
Poster number: 7
Background:
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 longterm therapies.
Methods:
Results:
Mean time between two genotyping was 173 days (st.dev 146);
Mean therapy duration was 780 days (st.dev 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 5358%. 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 nth 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 nth power of T:  

0.1754  0.3294  0.0356  0.0470  0.0312  0.3813 
Conclusions:
Modelling in this way the firstorder 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 wellobserved 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 longterm 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 crossresistance.
References