Solvent-dependent segmental dynamics in intrinsically disordered proteins

Abstract

Protein and water dynamics have a synergistic relationship, which is particularly important for intrinsically disordered proteins (IDPs), although the details of this coupling remain poorly understood. Here, we combine temperature-dependent molecular dynamics simulations using different water models with extensive nuclear magnetic resonance (NMR) relaxation to examine the importance of distinct modes of solvent and solute motion for the accurate reproduction of site-specific dynamics in IDPs. We find that water dynamics play a key role in motional processes internal to "segments" of IDPs, stretches of primary sequence that share dynamic properties and behave as discrete dynamic units. We identify a relationship between the time scales of intrasegment dynamics and the lifetime of hydrogen bonds in bulk water. Correct description of these motions is essential for accurate reproduction of protein relaxation. Our findings open important perspectives for understanding the role of hydration water on the behavior and function of IDPs in solution.

Fig. 1. Comparison of experimental and simulated NMR relaxation rates at 278 to 298 K.

(A) Experimental ¹⁵N transverse spin relaxation rates R₂ (gray bars) measured on N_tail at different magnetic fields (columns) and temperatures (rows) are compared with the results of simulations C3P (blue line), C4P (orange), and A4P (purple). At all temperatures and fields, simulations in TIP4P/2005 capture the dynamics of N_tail better than simulations in TIP3P water (RMSD given in figs. S4 to S6). All rates are reported in s⁻¹. Rates at 950 MHz are not shown in the interests of space. (B) Experimental ¹⁵N longitudinal spin relaxation rates (R₁) measured on N_tail at different magnetic fields (columns) and temperatures (rows) [color code as in (A)]. All simulations reproduce, at least qualitatively, the sequence dependence of R₂ rates, although simulations are more accurate at room temperature than at lower temperature. All rates are reported in s⁻¹. (C) Experimental ¹⁵N{¹H} steady-state NOEs measured on N_tail at different magnetic fields (columns) and temperatures (rows) [color code as in (A)]. Simulations in TIP4P/2005 reproduce the experimental values better than C3P, at all temperatures and at all fields (RMSD given in figs. S4 to S6).

Fig. 2. Average time scales resulted from fitting segmental dynamics correlation functions in C3P (blue), C4P (orange), and A4P (purple).

Fig. 3. Illustration of inter- and intrasegment dynamics contributing to NMR relaxation.

(A) We consider a time-dependent gyration tensor for each segment (here represented by an ellipsoid), as defined in (36). The gyration tensor is diagonalized by a rotation matrix expressed as a function of time-dependent angles θ and φ that are used to compute a correlation function that reports on the time fluctuations of the orientation of the segment in the laboratory frame. (B) In the model presented in (30), all the information regarding segmental motions is encoded in the relative orientation of peptide planes. We label α₁, α₂ … α_n the n = N(N − 1)/2 time-dependent angles identified by two Cα-Cα vectors in a segment of N residues. We compute n correlation functions reporting on intrasegment dynamics.

Fig. 4. Comparison of intrasegment dynamics and longest relaxation active time scale.

Time scales associated with intrasegment dynamics at 298 K (red circles) in C3P (top), C4P (middle), and A4P (bottom) are compared with the longest time scale resulting from fitting segmental dynamics correlation functions (gray squares, see also fig. S7).

Fig. 5. Segmental motional models derived from C4P reproduce overall NMR relaxation rates better than segmental motional models derived from C3P.

(A) Top: Length and position of segments derived from C3P (green) and C4P (blue) at 278 K. Bottom: Difference in χ² of the central residue in the segment between C3P- and C4P-derived segmental models (χ²_C3P and χ²_C4P). (B and C) Similar representation for segments derived from ensembles of trajectories determined from C3P and C4P at 288 K and 298 K.

Fig. 6. Comparison of properties of water models.

Self-diffusion coefficients (A) and lifetime of hydrogen bonds (B) in TIP3P (blue circles) and TIP4P/2005 (orange squares) water.