Past exam of the genetics course of the University of Cambridge / 2024 / Paper 1 / 7 / b / Solution

The saturation concentration $c_{\mathrm{sat}}(T)$ is the dilute-phase coexistence concentration at the specified temperature and solution conditions. On increasing the overall concentration through this boundary, a macroscopic condensed phase can first coexist with the dilute phase. The other branch gives the dense-phase concentration $c_{\mathrm{dense}}(T)$.

At the thermodynamic critical point, the two branches meet: their concentration difference vanishes. Its coordinates define the critical concentration $c_c$ and critical temperature $T_c$. In the upper-critical model, $T>T_c$ admits no two-liquid coexistence. Thus $c_{\mathrm{sat}}$ is a temperature-dependent branch, whereas $c_c$ is the concentration at the endpoint.

Between coexistence concentrations, the lever rule gives the dense-phase volume fraction $v=(\bar{c}-c_{\mathrm{sat}})/(c_{\mathrm{dense}}-c_{\mathrm{sat}})$, assuming consistent concentration and volume definitions. Increasing total chromatin then primarily changes phase amounts rather than allowing the dilute phase to increase without bound.