Conformational Analysis 16

Assembling a molecule with a modelling kit makes it already clear that rotations

around single bonds can be easily carried out. The molecule will achieve a different

shape, or as the chemists say, it is transformed into a different conformation. In a realmolecule, rotations around these bonds are not fully free. They are subjected to

a potential and the molecule adopts during the rotation particular, energetically favor-

able arrangements. n-Butane represents the simplest case (Fig. 16.1). The central

torsion or dihedral angle determines the relative orientation of the two bonds to the

methyl groups to one another. If n-butane is rotated out of the arrangement with the two

bonds to the methyl groups in 180� orientation (trans), the methyl group at the “front”

carbon and the hydrogen atom at the “back” carbon will directly coincide which each

other at a rotation angle of 120� and 240� called “eclipsed”. In this geometry, they come

closer to one another, therefore this arrangement is unfavorable for steric reasons. At a

rotation angle of 60� and 300� the groups are again in a staggered geometry,which is an

energetically more favorable situation. This arrangement is somewhat less favorable

than the staggered trans orientation because of the spatial vicinity of themethyl groups,

which are now said to be “gauche” to one another. Finally along the rotation path an

orientation is adopted at 0� and 360� in which both methyl groups are exactly behind

one another. This is an even less favorable orientation.

16.1 Many Rotatable Bonds Create Large ConformationalMultiplicity

Multiple energy maxima and minima can be passed through during the course of

a full rotation about 360� depending on which atoms and groups are attached to the

rotatable bond. They are at different energy levels relative to one another. The

lowest minimum is called the global minimum, and the energetically higher minima

are called local minima. Knowledge about these minima is important because

molecules adopt geometries that correspond to such energy minima. Calculations

are necessary to find these minima. A possible method is in the systematic rotation

of all rotatable bonds, for instance in 10� steps. At each step the energy of the

G. Klebe, Drug Design, DOI 10.1007/978-3-642-17907-5_16,# Springer-Verlag Berlin Heidelberg 2013

335

molecule is calculated by using a force-field. All detected minima correspond to

possible conformations of the molecule.

Most drug-like molecules have many single bonds and therefore exhibit more

than one rotatable bond. For these bonds, multiple values of the torsion angle can be

adopted. These values have to be combined for all rotatable bonds in the molecule.

The number of possible combinations increases multiplicatively. The molecule

n-hexane has three rotatable bonds. If, analogous to n-butane, three local minima

are assumed for each rotatable bond (�60�, 80�, and 300�), we can expect 3 � 3 �3 ¼ 27 minima. To perform a systematic search for these minima in 10� steps

however, the evaluation of 36� 36� 36¼ 46,656 positions would be necessary. In

principle, the energy must be calculated for each of these positions. Not all angle

positions will, however, lead to reasonable geometries. It can happen that parts of

the molecule fold back upon itself, and parts will mutually superimpose. Such

collisions can be recognized by computer programs, and the geometry is discarded

from consideration. It is also easily imaginable that with an increasing number of

rotatable bonds, the number of local minima and adoptable geometries can dramat-

ically increase in a systematic search.

Energy(kJ/mol)

3,8 kJ

CH3CH3 CH3CH3CH3

CH3

CH3

CH3

CH3

CH3

CH3CH3CH3CH3

τ

0 60 120 180 240 300 360

Torsion Angle t [°]

gauche trans gauche

14,6 kJ

25,5 kJ

Fig. 16.1 Butane, CH3CH2CH2CH3, is made up of a linear chain of carbon atoms. If the terminal

methyl groups are covering one another after rotation around the central C—C bond, the torsion

angle about the central bond is 0�. At a 60� angle the “back” methyl group is half way between the

“front” methyl group and a hydrogen atom. This situation is called a “gauche” orientation. At 120�

a methyl group and a hydrogen atom are eclipsed to one another. At 180� the terminal methyl

groups are exactly opposite one another. Here the energetically most favorable situation, the transorientation, is achieved. From now on, the course of the rotation is mirror symmetrical, and ends in

the starting position at 360�. The orientations at 120� and 140� are energetically less favorable thanthe 180�-orientation by 14.6 kJ/mol. The gauche orientations at 60� and 300� are the least

favorable ones and are 25.5 kJ/mol higher in energy. If a minimization method is applied that

can only run “downhill,” the three minima on the potential curve can be reached by starting at the

110�, 130�, and 250� points.

