What Is the Optimal Value of the g-Ratio for Myelinated Fibers in the Rat CNS? A Theoretical Approach
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{"title"=>"What is the optimal value of the g-ratio for myelinated fibers in the rat CNS? A theoretical approach", "type"=>"journal", "authors"=>[{"first_name"=>"Taylor", "last_name"=>"Chomiak", "scopus_author_id"=>"16027991800"}, {"first_name"=>"Bin", "last_name"=>"Hu", "scopus_author_id"=>"7402045068"}], "year"=>2009, "source"=>"PLoS ONE", "identifiers"=>{"pui"=>"355713759", "issn"=>"19326203", "isbn"=>"1932-6203 (Electronic)\\r1932-6203 (Linking)", "doi"=>"10.1371/journal.pone.0007754", "scopus"=>"2-s2.0-70649084126", "pmid"=>"19915661", "sgr"=>"70649084126"}, "id"=>"7d328826-469b-3e14-90d0-7073ba642bc2", "abstract"=>"BACKGROUND The biological process underlying axonal myelination is complex and often prone to injury and disease. The ratio of the inner axonal diameter to the total outer diameter or g-ratio is widely utilized as a functional and structural index of optimal axonal myelination. Based on the speed of fiber conduction, Rushton was the first to derive a theoretical estimate of the optimal g-ratio of 0.6 [1]. This theoretical limit nicely explains the experimental data for myelinated axons obtained for some peripheral fibers but appears significantly lower than that found for CNS fibers. This is, however, hardly surprising given that in the CNS, axonal myelination must achieve multiple goals including reducing conduction delays, promoting conduction fidelity, lowering energy costs, and saving space. METHODOLOGY/PRINCIPAL FINDINGS In this study we explore the notion that a balanced set-point can be achieved at a functional level as the micro-structure of individual axons becomes optimized, particularly for the central system where axons tend to be smaller and their myelin sheath thinner. We used an intuitive yet novel theoretical approach based on the fundamental biophysical properties describing axonal structure and function to show that an optimal g-ratio can be defined for the central nervous system (approximately 0.77). Furthermore, by reducing the influence of volume constraints on structural design by about 40%, this approach can also predict the g-ratio observed in some peripheral fibers (approximately 0.6). CONCLUSIONS/SIGNIFICANCE These results support the notion of optimization theory in nervous system design and construction and may also help explain why the central and peripheral systems have evolved different g-ratios as a result of volume constraints.", "link"=>"http://www.mendeley.com/research/optimal-value-gratio-myelinated-fibers-rat-cns-theoretical-approach", "reader_count"=>197, "reader_count_by_academic_status"=>{"Unspecified"=>3, "Professor > Associate Professor"=>10, "Student > Doctoral Student"=>14, "Researcher"=>41, "Student > Ph. D. Student"=>72, "Student > Postgraduate"=>5, "Student > Master"=>20, "Other"=>4, "Student > Bachelor"=>16, "Lecturer"=>1, "Professor"=>11}, "reader_count_by_user_role"=>{"Unspecified"=>3, "Professor > Associate Professor"=>10, "Student > Doctoral Student"=>14, "Researcher"=>41, "Student > Ph. D. Student"=>72, "Student > Postgraduate"=>5, "Student > Master"=>20, "Other"=>4, "Student > Bachelor"=>16, "Lecturer"=>1, "Professor"=>11}, "reader_count_by_subject_area"=>{"Unspecified"=>13, "Agricultural and Biological Sciences"=>76, "Arts and Humanities"=>1, "Veterinary Science and Veterinary Medicine"=>1, "Business, Management and Accounting"=>2, "Chemistry"=>2, "Earth and Planetary Sciences"=>1, "Engineering"=>16, "Biochemistry, Genetics and Molecular Biology"=>7, "Materials Science"=>1, "Mathematics"=>1, "Medicine and Dentistry"=>31, "Neuroscience"=>28, "Pharmacology, Toxicology and Pharmaceutical Science"=>2, "Physics and Astronomy"=>12, "Psychology"=>2, "Immunology and Microbiology"=>1}, "reader_count_by_subdiscipline"=>{"Materials Science"=>{"Materials Science"=>1}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>31}, "Physics and Astronomy"=>{"Physics and Astronomy"=>12}, "Psychology"=>{"Psychology"=>2}, "Mathematics"=>{"Mathematics"=>1}, "Unspecified"=>{"Unspecified"=>13}, "Pharmacology, Toxicology