Thus, with mutation data from enough patients, it is possible to identify driver pathways without an estimate of the passenger mutation probability q.
In practice, any test that identifies driver genes by recurrent mutations requires a good estimate of the passenger mutation probability q.
For example, we assume a constant passenger mutation probability q across all genes, but models that allow q to vary by gene would be useful in applications and warrant further investigation.
Single-point mutants form during infection of a target cell x by wild type (WT) drug-susceptible virus v WT, due to reverse transcription with a per-position mutation probability q.
Theorem 1 shows that in the D > P model an estimate of the passenger mutation probability q and a sufficient number of patients are enough to identify the driver genes.
In this section we analyze a method that identifies the set of driver genes with no prior information on the passenger mutation probability q, and works for both the D > P and D=P models.
To compare the performance of the two algorithms, we measured the minimum number of patients required to detect the driver pathway over a range of estimates of the passenger mutation probability q.
Corollary 1 shows that with sufficient number of patients the set can be identified by finding the set of maximum weight, without an estimate of the passenger mutation probability q We previously showed in [ 11] that with an arbitrary mutation distribution identifying the set of maximum weight is NP-Hard.
In matrix notation, the quasispecies Equation 1 becomes p ˙ (t ) = Q T diag (f ) p (t ) − φ (p (t ), f ) p (t ) (2 with p = (p 1, …, p m ) T ∈ Δ m − 1 = { (x 1, …, x m ) T ∈ ℝ + m | ∑ i = 1 m x i = 1 }, the (m − 1 -dimensional probability simplex, average fitness φ(p(t), f) = p ⋅ f, and mutation probability matrix Q = (q ij).
This approach assumes a prior knowledge or a good estimate of the passenger mutation probability, the parameter q in our models.
