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Feb 2021

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A Method for Estimating the Potential Synaptic Connections Between Axons and Dendrites From 2D Neuronal Images
一种从二维神经元图像中估计轴突和树突之间潜在突触连接的方法   

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Abstract

Computational neuroscience aims to model, reproduce, and predict network dynamics for different neuronal ensembles by distilling knowledge derived from electrophysiological and morphological evidence. However, analyses and simulations often remain critically limited by the sparsity of direct experimental constraints on essential parameters, such as electron microscopy and electrophysiology pair/multiple recording evidence of connectivity statistics. Notably, available data are particularly scarce regarding quantitative information on synaptic connections among identified neuronal types. Here, we present a user-friendly data-driven pipeline to estimate connection probabilities, number of contacts per connected pair, and distances from the pre- and postsynaptic somas along the axonal and dendritic paths from commonly available two-dimensional tracings and other broadly accessible measurements. The described procedure does not require any computational background and is accessible to all neuroscientists. This protocol therefore fills the important gap from neuronal morphology to circuit organization and can be applied to many different neural systems, brain regions, animal species, and data sources.


Graphic abstract:



The processing protocol from 2D reconstructions to quantitated synaptic connections


Keywords: Synaptic connectivity (突触连接), Neuronal network (神经网络), Connection probabilities (连接概率), Contacts (联系), Convex hull (凸包), Propagation error (传播误差), Axonal-dendritic overlap (轴突-树突重叠)

Background

Synaptic connectivity is a key determinant of the interaction between neurons, and its quantitation is pivotal to understanding the organization of brain circuits and the relationship with network function (Ascoli and Atkeson, 2005). Current knowledge of synaptic probability relies on empirical evidence, which is limited by the number of simultaneously recorded neurons (e.g., by pair recording, octopatch, multielectrode array) and affected by experimental conditions (in vitro vs. in vivo, slice orientation and thickness, distance between cells, etc.). Connections in a particular brain region are often probed by evoked responses upon stimulation of the afferent fiber tracts; however, such tests do not allow the identification of the specific neuronal types involved (Moradi and Ascoli, 2020). Alternatively, synaptic connectivity can be calculated computationally by embedding three-dimensionally (3D) reconstructed neuronal morphologies into 3D brain atlases and counting the possible locations of axonal-dendritic overlap (Ropireddy and Ascoli, 2011). Nevertheless, this approach requires a large amount of labor-intensive data, is limited by the precision of the 3D registration, and has so far proven impractical to scale up.


Despite its importance, connectivity information remains incomplete for most animal species and neural systems (Rees et al., 2017). This protocol describes a simple process for the extraction of important quantitative synaptic parameters – namely the connection probability, number of contacts per connected pair, and distance from the pre- and postsynaptic somas along the neurite paths – from commonly available two-dimensional images of axonal and dendritic morphology. To the best of our knowledge, there are no alternative solutions available to obtain the same results. Initially, this approach was used to estimate hippocampal connectivity and demonstrated high correlation of the resulting estimates with sparsely available data (Tecuatl et al., 2021).


The overall workflow of the presented pipeline consists of seven main logical components: (i) quantitation of parcel-specific axonal and dendritic lengths; (ii) determination of parcel-specific axonal and dendritic path distances; (iii) measurement of parcel-specific axonal and dendritic convex hull volume; (iv) calculation of the average number of synapses per neuronal pair in each parcel; (v) calculation of the number of contacts per connected pair; (vi) calculation of the connection probability per neuronal pair; and (vii) calculation of the confidence intervals on these values by propagation of error analysis. All steps can be carried out on a basic desktop or laptop computer using readily available software (Figure 1).



Figure 1. Flow chart of the described pipeline. The procedure starts from 2D neuronal images that are processed to quantitate axonal and dendritic lengths, path distances from the soma by parcel, and convex hull volumes. From these quantitations, we calculate the number of synapses and contacts per neuronal pair and subsequently estimate the probabilities of connection from multiple neuronal pairs. The generated information is analyzed and presented as the mean and standard deviation.


Equipment

  1. Standard personal computer

    The described analysis was performed using a Bionic G32 144Hz All In One PC [i7-8700] with Windows 10. The recommended minimal configuration is AMD Ryzen 5 2600X Six-Core Processor 3.60 GHz, 16 GB RAM, 64-bit operating system.

Software

  1. GNU Image Manipulation Program, free access (GIMP 2.8; gimp.org/downloads/).

  2. Custom-made MATLAB algorithm, free access (github.com/Hippocampome-Org/QuantifyNeurites)

  3. Plot Digitizer, free access (plotdigitizer.sourceforge.net)

  4. Fiji: Shape Analysis plugin, free access (Wagner and Lipinski, 2013; imagej.net/Shape_Filter)

  5. Fiji: Simple Neurite Tracer plugin, free access (Longair et al., 2011; imagej.net/Simple_Neurite_Tracer:_Basic_Instructions)

  6. Fiji: 3D Convex Hull, free access (imagej.nih.gov/ij/plugins/3d-convex-hull)

  7. MATLAB: commercial license; 30-day free trial available (mathworks.com/products/get-matlab.html)


Image Dataset and Additional Requirements
  1. Required are figures containing drawings of neuronal morphology, such as dendritic and axonal arbors (Recipe 1). If both axons and dendrites originate from the same neuron, they need to be drawn in distinct colors. If the arbors invade multiple anatomical parcels, the figure must demarcate the parcel boundaries when parcel-specific data are required. IMPORTANT: All figures need to contain a calibration bar. The examples used in this protocol are accessible at hippocampome.org/php/data/Bio-protocol_sample_files.zip.

  2. Required are estimations of the volumes of anatomical parcels in which the neurons of interest are contained (Recipe 2). The examples used in this protocol are listed in Table 1 and accessible at bbp.epfl.ch/nexus/cell-atlas.

  3. Required are estimations of the average distance between presynaptic elements (boutons) along the axons and of the average distance between postsynaptic elements (spines of shaft densities) along the dendrites for the species and neural system of interest (Recipe 3). The examples used in this protocol are accessible at hippocampome.org/php/data/Bio-protocol_sample_files.zip.

Procedure

  1. Quantitation of parcel-specific axonal and dendritic lengths

    1. Generate the necessary PNG files with GIMP. From the original unmodified neuronal reconstruction (Recipe 1), manually segregate the axons and dendrites within each anatomical parcel. If parcel-specific information is not required, simply separate the axons from the dendrites to estimate the corresponding axonal and dendritic length (Video 1).


      Video 1. 2D image manipulation. GIMP is used to selectively erase axons or dendrites from the various parcels to isolate them for later analysis.

      1. Load a PDF into GIMP (e.g., File: Open “Harris-Stewart-2001-41-BrainRes-Fig2A.pdf”) (Figure 2A).

      2. Use GIMP to erase the extraneous parts of the figure (Figure 2B).

        1. Select the eraser tool from the Toolbox window.

        2. Select Hardness 100 from the Brushes window.

        3. Set the brush size to the desired size (e.g., 25) in the Tool Options windows (Figure 2B, red box).

        4. Hold down the left button of the mouse to erase parts of the figure.

        5. Save the XCF version of the erased figure that includes both kinds of neurites in all layers (e.g., File: Save As... “SCA_all_allColors_both”). IMPORTANT: The structure of the name should be preserved for the pixel count.

        6. Export the PNG version from the XCF version of the figure to the same folder (e.g., File: Export As... “SCA_all_allColors_both.png”). The PNG is selected as the file format of choice because its default background is transparent. This reduces any potential errors from accidentally counting pixels included in the background.

