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Reconstructing the Origin and the Diffusion of the SARS Epidemic

This example shows an analysis of the origin and diffusion of the SARS epidemic. It is based on the discussion of viral phylogeny presented in Chapter 7 of "Introduction to Computational Genomics. A Case Studies Approach" [1].

Introduction

SARS (Severe Acute Respiratory Syndrome) is a recently-emerged disease caused by a new type of coronavirus (SARS-CoV). It consists of a 29,571 base-long, single-stranded RNA and displays a characteristic spiky envelope protein that resembles a crown.

The first cases of SARS appeared in late 2002 in the Chinese province of Guangdong and grew into a major outbreak in the next few months (January through February 2003). The majority of the infected individuals acquired the disease in the Guangzhou Hospital. A doctor who had worked in this hospital traveled to Hong Kong in February 2003 and stayed at the Metropole Hotel. The doctor and a number of other hotel guests all became infected with the virus and traveled to different destinations (Vietnam, Canada, Singapore, Taiwan) carrying the disease and the virus.

By analyzing the phylogenetic relationships between the samples of SARS-CoV that were collected in late 2002 and in 2003, we can reconstruct the history of the SARS epidemic and understand how it spread throughout the world in such a short period of time.

Loading the Sequence Data of SARS Strains

We consider the nucleotide sequences of 13 strains of human SARS coronaviruses for which the location and the date of collection are known. The sequences correspond to the spike S protein, which is responsible for binding to specific receptors and is considered a major antigenic determinant. Because the Himalayan palm civet is believed to be the source of the human SARS-CoV, we also consider the sample derived from the palm civet. For the sake of convenience, the sequence data is stored in a MATLAB® structure called spike consisting of Header and Sequence fields for each viral strain. The data can also be downloaded from the GenBank® database using the accession numbers stored in the structure accNum.

% Load the genomic data for the human and palm civet SARS strains
load sarsdata.mat

% Display the accession numbers and collection dates of the sequence
% dataset.
disp('Genbank Acc. No.    Collection Date       Location')
disp(sprintf('%10s %22s %25s\n',accNum{reshape(1:42,14,3)'}))
Genbank Acc. No.    Collection Date       Location
  AY278489            DEC-16-2002               GZ 12/16/02
  AY394997            DEC-26-2002               ZS 12/26/02
  AY395004            JAN-04-2003               ZS 01/04/03
  AY394978            JAN-24-2003               GZ 01/24/03
  AY394983            JAN-31-2003               GZ Hospital
  AY304495            FEB-18-2002               GZ 02/18/03
  AY278554            FEB-21-2003        Metropole 02/21/03
  AY278741            FEB-26-2003            Hanoi 02/26/03
  AY274119            FEB-27-2003          Toronto 02/27/03
  AY283794            MAR-01-2003        Singapore 03/01/03
  AY291451            MAR-08-2003           Taiwan 03/08/03
  AY345986            MAR-19-2003        Hong Kong 03/19/03
  AY394999            MAY-15-2003        Hong Kong 05/15/03
  AY627048                                       Palm civet

Computing the Sequence Pair-Wise Distances

Obtain the distance matrix needed to build the phylogenetic tree by computing a symmetric matrix that holds pair-wise genetic distances with Jukes-Cantor corrections. Ignore sequence sites representing gaps.

JC_distances = seqpdist(spike,'method','jukes-cantor','alphabet','NT', ...
                           'indels','pairwise-delete','squareform',true);
numSeq = size(JC_distances,1);

By plotting the distance matrix, we can appreciate the presence of a subset of sequences that are more closely related to each other (central cluster, represented by the darker tones). The last sequence, which is associated to the Himalayan palm civet, is the most distant to the majority of the members of the set. This is expected because it is a nonhuman coronavirus.

figure;
imagesc(JC_distances);
colormap(bone);
colorbar;
title ('Pair-wise distances (spike protein nt sequences)');

Constructing a Neighbor-Joining Phylogenetic Tree

Using the distances computed above, construct a phylogenetic tree using the neighbor-joining method. In this case, we assume equal variance and independence of evolutionary distance estimates.

tree1 = seqneighjoin(JC_distances,'equivar',spike);
plot(tree1,'orient','left');
title('Neighbor-joining tree using Jukes-Cantor model');

The tree depicts the story of the epidemic. The early infections all occurred in Guangzhou and Zhongshan, labelled as GZ and ZS respectively. The international cases (Hong Kong, Singapore, Hanoi, Taiwan, Toronto) are all related to each other and seem to branch from the case traced back to the Metropole Hotel in Hong Kong.

Estimating the Date of Origin of the Epidemic

Because the date of collection of each SARS strain is known, we can observe the progression of the virus mutations over time. Consider the pair-wise distances according to the Kimura model, which distinguishes between transitional and tranversional mutation rates. Then, restrict your analysis to the distance of each human strain from the Himalayan palm civet's strain. Finally, plot the genetic distance versus the date of collection.

K_distances = seqpdist(spike,'method','Kimura','squareform',true, ...
                           'alphabet','NT','indels','pairwise-delete');

% sequence of the palm civet
civet = find(~cellfun(@isempty, strfind({spike.Header}, 'civet')));

d = regexp({spike.Header},'\d+/\d+/\d+','match','once');
for i = 1:numSeq-1
    % genetic distances with respect to the palm civet's strain
    scores(i,1) = K_distances(civet,i);
    % convert the collection dates into numbers
    dates(i,1) = datenum(d{i});
end

refDate = datenum('01/01/03','mm/dd/yy'); % reference date

figure();
plot(dates-refDate,scores,'k*');
ylabel('Genetic distance (relative to the palm civet)');
xlabel('Time distance from 01/01/03 (days)');
hold on;

In relation to the sequence of the palm civet, we observe that the genetic distance increases approximately in a linear manner with time. Perform a polynomial fitting and a least-square interpolation to outline the progression of the viral mutations over time and estimate the approximate date for the origin of the epidemic. The start of the infection corresponds more or less to the root of the polynomial fit, i.e., any date that is at zero genetic distance from the palm civet's sequence.

