From a696ccef018c1815ffe3d6944695aa76c54e6dbe Mon Sep 17 00:00:00 2001 From: Tom Bland <23723407+tsmbland@users.noreply.github.com> Date: Fri, 17 May 2024 12:11:56 +0100 Subject: [PATCH] Add readme for flexi model --- README.md | 5 ++- docs/README.md | 64 +++++++++++++++++++++++++++++++++ docs/model_flexi.md | 58 ++++++++++++++++++++++++++++++ docs/profiles.png | Bin 0 -> 115855 bytes docs/schematic.png | Bin 0 -> 579937 bytes docs/simulation comparison.png | Bin 0 -> 451023 bytes 6 files changed, 124 insertions(+), 3 deletions(-) create mode 100644 docs/README.md create mode 100644 docs/model_flexi.md create mode 100644 docs/profiles.png create mode 100644 docs/schematic.png create mode 100644 docs/simulation comparison.png diff --git a/README.md b/README.md index b6b0de0..464c297 100644 --- a/README.md +++ b/README.md @@ -71,7 +71,7 @@ Cortex positions are modelled as a spline with a user-specified number of evenly

-Cross-cortex intensity profiles at each position around the cortex are modelled as the sum of distinct cytoplasmic and membrane signal components: +In the default model, cross-cortex intensity profiles at each position around the cortex are modelled as the sum of distinct cytoplasmic and membrane signal components: an error function and Gaussian function respectively, representing the expected shape of a step and a point convolved by a Gaussian point spread function (PSF) in one dimension:

@@ -84,8 +84,7 @@ The program learns the amplitude of these two components at each position around

-Modelling the PSF as a Gaussian, and ignoring out-of-focus contributions, is a clear simplification of reality, but is a close enough approximation for many purposes (e.g. if you're interested in relative concentrations rather than absolute concentrations). Nevertheless, one can relax these assumptions (with some added caveats) if higher accuracy is required. -See [here](/~https://github.com/tsmbland/discco). +An additional model is included that can relax these assumptions if higher accuracy is required, see [here](/~https://github.com/goehringlab/par-segmentation/tree/master/docs/model_flexi.md) ## Publications diff --git a/docs/README.md b/docs/README.md new file mode 100644 index 0000000..af11605 --- /dev/null +++ b/docs/README.md @@ -0,0 +1,64 @@ +# DISCCo: Differentiable Image Simulation of the Cell Cortex + +[![CC BY 4.0][cc-by-shield]][cc-by] +[![Black](https://img.shields.io/badge/code%20style-black-000000.svg)](/~https://github.com/psf/black) +[![pre-commit](https://img.shields.io/badge/pre--commit-enabled-brightgreen?logo=pre-commit&logoColor=white)](/~https://github.com/pre-commit/pre-commit) +[![PyPi version](https://badgen.net/pypi/v/discco/)](https://pypi.org/project/discco) + +Quantification of membrane and cytoplasmic concentrations based on differentiable simulation of cell cortex images. +Designed for use on images of PAR proteins in C. elegans zygotes. + +This extends on the segmentation and straightening algorithm described [here](/~https://github.com/tsmbland/par-segmentation), and uses straightened cortices obtained by that method as input. + +## Installation + + pip install discco + +## Methods + +Our method is adapted from previous methods that model intensity profiles perpendicular to the membrane as the sum of distinct cytoplasmic and membrane signal components (Gross et al., 2018; Reich et al., 2019). Typically these two components are modelled as an error-function and Gaussian function respectively, representing the expected shape of a step and a point convolved by a Gaussian point spread function (PSF) in one dimension. Using this model, one can generate simulated images of straightened cortices as the sum of two tensor products which represent distinct membrane and cytoplasmic signal contributions (Figure 1): + +sim = ccyt ⊗ scyt + cmem ⊗ smem + +where ccyt and cmem are cytoplasmic and membrane concentration profiles and scyt and smem are, by default, error-function and Gaussian profiles. We impose the constraint that the cytoplasmic concentration ccyt is uniform throughout each image. +

+ + Figure 1: Schematic of differentiable model for image quantification +

+
+ +Using a differentiable programming paradigm, the input parameters to the model can be iteratively adjusted by backpropagation to minimize the mean squared error between simulated images and ground truth images. +As well as allowing the image-specific concentration parameters (ccyt and cmem) to be learnt, this procedure also allows the global signal profiles scyt and smem to be optimised and take any arbitrary form, allowing the model to generalise beyond a simple Gaussian PSF model and account for complex sample-specific light-scattering behaviors. In practice we find that this additional flexibility is necessary to minimise model bias and prevent underfitting: + +

