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Mapping the Electrostatic Potential of Muscarinic and Nicotinic Agonists with Artificial Neural Networks**

Johann Gasteiger* and Xinzhi Li

Signals in biological neural networks are transmitted between neurons by chemicals, called neurotransmitters, that are released at the terminus of the axon of one neuron, cross the synaptic gap, and then bind to receptors in the postsynaptic membrane of a dendrite of another neuron where they cause an electrical signal. Acetylcholine is such a neurotransmitter occurring in a variety of neuron types of the sympathetic and parasympathetic nervous system. It binds to at least two different receptors, the muscarinic and the nicotinic receptor.

The ring system makes muscarine structurally fairly rigid; thus it can only bind to the receptor that has been given its name. Scheme 1 shows muscarine and three other molecules that are agonists of muscarine and likewise bind only to the muscarinic receptor.

muscarine

atropine

scopolamine

pilocarpine

Scheme 1. Muscarine and three of its agonists, atropine, scopolamine, and pilocarpine.

Similarly, nicotine has such a rigid structure that it binds only to the nicotinic receptor as do the other three molecules of Scheme 2.

nicotine

(+)-anatoxin-a

mecamylamine

pempidine

Scheme 2. Four molecules that only bind to the nicotinic receptor: nicotine, anatoxin-a, mecamylamine, and pempidine.

In this study we report how similarities in the compounds that bind either to the muscarinic or nicotinic receptor can be found. Furthermore, dissimilarities between these two classes of compounds can be recognized.

The investigation of molecular electrostatic potentials (MEPs) is a commonly used method for unraveling the secrets of biological activity. Particularly, the MEP on a molecular surface is calculated and visualized by projection onto a computer screen. However, such projections are linear transformations and thus can only provide insight into one part of the three-dimensional molecular surface. To obtain a full picture of the entire MEP a series of observation points and associated projections is needed. We will show here that maps of the MEP obtained by Kohonen neural networks indicate characteristics common to muscarinic agonists or to nicotinic agonists. The neural network paradigm that was developed by Kohonen models an important feature of the human brain, namely, the development of maps of the sensory environment in the cortex of the brain[1][2]. The Kohonen network employs a competitive learning method that maps a point of a space (body, measurement space) into a single neuron of a two-dimensional network while conserving the topology of the information, that is, the neighborhood relationship of the points in the space.

The self-organizing formation of topological feature maps of Kohonen neural networks can be utilized as a method for the nonlinear transformation of a high-dimensional space into a one- or two-dimensional network[3][4]. In our application, points of the three-dimensional van der Waals surface of a molecule are mapped into a two-dimensional space. In order to have a two-dimensional space in which each neuron has the same number of neighbors the projection was made onto a space without boundaries: the surface of a torus. For easier visualization the torus will be cut along two perpendicular lines and the surface spread out to form a plane which gives a rectangular array of neurons (Fig. I ) [3][4].

Fig. 1. The surface of a torus is cut along two perpendicular lines and spread into a plane. The little boxes of the rectangle symbolize the neurons of the network.

Learning in a Kohonen network is an unsupervised process. In our case, only the three Cartesian coordinates of the points on the van der Waals surface of a molecule are used, but not the property existing at such a point (e.g., the MEP). With three input variables, each neuron j also has three weights wj=(wj1, wj2, wj3). Each point xs=(xs1, xs2, xs3) an the surface will be mapped into that central neuron cs that has weights, wcs=(wcs1, wcs2, wcs3), closest to xs with respect to the Euclidean distance [Eq. (1)]. The neuron cs is usually referred to as the winning neuron of the input xs.

(1)

The weights of all neurons are adjusted in the learning process iteratively for each randomly selected point xs on the molecular surface.

The basic methodology for obtaining Kohonen maps of the MEP of the molecules shown in Schemes 1 and 2 is as follows:

1. Three-dimensional atomic coordinates are calculated by the automatic 3D-structure generator CORINA[5][6].

2. Partial atomic charges are calculated by the empirical PEOE procedure[7][8].

3. The electrostatic potential at points of the van der Waals surface is calculated as classical coulomb potential. (Clearly, more sophisticated quantum mechanical methods and other molecular surfaces, such as the solvent accessible surface[9], can be used as well.)

4. 20000 points are randomly selected from the van der Waals surface with a grid of 100 points per Å2 and used for training a Kohonen map with 100 x 100 neurons.

In the self-organization of the Kohonen map, points that are close to each other on the van der Waals surface are mapped into the same or nearby neurons.

Two methods are used for visualizing the mapping of a molecular surface. In the first approach, a neuron of the two-dimensional Kohonen network (it is, in fact, the surface of a torus) is colored according to the value of the electrostatic potential observed at the points on the van der Waals surface that have been mapped into this neuron. A strongly negative potential is indicated in red; in order, yellow, green, blue, and purple indicate increasingly more positive values of the MEP. This leads to maps of the MEP of the entire molecular surface.

