Super-Resolved_Tomographic_Reconstruction

Simulations of subunit models of retinal ganglion cells and inference of their subunits with super-resolved tomographic reconstruction (STR).

This code accompanies the manuscript by Krüppel et al.: "Applying Super-Resolution and Tomography Concepts to Identify Receptive Field Subunits in the Retina". It implements the retinal ganglion cell simulations and the STR method described there and can be used to reproduce all presented simulation data. For a description of the model and method basics, please refer to the manuscript. The following description will outline the contents and use of the provided scripts and how to reproduce the presented data.

Subunit_Model.py

This script provides a class for a subunit model of a retinal ganglion cell. The class Subunit_Model can be used to generate an LNLNP model in a sandbox principle, allowing, for example, to try different subunit nonlinearities. It can easily be extended beyond the setups presented in the manuscript. More detailed tuning of the model can be done via the global parameter DEFAULT_PARAMS that controls, e.g., the noise level. The method response_to_flash calculates the response of the model cell to a flash of a given stimulus, e.g., a Ricker stripe stimulus.

Mexican_Hat.py

This script provides two functions that are requried to probe the receptive field of a simulated ganglion cell with a Mexican hat-shaped stimulus, illustrated in manuscript figure 1. The function Response_map performs such a probing and returns the responses of the model.

STR.py

The main STR analysis is implemented here. The main program instantiates a Subunit_Model and analyzes it with STR. It generates several plots depicting this analysis and saves them in a subfolder. One can change, for example, the global parameters to investigate how they affect the analysis.

Quantitative_STR.py

This script can be used to calculate average F-scores evaluating the reconstruction quality using certain model and analysis parameters. The results of each parameter combination are saved in a separate file in a subfolder, containing the parameter values in the file name.

Examples shown in figures

The default parameters are described in the manuscript and correspond to the default parameters in the scripts. Parameter changes, e.g., a different subunit nonlinearity, are mentioned in the text and can be implemented by changing the corresponding parameters in the script. In combination with the following seeds of the random number generators, this information can be used to replicate the results shown in the manuscript's figures. Each instantiation of a Subunit_Model has two seeds - one for generating the subunit layout and one for the Poisson spiking process.

• Fig 2 (top): 20 (layout seed), 2000 (Poisson seed)
• Fig 2 (center): 30, 3000
• Fig 2 (bottom): 46, 4000
• Fig 3: 4, 1025
• Fig 4I: 1101, 110
• Fig 4J: 100, 250
• Fig 5 (1st row): 1501, 151
• Fig 5 (2nd row): 1517, 150
• Fig 5 (3rd row): 1525, 150
• Fig 5 (4th row): 1531, 152
• Fig 5 (5th row): 1553, 150
• Fig 6A: [1602, 1702] (two superimposed layouts), 167
• Fig 6B: [1611, 1710], 166
• Fig 6C: [1620, 1720], 162
• Fig 6D: [1633, 1730] (subunits and photoreceptors), 160

Sample seeds were chosen to generate representative layouts and F-scores. The 1000 seeds for the calculation of average F-scores covered the range [0, 1000) for the layout (and [1000, 2000) for the second layout or photoreceptors) and [10000, 11000) for the Poisson process.