Optimisation of the diffusion tensor parameters

The parameters of the Brownian rotational diffusion tensor belong to the set $ \mathfrak{D}$. This set is the union of the geometric parameters $ \mathfrak{G}= \{\mathfrak{D}_{iso}, \mathfrak{D}_a, \mathfrak{D}_r\}$ and the orientational parameters $ \mathfrak{O}$,

$\displaystyle \mathfrak{D}= \mathfrak{G}\cup \mathfrak{O}.$ (15.4)

When diffusion is spherical solely the geometric parameter $ \mathfrak{D}_{iso}$ is optimised. When the molecule diffuses as a spheroid the geometric parameters $ \mathfrak{D}_{iso}$ and $ \mathfrak{D}_a$ and the orientational parameters θ (the polar angle) and φ (the azimuthal angle) are optimised. If the molecule diffuses as an ellipsoid the geometric parameters $ \mathfrak{D}_{iso}$, $ \mathfrak{D}_a$, and $ \mathfrak{D}_r$ are optimised together with the Euler angles α, β, and γ.

This category is defined as the optimisation of solely the parameters of $ \mathfrak{D}$. The model-free parameters of $ \mathfrak{F}$ are held constant. As all selected residues of the macromolecule are involved in the optimisation, this category is global and can be more complex than the optimisation of $ \mathfrak{F}_i$ or $ \mathfrak{T}_i$. The dimensionality of the problem nevertheless low with

dim$\displaystyle \mathfrak{D}= 1, \qquad \dim \mathfrak{D}= 4, \qquad \dim \mathfrak{D}= 6,$ (15.5)

for the diffusion as a sphere, spheroid, and ellipsoid respectively.

The relax user manual (PDF), created 2016-10-28.