336 16 Conformational Analysis

16.2 Conformations Are the Local Energy Minima ofa Molecule

It was shown in ▶Chap. 15, “Molecular Modeling” that the energy and geometry

of a molecule can be calculated with the help of a force field or a quantum

mechanical method. In this way every possible angle value combination about the

rotatable bonds in a molecule can be found that correspond to energetically

favorable states. The mathematical method that is used to search for such

a minimum geometry can only move downhill on the potential energy surface

(▶Sect.15.5). For this, the potential of n-butane should be considered again

(Fig. 16.1). If an angle of 130� is used as a starting value, the minimization ends

with a trans geometry. If an angle of 110� is started with, which is only 20� distant, theoptimization will lead to a gauche orientation. By doing this, two of the three possi-

bilities are detected. The third minimum that mirrors the gauche conformation is

reached if an angle of 350� is started from. In this way, all three conformations are

found for the simplest possible case.

How are complex molecules to be approached? In principle, in exactly the same

way. Because it is not known which torsion angles of the individual single bonds

will give access to potential minima, that is, stable conformations, the minimization

must be started from numerous angles for each of the single bonds. From these

values the minimization always goes “downhill”. The minima on the potential

surface are found in this way. The art is to efficiently define the starting points

from which a given geometry is minimized. This is a very laborious task, particu-

larly with large molecules. It is akin to a hiker in the mountains searching for the

deepest valley.

Adenosine monophosphate 16.1 serves as an example (Fig. 16.2). The analysis

concentrates on the five-membered ribose ring, the bond to nitrogen in the adenine,

and the three bonds of the sugar phosphate side chain. What conformations can this

molecule adopt? Rotations are performed about the open-chain bonds in 10� steps.In the systematic search for the ribose ring only those orientations are considered

that allow the ring to close. To get a rough overview of the hypothetically obtained

geometries, the distance between the center of the adenine scaffold and the phos-

phorus atom is measured in each generated geometry. This falls between 4.5 and

9.3 A for the more than 300,000 generated geometries. To estimate the energy content

of a molecule in an arbitrary geometry, its van der Waals energy (▶Chap. 15,

“Molecular Modeling”) is calculated. Such a calculation is quickly accomplished.

The energies of the 300,000 geometries are between 0 and 64 kJ/mol. The

so-generated structures are not yet in local potential minima. To achieve this, each

starting geometry must be minimized (cf., the potential energy curve of n-butane inFig. 16.1). The subsequently obtained conformations are compared to determine

whether the same local minima have been reached by starting from different points.

This is a rather laborious endeavor for 300,000 starting geometries! It is akin to letting

our hiker walk downhill from each level square to find the deepest valley. Hopefully

he is granted great longevity so that he lives long enough to see the results of the

search! Can this search be structured more effectively?

16.2 Conformations Are the Local Energy Minima of a Molecule 337

16.3 How to Scan Conformational Space Efficiently?

Sometimes rolling the dice is better than systematic probing! The hiker could

choose random places in the mountains from which to descend into the next valley.

With a little luck he will find the deepest valley with significantly less effort. Such

Monte Carlo methods are very popular in conformational analysis. For this the

starting angles for the conformation search are chosen purely randomly.Moleculardynamics serves as another approach. The hiker would have to climb into an

airplane that flies at high speed between the mountains and changes its direction

with each obstruction. After set time intervals, the hiker jumps from the airplane

and hikes to the base of the valley upon landing. The higher the airplane flies,

the fewer mountain peaks are encountered and the faster the mountains can

be crisscrossed. In the course of molecular dynamics a molecular trajectory

(▶Sect. 15.8) is followed, and the geometry is saved at predefined time intervals

to use them as starting points for energy minimizations in a conformational anal-

ysis. By increasing the temperature (i.e., flying higher) a larger area of conforma-

tional space can be searched in a shorter period of time.

16.4 Is It Necessary to Search the Entire ConformationalSpace?

Until now molecules have been considered in an isolated state. How does their

flexibility change when they are brought into an environment like the binding

pocket of a protein? In principle nothing changes in their conformational flexibility.

