Early changes of hepatitis B virus quasispecies during lamivudine treatment and the correlation with antiviral efficacy.J Hepatol. 2009 May;50(5):895-905.

20130701Journal

Evaluation of genomic diversity and complexityAdvice on calculation from base frequency data

A viral quasispecies is a group of viruses related by a similar mutation or mutations, competing within a highly mutagenic environment.

Hepatitis B virus (HBV)

3.2kb, double strand, circular DNA virus.HBV is the second most cause of hepatocellular carcinoma (HCC).HCC is the 3rd cause of cancer death in Japan.A nucleoside analog (lamivudine) therapy is available but we often encounter drug-resistance.

n=25

n=14

n=11

Experimental design and resultBaseline(0 week) 4 weeks

DNA cloning

ResponderLow HBV-DNALow AST, ALT

Non-responderHigh HBV-DNAHigh AST, ALT

???

What dynamic changes could occur during anti-viral therapy?

???

DNA cloning

DNA cloning

Lamivudine (anti-HBV drug)

n=14

n=11

Experimental design and result4 weeks

ResponderLow HBV-DNALow AST, ALT

Non-responderLow HBV-DNAHigh AST, ALT→ Responders were low

complexity and diversity. Non-responders were high.

↓ Responders were monoclonal. Non-responders were polyclonal.

Evaluation of quasispecies heterogeneity

complexity diversityShannon entropy (Sn) Genetic distance (d)

Synonymous substitution/site (dS or Ks)Non-Synonymous substitution/site (dN or Ka)

4/8 2/8 1/8

Evaluation of quasispecies heterogeneity

complexityShannon entropy (Sn)

𝑆𝑛=−∑𝑖

❑ 𝑝𝑖 ln𝑝𝑖

ln𝑁

𝑝𝑖

𝑁Frequency of clones in viral population

Total # of clones

p <- c(1,2,4)/8- sum(log(p)*p)/log(8)[1] 0.4583333

0 ~ monoclonal1~ polyclonal

Evaluation of quasispecies heterogeneity

diversityGenetic distance (d)Synonymous substitution/site (dS or Ks)Non-Synonymous substitution/site (dN or Ka)

Hamming distance

A A T G C T

A C T G T T Dist 2

Levenshtein distanceA A T G - C T

A C T G G T T

Transversion 1Transition 1Insertion 1(any cost can be set)

Dist 3

Evaluation of quasispecies heterogeneity

diversityGenetic distance (d)Synonymous substitution/site (dS or Ks)Non-Synonymous substitution/site (dN or Ka)

C G A

C A A

C C A

C T A

G G A

T G A

C G G

C G C

C G T

Arg(R)

Synonymous mutation

Possible dS sitesC G A

1/3 0/3 3/3

MethodsMiyata & YasunagaNei & GojoboriLiMaximum Likelihood

A G A

Evaluation of quasispecies heterogeneity

diversityGenetic distance (d)Synonymous substitution/site (dS or Ks)Non-Synonymous substitution/site (dN or Ka)

C G A

C A A

C C A

C T A

G G A

T G A

C G G

C G C

C G T

Arg(R)

MethodsMiyata & YasunagaNei & GojoboriLiMaximum Likelihood𝐿0

𝐿2All are non-synonymous.

1/3 is synonymous.

𝐿4𝐴𝑖𝐵𝑖

All are synonymous.

# of transition at

# of transversion atC G A

𝐿4𝐿0𝐿2

𝑑𝑆=𝐿2 𝐴2+𝐿4 𝐴4

𝐿2+𝐿4+𝐵4

𝑑𝑁=𝐿0𝐵0+𝐿2𝐵2

𝐿2+𝐿4+𝐴0

A G A

𝐿𝑖

𝐿𝑖

Synonymous mutation

Evaluation of quasispecies heterogeneity

diversityGenetic distance (d)Synonymous substitution/site (dS or Ks)Non-Synonymous substitution/site (dN or Ka)

C G A

C A A

C C A

C T A

G G A

T G A

C G G

C G C

C G T

Arg(R)

Synonymous mutation

MethodsMiyata & YasunagaNei & GojoboriLiMaximum Likelihood

𝑞𝑖 , 𝑗={0𝜋 𝑗

𝜋 𝑗𝜅𝜋 𝑗𝜔𝜋 𝑗𝜅𝜔

more than one mutationsynonymous transversion

synonymous transition

nonsynonymous transversionnonsynonymous transition

𝜔=𝑑𝑁𝑑𝑆

𝜅=𝑇 𝑠

𝑇 𝑣

𝑇 𝑠𝑇 𝑣

Transition rateTransversion rate

𝜋 𝑗

𝑞𝑖 , 𝑗Substitution frequency from codon i to j.

Equilibrium frequency of codon j.

𝜒2

𝐿𝑅=2 ln𝐿𝜔𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒

𝐿𝜔=1

distribution (df=1)

A G A

Clustering

Sorry!!!

n=14

n=11

Experimental design and result4 weeks

ResponderLow HBV-DNALow AST, ALT

Non-responderLow HBV-DNAHigh AST, ALT→ Responders were low

complexity and diversity. Non-responders were high.

↓ Responders were monoclonal. Non-responders were polyclonal.

Genotype estimation from frequency?

Cloning NGS

4/8 2/8 1/8

A T T G C G A T G C A C T G C T

A T T C G G A T G C G C T G C T

A T T G C G A A G C G C T G C T

?? ?? ??

A T T G C G A T G C A C T G C T

A T T ? ? G A T G C ? C T G C T

A T T G C G A ? G C ? C T G C T

A

G

C

T

0.95

0.05

0.98

0.02

0.90

0.10

Monte Carlo simulation?

Random samplingGenerate pseudosequenceRare mutation ??Linkage ??

NGS

?? ?? ??

A T T G C G A T G C A C T G C T

A T T ? ? G A T G C ? C T G C T

A T T G C G A ? G C ? C T G C T

A

G

C

T

0.95

0.05

0.98

0.02

0.90

0.10