle tracks into Brownian and motor-driven intervals by variational maximization of the Bayesian evidence. EUROPEAN BIOPHYSICS JOURNAL: EBJ 2015; 45:269-77. [PMID: 26538332 DOI: 10.1007/s00249-015-1091-0] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2015] [Revised: 10/06/2015] [Accepted: 10/13/2015] [Indexed: 11/26/2022]
Abstract
Many organelles and vesicles in live cells move in a start-stop manner when observed for ~10 s by optical microscopy. Changes in velocity and directional persistence of such particles are a potentially rich source of insight into the mechanisms leading to the start and stop states. Unbiased assessment of the most probable number of states, the properties of each state, and the most probable state for the particle at each moment can be accomplished by variational Bayesian methods combined with a hidden Markov model and a Gaussian mixture model. Our track analysis method, "vbTRACK", applied this combination of methods to particle velocity v or changes in the direction of travel evaluated from simulated tracks and from tracks of peroxisomes in live cells. When tested with numerical data, vbTRACK reliably determined the number of states, the mean and variance of the velocity or the direction of travel for each state, and the most probable state during each frame. When applied to the tracks of peroxisomes in live cells, some tracks separated into two states, one with high velocity and directionality, the other approximately Brownian. Other tracks of particles in live cells separated into several diffusive states with distinct diffusion constants.
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Affiliation(s)
- Matthew J Martin
- Department of Physics, Wake Forest University, Winston-Salem, NC, USA
| | - Amanda M Smelser
- Department of Physics, Wake Forest University, Winston-Salem, NC, USA
- Department of Biochemistry, School of Medicine, Wake Forest University, Winston-Salem, NC, USA
| | - George Holzwarth
- Department of Physics, Wake Forest University, Winston-Salem, NC, USA.
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13
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From individual to collective dynamics in Argentine ants (Linepithema humile). Math Biosci 2015; 262:56-64. [DOI: 10.1016/j.mbs.2015.01.007] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2014] [Revised: 01/04/2015] [Accepted: 01/05/2015] [Indexed: 11/23/2022]
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