and Pharmaceutical Science"=>{"Pharmacology, Toxicology and Pharmaceutical Science"=>2}, "Arts and Humanities"=>{"Arts and Humanities"=>1}, "Engineering"=>{"Engineering"=>16}, "Chemistry"=>{"Chemistry"=>2}, "Neuroscience"=>{"Neuroscience"=>28}, "Earth and Planetary Sciences"=>{"Earth and Planetary Sciences"=>1}, "Immunology and Microbiology"=>{"Immunology and Microbiology"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>76}, "Business, Management and Accounting"=>{"Business, Management and Accounting"=>2}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>7}, "Veterinary Science and Veterinary Medicine"=>{"Veterinary Science and Veterinary Medicine"=>1}}, "reader_count_by_country"=>{"Argentina"=>1, "United States"=>3, "United Kingdom"=>4, "France"=>3, "Portugal"=>1, "Germany"=>2, "Spain"=>1}, "group_count"=>4}

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  • {"files"=>["https://s3-eu-west-1.amazonaws.com/pstorage-plos-3567654/875807/Figure_1.tif"], "description"=>"<p><i>d<sub>i</sub></i> and <i>d<sub>o</sub></i> represent the inner and outer (i.e., <i>d<sub>i</sub></i> + total myelin sheath thickness) axon diameters respectively. <i>R<sub>m</sub></i> and <i>C<sub>m</sub></i> used in the model can be related to the axolemma (ax) and myelin (my) electrical components as follows: <i>R<sub>m</sub></i> = R<sub>ax</sub>+nR<sub>my</sub> and 1/<i>C<sub>m</sub></i> = 1/C<sub>ax</sub>+n/C<sub>my</sub>, where n is the number of myelin lamellae with a periodicity of 16 nm (naïve). R<sub>a</sub> depends on both the geometric properties of the inner core and the core resistivity (<i>p</i>). Axon electrical parameters; <i>p</i> = 70 Ω·cm, R<sub>ax</sub> = 4.7×10<sup>3</sup> Ω·cm<sup>2</sup>, R<sub>my</sub> = 800 Ω·cm<sup>2</sup> (per lamellae), C<sub>ax</sub> = 1 µF/cm<sup>2</sup>, C<sub>my</sub> = 0.6 µF/cm<sup>2</sup> (per lamellae). All values are based on published work (see <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007754#pone.0007754-Tasaki1\" target=\"_blank\">[30]</a>, <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007754#pone.0007754-Awiszus1\" target=\"_blank\">[59]</a>–<a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007754#pone.0007754-CurtisHaC1\" target=\"_blank\">[62]</a> and text).</p>", "links"=>[], "tags"=>["properties", "myelinated", "axon", "internodal", "schematic"], "article_id"=>546263, "categories"=>["Physiology", "Biological Sciences", "Neuroscience"], "users"=>["Taylor Chomiak", "Bin Hu"], "doi"=>["http://dx.doi.org/10.1371/journal.pone.0007754.g001"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"http://figshare.com/articles/_Geometrical_and_electrical_properties_of_a_myelinated_axon_internodal_segment_of_unit_length_and_a_schematic_of_the_equivalent_circuit_/546263", "title"=>"Geometrical and electrical properties of a myelinated axon internodal segment of unit length and a schematic of the equivalent circuit.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 03:50:57"}
  • {"files"=>["https://s3-eu-west-1.amazonaws.com/pstorage-plos-3567654/875898/Figure_2.tif"], "description"=>"<p>A: Relative efficiency index with increasing lamellae (i.e. increasing sheath thickness) without volume as a constraint (i.e., <i>δ</i> = 0). A global optimum does not exist. B: Top, a schematic illustrating a 2 µm inner diameter (<i>d<sub>i</sub></i>) axon with an increasing (1→3) myelin sheath thickness; where the total myelin sheath thickness equals the difference between the outer (<i>d<sub>o</sub></i>) and inner diameters (i.e., <i>d<sub>o</sub></i>-<i>d<sub>i</sub></i>). Bottom, relative efficiency index for different myelin sheath thicknesses. “2” represents the level of “optimized” (i.e, maximal efficiency) myelination for this particular axon. “1” and “3” illustrate that lower or higher levels of myelination provide a less efficient myelo-architectural design. Here volume is a constraint (<i>δ</i> = <i>β</i> = 1).</p>", "links"=>[], "tags"=>["optimized", "myelination"], "article_id"=>546364, "categories"=>["Physiology", "Biological Sciences", "Neuroscience"], "users"=>["Taylor Chomiak", "Bin Hu"], "doi"=>["http://dx.doi.org/10.1371/journal.pone.0007754.g002"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"http://figshare.com/articles/_The_model_can_predict_an_optimized_level_of_myelination_for_a_given_axon_/546364", "title"=>"The model can predict an optimized level of myelination for a given axon.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 03:51:31"}
