Fitness effects of HIV mutations
Lucy Crooks
Theoretical Biology, ETH Zurich
Drug-resistance in HIV
• Combination therapy (3 drugs) most effective if resistance
mutations have negative effects under some drugs
• How mutations interact to affect fitness also has an influence
through recombination
log Fitness AB  log log Alog B 
negative epistasis can accelerate evolution

epistasis is also relevant for theories of the evolution of
sexual reproduction
Aims
• estimate the fitness effects of HIV-1 mutations
• estimate interactions between these effects
17,000 sequences
+
fitness in 16 treatments
Data
• 400 positions
• 1,800 mutations
• 180,000 pairwise interactions
complex mutational
patterns
My Approach
• randomly split interaction terms into subsets
• fit a series of models each with main effects for all mutations
• remove terms with high p-values (t-test of coefficient)
repeat until few enough interactions to fit into one model
log  log  1m1  2m2 ... k mi m j 
• GLM with variance  mean
•p-value cut-off = 0.4
• significance tested by change in deviance (p>0.05)
Approach (2)
• fit remaining terms into one model
• sequentially remove sets of terms with highest p-values
• repeat until only significant terms remain (p>0.05)
Technical details
• each model run as separate job
• fitting done in R with model matrix generated in perl
• method is iterative weighted least squares using QR
decomposition (calls fortran routine dqrls)
• 1 processor, exclusive node use
• CPU time = 5 hours
Preliminary results
fitness effects of mutations in absence of drugs
Preliminary results (2)
epistasis in the absence of drugs
Outlook
• simplify the model
• test robustness of subset approach
• repeat analysis for 15 drug treatments
• find funding!