      3. Use GIMP to erase the axons from the figure based on the color code (axons are shown in red in Figure 2B) by repeating steps b i-iv (Figure 2C, Video 1).

        1. Save the XCF version of the figure with the dendrites in the layer of interest to the same folder (e.g., File: Save As... “SCA_SO_allColors_Ds.xcf”).

        2. Export the PNG version from the XCF version of the figure to the same folder (e.g., File: Export As... “SCA_SO_allColors_Ds.png”).

      4. Use GIMP to erase the dendrites from the figure based on the color code (dendrites are shown in black in Figure 2B) by repeating steps b i-iv (Figure 2D, Video 1).

        1. Save the XCF version of the figure with the axons in the layer of interest to the same folder (e.g., File: Save As... “SCA_SO_allColors_Ax.xcf”).

        2. Export the PNG version from the xcf version of the figure to the same folder (e.g., File: Export As... “SCA_SO_allColors_As.png”).

        3. Save the axonal and dendritic domains in distinct files for every layer and subregion to the same folder (Figure 2E and 2F).



      Figure 2. Preprocessing of images for the quantitation of axonal and dendritic lengths. A. The GIMP File menu is used to open an image file to be processed. B. Representative image is in preparation for processing (Harris et al., 2001), where the red box delimits the toolbox location and the circle represents the eraser tool. C, D. Shown are processed images containing only dendrites (C) or axons (D) in all the layers of the region of interest (in this example, the subiculum), which were obtained from the original image shown in (B). E, F. Shown are representative images displaying only dendrites (E) or axons (F) in the parcel of interest (in this case, the stratum moleculare of the subiculum), which were obtained from the original image shown in (B).


    2. Pixel counting using a custom-made MATLAB algorithm (Figure 3; Video 2).


      Video 2. Pixel count from 2D images. A custom-made MATLAB program is used to count all pixels included in the 16 color channels of an image.

      1. Place the separated images in the data folder.

      2. Open MATLAB, making sure that the current working folder is open (e.g., “dir_QuantifyNeurites_v2”) (Figure 3A1, red boxes).

      3. Run the command convert (Figure 3A1, green box).

      4. From the displayed menu, select the image to be worked on by typing the number and pressing enter (Figure 3A2).

      5. After the image is open, select the carousel mode to identify the color channels that contain pixels (Figure 3A3).

      6. Press m to choose the color channels that contain pixels (the number of pixels is displayed in brackets) (Figure 3B1).

      7. If the channel does not contain any pixels, just press the space bar to move to the next channel (Figure 3B2).

      8. Optional step: plot the image with the selected color channels to verify that the selected channels contain all of the pixels by typing p and pressing enter (Figure 3B3).

      9. A histogram with the total pixel count is displayed (Figure 3C1). The command window displays the selected channels and number of pixels.

      10. Optional step: save the images that contain the selected (Figure 3C2) and unselected (Figure 3C3) channels by typing s and pressing enter. The images are automatically saved to the output folder.

      11. Select a new image from the data folder by typing l and pressing enter.

      12. End the process by typing / and pressing enter.



      Figure 3. Pixel counting. A1. Shown is a MATLAB window with the open working folder “dir_QuantifyNeurites_v2” in a red box and the command window to run the command “convert” in a green box. A2. The displayed menu that appears after running the command “convert” to select the image to process. A3. The displayed menu options that appear in order to analyze the selected figure. B. Shown is a representative carousel mode, where the color number and the number of pixels present (B1) or absent (B2) are delimited within the blue boxes and where a final plot figure contains only the channels selected during the full run of the carousel mode. C. Presented are a histogram of the selected channels and the number of pixels per channel (C1) and the generated PNG files for the selected (C2) and unselected (C3) channels.


    3. Pixel length estimation using Plot Digitizer (Video 3).


      Video 3. Measuring a calibration bar in pixels. Plot Digitizer is used to measure the length in pixels of a neuronal reconstruction’s calibration bar. The X coordinates of the two ends of the calibration bar are recorded, and their difference is the final measurement in pixels.

      1. Open the original reconstruction with Plot Digitizer.

      2. Place the cursor over the start of the calibration bar and take note of the number.

      3. Do the same at the other end of the calibration bar.

      4. The difference between the numbers represents the length of calibration bar in pixels.

    4. Conversion from pixel number to length.

      1. Determine the mean neurite width by randomly selecting three locations for every neuron image, parcel, and neurite domain, measuring the branch width in pixels at each location, and averaging the three values (Video 4).


        Video 4. Neurite width estimation. Plot Digitizer is used to estimate the widths of axons and dendrites in each layer containing portions of a neuronal reconstruction. Three examples are measured for each layer to obtain an average estimate of the neurite width per layer.

      2. Calculate the pixel length in physical units, which is simply the nominal calibration scale-bar value (in µm) divided by the measured bar length in pixels.

      3. Obtain the parcel-specific neurite length by multiplying the pixel count for that neurite in the given parcel by the physical pixel length and dividing the result by the average branch width in pixels.

      4. Correct for the artifactual flattening of three-dimensional arbors into two-dimensional images by combining the parcel-specific length, lp, with the reported section thickness, ts, using Pythagoras’ formula:



        where represents the final corrected length.

  2. Determination of the axonal and dendritic path distances (Figure 4, Video 5)


    Video 5. Measuring somatic distance. Fiji with the Simple Neurite Tracer plugin is used to measure the length in pixels from the soma to the end of the selected axon or dendrite. Three examples are measured for each type of neurite to determine the average.

    1. Open the original file with Fiji: File – Open – File source (Figure 4A).

    2. Convert the image to binary: Process – Binary – Make Binary (Figure 4B).

    3. Open the plugin “Simple Neurite Tracer:” Plugins – Neuroanatomy – SNT (Figure 4C).

    4. Open the image in the SNT command window: File – Choose tracing image – From (Figure 4D).

    5. Trace the distance along the dendrite/axon by clicking on the soma and at the end of the segment. If the tracing does not correspond with the structure, increase the accuracy by clicking multiple times along the segment: press y, and continue tracing along the path (Figure 4E).

    6. Once the tracing is complete, move on to the next one by accepting the trace. Press F to finish the tracing.

    7. The values are estimated in pixels (Path manager window, if values are not visible: tag – Morphometry – Length), so convert them to length using the pixel/length factor (Section 3, Figure 4E).

    8. When all traces are done, save them for future reference. File – Export as – swc or traces.



      Figure 4. Determining the somatic distances and convex hull volumes. A. Shown are the Fiji menu steps to open an image for path tracing (e.g., a CA1 pyramidal neuron; Bannister and Larkman, 1995). B. Displayed are the menu steps to convert the image into a binary image. C. Presented are the menu steps to run the Simple Neurite Tracer plugin. D. Shown are the Simple Neurite Tracer steps to load the open image for tracing. E. Presented is a representative Simple Neurite Tracer console that shows one path in blue (middle), with the options to finish the path and continue tracing on the console (left), and the path manager, with all the traces that correspond to the different parcels of the original image (right). F. Shown are the menu steps to run the Hull And Circle plugin for the dendrites located in the parcel of interest (e.g., CA1 stratum oriens; green box) for the convex hull measurement. G. The Hull And Circle toolbox (left) is used to scan the current image, where the image with the delimited area is shown in green and the bottom panel shows the emerging results window.


  3. Determining the convex hull volume from 2D reconstructions (Figures 4F and 4G, Video 6)

    1. Open the generated segmented images that only contain axons or dendrites (PNG file) with Fiji: File – Open – File source.

