RNA molecules in monovalent salt solutions generally adopt a set of partially folded conformations containing only secondary structure, the intermediate or I state. Addition of Mg2+ strongly stabilizes the native tertiary structure (N state) relative to the I state. In this paper, a combination of experimental and computational approaches is used to estimate the free energy of the interaction of Mg2+ with partially folded I state RNAs and to consider the possibility that Mg2+ favors "compaction" of the I state to a set of conformations with a higher average charge density. A sequence variant with a drastically destabilized tertiary structure was used as a mimic of I state RNA; as measured by small-angle X-ray scattering, it adopted a progressively more compact conformation over a wide Mg2+ concentration range. Average free energies of the interaction of Mg2+ with the I state mimic were obtained by a fluorescence titration method. To interpret these experimental data further, we generated molecular models of the I state and used them in calculations with the nonlinear Poisson-Boltzmann equation to estimate the change in Mg2+-RNA interaction free energy as the average I state dimensions decrease from expanded to compact. The same models were also used to reproduce quantitatively the experimental difference in excess Mg2+ between N and I states. On the basis of these experiments and calculations, I state compaction appears to enhance Mg2+-I state interaction free energies by 10-20%, but this enhancement is at most 5% of the overall Mg2+-associated stabilization free energy for this rRNA fragment.

Analysis of Raman and neutron scattering spectra of lysozyme demonstrates that the protein dynamics follow the dynamics of the solvents glycerol and trehalose over the entire temperature range measured 100-350 K. The protein's fast conformational fluctuations and low-frequency vibrations and their temperature variations are very sensitive to behavior of the solvents. Our results give insight into previous counterintuitive observations that protein relaxation is stronger in solid trehalose than in liquid glycerol. They also provide insight into the effectiveness of glycerol as a biological cryopreservant.