Many of the assumptions made in TNT are shared by most of the available
macromolecular refinement packages. These assumptions include the notions
that anomalous scattering and anisotropic temperature factors can be ignored
(the noteworthy exception being SHELXL, described in the accompanying chapter
by G. Sheldrick). In addition, the model is refined against the amplitude
of the structure factor, rather than the more statistically correct intensity
of the diffracted ray.
In some instances, where authors initially made differing assumptions, one particular assumption won out over time. While the simultaneous refinement against diffraction data and stereochemical knowledge was quite radical when first introduced in PROLSQ[Hendrickson & Konnert, 1980], it has now been incorporated within all packages as the best way to compensate for the lack of high-resolution data.
The convergence of assumptions continues as more experience in refinement
is acquired. In the past there has been a strong dichotomy between the
refinement packages that minimize a least-squares residual and those that
minimize empirical energy functions. The most popular refinement program,
X-PLOR [Brünger et
al., 1987], uses the formalism of energy minimization to ensure
that the model is consistent with ideal stereochemistry. However, when
Brünger adopted the standard parameters of Engh
& Huber (1991) he abandoned the ``force constants'' of an energy
function and began using the 
's of least-squares. Now all the major refinement packages are least-squares
refinement packages.
The structure of TNT embodies several assumptions that differ from those found in other packages.
One cannot determine mathematically the importance of local minima in the refinement function. The function is extremely complicated and exists in a space of many thousands of dimensions. No one has performed an analysis of the distance between nor the height of the barriers between the local minima. Objectively, one cannot rule out their importance but if one assumes they are not a problem, the programming code becomes simpler to write and much quicker to execute.
Some support can be found for the assumption that entrapment in local minima is not significant. The minimization method used in TNT proceeds to the local minimum while that of X-PLOR has the capability to leap from one minimum to another. In spite of this difference the final models from each program are quite similar.
The minimization methods used in crystallographic refinement -- Conjugate Gradient [Fletcher & Reeves, 1964, Powell, 1977, Konnert, 1976], and Preconditioned Conjugate Gradient (also known as Conjugate Direction) [Axelsson & Barker, 1984, Tronrud, 1992] -- require, in theory, many thousands of cycles to reach the local minimum if that minimum is described by a perfectly quadratic function; it is not. There is no way to estimate how much better our models would be if we could run this many cycles of refinement. The minimizer in TNT has been constructed to be the most powerful (in terms of using more second derivatives of the function) of the packages available for refinement at non-atomic-resolution. Since it uses more of the second derivatives of the function, it will approach the local minimum in fewer cycles.
Any refinement package is limited by the fact that it can only change the values of the parameters of the model -- it can neither add nor remove parameters. The number of amino acids, amino acid sequence, and the common occurrence of unmodeled electron density are examples of properties of a model that cannot be changed automatically. While TNT is very good at optimizing the fit of atoms to their density it does not attempt to tear the atoms out of density and place them in nearby unexplained density.
The programs in TNT are not a replacement for the examination of a model using a molecular-graphics program. TNT provides tools to ease the job of rebuilding, but it can never eliminate the need for this vital step in the refinement of a macromolecular model.
The low-resolution portion of the diffraction data includes some of
the strongest reflections. Their ommission will cause distortions in the
appearance of any 
map, and these distortions will appear principally on or near the surface
of the molecule. The calculation of an appropriate map requires that these
terms be included. However, the low resolution reflections can be used
only if the model includes compensation for the scattering of the disordered
solvent in the crystal.
By default, TNT includes a model for this scattering, and the use of all low resolution data is encouraged. Section 4 describes the disordered-solvent model used in TNT.