Does the word "restraint" have any special meaning in the case of protein or biochemistry?

Question

The following screenshot is taken from the book The Encyclopedia of Physical Science & Technology, volume: Biochemistry, Edition: 3rd, Page-197.

The text says:

FIGURE 3 Schematic representation of the peptide bond and the observed restraints on the conformational.

On the other hand, the research article

• Discrete restraint‐based protein modeling and the Cα‐trace problem. (2003)

also mentions and repeatedly uses the word restraint.

^{Abstract
We present a novel de novo method to generate protein models from sparse, discretized restraints on the conformation of the main chain and side chain atoms. We focus on Cα-trace generation, the problem of constructing an accurate and complete model from approximate knowledge of the positions of the Cα atoms and, in some cases, the side chain centroids. Spatial restraints on the Cα atoms and side chain centroids are supplemented by constraints on main chain geometry, φ/ξ angles, rotameric side chain conformations, and inter-atomic separations derived from analyses of known protein structures. A novel conformational search algorithm, combining features of tree-search and genetic algorithms, generates models consistent with these restraints by propensity-weighted dihedral angle sampling. Models with ideal geometry, good φ/ξ angles, and no inter-atomic overlaps are produced with 0.8 Å main chain and, with side chain centroid restraints, 1.0 Å all-atom root-mean-square deviation (RMSD) from the crystal structure over a diverse set of target proteins. The mean model derived from 50 independently generated models is closer to the crystal structure than any individual model, with 0.5 Å main chain RMSD under only Cα restraints and 0.7 Å all-atom RMSD under both Cα and centroid restraints. The method is insensitive to randomly distributed errors of up to 4 Å in the Cα restraints. The conformational search algorithm is efficient, with computational cost increasing linearly with protein size. Issues relating to decoy set generation, experimental structure determination, efficiency of conformational sampling, and homology modeling are discussed.}

I have two questions:

1. Does the word restraint mean the same things in the above two sources?
2. Was the word restraint used as a general term that means a measure or condition that keeps someone or something under control, or does it mean any specific property of protein or a biochemical element?

Answer 1

[OP] Does the word restraint mean the same things in the above two sources?

Restraint is used in two contexts in chemistry in general, and biochemistry specifically. Your first example shows the first context, and your second example shows the second.

The first context is in the analysis of observed conformations. Some conformations are not observed because they would result in clashes of non-bonded atoms or would require to break a partial double bond, as is the case for the peptide bond. We rationalize this observation by saying that there is a restraint. There may or may not be a theoretical model explaining the restraint.

The second context is related and refers to restraints applied in simulating the dynamics of molecules, e.g. in molecular dynamics. The restraints could be based on generally known properties (like trying to keep the bond distances in a reasonable range with a quadratic penalty function), or on specific experimental data (like turning an observed NOE from NMR data into a distance restraint of non-bonded atoms, or having a penalty function based on X-ray diffraction data).

So you can distinguish the two contexts of "restraint" based on whether nature imposes the restraints on a real molecule, or researchers impose it on a model of a molecule.

[OP] Was the word restraint used as a general term that means a measure or condition that keeps someone or something under control, or does it mean any specific property of protein or a biochemical element?

The general definition explains pretty well what is meant (in either context). For a specific type of molecule (like a protein), there are specific restraints that you would expect from the combined knowledge on that type of molecule.

Answer 2

In molecular simulations, a restraint is a potential energy term introduced to limit the range of possible values that a geometrical feature of a molecular structure is allowed to have. In practice it is a penalty function that makes extending the value of the geometrical feature (typically a distance, angle or dihedral) beyond a specified ideal range incur an increasing or very large value of potential energy, thereby discouraging such values. The ideal range can be described mathematically as $x = x_{\textrm{ideal}}$, $x \leq x_{\textrm{max}}$ or $x \geq x_{\textrm{min}}$ , sometimes in combination. The restraints$^*$ do not imply that the value of $x$ cannot deviate from the ideal point or range, same as a pendulum might swing away from an energy minimum. However by imposing a sufficiently large penalty such a restraint may become a strict constraint $^*$.

The potential itself can take many forms, commonly a quadratic function that increases away from a central value, sometimes with a cutoff penalizing extreme values, and sometimes with a constant intermediate potential.

The meaning of restraint can be understood as being roughly the same as in ordinary contexts, a device that keeps something from straying from a desired region, for instance a leash for a dog on a leash. It allows the dog to move around but not just anywhere. The word has the same meaning in both contexts in the question (as explained by Karsten) but in one case it refers to the actual potential function that limits observed values of a geometry (in the figure, backbone dihedral values $\phi$ and $\psi$) whereas in the second it refers to potential functions used during a simulation to reflect what is already known about geometrical features (typical bond lengths, angles, dihedrals, minimum vdW contact distances) or other new experimental information (typically distances between atoms on the same or different residues), but both ultimately obtained via experiments, same as in the first example.

$^*$ [edited] In the nomenclature of molecular simulations, constraint may have a more specific meaning and refer to geometric features that are enforced to have a fixed value. For instance, from the Biosym Discovery manual:

The seminal difference between a constraint and a restraint is that a constraint is an absolute restriction imposed on the calculation, while a restraint is an energetic bias that tends to force the calculation toward a certain restriction.