In the second approach, the van der Waals surface is dissected into areas originating from the individual atoms of a molecule. Those parts of the surface belonging to a specific atom or group of atoms are distinguished by color. A neuron of a Kohonen map is colored according to the particular atom surface assignment (ASA) of the origin of the point mapped into this neuron. In this way, the nonlinear mapping of certain parts of the molecular surface can be identified.

Figure 2a shows a Kohonen map of the MEP on the van der Waals surface of muscarine. With this map, the entire MEP can be viewed in a single picture, quite in contrast to the usual representations of MEP that need a series of different viewpoints to obtain an overall impression of the MEP.

Fig. 2. Maps of the van der Waals surface of muscarine. For details see text.

The map of Figure 2a was obtained by cutting the surface of a torus at two perpendicular lines (see Fig. 1). Such cuts can be made at arbitrary lines and thus the map of Figure 2a can be shifted into any direction. In fact, Figure 2a was obtained by centering the map on the large positive part of the MEP of muscarine - effectively putting the positively charged nitrogen into the center of the map. Figure 2b shows the same map, now centered on the negative part of the MEP. In order to show this self-containment of the Kohonen maps we have found it quite useful to put several identical maps together like tiles. This is shown in Figure 3 where Figure 2a has been replicated four times. Both Figure 2a and 2b can clearly be distinguished as parts of Figure 3.

Fig. 3. Four identical maps of the MEP of muscarine put together like tiles.

While the neurons in the Kohonen map of Figure 2a and Figure 2b have been identified by the MEP observed at the points on the van der Waals surface, these Kohonen maps can be associated with any other molecular surface property. Figure 2c and Figure 2d show the very same maps of Figures 2a and 2b, now indicating the atomic surface assignment (ASA).

These ASA maps give a clearer picture of how the nonlinear transformation leads to the self-organization of the neurons. The representative surface was colored in such a way that those parts mapped by hydrogen are shown in purple and those by carbon in dark blue. The contribution of nitrogen to the van der Waals surface is indicated in green and that of the two oxygen atoms in red. Clearly, the van der Waals surface is dominated by hydrogen atoms. The carbon atoms, and particularly the nitrogen atom, are buried deeper in the molecule and are much less visible, but can still be located. The two oxygen atoms, on the other hand, can be clearly identified.

The Kohonen maps of the electrostatic potential on the van der Waals surfaces of the eight structures shown in Schemes 1 and 2 are given in Figure 4. To allow for a correct comparison, the neutral molecules were protonated at the most basic site, since this also occurs when they are bound to their receptors[10][11]. The large positive MEP associated with the positively charged quaternary nitrogen atom clearly has a profound influence on the binding of these substrates to their respective receptors. Therefore, the maps of the MEP of these eight molecules have been arranged so that this positive MEP is in the center of the image in order to see variations at this binding site most directly.

Fig 4. Kohonen maps of (top row) muscarine and the protonated forms of atropine, scopolamine, pilocarpine and of (bottom row) the protonated form of nicotine, anatoxin-a, mecamylamine, and pempidine.

A detailed discussion of these Kohonen maps goes beyond the scope of this paper. However, it can be seen that the maps of the four muscarinic compounds shown in the top row have some distinct common features. A regular rhomboid pattern of white lines indicating empty neurons is centered in the map. These empty neurons result from topological distortions occurring during the mapping of the molecular surface onto the topologically different surface of a torus[12]. The rhomboid pattern of empty neurons in the maps of the muscarinic compounds encloses the blue area of the positive MEP.

The maps of the four nicotinic compounds in the bottom row of Figure 4 have rather irregular patterns of empty neurons. The topological distortions indicated by these empty neurons occur directly adjacent to those parts of the molecular surface having the largest positive MEP; that is, the pattern of the white lines of empty neurons cuts through the blue and purple areas. Furthermore, the blue areas are more elongated than for the muscarinic compounds and in some cases extend across the entire area of the map.

The similarities in the Kohonen maps of the MEPs of the agonists either of muscarine or of nicotine, and the clear differences between the two series of compounds suggest the following:

1. The MEP is a crucial factor in the binding of these molecules to their receptors.

2. The Kohonen maps retain essential features of the MEP and thus can help in screening biologically active compounds.

The self-organization in Kohonen networks enables the projection of properties of molecular surfaces. The mapping of MEP can give important insights into the similarity of molecules essential for biological activity. The present study shows that artificial neural networks can be employed to shed light on essential mechanisms of information processing in biological neural networks.

Received: November 16, 1993 [Z 6504 IE]
German Version: Angew. Chem. 1994, 106, 671

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