It could be that minima are found at different positions that have different relative

energies because of electrostatic and steric interactions in the binding pocket. This

begs the question of whether the torsion angles in all areas must be sought for

NN

NH2

O

P

O−

OHO

NNO

O

16.1OHOH

t1 t4

t2t3

Fig. 16.2 Adenosine monophosphate 16.1 exhibits the conformationally flexible ribose ring and

four open-chain torsion angles, t1–t4. Rotations are performed and the center of the around these

torsion angles during the conformational analysis. To get a rough description of the attained

geometry, the distance between the phosphorus atom in the side chain and the adenine scaffold

(N

) is measured.

338 16 Conformational Analysis

a ligand that is in a binding pocket. If energy minima occur preferentially at

particular torsion angles, it is reasonable to limit the search to these angles. The

hiker could, for example, get the impression that the villages are predominantly

found in valleys and hardly ever on peaks or slopes. Because of this, all of the

villages would be worthwhile as starting points for his minimum search.

Ligands in the binding pocket of a protein are under the influence of directional

interactions from the amino acids that are located there. Similar conditions are

found for molecules in a crystal lattice. There, the environment is built of identical

copies of neighboring molecules (▶Chap. 13, “Experimental Methods of Structure

Determination”). These undergo directional interactions with the molecule, analo-

gously to the amino acids in the binding pocket. Interestingly, the molecular

packing density in the interior of a protein is similar to organic molecules in

a crystal lattice. As was already mentioned in ▶ Sect. 13.9, the crystal structures

of numerous organic molecules are known and stored in a database. Experience has

unfortunately shown that the conformation of a flexible molecule in a crystal

structure is often not identical, or even similar to the geometry of the molecule in

the binding pocket of a protein. The same is true for conformations that have been

found in solution.

The receptor-bound conformation of a molecule cannot be unambiguously

derived from its small-molecule crystal structure or from that in solution. None-

theless, much can be learned from crystal structures. As an example, not the entire

molecule should be considered, but rather individual torsion angles. The potential

energy for the central torsion angle of n-butane is shown in Fig. 16.1. If the

angles for multiple C—CH2—CH2—C fragments are extracted from a database

of small-molecule crystal structures, they gather overwhelmingly in areas where the

potential energy curve shows local minima. Adenosine monophosphate 16.1 has

four open-chain torsion angles t1–t4 (Fig. 16.2). The bond between the ribose

ring and the adenine scaffold forms the torsion angle t4. A further fragment is the

phosphate group with the oxygen and the attached carbon in the chain (t3).This fragment occurs in the database in a large variety of different structures.

A representative picture can be expected because this fragment occurs in very

many different environments when enough crystal structures are considered. The

results of such searches for the four torsion angles t1–t4 are shown in Fig. 16.4 as

frequency distributions, so-called histograms. Experience has shown that clearly

preferred values occur for many torsion angles. That is the case here for t1, t2, andt3. The question can be raised as to why this statistical evaluation is not better

performed on ligands that are taking part in crystallographically studied protein–

ligand complexes. Unfortunately the diversity of these data is still limited, and the

data are usually not accurate enough for the desired evaluation. Nevertheless,

comparative studies have shown that the same torsion angles are preferentially

found in protein–ligand complexes and small-molecule crystal structures

(Fig. 16.3).

The experience that torsion angles prefer particular values can be used for the

conformational search. The angle t4 between the ribose ring and the adenine

scaffold shows a broad distribution over many possible values (Fig. 16.4).

16.4 Is It Necessary to Search the Entire Conformational Space? 339

Unfortunately, the search cannot be narrowed here. This looks better for the other

angles t1–t3. There, only specific values occur. If the systematic search is limited to

these areas, and a search in 10� steps is carried out around the average value, it wouldonly be necessary to generate 6,340 geometries. Almost the same distance between

phosphorus and adenine is covered with 5.9–9.3 A as in the unrestricted search.

If a van der Waals energy calculation is carried out on these geometries, values

between 0 and 16.3 kJ/mol are obtained. In contrast to the results from Sect. 16.2, all

the geometries that correspond to the energetically unfavorable areas are discarded.

