I just realised that so far it's been quite math heavy. So now for something different, inspired by Molecular Biology of the Cell (Alberts et. al), 5th edition.
Cells rely on different gradients (voltage, concentration) to drive processes. The gradients are maintained by active and passive transport across the membranes. K+ leak channel takes care of a part of them. The cool bit is in its selectivity - this channel conducts K+ 10000 times better than Na+, while both ions are almost uniform spheres of similar diameter.
Firstly, the channel is selective for cations by the virtue of negatively charged amino acids at its entrance. Then there is a maximum size limit of how fat of an ion can fit through, the skinny ones make it past the first hurdle into the vestibule. But how do you make sure smaller cations do not slip by?
All cations are associated with the polar water molecules. To get through the vestibule, the ion has to shed the water molecules. For K+, this is exactly balanced by bonds created with carbonyl oxygens. Na+, however, is too small to create the bonds, thus it is energetically unfavorable for it to pass on from the vestibule. Neat!
It is in fact a specific conformation of the channel filter that is vital for preventing sodium conduction, not just ion size. Chloride channels use the same principle to maintain anion selectivity although constructed differently- mainly using charged residues on the ends of the alpha helix for ion stability inside the membrane and filters containing multiple ions to mediate conduction.
ReplyDeleteI should have been more specific - I was just talking about the potassium leak channel. Then that specific conformation is highly selective for potassium conduction because of the ion size - the charges are identical, and there are no more distinguishable characteristics for the atom.
ReplyDeleteNow let's see you comment math :) And good luck in warm place! Hope I can read more bio stuff tomorrow..
Fair enough, while we're on the topic of ion channel selectivity:
ReplyDeleteI came across this paper Shrivastava et al. Biophysical Journal 2002 83:633 where they dissected differences in interactions of the bacterial potassium channel (KScA) as a selectivity filter for K+ compared with Na+ ions using molecular dynamics simulations- In particular, differences in K+ ions and water molecules within the filter where they undergo concerted single-file motion during translocation between adjacent sites within the filter on a nanosecond timescale. In contrast, Na+ ions remain bound to sites within the filter and do not exhibit translocation on a nanosecond timescale. The molecular interactions with the channel also differs- K+ ions prefer to sit within a cage of eight oxygen atoms of the filter, whilst Na+ ions prefer to interact with a ring of four oxygen atoms plus two water molecules. All these differences in interactions in the selectivity filter contribute to the selectivity of KcsA for K+ ions 1. the differences in dehydration energy between K+ and Na+
2. the block of KcsA by internal Na+ ions. In the simulations, the selectivity filter exhibits significant flexibility in response to changes in ion/protein interactions, with greater distortion induced by Na+ than by K+ ions.
Biology is the new physics for mathematicians. I know I'm treading a landmine here :>
Nah, I don't see mathematicians take over biology. Theoretical physics is math, and some of the most advanced math there is. But any modelling in biology is only good for generating new hypothesis and questioning the underlying assumptions. I don't see where a de novo theory would come from that would explain a big bit of biology, so I can only see mathematical models fail (and be instructive as to why they fail), and describe what we already know in a rigorous model, hopefully leading for something that can be checked in the lab.
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