Past exam of the biological physics course of the University of Oxford / 2018 / 6

PALM separates emitters in time. A sparse subset of photoactivatable or photoconvertible labels is switched on so that its diffraction-broadened images can be fitted individually; repeated activation, imaging and localization builds a map from many isolated detections. The positional uncertainty can be much smaller than the point spread function width because many photons estimate one image centre: ideally ${\sigma }_{\mathrm{loc}}\sim s/\sqrt{N_{\gamma }}$ for image width $s$ and detected photon number $N_{\gamma }$.

That is fluorescence localization precision, not automatically the structural resolution of the reconstructed cell. Pixelation, background, imperfect optics, drift, label linkage, blinking and labelling density matter. Repeated localizations of one molecule cannot fill unlabelled gaps; a crowded frame with overlapping images cannot simply be treated as many isolated emitters. For a static structural map, the structure must remain sufficiently stable while the many frames are accumulated, or its time dependence must be reconstructed explicitly.

For mobility in living cells, keep activated proteins observable for successive frames and link isolated positions into trajectories before bleaching. Repeating this for successive sparse subsets yields many trajectories without making the entire protein population simultaneously fluorescent. This is the sptPALM strategy.^[ref]

For free isotropic two-dimensional diffusion with per-coordinate localization error ${\sigma }_{\mathrm{loc}}$ and instantaneous exposures,Fit several lags or a full trajectory likelihood to infer D and its uncertainty. Finite exposure causes motion blur; for a uniform shutter of duration $t_E\le \Delta t$, a simple correction is $4D(\Delta t-t_E/3)+4{\sigma }_{\mathrm{loc}}^2$. Confinement, directed motion and switching binding states change the lag dependence. Short tracks, missed detections and false linking in crowded regions can mimic apparent heterogeneity, so mobility classes require explicit measurement-error and tracking controls. A trajectory map recovers dynamics; it is not identical to a static PALM density map.

The RNA world hypothesis proposes an early stage in which RNA-like molecules carried heritable sequence information and also performed important catalytic functions, before the present division of labour among DNA, RNA and proteins. Complementary base pairing supplies a route to template-directed information copying, while sequence-dependent RNA folding can create catalytic structures. This helps address the apparent circularity of requiring protein enzymes to copy genes whose expression already requires an elaborate protein-synthesis apparatus.

Modern biology supplies evidence for the necessary capacities. Ribozymes catalyse reactions, and self-splicing introns demonstrate RNA-dependent processing without a dedicated protein enzyme for that chemistry. The ribosome's peptidyl-transferase centre is built principally from RNA, with catalytic geometry located in its RNA core; structural work provides direct evidence that this central protein-synthesis chemistry is RNA based.^[ref] RNA also remains central as messenger, adaptor and regulatory material. These observations make RNA catalysis and information storage physically plausible rather than assuming that all catalysts must be proteins.

They do not prove a complete historical sequence. A viable early system still needs plausible nucleotide supply and activation, polymerization, template copying with sufficient fidelity, product-strand separation, compatibility of catalytic and copying conditions, an energy source and some means of maintaining useful combinations. RNA's chemical lability and the challenge of separating paired products are constraints, not details supplied automatically by base pairing. The first hereditary chemistry might also have involved related polymers or cooperative RNA–peptide systems rather than an exclusively RNA organism.

The later advantages of DNA as a relatively stable storage medium and proteins as catalysts with chemically varied side chains help explain the present division of labour. The hypothesis is therefore a testable family of evolutionary scenarios supported by molecular capabilities and biological relics, not a direct observation of prebiotic life or proof that an isolated modern RNA already self-replicates autonomously.

A stable native conformation is favoured when its Gibbs free energy, including the protein and its surrounding solvent, is lower than that of competing conformational ensembles under the specified conditions:Folding greatly reduces the chain's conformational entropy, an unfavourable contribution. It can nevertheless gain favourable hydrogen-bonding and packing interactions, van der Waals contacts, screened electrostatic interactions and solvent free energy. In aqueous globular proteins, burying nonpolar surface reduces the cost of exposing it to water; the hydrophobic effect is not an extra covalent attraction between all hydrophobic residues. Hydrogen bonds and ionic contacts must be judged relative to the interactions those groups made with solvent before folding, so merely counting bonds in the folded structure does not determine stability.

The protein primary structure determines which contacts and protein secondary structures can cooperate. A free-energy landscape biased towards compatible contacts permits many routes towards the native ensemble, rather than an exhaustive random search through every conformation. Folding funnels describe this bias, while barriers explain metastability and folding rates. Reversible denaturation/refolding experiments show that some proteins can recover native structure and activity when suitable conditions are restored, supporting a sequence-encoded thermodynamic tendency without asserting that every protein folds unaided.

“Stable” means an equilibrium preference and a useful lifetime, not one perfectly rigid shape. Native proteins fluctuate and can have several functional conformations; the unfolded ensemble remains populated with relative weight depending on its full free energy. Changes of temperature, pH, salt, solvent, ligands or pressure alter the balance, and molecular chaperones can prevent protein aggregation or assist kinetic access without supplying a different primary sequence. Membrane proteins require their appropriate environment, and intrinsically disordered proteins need not possess one stable folded state in isolation.

Thus a released stretched chain can gain configurational entropy on first recoiling yet later favour a more ordered native structure because the total free energy balance, including solvent, is different. Equilibrium stability, barriers to unfolding and resistance to irreversible protein aggregation are distinct properties. The existence of a native minimum alone does not guarantee rapid, reversible folding under every experimental condition.