Diseño de un sedimentador vertical

Once an homologous fold adopted by a target sequence has been identified, the three-dimensional structure can be modelled. INSIGHT II (release 97.0; Biosym/MSI, San Diego, USA) is a suite of molecular graphics and computational chemistry software that is used for building and refining domain models. The homologous (or analogous) fold structure is used as a template, from which an atomic coordinate model is built by a rigid fragment assembly method that is implemented using the HOMOLOGY program. HOMOLOGY imports the template structure and facilitates the alignment of its sequence to that of the protein structure to be modelled.

The stmcturally conserved regions (SCRs) in the core of the fold must be defined. The atomic coordinates of the template SCRs are then copied to the model, except when differences occur between the sidechain atoms of the two proteins, in which case these are modelled from a library of amino acid structures.

The loops whichjointhe SCRs are modelled next. The conformations of SCRs are restricted by hydrogen bonding constraints, but such conformational restriction is not usually observed for loops and they therefore exhibit a higher degree of sequence and structural divergence between homologous proteins. Consequently loops are more difficult to model. Where possible, loops from the template structure are used. This type of loop is termed a designated loop in HOMOLOGY and the template coordinates for designated loops are copied to the target model.

Other loops are termed searched loops, and these occur when the loop length is different between the template and target proteins. Searched loops are modelled using a database of compatible loop structures (Hobohm and Sander, 1994). HOMOLOGY provides an algorithm that enables the database to be searched for loops that have the desired length and which best satisfy the geometric constraints required to join two SCRs. This search

algorithm calculates an a-carbon distance matrix for the model residues on either side of a loop and this is compared to a-carbon distance matrices from structures in the database. The database loop structures that give the best fit to a model loop are defined as those with the lowest root mean-squared (RMS) distance values:

RMS d is ta n c e =

^ N [ x - x , f + { y - J o / + '

i = i N

Equation 3.8

where the summation is performed for 1 to pairs of a-carbon atoms between the two structures; and x, y, z and Xq, yo, Zo are the atomic coordinates of each corresponding a- carbon atom between the two structures. The selection of a loop structure is typically governed by conditions such as: suitable mainchain torsion angles and distances between a- carbon atoms at the points where loops are joined to SCRs; the loop does not contain secondary structure; there is no gross steric overlap of the loop with other regions of the model. When a searched loop is selected, its coordinates are copied to the model.

After atomic coordinates have been assigned to every model residue, manual rotamer searches can be used to relieve steric overlap. HOMOLOGY contains a library of commonly occurring sidechain rotamers and these are tested individually in an attempt to reduce the steric overlap of poorly modelled sidechains.

3.8.1 Model refinement

A model that has been built using a rigid fragment assembly method may contain structural artefacts. These include the substitution of large sidechains for small ones, strained peptide bonds between segments taken from different reference proteins, and non-optimum conformations for the loops. In order to overcome these artefacts, models can be refined using energy minimization.

DISCOVER is a molecular simulation program within IN SIGHT II that can perform many routines, including energy minimisation, template forcing, torsion forcing, and dynamic

trajectories as well as the calculation of interaction energies, derivatives, mean square displacements, and vibrational frequencies (DISCOVER 2.9.7/95.0/3.0.0 user guide). The consistent-valence forcefield was used to represent the potential energy of the molecular system. This forcefield contains terms which describe the energies necessary to stretch a bond, distort the angle between three atoms, rotate atoms about their bond axis, and move an atom out of the plane defined by the three atoms to which it is bonded, as well as extra terms that describe the energies representing the coupling effects of one of the above energies with another (cross terms), and associated with the attractive, repulsive and electrostatic forces between atoms that are not bonded to one another (charges). Energy minimization is used to produce a model that is chemically and conformationally reasonable.

The first stage of protein minimization would commonly be splice repair. This minimizes the energy of the peptide bonds at the junctions between regions from different reference structures. Bond lengths and mainchain omega torsion angles are displayed by the program so that the progression of the minimization can be monitored. The relax option enables different minimization strategies to be set up. The model is divided into individual fragments from different reference structures, SCRs and loops, mainchains and sidechains, and mutated sidechains and non-mutated sidechains, and from these different regions can be selected for minimization.

3.8.2 Structure validation

After building an atomic coordinate model, whether by means of X-ray crystallography, NMR or homology modelling techniques, it is important to assess its quality. PROCHECK (Laskowski et al., 1993) is a suite of programs that assesses a PDB-format atomic coordinate file using stereochemical parameters derived from high-resolution protein crystal structures (Morris et al., 1992), and bond lengths and bond angles derived from a comprehensive analysis of small-molecule structures (Engh and Huber, 1991). The stereochemical quality of the model is output as a residue-by-residue listing that enables the clear identification of regions that are in error. A useful feature of PROCHECK is that it produces a Ramachandran plot of the ^ (phi) and \\f (psi) mainchain torsion angles

(Ramachandran and Sassiekharan, 1968).

3.8.3 Surface electrostatic potentials

Electrostatic interactions play a central role in a variety of biological processes (Honig and Nicholls, 1995). DELPHI is part of the INSIGHT II suite of programs and is used to calculate the electrostatic properties of charged molecules. The output from DELPHI can be mapped onto the molecular surface of the protein via its interface with INSIGHT II. The electrostatic potential in and around macromolecules can be calculated using a finite difference solution to the Poisson-Boltzmann equation:

V-[e(r)V-(p (r)] - e(r)K(r)^ sinh[(p(r)] + 47i:p^(r)/A^gr= 0 Equation 3.13

where cp(r) is the electrostatic potential at any point in space, and has units of k^Tle {k^ is the Boltzmann constant; Tis the absolute temperature and e is the elementary charge); e is the relative permittivity; and p^is fixed charge density (in proton charge units). The term = 1A,^ = Sizq^I/ekT, where X is the Debye length and lis the ionic strength of the bulk solution. The variables (p, e , k and p are all functions of the vector r.

The molecular surface is defined as the contact surface formed between the van der Waals envelope of the molecule and a probe molecule of 1.4 À radius. All internal regions are assigned a low value of e (around 2-4), whereas exterior regions are assigned the standard relative permittivity of water (e of around 80). Using iterative procedures for the solution of equation 3.13, cp(r) can be calculated for a molecule in solution of arbitrary ionic strength. In the context of proteins, unique patterns of (p(r) are seen in many cases to have an important functional role (Honig and Nicholls, 1995).

Chapter 4