The Sulston score is an equation used in DNA mapping to numerically assess the likelihood that a given "fingerprint" similarity between two DNA clones is merely a result of chance.
That is, low values imply that similarity is significant, suggesting that two DNA clones overlap one another and that the given similarity is not just a chance event.
The name is an eponym that refers to John Sulston by virtue of his being the lead author of the paper that first proposed the equation's use.
[1] Each clone in a DNA mapping project has a "fingerprint", i.e. a set of DNA fragment lengths inferred from (1) enzymatically digesting the clone, (2) separating these fragments on a gel, and (3) estimating their lengths based on gel location.
For each pairwise clone comparison, one can establish how many lengths from each set match-up.
Consequently, two fragments whose lengths match may still represent different sequences.
The problem is instead one of using matches to probabilistically classify overlap status.
Biologists have used a variety of means (often in combination) to discern clone overlaps in DNA mapping projects.
While many are biological, i.e. looking for shared markers, others are basically mathematical, usually adopting probabilistic and/or statistical approaches.
The Sulston score is rooted in the concepts of Bernoulli and binomial processes, as follows.
measured fragment lengths, respectively, where
Thus, for a given comparison between two clones, one can measure the statistical significance of a match of
fragments, i.e. how likely it is that this match occurred simply as a result of random chance.
Very low values would indicate a significant match that is highly unlikely to have arisen by pure chance, while higher values would suggest that the given match could be just a coincidence.
These two lengths are arbitrarily selected from their respective sets
We assume that the gel location of fragment
Now, let us expand this to compute the probability that no length on clone
This can be restated verbally as: length 1 on clone
Since each of these trials is assumed to be independent, the probability is simply Of course, the actual event of interest is the complement: i.e. there is not "no matches".
This event is taken as a Bernoulli trial having a "success" (matching) probability of
However, we want to describe the process over all the bands on clone
is constant, the number of matches is distributed binomially.
observed matches, the Sulston score
In a 2005 paper,[2] Michael Wendl gave an example showing that the assumption of independent trials is not valid.
So, although the traditional Sulston score does indeed represent a probability distribution, it is not actually the distribution characteristic of the fingerprint problem.
Wendl went on to give the general solution for this problem in terms of the Bell polynomials, showing the traditional score overpredicts P-values by orders of magnitude.
(P-values are very small in this problem, so we are talking, for example, about probabilities on the order of 10×10−14 versus 10×10−12, the latter Sulston value being 2 orders of magnitude too high.)
This solution provides a basis for determining when a problem has sufficient information content to be treated by the probabilistic approach and is also a general solution to the birthday problem of 2 types.
A disadvantage of the exact solution is that its evaluation is computationally intensive and, in fact, is not feasible for comparing large clones.
[2] Some fast approximations for this problem have been proposed.