Lecture notes. Written from the material of MIT 8.592J, licensed CC BY-NC-SA 4.0. These are notes, not a transcript: the material has been reorganised and rewritten. This adaptation carries the same licence, and the original is linked above.
5. The Charge Environment of the Cell¶
What this covers¶
This is the opening lecture of the structural half of the course. It states why the physics of charge, not just sequence, has to enter the story of a biomolecule, and it introduces the two pictures the course builds on: the electrostatic environment inside a cell, and the geometry for computing the field of a charged membrane. It assumes only elementary electrostatics — Coulomb's law and the idea of a surface charge density. The material supplied for this lecture is short — one slide of text and two hand-drawn figures — and this chapter says only what they contain.
From sequence to structure¶
The information a living system needs to reproduce itself is carried in the sequence of its macromolecules. But that sequence only does anything once it is turned into a physical structure — a folded protein, a wound strand of DNA, a bounded cell — and the forces that do the turning are physical forces. Identifying which forces matter, and how they act, is the subject of this half of the course.
Coulomb interactions as the relevant force¶
Of the fundamental interactions, only the electromagnetic one matters at the scale of a cell: gravity is far too weak, and the nuclear interactions do not reach beyond the nucleus of an atom. So every force that shapes a macromolecule of life is some manifestation of the Coulomb interaction between electrons and nuclei — the strong covalent bonds that hold together the primary chain of a molecule, and the weaker hydrogen bonds. The slide's text breaks off mid-sentence immediately after naming hydrogen bonds, so whatever the lecture went on to list — presumably further electrostatic effects such as interactions between charged side groups, or effects mediated by the solvent — is not part of the material supplied for this chapter.
The charge environment of the cell¶
The first figure, captioned "the 'charge environment' of the cell is quite complicated," makes the electrostatic picture concrete. A cell, bounded by its membrane, contains large charged molecules — macroions — such as DNA and folded proteins. The figure sorts macroions into two kinds: an "acid," a macroion such as DNA whose backbone has given up protons and so carries a fixed negative charge, and a "polyampholyte," a macroion such as a protein whose different side groups can carry positive or negative charge, so that the molecule as a whole is a mix of both. Around a charged macroion, small mobile ions of the opposite sign accumulate; the figure labels this local screening layer a "neutralizing cloud." The rest of the cell's interior is not empty either: it holds dissolved salt (the figure lists the cations Na⁺, K⁺, Mg²⁺ and the anion Cl⁻), which dissociates into free ions that can move to screen any charge in the cell. The point of the figure is that a macromolecule's charge is never isolated — it always sits inside a bath of mobile counterions and salt.
Setting up: a charged membrane¶
The second figure turns from this qualitative picture to a specific calculation. It is headed "Solution for a membrane with a uniform surface charge," and gives the surface charge density as
a single electronic charge \(-e\) spread over an area \(d^2\). Above the plane it places a charge
i.e. a singly-charged cation, at some height along a \(y\)-axis perpendicular to the membrane. This is as far as the supplied material goes: the figure establishes the geometry — a uniformly charged plane and a point charge held above it along \(y\) — but the field or potential that the heading promises is not part of the text or figure supplied for this lecture.
Sources¶
- Slides:
computational-biology/mit-ocw/8592j/lectures/09-slides.md, "2 Structure", section 2.1 "Coulomb interactions", together with both figures extracted from the same slide deck (09-slides/figures/p002-1.png, the cell's charge environment;09-slides/figures/p005-1.png, the charged-membrane geometry). This markdown is itself a model's reconstruction of a PDF slide deck that has no text layer, and its own banner flags that "every equation is unverified" and that the prose is a paraphrase in places; the running text is quoted here as supplied, and it breaks off mid-sentence after "...the weaker hydrogen bonds (" — the original lecture evidently continued past this point, but that content was not part of the material supplied for this chapter. - No transcript, written notes, or exercises were supplied for this lecture.
- Course: MIT OpenCourseWare 8.592J, Statistical Physics in Biology (Spring 2011).
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