Past exam of the genetics course of the University of Cambridge 2024 Paper 1 7 b Solution 2026-10-20
The saturation concentration 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 .
At the thermodynamic critical point, the two branches meet: their concentration difference vanishes. Its coordinates define the critical concentration and critical temperature . In the upper-critical model, admits no two-liquid coexistence. Thus is a temperature-dependent branch, whereas is the concentration at the endpoint.
Between coexistence concentrations, the lever rule gives the dense-phase volume fraction , assuming consistent concentration and volume definitions. Increasing total chromatin then primarily changes phase amounts rather than allowing the dilute phase to increase without bound.
Past exam of the genetics course of the University of Cambridge 2024 Paper 1 7 d Solution 2026-10-20
In the regime where salt promotes chromatin condensation by screening repulsion between DNA-rich surfaces, reducing salt from 0.15 M to 0.1 M weakens the effective attraction. In the schematic upper-critical model this means a lower critical temperature and a smaller coexistence region; at a fixed suitable temperature the dilute-phase saturation concentration rises. The second curve is therefore drawn inside and below the first. The magnitude of the shift is not specified by the question.
This direction has a microscopic basis: reducing ionic strength increases the range of electrostatic repulsion between negatively charged DNA segments. Modelling of interacting arrays supports a role for screening and nucleosome contacts in stabilizing chromatin-rich phases.[ref]
Nucleosome plasticity is a critical element of chromatin liquid-liquid phase separation and multivalent nucleosome interactions by Stephen E. Farr and others. Salt-dependent coexistence and the role of nucleosome breathing
In the idealized limit of unscreened DNA-DNA repulsion, the ordinary condensed phase can disappear, rather than simply acquiring an arbitrarily small positive critical temperature. However, zero added NaCl is not literally zero counterions: charged chromatin requires charge compensation, and buffer ions and counterions associated with the preparation remain. Salt also screens attractive interactions, and very high salt can alter nucleosome stability. The proposed shift applies to the stated low-salt screening regime, not a universal monotonic law at every salt concentration.