Session V21 - Proteins: Computation and Dynamics.
ORAL session, Thursday morning, March 15
Room 604, Washington State Convention Center
We monitor the collective motions of the proteins, and relate the topological characteristics to the flexibility and stability of the protein molecule.^1,2 For modeling purposes, we follow the backbone topology of a compact globular protein and pick the C^\alpha atom at each residue. To define the non-bonded contacts, the first coordination sphere of each C^\alpha with 7 Åradius is considered. Now, C^\alpha's are the nodes and the contacts are the branches; thus, we create an equivalent connected digraph from a folded protein. We accordingly consider first the equilibrium of each residue: A \Delta f = 0, then the compatibility equation between the fluctuation of a residue and fluctuations of its contacting bonds: A^T \Delta R = \Delta r; and finally the constitutive relation for each bonded and nonbonded contact: K \Delta r + C \dot\Delta r = \Delta f. In this formulation, A is the incidence matrix of the connected digraph of the protein molecule, K and C are diagonal matrices whose entries are, respectively, the rigidities and the viscous dissipations of the contacts. In addition, the forces at each bond f, positional movements of each residue R, and the bond displacements r are analogous to the branch current vector, node-to-datum voltage vector, and branch voltage vector, respectively, of the circuit theory; and, therefore, the equilibrium and the compatibility equations are the Kirchhoff's Law of Currents and Voltages, respectively. For homogeneous, elastic interactions, the global rigidity of a protein is represented by the Kirchhoff Matrix, that is the incidence matrix multiplied by its transpose. This procedure lends a great helping hand to elucidate the structural dynamic mechanisms for biological activities.^3,4 Illustrative examples are presented and validated by experimental results, and the qualitative differences between one- and three-dimensional formulations are discussed.
1. Bahar, I., Atilgan A.R., Demirel, M.C., and Erman, B., Phys. Rev. Lett., 80, 2733, 1998.
2. Yilmaz, L.S. and Atilgan, A.R., J. Chem. Phys., 113, 4454, 2000.
3. Bahar, I., Erman, B., Jernigan, R.L., Atilgan, A.R., and Covell, D., J. Mol. Biol., 285, 1023, 1999.
4. Baysal, C. and Atilgan, A.R., Proteins, to appear, 2001.