Vaciados y excavaciones

Structural rigidity defines the resistance of a material to structurally deform in response to a mechanical force. The structural rigidity of a protein depends on the

curvature of the potential well of the energy profile, the height of the energy barrier, ∆G‡, and the distance xu separating its folded state from the transition state (Figure

4.5). An energy landscape describes the energy of a protein structure as a function of

its conformational entropy (Dill, 1997). Accordingly, the width of an energy valley defines the conformational entropy of a protein structure. With increasing (decreasing) width of an energy valley a protein structure can adopt more (less) conformational substates owing to an increase (decrease) in its flexibility (Wolynes et al., 1995; Dill, 1997). Because different functional states have different conformational states, structural rigidity is intrinsically related to the function of a protein.

We assumed a parabolic potential of the energy minimum and a sharp transition barrier for all unfolding intermediates of OmpG (To approximate the rigidity of the individual structural segments (β-hairpins and β-strands) of the unfolding intermediates we calculated their spring constants using Equation 4.3. The spring constants of the β-hairpins and β-strands of OmpG ranged from 0.3 to 2.6 N/m (Table 4.1). The spring constants of transmembrane α-helices of bacteriorhodopsin ranged from 0.5 to 7.3 N/m (Sapra et al., 2008a), of bovine rhodopsin from 0.9 to 3.8 N/m (Sapra et al., 2008b) and of SteT from 0.2 to 2.8 N/m (Bippes et al., 2009). Thus, we conclude that β-hairpins and β-strands of OmpG that show a similar structural flexibility as transmembrane α-helices . Changing OmpG from the open to the closed state did not significantly affect the mechanical properties of most of the β-hairpins

and β-strands.

As discussed in the previous section, the average rigidity of the unfolding intermediates decreased with the increasing number of secondary structures unfolded.

Figure 4.10 Unfolding energy landscape of OmpG being set in the open (pH 7.0, red) and closed (pH 5.0, black) conformation: Upon applying a sufficiently high mechanical force to the N-terminal

end, the structural segments of OmpG start unfolding sequentially. Individual unfolding intermediates of OmpG are trapped in energy valleys (rainbow colored). Structures forming the unfolding intermediates along the unfolding pathway are shown for each energy valley. For simplicity we have assumed the energy valleys stabilizing the folded native state of OmpG in the open (pH 7.0) and closed (pH 5.0) state to be the same (valley indicated by black number 1). Overcoming each energy barrier that separates two energy valleys from each other induces the unfolding of a β-hairpin. The first four unfolding steps (stepwise unfolding of β-hairpins I, II, III, and IV) that guide one unfolding intermediate to the other are the same for OmpG in the open and closed states. After this, the unfolding pathway differs for OmpG being set in the open (top, red pathway at pH 7.0) and the closed (bottom, black pathway at pH 5.0) state. In the open conformation, unfolding of β-hairpin IV is followed by the unfolding of β-hairpins V (transition from energy valley numbered with black 5 to energy valley numbered red 6), then VI (transition from energy valley numbered with red 6 to energy valley numbered black 7), and finally VII (transition from energy valley numbered with black 7 towards completely unfolded OmpG). In the closed conformation, unfolding of b-hairpin IV is followed by the unfolding of β-hairpin V together with β-strand S11 (transition from energy valley numbered with black 5 to energy valley numbered black 6), then of β-strand S12 (transition from energy valley numbered with black 6 to energy valley numbered black 7), and finally of β-hairpin VII (transition from energy valley numbered with black 7 towards completely unfolded OmpG). Because the parameters characterizing the unfolding of β-hairpin VII do not differ between OmpG being set in the open or in the closed state we assume that the last unfolding step is the same for both unfolding pathways. The schematic representation of the unfolding energy landscape was reconstructed from parameters revealed by SMFS and DFS (Fig. 4.4 and Table 4.1). Shown is only the predominant (main)

A possible reason for this decrease in the rigidity could be the breaking of the inter- strand hydrogen bond network as unfolding proceeds.

The first β-hairpin is the most rigid, and as hydrogen bonds are broken the remaining β-strands get flexible. The contribution of the inherent rigidity of each structural segment, i.e., the rigidity of structural segments in the absence of hydrogen bonds, is a daunting experimental task. However, it may be assumed that the rigidity of the last β-hairpin VII is the approximate inherent rigidity of a β-hairpin in OmpG, and that the rigidity increases with increasing complexity of the hydrogen bond network. A greater flexibility of the structure denotes more conformations being trapped by many local minima in a rough energy landscape. The accompanying decrease in the spring constant, κ, (Table 4.1) also signifies the highly frustrated nature of the energy landscape. In contrast, a more rigid structure is indicative of a minimally frustrated, smooth energy landscape.The rigidity or the spring constant of the structural segment constituted of β-strands S9-S11 and part of loop L6 at pH 5 was calculated to be three times more than that of β-hairpin V (β-strands S9-S10) at pH 7. It may be assumed that the extra mechanical rigidity of the gating region in the closed state reduces its structural fluctuations to ensure that the gated pore remains closed. In the open conformation, however, this may not be a necessity and a flexible loop L6 can be tolerated by the organism. Thus, a change in conformation of OmpG changes its mechanical properties to ensure an efficient functional state.

4.2.3.6 Mapping the unfolding energy landscapes of OmpG in the open and closed