MDS with T-cell epitope as input for antigenic map

[JianiC]

Ancestral Sequence reconstruction

Benefits for Beast https://groups.google.com/g/beast-users/c/P4_buh3u_5A

a pilot test with Smith.et.,al data

1. EPICC score was calculated only with the shared epitopes
2. n*n matrix was visualized with MDS and the compressed MDS data were used in the K-means Clustering Try with K=10 based on different methods to find the optimal number of K
3. pair with Phylogenetic tree with same sequences

   Do not really observed monophylatic cluster on the phylogenetic tree, but seems there are some genetic diversity accumulate within the immune-cluster???

   

4. the distance to the reference sequence (BI_16190_68 used in Smith Paper) was measured form the MDS with straight line distance between points. MDS is used to covert similarly to dissimilarity, with EPICC estimate itself, the latest esolate has less similar to the reference, but not same after using MDS method to get the distance? ref: EPICC (similarly) estimate against BI_16190_68 Try to find the optimal number of cluster used for K-means cluster

[JianiC]

Edit:

1. Normalize the input: Shared epitope content *2/(epitope content i+ epitope content j), so the input is the proportion of shared T-cell immunity between two strains
2. change the equation to calculate distance : There are many different ways to convert a similarity or dissimilarity into the distance. By default with mds <-data %>% dist() %>% cmdscale(k=2) where distance is calculated with euclidean distances between the rows ( shortest distance between two point)

Now, I treat the similarity proportion as a correlation matrix where corr=sqrt(data) dist = sqrt(2*(1-corr)) where the percentage of shared variance is represented by the square of the correlation coefficient, r2

3. I also try with less number of clusters, however, there still seems some problems, maybe other cluster methods need to be considered.

I could at least observe the gradual evolution of the T-cell immunity now, similar to Smith paper Next: Try with RSV, also ask for comments with these calculations

[JianiC]

New version

Simplify the dist calculation : dist=1-similarity

In smith paper, they also adjust the cluster determined from k-means to manually make it match the phylogeny

from a T-cell immunity mds plot color by antigenetic cluster defined by Smith paper

[JianiC]

3 D map cluster

still can not separate all of the cluster, but seems to be helpful

[JBahl]

Hmm - can you add a fourth dimension? Year of isolation?

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3 D map cluster

still can not separate all of the cluster, but seems to be helpful [Screen Shot 2020-11-02 at 4 11 23 PM]https://user-images.githubusercontent.com/47227610/97919820-72fbcf00-1d26-11eb-8786-3c6f1a1d783d.png

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[JianiC]

not a real 4d plot, but the color has been used as legend

[JianiC]

alternatively try to build mds with euclidean distances

difference compared with n*n matrix

with n*n comparasion, the distance was just calculate with 1- similarity, to correct what I have done it is not mds, it is just PCA Maybe for my RSV research, try to use the clade represent sequence in RSV ??? Here, the cross-immunity to each sequence was take as a features, and the relative distance between each strains were calculated using euclidean distance algorithm, (minimal length between each point) locations of the vaccine strain were added

new issue, the T-immunity distance do not follow linear clock signal

To address the comments from Friday meeting

K-means: to further evaluate the quality of the clustering

1. Elbow method : minimize total within-cluster sum of square 2.Average Silhouette Method: maximize the average silhouette values
2. gap statistics: total intracluster variation for different values of k with their expected values under null reference distribution of the data

Density based clustering rationale: k-means: severely affected by the presence of noise and outliers in the data. But for MDS, classification should be used K-means, because k-means is also based on euclidean distance