How can it be confirmed that this restricted search also covers that part of the

conformational space that includes the receptor-bound conformations? Adenosine

monophosphate 16.1 often occurs as a substructure of cofactors in protein com-

plexes so that there is enough information about receptor-bound conformations for

this particular example. They come from crystal structures of proteins with these

bound cofactors. The distance range of 5.9–9.2 A between the adenine scaffold and

the phosphorus in the receptor-bound structures covers the same range that was

detected in the enhanced systematic search. It can therefore be assumed that enough

geometries were generated that satisfactorily populate the local minima of the

bound state of adenosine monophosphate. Reflecting back to the initial butane

example (Fig. 16.1), this means that the starting points were well distributed so

that all minima were reached.

16.5 The Difficulty in Finding Local Minima Corresponding tothe Receptor-Bound State

As already described, the local minima in a systematic conformational search are

obtained by subjecting all of the generated geometries to a force-field optimization.

There can be problems with this approach. To explain this, a different molecule,

citric acid 16.2 can be considered, in the binding pocket of citrate synthase. Seven

Fre

quen

cy [%

]

60

80

0

20

40

0 30 60 90 120 150 180 210 240 270 300 330 360

Torsion Angle t [°]

Fig. 16.3 A value distribution for the torsion angles with clusters at 60�, 180�, and 300� is derivedfrom a database of small-molecule crystal structures for the C—CH2—CH2—C fragment. Most

values are found at 180�. Torsion angles between 0� and 360� are entered as the relative frequencyin percent. The maxima of the distribution are at the points where the potential curve of n-butane(Fig. 16.1) shows its energy minima.

340 16 Conformational Analysis

hydrogen bonds are formed by its three carboxylate groups and the hydroxyl group

to three histidine and two arginine residues of the protein (Fig. 16.5). If the free, not

to the protein bound citrate molecule is considered and its geometry is minimized in

an isolated state, it takes on a conformation with internally saturated hydrogen

bonds (▶Sect. 15.5). Of course, a different geometry can be started from, but in

all cases, conformations with intramolecular hydrogen bonds will result upon

minimization. Such hydrogen bonds rarely occur in the protein-bound state.

Therefore the conformation that was obtained after minimization in the isolated

state has no relevance for the conditions in the protein.

As a general rule, ligands rarely bind to proteins in a conformation exhibiting

intramolecular hydrogen bonds. The H-bond-forming groups are generally

involved in interactions with the protein.

To circumvent the problem of intramolecular H-bond formation, a minimization

of the generated starting structure can be neglected, and all geometries from the

systematic search can be used for further comparison (▶Chap. 17, “Pharmacophore

Hypotheses and Molecular Comparisons”). Then, however, very many geometries

must be examined. This would severely limit the scope of such comparisons for

NN

NH2

OP−O

HO

NNOO

16.1OHHO

t1 t4

t2t3

40

60

20

30

40

0

20

0

10

Fre

quen

cy [%

]

Fre

quen

cy [%

]

0 30 60 90 120 150 180 210 240 270 300 330 360

Fre

quen

cy [%

] 60

0

20

40

Torsion Angle t [°]

0 30 60 90 120 150 180 210 240 270 300 330 360

Torsion Angle t [°]

Fre

quen

cy [%

] 15

0

5

10

0 30 60 90 120 150 180 210 240 270 300 330 360

Torsion Angle t [°]

0 30 60 90 120 150 180 210 240 270 300 330 360

Torsion Angle t [°]

Fig. 16.4 The frequency distribution of the torsion angles of the open-chain bonds of adenosine

monophosphate as found in the crystal structures of small organic molecules. The torsion-angle

histograms are constructed for fragments that are representative for corresponding portions of the

test molecule. There are clearly preferred values for the angles t1–t3, but a broad distribution of allpossible angles is found for t4. This knowledge is used in the conformational analyses and limits

the search for t1–t3 to the preferred value ranges.

16.5 The Difficulty in Finding Local Minima 341

computational reasons. Furthermore, such generated results would likely describe

rather distorted geometries. The force field responsible for the formation of intra-

molecular H-bonds could be neglected. But how reliable would such a reduced

force field be? An attempt can be made to summarize the geometries that were

generated in a systematic search so that groups with similar conformations are

described by one representative member.