    2. Convert the image to binary: Process – Binary – Make Binary.

    3. Open the plugin: Plugins – Shape Analysis – Hull And Circle (Figure 4F).

    4. From the new window, select the option Scan current Image or Roi (Figure 4G).

    5. A new window containing the results is generated (Hull and Circle Results, Figure 4G).

    6. Save the results: File – Save as.

    7. An image with the calculated hull volume is displayed. This image cannot be saved, but it provides information about how the resulting convex hull area was calculated (Figure 4G).

    8. Convert the area measurements from pixel units to µm2 and multiply the resulting values by the reported slice thickness, assuming that the reconstruction is located in the middle of the slice.


      Video 6. Convex hull estimation. Fiji with the Hull and Circle plugin is used to measure the convex hull area in pixels from the region of interest in 2D neuronal reconstructions.

  4. Determining the convex hull volume from 3D reconstructions

    1. Directly estimate the real volume using the 3D Convex Hull plugin.


  5. Calculating the average number of synapses per neuronal pair.

    1. Calculate the average number of synapses per pair of presynaptic and postsynaptic neurons, Ns, from their parcel-specific axonal and dendritic lengths, by separately estimating the number, Nsx, of axonal-dendritic overlaps in each parcel x (Tecuatl et al., 2021). For any x, the value Nsx can be derived as the product of three factors:

      1. The probability that presynaptic and postsynaptic elements occur within a given interaction distance, r, is the ratio between the volume of the interaction sphere, within which the two elements are found, and the volume of the entire parcel, Vx (Recipe 2).

      2. The number of presynaptic elements (axonal boutons) in a given anatomical parcel is specified by the presynaptic axonal length in parcel x, Lax, divided by the average distance between consecutive presynaptic boutons, bd (Recipe 3; example files are accessible at hippocampome.org/php/data/Bio-protocol_sample_files.zip).

      3. The number of postsynaptic elements (dendritic spines or shafts) in the same parcel is given by the postsynaptic dendritic length in x, Ldx, divided by the distance between postsynaptic elements, sd.

    2. To calculate the average number of synapses per pair of presynaptic and postsynaptic neurons in a specific parcel, use the following formula:



    3. The total count of synapses per directed neuron pair, Ns, is just the sum of the number per parcel, Nsx, over all parcels.


  6. Calculate the number of contacts per connected pair.

    1. Assume that a given pair of neurons forms at least a single synaptic contact, and calculate the expected number of additional contacts for that pair as:



      where the volumetric ratio between the sphere defined by the radius of interaction r and Vo represents the chance of an encounter for any given pair of axonal boutons and dendritic spines or shafts, and Lax/bd and Ldx/sd correspond, respectively, to the number of axonal boutons and dendritic spines or shafts in parcel x.

    2. Determine the volume of the intersection, Vo, by:



      where Vdx and Vax are the dendritic and axonal convex hull volumes in parcel x.

    3. Calculate the overall number of contacts per connected pair as the sum of the contacts in each parcel augmented by one, reflecting the initial assumption that the neuronal pair is connected:



      where the symbol Σx represents the sum over all parcels.


  7. Calculate the connection probabilities

    1. Compute the connection probability for a pair of neuronal types in parcel x by dividing the average number of synapses per neuronal pair by the number of contacts per connected pair in the same parcel:



    2. Determine the overall probability of connection for a pair of presynaptic and postsynaptic neurons in any parcel by the sum of inclusive events:



      where the symbol Πx represents the product over all parcels.


      Table 1. List of all representative files

      File name Type Description   Use
      Neurite Quantitation.xlsx XLSX Spreadsheet to collect the data from the pixel count, pixel length estimation, convex hull area, and neurite path distance  Data collection of pixel count to estimate axonal/dendritic length and somatic distance
      Bouton distance.docx DOCX List of reported ultrastructural measurements for axonal bouton distance in the hippocampal formation   Estimation of the number of synapses and contacts per neuronal pair
      Dendritic spine distance.docx DOCX List of reported ultrastructural measurements for dendritic spine distance in the hippocampal formation   Estimation of the number of synapses and contacts per neuronal pair
      Harris-Stewart-2001-41-BrainRes-Fig2A/Harris-Stewart-2001-41-BrainRes-Fig2A.pdf PDF Original file that contains the neuronal reconstruction from a Subiculum CA1 Projecting Pyramidal cell   Image manipulation with GIMP
      Harris-Stewart-2001-41-BrainRes-Fig2A/Harris-Stewart-2001-41-BrainRes-Fig2A.xcf XCF File generated with GIMP for manipulation   Exported file without modifications
      Harris-Stewart-2001-41-BrainRes-Fig2A/Harris-Stewart-2001-41-BrainRes-Fig2A.png PNG Exported PNG file without modifications from the XCF version 
        1. Scale bar conversion with Plot Digitizer
        2. Somatic distance estimation with SNT
      Harris-Stewart-2001-41-BrainRes-Fig2A/Sub_CA1 projecting Pyramidal_all_allcolors_both.xcf XCF File saved with GIMP for manipulation that includes brain region, cell type, and parcel information   Segregation of axons and dendrites with GIMP
      Harris-Stewart-2001-41-BrainRes-Fig2A/Sub_CA1 projecting Pyramidal_all_allcolors_Ds.xcf XCF File that contains only dendrites in all the parcels   Segregation of dendrites based on parcel borders with GIMP
      Harris-Stewart-2001-41-BrainRes-Fig2A/Sub_CA1 projecting Pyramidal_all_allcolors_Ds.png PNG Exported PNG file with only dendrites from the XCF version   Dendritic somatic distance estimation with SNT, if you cannot discern axons and dendrites from Harris-Stewart-2001-41-BrainRes-Fig2A.png file
      Harris-Stewart-2001-41-BrainRes-Fig2A/Sub_CA1 projecting Pyramidal_SM_allcolors_Ds.xcf XCF File that contains only dendrites in SUB:SM   Saved file with dendrites in Sub:SM for future edits if needed
      Harris-Stewart-2001-41-BrainRes-Fig2A/Sub_CA1 projecting Pyramidal_SM_allcolors_Ds.png PNG Exported PNG file with only dendrites in Sub:SM
      1. Pixel count with MATLAB
      2. Convex hull area estimation with Fiji: Hull And Circle
      Harris-Stewart-2001-41-BrainRes-Fig2A/Sub_CA1 projecting Pyramidal_SP_allcolors_Ds.xcf XCF File that contains only dendrites in Sub:SP Saved file with dendrites in Sub:SP for future edits if needed
      Harris-Stewart-2001-41-BrainRes-Fig2A/Sub_CA1 projecting Pyramidal_SP_allcolors_Ds.png PNG Exported PNG file with only dendrites in Sub:SP
      1. Pixel count with MATLAB
      2. Convex hull area estimation with Fiji: Hull And Circle
      Harris-Stewart-2001-41-BrainRes-Fig2A/Sub_CA1 projecting Pyramidal_all_allcolors_Ax.xcf XCF File that contains only axons in all the parcels Segregation of axons based on parcel borders with GIMP
      Harris-Stewart-2001-41-BrainRes-Fig2A/Sub_CA1 projecting Pyramidal_all_allcolors_Ax.png PNG Exported PNG file with only axons from the XCF version Axonal somatic distance estimation with SNT, if you cannot discern axons and dendrites from Harris-Stewart-2001-41-BrainRes-Fig2A.png file
      Harris-Stewart-2001-41-BrainRes-Fig2A/Sub_CA1 projecting Pyramidal_SM_allcolors_Ax.xcf XCF File that contains only axons in Sub:SM Saved file with axons in Sub:SM for future edits if needed
      Harris-Stewart-2001-41-BrainRes-Fig2A/Sub_CA1 projecting Pyramidal_SM_allcolors_Ax.png PNG Exported PNG file with only axons in Sub:SM
      1. Pixel count with MATLAB
      2. Convex hull area estimation with Fiji: Hull And Circle
      Harris-Stewart-2001-41-BrainRes-Fig2A/Sub_CA1 projecting Pyramidal_SP_allcolors_Ax.xcf XCF File that contains only axons in Sub:SP Saved file with axons in Sub:SP for future edits if needed
      Harris-Stewart-2001-41-BrainRes-Fig2A/Sub_CA1 projecting Pyramidal_SP_allcolors_Ax.png PNG Exported PNG file with only axons in Sub:SP
      1. Pixel count with MATLAB
      2. Convex hull area estimation with Fiji: Hull And Circle
      Harris-Stewart-2001-41-BrainRes-Fig2A/Sub_CA1 projecting Pyramidal_PL_allcolors_Ax.xcf XCF File that contains only axons in Sub:PL Saved file with axons in Sub:PL for future edits if needed
      Harris-Stewart-2001-41-BrainRes-Fig2A/Sub_CA1 projecting Pyramidal_PL_allcolors_Ax.png PNG Exported PNG file with only axons in Sub:PL
      1. Pixel count with MATLAB
      2. Convex hull area estimation with Fiji: Hull And Circle
      Harris-Stewart-2001-41-BrainRes-Fig2A/Sub_CA1 projecting Pyramidal_CA1 SLM_allcolors_Ax.xcf XCF File that contains only axons in CA1:SLM Saved file with axons in CA1:SLM for future edits if needed
      Harris-Stewart-2001-41-BrainRes-Fig2A/Sub_CA1 projecting Pyramidal_CA1 SLM_allcolors_Ax.png PNG Exported PNG file with only axons in CA1:SLM
      1. Pixel count with MATLAB
      2. Convex hull area estimation with Fiji: Hull And Circle
      Harris-Stewart-2001-41-BrainRes-Fig2A/Sub_CA1 projecting Pyramidal_CA1 SR_allcolors_Ax.xcf XCF File that contains only axons in CA1:SR Saved file with axons in CA1:SR for future edits if needed
      Harris-Stewart-2001-41-BrainRes-Fig2A/Sub_CA1 projecting Pyramidal_CA1 SR_allcolors_Ax.png PNG Exported PNG file with only axons in CA1:SR
      1. Pixel count with MATLAB
      2. Convex hull area estimation with Fiji: Hull And Circle
      Bannister-Larkman-1995-150-JCompNeurol-Fig10A/Bannister-Larkman-1995-150-JCompNeurol-Fig10A.pdf PDF Original file that contains the neuronal reconstruction from a CA1 Pyramidal cell Image manipulation with GIMP
      Bannister-Larkman-1995-150-JCompNeurol-Fig10A/Bannister-Larkman-1995-150-JCompNeurol-Fig10A.png PNG Exported PNG file without modifications from the XCF version Somatic distance estimation with SNT
      Bannister-Larkman-1995-150-JCompNeurol-Fig10A/Bannister-Larkman-1995-150-JCompNeurol-Fig10A.traces TRACES File that includes the tracings and measurements associated with the neuronal reconstruction Saved tracings for reference and review if needed
      Bannister-Larkman-1995-150-JCompNeurol-Fig10A/Hull And Circle Results.csv CSV File with measurements for the convex hull area associated with the neuronal reconstruction Saved measurements for reference and review if needed
      Martina-Jonas-2000-295-Science-Fig1C.pdf PDF Original file that contains the neuronal reconstruction from a CA1 O-LM interneuron Image manipulation with GIMP
      Somogyi-Klausberger-2005-9-JPhysiol-Fig3A.pdf PDF Original file that contains the neuronal reconstruction from a CA1 Bistratified interneuron Image manipulation with GIMP

