| Summary: | Atomistic simulations can not achieve the time and length scales of many important biological problems. There is much interest in simple coarse-grained models that can capture the essential mechanical properties of proteins. Building upon the work of previous authors, that applied Combinatorial Rigidity Theory to proteins, a methodology is suggested to identify residues that play an important role in the rigidity of inhibitors from the Bowman-Birk family. This work points out that rigidity effects are non-local and thus the global tOpology of the constraint network is an additional factor to have in consideration when performing mutations. Concepts from Infinitesimal Rigidity are applied to proteins. An exact algorithm for rigidity analysis is described which takes advantage of the sparsity of the Rigidity Matrix. For large proteins, a nonexact, but efficient algorithm is also proposed which scales Iinearfy with the number of atoms. The great advantage of Infinitesimal Rigidity is that it can be used to stUdy a very general class of distance constraint network, denominated generic framework. Taking advantage of this fact, rigid decompositions of Adenylate Kinase and the Hemoglobin Dimer were obtained from multiple experimental conformations. A methodology to predict collective motions from a coarse-grained Rigidity Matrix is suggested. Good agreement was found with predictions based on Elastic Network Models. A simulation methodology was implemented, based on rigid body dynamics, to test rigid decompositions obtained with different methods. The results have shown that, if the rigid bodies are defined with Rigidity Theory algorithms, relevant properties of unconstrained atomistic simulations can be replicated. The studies were performed for Adenylate Kinase and the Ribosomal Protein L11C76.
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