16.6 An Effective Search for Relevant Conformations by Usinga Knowledge-Based Approach

A knowledge-based approach analyzes first the experimentally determined confor-

mations and generates for new molecules only those conformations that are con-

sistent with the experimental knowledge base. In this way, many geometries are

never generated from the very beginning. The example of adenosine

monophosphate 16.1 is once again invoked. The approach recognizes a flexible

five-membered ring and four open-chain rotatable bonds. Energetically favorable

conformations of the ring are chosen from a database. This database contains many

different ring systems as they are found in, for example, crystal structures of

organic molecules. In the case at hand, the approach suggests the five energetically

most favorable ring conformations from which two are in fact found in the protein-

bound cofactors. For the open-chain part of the molecule the method is guided by

the above-mentioned frequency distribution of the dihedral angle (Fig. 16.4). The

starting geometries are only generated in areas in which these distributions show

significant frequencies. The distribution is still rather crude. In a final step, the

generated geometries are optimized by readjusting the torsion angles. Clashes

between non-covalently bound atoms are avoided. At the same time the adjusted

dihedral angles are kept as close as possible to the preferred values. This approach

gets by with relatively few conformations. They are rather evenly distributed in the

part of the conformational space that is relevant for receptor-bound conformations

(Fig. 16.6).

N

NHis 238Arg 329

N

HN

NNH

OHOO

H

H

HNH H

His 320

+

NH O−OO−

HNO−

HN

H

Arg 401 +

N

N16.2 His 274

Fig. 16.5 Interactions

between citric acid 16.2 and

the enzyme citrate synthase.

The molecule is bound by

seven hydrogen bonds to three

histidine and two arginine

residues.

342 16 Conformational Analysis

16.7 What Is the Outcome of a Conformational Search?

Many drug-like molecules are flexible. They can adopt markedly different confor-

mations depending on the surrounding environment. Usually the receptor-bound

geometry is not in the energetically most favorable conformation found for the

isolated state, but will fall in an energetically favorable area. For the conformational

analysis, this means that it is not necessarily the deepest minimum that is sought.

Rather, it should be the “relevant” minimum that corresponds to the bound state.

There is only a chance of finding it when the criteria for the search are known.

There is no difference in the difficulty of finding the energetically most

favorable conformation, or the one that “fits” best the binding site. An important

tool in the search for novel lead structures is the docking of candidate molecules

into the binding pocket of a given protein. Programs that are able to use this

approach must be able to handle the conformation problem. Meanwhile, a large

variety of methods have been developed that allow efficient docking searches on

computer clusters, particularly for molecules of drug-like size.

Fig. 16.6 Eighty-one

conformers (upper part) from

experimentally determined

protein–ligand complexes are

superimposed upon one

another to illustrate the areas

in space that adenosine

monophosphate 16.1 can

adopt in a protein-bound state.

The ribose ring is located in

the center, for which two ring

conformations occur. The

possible orientations of the

adenine ring are shown on the

top, and the conformations of

the flexible phosphate chain

are on the bottom. Similar

coverage of the

conformational space is

achieved with a manageable

number of 14 conformations

(lower part), which were

generated by a knowledge-

based approach.

16.7 What Is the Outcome of a Conformational Search? 343

16.8 Synopsis

• Drug-like molecules exhibit multiple rotatable bonds. Rotations around these

bonds drive the molecules into different conformations that correspond to local

minima on the energy surface of the molecule.

• The receptor-bound conformation of a drug-like molecule is the starting

point for any drug-design considerations. Therefore, many methods have been

developed to perform conformational analyses. Systematic searches by incre-

mental rotations about each single bond torsion angle will produce a huge

amount of geometries that need to be optimized to the local minima on the

energy surface.

• The conformation of a drug-like molecule frequently changes with the environ-

ment. Usually the conformation in the protein-bound state differs from that in

solution, in the gas phase, or in the small-molecule structure.

• Considering torsional fragments in small molecules and analyzing them across

databases of crystal structures by statistical means reveals clear-cut torsional

preferences for many examples. Such knowledge can be exploited to perform

a conformational search more efficiently. Not all values around a rotatable bond

have to be tested, and the search can be limited to the ranges that are known to be

preferred.

• A further obstacle in the conformational search of the protein-bound conforma-

tion of a drug-like molecule is that the molecule will interact with its environ-

ment. This environment, the protein’s binding pocket, is often polar and will

involve the bound ligand in multiple hydrogen bonds.

• Using a knowledge base on torsional preferences of small organic molecules

can significantly enhance the conformational search, particularly during

docking, in molecular comparisons, or in database searches based on predefined

pharmacophores.

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