Data analysis

  1. Calculate the standard deviation for the average number of synapses per neuronal pair using the mean and standard deviation from all measurements for the presynaptic axonal and postsynaptic dendritic lengths.

    1. Compute the number of synapses for a given parcel x utilizing Equation (2) for Nsx.

    2. Consider r, Vx, bd, and sd to be constants.

    3. Calculate the standard deviation of Nsx by propagating the standard deviations of Lax and Ldx using the formulas for products and constants,




    4. Determine the total number of synapses by summing across all parcels, and compute the associated standard deviation using the formula for sums,



  2. Calculate the standard deviation for the number of contacts per connected pair using the mean and standard deviation from all measurements for the presynaptic axonal and postsynaptic dendritic lengths and for the convex hull volumes for the presynaptic axons and the postsynaptic dendrites.

    1. Compute the number of contacts for a given parcel x utilizing Equation (3) for Ncx. Determine the standard deviation for the average volume of intersection using the formulas for sums and constants,



    2. Calculate the standard deviation for the number of contacts for a given parcel x utilizing the formulas for products, quotients, and constants,




    3. Determine the total number of contacts using Equation (5), and compute the associated standard deviation using the formula for sums,



  3. Calculate the standard deviation for the connection probabilities for a pair of neuronal types in parcel x from Equation (6).

    1. Compute the standard deviation for the connection probability using the formula for constants,



    2. Determine the total connection probability from Equation (7), and calculate the associated standard deviation using the formulas for differences and products,

Notes

The accuracy of this procedure is limited by the incompleteness of axonal reconstructions and variability in neurite diameter.

This protocol can be used only for dendritic targeting connections: perisomatic connections cannot be estimated with this approach (but see Brown et al., 2012 for those cases).

The computation of standard deviation in the above Data Analysis are performed manually for each pair of neuronal types. The time required to carry out this operation by applying the provided formulas is negligible relative to the time required to trace the neurons from microscopic images.

Recipes

  1. Neuronal reconstructions

    Include representative two-dimensional neuronal tracings for each neuronal type from peer-reviewed publications based on the following inclusion criteria:

    1. Reconstructions should be representative of the neuronal type. At least one axonal reconstruction per presynaptic neuron type and one dendritic reconstruction per postsynaptic type must be included.

    2. Images should contain a calibration scale bar and clear demarcations of relevant layers and subregional boundaries. The latter is optional and only required for parcel-specific estimates.

    3. For tracings including both axons and dendrites, the two neurite types must be unambiguously discernable. Likewise, in tracings including multiple neurons, each neurite type must be unambiguously ascribable to a single neuron.

    4. Species (e.g., rat vs. mouse) and developmental stage (e.g., young vs. adult) should be consistent for all the neuronal types.

    Thousands of neuronal reconstructions are also available through open access databases such as MouseLight (ml-neuronbrowser.janelia.org) for mouse, Mapzebrain (fishatlas.neuro.mpg.de/neurons) for zebrafish, FlyCircuit for drosophila (flycircuit.tw), Insect Brain Database for insects (insectbraindb.org), and NeuroMorpho.Org for over 60 different species (Akram et al., 2018).

  2. Volume estimations

    We use the anatomical volumes for the mouse brain reported from the Blue Brain Cell Atlas (bbp.epfl.ch/nexus/cell-atlas). Other sources are suitable for different species, such as rat (scalablebrainatlas.incf.org/rat/PLCJB14), drosophila (v2.virtualflybrain.org), and zebrafish (fishatlas.neuro.mpg.de). Independent studies that report parcel-specific volume estimations can also be considered (e.g., Ropireddy et al., 2012). NOTE: differences in brain sizes have been reported between males and females as well as among strains (Wang et al., 2020).

