A Laboratory-free Approach - In Silico Prediction

The initial expansion of interest in model compounds just predated the rapid rise in computing power. This later development meant that three-dimensional computer modelling of compounds could at last be achieved at a rate that made it practicable. The development in computer speed gave rise to a parallel development of sophisticated computer software for modelling.

The simplest approach to modelling treats molecules as solid spheres of characteristic radii joined by springs of characteristic length with the classical Hooke's Law dominant in the development of predictive equations for what is called molecular modelling. This very classical contrived approach has proved both resilient and surprisingly useful. Perhaps our capacity, using electron microscopy, to at last 'see' individual atoms which appear for all the world as spheres provides some justification of the simplicity of this approach. This

Figure 8.16

Comparison of the zinc (II) ion environment of the enzyme carbonic anhydrase and of a small molecule model that employs a triaza-macrocycle to supply the N-donor ligand set.

classical form of molecular modelling remains both very accessible and of value, since the great computational speed achievable with the simple equations employed allows the procedure to be used for conformational energy searching, molecule-protein docking and molecular dynamics that all demand a large number of energy calculations.

More elaborate modelling based on a pure theoretical model for the atom, an ab initio (from the beginning) approach, is limited by computer power, and as yet finds limited application in coordination and biological chemistry. However, a middle ground approach, using density functional theory (DFT) which has a more limited theoretical base, has grown in popularity and applicability. These so-called 'in silico' (or silicon chip-based) approaches may present the future for an important aspect of chemistry - prediction of function. A screen-based model to probe a large family of related compounds certainly is more attractive than many hours of tedious repetitive laboratory work involving synthesis and testing to discover the most efficient compound for a particular task.

Let's explore the simplest type of 'in silico' technology, the so-called molecular me- chanics, which treats atoms and their electron sets as hard spheres and bonds as springs. Because molecules have preferred bond distances and angles, all deformations away from ideal cost energy, and it is the sum of all deformations and other unfavourable nonbonded interactions that add up to an overall energy associated with stability. Comparison of calculated energies for different isomers of the same molecule, for example, allows prediction of the most stable isomer. This is a valid application, as is the calculation of en- ergy for different conformations of a molecule. However, comparisons of energy between different molecules is inappropriate, since they will contain different numbers of atoms and bonds and thus will differ inherently, so that their relative energies offer little real meaning.

The total strain energy of a system can be considered to arise from bond length distortion (stretching or compressing a bond away from its ideal, represented here as Es), bond angle distortion (bending bonds to open out or close up an ideal angle; Ebend), torsional effects (twisting of groups around a particular bond relative to each other; Etor) and nonbonded contributions (van der Waals attraction, steric repulsion and electrostatic attraction or repulsion; Enb). This can be expressed by (8.5).

Etotal = Estr + Ehend + Etor + Enb (8.5)

The origins of these effects are represented simplistically in Figure 8.17. Each of the contributions may be represented by simple classical equations (e.g. Ebend =ε{k_θ (θ - θ⁰)₂} where ka is the force field parameter and 9, the ideal angle summed for all angles in the system under examination). The full sets of equations are not pursued here but can be found in specialist texts and web sites.

Software packages work by varying atom locations by small amounts, performing a calculation and comparing it with the previous calculation. A stepwise process leads to a minimum. This may be the global minimum for the system (that is the best solution), or a local minimum (a low-energy situation, but not the lowest-energy minimum available). The latter can be tested for by starting from a quite different shape and allowing the process to repeat. An array of sophisticated approaches is employed in software packages, but in the end this is still really a classical ball-and-stick modelling method, with inherent limitations. Despite this, the approach is efficient and the outcomes, with 'training' of the system through the use of appropriate force field parameters, are surprisingly good if using packages developed with suitable parameters for metal ions as well as nonmetallic elements. 'Docking' (directed noncovalent bonding) between even large biomolecules and complexes

Figure8.17 Representation of effects operating in molecular mechanics(left). An example of binding of a copper complex to a phosphate group on the backbone of a DNA strand optimised using molecular mechanics methodology appears at right.

Can be probed for example (Figure8.17). Modelling is set to expand its reach from a dominant use with pure organic systems to include metal complexes now that software packages appropriate for dealing successfully with metal ions have  been established.

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