Tendencias de los estudios de Gestión de Riesgo

The results presented in this chapter on the rigidity and flexibility reveal that the rigidity dilution of the selected proteins is unique for each case. For example, the RCD distribution of the membrane protein displays a unique rigidity distribution. It shows a sharp change in the rigidity distribution. Hence, the selection of Ecut must be done based of the RCD graph. Further, the proteins displaying the highest mobility, in terms of xRMSD, have a very different pattern of rigidity dilution. This reinforces previous studies [48] which concluded that each protein structure needs to be examined individually and that the Ecut used for simulating protein motion must be chosen on a case by case. The choice of theEcutto explore protein mobility depends on the RCD, on theEcutranges and on what question we are investigating. For all the proteins investigated in this chapter, the Ecut is chosen to identify at least oneEcutat which the protein is mostly rigid and oneEcutat which the protein is mostly flexible in order to quantify and compare protein mobility. In the next chapter however, we choose moreEcutfrom the RCD graph for extensively studying yeast PDI mobility under different rigid cluster constraints.

4.4.2 Significance of rigidity-analysis energy cutoff

In the case of small loop motion, it is clear that lowering the rigidity-analysis energy cutoff — thus making the structure more flexible as less hydrogen bonds are included in the rigid clusters— increases the amplitude of flexible motion, as one might expect. In the case of large domain motion, however, the most important criterion appears to be whether the domains are mutually rigid or not,. In general, the rigidity analysis of protein structures can thus add value to the simulation of flexible motion by identifying the constraints that must be eliminated in order for two residues to become independently mobile.

The proteins that undergo a large conformational change, i.e. PDI and pGLIC, display a different dependence with respect to the cutoff energy. In the case of PDI the amplitude of flexible motion for the lowest-frequency modes is almost unaffected by the choice of theEcut provided it is set at a reasonable value of Ecut which rep- resents each domain as a number of separate small rigid clusters. This conclusion can also be drawn in the case of the ligand-gated ion channel protein.

4.4.3 RMSD

RMSD is a standard measure of structural similarity between two proteins. However, the results presented in this chapter focus on using RMSD to characterise protein motion; this reveal its limitations to correctly describe protein large conformational changes. Visual inspection of the overlapped conformers revealed three types of mo- tion which are not differentiated by using RMSD as a mobility measure. The most clear example is the comparison of RMSD values and conformer motion between BPTI and pLGIC; 58 and 1605 residue long respectively. The motion for BPTI is restricted to the motion of a small loop, whereas the membrane protein displays a domain motion where the intracellular domain moves with respect to the extracel- lular domain. The RMSD values for BPTI range≈1.5–4.5˚A whereas for pLGIC ≈ 0.7–2.5˚A. The displacement of the overlapped conformers indicated a larger motion for the membrane protein than for BPTI, yet the RMSD measures suggest the con- trary. This is due to the least-squares fitting routinely used to compare two very similar structures that averages and minimizes the structural variation; which in this case is performed by usingPyMOL intra fit command.

4.4.4 xRMSD

xRMSD characterises protein motion so that it correlates with the observed motion from the overlapping conformers. Furthermore, the results of comparing the xRMSD mobility of two proteins with similar number of residues (PDI and Antitrypsin) dismiss the possibility that the different types of motion here mentioned are due to the protein size. In addition, the results for the mobility characterisation are consistent not only for the lowest frequency mode but for the other modes too. Therefore, xRMSD properly identifies the character of protein motion and can be used as an useful measure to identify conformational change in proteins.

4.5

Conclusions

The reported hybrid method is able to explore protein motion by integrating both rigidity constraints fromFirstand low-frequency mode eigenvectors obtained using Elnemo, into the geometric simulation Froda. In order to illustrate the method, we have applied it here to a diverse selection of proteins whose flexible motion ranges from small loop motion (BPTI, cytochrome-c) and large loop motion (a kinesin and an antitrypsin) to large motions of entire domains (protein disulphide isomerase and a transmembrane pore protein). Detailed studies of dynamics in relation to func-

tion of particular proteins are currently in progress [66, 67]. The combined method can rapidly explore motion to large amplitudes in an all-atom model of the protein structure, maintaining steric exclusion and retaining the covalent and non-covalent bonding interactions present in the original structure. Significant amplitudes of motion are achieved with only CPU-minutes of computational effort even in a pen- tameric pore protein with more than 1600 residues. The amplitude of motion that can be achieved by flexible loops increases as the rigidity-analysis energy cutoff is lowered. For large-scale motion of domains, the most important criterion is that the energy cutoff should be low enough that different domains do not form a single rigid body. RMSD, a measure of structural similarity, does not properly reflect the scale of flexible motion between different proteins; this is better captured by an extensive measure, xRMSD, which reflects both the size of the protein and the amplitude of its motion. Examination of the behaviour of the elastic network eigenvectors during the motion shows many examples of mode mixing, so that a given vector of motion can change from being a pure mode to a mixed one after quite small displacements, without losing its character as an “easy” direction for flexible motion.