Constant gap weight model

The simplest choice is the constant gap weight, where each individual space is free, and each gap is given a weight of W_s independent of the number of spaces in the gap. Letting $\sigma$ denote the weights of match and mismatch only ( ${\sigma(x, -) = \sigma(-, x) = 0}$ for every character x). Thus we have to find an alignment that maximzes:

$$\Sigma \sigma(S'_{i}, T'_{i})+ W_{g} \times \char93 gaps$$

where S' and T' represent S and T after inserting space. A generalization of the constant gap weight model is to add a weight W_s for each space in the gap. In this case, W_grepresents the cost of starting a gap, and W_s represents the cost of extending the gap by one space.This leads us to the affine gap weight model. This is called affine gap weight model because the weight contributed by a single gap of length q is given by the affine function W_g + q W_s. The constant gap weight model is simply the affine model with W_s = 0 . Thus we have to find an alignment that maximizes:

$${\Sigma \sigma(S'_{i}, T'_{i}) + W_{g} \times \char93 gaps + W_{s} \times \char93 spaces}$$

while S' and T' represent S and T after inserting space and ${\sigma(x, -) = \sigma(-, x) = 0}$ for every character x.

It has been suggested that some biological phenomena are better modeled by a gap weight function where each additional space in a gap contributes less to the gap weight than the preceding space. In other words, a gap weight that is a convex, but not affine function of its length. An example is the function $W_{g} + {\log q}$, where q is the length of the gap. Finally, the most general gap weight that might be considered is the arbitrary gap weight, where the weight of a gap is an arbitrary function ${\omega(q)}$ of its length q. The constant, affine and convex weight models are ofcourse restricted cases of the arbitrary weight model.