Gaussian network model

The Gaussian network model (GNM) is a representation of a biological macromolecule as an elastic mass-and-spring network to study, understand, and characterize the mechanical aspects of its long-time large-scale dynamics. The model has a wide range of applications from small proteins such as enzymes composed of a single domain, to large macromolecular assemblies such as a ribosome or a viral capsid. Protein domain dynamics plays key roles in a multitude of molecular recognition and cell signalling processes.Protein domains, connected by intrinsically disordered flexible linker domains, induce long-range allostery via protein domain dynamics.The resultant dynamic modes cannot be generally predicted from static structures of either the entire protein or individual domains. The Gaussian network model (GNM) is a representation of a biological macromolecule as an elastic mass-and-spring network to study, understand, and characterize the mechanical aspects of its long-time large-scale dynamics. The model has a wide range of applications from small proteins such as enzymes composed of a single domain, to large macromolecular assemblies such as a ribosome or a viral capsid. Protein domain dynamics plays key roles in a multitude of molecular recognition and cell signalling processes.Protein domains, connected by intrinsically disordered flexible linker domains, induce long-range allostery via protein domain dynamics.The resultant dynamic modes cannot be generally predicted from static structures of either the entire protein or individual domains. The Gaussian network model is a minimalist, coarse-grained approach to study biological molecules. In the model, proteins are represented by nodes corresponding to α-carbons of the amino acid residues. Similarly, DNA and RNA structures are represented with one to three nodes for each nucleotide. The model uses the harmonic approximation to model interactions. This coarse-grained representation makes the calculations computationally inexpensive. At the molecular level, many biological phenomena, such as catalytic activity of an enzyme, occur within the range of nano- to millisecond timescales. All atom simulation techniques, such as molecular dynamics simulations, rarely reach microsecond trajectory length, depending on the size of the system and accessible computational resources. Normal mode analysis in the context of GNM, or elastic network (EN) models in general, provides insights on the longer-scale functional dynamic behaviors of macromolecules. Here, the model captures native state functional motions of a biomolecule at the cost of atomic detail. The inference obtained from this model is complementary to atomic detail simulation techniques. Another model for protein dynamics based on elastic mass-and-spring networks is the Anisotropic Network Model. The Gaussian network model was proposed by Bahar, Atilgan, Haliloglu and Erman in 1997. The GNM is often analyzed using normal mode analysis, which offers an analytical formulation and unique solution for each structure. The GNM normal mode analysis differs from other normal mode analyses in that it is exclusively based on inter-residue contact topology, influenced by the theory of elasticity of Flory and the Rouse model and does not take the three-dimensional directionality of motions into account. Figure 2 shows a schematic view of elastic network studied in GNM. Metal beads represent the nodes in this Gaussian network (residues of a protein) and springs represent the connections between the nodes (covalent and non-covalent interactions between residues). For nodes i and j, equilibrium position vectors, R0i and R0j, equilibrium distance vector, R0ij, instantaneous fluctuation vectors, ΔRi and ΔRj, and instantaneous distance vector, Rij, are shown in Figure 2. Instantaneous position vectors of these nodes are defined by Ri and Rj. The difference between equilibrium position vector and instantaneous position vector of residue i gives the instantaneous fluctuation vector, ΔRi = Ri - R0i. Hence, the instantaneous fluctuation vector between nodes i and j is expressed as ΔRij = ΔRj - ΔRi = Rij - R0ij. The potential energy of the network in terms of ΔRi is where γ is a force constant uniform for all springs and Γij is the ijth element of the Kirchhoff (or connectivity) matrix of inter-residue contacts, Γ, defined by rc is a cutoff distance for spatial interactions and taken to be 7 Å for amino acid pairs (represented by their α-carbons).