  • {"files"=>["https://s3-eu-west-1.amazonaws.com/pstorage-plos-3567654/876027/Figure_3.tif"], "description"=>"<p>A: Example relative efficiency index curves for increasing diameter axons (1.5-blue, 2.5-green and 3.5-grey) illustrating that the optimized level is scaled to axon inner diameter as indicated by the shifting of the peak or theoretical global maxima. For clarity, only 1.5, 2.5 and 3.5 µm caliber axon efficiency curves are shown. B: The theoretical predicted relationship between the inner (<i>d<sub>i</sub></i>) and outer (<i>d<sub>o</sub></i>) axon diameter for optimized axon myelo-architecture of increasing caliber when volume is a constraint (<i>δ</i> = <i>β</i> = 1). The model predicts that d<sub>o</sub> and d<sub>i</sub> are significantly correlated (correlation coefficient r = 1.0, R<sup>2</sup> = 0.99; p<0.0001), where <i>d<sub>i</sub></i> = (0.76–0.77)<i>d<sub>o</sub></i>. <i>d<sub>o</sub></i> = <i>d<sub>i</sub></i> + total sheath thickness. Blue, green and grey triangles correspond to their respective curve in panel a. C: a representative TEM image illustrating a relatively thin myelin sheath thickness for most CNS axons. Scale bar  = 1 µm. D: Experimentally determined axon myelo-architecture for different axon calibers from rat brain. The experimentally determined relationship between the inner and outer axon diameters from the rat brain. Values are corrected for tissue shrinkage resulting from the fixation process (see <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007754#s4\" target=\"_blank\">Methods</a>) to compare to the model prediction for naïve axons (<a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007754#pone-0007754-g003\" target=\"_blank\">Figure 3B</a>). The red line represents the theoretically predicted relationship for optimized axon myelo-architectural design (model fit to experimental data: R<sup>2</sup>>0.96 for each). Inset: a typical example of a brain white matter axon indicating both d<sub>i</sub> and d<sub>o</sub>. Midbrain: myelinated axons from the rat brainstem; forebrain: myelinated axons from the rat internal capsule. Summarized experimental values are listed for <i>d<sub>i</sub></i>, <i>d<sub>o</sub></i> and the sheath thickness (all in µm units). Inset scale bar  = 0.5 µm.</p>", "links"=>[], "tags"=>["predictions", "optimized", "axon", "myelo-architectural", "calibers"], "article_id"=>546484, "categories"=>["Physiology", "Biological Sciences", "Neuroscience"], "users"=>["Taylor Chomiak", "Bin Hu"], "doi"=>["http://dx.doi.org/10.1371/journal.pone.0007754.g003"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"http://figshare.com/articles/_Model_predictions_for_optimized_axon_myelo_architectural_design_i_e_g_ratio_for_different_axon_calibers_of_central_white_matter_/546484", "title"=>"Model predictions for optimized axon myelo-architectural design (i.e., g-ratio) for different axon calibers of central white matter.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 03:52:13"}
  • {"files"=>["https://s3-eu-west-1.amazonaws.com/pstorage-plos-3567654/876122/Figure_4.tif"], "description"=>"<p>A: Efficiency index curves for a 1 µm diameter axon where δ = β = 1 (CNS-black curve) and where volume is less of a constraint <i>δ</i> = 0.6β (PNS-grey curve). Note that the peak is shifted to the right indicating that when volume is less of a constraint then the optimal sheath thickness is larger. B: Plots of <i>d<sub>i</sub></i> versus <i>d<sub>o</sub></i> representing different neural systems. In grey (circles) is when volume is less of a constraint (<i>δ</i> = 0.6<i>β</i>). In black (triangles) is when volume is as equally important as the other parameters (<i>δ</i> = <i>β</i> = 1) in defining an optimal structure (re-plotted from previous figure for comparison). The slopes of the lines, which represent the g-ratio, correspond to approximately 0.58–0.59 for the grey (PNS; correlation coefficient r = 1.0, R<sup>2</sup> = 0.99; p<0.0001) and 0.76–0.77 for the black (CNS). Curves were generated using the parameters defined in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007754#pone-0007754-g001\" target=\"_blank\">Figure 1</a> and were the same for both the “CNS” and “PNS” plots with the exception of <i>δ</i>.