  3. Ultrastructural parameters

    Dendritic spine or shaft postsynaptic density distance and axonal inter-bouton distance can have huge variability among species, brain regions, and neuronal types. For greater accuracy, collect specific values from the literature for the synapses of interest (see e.g., the files at hippocampome.org/php/data/Bio-protocol_sample_files.zip for the examples used in this protocol description).

Acknowledgments

This work was supported in part by NIH grants R01NS39600 and U01MH114829. Carolina Tecuatl thanks the Consejo Nacional de Ciencia y Tecnología, México for providing fellowship 253060, allowing this project to start during her PhD training. This methodology was used in Tecuatl et al. (2021) “Comprehensive estimates of potential synaptic connections in local circuits of the rodent hippocampal formation by axonal-dendritic overlap.”

Competing interests

The authors declare no competing financial interests.

Ethics

All original data analyzed using this protocol were published previously in accordance with the authors’ respective ethics committees.

References

  1. Akram, M. A., Nanda, S., Maraver, P., Armananzas, R. and Ascoli, G. A. (2018). An open repository for single-cell reconstructions of the brain forest. Sci Data 5: 180006.
  2. Ascoli, G. A. and Atkeson, J. C. (2005). Incorporating anatomically realistic cellular-level connectivity in neural network models of the rat hippocampus. Biosystems 79(1-3): 173-181.
  3. Bannister, N. J. and Larkman, A. U. (1995). Dendritic morphology of CA1 pyramidal neurones from the rat hippocampus: I. Branching patterns. J Comp Neurol 360(1): 150-160.
  4. Brown, K. M., Sugihara, I., Shinoda, Y. and Ascoli, G. A. (2012). Digital morphometry of rat cerebellar climbing fibers reveals distinct branch and bouton types. J Neurosci 32(42): 14670-14684.
  5. Harris, E., Witter, M. P., Weinstein, G. and Stewart, M. (2001). Intrinsic connectivity of the rat subiculum: I. Dendritic morphology and patterns of axonal arborization by pyramidal neurons. J Comp Neurol 435(4): 490-505.
  6. Moradi, K, Ascoli, GA. A comprehensive knowledge base of synaptic electrophysiology in the rodent hippocampal formation. Hippocampus. 2020; 30: 314- 331.
  7. Longair, M. H., Baker, D. A. and Armstrong, J. D. (2011). Simple Neurite Tracer: open source software for reconstruction, visualization and analysis of neuronal processes. Bioinformatics 27(17): 2453-2454.
  8. Rees, C. L., Moradi, K. and Ascoli, G. A. (2017). Weighing the Evidence in Peters' Rule: Does Neuronal Morphology Predict Connectivity? Trends Neurosci 40(2): 63-71.
  9. Ropireddy, D. and Ascoli, G. A. (2011). Potential Synaptic Connectivity of Different Neurons onto Pyramidal Cells in a 3D Reconstruction of the Rat Hippocampus. Front Neuroinform 5: 5.
  10. Ropireddy, D., Bachus, S. E. and Ascoli, G. A. (2012). Non-homogeneous stereological properties of the rat hippocampus from high-resolution 3D serial reconstruction of thin histological sections. Neuroscience 205: 91-111.
  11. Tecuatl, C., Wheeler, D. W., Sutton, N. and Ascoli, G. A. (2021). Comprehensive estimates of potential synaptic connections in local circuits of the rodent hippocampal formation by axonal-dendritic overlap. J Neurosci 41(8): 1665-1683.
  12. Wagner, T. and Lipinski, H. (2013). IJBlob: An ImageJ Library for Connected Component Analysis and Shape Analysis. J Open Res Softw 1(1): e6.
  13. Wang, N., Anderson, R. J., Ashbrook, D. G., Gopalakrishnan, V., Park, Y., Priebe, C. E., Qi, Y., Laoprasert, R., Vogelstein, J. T., Williams, R. W. and Johnson, G. A. (2020). Variability and heritability of mouse brain structure: Microscopic MRI atlases and connectomes for diverse strains. Neuroimage 222: 117274.

简介

[摘要]计算神经科学目的到模型,复制,并预测网络对于不同的神经元集合动力学通过蒸馏知识衍生自electrophysiol ö gical和形态学证据。然而,nalyses和仿真经常保持暴对直接的实验约束稀疏限制必要参数,如电子显微镜和电生理学对/多重记录证据ö ˚F连接的统计信息。值得注意的是,可用的数据是特别稀缺关于所识别的神经元之间的突触连接的定量信息人类型。在这里,我们提出了一个用户友好的数据驱动管道来估计连接概率、每个连接对的接触数量,以及从常用二维追踪和其他广泛访问的轴突和树突路径上与突触前和突触后体细胞的距离。测量。所描述的过程不需要任何计算的背景和可以访问到所有的神经科学家。因此,该协议填补了从神经元形态到电路组织的重要空白,可应用于许多不同的神经系统、大脑区域、动物物种和数据源。


图文摘要:

该p rocessing协议从2D重建到孔定量达ED突触连接

[背景]突触connecti VITY是的关键决定因素之间的相互作用的神经元,并且其孔定量吨通货膨胀就是枢轴理解荷兰国际集团脑回路的组织和所述RELAT ionship与网络功能(阿斯科利和Atkeson ,2005) 。突触概率的当前知识依赖于经验证据,这是有限的,通过同时记录的数量的神经元(例如,通过一对记录,octopatch ,多电极阵列)和受实验条件(体外VS 。体内,切片取向和厚度,细胞之间的距离等)。Ç在特定脑区域onnections被经常概率通过诱发反应编后的刺激传入纤维束; 然而,这种测试不允许进行特定的神经元的鉴定人参与类型(莫拉迪和阿斯科利,2020年)。或者,可以通过将三维 (3D) 重建的神经元形态嵌入 3D 脑图谱并计算轴突 - 树突重叠的可能位置来计算突触连接(Ropireddy和 Ascoli,2011)。然而,这种方法需要大量劳动密集型数据,受到 3D 配准精度的限制,并且迄今为止被证明不切实际。

尽管它很重要,但对于大多数动物物种和神经系统来说,连接信息仍然不完整(Rees等,2017)。这个协议描述一个简单的过程的提取的离子重要定量突触参数 ——即连接概率、每个连接对的接触数量以及沿神经突路径与突触前和突触后胞体的距离——来自轴突和树突形态的常用二维图像。据我们所知,没有其他解决方案可用于获得相同的结果。最初,被用来估计海马连通性和结果的证实高相关性这种方法荷兰国际集团与稀疏可用数据估计(Tecuatl等人,202 1 )。

所呈现流水线的总体工作流程由七个主要逻辑组件:(我)●条款依照它ATION包裹特异性轴突和树突长度; (ii)确定包裹特定的轴突和树突路径距离;(ⅲ)的测量包裹特异性轴突和树突凸ħ ULL体积; (ⅳ)ç alculati ø Ñ的平均数量的每神经元突触人对在每个包裹; (V)C alculat的离子每连接一对触点的数目; (ⅵ)每个神经元的连接概率的计算人对; (vii)通过误差分析的传播计算这些值的置信区间。所有步骤都可以使用现成的软件在基本台式机或笔记本电脑上执行(图 1)。


图 1. 所述管道的流程图。从2D神经影像的步骤开始被加工到孔定量泰特轴突和树突长度,从通过包裹胞体,和凸包卷路径距离。从第Ë本身孔定量吨ations ,我们计算突触和神经元每触点的数量人对和随后估计来自多个神经元连接的概率人对。生成的信息被分析并表示为平均值和标准偏差。

