Synaptic Probabilities Calculations

Synaptic probabilities calculations

The synaptic probabilities calculations are described as “error propagation” calculations. The author of this document is not sure of the reason why they were given that description.

Overall procesing strategy

The calculations create several temporary SQL tables (views) that are used to store intermediary values. The only permanent table added is SynproParcelVolumes. The views are meant to be temporary data storage that can be deleted then automatically added again with the build_error_prop.sh script as described below. This helps avoid taking up database space with intermediary tables when that is not needed.

Usage note: while each implementation step is listed below, it is recommended to run build_error_prop.sh to run all steps unless there is interest in inspecting an individual intermediate table. The build_error_prop script uses mysql_user, mysql_password, and mysql_db_name found in database_save.sh in the base csv2db_import directory. This is a file that a user creates based on the example_database_save.sh file. If these variables are not retrieved correctly from database_save.sh then they can be manually specified in the build_error_prop script. A purpose of database_save.sh is to store login credentials in a file that is ignored by github uploads. If you manually include the credentials in the build_error_prop script be sure to avoid uploading them to github if you upload files from this project to there.

Csv file note:
In SynproParcelVolumes.csv for EC subregion the “L” in layer names was removed to match the way that is described in the neurite_quantified tables. This allows compatibility for queries.

Step 1

Define the parcel-independent constants to be used throughout the NxN calculations.
a. Inter-bouton distance: length_bouton = 6.2 (or value specific to neuron pair and parcel).
b. Dendritic spine distance: length_spine = 1.09.
c. Radius of interaction: radius_int = 2.
d. Volume of interaction: volume_int = (4/3) * pi * radius_int^3.
e. Constant: c = volume_int / (length_bouton * length_spine).

Implementation:
The length_bouton, which is the inter-buton distance (IBD), is specific to the neuron pair, subregion, and layer ever since cross-subregion connections were added. The table SynproIBD supplies the IBD values and is created when the hippocampome database is built. In nps.sql and number_of_contacts.sql scripts described later the formula ((4/3)*PI()*8/(ibd*1.09)) provides the c (constant) factor in calculations.

Step 2

Select the first parcel for performing the NxN calculations.
a. Query the database for the needed values.
  i. You need to read from the database all of the axonal length values for the “From” neuron type. This information is already being read from the database for the Number of Potential Synapses Evidence Page and the Number of Contacts Evidence Page. Find the mean value for all of these axonal lengths (axonal_length_mean_[parcel]) and calculate the standard deviation (axonal_length_stdev_[parcel]).
  ii. You need to read from the database all of the dendritic length values for the “To” neuron type. This information is already being read from the database for the Number of Potential Synapses Evidence Page and the Number of Contacts Evidence Page. Find the mean value for all of these axonal lengths (dendritic_length_mean_[parcel]) and calculate the standard deviation (dendritic_length_stdev_[parcel]).
  iii. You need to read from the database all of the axonal convex hull volume values for the “From” neuron type. This information is already being read from the database for the Number of Contacts Evidence Page. Find the mean value for all of these axonal convex hull volumes (axonal_volume_mean_[parcel]) and calculate the standard deviation (axonal_volume_stdev_[parcel]).
  iv. You need to read from the database all of the axonal convex hull volume values for the “To” neuron type. This information is already being read from the database for the Number of Contacts Evidence Page. Find the mean value for all of these dendritic convex hull volumes (dendritic_volume_mean_[parcel]) and calculate the standard deviation (dendritic_volume_stdev_[parcel]).

Implementation:
Run lengths_hull_vols.sql to get length values and convex hull volume values for each neuron class in each parcel that is reported for.
Run split_layers c++ program and other steps listed under “reformat number_of_contacts data” in build_error_prop.sh. This splits more than one parcel listed for a neuron pair unto more than one row in number_of_contacts. This helps with the sequence of data processing. This was added to assist in processing using the layers column to accomidate cross-subregion connections.
Run order_of_pairs.sql to create a list of all neuron pairs and parcels they are in.
Run pairs_lengths_hull_vols.sql to join the values with the list of axon-dendrite pairs.

b. Read in needed values from stored data/ files
i. You need to read the parcel volume (volume_[parcel]) from the first line of either data/[parcel]-Table-1.csv or data/[parcel]-Table-2.csv.

Implementation:
Run create_synpro_parcel_volumes.sql to create SynproParcelVolumes table.
Import SynproParcelVolumes.csv to add data to table.

Step 3

Determine the total number of parcels (n_parcels) involved in the interaction between the “From” and “To” neuron types in the relevant subregion.

