James X. Li

Ideally t-SNE embedding grows, during its learning process, from a tine spot to a short bar that then elongates, splits and expands to a cluster of various shapes with gradient boarder. The following is an embedding of 6K proteins based on their 3D coordinates:

Protein Atlas with t-SNE: We can vectorize amino-acid chains with Fourier-Transform and embed them with t-SNE into 2D space. Here is a map of ca. 100K AA-chains. The map reveals the similarity between the 3D structures.

UnFolding protein with t-SNE: The following video clip shows the 3D structure of a protein complex (6EMK, rcsb.org/3d-view/6EMK). The t-SNE embedding shows clearly the C2 symmetry between upper and lower halves.

t-SNE for un-folding protein 3D structure: When we add the sequential index as the forth dimension to the 3D coordinates of polypeptides, t-SNE can produce 2D maps which unfold their 3D structures; and reveal more sub-clusters with their distinguished shapes.

t-SNE for 2D protein maps: In order to facilitate the exploration of 3D folding structure of protein polymers, we can use t-SNE to create 2D maps for protein polymers. Here are the steps:

t-SNE & scRNA-seq analysis: From expression matrix to network of dominant & pilot genes. Labeling cell clusters with dominant genes; and labeling links between them with pilot genes we get a network that indicates the major variation of gene expressions.

t-SNE & scRNA-seq Analysis: t-SNE embedding annotated with dominant genes offers an effective way for comparative study of cell groups. The following video shows the basic steps:

If you run t-SNE with large perplexity, say 0.2*N, you can get almost a "perfect" embedding. Mapping the 3D sphere to 2D plane was the defining feature of t-SNE that drove my attention to it.

t-SNE for ribosome gene (rRNA) expression: t-SNE embedding forms cell clusters with 1 to 3 dominant genes; and neighboring clusters often differ only on 1 or 2 dominant genes. Annotating links between clusters by those differences leads to a kind of directed correlation-graph:

This example shows also the importance of the perplexity parameter for t-SNE. The following maps show the t-SNE embeddings with perplexity running from 4000 to 50. It is clear that the resulting maps gradually lost large part of local and global structural information.

t-SNE & MT genes (Continued): Restricting the gene-set to 4 genes we obtain a cluster map with more details: a kind of "fiber" patter which indicate 1 to 3 co-regulated characteristic genes. Moreover, all "fibers" point roughly to a common low expressed region.

Further study shows that these clusters are mainly formed by 3 differently expressed genes, ATP8, ND4L and ND6. More interestingly, clusters are arranged in a way that minimizes changes between neighboring clusters; and that leads to a kid of Gray encoding of the clusters.

t-SNE & MT genes: t-SNE maps of scRNA expression of mitochondrial genes reveal remarkably uniform structure across different tissues and cells; and t-SNE embeddings clearly outperform PCA for discerning these cluster structures.

Profiling scRNA expressions with t-SNE: When restricted to subsets of biologically similar genes, high-fidelity t-SNE can capture a plethora of embeddings with amazingly fine structures:

With a little larger perplexity, you can get clean embedding with t-SNE too. This example demonstrates clearly the importance of large perplexity.