关键字:突触连接, 神经网络, 连接概率, 联系, 凸包, 传播误差, 轴突-树突重叠



设备

标准个人电脑
所描述的分析是使用带有 Windows 10的Bionic G32 144Hz 一体机 [i7-8700] 进行的。推荐的最低配置是 AMD Ryzen 5 2600X 六核处理器 3.60 GHz、16 GB RAM、64 位操作系统。

软件

GNU 图像处理程序,免费访问(GIMP 2.8;gimp.org/downloads/ )。
定制MATLAB算法,免费获取(github.com/Hippocampome-Org/QuantifyNeurites)
绘图数字化仪,免费访问( plotdigitizer.sourceforge.net )
斐济:形状分析插件,免费获取(Wagner and Lipinski, 20 13; imagej.net/Shape_Filter)
斐济:简单的 Neurite Tracer 插件,免费访问(Longair等人2011;imagej.net/Simple_Neurite_Tracer:_Basic_Instructions)
斐济:3D Convex Hull ,免费访问( imagej.nih.gov/ij/plugins/3d-convex-hull )
MATLAB:商业许可;提供 30 天免费试用 ( mathworks.com/products/get-matlab.html )


图像数据集和附加要求

需要的是包含神经元形态图的图形,例如树突和轴突乔木(配方1 )。如果轴突和树突都来自同一个神经元,则需要以不同的颜色绘制它们。如果乔木侵入多个解剖宗地,则在需要宗地特定数据时,图形必须划定宗地边界。重要提示:所有数字都需要包含校准条。本协议中使用的示例可在hippocampome.org/php/data/Bio-protocol_sample_files.zip访问。
需要估计包含感兴趣神经元的解剖包的体积(方法2 )。本协议中使用的示例列在表 1 中,可在bbp.epfl.ch/nexus/cell-atlas 上访问。
所需的是估计沿轴突的突触前元件 (boutons)之间的平均距离和沿树突的突触后元件 (轴密度的棘)之间的平均距离, 以了解感兴趣的物种和神经系统 (Recipe 3 )。本协议中使用的示例可在hippocampome.org/php/data/Bio-protocol_sample_files.zip访问。


程序

孔定量吨的通货膨胀特定包裹-轴突和树突长度
使用 GIMP 生成必要的 PNG 文件。从原始未修改的神经元重建(方法1 )中,手动分离每个解剖包裹内的轴突和树突。如果包裹-特定信息不是必需的,SIMPL ÿ分离的轴突从所述估计对应轴突和树突长度树突(视频1)。                           


视频 1. 2D 图像处理。GIMP 用于从各个包裹中选择性地擦除轴突或树突,以将它们隔离以供以后分析。

一种。将 PDF 加载到 GIMP(例如,文件:打开“Harris-Stewart-2001-41-BrainRes-Fig2A.pdf”)(图 2A)。                   

湾 使用 GIMP 擦除图形的无关部分(图 2B)。     

                                          从工具箱窗口中选择橡皮擦工具。
从画笔窗口中选择硬度 100 。
画笔大小设置为所需的尺寸(例如,在25)工具选项窗口(图2B,红色框)。
按住鼠标左键可擦除部分图形。
保存擦除图形的 XCF 版本,其中包括所有层中的两种神经突(例如,文件:另存为... “ SCA_all_allColors_both ”)。重要提示:名称的结构应保留用于像素计数。
将 PNG 版本从图形的 XCF版本导出到同一文件夹(例如,文件:导出为... “SCA_all_allColors_both.png”)。选择 PNG 作为首选文件格式,因为其默认背景是透明的。这减少了因意外计算背景中包含的像素而导致的任何潜在错误。
C。通过重复步骤 b i -iv (图 2C,视频 1),使用 GIMP根据颜色代码(轴突在图 2B 中以红色显示)从图中擦除轴突。     

                                                                                    将图形的 XCF 版本与感兴趣层中的树突保存到同一文件夹(例如,文件:另存为... “ SCA_SO_allColors_Ds.xcf ”)。
将 PNG 版本从图形的 XCF版本导出到同一文件夹(例如,文件:导出为... “SCA_SO_allColors_Ds.png”)。
d. 通过重复步骤 b i -iv (图 2D,视频 1),使用 GIMP根据颜色代码(树突在图 2B 中以黑色显示)擦除图中的树突。     

                            将图形的 XCF 版本与感兴趣层中的轴突保存到同一文件夹(例如,文件:另存为... “ SCA_SO_allColors_Ax.xcf ”)。
将 PNG 版本从图形的xcf版本导出到同一文件夹(例如,文件:导出为... “SCA_SO_allColors_As.png”)。
保存在每一个层和分不同的文件的轴突和树突域到相同的文件夹(图2E和2 F)。


图2为图像的预处理的孔定量吨轴突和树突长度的通货膨胀。A. GIMP File 菜单用于打开要处理的图像文件。B.代表性图像正在准备处理(Harris et al ., 2001),其中红色框界定工具箱位置,圆圈代表橡皮擦工具。丙、丁。显示的是处理后的图像,在感兴趣区域的所有层(在本例中为下突)中仅包含树突 ( C ) 或轴突 ( D ),这些图像是从 ( B ) 中显示的原始图像中获得的。E,F 。示出的是- [R具有代表性的仅显示树突(图像ë )或轴突(˚F在感兴趣的包裹)(在这种情况下,该层moleculare下托),它是从(所示的原始图像而获得的乙)。

使用定制的 MATLAB 算法进行像素计数(图 3;视频 2)。


视频 2. 来自 2D 图像的像素数。定制的 MATLAB 程序用于计算图像的 16 个颜色通道中包含的所有像素。

一种。将分离的图像放在数据文件夹中。     

湾 打开 MATLAB,确保当前工作文件夹已打开(例如,“dir_QuantifyNeurites_v2”)(图 3A1,红色框)。     

C。运行命令转换(图 3A1,绿色框)。     

d. 从显示的菜单中,通过键入数字并按Enter来选择要处理的图像(图 3A2)。     

e. 图像打开后,选择轮播模式以识别包含像素的颜色通道(图 3A3)。     

F。按m选择包含像素的颜色通道(像素数显示在括号中)(图 3B1)。       

G。如果通道不包含任何像素,只需按空格键移动到下一个通道(图 3B2)。     

H。可选步骤:使用选定的颜色通道绘制图像,通过键入p并按Enter来验证选定的通道是否包含所有像素(图 3B3)。     

一世。显示包含总像素数的直方图(图 3C1)。命令窗口显示选定的通道和像素数。       

j. 可选步骤:通过键入s并按Enter保存包含选定(图 3C2)和未选定(图 3C3)通道的图像。图像会自动保存到输出文件夹。       

克。小号的选民,从数据文件夹中的新图像通过典型ING升,按ING进入。     

湖 Ë次过程的典型ING /并按ING进入。       



图3. 像素计数。A1 。显示的是一个MATLAB 窗口,红色框中是打开的工作文件夹“dir_QuantifyNeurites_v2”,绿色框中是运行命令“ convert ”的命令窗口。A2 。该d isplayed菜单显示运行命令“后转换”选择图像处理。A3 。该d isplayed菜单选项中出现的顺序来分析所选择的人物。乙。显示的是代表性的轮播模式,其中颜色编号和存在 ( B1 ) 或不存在 ( B2 )的像素数在蓝色框中分隔,最终绘图仅包含在轮播模式完整运行期间选择的通道. Ç 。呈现的是所选通道的ah柱状图和每个通道的像素数 ( C1 ) 以及为所选 ( C2 ) 和未选择 ( C3 ) 通道生成的 PNG 文件。

