The role of topology on protein thermal stability

Abstract

For several decades, experimental and computational studies have been used to investigate the potential functional role of knots in protein structures. A property that has attracted considerable attention is thermal stability, i.e., the extent to which a protein retains its native conformation and biological activity at high temperatures, without undergoing denaturation or aggregation. Thermal stability is quantified by the melting temperature Tm, an equilibrium property that corresponds to the peak of heat capacity in differential scanning calorimetry (DSC) experiments. Experimental and computational studies report conflicting effects of knotting on protein thermal stability. Here, we use extensive Monte Carlo simulations of a simple C-alpha model of protein YibK, with energetics modeled by the Go potential, to show that Tm does not depend on the topological state of the protein. Our simulations further support the view that the discrepancy between the experimental and computational results stems from a pronounced separation of timescales for unknotting and unfolding that is inherent to deeply knotted proteins like YibK. In particular, the timescale separation implies that the complete unfolding-untying transition may not be accessible within the duration of a DSC experiment, whose apparent Tm measurements likely reflect a non-equilibrium distribution lacking unfolded states that are also unknotted.

Figures (5)

• Figure 1: Model systems used in the present study. Cartoon representation (left) and bead and stick representation (right) of the native structure of protein YbeA (PDB id: 1ns5, chain A) (A), and YibK (PDB id: 1mxi, chain A) (B) with the knotted core colored in orange and the knot tails (number of residues that must be removed from the chain termini to untie the knot) colored in red (C-terminus) and blue (N-terminus). Each bead represents a C$_\alpha$ atom and rigid sticks represent pseudo-bonds connecting pairs of C$_\alpha$ atoms. The size (measured in number of beads) of the knot tails and knotted core is indicated. In both proteins, the knotted topology results from threading the C-terminus through the knotted core.
• Figure 2: Control systems used in the present study. Unknotted control systems CP-YbeA (PDB ID: 1ns5) and CP-YibK (PDB ID: 6ahw) obtained experimentally by Hsu and co-workers through circular permutation of YbeA (PDB ID: 1ns5) and YibK (PDB ID: 1mxi), respectively (A), and in silico unknotted control system IS-YibK, obtained through computer modeling from YibK (PDB ID: 1mxi)(B). The knotted structures are all shown in blue, the unknotted structures obtained experimentally by CP are shown in green, and the unknotted structure obtained in silico is shown in red.
• Figure 3: Equilibrium properties as a function of temperature obtained from Monte Carlo simulations. Dependence of the internal energy ($U$), entropy ($S$), free energy ($F$), and heat capacity ($C_V$) on temperature ($T$) for the knotted (K) and unknotted (U) model systems of YbeA (A-D) and YibK (E-H). The melting temperature, $T_m$, is indicated on the corresponding heat capacity curves.
• Figure 4: Free energy profiles obtained from Monte Carlo simulations. Dependence of the free energy ($F$) on the fraction of native contacts $Q$ at the melting temperature ($T_m$) for the YbeA (A) and YibK (B) model systems.
• Figure 5: Depedence of the heat capacity (A) and of the knotting probability (B) on the simulation temperature for YibK. The MC simulation that does not preserve the linear topology of the chain (NLTyp) requires 200$\times 10^6$ MC steps to equilibrate (the curves do not change for a larger number of MC steps). On the other hand, a simulation that preserves the linear topology of the chain requires 12$\times 10^9$ MC steps to equilibrate. Interestingly, a non-equilibrated simulation predicts an apparent $T_m$ that is smaller, and a transition that is clearly less sharp (as denoted by the shape of the knotting probability curve) than that predicted by the equilibrated sampling.