</p>", "links"=>[], "tags"=>["g-ratio", "neural"], "article_id"=>546585, "categories"=>["Physiology", "Biological Sciences", "Neuroscience"], "users"=>["Taylor Chomiak", "Bin Hu"], "doi"=>["http://dx.doi.org/10.1371/journal.pone.0007754.g004"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"http://figshare.com/articles/_Optimized_g_ratio_for_different_neural_systems_/546585", "title"=>"Optimized g-ratio for different neural systems.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 03:52:46"}
  • {"files"=>["https://s3-eu-west-1.amazonaws.com/pstorage-plos-3567654/876241/Table_1.xls"], "description"=>"<p>Some previously published g-ratio values for myelinated axons. The data are reported as the mean value (or range of means - except for the anterior commissure that only reported a range). Note that mean values are in good agreement with our predictions (g-ratio<i><sub>observed</sub></i>≈0.76–0.81) for CNS and some PNS axons. Sources: a, <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007754#pone.0007754-Arnett1\" target=\"_blank\">[10]</a>; b, <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007754#pone.0007754-Benninger1\" target=\"_blank\">[12]</a>; c, <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007754#pone.0007754-Mason1\" target=\"_blank\">[16]</a>; d, <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007754#pone.0007754-Waxman3\" target=\"_blank\">[32]</a>; e, <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007754#pone.0007754-Guy1\" target=\"_blank\">[15]</a>; f, <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007754#pone.0007754-Chau1\" target=\"_blank\">[36]</a>; g, <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007754#pone.0007754-Blakemore2\" target=\"_blank\">[13]</a>; h, <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007754#pone.0007754-Ehrlich1\" target=\"_blank\">[63]</a>; i, <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007754#pone.0007754-Grandis1\" target=\"_blank\">[64]</a>; j, <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007754#pone.0007754-Michailov1\" target=\"_blank\">[65]</a>; k, <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007754#pone.0007754-Wallace1\" target=\"_blank\">[66]</a>; l, <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007754#pone.0007754-Jeronimo1\" target=\"_blank\">[67]</a>; m, <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007754#pone.0007754-Malik1\" target=\"_blank\">[68]</a>; n, <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007754#pone.0007754-Fahrenkamp1\" target=\"_blank\">[69]</a>; o, <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007754#pone.0007754-Thomas1\" target=\"_blank\">[70]</a>; p, <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007754#pone.0007754-Kerns1\" target=\"_blank\">[58]</a>; q, <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007754#pone.0007754-Fraher1\" target=\"_blank\">[71]</a>. <sup>†</sup>signifies data from the present study (rat internal capsule raw data; 0.78±0.01 SEM, n = 85; and rat brainstem raw data; 0.81±0.01 SEM, n = 70).</p>", "links"=>[], "tags"=>["summarized", "g-ratio"], "article_id"=>546703, "categories"=>["Physiology", "Biological Sciences", "Neuroscience"], "users"=>["Taylor Chomiak", "Bin Hu"], "doi"=>["http://dx.doi.org/10.1371/journal.pone.0007754.t001"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"http://figshare.com/articles/_Some_summarized_experimental_g_ratio_data_/546703", "title"=>"Some summarized experimental g-ratio data.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-21 03:53:26"}

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Relative Metric

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