使用Plot Digitizer估计像素长度(视频 3)。


视频 3.以像素为单位测量校准条。Plot Digitizer 用于测量神经元重建校准条的像素长度。记录校准条两端的 X 坐标,它们的差值以像素为单位的最终测量值。

一种。使用 Plot Digitizer 打开原始重建。     

湾 将光标放在校准条的开头并记下数字。     

C。在校准条的另一端做同样的事情。     

d. 数字之间的差异代表校准条的长度(以像素为单位)。     

从像素数到长度的转换。
一种。确定由所述平均神经突宽度随机选择荷兰国际集团为每个神经元的图像,包裹,和神经突域的三个位置; MEASUR荷兰国际集团在每个位置处的像素的分支宽度; 和averag荷兰国际集团三个值(视频4)。     



视频 4.神经突宽度估计。Plot Digitizer 用于估计包含神经元重建部分的每一层中轴突和树突的宽度。每层测量三个例子以获得每层神经突宽度的平均估计。

湾 以物理单位计算像素长度,这只是标称校准比例尺值(以微米为单位)除以以像素为单位的测量条长度。     

C。通过将给定包裹中该神经突的像素数乘以物理像素长度并将结果除以像素的平均分支宽度,获得包裹特定的神经突长度。     

d. 正确的人为通过组合包裹特异性长度压扁三维乔木成二维图像,升p ,与文献报道的截面厚度,吨小号,利用毕达哥拉斯式:     

 (1)

其中代表最终校正的长度。

的判定的一个xonal和树突状路径的距离(图4中,视频5)


视频 5. 测量体细胞距离。斐济与简单轴突示踪插件是用来从细胞体到的端部测量的像素长度的选定轴突或树突。三个例子为每种类型的神经突,以确定测量的平均值。

用斐济打开原始文件:文件 - 打开 - 文件源(图 4A)。
将图像转换为二进制:处理 - 二进制 - 生成二进制(图 4B)。
打开插件“Simple Neurite Tracer:”插件-神经解剖-SNT (图4C)。
在 SNT 命令窗口中打开图像:文件 - 选择跟踪图像 - 从(图 4D)。
通过单击体细胞和段的末尾跟踪树突/轴突的距离。如果跟踪与结构不对应,请通过沿线段多次单击来提高精度:按y ,然后继续沿路径跟踪(图 4E)。
跟踪完成后,通过接受跟踪移动到下一个。按F完成跟踪。
这些值以像素为单位估计(路径管理器窗口,如果值不可见:标记 – 形态测量 – 长度),因此使用像素/长度因子将它们转换为长度(第3部分,图 4E)。
完成所有跟踪后,保存它们以备将来参考。文件 – 导出为– swc或 traces 。


图4.确定的š omatic距离和凸包卷。一个。显示了斐济菜单步骤,用于打开路径跟踪图像(例如,CA1 锥体神经元;Bannister和Larkman ,1995)。乙。显示的是将图像转换为二进制图像的菜单步骤。Ç 。显示的是运行 Simpl e Neurite Tracer 插件的菜单步骤。d 。显示的是加载打开的图像以进行跟踪的简单神经突跟踪器步骤。乙。呈现的是具有代表性的Simple Neurite Tracer 控制台,以蓝色显示一条路径(中间),控制台上有完成路径和继续追踪的选项(左),以及路径管理器,以及对应于不同地块的所有追踪原始图像(右)。˚F 。显示的是菜单的步骤来运行赫尔和圈为位于感兴趣包裹树突插件(例如,CA1地层东方明珠Oriens ;对于凸绿盒)^ h ULL测量。格。所述船体和圈工具箱(左)被用来扫描当前图像,其中所述图像与所述分隔区域在绿色和底面板显示新兴结果窗口被示出。

确定的C onvex ħ ULL体积从2D重建(图4F和4 G,视频6)
使用斐济打开生成的仅包含轴突或树突(PNG 文件)的分割图像:文件 - 打开 - 文件源。
将图像转换为二进制:处理 - 二进制 - 生成二进制。
打开插件:Plugins – Shape Analysis – Hull And Circle (图 4F)。
从新窗口中,选择选项扫描当前图像或 Roi (图 4G)。
将生成一个包含结果的新窗口(Hull 和 Circle 结果,图 4G)。
保存结果:文件 – 另存为.
与计算出的图像ħ显示ULL体积。该图像不能保存的,但它提供了有关所得凸如何信息ħ ULL面积计算(图4G)。
将从像素单元的区域测量以微米2和乘法结果荷兰国际集团所报告切片厚度值,假设该重建位于切片的中部。


从3D 重建确定凸包体积
使用 3D Convex Hull 插件直接估计真实体积。


计算一个每神经元突触verage数人对。
Ç alculate每对突触前和突触后神经元的突触的平均数目Ñ小号,从它们的具体包裹-轴突和树突长度,通过单独地估计数,Ñ SX ,轴突树突重叠在每个包裹X (Tecuatl等人., 202 1 ) . 对于任何x ,值N sx可以导出为三个因子的乘积:
一个给定的相互作用距离内发生突触前和突触后的元素的概率,[R ,是相互作用球的体积之间的比率,在其内两个元件中发现,并且整个包裹的体积,V X (配方2 )。
在突触前的元素(轴突终扣)的数量一个给定解剖包裹指定通过在包裹的突触前轴突长度X ,大号斧,通过连续的突触前突触小结,间的平均距离除以b d (配方3 ;实施例的文件是在hippocampome访问.org/php/data/Bio-protocol_sample_files.zip )。
在相同的包裹突触后元素(树突棘或轴)的数量是通过在突触后树突长度给定X ,大号DX ,由距离betwee划分Ñ突触后的元素,š d 。
要计算特定包裹中每对突触前和突触后神经元的平均突触数,请使用以下公式:


                                                                                                  (2)

每涉及神经元突触对的总数,Ñ小号,是每包裹的数量,只是总和Ñ SX ,在所有的包裹。


计算每个连接对的触点数。
假设该给定的对神经元形成至少单突触接触,并计算的该对附加的触头的预期数量为:


                                                                       (3)

其中由相互作用半径r和V o定义的球体之间的体积比表示任何给定的轴突束和树突棘或轴的相遇机会,并且L ax / b d和L dx / s d对应,分别对应于包裹x 中的轴突束和树突棘或轴的数量。

确定吨的他体积的交集,V Ó ,通过:


                                                                       ( 4 )

其中V DX和V斧是树突和轴突凸包卷在包裹X 。

计算Ť他每连接一对触头的总数一个š由一个增强在每个包裹的接触,反映了初始假设神经元的总和人对连接:
                                           ( 5 )

其中符号Σ x代表所有地块的总和。

计算连接概率
计算吨他一对神经元的连接概率人在包裹类型X除以每神经元的突触的平均数人通过在相同的包裹每连接一对触点的数目对:


                                                                                    ( 6 )

测定T他总在任何包裹一对前和突触后神经元通过包容性的事件和连接的可能性:


                                                         ( 7 )

其中符号𝛱 x代表所有包裹的产品。

表 1. 所有代表性文件的列表

请在正文中引用表 1。

数据一nalysis

计算平均数每神经元的突触的标准偏差人使用从突触前轴突和突触后树突长度所有测量的平均值和标准偏差对。
使用N sx 的等式 (2)计算给定包裹x的突触数量。
将r 、V x 、b d和s d视为常数。
使用乘积和常数的公式通过传播L ax和L dx的标准差来计算N sx的标准差,


( 8 )

( 9 )

通过对所有包裹求和来确定突触的总数,并使用求和公式计算相关的标准偏差,


(1 0 )

