PMC

Modulating frustration: a substantive theory of tinnitus tolerance.

The theory of ideological obsession: from needs frustration to violent extremism.

a Five tetrahedra can almost form a pentamer; 20 tetrahedra can almost form an icosahedron. b A 2D example of geometric frustration: pentagons do not tile Euclidean surface, but can form a regular crystal (dodecahedron) on the 2-sphere S². c CdTe tetrahedral NPs (yellow tetrahedra) are coated with a layer of chiral ligands (l- or d-Cysteine). The blue-shaded areas represent the soft interaction regions where coordination bridges between ligands can form. d Elastic deformations in this continuum theory represent distortions of the soft ligand interactions.

The global effects of frustration can be quantified with energy landscape theory. A frustrated heteropolymer will have the energy distribution drawn from a random energy landscape, a Gaussian with some mean Ē and a standard derivation ΔE. The energy of the lowest energy states E_g can be estimated given the size of the configuration space and the variance of the energy distribution. A large protein whose energy is just E_g will have quite a few kinetic traps of nearly the same stability. Therefore, if a protein is to fold robustly, its ground state energy must be substantially below E_g. If the energy of the completely folded state E_f is substantially below this estimate we can predict that frustration effects will be minimal for this sequence (). The condition that E_f is below E_g is known as the gap condition for folding. Comparing E_f and E_g and requiring them to be well separated (δE) provides one way of quantitatively stating the Principle of Minimal Frustration.