Implementation:
Run number_of_parcels.sql

Calculate the mean potential volume of overlap and its standard deviation.
i. Calculate the overlap volume mean: overlap_volume_mean_[parcel] = (axonal_volume_mean_[parcel] + dendritic_volume_mean_[parcel]) / 4.
ii. Calculate the overlap volume standard deviation: overlap_volume_stdev_[parcel] = sqrt(axonal_volume_stdev_[parcel]^2 + dendritic_volume_stdev_[parcel]^2).

Implementation:
Run volume_of_overlap.sql

Step 4

Calculate the number of potential synapses, number of contacts, and connection probability values for the matching matrices.

a. Calculate the mean number of potential synapses (NPS) and its standard deviation.
i. Calculate the NPS mean: NPS_mean_[parcel] = c * axonal_length_mean_[parcel] * dendritic_length_mean_[parcel] / volume_[parcel].
ii. Calculate the NPS standard deviation: NPS_stdev_[parcel] = NPS_mean_[parcel] * sqrt((axonal_length_stdev_[parcel] / axonal_length_mean_[parcel])^2 + (dendritic_length_stdev_[parcel] / dendritic_length_mean_[parcel])^2).

Implementation:
Run nps.sql

b. Calculate the mean number of contacts (NC) and its standard deviation.
i. Calculate the NC mean: NC_mean_[parcel] = (1/n_parcels) + (c * axonal_length_mean_[parcel] * dendritic_length_mean_[parcel]) / overlap_volume_mean_[parcel].
ii. Calculate the NC standard deviation: NC_stdev_[parcel] = NC_mean_[parcel] * sqrt((axonal_length_stdev_[parcel] / axonal_length_mean_[parcel])^2 + (dendritic_length_stdev_[parcel] / dendritic_length_mean_[parcel])^2 + (overlap_volume_stdev_[parcel] / overlap_volume_mean_[parcel])^2).

Implementation:
Run number_of_contacts.sql

c. Calculate the mean connection probability (CP) and its standard deviation.
i. Calculate the CP mean: CP_mean_[parcel] = NPS_mean_[parcel] / NC_mean_[parcel].
ii. Calculate the CP standard deviation: CP_stdev_[parcel] = CP_mean_[parcel] * sqrt((NPS_stdev_[parcel] / NPS_mean_[parcel])^2 + (NC_stdev_[parcel] / NC_mean_[parcel])^2).

Implementation: Run connection_probability.sql

Step 5

Sum values across all n_parcels parcels.
a. Calculate the total mean number of potential synapses and its standard deviation.
i. NPS_mean_total = NPS_mean_[parcel1] + NPS_mean_[parcel2] + …
ii. NPS_stdev_total = sqrt(NPS_stdev_[parcel1]^2 + NPS_stdev_[parcel2]^2 + …).

Implementation: Run total_nps.sql

b. Calculate the total mean number of contacts and its standard deviation.
i. NC_mean_total = NC_mean_[parcel1] + NC_mean_[parcel2] + …
ii. NC_stdev_total = sqrt(NC_stdev_[parcel1]^2 + NC_stdev_[parcel2]^2 + …).

Implementation: Run total_noc.sql

c. Calculate the total mean connection probability and its standard deviation.
i. CP_mean_total = 1 – ((1 - CP_mean_[parcel1]) * (1 - CP_mean_[parcel2]) * …)
ii. CP_stdev_total = CP_mean_total * sqrt((CP_stdev_[parcel1] / CP_mean_[parcel1])^2 + (CP_stdev_[parcel2] / CP_mean_[parcel2])^2 + …).

Implementation: Run total_cp.sql

Step 6

Export views into tables for perminant storage in the database.
The method of SET STATEMENT max_statement_time=0 FOR SELECT * FROM \ $DB.<table_name> INTO OUTFILE '$EXP_DIR/<table_name>.csv';" > export_table.sql then mysql -h $ADDR -u $USER -p$PASS $DB < export_table.sql as included in build_prop_error.sh under the exporting tables section enables converting the views into tables. Once they are tables they can then be exported into csv files. Specifically, the csv files SynproCP.csv, SynproCPTotal.csv, SynproNOC.csv, SynproNOCTotal.csv, SynproNoPS.csv, SynproNPSTotal.csv, and SynproPairsOrder should be created. Then those files should be tranfered to /iconv/latin1 of the csv2db software. The csv2db software will use those csv files to create tables for them when the database is built.

Php files

Related php files are synapse_probabilities.php, synapse_probabilities_ps.php, synapse_probabilities_sd.php, synapse_probabilities_dal.php, synapse_probabilities_noc.php, synapse_probabilities_sypr.php
These files display the synaptic probabilities related values that are created through the error propagation calculations.