Authortwheeler

Let’s stop being sloppy about uncertainty

Let’s draw a line. Across the calendar, I mean. Let’s all pledge that from today on we’re going to give honest accounting of the uncertainty in our data. I mean ‘honest’ in the sense that if someone tried to reproduce our data in the future, their confidence interval and ours would overlap.

There are a few conceptual issues to address up front. Let’s set up our discussion in terms of some variable q which we measure in a molecular dynamics (MD) simulation at successive configurations: q_0, q_1, q_2, and so on. Regardless of the length of our simulation, we can measure the average of all the values \overline{q}= \displaystyle\sum_{i=1}^{M} q_i. We can also calculate the standard deviation σ of these values in the usual way as the square root of the variance. Both of these quantities will approach their “true” values (based on the simulation protocol) with enough sampling – with large enough M.

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What I have against (most) PMF calculations

Such a beautiful thing, the PMF. The potential of mean force is a ‘free energy landscape’ – the energy-like-function whose Boltzmann factor exp[ -PMF(x) / kT ] gives the relative probability* for any coordinate (or coordinate set) x by integrating out (averaging over) all other coordinates. For example, x could be the angle between two domains in a protein or the distance of a ligand from a binding site.

The PMF’s basis in statistical mechanics is clear. When visualized, its basins and barriers cry out “Mechanism!’’ and kinetics are often inferred from the heights of these features.

Yet aside from the probability part of the preceding paragraph, the rest is largely speculative and subjective … and that’s assuming the PMF is well-sampled, which I highly doubt in most biomolecular cases of interest.

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Biology for quants, again. Required reading, Part 2.

“Proteins don’t know biology” is one of those things I’m overly fond of saying. Fortunately, it’s true, and it gives quantitative folks a foot in the door of the magical world of biology. And it’s not only proteins that are ignorant of their role in the life of a cell, the same goes for DNA, RNA, lipids, etc. None of these molecules knows anything. They can only follow physical laws.

Is this just a physicist’s arrogance along the lines of, “Chemistry is just a bunch of special cases, uninteresting consequences of quantum mechanics”? I hope not. To the contrary, you should try to see that cells employ basic physics, but of a different type than what we learned (most of us, anyway) in our physical sciences curricula. This cell biophysics is fascinating, not highly mathematical, and offers a way of understanding numerous phenomena in the cell, which are all ‘special cases’ … but special cases of what?

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