计算的标准偏差用于使用从对突触前轴突和突触后树突长度所有测量的平均值和标准偏差每连接一对触头的数目和用于凸ħ ULL体积为突触前轴突和突触后树突。
使用N cx 的等式 (3)计算给定地块x的联系人数量。确定的标准偏差为使用公式总和和常数交叉点的平均体积,


(1 1 )

(1 2 )

使用乘积、商和常数的公式计算给定包裹x的联系数量的标准偏差,


(1 3 )

(1 4 )

使用公式 ( 5 )确定联系总数,并使用总和公式计算相关的标准偏差,


(1 5 )

计算用于连接概率的标准偏差为一对神经元的人在包裹类型X从公式(6 )。
计算的标准偏差为使用式为常量的连接概率,


(1 6 )

根据公式 ( 7 )确定总连接概率,并使用差值和乘积公式计算相关标准偏差,


(1 7 )

(1 8 )

( 19 )

笔记

精度此的过程是升IMIT编通过轴突重建的不完备性和可变性神经突直径。

  该协议只能用于树突靶向连接:不能用这种方法估计perisomatic连接(但这些情况见 Brown等人,2012)。

                                            在数据分析上述标准偏差的计算是对于每对神经元的手动执行人类型。相对于从显微图像追踪神经元所需的时间,通过应用提供的公式执行此操作所需的时间可以忽略不计。

食谱

神经元重建
包括用于每个神经元代表二维神经元描记人从同行评审出版物型基于下列入选标准:

重建应代表神经元的人型。必须包括每个突触前神经元类型至少一次轴突重建和每个突触后类型一次树突重建。
图片应包含校准比例尺和相关层的明确分界小号和次区域界限。后者是可选的,仅针对特定包裹的估算才需要。
对于包括轴突和树突的追踪,这两种神经突类型必须是明确可辨别的。同样,在包括多个神经元的追踪中,每个神经突类型必须明确归因于单个神经元。
物种(例如,鼠与鼠标)和发育阶段(例如,年轻的成年对比),应该是所有的神经元一致的人的类型。
数千神经重建的也可通过开放式访问数据库如MouseLight (ml-neuronbrowser.janelia.org)对于小鼠,Mapzebrain (fishatlas.neuro.mpg.de/neurons)斑马鱼,FlyCircuit对于果蝇(flycircuit.tw),昆虫脑数据库昆虫(insectbraindb.org),和NeuroMorpho.Org超过60不同的物种(阿克拉姆等人。,2018)。

体积估计
我们使用 Blue Brain Cell Atlas ( bbp.epfl.ch/nexus/cell-atlas )报告的小鼠大脑的解剖体积。其他来源适用于不同的物种,例如大鼠 (scalablebrainatlas.incf.org/rat/PLCJB14)、果蝇 ( v2.virtualflybrain.org ) 和斑马鱼 ( fishatlas.neuro.mpg.de )。也可以考虑报告地块特定体积估计的独立研究(例如,Ropireddy等,2012)。注:在脑容量的差异已报告的男性和女性之间以及中(王株等。,2020)。

超微结构参数
树突棘或轴突触后密度距离和轴突间- b Ø uton距离可以有巨大的中变异的物种,脑区,神经元人的类型。为了获得更高的准确性,请从感兴趣的突触的文献中收集特定值(例如,请参见hippocampome.org/php/data/Bio-protocol_sample_files.zip 中的文件,了解本协议描述中使用的示例)。

           

致谢

这项工作得到了 NIH 赠款 R01NS39600 和 U01MH114829 的部分支持。Carolina Tecuatl感谢Consejo Nacional de Ciencia y Tecnología ,墨西哥提供奖学金 253060,允许在她的博士培训期间启动该项目。Tecuatl等人使用了这种方法。(202 1 ) “通过轴突-树突重叠对啮齿动物海马形成局部回路中潜在突触连接的综合估计。”

利益争夺

作者声明没有相互竞争的经济利益。

伦理

使用该协议分析的所有原始数据均已根据作者各自的伦理委员会发布。

参考

1. Akram, MA, Nanda, S., Maraver, P., Armanzas, R. 和 Ascoli, GA (2018)。大脑森林单细胞重建的开放存储库。科学数据5:180006。     

2. Ascoli, GA 和Atkeson , JC (2005)。在大鼠海马的神经网络模型中加入解剖学上真实的细胞水平连接。生物系统79(1-3):173-181。     

3. Bannister, NJ 和Larkman , AU (1995)。来自大鼠海马的 CA1 锥体神经元的树突形态:I. 分支模式。J Comp Neurol 360(1):150-160。     

4. Brown, KM, Sugihara, I., Shinoda, Y. 和 Ascoli, GA (2012)。大鼠小脑攀缘纤维的数字形态测量显示不同的分支和布顿类型。J Neurosci 32(42):14670-14684。                   

5. Harris, E., Witter, MP, Weinstein, G. 和 Stewart, M. (2001)。大鼠下托的内在连通性:I. 锥体神经元的树突形态和轴突分枝模式。J Comp Neurol 435(4):490-505。                   

6.莫拉迪,K,阿斯科利,乔治亚州。啮齿动物海马形成中突触电生理学的综合知识库。海马体。2020 年;30:314–331。     

7. Longair , MH, Baker, DA 和 Armstrong, JD (2011)。Simple Neurite Tracer:用于神经元过程重建、可视化和分析的开源软件。生物信息学27(17):2453-2454。     

8. Rees, CL, Moradi, K., & Ascoli, GA (2017)。权衡彼得斯规则中的证据:神经元形态学能预测连通性吗?。神经科学趋势,40(2), 63–71。       

9. Ropireddy , D. 和 Ascoli, GA (2011)。在大鼠海马体的 3D 重建中,不同神经元与锥体细胞的潜在突触连接。前神经信息5:5。     

10. Ropireddy ,D.,Bachus ,SE和阿斯科利,GA(2012)。来自薄组织切片的高分辨率 3D 连续重建的大鼠海马体的非均匀体视特性。神经科学205:91-111。 

11. Tecuatl , C., Wheeler, DW, Sutton, N. 和 Ascoli, GA (202 1 )。通过轴突-树突重叠对啮齿动物海马形成局部回路中潜在突触连接的综合估计。J Neurosci 41(8):1665-1683。               

12. Wagner, T. 和 Lipinski, H. (2013)。IJBlob:用于连接组件分析和形状分析的 ImageJ 库。J Open Res Softw 1(1): e6。 

13. Wang, N., Anderson, RJ, Ashbrook, DG, Gopalakrishnan, V., Park, Y., Priebe, CE, Qi, Y., Laoprasert , R., Vogelstein , JT, Williams, RW 和 Johnson, GA (2020)。小鼠大脑结构的变异性和遗传性:不同品系的显微 MRI 图谱和连接组。神经影像222:117274。   
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Copyright: © 2021 The Authors; exclusive licensee Bio-protocol LLC.
引用: Readers should cite both the Bio-protocol article and the original research article where this protocol was used:
  1. Tecuatl, C., Wheeler, D. W. and Ascoli, G. A. (2021). A Method for Estimating the Potential Synaptic Connections Between Axons and Dendrites From 2D Neuronal Images . Bio-protocol 11(13): e4073. DOI: 10.21769/BioProtoc.4073.
  2. Tecuatl, C., Wheeler, D. W., Sutton, N. and Ascoli, G. A. (2021). Comprehensive estimates of potential synaptic connections in local circuits of the rodent hippocampal formation by axonal-dendritic overlap. J Neurosci 41(8): 1665-1683.
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