[P,S] = polyfit(dates-refDate,scores,1);
x = [-max(dates-refDate):.1:max(dates-refDate)];
[y,delta] = polyconf(P,x,S); % estimate 95% prediction interval

plot(x,y,'b-');
plot(x,y+delta,'r-',x,y-delta,'r-'); % confidence interval
line([-max(dates-refDate) max(dates-refDate)],[0 0],'LineStyle', ':');
title('Estimate of origin of SARS epidemic');


originDist=roots(P);% estimated distance between origin and reference date
estimated_origin = datestr(floor(originDist+refDate))
% dates(civet)=originDist+refDate;
plot(originDist, 0,'*b');
annotation(gcf,'textarrow', [0.245 0.245], [0.30 0.35], ...
           'String', {'estimated origin'}, 'color', [0 0 1]);
estimated_origin =

17-Sep-2002

Rerooting the Phylogenetic Tree

Because the disease caused by the novel strain of human SARS-CoV appears to have originated in the palm civet, we can assume that the location of the root for the human strains' phylogenetic tree is next to the node associated with the Himalayan palm civet.

civetNode = getbyname(tree1,'civet');
tree2 = reroot(tree1,civetNode,0);
plot(tree2,'orient','left');
title('Rerooted Neighbor-joining tree using Jukes-Cantor model');

The rerooted tree better illustrates the progression of the SARS epidemic. Starting with the early infections in the Guangdong province in 2002 (GZ 12/16/02 and ZS 12/26/02), the virus spread in the Guangzhou Hospital in early 2003 (GZ Hospital 01/31/03) and reached Hong Kong via the doctor who worked in the mentioned hospital and who stayed at the Metropole Hotel (Metropole 02/21/03). The virus was then carried across the borders via infected guests of the Metropole Hotel.

Observing the Phylogenetic Tree as It Builds

Assuming that the samples represent the SARS coronavirus at different points in time, we can observe the virus evolution as the phylogenetic tree (built on the basis of genetic distances) is created. We can simulate the various steps in the tree reconstruction. The movie function animates the tree building process.

d = regexp({spike.Header},'\d+/\d+/\d+','match','once');
d{end} = datestr(estimated_origin, 'mm/dd/yy');
allDates = datenum(d);
[dummy,order] = sort(allDates); % sort according to collection date

for i = 2:numSeq
    sp = order(1:i);
    tr1 = seqneighjoin(JC_distances(sp,sp),'equivar',spike(sp));
    tr2 = reroot(tr1,getbyname(tr1,'civet'),0);
    h = plot(tr2,'leaflabels',true,'terminallabels',false);
    h1 = findobj(h.leafNodeLabels,'string',spike(sp(i)).Header);
    h1.Color = 'r';
    axis([-.0002 .0045 0 15])
    fs(i-1) = h.axes.Parent;
    M(i-1) = getframe(fs(i-1));
end
close(fs) % close figures
% movie(figure,M,1,1) % <== uncomment this line to play the animation

Visualizing the Diffusion of the Virus via a Directed Graph

We can also visualize the diffusion of the virus using a directed graph, where each node represents an infected individual and weights of edges are associated to the genetic distance between sequences. First, create an adjacency matrix based on the date of collection of the samples, such that possible paths run through nodes that are compatible in terms of the collection dates. Then, use the previously computed Jukes-Cantor distances to assign weights to the edges between nodes. And finally, determine the shortest path from the node associated with the palm civet and every other node.

 % adjacency matrix based on collection dates
gValid = bsxfun(@lt,allDates,allDates');
% weight matrix for the graph
g1 = sparse((gValid .* JC_distances));

% find shortest paths from civet node to all nodes
[dist,paths,pred_tree] = graphshortestpath(g1,civet);
% create adjacency matrix for the winning shortest path
g2 = sparse(pred_tree(1:13),1:13,1,14,14).*g1;
% plot the graph
spikeGraph = view(biograph(g2,{spike.Header}));

% nodes relative to Guangdong province (GZ and ZS)
guangdong = find((~cellfun(@isempty, strfind({spike.Header}, 'GZ'))) |...
    (~cellfun(@isempty, strfind({spike.Header}, 'ZS'))));
% node relative to the Metropole Hotel
metropole = find(~cellfun(@isempty, strfind({spike.Header}, 'Metropole')));
% node relative to the Guangzhou Hospital
hospital = find(~cellfun(@isempty, strfind({spike.Header}, 'Hospital')));

% highlight some of the important nodes
set(spikeGraph.Nodes(civet),'Color',[1 1 1]) % white (palm civet)
set(spikeGraph.Nodes(guangdong),'Color',[1 .7 .7]) % pink (Guangdong)
set(spikeGraph.Nodes(metropole),'Color',[0.8 0.8 1]) % lavander (Metropole Hotel)
set(spikeGraph.Nodes(hospital),'Color',[1 0.3 0.3]) % red (GZ Hospital)

This graph highlights the crucial role played by some of the infection events:

  • The Himalayan palm civet is the source of the infection

  • The Metropole Hotel is the root of the branching for the international epidemic

  • The Guangzhou Hospital represents the bridge connecting the province of Guangdong (GZ and ZS) and the Metropole Hotel in Hong Kong.

References

[1] Cristianini, M. and Hahn, M.W. "Introduction to Computational Genomics: A Case Studies Approach", Cambridge University Press, 2007.

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