Video 1-6: Real Spectra

0:04 I'd like to finish this first part with a few remarks on what we did not actually achieve. Uh if you look at where we came from, take mass spectrometry to uh sequence a protein. Uh what you're really starting with looks rather more like this. So you have on the x-axis the different remember it's molecular weight but actually it's a weight divided by charge ratio that you see because we have these ionized particles that then the magnetic field uh pulls in a certain direction and depending how much impulse they have they go a long white curve or a shorter curve. uh but the magnetic field also pulls stronger if they are more charged. So that's one issue and this is a lot of mess because some of these peaks are clear and distinct but then there's not so obvious uh a threshold where you want to say this is still a peak and this is just noise.

1:06 Uh if you take this this is a concrete example from this um bioinformatics algorithms book. So it's a it's an an actual molecule where where they got the data from. If you look at the values of the peaks that are visible and take generously most of them, then you get these numbers. And if you round them, then the bold ones correspond to real numbers that you would expect for this protein to see. And the other 2/3 are just uh noise or contamination or things you don't actually uh should expect for this molecule. And what we were working with is the ideal spectrum where you get every position you get a a fragment and you can measure the weights exactly. So there's a bunch of complications that mean the algorithm that we developed can't be applied directly because we had a yes no procedure, right? we accepted the perfect ideal spectrum and uh if there was some measurement error or one of these peaks got lost we would just tell the user n can't do it your fault.

2:18 It's uh uh in this case not very useful. So what you have to do instead is uh tweak the algorithms so that they don't insist on having an exact solution but find uh a candidate sequence of of weights that matches best the spectrum that you have. That makes the problem a tiny tad more spicy still. But I decided um we're going to stop here. The clean version was already an exponential time problem from the looks of it even if unproven. So for this real version, you can't expect to have a very efficient solution and you might even have to give up correctness in the sense that you find the exact best solution according to some criterion and then um people work with huristics and try to doublech checkck the results with external techniques.

3:29 I guess the lesson should just be uh you have to uh not just learn the algorithms but also see where they make assumptions and how that can fail and how the results you get might have to be double checked. And ideally, of course, you can work around the restrictions and improve the algorithms.