The Gaussian network model (GNM) is a representation of a biological
macromolecule
A macromolecule is a very large molecule important to biophysical processes, such as a protein or nucleic acid. It is composed of thousands of covalently bonded atoms. Many macromolecules are polymers of smaller molecules called monomers. The ...
as an elastic mass-and-
spring
Spring(s) may refer to:
Common uses
* Spring (season)
Spring, also known as springtime, is one of the four temperate seasons, succeeding winter and preceding summer. There are various technical definitions of spring, but local usage of ...
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
Domain may refer to:
Mathematics
*Domain of a function, the set of input values for which the (total) function is defined
**Domain of definition of a partial function
**Natural domain of a partial function
**Domain of holomorphy of a function
* Do ...
, to large
macromolecular assemblies
The term macromolecular assembly (MA) refers to massive chemical structures such as viruses and non-biologic nanoparticles, cellular organelles and membranes and ribosomes, etc. that are complex mixtures of polypeptide, polynucleotide, polys ...
such as a
ribosome
Ribosomes ( ) are macromolecular machines, found within all cells, that perform biological protein synthesis (mRNA translation). Ribosomes link amino acids together in the order specified by the codons of messenger RNA (mRNA) molecules to ...
or a viral
capsid
A capsid is the protein shell of a virus, enclosing its genetic material. It consists of several oligomeric (repeating) structural subunits made of protein called protomers. The observable 3-dimensional morphological subunits, which may or may ...
. Protein domain dynamics plays key roles in a multitude of molecular recognition and
cell signalling
In biology, cell signaling (cell signalling in British English) or cell communication is the ability of a cell to receive, process, and transmit signals with its environment and with itself. Cell signaling is a fundamental property of all cellula ...
processes.
Protein domains, connected by intrinsically disordered
flexible linker
In molecular biology, an intrinsically disordered protein (IDP) is a protein that lacks a fixed or ordered three-dimensional structure, typically in the absence of its macromolecular interaction partners, such as other proteins or RNA. IDPs rang ...
domains, induce long-range
allostery
In biochemistry, allosteric regulation (or allosteric control) is the regulation of an enzyme by binding an effector molecule at a site other than the enzyme's active site.
The site to which the effector binds is termed the ''allosteric site ...
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
Nucleotides are organic molecules consisting of a nucleoside and a phosphate. They serve as monomeric units of the nucleic acid polymers – deoxyribonucleic acid (DNA) and ribonucleic acid (RNA), both of which are essential biomolecules wi ...
. 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
Enzymes () are proteins that act as biological catalysts by accelerating chemical reactions. The molecules upon which enzymes may act are called substrates, and the enzyme converts the substrates into different molecules known as products. A ...
, occur within the range of nano- to millisecond timescales. All atom simulation techniques, such as
molecular dynamics
Molecular dynamics (MD) is a computer simulation method for analyzing the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic "evolution" of the ...
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 Anisotropic Network Model (ANM) is a simple yet powerful tool made for normal mode analysis of proteins, which has been successfully applied for exploring the relation between function and dynamics for many proteins. It is essentially an Elasti ...
.
Gaussian network model theory
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
The Rouse model is frequently used in polymer physics.
The Rouse model describes the conformational dynamics of an ideal chain. In this model, the single chain diffusion is represented by Brownian motion of beads connected by harmonic springs. The ...
and does not take the three-dimensional directionality of motions into account.
Representation of structure as an elastic network
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, R
0i and R
0j, equilibrium distance vector, R
0ij, instantaneous fluctuation vectors, ΔR
i and ΔR
j, and instantaneous distance vector, R
ij, are shown in Figure 2. Instantaneous position vectors of these nodes are defined by R
i and R
j. The difference between equilibrium position vector and instantaneous position vector of residue i gives the instantaneous fluctuation vector, ΔR
i = R
i - R
0i. Hence, the instantaneous fluctuation vector between nodes i and j is expressed as ΔR
ij = ΔR
j - ΔR
i = R
ij - R
0ij.
Potential of the Gaussian network
The potential energy of the network in terms of ΔR
i is
: