Energy landscape
Encyclopedia
In physics
, an energy landscape is a mapping of all possible conformations of a molecular entity
, or the spatial positions of interacting molecule
s in a system, and their corresponding energy levels, typically Gibbs free energy
, on a two- or three-dimensional Cartesian coordinate system
.
In mathematical terms, an energy landscape can be defined as a pair (X, f) consisting of a topological space
X representing the physical states or parameters of a system together with a continuous function
f: X → Rn representing the energies associated to these states or parameters such that the image of f represents a hypersurface
in Rn.
The term is useful when examining protein folding
; while a protein can theoretically exist in a nearly infinite number of conformations along its energy landscape, in reality proteins fold (or "relax") into secondary and tertiary structures that possess the lowest possible free energy
. The key concept in the energy landscape approach to protein folding is the folding funnel
hypothesis.
In glass
ing models, the local minima
of an energy landscape correspond to metastable
low temperature states
of a thermodynamic system
.
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, an energy landscape is a mapping of all possible conformations of a molecular entity
Molecular entity
According to the IUPAC Gold Book a molecular entity is "any constitutionally or isotopically distinct atom, molecule, ion, ion pair, radical, radical ion, complex, conformer, etc., identifiable as a separately distinguishable entity"....
, or the spatial positions of interacting molecule
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...
s in a system, and their corresponding energy levels, typically Gibbs free energy
Gibbs free energy
In thermodynamics, the Gibbs free energy is a thermodynamic potential that measures the "useful" or process-initiating work obtainable from a thermodynamic system at a constant temperature and pressure...
, on a two- or three-dimensional Cartesian coordinate system
Cartesian coordinate system
A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length...
.
In mathematical terms, an energy landscape can be defined as a pair (X, f) consisting of a topological space
Topological space
Topological spaces are mathematical structures that allow the formal definition of concepts such as convergence, connectedness, and continuity. They appear in virtually every branch of modern mathematics and are a central unifying notion...
X representing the physical states or parameters of a system together with a continuous function
Continuous function
In mathematics, a continuous function is a function for which, intuitively, "small" changes in the input result in "small" changes in the output. Otherwise, a function is said to be "discontinuous". A continuous function with a continuous inverse function is called "bicontinuous".Continuity of...
f: X → Rn representing the energies associated to these states or parameters such that the image of f represents a hypersurface
Hypersurface
In geometry, a hypersurface is a generalization of the concept of hyperplane. Suppose an enveloping manifold M has n dimensions; then any submanifold of M of n − 1 dimensions is a hypersurface...
in Rn.
The term is useful when examining protein folding
Protein folding
Protein folding is the process by which a protein structure assumes its functional shape or conformation. It is the physical process by which a polypeptide folds into its characteristic and functional three-dimensional structure from random coil....
; while a protein can theoretically exist in a nearly infinite number of conformations along its energy landscape, in reality proteins fold (or "relax") into secondary and tertiary structures that possess the lowest possible free energy
Thermodynamic free energy
The thermodynamic free energy is the amount of work that a thermodynamic system can perform. The concept is useful in the thermodynamics of chemical or thermal processes in engineering and science. The free energy is the internal energy of a system less the amount of energy that cannot be used to...
. The key concept in the energy landscape approach to protein folding is the folding funnel
Folding funnel
The folding funnel hypothesis is a specific version of the energy landscape theory of protein folding, which assumes that a protein's native state corresponds to its free energy minimum under the solution conditions usually encountered in cells...
hypothesis.
In glass
Glass
Glass is an amorphous solid material. Glasses are typically brittle and optically transparent.The most familiar type of glass, used for centuries in windows and drinking vessels, is soda-lime glass, composed of about 75% silica plus Na2O, CaO, and several minor additives...
ing models, the local minima
Maxima and minima
In mathematics, the maximum and minimum of a function, known collectively as extrema , are the largest and smallest value that the function takes at a point either within a given neighborhood or on the function domain in its entirety .More generally, the...
of an energy landscape correspond to metastable
Metastability
Metastability describes the extended duration of certain equilibria acquired by complex systems when leaving their most stable state after an external action....
low temperature states
Thermodynamic state
A thermodynamic state is a set of values of properties of a thermodynamic system that must be specified to reproduce the system. The individual parameters are known as state variables, state parameters or thermodynamic variables. Once a sufficient set of thermodynamic variables have been...
of a thermodynamic system
Thermodynamic system
A thermodynamic system is a precisely defined macroscopic region of the universe, often called a physical system, that is studied using the principles of thermodynamics....
.