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. 2009 Feb;96(3):1076-82.
doi: 10.1529/biophysj.107.125369.

Monte Carlo simulations of proteins in cages: influence of confinement on the stability of intermediate states

Pedro Ojeda  1 , Martin E Garcia, Aurora Londoño, Nan-Yow Chen
Affiliations

Monte Carlo simulations of proteins in cages: influence of confinement on the stability of intermediate states

Pedro Ojeda et al. Biophys J. 2009 Feb.

Abstract

We study the folding of small proteins inside confining potentials. Proteins are described using an effective potential model that contains the Ramachandran angles as degrees of freedom and does not need any a priori information about the native state. Hydrogen bonds, dipole-dipole-, and hydrophobic interactions are taken explicitly into account. An interesting feature displayed by this potential is the presence of metastable intermediates between the unfolded and native states. We consider different types of confining potentials to describe proteins folding inside cages with repulsive or attractive walls. Using the Wang-Landau algorithm, we determine the density of states and analyze in detail the thermodynamical properties of the confined proteins for different sizes of the cages. We show that confinement dramatically reduces the phase space available to the protein and that the presence of intermediate states can be controlled by varying the properties of the confining potential. Cages with strongly attractive walls destabilize the intermediate states and lead to a two-state folding into a configuration that is less stable than the native structure. However, cages with slightly attractive walls enhance the stability of native structure and induce a folding process, which occurs through intermediate configurations.

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Figures

Figure 1
Figure 1
Ground-state structure (β-sheet) of the peptide 1NJ0 (Eg ∼ −132.0).
Figure 2
Figure 2
Free energy as a function of the configurational energy E for the bulk (Rc → ∞) showing the presence of the native (N), the intermediate (I1, I2), and the unfolded (U) states.
Figure 3
Figure 3
(a) Logarithm of the density of states (DOS) g(E) of the protein inside the confining potential V1(r) and for different values of Rc (15 Å, 20 Å, 25 Å) as well as for the bulk case. One notices the remarkable decrease of the DOS for decreasing Rc. (b) Specific heat for the bulk case and for confining potentials with radii 15 Å, 20 Å, and 25 Å. Tf = 321 K is the transition temperature in the bulk case. Tf increases as the radius Rc decreases. The confining potential in panels a and b is purely repulsive.
Figure 4
Figure 4
Contour plots of the free energy landscape F(E, Q) as a function of the configurational energy E and the end-to-end distance Q for a purely repulsive confining potential. Plots a–d correspond to the bulk case and cages of radius 15 Å, 20 Å, and 25 Å, respectively. The unfolded states are strongly affected when the size of the cage decreases. The native state and the intermediates are only slightly modified. The contour lines represent the free energy difference with respect to the native state and are given in Kcal/mol K.
Figure 5
Figure 5
(a) Logarithm of the DOS g(E) for different degrees of hydrophobicity (ɛ = 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0) and for the bulk case. Notice the abrupt decay of g(E) by ∼13 orders of magnitude as ɛ goes from 0.0 to 1.0. For high values of ɛ, the protein tends to be in the unfolded state. (b) Specific heat of the protein for different values of ɛ, 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0, compared to the bulk case. Tf = 321 K is the transition temperature for the bulk. Notice how Tf and the peak of the specific heat decrease as ɛ goes from 0 (purely repulsive wall) to 1 (strongly attractive wall).
Figure 6
Figure 6
Contour plots of the free energy landscape F(E, Q) for a cage with attractive inner surface. Different degrees of hydrophobicity are displayed in plots a–d, corresponding to ɛ = 0.0, ɛ = 0.4, ɛ = 0.6, and ɛ = 0.8, respectively. The native and the intermediates states are slightly modified for 0.0 < ɛ < 0.4 but for larger values of ɛ the intermediate states disappear and the native structure is deformed. As a consequence, F(E, Q) represents a two-states landscape. The contour lines represent the free energy difference with respect to the native state and are given in Kcal/mol K.
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