Past exam of the biological physics course of the University of Oxford / 2015 / 8

A time-calibrated phylogenetic tree combines evidence about ancestry with evidence about elapsed time. First identify homologous RNA or protein sequences, preferably orthologous loci whose splits reflect the species divergences of interest. A multiple sequence alignment proposes corresponding ancestral positions. Conserved ribosomal RNA can compare distant lineages, whereas faster-evolving regions help resolve recent splits; amino acid alignments can retain useful deep information after many nucleotide sites have changed repeatedly.

A phylogenetics model estimates a topology and branch lengths in substitutions per site, using explicit substitution probabilities rather than treating every observed mismatch as one historical change. Repeated substitutions, unequal rates among sites, selection, and compositional bias can make observed mismatch fractions underestimate the amount of change. Multiple loci help test consistency; a single gene tree can disagree with the species history through duplication, incomplete lineage sorting, or horizontal transfer.

A molecular clock converts branch change to time through an evolutionary rate. For two equally evolving lineages, an expected distance $d$ and rate $\mu$ give a divergence time $t=d/(2\mu )$, but sequence information alone usually identifies a rate-time product, not its two factors separately. A fossil securely assigned to a descendant clade supplies a dated constraint: the ancestral split must be at least as old as that fossil. The oldest known fossil is normally a minimum age, not proof that the lineage originated exactly then.

Several independent fossil constraints, their dating and placement uncertainty, and a relaxed molecular clock permit rates to vary while estimating divergence times with uncertainty intervals. Geological absence alone is a weak upper bound when preservation or sampling is poor. Conflicting loci, uncertain alignments, saturation, model misspecification, and uncertain fossil assignments should be investigated rather than hidden by a precise-looking time axis. The resulting phylogenetic tree is a joint inference from sequences, evolutionary assumptions, and geological evidence.

An ion channel is a selective permeation pathway, not simply an aqueous hole of fixed diameter. A hydrated ion entering a narrow selectivity filter must lose or reorganize some hydration water. The energetic cost can be offset by interactions with charged or polar groups in the pore. Different ionic radii, valences, hydration free energies, and coordination geometries therefore produce different permeation barriers and binding affinities.

A classical potassium selectivity filter presents oxygen ligands that stabilize relatively dehydrated potassium in configurations resembling its aqueous coordination. Smaller sodium does not automatically pass more easily: its hydration is stronger and the filter need not provide a compensating configuration at equally low free energy. Filter flexibility and multi-ion occupancy matter, so the explanation is an energetic balance, not the assertion that a rigid hole simply blocks every larger or smaller sphere. Ion-ion interactions and coupled displacement can permit rapid conduction while maintaining selectivity.^[ref]

Other ion channels use different arrangements. Fixed negative groups can strongly favor divalent calcium over monovalent ions; occupancy and competition then influence both selectivity and throughput. Selectivity is distinct from activation or ion-channel inactivation, which control access or availability. Selective passive flux follows an electrochemical potential gradient; it does not by itself pump ions uphill. Selectivity allows cells to establish particular membrane potentials, generate action potentials, regulate calcium signals, and control solute balance without dissipating every ionic gradient whenever one pathway opens.

Single-molecule experiments expose distributions and ordered events that an ensemble average can hide. Several distinct biological systems make this advantage concrete.

These methods also have limitations: the attached probe or applied load may perturb the molecule, inactive or heterogeneous molecules may be overrepresented, and finite temporal resolution can hide fast steps. Repeated independent trajectories and appropriate controls are needed to connect a single observed event to a reproducible mechanism. The gain is access to trajectories and heterogeneity, rather than an assumption that one molecule alone represents every molecule.