Temperature Dependence of Normal Mode Reconstructions of Protein Dynamics

Normal mode (NM) analysis is a widely used technique for reconstructing conformational changes of proteins from the knowledge of native structures. In this Letter, we investigate to what extent NMs capture the salient features of the dynamics over a range of temperatures from close to $T=0$ to above unfolding. We show that the use of normal modes at room temperature is justified provided proteins are cooperative, that is, globular and highly structured. On the other hand, it is imperative to consider several modes in order to eliminate the unpredictable temperature dependence of single-mode contributions to the protein fluctuations.

Figure 1

Cartoon representations of three of the analyzed structures, along with the corresponding PDB codes.

Figure 2

(a) First nine thermal involvement coefficients for lysozyme (PDB code 166L), $N=162$, $T_f=0.75$, as functions of the reduced temperature. (b) Relative TICs for the odorant binding protein LUSH (PDB code 1OOI), $N=124$, $T_f=0.86$. In the lower panel TICs are normalized to the $T=0$ values (see text). In all graphs horizontal lines mark single [${\Theta }_k(0)$] and aggregated [$\sum _{m=1}^{3,5}{\Theta }_m(0)$] TICs.

Figure 3

Cumulative involvement coefficient over the first three modes. (a) PDZ III domain, $N=85$, $T_f=0.67$, PDB code 1BFE (solid line) and different independent surrogates (symbols). (b) Peptide-binding fragment from Hsp40, $N=171$, $T_f=0.96$ (PDB code HDJ1) and TATA-box Zinc-finger binding protein, $N=177$, $T_f=0.89$ (PDB code 1G2F).

Figure 4

Cumulative involvement coefficient with the full potential (filled circles) and without dihedral forces (empty circles) normalized to the zero-temperature values. Arrows mark the unfolding temperature calculated with the full force field. Upper panel: Lysozyme, ($64\%\alpha$, $9\%\beta$), $N=162$, $T_f=0.754$ (PDB code 166L). Lower panel: $ϵ$-subunit of the F1-ATPase, ($26\%\alpha$, $37\%\beta$), $N=138$, $T_f=0.99$ (PDB code 1BSN). Also marked is the temperature $T^{*}$, at which a first structural rearrangement occurs with the loss of about 25% of native contacts.