COILS

The coils program is based on scoring tables $S^h(a)$ that are used to compute the probability score for each segment of a protein sequence (see [1]), and some parameters that define Gaussian probabilities. Then the main parameters are:

• $\mu_{cc}, \mu_{g}$ the average scoring values of the coiled-coil and globular protein sets;
• $\sigma_{cc}, \sigma_{g}$ the standard deviation of the scoring values for the coiled-coil and globular protein sets;
• $S^h(a)=$ the score for the residue type $a$ in the heptad position $h$ (from 1 to 7).

So that the probability of a coiled-coil segment of length $W$ starting at position $i$ in a given sequence is computed as

$$Pr_i=\frac{G_{cc}}{G_{cc}+c\cdot G_{g}}$$ (1)

where $c$ is the bias for the most abundant globular class ($g$) and $G_{cc}$ and $G_{g}$ are defined as

$$G_{cc}=\frac{1}{\surd{2}\sigma_{cc}}e^{-\frac{(x_i-\mu_{cc})^2}{\sigma_{cc}^2}}$$ (2)

$$G_{g}=\frac{1}{\surd{2}\sigma_{g}}e^{-\frac{(x_i-\mu_{g})^2}{\sigma_{g}^2}}$$ (3)

The score $x_i$ is computed using the matrix $S^h(a)$ ([1]) along the segment $W$ starting at position $i$ as

$$x_i=(\prod_{h=1}^W f(a_{i+h},h)^{e_h})^{1/N}$$ (4)

where $e_h$ is the exponential weight of the position $h$ (if not weighted is simply $e_h=1$) and $N$ is the normalization factor $N=\sum_{h=1}^W e_h$. The function $f$ is in the case of COILS program is simply

$$f(a_{i+h},h)=S^h(a_{i+h})$$ (5)

where $S^h(a_{i+h})$ is the element of the COILS scoring table accounting for the residue type $a_{i+h}$ in the $h^{th}$ heptad position.