+ +
+ Figure 2: Example of ground truth and simulated images. Naive model refers to a mechanistic optical model with a Guassian PSF. Gaussian noise has been added to simulated images to allow for closer visual comparison to the ground truth image. + +

+
+ +An additional step, described in the paper, puts the cytoplasmic and membrane concentrations outputted by the model into biologically meaningful units, which has great utility for mathematical models. + +For full details of the model and training procedures, see the paper: + +[Optimized dimerization of the PAR-2 RING domain drives cooperative and selective membrane recruitment for robust feedback-driven cell polarization](https://www.biorxiv.org/content/10.1101/2023.08.10.552581v1) (preprint) + +And the accompanying [GitHub repository](/~https://github.com/goehringlab/2023-Bland-par2). + +Limitations: +- Relies on a few assumptions about the system (uniform cytoplasmic concentration, rotational symmetry) +- Requires several calibrations with a few different samples + + +## License + +This work is licensed under a +[Creative Commons Attribution 4.0 International License][cc-by]. + +[![CC BY 4.0][cc-by-image]][cc-by] + +[cc-by]: http://creativecommons.org/licenses/by/4.0/ +[cc-by-image]: https://i.creativecommons.org/l/by/4.0/88x31.png +[cc-by-shield]: https://img.shields.io/badge/License-CC%20BY%204.0-lightgrey.svg + diff --git a/docs/model_flexi.md b/docs/model_flexi.md new file mode 100644 index 0000000..8b481f1 --- /dev/null +++ b/docs/model_flexi.md @@ -0,0 +1,58 @@ +# Flexi model + + iq = ImageQuant(method='flexi') + +Quantification of membrane and cytoplasmic concentrations based on differentiable simulation of cell cortex images. +Designed for use on images of PAR proteins in C. elegans zygotes. + +This extends on the default segmentation and straightening algorithm described [here](/~https://github.com/goehringlab/par-segmentation), and uses straightened cortices obtained by that method as input. + + +## Methods + +This method is adapted from previous methods that model intensity profiles perpendicular to the membrane as the sum of distinct cytoplasmic and membrane signal components (Gross et al., 2018; Reich et al., 2019). Typically these two components are modelled as an error-function and Gaussian function respectively, representing the expected shape of a step and a point convolved by a Gaussian point spread function (PSF) in one dimension. Using this model, one can generate simulated images of straightened cortices as the sum of two tensor products which represent distinct membrane and cytoplasmic signal contributions (Figure 1): + +sim = ccyt ⊗ scyt + cmem ⊗ smem + +where ccyt and cmem are cytoplasmic and membrane concentration profiles and scyt and smem are, by default, error-function and Gaussian profiles. We impose the constraint that the cytoplasmic concentration ccyt is uniform throughout each image. +

+ + Figure 1: Schematic of differentiable model for image quantification +

+
+ +Using a differentiable programming paradigm, the input parameters to the model can be iteratively adjusted by backpropagation to minimize the mean squared error between simulated images and ground truth images. +As well as allowing the image-specific concentration parameters (ccyt and cmem) to be learnt, this procedure also allows the global signal profiles scyt and smem to be optimised and take any arbitrary form, allowing the model to generalise beyond a simple Gaussian PSF model and account for complex sample-specific light-scattering behaviors. In practice we find that this additional flexibility is necessary to minimise model bias and prevent underfitting: + +

+ +
+ Figure 2: Example of ground truth and simulated images. Naive model refers to a mechanistic optical model with a Guassian PSF. Gaussian noise has been added to simulated images to allow for closer visual comparison to the ground truth image. + +

+
+ +An additional step, described in the paper, puts the cytoplasmic and membrane concentrations outputted by the model into biologically meaningful units, which has great utility for mathematical models. + +For full details of the model and training procedures, see the paper: + +[Optimized dimerization of the PAR-2 RING domain drives cooperative and selective membrane recruitment for robust feedback-driven cell polarization](https://www.biorxiv.org/content/10.1101/2023.08.10.552581v1) (preprint) + +And the accompanying [GitHub repository](/~https://github.com/goehringlab/2023-Bland-par2). + +Limitations: +- Relies on a few assumptions about the system (uniform cytoplasmic concentration, rotational symmetry) +- Requires several calibrations with a few different samples + + +## License + +This work is licensed under a +[Creative Commons Attribution 4.0 International License][cc-by]. + +[![CC BY 4.0][cc-by-image]][cc-by] + +[cc-by]: http://creativecommons.org/licenses/by/4.0/ 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