Title of my thesis

Your Name

Abstract

Here is the abstract: We aim to do probabilistic modeling of eigenvectors obatained from the ICE method in Hi-C analysis. The idea is to capture some of the variance lost when hard-labeleling the bins based on only the sign of the eigenvector.

This model infers A/B chromatin compartment structure from the first eigenvector (E1) of the Hi-C contact matrix using a Bayesian framework.

Goals - Replace hard sign-thresholding of E1 with a probabilistic compartment assignment. - Quantify uncertainty in compartment calls for each genomic bin. - Allow for modeling of missing E1 values due to low signal.

Assumptions - Each bin belongs to one of two latent states: A or B compartment. - E1 values are generated from Gaussian distributions specific to each compartment. - Prior belief: A has positive E1 values (μ ≈ 0.5), B has negative (μ ≈ -0.5). - Bins are initially treated as independent - Spatial depency are added later (Gaussian Random Walk)

Introduction

Chromatin architecture is of high interest in molecular biology, and increasingly so in molecular evolution. A high-throughput method for mapping the 3D organization of the genome was proposed by Lieberman-Aiden et al. (2009). Here, chromatin interactions from Hi-C sequencing is used to generate an interaction matrix of valid Hi-C contacts, and PCA is performed on the covariance matrix of the observed and expected matrix. The following rationale is proposed and experimentally supported; if clustering into 2 types (A/B compartments), genomic positions that interact will have a positive value in the covariance matrix, and vice versa for positions that do not interact. Then, when PCA is performed, the first principal component captures the variance that arise from being in different compart by its sign. The direction of the eigenvector (the sign) is then phased with a biologically relevant measure (such as GC content) to establish that the A compartment is largely the active chromatin and B is largely inactive.

Methods

Here are methods

Method 1

The first method with a code block

# Python code 
e = mc**2

print(e)

Results

Results are written here

Discussion

The discussion

Conclusion

I am concluding this analysis

Bon mot

Nothing in Biology Makes Sense except in the Light of Evolution

- Theodosius Dobzhansky

References

Lieberman-Aiden, Erez, Nynke L. Van Berkum, Louise Williams, Maxim Imakaev, Tobias Ragoczy, Agnes Telling, Ido Amit, et al. 2009. “Comprehensive Mapping of Long-Range Interactions Reveals Folding Principles of the Human Genome.” Science 326 (5950): 289–93. https://doi.org/10.1126/science.1181369.