Modelling in-vivo HIV evolutionary mutational pathways under AZT-3TC regimen through Markov Chains

Poster number: 7

M. Prosperi(1), M. Zazzi(2), A. Gonnelli(3), M. Trezzi(4), P. Corsi(5), M. Morfini(6), A. Nerli(7), M. De Gennaro(8), A. Giacometti9, G. Ulivi(1), S. Di Giambenedetto(10), A. De Luca(10)

  1. Faculty of Computer Engineering - University of Roma TRE
  2. Department of Molecular Biology - University of Siena
  3. Infectious Diseases Unit - Siena Hospital
  4. Infectious Diseases Unit - Grosseto Hospital
  5. Infectious Diseases Unit - Careggi Hospital
  6. Hematology Unit - Careggi Hospital
  7. Infectious Diseases Unit - Prato Hospital
  8. Infectious Diseases Unit - Lucca Hospital
  9. Clinical Infectious Diseases Unit - Ancona Hospital
  10. Infectious Diseases Unit – Catholic University Sacro Cuore of Rome


During most antiretroviral treatments HIV can follow different mutational pathways to develop resistance, depending on drug pressure, viral population size, fitness and replicative capacity of the resistant mutants. Knowledge about the probability and time needed to select different resistant strains, joined with pathways description, can increase confidence about long-term therapies.


  • 392 genotype-genotype consecutive pairs extracted from the ARCA data base under AZT-3TC treatment (with a backbone of NNRTIs or PIs, but not any other NRTI)

  • 18 codons considered from IAS/USA NRTI resistance list:


  • first order Markov Chain model


Mean time between two genotyping was 173 days ( 146);

Mean therapy duration was 780 days ( 499);

119 different patterns discovered among the 784 genotypes;

Complete Markov chain transition matrix estimated by relative frequencies, with time step t = 6 months;

5 states selected according to uncertainity measure on counts < 20%:

{184}; {wildType}; {70,184}; {41,184,215}; {70}; other states unified in {other}.

From the chain graph, state {184} appears to be the most conservative, followed by {wildType} and {41,184,215}, in the range 53-58%. When the mutation K70R is acquired, either with M184V or alone, chances to develop further mutations are higher. States with K70R are also antagonist with states containing M41L and T215Y (in agreement with the previously reported TAM1 vs. TAM2 patterns), while M184V can coexist with both states. From {wildType} there is 0.47 probability to accumulate other mutations, with 0.14 belonging to {184}, while there is little chance to acquire suddenly the {41,184,215} or {70,184} or {70}. Reversions to {wildType} are in the order of 0.1.

The limit of the n-th power of the transition matrix exists and the rows are identical, this means that the process is Complete Ergodic, the system state ad infinitum does not depend on the initial one.

The transition matrix T is (states are ordered as above):
0.5854 0.2439 0.0244 0 0 0.1463
0.1419 0.5743 0.0270 0.0203 0.0270 0.2095
0.0625 0.1250 0.3750 0 0.0625 0.3750
0.0667 0.1333 0 0.5333 0 0.2667
0.0909 0.0909 0.0455 0 0.3182 0.4545
0.0467 0.2200 0.0200 0.0400 0.0267 0.6467

And the n-th power of T:
0.1754 0.3294 0.0356 0.0470 0.0312 0.3813


Modelling in this way the first-order Markov chain requires a large number of states, thus leading to possible wrong estimations for the transition matrix considering the relatively small set of genotype pairs (119 different states having 392 transition pairs), so dimension reduction must be further investigated (clustering could be reasonable for conservative states, as Foulkes and De Gruttola pointed out, but not for intermediate evolution). Anyway, most and well-observed mutations and mutational pathways have been correctly detected, as the antagonisms between TAM1 and TAM2 patterns, the low fitness of 184 et cetera.

Further optimisation of such a model allows to estimate the probability of following different mutational pathways during a long-term treatment, thus increasing the physician confidence about the durability of the treatment, the most likely evolutionary pathway that the virus population will follow and the risk to develop cross-resistance.